Characterizing the Crush Performance of Composite Flat ...

March 2022

Characterizing the Crush

Performance of Composite Flat

Plates and Profiles

A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy

Jonas Lausch

M. Eng. (UAS Ingolstadt, Germany) B. Eng. (UAS Ingolstadt, Germany)

School of Engineering College of Science, Technology, Engineering, and Maths

RMIT University

ii

"Each time new experiments are observed to agree with the

predictions, the theory survives, and our confidence in it is

increased: but if ever a new observation is found to disagree,

we have to abandon or modify the theory. At least that is what

is supposed to happen, but you can always question the

competence of the person who carried out the observation."

–

Stephen Hawking 1988

iii

Declaration

I certify that except where due acknowledgement has been made, this research is that

of the author alone; the content of this research submission is the result of work which has

been carried out since the official commencement date of the approved research program;

any editorial work, paid or unpaid, carried out by a third party is acknowledged; and, ethics

procedures and guidelines have been followed.

In addition, I certify that this submission contains no material previously submitted

for award of any qualification at any other university or institution, unless approved for a

joint-award with another institution, and acknowledge that no part of this work will, in the

future, be used in a submission in my name, for any other qualification in any university or

other tertiary institution without the prior approval of the University, and where applicable, any partner institution responsible for the joint-award of this degree.

I acknowledge that copyright of any published works contained within this thesis

resides with the copyright holder(s) of those works.

I give permission for the digital version of my research submission to be made

available on the web, via the University’s digital research repository, unless permission has been granted by the University to restrict access for a period of time.

Jonas Lausch

Ingolstadt, 28 March 2022

iv

Acknowledgment

I would like to express my sincere gratitude and heartfelt thanks to my senior

supervisor Dr. Monir Takla at RMIT. Without his guidance and support throughout this

thesis would not have been possible. His ingenuity, attention to detail, and exceptional

motivational abilities in his role as a senior supervisor have been invaluable in helping me

through my research. He has been and continues to be a highly committed and caring mentor to me. At this point, I also have to express my appreciation to Prof. Jörg Wellnitz

from the THI. Without his recommendation, I would still be searching for my supervisor.

I also would like to sincerely thank my associate, Prof. Hans-Georg Schweiger, at THI

for his support, thoughtful advice, and positive criticisms throughout my Ph.D. project.

Special thanks to him for providing the environment and equipment to conduct my research.

Throughout my candidature, I had the privilege of working with some fantastic

colleagues and friends at THI. Each of them has been a pleasure to know. I would like to

thank you for the wonderful sources of motivation and encouragement in exchanging ideas,

problem-solving, scientific collaboration, and, importantly, the splendid working atmosphere.

I also would like to thank Ludger Lagermann from EDAG Engineering GmbH for

providing me the opportunity and trust to do the Ph.D.

My particular thanks to my parents and siblings, especially to my brother Dr. Tobias Lausch, for their continued support and encouragement. Particularly heartfelt thanks to my

incredible wife, Eva, and my marvelous daughters, Carlotta, and Florentina, for they have

endured the most. I would like to thank my wife for her confidence and care. She knows she

is the person behind my success.

This work was supported by the German Federal Ministry of Education and Research

[grant number 13FH7I04IA] through the funding program “Forschung an

Fachhochschulen”. The third-party funding source of the project is the EDAG Engineering

GmbH. Many thanks for the support through a fee-exemption scholarship awarded by RMIT

University under the dual agreement between the THI and RMIT.

v

Table of Contents

Declaration iii

Acknowledgment iv

Table of Contents v

List of Figures viii

List of Tables xi

List of Abbreviation xii

List of Symbols xiii

ABSTRACT 1

CHAPTER 1. INTRODUCTION 3

1.1. Motivation and Rationale 3

1.2. Research Questions 5

1.3. Thesis Outline 8

1.4. Study Limitations 10

1.5. References 10

CHAPTER 2. CRUSH TESTING APPROACH FOR FLAT PLATE FIBROUS MATERIALS 16

2.1. Introduction 16

2.2. Testing Approach 19

2.3. Experimental Setup 24

2.4. Results and Discussion 27

2.4.1. Crushing Behavior 27

2.4.2. Approach Validation 30

2.4.3. Usability for Different Materials 34

2.5. Conclusion 37

2.6. References 38

vi

CHAPTER 3. CRUSH CHARACTERISTICS OF FLAT PLATE DISCONTINUOUS CARBON

COMPOSITES 43


3.2. Methodology 46

3.2.1. Experimental Design 46

3.2.2. Material and Manufacturing Process 48

3.2.3. Experimental Setup 48

3.2.4. Measurements and Analysis of Results 51

3.3. Discussion of Results 53


3.3.2. CPIT Results 55

3.3.3. Effect of the Fiber Length & Fiber Mass Content 58

3.3.4. Effect of the In-Plane Fiber Orientation 60

3.3.5. Interaction between the Loading Rate Influence and the Specimen Thickness 61

3.3.6. Comparison of the SEA Values 63

3.4. Conclusion 66

3.5. References 68

CHAPTER 4. INSIGHT INTO CRUSH PERFORMANCE COMPARISON OF COMPOSITE

PROFILES AND FLAT PLATES 74


4.2. Methodology 79

4.2.1. Testing Approach 79

4.2.2. Experimental Design 85

4.2.3. Experimental Test Setup 88 4.3. Results and Discussion 89


4.3.2. Right-Angled Profiles 92

4.3.3. Comparison of Right-Angled Profiles and Flat Plates 97

4.3.4. Circular Tubes 99

4.4. Conclusion 102

4.5. References 104

vii

CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS 109

5.1. Conclusions 109

5.2. Future Work 113

5.3. References 115

APPENDIX 117

A. List of Publication 117

B. Accuracy Analysis 118

B.1. Crush Testing Approach for Flat Plate Fibrous Materials 118

B.2. Crush Characteristics of Flat Plate Discontinuous Carbon Composites 119

B.3. Insight into Crush Performance Comparison of Composite Profiles and Flat Plates 121

viii

List of Figures

Figure 2-1: Schematic representation of different test rig designs:

a) from Ref. [22];

b) from Ref. [29];

c) from Ref. [30] adapted from (a). 17

Figure 2-2: Force components of a moving impactor. 20

Figure 2-3: a) Schematic illustration of the proposed approach;

b) force-width relationship of different materials from Ref. [39]. 22

Figure 2-4: Schematic representation of the test rig and overview of the whole setup. 24

Figure 2-5: Detailed configuration for all three crushing widths w. 25

Figure 2-6: Crush test procedure for the selected crushing widths for PW(90/0/90/0�)S. 28

Figure 2-7: Crushing specimen of two crushing widths for LDF, MDF, and PW(90/0/90)S. 29

Figure 2-8: Crush test procedure for the selected crushing widths for the DCFC. 30

Figure 2-9: PW(90/0/90/0�)S for the three used widths w:

a) average measured force 𝐹𝐹 vs. crushing stroke s;

b) the total work done E by the measured force F over the SCR. 31

Figure 2-10: Calculating the edge energy for a hypothetical specimen of zero crushing

width at specific strokes for PW(90/0/90/0�)S. 31

Figure 2-11: Properties of PW(90/0/90/0�)S vs. crushing stroke sSCR:

a) energy absorption components crushing energy EC and edge energy EE;

b) calculated SCE. 33

Figure 2-12: Energy absorption components vs. sSCR of LDF, MDF, PW(90/0/90)S, and DCFC. 34

Figure 2-13: SCE of all used materials. 35

Figure 2-14: Calculating the edge energy for a hypothetical specimen of zero crushing

width for LDF, MDF, PW(90/0/90)S, and DCFC. 36

ix

Figure 3-1: Quasi-static test setup:

a) schematic representation from Ref. [40];

b) overview of the test rig;

c) setup of different crushing widths. 50

Figure 3-2: Overview of the dynamic test setup. 51

Figure 3-3: Examples of typical fracture behavior of the crushing frond. 54

Figure 3-4: Examples of typical fracture behavior due to friction and shearing at the edge

of the impactor. 55

Figure 3-5: Examples of measured force responses for different loading rates. 55

Figure 3-6: a) Calculated average crushing force for the largest crushing width; b) calculated average edge force. 57

Figure 3-7: a) Calculated average crushing force for the largest crushing width;

b) calculated average edge force. 57

Figure 3-8: Effect of fiber length on SEAC. 58

Figure 3-9: Effect of fiber mass content on SEAC. 59

Figure 3-10: Effect of the in-plane fiber distribution on SEAC. 60

Figure 3-11: Effect of the loading rate and thickness on SEAC. 62

Figure 3-12: Distribution of the SEA vs. thickness. 64

Figure 4-1: SEAM of flat plates and profiles with different crushed segment widths per tearing for different materials from Ref. [13, 33, 34, 37, 40]. 77

Figure 4-2: Schematic representation of the different test setups:

a) flat plate knife-edge supporting frame from Ref. [37, 40];

b) flat plate full lateral supporting frame from Ref. [33, 34];

c) investigated profiles by Feraboli et al. [13]. 78

Figure 4-3: Comparison between the fracture mode of a fully constrained flat plate

specimen and a crush-tested profile. 80

Figure 4-4: Representation of the individual force components, tearing and crushing,

based on the linear regression of the results of the crush-tested profiles from Feraboli

et al. [13]. 81

Figure 4-5: Separation of the crushing force of the profile flat segments from the results

from Feraboli et al. [13]. 82

Figure 4-6: Overview of the investigated specimen geometries and dimensions. 86

Figure 4-7: Overview of the quasi-static test setups for the flat plate specimens from Ref.

[33] and profile crush testing. 89

x

Figure 4-8: Examples of typical fracture behavior of the crushing frond and the tearing

modes. 91

Figure 4-9: Examples of:

a) measured force F of all specimens of angle-shaped profile A27275;

b) average force 𝐹𝐹 of all angle-shaped profiles. 92

Figure 4-10: Linear regression models of the measured force for each specimen of the

right-angled profiles. 94

Figure 4-11: a) measured force F;

b) SEAM distributions against the segment width of all right-angled profiles and

corresponding hypothetical corner-free profiles. 96

Figure 4-12: Comparison against the segment widths per tearing wx between the right-

angled profiles and the corresponding flat plate of:

a) the measured force per tearing Fx;

b) the SEAM based on the measured force F and the SEAC based on the crushing force FC. 99

Figure 4-13: Examples of the different tearing occurrences at the circular tubes crushing

fronds. 100

Figure 4-14: Comparison of the measured results of the tubes with those of the right-

angled profiles and the corresponding flat plates: a) measured force F;

b) SEAM. 101

xi

List of Tables

Table 2-1: Overview of the test configurations for the different materials. 26

Table 2-2: Summary of the measured and calculated data for the SCR of all materials. 36

Table 3-1: Overview of the test setups for the different material configurations. 47

Table 3-2: Overview of the drop tower weights used. 50

Table 3-3: Overview of the results for the investigated fiber length, fiber mass content, thickness, and loading rate configurations. 65

Table 4-1: Overview of the test setups for the different profile and flat plate

configurations. 87

Table 4-2: Overview of the measured results of the different profile- and flat plate-

configurations. 93

Table 4-3: Overview of the results by utilizing the linear regression for the different

configurations. 95

Table 4-4: Overview of the measured results of the different tubes. 101

Table B.1-1: Summary of the mean values, the standard deviation, and the total

uncertainty for the calculated energy of all used materials. 118

Table B.2-1: Overview of the uncertainty of each configuration. 120

Table B.3-1: Overview of the uncertainty of each configuration. 122

xii

List of Abbreviation

BEV Battery Electric Vehicle

CPIT Crush Property Isolation Technique

DCFC Discontinuous Carbon Fiber Composites

FL Fiber Length

PD In-Plane Production Direction FMC Fiber Mass Content

GRP Glass-Fiber-Reinforced Pultrusion Plastic

LDF Low-Density Fiberboard

LR Loading Rate

MDF Medium-Density Fiberboard PAN Polyacrylonitrile

PW Plywood

RMIT Royal Melbourne Institute of Technology

SCE Specific Crushing Energy

SCR Sustained Crushing Region SEA Specific Energy Absorption

SD Standard Deviation

THI Technische Hochschule Ingolstadt

UAS University of Applied Science

xiii

List of Symbols

A Cross-Sectional Area mm² CV Coefficient of Variation % do Outer Diameter mm di Inner Diameter mm d/t Diameter to Thickness Ratio - df Degree of Freedom - E Total Energy Associated to the Measured Force J EC Crushing Energy Associated to the Crushing Force J EE Edge Energy Associated to the Edge Force J F Measured Force from Crush Testing Flat Plates or Profiles kN 𝑭𝑭� Mean Value of the Measured Forces kN FC Crushing Force Caused by Frond Formation kN FE Edge Force Caused by Shearing and Friction at the Edge of the Impactor of

Fully Supported Flat Plates kN FT Tearing Force at the Profile Corner kN FX Measured Force per Tearing kN M Crushing Force per Unit Segment Width N/mm p Significance Value - p2a Peak to Average Value - R² Coefficient of Determination - s Crushing Stroke mm s1/s2 Boundaries of the Sustained Crushing Region mm SCE Specific Crushing Energy J/mm SEA Specific Energy Absorption kJ/kg SEAC SEA Corresponding to the Crushing Force kJ/kg SEAM SEA Corresponding to the Measured Force kJ/kg t Specimen Thickness mm w Crushing Width (Flat Plate) / Segment Width (Profile) mm 𝒘𝒘� Mean Value of the Crushing / Segment Widths mm w0 Hypothetical Zero Crushing Width mm wx Segment Width per Tearing mm x Number of Tearing Occurrences - ρ Specimen Density kg/m³

1

Abstract

Lightweight materials have always been of interest to the automotive industry.

Besides the beneficial properties of such materials, higher material and manufacturing costs

emerge, which are significantly reflected in the testing procedure and, therefore, demand

cost-effective methods to accurately determine the crush properties of these materials.

Flat plate specimens offer potential cost savings due to their easy manufacturability. By investigating the crushing morphology of a fully supported flat plate specimen, it is found

that two factors influence the energy absorption process during crush testing. One is the

formation of the crushing frond, and the other is the partial separation of the specimen due

to the support and the impactor. Conducting crush tests with different crushing widths

revealed that the crushing force consists of a linear but non-proportional force-width relationship, implying that the tearing at the edge of the impactor is independent of the

crushing width. Subtracting this tearing component from the original measured force

results in the crushing component, which represents the frond formation. The specific

energy absorption (SEA) is often used to compare the potential of different materials.

Contrary to the name, the SEA usually depends on the specimen geometry or the used test setup. Such dependency can be observed when the SEA is calculated from the measured

force of flat plates with different crushing widths, resulting in decreased SEA values. On the

other hand, calculating the SEA from the isolated crushing component leads to consistent

values for different crushing widths.

In order to validate the proposed approach, a comprehensive study is conducted for

several parameters of discontinuous carbon fiber composite flat plates manufactured by

compression molding. The effect of fiber length on fracture toughness agrees with the

general results found in the literature. Increasing the fiber mass content resulted in a

slightly insignificant energy absorption increase. Mainly both parameters affect the standard deviation, as they influence the homogeneity of the fiber distribution. The in-plane

fiber distribution due to different production directions shows almost no influence on

fracture toughness. Increasing the specimen thickness leads to an increase in fracture

toughness as the level of fragmentation decreases and the coherence of the frond formation

during the crushing process increases. Dynamic testing of the specimens revealed a loading

2

rate dependency due to an increase in fragmentation and separation of individual layers of

the crushing frond.

Although the flat plate crush testing methods are very helpful for developing

structural components, the obtained properties need to be transferred accurately. Testing

self-supporting structures do not need an extra test frame, but the obtained results also have geometric dependencies. The crushing morphology of right-angled profiles is typically

composed of tearing at the corner and forming a crushing frond in the flat segments. This

mechanism implies that the corner tearing is most likely independent of the profile width

and depends only on the number of corners in the profile. Accordingly, a technique was

developed and utilized to isolate the width-independent tearing component at the corner from the width-dependent crushing component of the flat segments. This separation allows

for characterizing the geometric dependency of crush-tested profiles on the tearing

occurrences. In addition, the crush properties of profiles with different shapes and

dimensions can be predicted from crush testing a few specimens of different sizes, as long as the corner geometry is identical. The SEA calculated from the crushing force of the flat

segments showed to be practically the same for different values of segment width of right-

angled profiles and flat plates, which explains the differences in crush performance when

comparing the properties obtained from testing composite profiles and flat plates.

3

Chapter 1. Introduction

1.1. Motivation and Rationale

Modern automotive designs, including battery-electric vehicles (BEV), are becoming

the focus of car manufacturers [1–6]. New designs also need to satisfy increasingly stringent regulations [7, 8], aiming to improve safety [7, 9] while minimizing emissions via reducing

or eliminating fuel consumption. Interest in lightweight materials became the focus of

automotive designers in their attempt to satisfy such conflicting demands [3, 6, 7, 9–13]. For

example, reducing the mass of a vehicle frame has a direct influence on the capacity and,

consequently, the mass of the batteries [1, 3, 6, 7, 9, 12]. In addition to reducing weight, fiber-reinforced composite materials have an excellent crush performance, and accordingly,

an outstanding specific energy absorption (SEA) capacity [14–20], which is particularly

beneficial to BEVs as additional protection against impact is needed for the battery [7, 8]. In

particular, discontinuous carbon fiber composites are gaining more interest due to their

manufacturability [21] when design space is limited.

Material and Manufacturing costs demand a cost-effective method to determine the

crushing properties of these materials accurately [6, 16]. In general, crush tests are carried

out on specific components under specific conditions to evaluate the functionality and

determine the SEA of those components. The disadvantages of such tests carried out at the

component level are the high production costs of the prototypes, the manufacturing tools, and the general informative value of such tests, as it is mostly only related to the specific

component and condition. Therefore, Jackson et al. [22] proposed using flat plate test

specimens as they are less expensive and easier to fabricate than corrugated or profiled

specimens to generate a deeper understanding of the parameters influencing the behavior and properties of the materials. The contradiction in this statement is due to the

dependence of the test results on the test methods used and the fact that no standard test

approach has prevailed so far.

According to Feraboli [23], the results of the flat-plat approaches, as well as those of

the profiles, are structure-dependent and, therefore, extrinsic values, which provide difficulties in comparing the obtained results. For example, the investigation of various

channel sections [13] showed geometry-dependent crushing morphologies and, therefore,

a variation in SEA. In addition, the two established methods for obtaining the SEA of flat

1.1 Motivation and Rationale

4

plate specimens vary in results. The first method is based on a proposal from NASA Langley

Research Center [22, 24, 25]. Here, supporting rods stabilize the specimens, whereby an

inadvertently included component is reflected in higher SEA results [23, 25–27]. The

further development of the method by Engenuity LTD. [28] introduced the unsupported

height to dislodge the effect of the supporting rods and therefore enable the specimen to deform freely. The unsupported height turned out to be a fixture-related parameter [29].

With increasing height, the SEA decreased, and finally, catastrophic buckling of the

specimens occurred.

Due to the complexity of the fracture mechanisms, the test setups, and the geometrical

differences, comparisons between the SEA of flat plate specimens and those of self-supporting structures, like tubes, used to be difficult and provided conflicting results. For

example, Lavoie et al. [25] observed material-related differences between crush-tested

plates and profiles. They suggested that plate testing was only usable for screening different

materials but not as a general alternative for structural testing. Cauchi and Hogg [30] investigated the effect of plate geometry on crush testing flat plate composites. They also

investigated the similarity of the nonlinear relationship between the SEA and the specimen

width-to-thickness ratio in flat plates to that between the SEA and the diameter-to-

thickness or width-to-thickness ratio in circular and square profiles.

A similar conclusion follows from comparing the crush testing methods of plates and profiles of several investigations on discontinuous carbon fiber composite [31–38]. Jacob et

al. [31–34] developed an approach for flat plate specimen testing to isolate the frond

splaying crushing mode, which is similar to that observed when testing tubes. They

investigated various mechanisms, e.g., increasing the tow size reduces the SEA, and

increasing the widths of the specimen results in a little higher SEA. They concluded that fiber distribution and length play a crucial role in crush resistance and substantially affect

SEA and therefore recommended studying its effect in detail. In addition to the material

parameters, they examined significant influences of the test setup on the results due to the

choice of the constraints of the specimen and the radius at the base plate. Contradicting, the

SEA values for the tubes [35–38] showed to be higher than those measured by Jacob et al. [32–34] for flat plate specimens. No attempt was made to explain the discrepancies,

probably due to a large number of influencing parameters. The most significant changes in

the SEA were caused by changes in the tube’s thickness. Nonetheless, the tubes’ geometry

had a significant influence since the circular tubes showed higher SEA values than the

1.2 Research Questions

5

square ones. No significant decrease of the SEA was observed in the tubes due to longer

fiber bundles, as in the case of a flat plate specimen.

Nevertheless, the essential focus in the literature for crush testing composites has

been on circular tubes. According to Feraboli et al. [13], the utilization of the tubes is mainly

attributed to the self-supporting structure since no additional test fixtures are required. Various studies [39–46] investigated the geometric effect of tubes or beams on their crush

performance. This effect, however, has mostly been attributed to their profile dimensions-

to-thickness ratios. Although such a ratio is defined for circular tubes, there is no precise

definition for square or other-shaped profiles, which makes comparing the general

performance even more difficult.

1.2. Research Questions

The demand for cost-effective methods for the precise characterization of the

crushing properties comes with contradicting results, specimen geometry dependencies, and influencing factors due to the test setups. These contradictions represent significant

research gaps, which lead to a variety of questions on how to characterize the crush

performance of composite flat plates and profiles appropriately.

How to accurately and consistently characterize the crush energy absorption

properties of flat plates made of fibrous materials?

For the practical use of flat plate crush testing results, the accuracy and consistency

of such results compared to those obtained from profile testing are decisive factors. The

cost-efficiency of the adopted testing methods is not of benefit, as long as the results are not

reliably obtained. The value of the SEA obtained from testing the flat plate specimen is affected by the testing methods and conditions, e.g., the used trigger, clamping conditions,

or geometry. Therefore, the SEA is not an explicit material property, and comparing the SEA

values obtained from different methods is rather difficult. The selection of a suitable test

method depends on the intended usage of the proposed material in a component. For

example, the supporting mechanism of 90° plies cannot be observed using the method of unsupported height. Testing the component itself or substitutional structures like tubes

would give more reliable predictions of the material behavior but would also be more

expensive. Although various methods for examining flat plate specimens are known within

the literature, the relation of the boundaries- and influencing conditions of the different

testing methods are not provided. The need to accurately and consistently characterize the


6

crush energy absorption properties of flat plates is crucial to understanding the relevance

of the methods in different applications.

How to eliminate the effect of the testing setup on the obtained crush

properties?

Feraboli [29] mentioned that the supporting of the flat plate specimen along the crushing stroke is only a compromise between increased friction of a fully clamped

specimen and an inefficient clamping, which leads to unstable crushing due to premature

buckling. Both established testing methods, the fully supporting test rigs [22, 24–27, 47]

and the test rigs using the unsupported height [23, 28, 29, 31–34, 48], induce their test rig-

related characteristics in the obtained results stated by Feraboli [23]. Based on the knowledge of the different test methods, a crush testing approach for characterizing fully

constrained flat plate specimens, which eliminates the effect of the edge constraints, is

needed to be developed to increase the reliability of the results obtained from such tests.

Such a crush testing approach is needed to accurately and consistently characterize the crush energy absorption properties of flat plates.

What are the effects of different testing parameters on the SEA of a composite

material obtained from crush testing flat plates?

This research question is related to developing a novel method for determining the

SEA of flat plate specimens. Such a method needs to be investigated and compared with the already established methods of flat plate and profile testing for evaluating material

usability. Therefore, the effect of various parameters on the energy absorption mechanism

of fully constrained flat plate specimens utilizing the developed approach must first be

investigated.

What differentiates the obtained results from those obtained using other established methods for crush testing composite flat plates and profiles?

Based on the results of a parameter study, the newly developed method is to be

compared between the unsupported height method for flat plate testing and profile testing.

This comparison is intended to help improve the understanding of the differences and

similarities between these methods and increase the usability of flat plate testing due to the given explanations of the various effects. Additionally, understanding these circumstances

and relations should allow for interpreting the contradicting results, the specimen geometry


7

dependencies, and the influencing factors due to the test setups. This missing knowledge

represents a substantial part of the research gap dealing with the flat plate crush testing

methods and needs to be investigated.

How to evaluate and interpret the geometric effects of the crush-tested profiles

on the obtained results?

The geometric effect in contrast to the SEA has been investigated by various studies

[13, 49, 50] under different circumstances. They agreed on the occurrence of two

components, the tearing at the corner and the crushing of the flat segments of the profile.

The comparison relative to a reference corner segment showed a nonlinear decreasing SEA

of the profiles when increasing the widths of the flat segment. In addition, Feraboli et al. [13] calculated the SEA of the flat segments for each profile. These SEA values of the flat

segments were consistent despite a high degree of variation but very low compared to the

SEA of the reference corner segment. They concluded that a significant amount of energy is

absorbed in the corner segment. They also depicted a linear increase of the SEA with the degree of curvature of the cross-section of the profiles. Therefore, they concluded that the

SEA is highly dependent on the degree of curvature of the profile geometry. Thus, the values

for flat and curved segments must be considered separately. Although these results already

provide information about the geometric effects of profiles, they only apply to the reference

corner segment, leading to an additional research gap to universally evaluate and interpret the geometric effects of crush-tested profiles.

What is the relationship between the crush performance of flat plates and that

of profiles of different shapes?

Feraboli et al. [13] also observed the geometric effects on the SEA of the profiles in

comparison to flat plates. Therefore, they compared the SEA of the flat segments from the profiles with those of flat plate specimens of the same material using the method of

unsupported height. The results showed to be similar to those of the flat plate specimens

but slightly lower. Therefore, they concluded that flat plate testing led to overestimating the

energy absorption due to additional effects of the test fixture, so far not been investigated

in detail. However, comparing the crushing morphology of the profile flat segments to that of the flat plate specimens from the literature [13, 35, 38, 40, 41, 44, 49–51, 53–56] is

practically identical. In addition, the behavior of the nonlinear decreasing SEA of the profiles

when increasing the widths of the flat segment showed to be similar to that of fully

1.3 Thesis Outline

8

supported flat plate specimens [27, 44, 51, 52]. Therefore, it can be predicted that the

isolated crushing force of a flat segment of a profile is also likely to be proportional to the

width of the segment, similar to the case of flat plate specimens [52]. However, the literature

does not provide a concrete relationship between the results obtained from testing flat

plates and those obtained from testing profiles of different shapes. This context represents a research gap that needs to be investigated.

How to predict the crush behavior of a composite profile using that obtained

from testing other profiles, and what are the limitations?

Originating from the geometric effects of the crush-tested profiles, separating the

tearing component of the profile corner and the crushing component of the profile flat segments would not only allow for a comparison with crush-tested flat plate specimens. The

crush resistance of a profile could be considered as a combination of resistance of the

corners and that of the flat segments. Once these properties are determined, the behavior

of a right-angled profile with a given number of tearing occurrences and a defined length of the flat segments could be predicted. The resulting research gap could benefit significantly

by examining this connection, as the experimental effort needed to characterize the crush

properties of self-supporting profiles or flat plates can be simplified immensely and reduced

substantially.

1.3. Thesis Outline

The following chapters explain the research done in order to address the above stated

research questions. Each chapter thereby presents an individual published peer-reviewed

article. Therefore, each chapter has its own introduction, methodology, discussion of results, and conclusion sections. The individual articles are slightly adjusted to present a

uniform and consistent nomenclature within the thesis. However, the original research

articles are referenced individually.

Chapter 2 presents a novel crush testing approach to obtain crush properties of flat

plate fibrous materials. To validate the proposed approach, fully constrained specimens of different materials were crushed. The inevitable edge force component, included in the

measured force, emanating from shearing, tearing, and friction at the edges of the impactor,

is isolated and deducted, resulting in the crushing force. An approximately linear

relationship between the energy associated with the measured force and the crushing width

was observed, suggesting a width-independent energy component associated with the

1.3 Thesis Outline

9

shearing and tearing at the edge of the impactor. Consistent specific energy absorption

(SEA) properties of fully supported flat plate specimens were obtained when adopting the

proposed approach, which was labelled as the Crush Property Isolation Technique (CPIT).

Chapter 3 provides an investigation of the effect of fiber length, fiber mass content,

in-plane fiber distribution, plate thickness, and loading rate on the energy absorption mechanism of discontinuous carbon fiber composite flat plate specimens, utilizing the crush

property isolation technique, which was introduced in Chapter 2. Similar crushing

morphology was obtained for flat plate testing as for discontinuous carbon fiber tubes. Fiber

length and fiber mass content showed only a minor effect on the specific energy absorption

(SEA). Results obtained for the in-plane fiber distribution showed to be consistent. SEA values increased substantially with increased plate thickness. A loading rate dependency

between static and dynamic loading could be observed as a decrease in the SEA values when

increasing plate thickness.

Chapter 4 investigates the correlation between the specific energy absorption (SEA) behavior of various right-angled profiles, e.g., those with angle-, channel-, and square

geometries. The behavior is also compared with that of flat plates and circular tubes. A novel

approach is proposed, which allows for utilizing the results obtained from a small number

of profile crush tests to predict the crush properties of other profiles. The proposed

approach is to separate the effect of the resistance at the profile corners from the crushing force of the profile flat segments. A generic crush property of a corner and that of a flat

segment, calculated from crush testing a few profile specimens, has been utilized to predict

the crush properties of right-angled profiles with different shapes and dimensions. The

predicted crush properties of numerous profiles of different shapes and sizes proved to be

practically identical to those obtained experimentally. The calculated crushing SEA of the profile flat segments has also proved to be identical to that of flat plates.

Chapter 5 concludes the work with a summary of the individual investigations and

accounts for the results in context by highlighting the advantages, applications, and

limitations of the outcome. In addition, the future scope based on the thesis outcome is

discussed.

The Appendix contains the accuracy analysis of the corresponding experimental

investigations of the studies of Chapters 2 to 4.

1.4 Study Limitations

10

1.4. Study Limitations

The research focuses on accurately and consistently obtaining the crush energy

absorption properties of flat plates and profiles for different specimen widths and profile dimensions while describing the geometric effects.

However, the research focuses on comparing the characteristics of suitably crushed

specimens and not investigating the material-related boundary conditions, e.g., buckling.

In crush testing right-angled profiles, the research focuses on comparing the

characteristics of profiles of different geometries but having the same shell thickness, and corner geometry. This limitation applies equally when comparing the characteristics of flat

plates to those of profiles.

Moreover, the research is limited to profiles, the corner tearing of which is

predictable. Therefore, in the case of circular profiles, where the crush behavior mechanism

differs significantly, only limited investigation is conducted.

1.5. References

[1] Kampker A, Kreisköther K, Treichel P, Möller T, Boelsen Y. Elektromobilität -- Trends und Herausforderungen der zukünftigen Großserienproduktion. In: Frenz W, editor. Handb. Ind. 4.0 Recht, Tech. Gesellschaft, Berlin, Heidelberg: Springer Berlin Heidelberg; 2020, p. 661–80. doi:10.1007/978-3-662-58474-3_34.

[2] Ou S, Lin Z, He X, Przesmitzki S, Bouchard J. Modeling charging infrastructure impact on the electric vehicle market in China. Transp Res Part D Transp Environ 2020;81:102248. doi:10.1016/j.trd.2020.102248.

[3] Gröger O, Gasteiger HA, Suchsland J-P. Review—Electromobility: Batteries or Fuel Cells? J Electrochem Soc 2015;162:A2605–22. doi:10.1149/2.0211514jes.

[4] Zarazua de Rubens G, Noel L, Kester J, Sovacool BK. The market case for electric mobility: Investigating electric vehicle business models for mass adoption. Energy 2020;194:116841. doi:10.1016/j.energy.2019.116841.

[5] Schwabe J. Risk and counter-strategies: The impact of electric mobility on German automotive suppliers. Geoforum 2020;110:157–67. doi:10.1016/j.geoforum.2020.02.011.

[6] Smith B, Spulber A, Modi S, Fiorelli T. Technology Roadmaps: Intelligent Mobility Technology, Materials and Manufacturing Processes, and Light Duty Vehicle Propulsion. Cent Automot Res 2017. doi:10.1044/leader.ppl.22062017.20.

1.5 References

11

[7] Redelbach M, Klötzke M, Friedrich HE. Impact of lightweight design on energy consumption and cost effectiveness of alternative powertrain concepts. Eur. Electr. Veh. Congr., Brussels, Belgium: 2012, p. 1–9.

[8] Fischer- J, Gereon W, Editors M. Advanced Microsystems for Automotive Applications 2013. Heidelberg: Springer International Publishing; 2013. doi:10.1007/978-3-319-00476-1.

[9] Höhne K, Hirtz E. With System Integration and Lightweight Design to Highest Energy Densities, Springer, Heidelberg; 2013, p. 205–14. doi:10.1007/978-3-319-00476-1_20.

[10] Elmarakbi A, editor. Advanced Composite Materials for Automotive Applications. Chichester, UK: John Wiley & Sons Ltd; 2013. doi:10.1002/9781118535288.

[11] Obradovic J, Boria S, Belingardi G. Lightweight design and crash analysis of composite frontal impact energy absorbing structures. Compos Struct 2012;94:423–30. doi:10.1016/j.compstruct.2011.08.005.

[12] Justen R, Schöneburg R. Crash safety of hybrid-and battery electric vehicles. 22th ESV-Conference, 2011, p. 11–0096.

[13] Feraboli P, Wade B, Deleo F, Rassaian M. Crush energy absorption of composite channel section specimens. Compos Part A Appl Sci Manuf 2009;40:1248–56. doi:10.1016/j.compositesa.2009.05.021.

[14] Eichlseder W, Schöneburg R. Anforderungen an den Leichtbau im Fahrzeug. Leichtbau der Fahrzeugtechnik, Wiesbaden: Springer Fachmedien Wiesbaden; 2013, p. 119–75. doi:10.1007/978-3-8348-2110-2_4.

[15] Dieringa H, Drechsler K, Evertz T, Flaxa V, Furrer P, Gadow R, et al. Die Leichtbauwerkstoffe für den Fahrzeugbau. Leichtbau der Fahrzeugtechnik, Wiesbaden: Springer Fachmedien Wiesbaden; 2013, p. 199–442. doi:10.1007/978-3-8348-2110-2_6.

[16] Hull D. A unified approach to progressive crushing of fibre-reinforced composite tubes. Compos Sci Technol 1991;40:377–421. doi:10.1016/0266-3538(91)90031-J.

[17] Kumar AP, Mohamed MN. Crush Performance Analysis of Combined Geometry Tubes under Axial Compressive Loading. Procedia Eng 2017;173:1415–22. doi:10.1016/j.proeng.2016.12.203.

[18] Isaac CW, Ezekwem C. A review of the crashworthiness performance of energy absorbing composite structure within the context of materials, manufacturing and maintenance for sustainability. Compos Struct 2021;257:113081. doi:10.1016/j.compstruct.2020.113081.

1.5 References

12

[19] Bru T. Behaviour and material properties of composites for crash modelling. Chalmers University of Technology, 2016.

[20] Mamalis A., Robinson M, Manolakos DE, Demosthenous GA, Ioannidis MB, Carruthers J. Crashworthy capability of composite material structures. Compos Struct 1997;37:109–34. doi:10.1016/S0263-8223(97)80005-0.

[21] Xiao Z. Advancements in discontinuous carbon fibre composite technologies for high- volume manufacturing processes. University of Nottingham, 2018.

[22] Jackson K, Morton J, Lavoie JA, Boitnott R. Scaling of Energy Absorbing Composite Plates. AHS 48th Annu. Forum, Washington D.C.: 1992.

[23] Feraboli P. Current Efforts in Standardization of Composite Materials Testing for Crashworthiness and Energy Absorption. 47th AIAA/ASME/ASCE/AHS/ASC Struct. Struct. Dyn. Mater. Conf. 14th AIAA/ASME/AHS Adapt. Struct. Conf. 7th, Reston, Virigina: American Institute of Aeronautics and Astronautics; 2006. doi:10.2514/6.2006-2217.

[24] Jackson K, Morton J, Lavoie JA, Boitnott R. Scaling of Energy Absorbing Composite Plates. J Am Helicopter Soc 1994;39:17–23. doi:10.4050/JAHS.39.17.

[25] Lavoie JA, Morton J, Jackson K. An Evaluation of the Energy Absorption of Laminated Composite Plates. Proc Inst Mech Eng Part G J Aerosp Eng 1995;209:185–94. doi:10.1243/PIME_PROC_1995_209_289_02.

[26] Daniel L, Hogg P., Curtis P. The crush behaviour of carbon fibre angle-ply reinforcement and the effect of interlaminar shear strength on energy absorption capability. Compos Part B Eng 2000;31:435–40. doi:10.1016/S1359-8368(00)00026-3.

[27] Daniel L, Hogg P., Curtis P. The relative effects of through-thickness properties and fibre orientation on energy absorption by continuous fibre composites. Compos Part B Eng 1999;30:257–66. doi:10.1016/S1359-8368(98)00066-3.

[28] Barnes G. Composite crush coupon testing. Proc. 49th MIL-HDBK-17 Coord. Meet. Work. Gr., Santa Monica, CA: 2005.

[29] Feraboli P. Development of a Modified Flat-plate Test Specimen and Fixture for Composite Materials Crush Energy Absorption. J Compos Mater 2009;43:1967–90. doi:10.1177/0021998309343025.

[30] Cauchi Savona S, Hogg PJ. Effect of fracture toughness properties on the crushing of flat composite plates. Compos Sci Technol 2006;66:2317–28. doi:10.1016/j.compscitech.2005.11.038.

1.5 References

13

[31] Jacob GC, Starbuck JM, Simunovic S, Fellers JF. New Test method for determining energy absorption mechanisms in polymer composite plates. Polym Compos 2003;24:706–15. doi:10.1002/pc.10064.

[32] Jacob GC, Starbuck JM, Fellers JF, Simunovic S. Energy Absorption in Chopped Carbon Fiber Epoxy Composites for Automotive Crashworthiness. Polym J 2003;35:560–7. doi:10.1295/polymj.35.560.

[33] Jacob GC, Starbuck JM, Fellers JF, Simunovic S. Effect of fiber volume fraction, fiber length and fiber tow size on the energy absorption of chopped carbon fiber-polymer composites. Polym Compos 2005;26:293–305. doi:10.1002/pc.20100.

[34] Jacob GC, Starbuck JM, Fellers JF, Simunovic S, Boeman RG. Crashworthiness of various random chopped carbon fiber reinforced epoxy composite materials and their strain rate dependence. J Appl Polym Sci 2006;101:1477–86. doi:10.1002/app.24224.

[35] Turner T, Harper L, Warrior N, Caliskan A. Energy Absorption Performance of Meso-Scale Discontinuous Carbon Fibre Composites. Int J Veh Struct Syst 2011;3:80–6. doi:10.4273/ijvss.3.2.02.

[36] Cutting RA, Rios-Tascon F, Goodsell JE. Experimental investigation of the crush performance of prepreg platelet molding compound tubes. J Compos Mater 2020:002199832092941. doi:10.1177/0021998320929418.

[37] Cutting RA, Sharma V, Goodsell JE. Crush Response of Prepreg Platelet Molding Compound Tubes. Am. Soc. Compos. 2018, Lancaster, PA: DEStech Publications, Inc.; 2018. doi:10.12783/asc33/26074.

[38] Cutting RA, Goodsell JE, Pipes RB. Failure Morphology and Energy Absorption of Prepreg Platelet Molding Compound Tubes. Proc 18th Annu SPE Automot Compos Conf Exhib 2018:1–16.

[39] Yang Y, Nishikawa Y, Nakai A, Ishiaku US, Hamada H. Effect of Cross-Sectional Geometry on the Energy Absorption Capability of Unidirectional Carbon Fiber Reinforced Composite Tubes. Sci Eng Compos Mater 2008;15:249–63. doi:10.1515/SECM.2008.15.4.249.

[40] Yang H, Lei H, Lu G, Zhang Z, Li X, Liu Y. Energy absorption and failure pattern of hybrid composite tubes under quasi-static axial compression. Compos Part B Eng 2020;198:108217. doi:10.1016/j.compositesb.2020.108217.

[41] Yan L, Chouw N. Crashworthiness characteristics of flax fibre reinforced epoxy tubes for energy absorption application. Mater Des 2013;51:629–40. doi:10.1016/j.matdes.2013.04.014.

1.5 References

14

[42] Hamada H, Ramakrishna S. Scaling effects in the energy absorption of carbon-fiber/PEEK composite tubes. Compos Sci Technol 1995;55:211–21. doi:10.1016/0266-3538(95)00081-X.

[43] Pickett L, Dayal V. Effect of tube geometry and ply-angle on energy absorption of a circular glass/epoxy crush tube - A numerical study. Compos Part B Eng 2012;43:2960–7. doi:10.1016/j.compositesb.2012.05.040.

[44] Cauchi Savona S, HOGG P. Investigation of plate geometry on the crushing of flat composite plates. Compos Sci Technol 2006;66:1639–50. doi:10.1016/j.compscitech.2005.11.011.

[45] Farley GL. Effect of Specimen Geometry on the Energy Absorption Capability of Composite Materials. J Compos Mater 1986;20:390–400. doi:10.1177/002199838602000406.

[46] Farley GL, Jones. RM. Energy-Absorption Capability of Composite Tubes and Beams. NASA Tech Memo 1989;101634:0–250.

[47] Lavoie JA, Morton J. A CRUSH TEST FIXTURE FOR INVESTIGATING ENERGY ABSORPTION OF FLAT COMPOSITE PLATES. Exp Tech 1994;18:23–6. doi:10.1111/j.1747-1567.1994.tb00316.x.

[48] Joosten MW, Dutton S, Kelly D, Thomson R. Experimental evaluation of the crush energy absorption of triggered composite sandwich panels under quasi-static edgewise compressive loading. Compos Part A Appl Sci Manuf 2010;41:1099–106. doi:10.1016/j.compositesa.2010.03.010.

[49] Laananen DH, Bolukbasi AO. Prediction of energy absorption in composite stiffeners. Compos Struct 1995;32:173–86. doi:10.1016/0263-8223(95)00068-2.

[50] Bolukbasi AO, Laananen DH. Energy absorption in composite stiffeners. Composites 1995;26:291–301. doi:10.1016/0010-4361(95)93672-7.

[51] Lausch J, Takla M, Schweiger H-G. Crush characteristics of flat-plate discontinuous carbon composites. Compos Part A Appl Sci Manuf 2021;147:106431. doi:10.1016/j.compositesa.2021.106431.

[52] Lausch J, Takla M, Schweiger H-G. Crush testing approach for flat-plate fibrous materials. Compos Part B Eng 2020;200:108333. doi:10.1016/j.compositesb.2020.108333.

[53] Palanivelu S, Paepegem W Van, Degrieck J, Vantomme J, Kakogiannis D, Ackeren J Van, et al. Crushing and energy absorption performance of different geometrical shapes of small-scale glass/polyester composite tubes under quasi-static loading conditions. Compos Struct 2011;93:992–1007. doi:10.1016/j.compstruct.2010.06.021.

1.5 References

15

[54] Palanivelu S, Van Paepegem W, Degrieck J, Van Ackeren J, Kakogiannis D, Van Hemelrijck D, et al. Experimental study on the axial crushing behaviour of pultruded composite tubes. Polym Test 2010;29:224–34. doi:10.1016/j.polymertesting.2009.11.005.

[55] Paul D, Ramachandran V, Gupta NK. Improvements in the crushing behaviour of glass fibre-epoxy composite tubes by the addition of hollow glass particles. Thin-Walled Struct 2019;141:111–8. doi:10.1016/j.tws.2019.03.033.

[56] Imbsweiler D. Experimentelle Untersuchung und numerische Simulation des Crashverhaltens von SMC-Strukturen. Kaiserslautern: IVW; 2002.

16

Chapter 2. Crush Testing Approach for Flat Plate Fibrous Materials

This chapter presents a novel crush testing approach to accurately and consistently

obtain the crush energy absorption properties of flat plate fibrous materials. An

approximately linear relationship between the measured force and the crushing width was

observed, suggesting a width-independent component due to the shearing and tearing at

the edge of the impactor. This inadvertently included component can be isolated and deducted by utilizing linear regression, resulting in the sole crushing performance of the

frond formation of the flat plate.

The work related to this chapter has been published and peer-reviewed in the Journal

Composites Part B: Engineering. The corresponding article can be cited as:

Lausch J, Takla M, Schweiger H-G. Crush testing approach for flat-plate fibrous materials. Compos Part B Eng 2020;200:108333. doi:10.1016/j.compositesb.2020.108333.

2.1. Introduction

Today’s automotive industry faces continuous development due to new technologies, like electromobility [1–6]. Lightweight materials play an increasingly important role in

reducing fuel consumption while increasing safety through better energy absorption [3, 6–

12]. Battery electric vehicles (BEV), in particular, benefit from a lighter body because it

directly affects the required battery capacity and consequently its mass [1, 3, 6, 8, 10, 11].

Furthermore, BEVs need additional safety precautions in order to reduce intrusion levels and battery damage in side-impacts [10, 13]. Due to their high specific energy absorption

(SEA) capacity, fiber composites are predestined for this task [14, 15]. Material and

Manufacturing costs demand a cost-effective method to determine the crushing properties

of these materials accurately [6, 16]. Jackson et al. [17] proposed using flat plates test

specimens as they are less expensive and easier to fabricate than corrugated or profiled specimens. Numerical modeling was used to describe different crush failure modes in detail,

which can be introduced to crash simulations [18, 19] to reduce the need for costly crash

tests.

2.1 Introduction

17

A coupon-level test method was developed by Jackson et al. [17, 20] for characterizing

the energy absorption of flat plate specimens. The main problem with testing flat plate

specimens is global buckling, which needs to be prevented in order to ensure sustained

crushing under compressive loading [17, 20]. Therefore, buckling analysis was needed to

determine the appropriate plate dimensions. Jackson et al. [17] utilized lateral support rods in the developed test rig. This first design resulted in jamming the tested plate between the

rods, resulting in an increase in the measured load [20, 21]. Using knife-edges as supports,

as shown in Figure 2-1-a, produced better results [21, 22]. Lavoie et al. [22] suggested that

this test method was suitable for comparing the energy-absorbing potential of different

material systems and trigger mechanisms. However, they observed material-related differences when comparing the results with those of self-supporting structures such as

tubes. Daniel et al. [23, 24] constructed a test rig for variable specimen width and thickness.

They developed an empirical relationship between the unsupported width of a specimen

and its SEA. However, they did not provide an explanation for such a relationship but concluded that plate stability is a major factor for its overall strength. Feraboli [25]

attributed the link between decreasing SEA and increasing the unsupported width to the

knife-edge support rods.

Figure 2-1: Schematic representation of different test rig designs: a) from Ref. [22]; b) from Ref. [29]; c) from Ref. [30] adapted from (a).

Barnes [26] changed the supporting method to fully constrained clamping.

Additionally, he introduced the unsupported height as a new parameter by adding a variable

spacer between the base plate and the clamping fixture. Increasing the unsupported height resulted in horizontal buckling instability, which reduced the SEA. The changes made by

Barnes [26] to the test rig developed by Jackson et al. [17, 20–22] were also explained by

2.1 Introduction

18

Feraboli [25]. Jacob et al. [27–30] designed a test rig, schematically shown in Figure 2-1-b,

which isolates the frond splaying mode in one direction, like the crushing mode from

composite tubes. They also used full lateral roller support to reduce friction. They used a

rounded base plate to provoke frond splaying. They also examined the influence of three

constraint conditions: tight, loose, and no constraint. They also tested different specimen widths. Jacob et al. [30] referred the decrease in SEA of smaller specimens to the fiber length

of the discontinuous carbon composites, which is independent of the test rig but needed to

be considered in its design. Feraboli [31] developed a test rig, schematically shown in Figure

2-1-c, based on the works from Daniel et al. [23, 24] and Barnes [26]. He concluded that the

SEA is greatly affected by the unsupported height of the plate and the interlaminar toughness of the material.

The value of the SEA of the flat plate specimen is affected by the testing methods and

conditions, e.g., the used trigger, clamping conditions, or geometry. Therefore, The SEA is

not an explicit material property, and comparing the values obtained from different methods is rather difficult. The selection of a suitable test method depends on the intended

usage of the proposed material in a component. For example, the mechanism of 90° plies

cannot be observed using the method of unsupported height. Using the component itself or

substitutional structures like tubes would give more reliable predictions of the material

behavior but would be more expensive. Feraboli [31] mentioned that clamping the flat plate specimen against the knife-edge is only a compromise between increased friction of a fully

clamped specimen and an inefficient clamping, which leads to unstable crushing due to

premature buckling. According to Feraboli [25], both testing methods, the fully supporting

test rigs using knife-edge support rods, like [17, 20–24], and the test rigs using the

unsupported height, like [25–32], induce their test rig related characteristics in the obtained results. When fully supporting the edges of the specimen, an inadvertent force at the

supporting rods is included in the measured results. So far, the amount of this force has not

been identifiable yet. The other method using the unsupported height to circumvent the

inadvertently included force requires an in-depth characterization of the effect of the

unsupported height on the occurrence of buckling.

This work, therefore, investigates a novel crush testing approach for characterizing

fully constrained flat plate specimens by nullifying the inadvertently included forces

resulting from the edge constraints, thereby increasing the reliability of such tests. The

crushing force, the associated energy, and the SEA are isolated from the inadvertently

included components. The crush properties obtained by using this approach are placed

2.2 Testing Approach

19

between the properties obtained using the unsupported height and those obtained by

crushing tubes. Specific crushing energy (SCE) per unit width can also be obtained using

this approach.

2.2. Testing Approach

According to Feraboli [25, 31, 33], when testing fully supported flat plate specimens,

an edge force component is inadvertently included in the measured force caused by tearing

at the clamping rods, e.g., when using the test rig shown in Figure 2-1-a. The failure modes,

defined in fracture mechanics [34] and illustrated by Cauchi Savona and Hogg [35] for flat plate specimens, indicate that fracture starts with a midplane splitting. After the formation

of the splaying frond, splitting occurs at the midplane and within the frond. Additionally,

different delamination and friction mechanisms occur inside the frond, including bending

and fracture of the fibers. In addition, the force component due to friction at the edge of a

moving impactor between the rods and the flat plate specimen is implicit in the inadvertently included force and is very difficult to measure. The shear forces are also

difficult to measure when the guided edges of the specimen are also deforming, as the

additional resistance depends on the amount of lateral deformation, the edge clearance, and

other testing parameters. The edge force FE is not the targeted material property and should

be separated from the measured total force F in order to obtain reliable material crushing characteristics. The measured force F consists of the crushing force FC and the edge force FE,

which are shown in Figure 2-2. Calculating the SEA property of the tested material using the

measured force leads to artificially high values, and the calculated material property

becomes a function of the test rig design and the dimensions of the specimen.


20

Figure 2-2: Force components of a moving impactor.

In order to obtain the specific energy absorption property, the different components

of the measured force and the consequently calculated energy components need to be

isolated and separated. The calculated work done by the impactor is adopted as the basis

for comparison in the analysis. Using the energy rather than the measured force provides a

better illustration of the proposed method as the high level of fluctuation in the measured force, which is typical for composite and laminated materials [19], may conceal the

significance of the proposed approach. The total work done by the measured force F along

the sustained crushing region (SCR) of a specified crushing width w will be referred to as

the total energy E. Part of the work is converted to the energy dissipated in crushing the

specimen, and the remainder is dissipated at the clamped edges due to shearing and friction losses. The total energy E is calculated by integrating the measured force F along the

traveling stroke s between the given boundaries s1 and s2 of the SCR,

𝐸𝐸(𝑠𝑠,𝑤𝑤) = ∫ 𝐹𝐹(𝑠𝑠 ,𝑤𝑤) 𝑑𝑑𝑑𝑑 ,

𝐸𝐸(𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆,𝑤𝑤) = ∫ 𝐹𝐹(𝑠𝑠,𝑤𝑤)𝑠𝑠2𝑠𝑠1 𝑑𝑑𝑑𝑑.

(2-1)

The total energy E can be divided into two components; the crushing energy EC, associated

with the crushing force, and the edge energy EE, associated with the edge force.


21

The edge energy depends on the thickness and material of the plate, the surface of the

impactor, as well as the test parameters. Since the shearing and tearing occur only at the

constrained side edges of the plate, it is expected to be practically independent of the

crushing width w of the impactor. Therefore, the edge energy should be effectively

independent of the crushing width. Extrapolating the energy consumed by two flat plate specimens with different crushing widths, (wa and wb), to a hypothetical specimen of zero

crushing width w0 results in the edge energy dissipated along the SCR of the crushing stroke

s of

𝐸𝐸𝐸𝐸 (𝑠𝑠) = 𝐸𝐸(𝑠𝑠,𝑤𝑤𝑎𝑎)−𝐸𝐸�𝑠𝑠,𝑤𝑤𝑏𝑏�

𝑤𝑤𝑎𝑎−𝑤𝑤𝑏𝑏∗ (𝑤𝑤0 − 𝑤𝑤𝑎𝑎) + 𝐸𝐸(𝑠𝑠,𝑤𝑤𝑎𝑎) . (2-2)

Figure 2-3-a is a simplified schematic diagram illustrating how the crush energy and

edge energy components are calculated from the total energy. The upper line, which represents the apparent energy E, is obtained by fitting the energy values calculated from

force measurements at a specific impactor travel distance for specimens with different

widths (wa and wb). Although the energy-width relationship might not be linear for

extremely narrow or wide specimens, an almost linear relationship is practically valid

within a reasonable range of the crushed width. The approach can be used for a wide range of widths. However, very narrow specimens might have additional forces due to

accumulated debris and higher friction. On the other hand, very wide specimens tend to

buckle, whereby the crushing force decreases. Therefore, both extremes should be avoided.

Extrapolation to the hypothetical zero-width point, shown as a dotted line, determines the

width-independent energy associated with the edge forces. Reducing the calculated edge energy component EE from the total energy E, blue curve, results in the lower green line,

which represents the crushing energy EC, characterizing the material property. The offset

between the two lines is the edge energy EE consumed at the edges of the impactor due to

shearing and friction, which needed to be deducted so that the crushing energy component

EC could be isolated. While scaling of the specimens usually leads to a reduction in the obtained material strength [36], it should be noted that scaling includes every volume

aspect; width, height, and thickness. By only scaling the width, no significant size effects of

the investigated material strength and Young’s modulus were noticed [36–38], which

means that the measured force, which is used to calculate the strength and Young’s modulus

scales linearly with the width. Also, when Jacob et al. [28] investigated the effect of different specimen widths using unsupported height, the results showed almost the same SEA values

for different widths. Significant changes could only be noticed when using the

unconstrained condition at the rounded base plate. The slightly higher SEA of the widest


22

specimen was attributed to the fiber length. Since the results obtained using this method

only contain crushing forces and no shearing and tearing forces, a linear relationship

between the crushing force and the width of the specimen could be found, resulting in

almost the same SEA values for specimens with different widths.

Significant results were obtained by Cauchi, Savona, and Hogg [39], who examined the width-to-thickness ratio effect on the SEA for various glass-fiber-reinforced layups

using a modified test rig with knife-edge supporting rods along the stroke. The forces vs.

crushing widths, recalculated from the data available in [39], are illustrated in Figure 2-3-b,

which clearly indicates a mostly linear, albeit non-proportional force-width relationship.

The force distribution of the material combinations states linear correlation with the specimen width. Accordingly, a linear relationship between the measured forces and the

specimen width can be assumed, at least within a reasonable range of width values. Linear

extrapolation to the point of hypothetical zero-width is merely used to calculate the edge

force/energy, but the actual used range for experimental testing should avoid very narrow specimens, as indicated above. Researchers who adopt this approach in the future should

make sure that the selected width range lies within the linear section of the curve.

Figure 2-3: a) Schematic illustration of the proposed approach; b) force-width relationship of different materials from Ref. [39].

The crushing energy at the specified impactor travel s along the SCR for the specified

specimen crushing widths (wa and wb) is calculated by subtracting the edge energy from the total work done for the specified crushing width

𝐸𝐸𝐶𝐶 (𝑠𝑠,𝑤𝑤𝑎𝑎) = 𝐸𝐸(𝑠𝑠,𝑤𝑤𝑎𝑎) − 𝐸𝐸𝐸𝐸 (𝑠𝑠) ; 𝐸𝐸𝐶𝐶 (𝑠𝑠 ,𝑤𝑤𝑏𝑏) = 𝐸𝐸(𝑠𝑠 ,𝑤𝑤𝑏𝑏) − 𝐸𝐸𝐸𝐸 (𝑠𝑠) . (2-3)


23

Dividing the crushing energy by the corresponding crushing width leads to the

Specific Crush Energy (SCE), representing the actual energy absorption per unit width along

the SCR of the crushing stroke s

𝑆𝑆𝑆𝑆𝐸𝐸(𝑠𝑠) = 𝐸𝐸𝑆𝑆(𝑠𝑠,𝑤𝑤𝑎𝑎)

𝑤𝑤𝑎𝑎=

𝐸𝐸𝑆𝑆�𝑠𝑠,𝑤𝑤𝑏𝑏�

𝑤𝑤𝑏𝑏. (2-4)

For multiple crushing widths, the mean edge energy over the stroke, as well as the

SCE, can be calculated with the least mean square method. Based on the assumption of

constant edge energy and linear relation between the total dissipated energy and the crushing width, the edge energy EE is given as the intercept and the SCE as the slope:

𝐸𝐸𝐸𝐸 (𝑠𝑠) = 𝐸𝐸�(𝑠𝑠,𝑤𝑤�) −𝑆𝑆𝑆𝑆𝐸𝐸(𝑠𝑠)𝑤𝑤�. (2-5)

with

𝑆𝑆𝑆𝑆𝐸𝐸(𝑠𝑠) = ∑ (𝑤𝑤𝑖𝑖𝑛𝑛𝑖𝑖 −𝑤𝑤�)(𝐸𝐸�𝑠𝑠,𝑤𝑤𝑖𝑖�

−𝐸𝐸� (𝑠𝑠,𝑤𝑤� ))

∑ (𝑤𝑤𝑖𝑖−𝑤𝑤�)2𝑛𝑛𝑖𝑖

, (2-6)

The SEA is calculated for both the total work done and the actual crushing energy in

order to identify the value of discrepancy. The material SEA associated with the crushing

energy SEAC is calculated by dividing the crushing energy by the specimen thickness t,

density ρ, crushing width w, and SCR stroke sSCR or by dividing the SCE by the specimen thickness, density, and SCR stroke

SEA𝐶𝐶 =𝐸𝐸𝑆𝑆(𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆,𝑤𝑤𝑎𝑎)

𝑡𝑡∗𝜌𝜌∗𝑤𝑤𝑎𝑎 ∗𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆=

𝐸𝐸𝑆𝑆(𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆,𝑤𝑤𝑏𝑏)

𝑡𝑡∗𝜌𝜌∗𝑤𝑤𝑏𝑏∗𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆=

𝑆𝑆𝐶𝐶𝐸𝐸 (𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆 )

𝑡𝑡∗𝜌𝜌∗𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆. (2-7)

The apparent SEA corresponding to the total “measured” work SEAM is calculated by

integrating the measured force along the SCR and dividing it by the specimen thickness, density, crushing width, and SCR stroke

SEA𝑀𝑀(𝑤𝑤) =∫ 𝐹𝐹(𝑠𝑠,𝑤𝑤)𝑠𝑠2𝑠𝑠1

𝑑𝑑𝑠𝑠

𝑡𝑡∗𝜌𝜌∗𝑤𝑤∗𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆. (2-8)

It should be noted that the material SEAC (Crush Specific Energy Absorption) is

obtained from the isolated crushing energy component, while the apparent SEAM (Measured

Specific Energy Absorption) is calculated from the measured force.

2.3 Experimental Setup

24

2.3. Experimental Setup

The design of the test rig is based on the three-sided clamping construction used by

Feindler [40] and adapted to include a longer crushing stroke, as shown in Figure 2-4. The flat plate specimen is firmly mounted via screw connections of the two profiled blocks. The

free top side is loaded vertically between the fixed lateral blocks. The load is applied via

impactors of different crushing widths through a Z100SL; way steered, 100 kN, screw jack

system, made by ZIMM Maschinenelemente GmbH + Co KG. The impactor is directly

attached to the end of the spindle of the screw jack system. The stroke of the impactor is measured by the linear encoder BG200, made by Kami GmbH, with 5 µm steps. The linear

encoder is attached to the top of the spindle and measures the vertical movement of the

spindle directly. The test rig is mounted on four calibrated 20 kN force sensors of the type

KD80s that are used with the measuring amplifier GSV-8DS SUBD15HD, both from ME-

Meßsysteme GmbH. All the sensors and the measuring amplifier have an accuracy class of 0.05%. Both stroke and force are logged at 50 Hz and afterward resampled to a common

base of 5 µm steps for further evaluation.

Figure 2-4: Schematic representation of the test rig and overview of the whole setup.


25

The test rig is capable of holding specimens from 2.0 mm to 14.0 mm thickness. The

total width of all flat plate specimens is 80.0 mm. The engineered wood specimens are

100.0 mm long, and the composite specimens are 150.0 mm long. Part of the width is

constrained on each side by the profiled blocks. The crushing width is defined by the width

of the used impactor and is only part of the total specimen width. A clearance of 5.0 mm is used between the clamped edge and the impactor to prevent material jamming between

them. The impactors are milled from steel blocks with a flat crushing surface and different

crushing widths.

In general, a crush test is carried out on a specific component under specific

conditions to evaluate the functionality and determine the SEA of that component. The general usage of the developed test rigs for testing flat plate specimens so far was to

examine the material behavior under various circumstances to generate a deeper

understanding of the parameters that influence the material behavior. This article focuses

on presenting the concept of the new approach and validating its applicability for different materials, rather than examining the influence of different circumstances. Therefore,

validation of the proposed approach focuses on a quasi-static rate of 5 mm/min. While the

influence of loading rate is not addressed in this study, the work paves the way for

researchers to address the effect of different parameters, including loading rate, plate

thickness, and material composition.

As illustrated in Figure 2-5, the crushing widths of 23.6 mm and 36.0 mm need

additional plates in order to maintain the 5-mm clearance between the impactor and the

clamping blocks in all tests. In addition, an essential prerequisite is that the testing process

and conditions, such as the surface quality of the impactor and the thickness of the

specimen, are identical for the selected crushing widths.

Figure 2-5: Detailed configuration for all three crushing widths w.


26

Saka [41] stated that wood, especially engineered wood, can be considered a natural

composite material due to its structure and composition. Other researchers conducted

mixed experimental testing on both wooden and composite plates [42-44]. Considering the

different similarities, e.g., the layer structure of the plywood (PW) compared to fiber

composite laminates, engineered wood materials were initially used here to validate the proposed approach. The distribution of short fibers of low-density fiberboard (LDF) and

medium-density fiberboard (MDF) is also comparable to that of short fiber-reinforced

composite materials. In addition, to confirm that the proposed approach is feasible and

applicable to composite materials, it was also validated using discontinuous carbon fiber

composite (DCFC). The successful application of the proposed approach to such a range of different materials adds to the credibility of adopting it for testing different fibrous flat plate

materials. This also motivates researchers to use the proposed approach for testing other

flat plate materials, where buckling represents a limitation on the testing process.

In order to validate the proposed approach, three different test series were conducted. A detailed plan of the experiments is included in Table 2-1. The first test series

is performed on flat plate specimens made of beech plywood with an overall thickness of

8.8 mm and layer structure of (90/0/90/0�)S, where 0° corresponds to the vertical crushing

direction, s denotes symmetry. The outer layers have 0.9 mm thickness, and each of the

internal five layers is 1.4 mm thick.

Table 2-1: Overview of the test configurations for the different materials.

Material Density ρ / kg/m³

Thickness t / mm

Chamfered Trigger

Crushing Stroke s / mm

Crushing Width w / mm

No. of Tests

PW(90/0/90/0�)S 705.84 8.8 45° double 80 23.6; 36.0; 48.2 4

LDF 816.04 7.7 45° double 80 23.6; 48.2 3

MDF 807.50 7.8 45° double 80 23.6; 48.2 3

PW(90/0/90)S 670.08 8.4 45° double 80 23.6; 48.2 3

DCFC 1496.20 2.5 45° single 110 23.6; 36.0; 48.2 4/5

The second series of experiments have been conducted to further develop the

proposed approach for testing materials with different types of internal supporting

structures. Three additional engineered wood materials were tested, LDF, manufactured

from several kinds of wood chips, MDF, made of different softwood with an overall fiber length of 1 mm, and pine PW with a different layer structure (90/0/90)S. The LDF specimens

2.4 Results and Discussion

27

are 7.7 mm thick, the MDF specimens are 7.8 mm thick, and the PW(90/0/90)S specimens

are 8.4 mm thick with 1.4 mm per layer.

The proposed approach was also used to test a DCFC material in order to investigate

its relevance to composite materials of automotive applications. The tested flat plate

specimens are made by compression molding of the Polynt-SMCarbon 80 CF50-12K with an overall thickness of 2.5 mm. The material consists of a fiber mass content of 47.0% and a

fiber length of 50 mm. Due to the examination of double peaks in the load curves, the trigger

is altered to a 45° single-sided chamfer, which reduces the effect of the initial impact.

2.4. Results and Discussion

2.4.1. Crushing Behavior

The presented crush testing test is used to determine the energy absorption behavior of the material when crushing fully-supported flat plate specimens of different crushing

widths. The approach is to simply isolate the inadvertently included edge force and deduct

it from the measured result.

Figure 2-6 shows two different stages of the crushing strokes for each of the selected

crushing widths of the PW(90/0/90/0�)S. The top row of pictures shows the crushing at

5 mm impactor stroke, where the crushing force reaches a peak, as shown in Figure 2-9-a,

which displays the curves representing the average forces obtained from sets of specimens of the selected crushing widths. All selected crushing widths show the same initial damage

pattern. Shearing of the flat plate specimen starts to occur at the sides of the impactor. The

outer layer of the material has separated from the inner layers and is torn off at the clamps.

A curved bulge is visible underneath the impactor, forming a frond splaying crushing mode.

The bottom row of pictures shows the crushing failure at half the crushing stroke (40 mm). Shearing can be observed between the sides of the impactor and the clamped edges. The

90° outer layer is torn out in the clearance zone. Therefore, it is necessary for the clearance

to be the same for all specimens. Furthermore, shearing off the 0° layers and tearing off the

90° layers can be examined for the inner layers of the material. The crushing frond is formed

by combined lamina bending and transverse shear crushing, as explained by Farley [45]. In the illustrated tests, laminar buckling shows mainly in the specimens with the crushing

width of 36.0 mm and 48.2 mm, and transverse shear crushing mode is more noticeable in

the specimen with the 23.6 mm crushing width. No significant difference is observed

between the shear failure modes of the specimens with different crushing widths. A


28

combination of both crushing modes, transverse shearing, and lamina bending, occurred

simultaneously in all tested flat plate specimens.

Figure 2-6: Crush test procedure for the selected crushing widths for

PW(90/0/90/0�)S.

The second series of crush tests for LDF, MDF, and PW(90/0/90/0�)S is shown in

Figure 2-7 for both selected crushing widths. Each material shows similar edge shearing and tearing damage patterns and crushing frond damage patterns for both selected

crushing widths of this material. The damage pattern of the individual materials, however,

is different. Crushing the LDF specimens results in material crumbling and, therefore,

cannot be attributed to a unique crushing mode. Crushed MDF specimens depict a tendency

to build a layer splaying structure like the lamina buckling crushing mode, although the material consists of random short fibers and, therefore, no layer structure as in PW. The

specimens of the PW(90/0/90)S have a combined transverse-shearing and lamina-bending

damage pattern similar to that of the PW(90/0/90/0�)S specimens.


29

Figure 2-7: Crushing specimen of two crushing widths for LDF, MDF, and PW(90/0/90)S.

Figure 2-8 shows the crushing process of the DCFC. Similar to the PW and MDF

specimens, the material tends to crush in a two-sided frond splaying mode. Due to the

random structure of the fiber distribution and orientation, it is difficult to depict a specific crushing type. The frond splays are coherent, but their layer structure has fragile

connections like the MDF. Only one thick interrelated splaying builds up on either side, in

contrast with the frond splaying crushing mode in carbon laminate materials [33], where

several individual fronds are shaped. The fibers show fiber bundle pull out, longitudinal

splitting, and bundle rupture, similar to the case of standard coupon testing. Fiber delamination occurs depending on the in-plane orientation in the crushing direction. In the

off-plane direction, the behavior changes to longitudinal splitting, which is related to matrix

failure. Fiber rupture can be observed in the off-plane bundles. Fiber bundle tearing can be

observed in the outer material layer at the clearance zone. The inner layer shows a

combination of shearing and torn fibers.


30

Figure 2-8: Crush test procedure for the selected crushing widths for the DCFC.

2.4.2. Approach Validation

Figure 2-9-a shows the curves representing the average forces obtained from sets of

specimens of the selected crushing widths vs. stroke responses of the PW(90/0/90/0�)S flat

plate specimens that were used in the first test series. The specimen of 48.2 mm crushing

width shows a significantly high initial double peak force when a 45° double-chamfered

trigger is used. The 23.6 mm crushing width specimen shows a single peak force, slightly higher than the average value of the force along the SCR of the examined specimens. In

general, the peak to average force ratio increases with crushing width, as shown in Table

2-2. The average value of the force, measured along the SCR from testing a set of specimens

of a selected crushing width, is listed in Table 2-2 as 𝐹𝐹� and is used to calculate the peak to

average force ratio. In order to obtain consistent crush behavior, a SCR is considered in

energy calculations, as highlighted in Figure 2-9-a. To reduce the influence of the trigger, the SCR starts at an impactor travel stroke of twice the thickness of the used specimen. To

prevent deviations caused by accumulated debris of the crushing frond, leading to larger

measured forces, the SCR excludes at the end of the stroke a distance equal to the plate

thickness. The definition of SCR is also used for the other test series.

The curves for the work done vs. stroke over the SCR, shown in Figure 2-9-b, are obtained by integrating the measured impactor force along the SCR. The resulting energy

curves have much less fluctuation than the measured force curves. Therefore, the energy vs.

stroke curves will be adopted to illustrate the new approach. In addition, in crash analysis,

the energy absorption capacity is usually the most significant material property used for

comparing the crash behavior of different materials [19]. Figure 2-9-b shows that the energy increases almost linearly with the crushing stroke.


31

Figure 2-9: PW(90/0/90/0�)S for the three used widths w: a) average measured force 𝐹𝐹� vs. crushing stroke s; b) the total work done E by the measured force F over the SCR.

Fitting the three energy values corresponding to the three selected crushing widths,

calculated at a specific impactor stroke s, and extrapolating to a hypothetical zero-crushing

width leads to a non-zero energy value. The obtained energy value, which corresponds to

the specified impactor travel distance s, is the energy consumed at the specimen edges due to material splitting and friction as there would be hypothetically no material crushed by

the impactor. This value represents the energy dissipated by the edge force component,

resulting from friction and shearing at the constrained edges. The approach is based on

assuming that the energy dissipated at the edges remains the same within the adopted range of crushing width. While the assumption is practically accurate within the selected

width range, the relation might become nonlinear for extremely narrow specimens.

Examples of the non-zero energy values extrapolated to zero crushing width at different

stages along the crushing stroke are shown in Figure 2-10.

Figure 2-10: Calculating the edge energy for a hypothetical specimen of zero crushing width at specific strokes for PW(90/0/90/0�)S.


32

This outcome confirms the basic concept that the energy associated with the

measured force is composed of the crushing energy, which is a material characteristic that

obviously increases with the crushing width, and a width-independent energy component

dissipated by shearing and friction at the constrained edges. The distribution of the different

energy components is illustrated in Figure 2-11-a for all three crushing widths. The edge energy component over the whole stroke, shown in red, is calculated as the intercept

(equation (2-5)) of energy associated with the measured force of all three crushing widths.

The crushing energy component for the different crushing widths is calculated by

subtracting the edge energy component from the associated total work done by the

impactor. For a better comparison of different proportions of the components, the same color is chosen per crushing width. Accordingly, the crushing energy component is shown

as a solid line, and the associated total work done as a dashed line. It is evident that the

crushing energy increases almost linearly over the crushing stroke for all selected crushing

widths. The noticeable variations can be easily explained due to the natural inhomogeneous structure of the material. As the edge energy is practically width-independent and the

crushing energy is proportional to the material volume, the proportion of the edge energy

decreases for larger crushing width, but its effect on the total energy remains significant,

which interprets the remarks of Daniel et al. [23] that the SEA increases for smaller

specimens.

The crushing energy per unit width of the tested flat plate specimen is calculated by

dividing the crushing energy on the corresponding crushing width, which results in an

almost identical behavior for all three crushing widths, as depicted in Figure 2-11-b. The

average of these curves represents the SCE. The consistent behavior of the calculated SCE

for the selected crushing widths confirms the basic concept that the energy associated with the measured force is composed of the material crushing energy, which obviously increases

with the crushing width and a practically width-independent edge energy. Such consistent

behavior of the calculated crushing energy for all crushing widths proves that the proposed

approach is capable of predicting reliable crushing properties of flat plate composites that

can be used for comparing the crush properties of different materials.


33

Figure 2-11: Properties of PW(90/0/90/0�)S vs. crushing stroke sSCR: a) energy absorption components crushing energy EC and edge energy EE; b) calculated SCE.

In order to explain the significance of the proposed crush testing approach, the

consistent width-independent crush behavior calculated after removing the effect of the edge forces is compared with the properties obtained when using the raw measured forces.

Including the edge energy in calculating the SEA property of the plate leads to a seriously

inconsistent outcome. Comparing the SEA values listed in Table 2-2 shows a deviation of

114% for the 23.6 mm crushing width, 73% for the 36.0 mm crushing width, and 56% for

the 48.2 mm crushing width. It is evident that because the crushing force is proportional to the crushing width while the edge energy remains practically the same for any width within

the considered range, the impact of the edge energy increases for specimens with smaller

crushing width as its proportion increases in comparison with the total energy associated

with the measured force. The contribution of the edge energy for very wide specimens

would still have a significant influence on the calculated SEA. In addition, excessive crushing width would trigger lateral buckling.

Therefore, the properties obtained when using the total measured force for fully

supported flat plate specimens depend on the dimensions of the specimens. The comparison

between the properties obtained from the measured forces and those calculated after

discounting the edge forces, displayed in Table 2-2, confirms this outcome. This clarifies the unexplained observation by Daniel et al. [23], where an increase in SEA was observed when

crushing plates of smaller crushing widths.


34

2.4.3. Usability for Different Materials

The proposed approach is further validated experimentally by testing materials with

different fibrous structures. Figure 2-12 shows the energies calculated from the measured force as well as the calculated crushing and edge energies for the used crushing widths for

LDF, MDF, PW(90/0/90)S, and the DCFC over its corresponding SCR. The crushing energy

per unit width of all examined materials is shown in Figure 2-13. Due to defining the start

of the SCR to be twice the thickness of the used specimen, comparing the SCE of the different

materials along the crushing stroke sSCR is not feasible. Therefore, the illustration of the SCE of each material has to take place along the range of the SCR of the corresponding material,

considering the starting point to be 0 mm. As previously demonstrated, the edge energy

remains a significant part of the total energy for all materials and should be separated from

the actual crushing energy before calculating the SEA value of the material.

Figure 2-12: Energy absorption components vs. sSCR of LDF, MDF, PW(90/0/90)S, and DCFC.


35

Figure 2-13: SCE of all used materials.

The edge energy is not only a test rig-related property. For example, changing the

clearance between the clamps and the impactor leads to a different tearing pattern of the outer layer of the material. In addition, the actual amount of the edge energy depends on

the structural integrity of the composite material and its capacity to resist forces such as

shearing and friction between the flat plate specimen and the impactor. All these factors

have a negligible effect on the final outcome when using the crush testing approach, as the

edge forces are isolated and discounted. This is clarified in Figure 2-14 for all tested materials, which show similar behavior of the edge energy. The values of the crushing

energy and the edge energy are shown in Table 2-2 for all materials. The results show that

the crushing energy represents only around 50% to 60% for the 23.6 mm impactor, around

60% for the 36.0 mm impactor, and around 60% to 80% for the 48.2 mm impactor.

Comparing the SEA values obtained using the proposed approach SEAC with those obtained from the directly measured force SEAM, shows a deviation of around 60% to 110% for the

23.6 mm crushing width, around 70% for the 36.0 mm crushing width, and still 30% to 60%

for the wide 48.2 mm crushing width. These deviations illustrate the significant benefits of

using the proposed approach since using the measured forces of fully supported flat plate specimen to calculate the SEA leads to setup-dependent results, in particular when testing

narrow plates. Testing wide plates obviously reduces the error but does not eliminate it as

the proportion of the contribution of the width-independent edge component decreases. On

the other hand, increasing the width leads to an increased risk of lateral buckling. In all

tested materials, the SEA calculated from the crushing energy is consistent, while that calculated from the total energy depends on the width of the tested specimen.


36

Figure 2-14: Calculating the edge energy for a hypothetical specimen of zero crushing width for LDF, MDF, PW(90/0/90)S, and DCFC.

Table 2-2: Summary of the measured and calculated data for the SCR of all materials.

Material w

/ mm SCR

/ mm

𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆)

/ kN

SD of 𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆)

/ kN

p2a of 𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆)

/ -

E / J

EC / J

EE / J

SEAM

/ kJ/kg SEAC

/ kJ/kg SCE

/ J/mm

PW(90/0/90/0�)S 23.6 17.6

– 71.2

6.34 1.46 1.34 340 160 180

43.3 36.0 7.82 2.16 1.54 419 239 35.0 20.2 6.7 48.2 9.43 2.99 1.57 505 325 31.5

LDF 23.6 15.4 - 1.28 0.39 1.51 73 45

28 8.6

5.3 1.9 48.2 72.3 2.08 0.42 1.67 119 90 6.9

MDF 23.6 15.6 - 2.30 0.55 1.40 148 75

73 15.5

7.8 3.2 48.2 80.0 3.52 0.75 1.44 227 153 11.6

PW(90/0/90)S 23.6 16.8 - 3.33 0.49 1.76 182 105

77 25.0

14.5 4.5 48.2 71.6 5.33 1.01 2.14 292 215 19.7

23.6 5.0 5.77 1.37 1.23 606 302 65.3

DCFC 36.0 - 7.21 1.73 1.28 757 453 304 53.5 32.3 12.7 48.2 110.0 8.74 2.29 1.44 918 614 48.5

2.5 Conclusion

37

2.5. Conclusion

The cost-effective characterization of the crushing SEA capacity of flat plate fibrous

materials has so far only been possible using the method of the unsupported height [25-32], but with accompanying an in-depth investigation of the effect of the unsupported height on

the measured material properties in order to ensure that buckling does not occur, which

imposes a limit on the unsupported height of the specimen. Test rigs, using fully-supporting

guide systems [17, 20-24], which are used to prevent the specimen from buckling,

inadvertently include forces resulting from shearing and friction, namely edge forces. A novel crush testing approach is proposed and validated in this study to characterize fully

supported flat plate specimens of fibrous materials. It isolates and nullifies the

inadvertently included edge forces to determine the crushing energy and associated SEA of

the flat plate material. Therefore, this approach enhances the usability and credibility of

simple test rigs in characterizing the crushing SEA of flat plate specimens.

The inadvertently included edge forces are generated by shearing and tearing of the

crushed part from the fully clamped edges and friction, which occurs between the flat plate

specimen and the impactor. The energy associated with the edge forces has shown to be

practically independent of the width of the tested plate within a reasonable range of plate

width. The crush energy absorbed per unit width was found to remain consistent for the tested specimens of different widths. The proposed crush testing analysis eliminates the

edge forces by testing two or more specimens with different crushing widths. Simple test

rig designs can be used as the eliminated edge forces do not affect the outcome. The

obtained crushing energy is consistent for different values of the plate width.

Validating the proposed approach via experimental testing of different materials

proves its feasibility for the characterization of a range of fibrous materials. A near-

proportional relationship between the crushing energy and the crushing width could be

obtained. Experimental testing results revealed that the splitting energy at the edge of the

impactor is practically independent of the crushing width, which interprets the unexplained observation in the literature that the SEA increases when crushing plates of smaller

crushing widths. By adopting the proposed approach, there is no need to accept the increase

of SEA for smaller plate width. The results show that the SEAM, calculated from the

measured force, is not consistent in contrast with the consistent SEAC, calculated from the

crushing energy.

2.6 References

38

The significance of the proposed approach is manifested not only in the consistency

of the calculated material characteristics and its applicability on a range of flat plate fibrous

materials but also in its simplicity. Fully clamped flat plate specimens can be tested using

simple test rigs without excessive concerns about the forces generated at the edges as they

are isolated and eliminated. The approach also allows for a wide range of plate widths and long crushing strokes without concerns about buckling or inconsistency in test results due

to the edge forces.

2.6. References










2.6 References

39







[16] Ehrenstein GW. Faserverbund-Kunststoffe : Werkstoffe, Verarbeitung, Eigenschaften. Hanser; 2006.


[18] Israr HA, Rivallant S, Bouvet C, Barrau JJ. Finite element simulation of 0°/90° CFRP laminated plates subjected to crushing using a free-face-crushing concept. Compos Part A Appl Sci Manuf 2014;62:16–25. doi:10.1016/j.compositesa.2014.03.014.

[19] Velecela O, Found MS, Soutis C. Crushing energy absorption of GFRP sandwich panels and corresponding monolithic laminates. Compos Part A Appl Sci Manuf 2007;38:1149–58. doi:10.1016/j.compositesa.2006.06.002.




2.6 References

40










[32] Joosten MW, Dutton S, Kelly D, Thomson R. Experimental evaluation of the crush energy absorption of triggered composite sandwich panels under quasi-static edgewise compressive loading. Compos Part A Appl Sci Manuf 2010;41:1099–106. doi:10.1016/j.compositesa.2010.03.010.

2.6 References

41

[33] Feraboli P. Development of a corrugated test specimen for composite materials energy absorption. J Compos Mater 2008;42:229–56. doi:10.1177/0021998307086202.

[34] Perez N. Fracture Mechanics. Cham: Springer International Publishing; 2017. doi:10.1007/978-3-319-24999-5.


[36] Wisnom MR. Size effects in the testing of fibre-composite materials. Compos Sci Technol 1999;59:1937–57. doi:10.1016/S0266-3538(99)00053-6.

[37] Bing Q, Sun CT. Specimen size effect in off-axis compression tests of fiber composites. Compos Part B Eng 2008;39:20–6. doi:10.1016/j.compositesb.2007.02.010.

[38] Tiefenthaler M, Stelzer PS, Chung CN, Reisecker V, Major Z. Characterization of the fracture mechanical behavior of C-SMC materials. 16th Youth Symp. Exp. Solid Mech. YSESM 2018, vol. 18, 2018, p. 1–5. doi:10.14311/APP.2018.18.0001.


[40] Feindler N. Charakterisierungs-und Simulationsmethodik zum Versagensverhalten energieabsorbierender Faserverbundstrukturen. Lehrstuhl Für Carbon Compos 2012.

[41] SAKA S. Structure and Chemical Composition of Wood as a Natural Composite Material. Recent Res. Wood Wood-Based Mater., Elsevier; 1993, p. 1–20. doi:10.1016/B978-1-4831-7821-9.50007-1.

[42] Christoforo AL, Panzera TH, de Araujo VA, Fiorelli J, Lahr FAR. Timber beam repair based on polymer-cementitious blends. Eng Agric 2017;37:366–75. doi:10.1590/1809-4430-Eng.Agric.v37n2p366-375/2017.

[43] Mário Benedito F, Gustavo Freitas C, Túlio Hallak P, Juliano F, Vânia Regina Velloso S, Francisco Antonio Rocco L, et al. Numerical and Experimental Evaluation of the Use of a Glass Fiber Laminated Composite Materials as Reinforcement in Timber Beams. Int J Compos Mater 2014;4:73–82. doi:10.5923/j.cmaterials.20140402.06.

[44] Alves dos Santos Bravo CG, Nunes Branco LAM, Chahud E, de Moura Aquino VB, Pereira Geraldes Dias AM, Christoforo AL, et al. Carbon fiber-reinforced polymers as a tensile reinforcement of the Pinus elliotti and Manilkara huberi wood species. Maderas Cienc y Tecnol 2020:0–0. doi:10.4067/s0718-221x2020005000104.

2.6 References

42

[45] Farley GL, Jones RM. Crushing Characteristics of Continuous Fiber-Reinforced Composite Tubes. J Compos Mater 1992;26:37–50. doi:10.1177/002199839202600103.

43

Chapter 3. Crush Characteristics of Flat Plate Discontinuous Carbon Composites

This chapter presents an investigation of different testing parameters on the energy

absorption mechanism of discontinuous carbon composites. The crush property isolation

technique for fully supported flat plate specimens has been utilized for the investigation.

The determined effects of the parameters reflect those of discontinuous carbon fiber tubes

but on different energy absorption levels. In addition, the results shown here are comparable with those investigated so far using the method of unsupported height to

circumvent the deviation due to the supporting systems.


Composites Part A: Applied Science and Manufacturing. The corresponding article can be

cited as: Lausch J, Takla M, Schweiger H-G. Crush characteristics of flat-plate discontinuous

carbon composites. Compos Part A Appl Sci Manuf 2021;147:106431.

doi:10.1016/j.compositesa.2021.106431.

3.1. Introduction

New vehicle structures, such as those of battery-electric vehicles (BEV), are

increasing on the product list of the automotive industry [1–4]. These new vehicle types also have to satisfy increasingly strict regulations [5, 6]. The main focus is on reducing fuel consumption and thus emissions while increasing the safety of drivers, passengers, and

pedestrians [5, 7]. The need to meet such conflicting requirements increased the interest in lightweight materials [1, 4, 5, 7–11]. For example, reducing the mass of a BEV vehicle frame has a direct influence on the capacity and, thus, the mass of the batteries [1, 4, 5, 7, 10, 12].

Therefore, the energy absorption of the materials and, consequently, structural elements attracted special attention [13–15]. Lightweight materials such as fiber composite materials provide, in addition to weight advantages, additional benefits such as high specific energy

absorption capacity (SEA) [13, 16]. BEVs, in particular, benefit from the high crush energy absorption capacity as the battery cell itself requires additional protection against impact

3.1 Introduction

44

[5, 6]. When design space is limited, discontinuous carbon fiber composites are particularly

gaining more interest due to their manufacturability [17].

Various studies [18–35] investigated the parameters affecting the mechanical properties of discontinuous carbon fiber composites, e.g., resin types, manufacturing

processes, and fiber-related parameters, e.g., fiber mass content, fiber bundle dimension, and fiber orientation. The research focused on typical tension, compression, and bending

tests. Although the influence of individual parameters on the energy absorption mechanisms of laminate structures has already been investigated, only a few studies [36–44] have been conducted on the crush testing of discontinuous carbon fiber composites and

the parameters affecting their behavior using different manufacturing processes and geometries.

Two types of crush testing methods have been used to determine the energy

absorption properties of such materials. One approach is crushing flat plate specimens. The other is crushing tubes. Jacob et al. [36–39] developed an approach for flat plate specimen testing to isolate the frond splaying crushing mode, which is similar to that observed when

testing tubes. They tested different commercially available discontinuous carbon fiber materials manufactured by compression molding of chopped carbon fibers with epoxy as

resin. They examined different parameters such as fiber tow size, fiber mass content, fiber length, specimen width, and crushing speed. In relation to the test rig, they investigated the influence of the base plate radius as well as the specimen constraint at the base plate. The

results of the studies showed various mechanisms, e.g., increasing the tow size reduces the SEA, and increasing the widths of the specimen results in a little higher SEA. They concluded that fiber distribution and length play a crucial role in crush resistance. They also observed

a decrease in the SEA due to larger fiber length, which was attributed to the specimen width since the investigated fiber length was longer than the widths. The SEA varied with the fiber volume fraction. This effect was attributed to poor adhesion between the fiber and the

matrix but was not examined in detail. Nevertheless, they concluded that the fiber length had a substantial effect on SEA and therefore recommended studying its effect in detail.

They also found that increasing the loading rate increases fracture toughness and, therefore, SEA. Although all the materials examined by Jacob et al. [39] consisted of discontinuous carbon fiber with epoxy as resin, the SEA values were different. This variance showed that

the composition of the individual components and their interaction had a significant influence on the material properties. Similarly, Jacob et al. [45] studied the strain rate effect on carbon/epoxy materials, which showed contradicting results. Overall, the results of the

investigated flat plate specimen were significantly lower than those observed for tubes. In

3.1 Introduction

45

addition to the material parameters, they examined significant influences of the test setup

on the results due to the choice of the constraints of the specimen and the radius at the base plate.

In general, the results obtained from testing depend on the configuration of the test

rig. Feraboli [46] mentioned that supporting the flat plate specimen to prevent buckling is only a compromise between increased friction of a fully clamped specimen and insufficient

clamping, which leads to unstable crushing due to premature buckling. Increasing the radius of the base plate, the unsupported height of the established flat plate testing method, or reducing the level of constraint causes buckling and leads to decreasing SEA. Lausch et

al. [40] developed a technique for testing fully constrained flat plate specimens, which provides consistent results that are independent of the test rig configuration, further called the crush property isolation technique (CPIT). This technique allows identifying and isolating

the inadvertently included shearing and friction forces caused by the constraint at the edges of the specimen. Therefore, it is feasible to state that the obtained crushing force and the SEA are consistent. They validated the approach using several types of engineered wood

and a discontinuous carbon fiber material. However, they focused on validating the method rather than investigating the influence of parameters affecting the SEA of discontinuous

carbon fiber materials.

Turner et al. [41] investigated the crushing behavior of discontinuous carbon fiber composite tubes. While compression molding of chopped carbon fibers was used to

manufacture flat plate specimens, resin transfer molding of epoxy resin in a preform was used for manufacturing the tubes. The preforms of chopped carbon fibers were produced using the directed fiber preforming process. They investigated different tube shapes and

thicknesses, as well as different fiber lengths. They also examined the behavior at different loading rates. The measured SEA values for the tubes showed to be more than double those measured by Jacob et al. [37–39] for flat plate specimens. No attempt was made to explain

the discrepancies, probably due to a large number of influencing parameters. The most significant changes in the SEA were caused by changes in the tube’s thickness. Nonetheless,

the tubes’ geometry had a significant influence since the circular tubes showed higher SEA values than the square ones. No significant decrease of the SEA was observed for the tubes due to longer fiber bundles, as in the case of a flat plate specimen. In addition, the SEA

decreased by around 25%-35% by increasing the loading rate. Only minimal effects on SEA were observed when changing various parameters in dynamic testing, although there were significant effects in the static test.

3.2 Methodology

46

Cutting et al. [42–44] focused on the crushing morphology and influence of the

geometry of discontinuous carbon fiber materials. They compared the behavior of a

thermoset prepreg platelet molding compound against that of several laminate layups using

bladder-molded tubes. All tubes of the different materials showed almost the same SEA

values but different load vs. stroke curves, where the discontinuous carbon fiber material showed the best, i.e., the smallest, peak to average (p2a) values. Due to the material

structure and the random distribution of the fiber bundle, the examined crushing mode

showed a mix of the splaying and the fragmentation failure modes of a combined 0° and 90°

unidirectional layup. The debris of the material consisted mainly of fragmented layers of

frond splaying, together with ruptured bundles and longitudinal splitting. They also observed a minor decrease in SEA by increased loading rate, similar to the observations

made by Turner et al. [41]. Furthermore, they observed an increasing trend of SEA by

increasing the thickness to diameter ratio of the investigate tubes.

This study aims to investigate the effect of various parameters on the energy absorption mechanism of fully constrained discontinuous carbon fiber composite flat plate

specimens manufactured by compression molding. The effects of the fiber length, fiber mass

content, in-plane fiber distribution, specimen thickness, and loading rate are evaluated

using the CPIT for fully constrained flat plate fibrous specimens.

3.2. Methodology

3.2.1. Experimental Design

The selected study parameters of the discontinuous carbon fiber composite are fiber length, fiber mass content, specimen thickness, in-plane fiber distribution, and loading rate.

A detailed plan of the experiments is included in Table 3-1. Two values of fiber length

(25 mm and 50 mm) have been used with two values of the fiber mass content (25% and

50%) to form four material configurations A, B, C, and D. These values are selected from the

literature [18-44]. They represent the typical nominal values of fiber mass content used by the manufactures of discontinuous carbon fiber composites.

The remaining parameters, which are specimen thickness, in-plane fiber distribution,

and loading rate, are studied for the material of 50 mm fiber length and 50% fiber mass

content (like configuration D, however, from a different material batch). Tests of flat plates

with thicknesses of 2.5 mm, 4.3 mm, 6.2 mm, and 8.0 mm are conducted in the test series E, F, and G. In order to investigate the effect of the in-plane fiber distribution in the test series

3.2 Methodology

47

E and F, specimens are cut out of the molded plate at 0° and 90°, where 0° corresponds to

the production direction, and 90° is orthogonal to it. The loading rate effect is studied in

configurations E and G, using a quasi-static 5 mm/min and a high speed of 8.89 m/s loading

rates.

Table 3-1: Overview of the test setups for the different material configurations.

3.2 Methodology

48

3.2.2. Material and Manufacturing Process

The tested flat plate specimens were manufactured by compression molding of the

discontinuous carbon fiber composite Polynt-SMCarbon 80 CFXX-12K. This material belongs to the family of chopped carbon fiber-reinforced sheet molding compounds. The

material components used here are 12k polyacrylonitrile (PAN) fibers with 800 tex and an

additional epoxy coating. Bishpenol A is used as the basis for the thermoset epoxy resin. For

the compression molding process, a tool occupation of 90% is used for the semi-finished

product, a molding pressure of 260 bar, a temperature of 145°C, and a curing time of around 120 s/mm is used in the manufacturing cycle to provide appropriate curing of the base

plates. It should be noted that due to the random distribution of the fiber bundles and the

variability of the compression molding process, the fiber mass content of different

specimens varies slightly. The average fiber mass content, the corresponding fiber volume

content, as well as the material density for each configuration, are listed in Table 3-1. For Configurations A to D, the manufactured base plates are of sizes 120x250 mm. For

Configurations E, F, and G, the base plates are of size 300x500 mm. The specimens are cut

out of the base plates with the Mutronic Diadisc 5200 table saw at a sufficient distance from

the edge of the base plate to avoid material flow effects.

It should be noted that the parameter “in-plane fiber distribution” is based on the random distribution of the fiber bundles in the semi-finished product. The 90%-high

occupancy of the press tool enables a low material flow, which reduces the inclusion of air

bubbles. Also, the material flow within the plates is minimized by restricting it to the edges

of the plates. Therefore, it can be assumed that the in-plane fiber distribution is random,

resulting in quasi-isotropic properties, based on the findings of Kravchenko et al. [47] and Sommer et al. [48] on the effect of material flow in tensile testing. The influence of material

flow and entrainment of the fiber bundles will not be further investigated as they are not

part of this study.

3.2.3. Experimental Setup

A schematic diagram of the test rig is shown in Figure 3-1. It is based on a design

suggested by Feindler [49]. The edges of the flat plate specimen are fully supported

(clamped) along the whole crushing stroke. In order to isolate the boundary-independent

crush energy, two or more different crushing widths are tested for every configuration. The tested specimens are 120 mm long for configuration A to D and 150 mm long for

configuration E, F, and G. All specimens are 80 mm wide. It should be noted, however, that

3.2 Methodology

49

the crushing width w is only a part of the specimen width and is determined by the width of

the used impactor. The rest of the width is constrained by side clamps. The configurations

E and G are investigated for the three crushing widths 23.6 mm, 36.0 mm, and 48.2 mm. The

other configurations are investigated for the crushing widths 23.6 mm and 48.2 mm. As a

failure trigger, a single-sided 45° chamfer is used for all specimens.

3.2.3.1. Quasi-Static Test Setup

The quasi-static test setup and the detailed configurations for the different crushing

widths are illustrated in Figure 3-1. The load is applied via a stroke-guided Z100SL, 100 kN screw-jack system, made by ZIMM Maschinenelemente GmbH + Co KG. The impactor is

screwed into the spindle. The linear encoder BG200, made by Kami GmbH, with 5 µm steps,

is used as a measuring device for the stroke. The load is measured via four 20 kN KD80s

force sensors from ME-Meßsysteme GmbH. The measuring amplifier GSV-8DS SUBD15HD

from ME-Meßsysteme GmbH is used for both stroke and load measurements. The accuracy class is 0.05% for the amplifier and all sensors. A sampling rate of 50 Hz is used for the

quasi-static test rate of 5 mm/min. For a joint stroke base, the tests are subsequently

resampled to 5 µm steps.

3.2.3.2. Dynamic Test Setup

The dynamic testing is conducted using the universal drop tower facility made by

FORM+TEST Prüfsysteme from the CARISSMA Automotive Research Center at the

Technische Hochschule Ingolstadt. In order to fully support the specimens along the

crushing stroke, the test rig is installed directly under the drop element of the drop-tower,

as shown in Figure 3-2. The load is applied via the impactors of the different crushing widths attached to the drop element of the drop-tower. The impactor's stroke is measured by two

RF603HS high-speed laser sensors, made by Riftek LLC, with a sensor rate of 180 kHz. The

test rig is mounted on a force-measuring plate with an M205C ICP® quartz force ring sensor

from PCB Piezotronics, Inc. The used measuring amplifier is NI PXIe-8840 with data

modules NI PXIe-4492 and PXIe 6376, made by National Instruments. Both stroke and force are logged at 200 kHz and subsequently filtered with a CFC-600 filter, based on the

recommendation of the SAE J211/1 (Ref. [50]). For further processing, the values are

resampled to a joint base of 5 µm steps. All dynamic tests are conducted at a drop height of

4.03 m to obtain an impactor speed of 8.89 m/s (32.0 km/h) at impact. The masses of the drop element are selected according to the values of the absorbed energy obtained in static

testing for each configuration and corresponding crushing widths, as shown in Table 3-2.

The aim is to provide almost the same crushing stroke for the different crushing widths.

3.2 Methodology

50

Figure 3-1: Quasi-static test setup: a) schematic representation from Ref. [40]; b) overview of the test rig; c) setup of different crushing widths.

3.2 Methodology

51

Table 3-2: Overview of the drop tower weights used.

Config. Mass of Drop Element / kg Crushing Widths w

23.6 mm 36.0 mm 48.2 mm

G1 14 16 20 G2 31 35 42 G3 41 55 62 G4 54 62 75

Figure 3-2: Overview of the dynamic test setup.

3.2.4. Measurements and Analysis of Results

The full clamping of the edges has a significant influence on the crush-tested flat plate

specimen. The original SEA value obtained from the measured force F is much higher than

expected due to the influence of the inadvertently included force component, further called edge force FE, caused by shearing and friction at the edge of the impactor. The CPIT for flat

plate fibrous materials, used here, presents a method to separate the crushing component

FC from edge force FE resulting from the clamped edges. Therefore, the measured force

consists of two components,

𝐹𝐹 = 𝐹𝐹𝐶𝐶 + 𝐹𝐹𝐸𝐸 . (3-1)

When utilizing this approach, it is recommended to define a sustained crushing region

(SCR) because no shearing takes place during the initiation peak, and different crushing and

shearing mechanisms appear during the transition phase. Therefore, it is unfeasible to calculate the different components of the measured force reliably before the crushing mode

becomes sustainable. In addition, deviations caused by accumulated debris of the crushing

3.2 Methodology

52

frond have to be excluded from the SCR. In order to ensure sufficient distance for the

sustainable crushing mode in static testing, the SCR starts at 25 mm of the crushing stroke.

In dynamic testing, the SCR starts at 40 mm due to higher fluctuations of the measured force.

The edge force FE is obtained as the non-zero intercept of a linear regression of

measured forces F for different crushing widths w along the traveling stroke s between the given boundaries s1 and s2 of the SCR,

F𝐸𝐸(𝑠𝑠) = 𝐹𝐹�(𝑠𝑠) −∑ (𝑤𝑤𝑖𝑖𝑛𝑛𝑖𝑖 −𝑤𝑤�)(𝐹𝐹�𝑠𝑠,𝑤𝑤𝑖𝑖�

−𝐹𝐹�(𝑠𝑠))

�∑ (𝑤𝑤𝑖𝑖−𝑤𝑤�)2𝑛𝑛𝑖𝑖 �

𝑤𝑤�, 𝑑𝑑 ∈ [𝑑𝑑1,𝑑𝑑2]. (3-2)

As per the definition of linear regression, the mean values of all wi and Fi(s) are

expressed as 𝑤𝑤� and 𝐹𝐹�(𝑠𝑠).

On the other hand, the crushing force FC depends on the crushing width. In other

words, it is the force that would be obtained in the case of hypothetical free edges if buckling

is prevented. The crushing force FC can be easily calculated from the slope of the linear

regression of the measured forces for different crushing widths multiplied by the

corresponding crushing widths along the SCR of the crushing stroke,

F𝐶𝐶(𝑠𝑠 ,𝑤𝑤) =∑ (𝑤𝑤𝑖𝑖𝑛𝑛𝑖𝑖 −𝑤𝑤�)(𝐹𝐹(𝑠𝑠,𝑤𝑤𝑖𝑖)−𝐹𝐹�(𝑠𝑠))

(∑ (𝑤𝑤𝑖𝑖−𝑤𝑤�)2𝑛𝑛𝑖𝑖 )

𝑤𝑤 , 𝑑𝑑 ∈ [𝑑𝑑1,𝑑𝑑2]. (3-3)

The SEA values for the crushing process (SEAC) can be calculated by dividing the integration of the crushing force FC along the SCR by the flat plate specimen thickness t,

density ρ, crushing widths w, and corresponding crushing stroke s of the SCR,

SEA𝐶𝐶 =∫ 𝐹𝐹𝑆𝑆(𝑠𝑠,𝑤𝑤𝑎𝑎)𝑠𝑠2𝑠𝑠1

𝑑𝑑𝑠𝑠

𝑡𝑡𝜌𝜌𝑤𝑤𝑎𝑎 𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆=

∫ 𝐹𝐹𝑆𝑆(𝑠𝑠,𝑤𝑤𝑏𝑏)𝑠𝑠2𝑠𝑠1

𝑑𝑑𝑠𝑠

𝑡𝑡𝜌𝜌𝑤𝑤𝑏𝑏𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆. (3-4)

For comparison and illustration purposes, the apparent SEA per unit mass (SEAM) is

calculated by dividing the integration of the measured force F along the SCR by the specimen

thickness, density, crushing widths, and crushing stroke of the SCR,


𝑑𝑑𝑠𝑠

𝑡𝑡𝜌𝜌𝑤𝑤𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆. (3-5)

3.3 Discussion of Results

53

3.3. Discussion of Results


Typical crush behavior is illustrated in Figure 3-3 for different testing configurations.

Images labeled with letters E and G demonstrate the influence of the loading rate (quasi-

static 5 mm/min, and high speed 8.89 m/s respectively), and those with numbers 1 and 4

compare the behavior of different specimen thicknesses (2.5 mm and 8.0 mm, respectively).

Supplementary Videos showing the crushing process of the Configuration corresponding to Figure 3-3 can be accessed through the following link:

https://www.sciencedirect.com/science/article/pii/S1359835X21001548?via%3Dihub#

s0105. The crushing fronds in static and dynamic testing are formed from several layers due

to different mechanisms like internal friction, delamination, splitting, and fracture of the fiber bundles. Since these bundles are randomly aligned, the damage pattern within the

crushing frond is also random. As a result, the crushing frond is usually fragmented but

mostly coherent. The observed crushing morphology is similar to that of the transfer and

bladder molded tubes [41–44]. The comparison between the crushing frond due to static

and dynamic testing shows that several individual layers are formed, or larger areas are disconnected for the dynamic tests, which means that the frond coherence is significantly

lower. Based on this observation, it can be proposed that the significantly lower coherence

of the crushing frond, resulting from dynamic loading, is reflected in the crushing

performance of the material. The phenomena of lower coherence and higher fragmentation

of the crushing frond are also observed in static tests of thicker specimens with lower crushing force.

In general, the specimens form an almost symmetric two-sided crushing frond in both

static and dynamic testing, which is similar to the generation of the crushing frond in tubes

[41–44], instead of the single-sided crushing frond formed when investigating flat plate

specimens by Jacob et al. [36–39]. Non-symmetric crushing occurred in static testing only for the 2.5 mm thin specimens (configuration E1 and F1), most likely due to the

disintegration of one side of the thin crushing frond. Inspecting the measured response of

the thin specimens shows no significant variation related to the different crushing fronds.

Obviously, the thickness of the crushing frond increases with increasing the thickness of the

specimen. In addition, the coherence of crushing fronds increases, and the level of fragmentation decreases with increasing specimen thickness. Therefore, partial

disintegration of the crushing frond of the thin specimens can be noticed.

https://www.sciencedirect.com/science/article/pii/S1359835X21001548?via%3Dihub#s0105

https://www.sciencedirect.com/science/article/pii/S1359835X21001548?via%3Dihub#s0105


54

Figure 3-3: Examples of typical fracture behavior of the crushing frond.

Figure 3-4 shows a typical fracture behavior due to shearing and friction at the edge

of the impactor. Similar to Figure 3-3, configurations labeled E and G show the influence of the loading rate (quasi-static 5 mm/min, and high speed 8.89 m/s respectively), and labels

with the numbers 1 and 4 show the effect of specimen thickness (2.5 mm, and 8.0 mm

respectively). The split edge shows various damage mechanisms. In the outer layers of the

material, the fiber bundles are ripped out while the bundles are sheared off in the core layers. The area of influence of the torn fiber bundles differs between static and dynamic

testing. Under static loading, most of the fiber bundles are mainly torn out, and only a few

are sheared off. The proportion of shearing increases with specimen thickness. Under

dynamic loading, the proportion of tearing out is limited to the outer semi-solid shell layers,

and most of the inside layers are sheared off. In addition, the surface of the breaking edge is very rough and tattered when crushed statically and is very smooth when crushed

dynamically.


55

Figure 3-4: Examples of typical fracture behavior due to friction and shearing at the edge of the impactor.

3.3.2. CPIT Results

The overall results are shown in Table 3-3 for each test configuration. Examples of the curves representing the measured forces and the average force obtained from sets of

specimens of the selected crushing widths are shown in Figure 3-5 for configurations E4

and G4. The average value of the force, measured along the SCR from testing a set of

specimens of a selected crushing width, is listed in Table 3-3 as 𝐹𝐹�.

Figure 3-5: Examples of measured force responses for different loading rates.


56

The average force obtained from static testing varies between 5.88 kN and 37.52 kN

across the investigated range of thickness (2.5 mm to 8.0 mm) and crushing width (23.6 mm

to 48.2 mm). In dynamic testing, the force is somewhat lower, ranging between 5.24 kN and

28.88 kN. It is obvious that the material properties exhibit a significant scattering due to the

random distribution of the fiber bundles. The coefficient of variation (CV) of the measured force in static testing is between 15.8% and 29.8%. Due to the nature of the high-speed

impact, the CV almost doubles in dynamic testing to be between 33.0% and 41.3%. As

mentioned in various studies [20, 34, 35], a decrease of the CV when increasing the

thickness could also be observed for the static crush testing. Besides, the descent from

23.2% (2.5mm thickness) to 19.2% (8mm thickness) is significantly lower than that mentioned in the studies for the tensile properties. Additionally, a slight increase of the CV

from 19.1% to 21.7% could be observed when increasing the crushing widths from 23.6 mm

to 48.2 mm. In dynamic testing, the CV does not change significantly when changing the

specimen thickness from 2.5 mm to 8.0 mm. Also, no relevant variation of the CV due to the different crushing widths (23.6 mm to 48.2 mm) could be observed. Therefore, the

fluctuation in dynamic testing results in an average CV of around 36%. A similar observation

was made for static and dynamic p2a-values. In static testing, the p2a-value decreases from

1.55 to 1.09 by increasing the specimen thickness (2.5 mm to 8.0 mm) and increases from

1.26 to 1.45 by increasing the crushing widths (23.6 mm to 48.2 mm). The p2a-value for the dynamic testing for any thickness and crushing width is around 2.11.

Utilizing the CPIT allows for separating the two force components, the crushing force

FC, which is needed for calculating the SEAC, and the edge force FE, which is inadvertently

included in the measured force F due to shearing and friction at the edge of the impactor.

For illustration purposes, the average values of the corresponding components, calculated over the SCR from testing a set of specimens, are shown in Figure 3-6 and Figure 3-7, as well

as listed in Table 3-3. The crushing forces increase from 6.55 kN for the 25 mm fiber length

and 25% fiber mass content (Configuration A) to 8.64 kN for the 50 mm fiber length and

50% fiber mass content (Configuration D) for the largest crushing width, illustrated in

Figure 3-6-a. Overall, the increase due to increasing fiber length is smaller than that due to increasing fiber mass content. Considering the wide ranges of both parameters, fiber length,

and fiber mass content, the increase in the crushing force is relatively insignificant.

Inspection of the edge forces shown in Figure 3-6-b shows similar behavior to that of the

crushing force. Overall, the edge force increases from 3.53 kN for specimens with 25 mm


57

fiber length and 25% fiber mass content (Configuration A) to 4.32 kN for specimens with

50 mm fiber length and 50% fiber mass content (Configuration D).

Figure 3-6: a) Calculated average crushing force for the largest crushing width; b) calculated average edge force.

The influence on the calculated edge and crushing forces of specimen thickness, in-

plane fiber distribution, and loading rate is illustrated in Figure 3-7. The most significant influence arises from the specimen thickness as the crushing force for configurations E and

F increases by approx. 4 times from 6.2 kN to 25.0 kN for the largest crushing width. The

influence of the loading rate is displayed by configuration G. Here, the increase of the

crushing force due to increasing specimen thickness is only around 3.5 times from 6.0 kN to 20.9 kN for the largest crushing width. Comparing configurations E and F, the effect of the

in-plane fiber distribution is shown to be insignificant. The changes in force due to various

specimen thicknesses in different configurations vary between -0.37 kN and 0.33 kN.

Figure 3-7: a) Calculated average crushing force for the largest crushing width; b) calculated average edge force.


58

Overall, the edge force for configurations E and F increases with increasing specimen

thickness by approx. 4.3 times from 2.9 kN to 12.3 kN. The results of configuration G show

the influence of the loading rate on the edge force, which is relatively small, with an increase

of 3.5 times from 2.3 kN to 7.9 kN.

3.3.3. Effect of the Fiber Length & Fiber Mass Content

Fiber length and fiber mass content are identified as significant factors influencing the

mechanical properties, e.g., tensile strength and Young’s modulus in tensile testing

[18, 20, 21, 23–25, 31, 33–35, 37, 38, 41]. The positive effect here on the tensile properties will improve with fiber length but become asymptotic at a certain value, attributed to the

critical fiber length [24, 35, 51–54]. The few studies investigating the effect of fiber length

on compression or flexural behavior observed only little contribution to the mechanical

properties [23, 24, 35, 52]. The bar charts in Figure 3-8 and Figure 3-9 show the influence

of these parameters on the SEAC of the investigated flat plate specimens. Figure 3-8 shows the influence of fiber length on the two sets of specimens with different fiber mass contents.

Figure 3-8: Effect of fiber length on SEAC.

Contrary to the findings from Jacob et al. for flat plate specimens [37, 38], the SEAC increases due to higher fiber lengths. It should be mentioned here that the findings from

Jacob et al. [37, 38] are attributed to the specimen width, which was smaller than the

investigated fiber lengths. For a fiber mass content of 25%, the increase of SEAC from 25 mm

to 50 mm fiber length is 2.6 kJ/kg. For the higher fiber mass content of around 50%, the

increase is 2.1 kJ/kg, respectively, for the same fiber length. The increase, however, is rather small and not significant compared to the standard deviation, which increases with

increased fiber lengths. This phenomenon coincides with the findings for tubes [41] that no

significant trend for the fiber length could be observed. In general, the influence of fiber


59

length on the SEAC can be attributed to the fiber distribution, which is less homogeneous for

longer fibers. The standard deviation, shown in Figure 3-8 as error bars for the different

configurations, reinforces this statement.

An interpretation of the effect of the fiber length can be obtained from considering the

different fracture mechanisms forming the crushing frond [55–57]. Crush failure mainly consists of midplane splitting, fiber-bending, -fracture, and delamination into individual

layers, including friction between those layers. These failure modes are mainly based on

crack initiation and -propagation. The fiber contributes mainly as a reinforcement, which

carries a substantial portion of the load under normal operating conditions. Accordingly,

the cohesion between the fiber and the matrix is an essential factor. Once cohesion is lost during crushing, the compressive load cannot be transmitted between the matrix and the

fibers, so eliminating the reinforcing effect of the fibers, and accordingly, the effect of fiber-

length diminishes. As a result, most of the crushing force is transmitted through the matrix.

This interpretation may explain why the fiber length has only a minor effect on the crushing SEAC.

Figure 3-9 shows the effect of increasing SEAC due to increasing fiber mass content

from 25% to 50%, where the increase in SEAC for a fiber length of 25 mm is 1.7 kJ/kg, while

the increase for the longer fiber length of 50 mm is 1.1 kJ/kg. Compared to the influence of

the fiber length, the increase seems to be less significant when considering the standard deviation, which reflects the effects of fiber distribution and fiber length. The standard

deviation decreases when decreasing the fiber length and when increasing the fiber mass

content. The effect of both parameters, fiber length and fiber mass content, on the SEAC is

relatively insignificant, similar to the findings for tubes [41].

Figure 3-9: Effect of fiber mass content on SEAC.


60

The standard deviation improves with increased fiber mass content, which is most

likely due to an improvement in the fiber distribution. Although there is also an increase in

the force components, as shown in Figure 3-6, this increase is not accompanied by an

increase in the SEAC due to the increase in material density resulting from higher fiber mass

content. The combination of a high fiber mass content with a short fiber length seems most appropriate for an engineering material as the resulting standard deviation of the material

properties is rather small. Also, the loss of 2.1 kJ/kg for the fiber length from 25 mm to

50 mm, investigated here, seems rather small, for example, resulting in a solid SEAC of

34.9 kJ/kg for Configuration C (25 mm fiber length, 50% fiber mass content).

3.3.4. Effect of the In-Plane Fiber Orientation

The in-plane properties of the material are based mainly on fiber distribution, which

is affected by the manufacturing process of the semi-finished product and the compression

molding process. The following comparison illustrates the influence of the manufacturing process of the semi-finished product on the SEA value. The SEAC values of configurations E

(0° production direction) and F (90° production direction), shown in Figure 3-10, are almost

identical for different thicknesses, as expected due to the random in-plane fiber distribution

resulting in quasi-isotropic properties [47, 48]. The difference of the SEAC per thickness

between configurations E and F is between -0.3 and 1.0 kJ/kg for the specimen thickness from 2.5 mm to 8.0 mm. This almost identical behavior demonstrates that random in-plane

fiber distribution is almost isotropic and, therefore, has no significant influence on the in-

plane material properties.

Figure 3-10: Effect of the in-plane fiber distribution on SEAC.


61

Taking the standard deviation of the configurations into account supports this finding,

as it shows no significant trend to a configuration. The standard deviation is between 2.3

and 8.5 kJ/kg for the specimen thickness from 2.5 mm to 8.0 mm, and thus, higher than the

differences of the SEAC per thickness between the configurations. This observation is similar

to the findings from Ref. [19, 22, 30, 32, 33, 35, 47, 48] for tensile behavior. Due to the positioning of the semi-finished product, material flow, and in particular fiber entrainment,

can happen during the compression molding process. This effect is not further investigated.

3.3.5. Interaction between the Loading Rate Influence and the Specimen Thickness

The thickness of the flat plate specimen is a significant factor influencing the material

properties, as illustrated in Figure 3-11. In static testing, the SEAC value of the flat plate

specimen is 34.0 kJ/kg for the 2.5 mm thick plate, increases linearly with around 1.9 kJ/kg per mm thickness to 44.5 kJ/kg for the 8.0 mm thick plate. The standard deviation increases

with increasing specimen thickness but relatively remains constant, with a CV of

approximately 11.0% per investigated thickness. The improvement in the crushing

performance when increasing specimen thickness can be directly attributed to the

development of the crushing frond, as the level of fragmentation of the crushing frond decreases while its coherence increases with increasing specimen thickness. In turn, the

generation of the crushing frond has a significant influence on several parameters related

to the energy absorption mechanism, including the midplane splitting, the delamination

into individual layers, the friction between those layers, and fiber-bending and fracture [55-57]. It can be assumed here that the SEAC values resulting from most crushing modes

depend linearly on the crushing width and thickness. The crushing modes related to

bending instead have a quadratic increase based on the section modulus on each side of the

split-thickness. However, the bending contribution is only minor, as illustrated in Figure 3-7

of the distribution of the crushing force along the specimen thickness investigated here. Within the range of specimen thickness investigated here, the increase in SEAC appears to

be linear. While the increase in the crushing force might appear as quadratic for extremely

thick specimens, catastrophic failure is very likely to occur for very thin specimens. In

addition, a very thick specimen will likely tend to only split at the midplane and bend

outwards without forming stable crushing fronds.


62

Figure 3-11: Effect of the loading rate and thickness on SEAC.

In general, the findings related to the effect of the thickness and the loading rate on

the SEAC coincide with the findings for tubes [41] but on different SEA levels. Also, the intensity of the effects is significantly lower for crush testing flat plate specimens as for

tubes. In the literature [18, 24, 26, 27, 31, 34, 35], various observations on the influence of

the specimen thickness are made mainly for tensile testing. The overall influences observed

from the literature due to increasing thickness are various improvements of the material

strength and stiffness and a decrease of the standard deviation. These thickness effects were attributed to an increased homogenous fiber distribution, which leads, according to

Kravchenko [21], to a higher possibility of having fiber bundles aligned in the loading

direction. Based on the observation of mode I intra-laminar fracture made by Ko et al. [27]

due to geometrically-scaled single edge notch tension tests, the effect of the thickness

converges for specimens with random discontinuous fiber distribution to a specimen's thickness of 3 mm. They observed no further increase in material strength and stiffness for

specimens thicker than 3 mm. They assumed that at this specific specimen thickness, almost

homogeneous fiber distribution was already formed across the specimen thickness, and

therefore thicker specimen showed no further increase. Compared to the findings here, the fracture toughness due to crush testing does not converge to a specific specimen thickness

as the mode I intra-laminar fracture due to single notch tension tests. In fact, the SEAC

increases linearly over a wide range of specimen thickness. The inspection of failure

mechanisms explains the observation that there is no specific thickness at which the SEAC

ceases to improve. In coupon level testing, increasing the specimen thickness leads to an increased homogenous fiber distribution; however, it could lead to a higher possibility of

material defects and thus failure initiation. In crush testing, the generation of the crushing

frond is affected by the homogeneity of the fiber distribution. In addition, the interaction


63

between internal friction, delamination, splitting, and fracture of the fiber bundle severely

affects the development of the crushing frond, its fragmentation, and its coherence.

The comparison of the SEAC obtained from static and dynamic testing shows a loading

rate dependency of the material, which increases by increasing the specimen thickness. For

the 2.5 mm thick specimens, the loading rate dependency is questionable, as the SEAC value obtained from dynamic testing is 33.2 kJ/kg, only 0.8 kJ/kg less than the 34.0 kJ/kg obtained

from static testing. Interestingly, the loading rate dependency increases with increasing

specimen thickness, which reduces the value obtained from dynamic testing for the 8.0 mm

thick specimen to 37.2 kJ/kg and increases the gap between the 44.5 kJ/kg obtained

respectively from static testing to be 7.3 kJ/kg. This loading rate dependency due to the specimen thickness is also reflected in the increase of SEAC per mm specimen thickness, as

the increase along the specimen thickness from 2.5 mm to 8.0 mm obtained from static

testing is 1.9 kJ/kg per mm, and the increase obtained from dynamic testing respectively is

only 0.7 kJ/kg per mm. An interpretation of this outcome is that dynamic testing leads to an increase in the degree of fragmentation and an increase in separation of individual layers of

the crushing frond, which also leads to a smaller increase in SEAC when increasing specimen

thickness in comparison with static testing and, additionally, explains the investigated

loading rate dependency. The increase of the degree of fragmentation and separation of

individual layers of the crushing frond can be taken from the comparison of the statically tested Configuration E and dynamically tested Configuration G from Figure 3-3, for example.

3.3.6. Comparison of the SEA Values

Due to utilizing the CPIT, it is possible to isolate the inadvertently included force

caused by shearing and friction at the edge of the impactor, as validated in Ref. [40], which generally allows for comparing the results with those obtained by the method of

unsupported height, e.g., those from Jacob et al. [36-39]. The method of unsupported height

avoids these edge forces by omitting the support of the specimen shortly before they are

crushed. As shown in Figure 3-12, the SEA determined by Jacob et al. [36-39] based on a

tight constraint and a small profile radius is on a similar level to the SEAC values calculated here from the crushing force. It should be noted here that looser constraints or wider radii

reported by Jacob et al. [36-39] resulted in significantly lower SEA values. However, due to

the occurrence of buckling, these results are not comparable. A comparison of the results of

the flat plate specimen and the profiles seem not relevant, as stated by Feraboli et al. [11]. The results obtained from crushing profiles can be different even from each other due to the

profile shape, dimensions, and wall thickness. In addition, the tearing effect of the profiles


64

differs from the shearing and friction at the edge of the flat plate specimens. The overall

response of the SEA of the profile specimens [41-44] to the measured parameters seems to

be similar to that of the SEAM of the flat plate specimens.

Figure 3-12: Distribution of the SEA vs. thickness.

When calculating the SEAM based on the measured force, the inadvertently included

component due to shearing and friction at the edge of the impactor affects the result. This

effect can be seen when comparing the results of SEAC and SEAM from Table 3-3. For all

Configurations statically tested (A till F), the proportion of the SEAC to SEAM is only around 50% for the 23.6 mm crushing widths, increases by increasing the width to 61% for the

36.0 mm width, and 67% for the 48.2 mm width. Here the increase in the proportions is

evident since the edge component is independent of the width, whereas the crushing

component increases linearly with the width. In dynamic testing, Configuration G, the

proportions of the SEAC to SEAM are slightly higher. For the 23.6 mm crushing width, the proportion is 57%, increases for the 36.0 mm width to 66%, and for the 48.2 mm width

increases to 72%. Comparing these proportions for static and dynamic testing percentage-

wise shows that in dynamic testing, more energy is absorbed due to crushing and less due

to shearing and friction at the edge of the impactor. It should be noted here that in dynamic testing, the SEA is generally lower than in static testing. Similar to the difference in the

development of the crushing frond for the static and dynamic testing, which explains the

loading rate dependency, there are also differences in the generation of the split edge due

to shearing and friction at the edge of the impactor. The comparison from Figure 3-4 clearly

indicates differences, as the split edge obtained from static testing is very rough and tattered, and the split edge obtained from dynamic testing is smooth. Therefore, it can be

interpreted that the rough and tattered split edge due to static testing is provoked by a


65

higher amount of shearing and friction forces at the edge of the impactor. Likewise, the

smooth split edge due to dynamic testing is provoked by less shearing and friction forces.

Table 3-3: Overview of the results for the investigated fiber length, fiber mass content, thickness, and loading rate configurations.

3.4 Conclusion

66

3.4. Conclusion

This study presents an experimental investigation of the various parameters which

affect the crush energy absorption mechanism of fully constrained discontinuous carbon fiber composite flat plates manufactured by compression molding. The effects of fiber

length, fiber mass content, in-plane fiber distribution, specimen thickness, and loading rate

have been evaluated and compared against the literature. Fully constrained flat plate

specimens have been tested using the crush property isolation technique [40], which allows

for separating the crush energy from the energy dissipated at the constrained edges due to shearing and friction losses.

The crushing morphology is found to be similar to that of transfer and bladder molded

tubes [41–44], which forms a fragmented but mostly coherent crushing frond. The degree

of fragmentation increases in dynamic testing compared to quasi-static testing, which leads

to lower frond coherence and, therefore, less energy absorption. The split edges also show a difference in the damage mode as the edge is very rough and tattered in static testing and

very smooth when crushed dynamically. This, in turn, is reflected in the proportions of the

crushing and edge force components for static and dynamic testing.

Increasing fiber length and fiber mass content leads to a minor increase in the SEA.

Still, the effect of both parameters is relatively insignificant, similar to the findings for tubes [41–44]. Due to the crushing morphology and the composition of the crushing load from

compression and bending, it can be interpreted that the development of the crushing frond

is essentially affected by the crack initiation and -propagation. This failure, in turn, results

mainly from the loss of coherence between the fibers and the matrix. Therefore it is plausible to assume that the SEA is only slightly affected by increasing the fiber lengths. The

increase in the fiber mass content leads to an increase in the measured force. However, this

increase does not lead to an increase in the SEA as the increase in the fiber mass content

also leads to an increase in density. In addition, the standard deviation increases with

increasing fiber length and decreases with increasing fiber mass content. This effect can be attributed to the changes in the homogeneity of the fiber distribution, which are affected by

the fiber length and fiber mass content. Considering the influence of the fiber length and

fiber mass content on the SEA and its standard deviation, a combination of high fiber mass

content and low fiber length represents an appropriate combination for engineering

materials as an energy absorber. In particular, the SEA of such a combination is still high.

3.4 Conclusion

67

The in-plane fiber distribution showed almost no influence on the SEA as expected,

based on the findings in Ref. [47, 48]. In particular, the observed SEA was practically the

same for the investigated specimen thickness, and therefore no significant influence could

be observed. Furthermore, due to the identical behavior, it can be concluded that the

random in-plane fiber distribution is almost isotropic.

The specimen thickness is a significant factor affecting the SEA values of such

materials, as increasing the thickness leads to an increase in SEA and, in addition, highlights

the dependency of the SEA values on the material composition. The effect of plate thickness

can be attributed to the mechanism of forming the crushing frond. Increasing the plate

thickness leads to increasing the thickness of the crushing frond, which results in a decrease in the level of fragmentation and an increase in its coherence. The fracture mechanisms,

which form the crushing frond, consist of the midplane splitting, the delamination into

individual layers, the friction between those layers, and fiber-bending and fracture. Most of

the crushing modes depend linearly on the crushing width and thickness. The crushing SEA component related to bending should have a quadratic increase with thickness caused by

the resulting increase in the section modulus of the crushing fronds. The apparent increase

of the SEA with thickness within the range of the tested specimen thickness seems linear.

For coupon level testing, it was assumed in literature [27] that when a specific thickness is

reached, the fibers are homogeneously distributed, and therefore, a further increase in the specimen thickness has no additional effect. In contrast to the results from the literature,

the results obtained here show that the increase of the SEA due to increasing specimen

thickness appears to be linear within the considered range. However, catastrophic failure is

very likely to occur for very thin specimens. In addition, a very thick specimen will likely

tend to only split at the midplane and bend outwards without forming stable crushing fronds. Dynamic testing of the specimen showed a loading rate dependency, which

increased with specimen thickness. The decrease of energy absorption in dynamic testing

of larger specimen thickness can be attributed to an increase of fragmentation and

separation of individual layers of the crushing frond. Therefore, it could be shown that the

development of the crushing frond and the failure mechanism related to this evolving severely affect the SEA of the material.

Utilizing the crush property isolation technique on discontinuous carbon fiber

composite flat plate specimens allows for calculating the SEA from the crushing component

(SEAC) of the measured load instead of the SEA from the measured load itself (SEAM). The

results shown here are comparable with those investigated so far using the unsupported

3.5 References

68

height, as in Ref. [36–39]. The effects of the fiber length, fiber mass content, specimen

thickness, and the loading rate on SEAC obtained here are also comparable to those obtained

for the tubes investigated in Ref. [41–44]. Moreover, the SEAC calculation from the crushing

component of the measured load leads to width-independent and consistent results. Even

though the energy absorption determined here of the SEAM for flat plate specimens and those for the profiles, as in Ref. [41–44], are different, as stated in Ref. [11], the general trend

seems to be similar, which adds to the credibility of the results and the utilized method.

3.5. References










3.5 References

69





[14] Carruthers JJ, Kettle AP, Robinson AM. Energy Absorption Capability and Crashworthiness of Composite Material Structures: A Review. Appl Mech Rev 1998;51:635–49. doi:10.1115/1.3100758.

[15] Farley GL, Jones RM. Crushing Characteristics of Continuous Fiber-Reinforced Composite Tubes. J Compos Mater 1992;26:37–50. doi:10.1177/002199839202600103.


[17] Xiao Z. Advancements in discontinuous carbon fibre composite technologies for high- volume manufacturing processes. University of Nottingham, 2018.

[18] Harper L, Qian C, Luchoo R, Warrior N. 3D geometric modelling of discontinuous fibre composites using a force-directed algorithm. J Compos Mater 2017;51:2389–406. doi:10.1177/0021998316672722.

[19] Li Y, Chen Z, Xu H, Dahl J, Zeng D, Mirdamadi M, et al. Modeling and Simulation of Compression Molding Process for Sheet Molding Compound (SMC) of Chopped Carbon Fiber Composites. SAE Int J Mater Manuf 2017;10:2017-01–0228. doi:10.4271/2017-01-0228.

[20] Ionita A, Weitsman YJ. On the mechanical response of randomly reinforced chopped-fibers composites: Data and model. Compos Sci Technol 2006;66:2566–79. doi:10.1016/j.compscitech.2006.01.019.

[21] Kravchenko SG. Failure Analysis in Platelet Molded Composite Systems. Purdue University, 2017.

3.5 References

70

[22] Chen Z, Tang H, Shao Y, Sun Q, Zhou G, Li Y, et al. Failure of chopped carbon fiber Sheet Molding Compound (SMC) composites under uniaxial tensile loading: Computational prediction and experimental analysis. Compos Part A Appl Sci Manuf 2019;118:117–30. doi:10.1016/j.compositesa.2018.12.021.

[23] Wan Y, Takahashi J. Tensile and compressive properties of chopped carbon fiber tapes reinforced thermoplastics with different fiber lengths and molding pressures. Compos Part A Appl Sci Manuf 2016;87:271–81. doi:10.1016/j.compositesa.2016.05.005.

[24] Selezneva M. Experimental and theoretical investigations of mechanical properties of randomly-oriented strand (ROS) composites. McGill University, Montreal, 2015.

[25] Wulfsberg J, Herrmann A, Ziegmann G, Lonsdorfer G, Stöß N, Fette M. Combination of carbon fibre sheet moulding compound and prepreg compression moulding in aerospace industry. Procedia Eng 2014;81:1601–7. doi:10.1016/j.proeng.2014.10.197.

[26] Tiefenthaler M, Stelzer PS, Chung CN, Reisecker V, Major Z. Characterization of the fracture mechanical behavior of C-SMC materials. 16th Youth Symp. Exp. Solid Mech. YSESM 2018, vol. 18, 2018, p. 1–5. doi:10.14311/APP.2018.18.0001.

[27] Ko S, Davey J, Douglass S, Yang J, Tuttle ME, Salviato M. Effect of the thickness on the fracturing behavior of discontinuous fiber composite structures. Compos Part A Appl Sci Manuf 2019;125:105520. doi:10.1016/j.compositesa.2019.105520.

[28] Schommer D, Duhovic M, Gortner F, Maier M. Advanced Simulation of Polymer Composite SMC Compression Molding using Fluid-Structure Interaction. 13th Int LS-DYNA Users Conf 2014:1–10.

[29] Martulli LM, Alves M, Pimenta S, Hine PJ, Kerschbaum M, Lomov S V, et al. Predictions of Carbon Fibre Sheet Moulding Compound (CF-SMC) Mechanical Properties Based on Local Fibre Orientation. ECCM18 - 18th Eur. Conf. Compos. Mater., 2018, p. 6.

[30] Corbridge DMM, Harper LTT, De Focatiis DSASA, Warrior NAA. Compression moulding of composites with hybrid fibre architectures. Compos Part A Appl Sci Manuf 2017;95:87–99. doi:10.1016/j.compositesa.2016.12.018.

[31] Harper LT, Turner TA, Warrior NA, Dahl JS, Rudd CD. Characterisation of random carbon fibre composites from a directed fibre preforming process: Analysis of microstructural parameters. Compos Part A Appl Sci Manuf 2006;37:2136–47. doi:10.1016/j.compositesa.2005.11.014.

[32] Nony-Davadie C, Peltier L, Chemisky Y, Surowiec B, Meraghni F. Mechanical characterization of anisotropy on a carbon fiber sheet molding compound

3.5 References

71

composite under quasi-static and fatigue loading. J Compos Mater 2018;0:002199831880461. doi:10.1177/0021998318804612.

[33] Nicoletto G, Riva E, Stocchi A. Mechanical Characterization of Advanced Random Discontinuous Carbon/Epoxy Composites. Mater Today Proc 2016;3:1079–84. doi:10.1016/j.matpr.2016.03.052.

[34] Eguemann N, Giger L, Masania K, Dransfeld C, Thiebaud F, Perreux D. Processing of characterisation of carbon fibre reinforced peek with discontinuous architecture. 16th Eur. Conf. Compos. Mater. ECCM 2014, 2014.

[35] Feraboli P, Peitso E, Deleo F, Cleveland T, Stickler PB. Characterization of Prepreg-Based Discontinuous Carbon Fiber/Epoxy Systems. J Reinf Plast Compos 2009;28:1191–214. doi:10.1177/0731684408088883.







[42] CUTTING R, SHARMA V, GOODSELL J. Crush Response of Prepreg Platelet Molding Compound Tubes. Am. Soc. Compos. 2018, Lancaster, PA: DEStech Publications, Inc.; 2018. doi:10.12783/asc33/26074.


3.5 References

72


[45] Jacob GC, Starbuck JM, Fellers JF, Simunovic S, Boeman RG. The effect of loading rate on the fracture toughness of fiber reinforced polymer composites. J Appl Polym Sci 2005;96:899–904. doi:10.1002/app.21535.


[47] Kravchenko SG, Sommer DE, Denos BR, Favaloro AJ, Tow CM, Avery WB, et al. Tensile properties of a stochastic prepreg platelet molded composite. Compos Part A 2019;124:105507. doi:10.1016/j.compositesa.2019.105507.

[48] Sommer DE, Kravchenko SG, Denos BR, Favaloro AJ, Pipes RB. Integrative analysis for prediction of process-induced, orientation-dependent tensile properties in a stochastic prepreg platelet molded composite. Compos Part A 2020;130:105759. doi:10.1016/j.compositesa.2019.105759.

[49] Feindler N. Charakterisierungs-und Simulationsmethodik zum Versagensverhalten energieabsorbierender Faserverbundstrukturen. Technische Universität München, 2012. doi:urn:nbn:de:bvb:91-diss-20121217-1108924-1-9.

[50] Society of Automotive Engineers. SAE J211/1--Instrumentation for Impact Test-Part 1-Electronic Instrumentation. SAE Int Warrendale, PA 2007.

[51] Selezneva M, Roy S, Lessard L, Yousefpour A. Analytical model for prediction of strength and fracture paths characteristic to randomly oriented strand (ROS) composites. Compos Part B Eng 2016;96:103–11. doi:10.1016/j.compositesb.2016.04.017.

[52] Visweswaraiah SB, Selezneva M, Lessard L, Hubert P. Mechanical characterisation and modelling of randomly oriented strand architecture and their hybrids – A general review. J Reinf Plast Compos 2018;37:548–80. doi:10.1177/0731684418754360.

[53] Tucker III CL, Liang E. Stiffness predictions for unidirectional short-fiber composites: Review and evaluation. Compos Sci Technol 1999;59:655–71. doi:10.1016/S0266-3538(98)00120-1.

[54] AVK - Industrievereinigung verstärkte Kunststoffe e. V. Handbuch Fasververbundkunststoffe / Composites. 2010.

3.5 References

73


[56] Nakatani T, Kameo K, Hamada H. Development of energy absorption parts with FRP tubes. Adv Compos Mater 1999;8:345–54. doi:10.1163/156855199X00326.

[57] Hamada H, Ramakrishna S, Satoh H. Crushing mechanism of carbon fibre/PEEK composite tubes. Composites 1995;26:749–55. doi:10.1016/0010-4361(95)98195-Q.

74

Chapter 4. Insight into Crush Performance Comparison of Composite Profiles and Flat Plates

This chapter presents an approach to evaluate and interpret the geometric effects of crush-tested profiles by separating the effect of the resistance at the profile corners from

the crushing force of the profile flat segments. Based on the separation, the generic crush

property of a corner and that of a flat segment can be utilized to predict the crush properties

of profiles with different shapes and dimensions regarding specific conditions. The calculated crushing SEA of the profile flat segments has also proven identical to that of flat

plates.


Composites Part B: Engineering. The corresponding article can be cited as:

Lausch J, Takla M, Schweiger H-G. Insight into crush performance comparison of composite profiles and flat plates. Compos Part B Eng 2022;233:109643.

doi:10.1016/j.compositesb.2022.109643.

4.1. Introduction

Modern automotive designs, including battery-electric vehicles (BEV), are becoming

the focus of car manufacturers [1–6]. New designs also need to satisfy increasingly stringent

regulations [7, 8], which aim at improving safety [7, 9] while minimizing emissions via

reducing or eliminating fuel consumption. Interest in lightweight materials became the

focus of automotive designers in their attempt to satisfy such conflicting demands [3, 6, 7, 9–13]. Reducing the automotive body weight reduces the energy needs and,

consequently, the BEV battery mass [1, 3, 6, 7, 9, 12]. In addition to reducing weight, fiber-

reinforced composite materials have an excellent crush performance, and accordingly, an

outstanding specific energy absorption (SEA) capacity [14–20], which is particularly

beneficial to BEVs as additional protection against impact is needed for the battery [7, 8].

4.1 Introduction

75

In order to determine the precise crushing properties of lightweight materials,

inexpensive methods need to be adopted [6, 21]. Flat plate specimens are particularly

suitable, as they are significantly cheaper and easier to manufacture than corrugated or

profiled specimens [22–25]. Crush testing of flat plates, however, involves several

difficulties. Various approaches [26–34], such as testing with an unsupported height or testing fully supported specimens using the Crush Property Isolation Technique (CPIT),

have already been found to circumvent the additional difficulties affecting the usability of

flat plate crush testing [22, 23, 26–33, 35–39]. As the name implies, the approach of the

unsupported height [26–32] enables the specimen to deform freely in the lateral direction,

but lateral buckling can occur depending on the selected height. Lateral support during crush testing of flat plates provides sustained crushing and prevents global buckling.

However, it results in an additional force due to splitting at the lateral constraints. The CPIT

[33, 34] isolates the inadvertently included force component caused by the test setup from

the crushing component.

Due to the complexity of the fracture mechanisms, the test setups, and the geometrical

differences, comparisons between the SEA of flat plate specimens and those of self-

supporting structures, like tubes, used to be difficult and provided conflicting results. For

example, Lavoie et al. [35] observed material-related differences between crush-tested

plates and profiles. They suggested that plate testing was only usable for screening different materials but not as a general alternative for structural testing. Cauchi and Hogg [40]

investigated the effect of plate geometry on crush testing flat plate composites. They also

investigated the similarity of the nonlinear relationship between the SEA and the specimen

width-to-thickness ratio in flat plates to that between the SEA and the diameter-to-

thickness or width-to-thickness ratio in circular and square profiles. Nevertheless, the essential focus in the literature for crush testing composites has been on circular tubes.

According to Feraboli et al. [13], the utilization of the tubes is mainly attributed to the self-

supporting structure since no additional test fixtures are required. Various studies [40–47]

have already dealt with the geometric effect of tubes or beams on their crush performance,

but this effect has mostly been attributed to their profile dimensions-to-thickness ratios. Although such a ratio is defined for circular tubes, there is no precise definition for square

or other-shaped profiles, which makes comparing the general performance even more

difficult.

An investigation of the geometric effects of edge-free segments and in-between edge

segments of profiles was carried out by Bolukbasi and Laananen [24, 25]. The observed

4.1 Introduction

76

experimental behavior of the profiles demonstrated that no buckling would occur if the

combined critical buckling stress of the edge-free and in-between edge segments was higher

than the measured sustained crushing stress of the corresponding flat plate specimens.

They also noticed differences between the profiles and the flat plate specimens caused by

the tearing but referred them to the different boundary conditions of the test setups and the geometrical shapes. In addition, to predict the sustained crushing stress of the profiles, they

developed a semi-empirical approach based on the results of the flat plates by parameter

fitting the cross-sectional proportion of the edge-free and in-between edge segments. They

concluded that using the semi-empirical approach for crush testing of flat plates can

potentially replace profile testing.

Feraboli et al. [13] examined the geometry effect of different profile shapes on their

crush behavior. Five different profiles were examined for this purpose: two different angle

profiles, two different channel profiles, and a square tube. They also considered the

occurrence of the two components, the tearing at the corner and the crushing of the flat segments. They divided each profile shape into flat and corner segments. They used the

smallest investigated angle profile as the reference corner segment. The different profiles

demonstrated a nonlinear decrease of the SEA when increasing the width of the flat

segment, similar to that of fully supported flat plate specimens [33, 34, 37, 40]. In addition,

they calculated the SEA of the flat segments of the different profiles based on the geometric relationship between each profile and the reference corner segment, which is the smallest

angle profile. The SEA of the flat segments was consistent despite a high degree of variation

but very low compared to the SEA of the corresponding corner segment. They concluded

that a significant amount of energy is absorbed in the corner segment, which they attributed

to fiber tensile fracture and tearing. They also concluded that the more contoured the specimen, the higher the absorbed energy. In order to validate the observations, they

compared the SEA of the flat segments from the profiles with those of flat plate specimens

of the same material using the method of unsupported height. Although the results showed

to be similar to those of the flat plate specimens but slightly lower, they concluded that flat

plate testing led to an overestimation of the energy absorption due to inadvertently included effects of the test fixture. They also depicted a linear increase of the SEA with the

degree of curvature of the cross-section of the profiles. Therefore, they concluded that the

SEA is highly dependent on the degree of curvature of the profile geometry, and thus the

values for flat and curved segments must be considered separately.

4.1 Introduction

77

The comparison between the results from Feraboli et al. [13] for different crush-

tested profiles with those of fully constrained flat plate specimens obtained from Ref

[33, 34, 37, 40], illustrated in Figure 4-1, shows that the SEA of the profiles behaves in a

nonlinear manner similar to that of the flat plates. According to the results obtained by using

the CPIT, this behavior can be attributed to the inadvertently included force component at the constrained edges of the impactor in fully constrained flat plate crush testing. The

support of the different flat plate test frames from Ref [33, 34, 37, 40] and the profiles

investigated by Feraboli et al. [13] are schematically shown in Figure 4-2. The CPIT implies

that the edge force resulting from tearing and friction at the edge of the impactor is

practically independent of the crushing width. The crushing component, on the other hand, is linearly proportional to the crushing width of the flat plate specimen. Therefore, the SEA

calculated from the combined total (measured) force, further called SEAM, decreases

hyperbolically when increasing the crushing width and converges towards the SEAC

calculated from the crushing component, as the proportion of the included width-independent edge-component decreases and diminishes. This effect is illustrated in Figure

4-1 for the different flat plate specimens.

Figure 4-1: SEAM of flat plates and profiles with different crushed segment widths per tearing for different materials from Ref. [13, 33, 34, 37, 40].

4.1 Introduction

78

Figure 4-2: Schematic representation of the different test setups: a) flat plate knife-edge supporting frame from Ref. [37, 40]; b) flat plate full lateral supporting frame from Ref. [33, 34]; c) investigated profiles by Feraboli et al. [13].

Feraboli et al. [13] attributed the nonlinear behavior of the profiles to the tearing failure mechanism at the corners. According to discussions in the literature

[13, 24, 25, 42, 43, 47–51] for various profiles, the crushing morphology is typically

composed of tearing at the corner and forming a crushing frond in the flat segments. The

literature also indicates that the tearing is mostly confined to the corners, which suggested

that the tearing force component included in the measured force is, most likely, independent of the width of the flat segments of the profile and depends only on the number of corners

in the profile. In the cases of angle-, channel-, or square profiles, the corner appeared to

serve as the catalyst for the tearing. An interpretation of corner tearing is that it is initiated

from shell buckling in the axial direction. As the two flat segments on both sides of the corner tend to buckle/bend outwards in two perpendicular directions, this exerts a large

horizontal tensile force at the corner, exceeding its fracture limit, initiating the tearing. In

4.2 Methodology

79

addition, flat segments of profiles and flat plates are correlated due to the similar crushing

morphologies of the crushing fronds. Comparing the crush testing results obtained from the

literature [13, 24, 25, 34, 40, 42, 43, 48–53] for various materials shows that the crushing

frond of a flat plate specimen is practically identical to that of a flat segment of a profile.

Therefore, it can be predicted that the isolated crushing force of a flat segment of a profile is also likely to be proportional to the width of the segment, similar to the case of flat plate

specimens [33]. While significant, the above observations have not been adequately utilized

so far to predict the crush behavior of a profile from testing other profiles.

The aim of this study is to examine the geometrical effects of crush-tested profiles and

to investigate the possibility of predicting the crush properties of profiles from crush testing other profiles of the same material. The correlation between the crush performance of

composite profiles and that of plates is also investigated. For this purpose, several profiles

of different shapes with different numbers of right-angled corners have been investigated.

Different angle-, channel-, square profiles, and flat plates have been crush-tested experimentally, and the results thoroughly analyzed. In addition, circular tubes have been

crush-tested experimentally to investigate the effect of shell curvature on its crush behavior

and determine any possible correlation.

4.2. Methodology

4.2.1. Testing Approach

While the proposed approach to investigate the geometrical effects of crush-tested

profiles originates from the separation concept of the CPIT for fully constrained flat plate specimens, it is a very different approach. The CPIT was utilized to isolate and discard the

width-independent edge (shearing/tearing) force component caused by the test setup from

the width-dependent crushing component, as shown in Figure 4-3. The proposed approach

for the prediction of profile crush properties is also based on separating the two force

components, namely the resistance to tearing at the profile corners and the crushing of the flat segments. However, the tearing component at the profile corner remains a substantial

part of the profile crush property, as highlighted in Figure 4-3. Therefore, the crush

resistance of a profile can be considered as a combination of resistance of the corners and

that of the flat segments. Once these properties are determined, the behavior of a right-

angled profile of a given number of tearing occurrences (corners) and a defined length of the flat segments can be predicted.

4.2 Methodology

80

Figure 4-3: Comparison between the fracture mode of a fully constrained flat plate specimen and a crush-tested profile.

The separation concept of the CPIT is based on the circumstance that one of the

fracture mechanisms is independent of the specimen width and the other component linear

dependent on the specimen width resulting in a linear, albeit non-proportional increase for

the measured values. Regarding the crush-tested profiles, the corner tearing can be interpreted as the width-independent component and the formation of the crushing frond

as the width-dependent one. Therefore, both components, the tearing at the profile corner

and the crushing of the flat segments of the profile, can be calculated using linear regression

of the results of different profiles of different shapes and sizes. Figure 4-4 uses the results of the crush-tested profiles from Feraboli et al. [13] as an example to show the tearing and

crushing components calculated from the linear regression of the measured forces. This

illustration also proves the occurrence of width-dependent and independent components,

4.2 Methodology

81

as the linear regression is calculated based on the experimental tests. It should be noted

here that comparing profiles with different thicknesses is not feasible as the specimen

thickness has a quadratic effect on the bending resistance of the crushing frond, as stated in

Ref. [34]. Despite the self-supporting structure of profiles, column buckling is likely to occur

for extremely slender profiles due to the decrease in critical buckling load, while catastrophic failure is likely to occur for extremely wide/short profiles. Therefore, in order

to avoid both extremes, the slenderness ratios of the tested profiles have been selected to

be within the range from 10 to 64.

Figure 4-4: Representation of the individual force components, tearing and crushing, based on the linear regression of the results of the crush-tested profiles from Feraboli et al. [13].

Due to the similarity of the crushing morphology of the profile flat segments to that of

the flat plate specimens, their SEA is also expected to be similar. Utilizing the technique to analyze the results of the profiles investigated by Feraboli et al. [13] leads to a consistent

SEA for the flat segments with almost the same value as that for the crush-tested flat plates.

In comparison, the proposed method by Feraboli et al. [13] for calculating the SEA of the flat

segments leads to lower values with higher variations, which is why they concluded that flat

plate testing overestimates the SEA of the materials. The comparison of the calculated SEA values is illustrated in Figure 4-5. This variation can be attributed to using the smallest

investigated angle profile as the reference corner segment, which leads to reducing the

corresponding size of the flat segments of the other profiles since the smallest angle profile

consists of a corner and two narrow flat segments. In addition, if the SEA value of the

smallest angle profile deviates from the expected average SEA obtained from the values of all profiles, such deviation would lead to a substantial increase in the fluctuation of the

calculated SEA of the flat segments of the other profiles. Further development of the

4.2 Methodology

82

proposed method from Feraboli et al. [13] towards using an approach based on linear

approximation takes the fluctuation into account, which experimental testing is usually

subjected to, and provides new insights into comparing the crush performance of various

composite profiles and flat plates.

Figure 4-5: Separation of the crushing force of the profile flat segments from the results from Feraboli et al. [13].

As proposed here, the measured force F due to profile crush testing consists of the

two components, the crushing component FC of the flat segments and the tearing component

FT of the corners,

𝐹𝐹𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝐹𝐹𝐶𝐶 + 𝐹𝐹𝑇𝑇 . (4-1)

For profiles of different sizes with an equal number of tearings, the linear approximation is directly applicable to separate the crushing and the tearing component.

However, to determine the crushing and the tearing component for profiles with different

shapes and, therefore, a different number of corners, the measured force as well as the total

segment width w have to be considered per number of corners or, alternatively, per number

of tearings x,

𝐹𝐹𝑥𝑥𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑃𝑃𝑃𝑃 = 𝐹𝐹𝑥𝑥

= 𝐹𝐹𝑆𝑆+𝐹𝐹𝑇𝑇𝑥𝑥

, (4-2)

and

𝑤𝑤𝑥𝑥 = 𝑤𝑤𝑥𝑥

. (4-3)

It should be noted that the dimension of the shell middle plane is used as the total

width w of the profile.

4.2 Methodology

83

Crush testing of fully supported flat plates also consists of two components. The

crushing component of the flat plate should be similar to that of the flat segments of the

profiles. However, the tearing mechanisms in a flat plate and profile crush testing are

fundamentally different, as shown in Figure 4-3, and should be treated accordingly. The

inadvertently included component FE in testing fully constrained flat plates is caused by the resistance to shearing as well as the additional friction at both edges of the impactor, while

the tearing at the corners of the profiles is caused by the tensile force acting at the profile

corner in the direction of the contour of the profile. It should also be noted here that the

shearing/tearing/friction force in testing fully supported plates is not a plate section

property as it is directly related to the testing arrangement and, therefore, needs to be isolated using the CPIT and discounted from the measured force to obtain the pure crushing

property of the plate. Therefore, its own value is not significant, as long as it remains

consistent in different tests of different plate widths.

On the other hand, the tearing force at the corners of the profiles, although not part of the axial crushing force itself, contributes significantly to the resistance of the profile to axial

shell buckling, which contributes substantially to elevating the level of axial crush resistance

of the profile and its crush energy absorption. Therefore, such contribution represents an

integral component of the profile section property and needs to be considered carefully. The

effect of the lateral tearing force at the profile corners on the total axial resistance of the profile will be simply termed “the tearing force”.

In crush testing of fully constrained flat plates, there are always two

shearings/tearings, one on each edge of the impactor,

𝐹𝐹𝑃𝑃𝑃𝑃𝑎𝑎𝑡𝑡𝑃𝑃 = 𝐹𝐹𝐶𝐶 + 𝐹𝐹𝐸𝐸 , (4-4)

and

𝐹𝐹𝑥𝑥𝑃𝑃𝑃𝑃𝑎𝑎𝑃𝑃𝑃𝑃 = 𝐹𝐹𝑆𝑆+𝐹𝐹𝐸𝐸2

. (4-5)

The least mean squares method has been adopted to calculate the approximately

linear relationship between the measured force F and the width w by using the results of

several specimens of different widths. In the resulting linear regression, the slope M

represents the force per unit width, and the intercept represents the resistance force associated with the corners of the profiles or the edges of the fully constrained flat plates,

as illustrated in Figure 4-4. As the frond formation is associated with the specimen width,

the corresponding crushing force FC, which is independent of the corner or edge forces, can

4.2 Methodology

84

be calculated by multiplying the slope M of the linear regression with the width w of the

corresponding flat segment of the plate or profile

𝐹𝐹𝐶𝐶 (𝑠𝑠,𝑤𝑤) = 𝑀𝑀(𝑠𝑠)𝑤𝑤, 𝑑𝑑 ∈ [𝑑𝑑1,𝑑𝑑2] (4-6)

with

𝑀𝑀(𝑠𝑠) =∑ (𝑤𝑤𝑖𝑖− 𝑤𝑤�) 𝑛𝑛𝑖𝑖 �𝐹𝐹𝑖𝑖(𝑠𝑠)−𝐹𝐹�𝑖𝑖(𝑠𝑠)�

�∑ (𝑤𝑤𝑖𝑖− 𝑤𝑤�)2𝑛𝑛𝑖𝑖 �

, 𝑑𝑑 ∈ [𝑑𝑑1,𝑑𝑑2]. (4-7)

In order to normalize the application of the results, the measured force F and the

segment width w have to be replaced by the corresponding values per tearing x. In order to

eliminate the effects of the initial peak and accumulated debris, the calculations consider

only the traveling stroke s between the given boundaries s1 and s2 of the Sustained Crushing Region (SCR). According to the literature [24, 25, 37, 38, 40, 41, 47, 52, 54], the calculation

along the SCR considers only the fluctuation of the material resistance to the crushing

process without the inclusion of any additional effects. Due to the definition of linear

regression, the mean values of all wi and Fi(s) are expressed as 𝑤𝑤� and 𝐹𝐹�(𝑠𝑠).

The tearing force FT at the corners of the profiles and the inadvertently included force FE at the edges of the impactor of the flat plates are calculated as the non-zero intercept of

the linear regression of the measured force-to-width plots

F𝑇𝑇 (𝑠𝑠) = [𝐹𝐹�𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃(𝑠𝑠) −∑ (𝑤𝑤𝑖𝑖− 𝑤𝑤�) 𝑛𝑛𝑖𝑖 �𝐹𝐹𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑃𝑃𝑃𝑃𝑖𝑖(𝑠𝑠)−𝐹𝐹�𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑖𝑖𝑃𝑃𝑃𝑃𝑖𝑖(𝑠𝑠)�


𝑤𝑤�],𝑑𝑑 ∈ [𝑑𝑑1,𝑑𝑑2], (4-8)

and

F𝐸𝐸(𝑠𝑠) = [𝐹𝐹�𝑃𝑃𝑃𝑃𝑎𝑎𝑡𝑡𝑃𝑃 (𝑠𝑠) −∑ (𝑤𝑤𝑖𝑖−𝑤𝑤�) 𝑛𝑛𝑖𝑖 �𝐹𝐹𝑃𝑃𝑃𝑃𝑎𝑎𝑃𝑃𝑃𝑃𝑖𝑖(𝑠𝑠)−𝐹𝐹�𝑃𝑃𝑃𝑃𝑎𝑎𝑃𝑃𝑃𝑃𝑖𝑖(𝑠𝑠)�


𝑤𝑤�], 𝑑𝑑 ∈ [𝑑𝑑1,𝑑𝑑2]. (4-9)

As mentioned before, these forces are different, both in nature and value. However,

the calculation method is fundamentally the same.

The crushing SEA “SEAC“ values for flat profile segments or flat plates can be calculated by dividing the integration of the crushing force FC with respect to the SCR by the

width w of the flat segments, the specimen thickness t, density ρ, and corresponding

crushing stroke s of the SCR. The average force multiplied by the corresponding crushing

stroke represents the absorbed energy. Based on the definition of the crushing force from

equation (4-6), the calculation can be simplified by dividing the slope M of the linear regression, representing the crushing force per unit segment width, by the specimen

thickness and density,

4.2 Methodology

85

SEAC =∫ 𝐹𝐹𝑆𝑆(𝑠𝑠,𝑤𝑤)𝑠𝑠2𝑠𝑠1

𝑑𝑑𝑠𝑠

𝑤𝑤𝑡𝑡𝜌𝜌𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆= 𝑀𝑀

𝑡𝑡𝜌𝜌. (4-10)

For comparison and illustration purposes, the apparent (measured) SEA per unit

mass (SEAM) is calculated by dividing the integration of the measured force F with respect

to the SCR by the specimen cross-sectional area, density, and crushing stroke of the SCR. In

addition, similar to dividing the measured force into components as explained in

equation (4-1), SEAM can also be expressed as the summation of crushing and tearing components,


𝑑𝑑𝑠𝑠

𝑤𝑤𝑡𝑡𝜌𝜌𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆=

∫ 𝐹𝐹𝑥𝑥(𝑠𝑠,𝑤𝑤𝑥𝑥)𝑠𝑠2𝑠𝑠1

𝑑𝑑𝑠𝑠

𝑤𝑤𝑥𝑥𝑡𝑡𝜌𝜌𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆=

∫ (𝐹𝐹𝑆𝑆(𝑠𝑠,𝑤𝑤)+𝐹𝐹𝑇𝑇(𝑠𝑠))𝑠𝑠2𝑠𝑠1

𝑑𝑑𝑠𝑠

𝑤𝑤𝑡𝑡𝜌𝜌𝑠𝑠𝑆𝑆𝑆𝑆𝑆𝑆= 𝑀𝑀

𝑡𝑡𝜌𝜌+ 𝐹𝐹�𝑇𝑇

𝑤𝑤𝑡𝑡𝜌𝜌. (4-11)

Tubes, on the other hand, have a circular profile shape, which does not have any

corners that can contribute to initiating the tearing. In addition, the shell curvature adds to

increasing the bending resistance of the complete crushing frond due to the local arch effect.

Under axial crushing load, the curved shell, which tends to buckle in the axial direction, has two choices; to bend inwards or outwards. In order for the curved shell to bend inwards, it

needs to sustain excessive horizontal compressive stress, which the composite material can

resist until contour buckling occurs. On the other hand, in order for the curved shell to

buckle/bend outwards, the cylindrical shell needs to increase its diameter, so creating

excessive tensile hoop stress, causing the profile to tear apart, creating a number of segments, which flatten independently and bend outwards. The number of created

segments, which is associated with the bifurcation mode, depends greatly on the tube

material, thickness, and dimensions, including shell thickness, diameter, and tube height. In

addition, material, geometric or loading imperfections can play a role in defining the

locations and regularity of the tearings. Accordingly, the collapse mechanism and failure modes of tubes are fundamentally different from those of flat plates or profiles with flat

segments connected at corners. Elaboration on quantifying the influence of these effects

would need special attention and requires an independent study.

4.2.2. Experimental Design

In order to investigate the effect of the number of profile corners on the energy

absorption capacity, six different angle profiles, six different channel profiles, three

different square profiles, and four different circular tubes have been investigated. In

addition, three different flat plate specimens have also been investigated to validate the proposed approach and highlight the relation between crush-tested profiles and flat plate

specimens. The different specimen geometries are illustrated in Figure 4-6 together with

4.2 Methodology

86

the cross-sectional dimensions. A detailed plan of the experiments is illustrated in Table 4-1.

The angle, channel, and square profiles are 5 mm thick and will be termed as right-angled

profiles due to the corner shape. The circular tubes are only 3 mm thick. Flat plates of 5 mm

and 3 mm thickness have been tested in order to be able to compare the properties of flat

plates with those of right-angled profiles and tubes, respectively. In order to be able to differentiate between the profiles, the assigned configuration name is made up of the first

letter of the geometry (Angle: A; Channel: C; Square: S; Tube: T; Flat plate: F) plus the

external dimensions a and b of the sides and the thickness t, as exemplified in Figure 4-6.

For example, an Angle profile with external dimensions of 37 mm and 37 mm and 5 mm

thickness is termed A37375. For tubes, the outer do, and inner di diameters are used as the dimensions, e.g., a Tube of 30 mm external diameter and 3 mm thickness is termed T30243.

For the flat plates, only the crushing width w is used with the thickness due to the

irrelevance of the total width, e.g., for a flat plate of 36 mm crushing width and 5 mm

thickness is termed T365.

Figure 4-6: Overview of the investigated specimen geometries and dimensions.

The material used here is commercially available glass-fiber-reinforced pultrusion

plastic (GRP) with a thermosetting polyester matrix. The layup consists of three layers. The outer layers are a combination of fiberglass mats and rovings with 1.0 mm thickness for the

5 mm-thick specimens and 0.6 mm for the 3 mm-thick specimens, respectively. The inner

layer is unidirectional in the profile direction, with a thickness of 3.0 mm for the 5 mm thick

profiles and 1.8 mm for the 3 mm thick profiles, respectively. The profile specimens are cut

4.2 Methodology

87

to a length of 130 mm to provide sufficient crushing stroke while preventing catastrophic

failure due to column buckling. The angle-, channel profiles, and the circular tubes are fixed

into a 20 mm epoxy base as additional support. The corners of all right-angled profiles have

a common 3.5 mm mean radius, which allows for comparison, as the tearing force at the

corner would depend on the corner shape. All flat plate specimens are 80 mm wide and 150 mm long, cut from the flat segments of a 100 mm x 100 mm square profile.

Table 4-1: Overview of the test setups for the different profile and flat plate configurations.

Config. Area

A / mm²

Total Segment Width

w / mm

Thickness t / mm

Density ρ / kg/m³

Crushing Stroke s / mm

SCR / mm

No. test

Expected Number

of Tearings x

A17175 137.5 27.5 5.0 1879.7 100 20 - 90 7 1 A27275 234.1 47.2 5.0 1877.5 100 20 - 90 7 1 A37375 333.2 67.7 4.9 1883.9 100 20 - 90 7 1 A47475 432.2 87.0 5.0 1883.8 100 20 - 90 7 1 A57575 540.1 107.8 5.0 1887.7 100 20 - 90 7 1 A67675 627.5 126.5 5.0 1887.4 100 20 - 90 7 1

C40125 265.0 51.5 5.1 1876.0 100 20 - 90 7 2 C50175 356.8 70.5 5.1 1893.0 100 20 - 90 7 2 C40265 396.6 79.2 5.0 1880.8 100 20 - 90 7 2 C60225 454.3 90.9 5.0 1882.2 100 20 - 90 7 2 C50315 498.6 98.4 5.1 1887.6 100 20 - 90 7 2 C60365 602.8 119.8 5.0 1879.3 100 20 - 90 7 2

S40405 682.8 135.3 5.0 1883.8 95 20 - 80 7 4 S50505 880.5 175.1 5.0 1883.5 95 20 - 80 7 4 S60605 1074.2 214.4 5.0 1886.4 95 20 - 80 7 4

F245 118.7 23.6 5.0 1882.3 100 20 - 100 7 2 F365 181.8 36.0 5.0 1882.2 100 20 - 100 7 2 F485 240.9 48.2 5.0 1888.5 100 20 - 100 7 2

T20143 162.7 53.0 3.1 1887.2 90 10 - 70 7 - T28223 243.3 78.5 3.1 1885.0 90 10 - 70 7 - T30243 259.5 84.3 3.1 1888.0 90 10 - 70 7 - T32263 275.2 90.0 3.1 1885.7 90 10 - 70 7 -

F243 74.1 23.6 3.1 1880.2 100 20 - 100 7 2 F363 111.7 36.0 3.1 1882.2 100 20 - 100 7 2 F483 149.3 48.2 3.1 1881.4 100 20 - 100 7 2

4.2 Methodology

88

It should be emphasized here that the crushing width of the flat plate specimen is only

a part of the specimen width and is determined by the width of the used impactor. The

remainder of the width is constrained by side clamps, as illustrated in Figure 4-7 for the flat

plate test setup. For all investigated profile and flat plate specimens, a single-sided 45°

chamfer is used as a failure trigger. The cross-sectional area, specimen thickness, and total width have been obtained via digital image processing of the cross-sectional area. In

addition, the eccentricity of the tubes has also been measured. The density of each specimen

is determined using the principle of hydrostatic equilibrium.

4.2.3. Experimental Test Setup

The quasi-static test setups for the flat plate specimens as well as the profiles are

shown in Figure 4-7. The test frame of the flat plate specimen is based on a design suggested

by Feindler [55] and described in detail in Ref [33]. This test frame provides full lateral

support of the flat plate specimens to prevent buckling along the crushing stroke. For the investigation of the different profiles, the test frame is replaced by steel plates with a

crushing area of 200x200 mm². The 100 kN stroke-guided Z100SL screw-jack system, made

by ZIMM Maschinenelemente GmbH + Co KG, is used to apply the load. The impactors or the

upper steel plates are connected to the spindle. The linear encoder BG200, made by Kami

GmbH, with 5 µm steps, is used to measure the stroke. The testing frame, used for testing the flat plates, or the lower steel plate, used for testing the profiles, are mounted on four

20 kN KD80s force sensors from ME-Meßsysteme GmbH. The measuring amplifier GSV-8DS

SUBD15HD, from ME-Meßsysteme GmbH, is used for measuring the stroke and the load.

The amplifier and all sensors have an accuracy class of 0.05%. For the quasi-static test rate

measurements of 20 mm/min, a sampling rate of 50 Hz is used. The tests are subsequently resampled to a joint stroke base of 5 µm steps.


89

Figure 4-7: Overview of the quasi-static test setups for the flat plate specimens from Ref. [33] and profile crush testing.

4.3. Results and Discussion


Typical crush behavior is illustrated in Figure 4-8 for each profile and flat plate. A

uniform crushing morphology is necessary when comparing and linking the crushing

behavior of different profiles and flat plates. Comparing the crushing morphologies of the

flat segments of the profiles with those of the flat plates indicates pertinent resemblance. In both cases, the specimens form almost symmetric two-sided crushing fronds, which are

composed of several layers due to the different fracture mechanisms and the material layup.

The outer layers made of the fiberglass mat and roving remain coherent and delaminate

from the inner UD-Layup. In addition, these outer fronds show fiber splitting and fracture

of the fiber mats and the roving. The inner UD-Layup does not only split into two individual fronds but also disintegrates into several individual bundles, which also split. Fiber fracture

also occurs occasionally in the bundles. This crushing morphology is similar to the behavior

found in the literature [16, 35, 37, 40, 48–51] for GRP profiles and flat plates.


90

The main difference between the crush-tested profiles and flat plates stems from the

tearing of the crushing frond. In profile testing, the corner tearing is triggered from the

buckling, leading to the bending of the flat segments in different directions. The outward

bending of the crushing frond exerts a large horizontal tensile force at the corner that

exceeds the fracture limit and causes the tearing. This behavior agrees with the findings of Feraboli et al. [13] for the corner tearing. The inside part of the crushing frond, which bends

inwards, exerts a large horizontal compression force at the corner, and at a certain point,

flips inwards due to buckling, inducing fiber fracture. Depending on the shape of the profile,

the inner side of the crushing frond is turned inwards, which essentially leads to blocking

the core of closed (square/rectangular/circular) profiles towards the end of the crushing stroke. The lateral tearing force at the corners is not part of the axial crushing force.

However, it delays shell buckling and formation of the crushing frond until a larger axial

load is reached, which also contributes to increasing the level of crush energy absorption.

As expected, the right-angled profiles tear open only at the corners, which can be seen from Figure 4-8. The angle-shaped profiles tear only at one location, the channel profiles tear at

two locations, and the square profiles tear at four locations.

On the other hand, the crushing frond in constrained flat plate testing is torn out of

the specimen due to the clamping at the edges of the impactor, which corresponds to an in-

plane shearing mode. The tearing resistance can be mostly related to the outer fiberglass mat-and-roving layer, as the lateral support of the inner UD-Layup is comparatively low.

The tearing in the crushed eccentric tubes is primarily observed at the minimum and

maximum thicknesses. However, the tubes show additional axial failure lines distributed

around the perimeter with variations in the number of occurrences, which represents a

behavior different from that of the other profiles. In addition to these axial failure lines, which lead to complete tearing of the crushing frond into separate segments, partial axial

tearing is also scattered in the crushing fronds.


91

Figure 4-8: Examples of typical fracture behavior of the crushing frond and the tearing modes.


92

4.3.2. Right-Angled Profiles

An overview of the measured results for all right-angled profiles and flat plates is

shown in Table 4-2. Examples of the diagrams representing the measured force against the SCR for the angle-shaped profile A27275, obtained from sets of specimens of the

corresponding configurations, are shown in Figure 4-9-a. The average force for a set of

specimens, measured against the crushing stroke of all angle-shaped profiles, is illustrated

in Figure 4-9-b. As expected, it is clearly visible that the measured force increases with

increasing the width of the flat segments of the angle-shaped profiles. The average values of the measured force with respect to the SCR, obtained from testing a set of specimens of the

corresponding configurations, are listed in Table 4-2 as 𝐹𝐹�. The general behavior of the

measured values of the different configurations is consistent with respect to the SCR,

despite the normal fluctuation due to experimental crush testing. The coefficient of

variation (CV) of the measured values of all configurations ranges from 5.3% to 18.2%. The

general peak-to-average (p2a) value of all configurations is around 1.5, with a CV of 14.9%.

According to the SCR definition, the crush initiation peak and the subsequent transition to a stable crush mode, as well as the increase at the end of the crushing stroke due to

accumulation of debris, are excluded from the following calculations.

Figure 4-9: Examples of: a) measured force F of all specimens of angle-shaped profile A27275;

b) average force 𝐹𝐹� of all angle-shaped profiles.


93

Table 4-2: Overview of the measured results of the different profile- and flat plate- configurations.

Config. Total Segment

Width w / mm

Segment Width per Tearing

wx / mm

Actual Tearings

x / -

𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆) / kN

(CV / %) 𝐹𝐹�𝑥𝑥 (𝑆𝑆𝐶𝐶𝑆𝑆) / kN

SEAM / kJ/kg

A17175 27.5 27.5 1 10.14 (12.9) 10.14 39.2 A27275 47.2 47.2 1 14.30 (13.4) 14.30 32.5 A37375 67.7 67.7 1 18.78 (14.4) 18.78 29.9 A47475 87.0 87.0 1 22.73 (15.4) 22.73 27.9 A57575 107.8 107.8 1 27.23 (18.2) 27.23 26.7 A67675 126.5 126.5 1 30.91 (13.1) 30.91 26.1

C40125 51.5 25.7 2 19.85 (15.9) 9.93 39.9 C50175 70.5 35.2 2 23.80 (14.9) 11.90 35.2 C40265 79.2 39.6 2 25.71 (8.5) 12.85 34.5 C60225 90.9 45.5 2 28.03 (16.1) 14.02 32.8 C50315 98.4 49.2 2 29.79 (11.6) 14.89 31.7 C60365 119.8 59.9 2 34.45 (9.5) 17.22 30.4

S40405 135.3 33.8 4 46.71 (7.5) 11.68 36.3 S50505 175.1 43.8 4 55.16 (6.8) 13.79 33.3 S60605 214.4 53.6 4 63.66 (5.3) 15.92 31.4

F245 23.6 11.8 2 9.81 (10.8) 4.91 43.9 F365 36.0 18.0 2 12.50 (12.0) 6.25 36.5 F485 48.2 24.1 2 15.02 (13.9) 7.51 33.0

F243 23.6 11.8 2 5.65 (8.7) 2.83 40.6 F363 36.0 18.0 2 7.06 (15.2) 3.53 33.6 F483 48.2 24.1 2 8.44 (16.6) 4.22 30.1

Utilizing the CPIT allows for separating the crushing force FC from the edge force FE at

the edges of the impactor of the fully constrained flat plate specimens. A linear and proportional relationship between the crushing component and the width of the flat plates

has been established in Ref. [33]. Using the separation concept for analyzing the behavior

of the profiles allows for separating the crushing force FC of the flat segments from the

tearing force FT at the profile corners. Figure 4-10 demonstrates the average measured

behavior against the total segment widths of the right-angled profiles (Angle, Channel, and Square) for each crushed specimen of the corresponding profile. Although the distribution

of the measured force of the specimens shows fluctuations for each configuration, it


94

indicates a linear, albeit non-proportional, increase of the measured force against the

segment width. This behavior also reveals an almost identical linear regression value for all

profiles. The corrected coefficient of determination of the linear regression of the different

configurations indicates a value between 0.73 and 0.94, which represents a strong

agreement between the linear regression model and the experimental data. The intercept, which is attributed to the tearing force, and the slope, which is attributed to the crushing

force per unit segment width, compose the linear regression, which represents the

measured data. All linear regression values of each configuration are shown in Table 4-3,

including the values for the flat plates and the later discussed general representation of the

right-angled profiles. These results of the linear regression models demonstrate that the crushing force per unit segment width is identical as the slope is consistent for all right-

angled profiles.

Figure 4-10: Linear regression models of the measured force for each specimen of the right-angled profiles.


95

Table 4-3: Overview of the results by utilizing the linear regression for the different configurations.

Config.

Slope M – Crushing Force

per Unit Segment Width / N/mm

(CV / %)

Number of Tearings

x / -

Intercept - Tearing Force

FT/FE / N (CV / %)

R² / - corr. R² / -

F-test / - (df / -)

SEAC / kJ/kg

Angles 210.5*** (3.9) 1 4412.2*** (15.6) 0.95 0.94 663.2*** (38) 22.5 Channels 213.3*** (9.4) 2 8799.0*** (20.1) 0.74 0.73 112.4*** (40) 22.4 Squares 214.2*** (9.8) 4 17706.9*** (21.0) 0.85 0.84 104.5*** (19) 22.6

Right-Angled Profiles

209.4***(2.4) 1 4554.0***(6.9) 0.94 0.94 1730.1***(101) 22.2

Flat Platest=5 211.6*** (7.3) 2 4840.3*** (11.9) 0.91 0.90 188.3*** (19) 22.3 Flat Platest=3 113.4*** (12.1) 2 2979.1*** (17.2) 0.78 0.77 67.8*** (19) 19.4

*p<0.05; **p<0.01; ***p<0.001

Figure 4-11-a shows a linear, albeit non-proportional, relationship between the

measured force and the width of the corresponding flat segments. In addition, the linear

change is the same for all profiles. In this Figure, the intercept, which is the profile resistance at a hypothetical zero-width, represents the isolated resistance caused by the mere corner

existence. It can be depicted from the Figure that the intercepts of different lines, which are

also practically parallel, are almost proportional to the number of corners in the

corresponding profiles. For example, the intercept of the Angle profile, which contains only

one corner, is 4.4 kN, while that of the Square profile, which contains four corners, is 17.7 kN, which is almost 4 times that of the Angle profile. A similar result can be obtained

for the Channel profile. This outcome is valid for all tested right-angled profiles of all

dimensions. Consequently, this Figure alone provides clear validation of the proposed

approach. Such an observation allows for calculating the behavior of a hypothetical corner-

free profile representing only flat segments. The behavior of the hypothetical corner-free profile can be calculated by extrapolation from the lines representing profiles with different

numbers of corners. In other words, the line representing the corner-free profile can be

obtained by subtracting the shift between two lines, of profiles with two consecutive

numbers of corners, from the line which represents the behavior of the angle-shaped

profiles, which have only one corner. The three different behaviors of the hypothetical corner-free profile, obtained by extrapolation of the three possible line combinations, are

almost identical. They are also linear and proportional, which is illustrated in Figure 4-11-

a. Such an outcome indicates that the tearing force per corner is the same for all tested right-


96

angled profiles and that the difference of the measured force between profiles is directly

proportional to the difference in the number of corners. It should be noted here that the

above-explained outcome is valid only when comparing right-angled profiles of the same

material, thickness, and corner geometry.

Figure 4-11: a) measured force F; b) SEAM distributions against the segment width of all right-angled profiles and corresponding hypothetical corner-free profiles.

The corresponding SEAM calculated from the measured force of the different configurations, illustrated in Figure 4-11-b, demonstrates a nonlinear behavior similar to

that shown in Figure 4-1 for different materials. This hyperbolic trend is based on the linear

regression values and explained by the relationship of the crushing and the tearing force in

equation (4-11). A simple interpretation of the nonlinearity is that the corner is not

associated with any mass. Accordingly, the SEAM calculated at zero-width is hypothetically infinity as the energy is attached to a zero-mass. This is not a concern as the width is

practically always larger than the material thickness. The effect of the corner tearing force,

which is the intercept of the linear regression, on the SEAM decreases hyperbolically with

increased segment width, which is expected due to the increased mass. The dashed curve

fitted to the experimental data represents the general behavior. Outside the range of the measured data, the fitted curve is an extrapolation of the experimental results and

represents an artificial trend.

Calculating the SEAM values of hypothetical corner-free profiles by removing the

effect of the corner tearing force from the SEAM removes the nonlinearity and reduces the

SEA to a consistent width-independent value, which is almost the same for all tested profiles, as illustrated in Figure 4-11-b. This is also a significant outcome, as it has been


97

derived from experimental measurements and is not just a theoretical assumption. The

results are similar to those obtained when crush testing unconstrained flat plates with free

edges or using the CPIT when crush testing fully constrained flat plates.

4.3.3. Comparison of Right-Angled Profiles and Flat Plates

Plotting the measured force per tearing Fx, or the SEAM against the width of the flat

segments per tearing wx, allows for comparing the behavior of the configurations of all right-

angled profiles independent of the number of occurrences of tearings, as illustrated in

Figure 4-12. Although the number of tearings, which occur at the corners, are different for different profiles, the relationships between the measured force per tearing and the

segment width per tearing of the different profiles are not only similar but also almost

identical. It follows that the tearing mode at the corners and the crushing mode of the flat

segments are practically independent of the right-angled profile shape. Therefore, the

tearing force is simply the measured force at zero width, and the generalized linear regression per tearing is independent of the profile shape. The linear regression results of

the generalized right-angled profile, presented in Table 4-3, display a strong agreement

between the linear regression model and the experimental data. Similarly, a consistent

hyperbolic decrease in the SEAM when increasing the width of the flat segments per tearing

is almost identical for all profiles.

Comparing the behavior of the tested right-angled profiles with that of the

corresponding flat plates, which were tested under constrained conditions, reveals a strong

resemblance in the linear regression, as illustrated in Figure 4-12-a. However, there is a

difference in the level of the measured force, and accordingly, the zero-width force, which

can be attributed to the test setup as the flat plates do not have any orthogonal corners, and the tearing occurs at the interface of both edges of the impactor with the fully constrained

plate, which relates the occurrence of tearing to the testing process rather than the plate

properties.

Figure 4-12-b illustrates the comparison between the SEAM based on the measured

force and the SEAC based on the crushing force of the flat segments of the different configurations. The calculated tearing force is assumed to be associated with the profile

corner, independent of the profile dimensions. Therefore, no unique SEA value can be

calculated for the tearing force, as it is not associated with a crushed mass. It is also evident

that the SEAC is practically the same for different values of segment width of all profiles and flat plates. This is an extremely significant outcome, which can be attributed to the linearly


98

proportional relationship between the crushing force and the segment width of a

hypothetical corner-free profile. It should also be emphasized here again that the tearing

force is not actually a separate axial force, but it is just the effect of the lateral tensile

resistance, associated with lateral profile elongation, on delaying the onset of shell buckling

and the formation of the crushing frond, which leads to increasing the axial crushing force. In other words, the flat segments on each side of the corner are practically unable to bend

or deflect laterally, in two perpendicular directions, until they separate at the corner.

On the other hand, the difference between the SEAM and the SEAC, which can be

attributed to the tearing force, is a hyperbolic function of the segment width, highlighted in

equation (4-11). Such behavior can be easily interpreted as the energy consumed by the tearing force is practically constant. Therefore, it represents a substantial component when

added to the small crushing energy consumed by a small segment width, so substantially

increasing the measured SEAM. When the same amount of energy consumed by the tearing

force is added to the larger crushing energy consumed by a larger segment width, its effect on the SEAM value becomes smaller as it is divided by a larger mass. For example, the

difference between the SEAM and the SEAC values for a 20 mm segment width is double that

of a 40 mm segment width and 4 times that of an 80 mm segment width. Therefore, the SEAM

converges towards the SEAC for a very large segment width. It should be noted here that the

individual values of the SEAC of each configuration illustrated in Figure 4-12-b vary by less than 1% from the average value of the SEAC given in Table 4-3 for the different profile types,

in spite of the variation in specimen thickness and density.

Since the crushing force of a flat segment and that of a flat plate of the same width are

identical, the corresponding SEAC is identical too. The difference between the SEAM of the

right-angled profiles and that of the flat plates, which can be attributed to the different tearing modes, is identified by a shift of the SEAM. In other words, using flat plates with

widths similar to those of profile segments would lead to noticeably lower values of the

SEAM. It should be noted here that crushing a very wide plate may lead to premature

buckling and, consequently, unstable crushing. It should also be noted that using the method

of unsupported height in testing the flat plates, although it increases the risk of lateral buckling, it avoids the inclusion of edge forces as these only appear if the edges of the flat

plate are fully supported by the test rig. Therefore, the measured force, in this case, would

be equal to the crushing force, resulting in consistent SEA values when plotted against the

specimen’s width, as in Ref. [29]. In addition, these SEA values are also equal to the SEAC of

the flat segments of profiles of the same crush-tested material and thickness. This


99

relationship of the SEAC between the flat segments of the right-angled profiles and the flat

plates also means that the crush properties of any corner-shaped profile can be determined

based on the crush properties of the flat plates, provided the tearing force of the

corresponding profile corner is known.

Figure 4-12: Comparison against the segment widths per tearing wx between the right-angled profiles and the corresponding flat plate of: a) the measured force per tearing Fx; b) the SEAM based on the measured force F and the SEAC based on the crushing force FC.

4.3.4. Circular Tubes

As stated in section 4.2.1, the crush behavior mechanism of tubes differs from that of

the right-angled profiles as tubes do not have straight segments and also no corners that would initiate tearing. This difference is reflected in the significantly different crush

behavior of the tubes. In order to be able to utilize the above-discussed approach, a uniform

crushing morphology is necessary. This also includes the existence of a specified number

and locations of corners, representing potential tearings, which is not relevant to circular

tubes. In particular, the formation of the tearing mode depends on a variety of factors, e.g., the wall thickness eccentricity or the bifurcation mode, which is also affected by the profile

material and dimensions, including shell thickness, diameter, and tube height. Material and

loading imperfections can also play a role in defining the locations and regularity of the

tearings. In addition, as illustrated in Figure 4-13, only some tearings are formed with respect to the whole crushing stroke. Additional partial tearings are formed, causing only

short splits or tearing of only parts of the outer layer of the crushing frond. The partial

tearing of the whole crushing frond layers can be identified by its relative proportion over

the crushing stroke. The partial tearing of the crushing fronds outer layer, on the other hand,


100

induces an additional crushing mechanism, which varies significantly in the number of its

occurrence and causes individual contribution to the crush resistance. Therefore, it is not

feasible to divide the crushing frond into separate segments, as the number of occurrences

of complete and partial tearings cannot be simply predicted. In addition, the effect of tearing

resistance varies from one tearing to another.

In addition, the bending resistance of the crushing fronds increases due to the arch

effect, or in other words, the increase in the second moment of area of the curved segment.

Accordingly, the measured force increases nonlinearly with increasing segment widths. In

addition, the crush resistance increases nonlinearly with increasing the tube diameter due

to the increased number of tearings associated with larger diameters, as illustrated in Figure 4-14. It should be noted here that the thickness of the investigated tubes is lower

than that of the investigated right-angled profiles. For comparison purposes, corresponding

3 mm thick flat plates are also included in Figure 4-14. An overview of the measured results

of the tubes is shown in Table 4-4. Due to the different crushing mechanisms and the unpredictable number of tearings in crush-tested tubes, the crush behavior of tubes cannot

be simply predicted. In contrast, the crush behavior of right-angled profiles is easily

predictable and can be calculated from the behavior of the flat segments and the tearing

force at the corners, obtained from testing a few specimens with different dimensions of

one profile shape.

Figure 4-13: Examples of the different tearing occurrences at the circular tubes crushing fronds.


101

Figure 4-14: Comparison of the measured results of the tubes with those of the right-angled profiles and the corresponding flat plates: a) measured force F; b) SEAM.

Table 4-4: Overview of the measured results of the different tubes.

Config. Outer

Diameter do / mm

Inner Diameter di / mm

Total Segment Width

w / mm

Diameter to thickness ratio

d/t / -

𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆) / kN

(CV / %) SEAM

/ kJ/kg

T20143 19.9 13.8 53.0 4.5 12.58 (7.5) 41.0 T28223 28.1 21.9 78.5 7.1 20.72 (6.8) 45.2 T30243 29.9 23.7 84.3 7.7 22.61 (10.1) 46.2 T32263 31.7 25.6 90.0 8.4 25.96 (9.7) 50.0

4.4 Conclusion

102

4.4. Conclusion

Cost-effective crush testing has always been an issue, especially with composite

materials. For this reason, attempts have been made to explain the fracture behavior of complex composite structures, such as self-supporting structures, like tubes or square

profiles, using simple test scenarios such as crush testing flat plates. This comparison has

been challenging and provides inconsistent results due to the different failure mechanisms,

the influences of the different test setups, and the geometric effects. However, it has been

shown constantly that the SEA behavior is nonlinear with respect to the width-to-thickness ratio of flat plates and profiles or diameter-to-thickness ratio of tubes.

The Crush Property Isolation Technique (CPIT) has been established for isolating the

crushing force from the total measured force in crush testing of fully-supported flat plates.

Due to the boundary condition, the inadvertent force at the edge of the impactor is included

and needs to be extracted. This article introduces a similar approach based on the separation concept of the CPIT to characterize the crush behavior of different self-

supporting right-angled profiles, e.g., angle-shaped, channel, and square profiles. This

separation allows for analyzing the crushing force of the flat segments and the corner

tearing force of the profiles, comparing and predicting the behavior of different profiles

using the results obtained from a few crush tests.

In self-supporting profiles, the corner resistance against tearing in the lateral

direction plays a major role in defining the axial crush resistance of the profile. The effect of

the lateral tensile resistance at the corner on supporting the flat segments of the profile

against lateral shell buckling, which has been termed as the tearing force, contributes to increasing the resistance against axial crushing, as the flat segments on each side of the

corner cannot practically bend or deflect laterally, in two perpendicular directions, until

they separate at the corner.

The introduced approach isolates the crushing force of the flat segments of the

profiles from the effect of the tearing force at the corners. The obtained results can be used to accurately predict the behavior of different profiles with different numbers of right-

angled corners. The compared profiles should be of the same material and shell-thickness

as well as the same corner geometry. The obtained results show that the isolated corner

property is also independent of the crushed width and has the same value for all corners of

the investigated profiles. Comparing the isolated crushing force and the SEA of the flat segments with those of independently crush-tested flat plates of the same material and

4.4 Conclusion

103

thickness have also shown a strong resemblance. This is also an interesting outcome, as

shell buckling has been a challenging factor in crush testing of flat plates, which needed

special precautions, and sometimes expensive special-purpose sophisticated test rigs. The

introduced approach allows for characterizing the behavior of flat plates by testing self-

supported profiles made of the same plate material and thickness, which does not require any sophisticated test rigs.

On the other hand, the crushing force of the profile flat segments and the flat plates is

directly proportional to their combined width. This behavior also explains the nonlinear

behavior of the SEA reported in the literature since the corner tearing resistance remains

the same for specimens of different sizes, which dilutes its effect on wider flat segments. Therefore, it results in a hyperbolic decay of SEA with increased width, which converges,

for very wide segments, towards the SEA calculated from the crushing force of the flat

segments. By removing the corner effect, the SEA becomes constant for all tested profiles.

The crush behavior of composite tubes has also been briefly investigated. The shell curvature of the tubes was found to increase the bending resistance of the crushing frond,

which delays shell buckling and formation of the crushing frond, so resulting in higher

forces and SEA values. Contrary to the right-angled profiles or the flat plates, additional

partial tearing of the crushing frond occurs in crush-tested tubes. In addition, the number

of tearings increases with increasing tube diameter-to-thickness ratio. Therefore, it can be concluded that the diameter-to-thickness ratio has a significant effect on the crush

properties of tubes.

The most significant outcome of this research is that the SEA, calculated from the

crushing force of the flat segments, is practically the same for different values of segment

width of all right-angled profiles and flat plates, which can be attributed to the linearly proportional relationship between the crushing force and the segment width of a

hypothetical corner-free profile. Therefore, the experimental effort needed to characterize

the crush properties of self-supporting profiles or flat plates can be simplified significantly

and reduced substantially as their behavior can be determined from the combined width of

flat segments and the number of corners, using data obtained from crush testing a few specimens with different dimensions of one self-supporting profile shape. This approach

can also be useful in predicting the crush properties of a prototype with a complicated

geometry from the basic properties of corners and flat segments, which would reduce the

number of needed prototypes substantially in manufacturing a new design.

4.5 References

104

4.5. References













4.5 References

105


[14] Eichlseder W, Schöneburg R. Anforderungen an den Leichtbau im Fahrzeug. Leichtbau der Fahrzeugtechnik, Wiesbaden: Springer Fachmedien Wiesbaden; 2013, p. 119–75. doi:10.1007/978-3-8348-2110-2_4.

[15] Dieringa H, Drechsler K, Evertz T, Flaxa V, Furrer P, Gadow R, et al. Die Leichtbauwerkstoffe für den Fahrzeugbau. Leichtbau der Fahrzeugtechnik, Wiesbaden: Springer Fachmedien Wiesbaden; 2013, p. 199–442. doi:10.1007/978-3-8348-2110-2_6.


[17] Kumar AP, Mohamed MN. Crush Performance Analysis of Combined Geometry Tubes under Axial Compressive Loading. Procedia Eng 2017;173:1415–22. doi:10.1016/j.proeng.2016.12.203.

[18] Isaac CW, Ezekwem C. A review of the crashworthiness performance of energy absorbing composite structure within the context of materials, manufacturing and maintenance for sustainability. Compos Struct 2021;257:113081. doi:10.1016/j.compstruct.2020.113081.

[19] Bru T. Behaviour and material properties of composites for crash modelling. Chalmers University of Technology, 2016.


[21] Ehrenstein GW. Faserverbund-Kunststoffe : Werkstoffe, Verarbeitung, Eigenschaften. Hanser; 2006.





4.5 References

106









[34] Lausch J, Takla M, Schweiger H-G. Crush characteristics of flat-plate discontinuous carbon composites. Compos Part A Appl Sci Manuf 2021;147:106431. doi:10.1016/j.compositesa.2021.106431.



4.5 References

107



[39] Feraboli P. Development of a corrugated test specimen for composite materials energy absorption. J Compos Mater 2008;42:229–56. doi:10.1177/0021998307086202.


[41] Yang Y, Nishikawa Y, Nakai A, Ishiaku US, Hamada H. Effect of Cross-Sectional Geometry on the Energy Absorption Capability of Unidirectional Carbon Fiber Reinforced Composite Tubes. Sci Eng Compos Mater 2008;15:249–63. doi:10.1515/SECM.2008.15.4.249.


[43] Yan L, Chouw N. Crashworthiness characteristics of flax fibre reinforced epoxy tubes for energy absorption application. Mater Des 2013;51:629–40. doi:10.1016/j.matdes.2013.04.014.

[44] Hamada H, Ramakrishna S. Scaling effects in the energy absorption of carbon-fiber/PEEK composite tubes. Compos Sci Technol 1995;55:211–21. doi:10.1016/0266-3538(95)00081-X.

[45] Pickett L, Dayal V. Effect of tube geometry and ply-angle on energy absorption of a circular glass/epoxy crush tube - A numerical study. Compos Part B Eng 2012;43:2960–7. doi:10.1016/j.compositesb.2012.05.040.

[46] Farley GL. Effect of Specimen Geometry on the Energy Absorption Capability of Composite Materials. J Compos Mater 1986;20:390–400. doi:10.1177/002199838602000406.

[47] Farley GL, Jones. RM. Energy-Absorption Capability of Composite Tubes and Beams. NASA Tech Memo 1989;101634:0–250.

[48] Palanivelu S, Paepegem W Van, Degrieck J, Vantomme J, Kakogiannis D, Ackeren J Van, et al. Crushing and energy absorption performance of different geometrical

4.5 References

108

shapes of small-scale glass/polyester composite tubes under quasi-static loading conditions. Compos Struct 2011;93:992–1007. doi:10.1016/j.compstruct.2010.06.021.

[49] Palanivelu S, Van Paepegem W, Degrieck J, Van Ackeren J, Kakogiannis D, Van Hemelrijck D, et al. Experimental study on the axial crushing behaviour of pultruded composite tubes. Polym Test 2010;29:224–34. doi:10.1016/j.polymertesting.2009.11.005.

[50] Paul D, Ramachandran V, Gupta NK. Improvements in the crushing behaviour of glass fibre-epoxy composite tubes by the addition of hollow glass particles. Thin-Walled Struct 2019;141:111–8. doi:10.1016/j.tws.2019.03.033.

[51] Imbsweiler D. Experimentelle Untersuchung und numerische Simulation des Crashverhaltens von SMC-Strukturen. Kaiserslautern: IVW; 2002.




[55] Feindler N. Charakterisierungs-und Simulationsmethodik zum Versagensverhalten energieabsorbierender Faserverbundstrukturen. Technische Universität München, 2012. doi:urn:nbn:de:bvb:91-diss-20121217-1108924-1-9.

109

Chapter 5. Conclusions and Recommendations

5.1. Conclusions

The objective of the research described in this thesis was to characterize the crush

performance of discontinuous carbon fiber composites used in the design of automotive structural components. Carbon fiber-reinforced sheet molding compound manufactured by

compression molding was selected as the discontinuous carbon fiber composite material

for the planned investigations. A thorough literature review was conducted about

discontinuous carbon fiber composites, their properties, and the effects of several material

parameters, like fiber length or fiber mass content, on their crush performance. In addition, a literature review of the approaches used in crush testing composite flat plates needed to

be conducted since flat plates were selected as the specimens to be tested. This review

revealed the problems and inconsistencies of the results obtained when using the

established crush testing methods of flat plates or profiles, exposing a significant research

gap. The arising questions needed to be answered before progressing with the research any further, as any new findings can only be significant if the test measurements are reliable and

the obtained material properties are independent of the testing setup. Therefore, the

research focused on developing a reliable testing approach, including designing an

appropriate test setup for the general characterization of flat plate fibrous materials. The

literature review and the arising research gaps also motivated further investigation into the correlation between the crush performance of composite profiles and that of flat plates. The

review outcome attracted special attention, as the crush testing approaches of flat plates or

profiles, available in the current literature, proved to result in inconsistency, strong

geometric dependency, and additional influences of the test setups.

A novel crush testing approach for flat plate specimens of fibrous materials is proposed and validated in Chapter 2. The main aim of the proposed approach was to

characterize the crush energy absorption properties of flat plates made of fibrous materials

accurately and consistently and to eliminate the effect of the testing setup on the obtained

crush properties.

5.1 Conclusions

110

By investigating the crushing morphology of a fully supported flat plate specimen, it

was evident that two phenomena influence the energy absorption process during crush

testing. One is the original formation of the crushing frond beneath the impactor, and the

other is the separation or shearing and friction of the material at the edge of the impactor.

Conducting crush tests with different crushing widths revealed a linear, albeit non-proportional relationship between the crushing force and the plate width. This relationship

implies that the shearing and friction force at the edge of the impactor is independent of the

crushing width. Therefore, it is possible to extrapolate the values of the measured crushing

force of two separate crushing widths to a hypothetical zero crushing width to obtain the

amount of shearing and friction that occurred during the crush testing. Deducting this shearing and friction component from the actual measured force results in the crushing

component that would be obtained from testing an unsupported specimen without having

the risk of axial buckling. Due to the linear and proportional relationship between the

crushing component and the crushing widths, the specific energy absorption (SEA) calculated from this isolated component is consistent and independent of the geometry of

the tested plate.

In comparison, the SEA calculated from the measured forces of a set of specimens

decreases with increasing the crushing widths, as the measured force includes the shearing

and friction components, similar to the case with the approaches using the supporting rods [1–5]. This phenomenon can now be interpreted as the shearing and friction component is

independent of the crushing widths. As a result, its proportion and, accordingly, its effect

decreases with increasing crushing width.

This outcome does not only explain the discrepancies in the results obtained by the

established methods for crush testing flat plates but also eliminates the dependency on the testing approach and provides a technique for obtaining consistent, robust, and reliable

results.

Once the reliable crush property isolation technique (CPIT) has been established, it

has been adopted to investigate the feasibility and applicability of the novel approach to

composite materials of automotive structural components, with the aim of evaluating the effects of different testing parameters on the value of the SEA of a composite material

calculated from crush testing flat plates, as illustrated in Chapter 3. In addition, the results

obtained using the CPIT are differentiated from those obtained using other established

methods for crush testing composite flat plates and profiles.

5.1 Conclusions

111

A comprehensive study has been conducted for several parameters of discontinuous

carbon fiber composite flat plates manufactured by compression molding. The effects of

fiber length, fiber mass content, in-plane fiber distribution, specimen thickness, and loading

rate have been evaluated. The crushing morphology is found to be similar to that of transfer

and bladder molded tubes [6–8], which forms a fragmented but mostly coherent crushing frond. The degree of fragmentation increases in dynamic testing compared to quasi-static

testing, which leads to lower frond coherence and, therefore, less energy absorption. The

split edges also show a difference in the damage mode as the edge is very rough and tattered

in static testing, however very smooth when crushed dynamically. This, in turn, is reflected

in the proportions of the crushing and edge energy components. The effect of fiber length on fracture toughness agrees with the general results found in the literature on the effect of

this parameter on discontinuous carbon fiber composites. In addition, a slight insignificant

increase in energy absorption could be observed when increasing fiber mass content, which

is less obvious than that observed, e.g., in tensile testing. The main effect of fiber length and fiber mass content appears in the standard deviation, which increases with increasing fiber

length and decreases with increasing fiber mass content. This effect can be attributed to the

homogeneity of the fiber distribution, which is affected by the fiber length and fiber mass

content. Considering the influence of the fiber length and fiber mass content on the fracture

toughness and its standard deviation, a combination of high fiber mass content and low fiber length represents an appropriate combination for engineering materials in terms of an

energy absorption structure. In particular, the SEA of such a combination is still high. The

in-plane fiber distribution showed almost no influence on fracture toughness. In particular,

the observed SEA was practically the same for the investigated specimen thickness, and

therefore no significant influence could be observed. Furthermore, due to the identical behavior, it can be concluded that the random in-plane fiber distribution is almost isotropic.

The specimen thickness is a significant factor affecting the SEA values of such materials, as

increasing the thickness leads to an increase in fracture toughness and, in addition,

highlights the dependency of the SEA values on the experimental testing setup. The effect of

plate thickness can be attributed to the mechanism of forming the crushing frond. Increasing the plate thickness leads to a direct increase in the thickness of the crushing

frond, which results in a decrease in the level of fragmentation and an increase in its

coherence. Dynamic testing of the specimen showed a loading rate dependency, which

changed with the specimen thickness. The decrease of energy absorption in dynamic testing

of specimens with larger thickness can be attributed to an increase of fragmentation and separation of individual layers of the crushing frond. The values of the SEA, calculated from

5.1 Conclusions

112

the crushing component of the measured force, proved to be consistent and width-

independent.

Having established the CPIT and used it to evaluate the crush properties of flat

composite plates, a similar, albeit different, technique has been developed for crush testing

composite profiles. Similar to the case with flat plates, the methods established in the literature for crush testing composite profiles provide inconsistent and geometry-

dependent results, influenced by the test setups. In addition, there have been strong

discrepancies between the SEA values obtained from testing flat plates and those obtained

from testing profiles made from the same material and thickness. There has also been no

acceptable interpretation of these discrepancies in the literature.

Therefore, crush testing of profiles and its relation to crush testing of flat plates has

been investigated in Chapter 4 in order to improve the usability of the crush testing methods

of both plates and profiles, where the geometric effects of the crush-tested profiles on the

obtained results are evaluated and interpreted. Also, the relationship between the crush performance of flat plates and that of profiles of different shapes has been studied. It was

also of interest to investigate whether the crush behavior of a composite profile can be

predicted from that obtained by testing other profiles of other geometries, and to determine

the associated limitations.

In crush testing self-supporting profiles, the corner resistance against tearing in the lateral direction plays a significant role in defining the axial crush resistance of the profile.

The effect of the lateral tensile resistance at the corner on supporting the flat segments of

the profile against lateral shell buckling, which has been termed as the tearing force,

contributes to increasing the resistance against axial crushing, as the flat segments on each

side of the corner cannot practically bend or deflect laterally, in two perpendicular directions, until failure occurs at the corner. According to the crushing morphology

discussed in the literature [9–12] for various profiles, the crushing morphology is typically

composed of tearing at the corner and forming a crushing frond in the flat segments. The

literature also indicates that the tearing is mainly confined to the corners, which suggested

that the tearing force component included in the measured force is, most likely, independent of the width of the flat segments of the profile and depends only on the number of corners

in the profile.

In the cases of angle-, channel-, or square profiles, the corner appeared to serve as the

catalyst for the tearing. Flat segments of profiles and flat plates are correlated due to the

5.2 Future Work

113

similar crushing morphologies of the crushing fronds. Comparing the crush testing results

shows that the crushing frond of a flat plate specimen is practically identical to that of a flat

segment of a profile. Therefore, it could be shown that the isolated crushing force of a flat

segment of a profile was also likely to be proportional to the width of the segment, similar

to the case of flat plate specimens. Consequently, a technique similar to the CPIT developed for crush testing flat plates was also developed to isolate the width-independent tearing

component from the width-dependent crushing component. Both components can be

calculated using linear regression of the results obtained from a few crush tests of

specimens of different sizes made of a selected profile. By isolating the tearing and crushing

components of right-angled profiles, it could be demonstrated that the geometric dependency of crush-tested profiles is related to the tearing occurrences and, accordingly,

the numbers of corners in a profile. By using the developed technique, it was possible to

predict the crush properties of right-angled profiles with different shapes and dimensions

from crush testing a few specimens of different sizes of a single profile shape with the same material and thickness. It is also demonstrated that the SEA calculated from the crushing

force of the flat segments is practically the same for different values of segment width of

right-angled profiles and flat plates, explaining the inconsistencies depicted in the literature

between the crush performance properties of composite profiles when compared to those

obtained for flat plates made from the same material and thickness. Therefore, by using the developed technique, the crush properties of composite flat plates can also be obtained from

crush testing self-supported profile specimens, without the need to design a build a

sophisticated test rig. These are significant outcomes that assist in substantial savings in

cost and time when characterizing the crush performance of composite profiles and flat

plates.

5.2. Future Work

The work presented in this thesis provides several essential and novel discoveries

related to experimental crush testing, all of which could benefit from being followed up by further research.

Utilizing the CPIT allows for obtaining consistent and accurate results from crush

testing fully supported flat plate specimens. Due to separating and discarding the

inadvertent forces of the supporting system, the crush properties of the frond formation can

be observed. This isolation is only possible as the support of the specimens increases the buckling stability. For the experimental investigation shown in this thesis, linear behavior

5.2 Future Work

114

while increasing the crushing width of the specimens could be shown. This linear increase

is a prerequisite for isolating the shearing and friction force at the edge of the impactor

through linear regression. In addition, the separation of the tearing and the crushing

components of the profiles is also based on the linear behavior for increasing segment width

or the number of tearing occurrences of the profiles. It is mentioned that an almost linear relationship is practically valid within a reasonable range of the crushed width. However,

very narrow specimens might have additional forces due to accumulated debris and higher

friction. On the other hand, very wide specimens tend to buckle, reducing the crushing force.

Therefore, both extremes should be studied to understand their effect and occurrence to be

able to consider the limitations when developing new components.

Another phenomenon, which has been observed experimentally but not investigated

in detail, is the effect of the specimen thickness. Increasing the specimen thickness showed

higher crushing forces and thus an increase in the corresponding SEA. Based on the

composition of the force components in the formation of the crushing frond, the thickness of the crushing frond has a quadratic effect on the bending resistance of the frond formation.

This effect is relevant because a smaller but thicker component has a higher energy

absorption potential.

The method for separating the corner tearing force and the crushing force of the flat

segments of the profiles is validated on right-angled profiles. This validation showed that the crush performance is predictable for profiles of various geometries as long as the corner

geometry is identical. It turned out that the corner acts as an initiator of the tearing. Within

a certain range of the corner angle, it can be assumed that the corner will act as the tearing

initiator. The limitations of the tearing initiation and additional effects of the corner angle

can be investigated in detail to improve the usability of the separation method.

Another influencing factor is the corner radius, which affects the tearing occurrence

and the tearing force. The tearing force itself contributes significantly to the resistance of

the profile to axial shell buckling, which contributes substantially to elevating the level of

axial crush resistance of the profile and its crush energy absorption. For the investigation

here, an identical small radius was used. This similarity is necessary for the comparability of the results of the differently shaped profiles. Due to the small corner radius, the effect on

the bending resistance, as with circular tubes, could be neglected. In addition, larger radii

also tend to generate two separate tearings at the profile corner. Therefore, the effect of the

lateral tearing force at the profile corners on the total axial resistance of the profile

regarding the corner radius should be further investigated.

5.3 References

115

This knowledge of the effect of the corner angle and radius should also help to

understand the influence of the diameter of the circular tubes on the bending resistance and

the tearing occurrences. The absence of a corner in the circular tubes leads to a random

distribution of the tearing of the crushing frond. Since changes in the diameter of the tube

simultaneously influence the bending resistance of the crushing frond, as well as the tearing occurrences, isolating these effects can be tricky. In addition, the thickness to diameter ratio

should be taken into account when examining the circular tubes.

5.3. References







[7] Cutting RA, Sharma V, Goodsell JE. Crush Response of Prepreg Platelet Molding Compound Tubes. Am. Soc. Compos. 2018, Lancaster, PA: DEStech Publications, Inc.; 2018. doi:10.12783/asc33/26074.


5.3 References

116





117

Appendix

A. List of Publication

Lausch J, Takla M, Schweiger H-G. Crush testing approach for flat-plate fibrous

materials. Compos Part B Eng 2020;200:108333. doi:10.1016/j.compositesb.2020.108333. (SCImago Journal Rank (SJR): 2.196; Impact Factor: 9.078)

Lausch J, Takla M, Schweiger H-G. Crush characteristics of flat-plate discontinuous

carbon composites. Compos Part A Appl Sci Manuf 2021;147:106431.

doi:10.1016/j.compositesa.2021.106431.

(SCImago Journal Rank (SJR): 1.884; Impact Factor: 7.664)

Lausch J, Takla M, Schweiger H-G. Insight into crush performance comparison of

composite profiles and flat plates. Compos Part B Eng 2022;233:109643.

doi:10.1016/j.compositesb.2022.109643.

(SCImago Journal Rank (SJR): 2.196; Impact Factor: 9.078)

The CRediT author statement published for each article clarifies the contribution for

each author. Since the participation in the articles has not changed, it is only shown here

once for all articles.

J. Lausch: Conceptualization, Methodology, Validation, Formal analysis,

Investigation, Writing – Original Draft, Writing – Review & Editing, Visualization, Project administration

M. Takla: Conceptualization, Methodology, Validation, Formal analysis, Investigation,

Writing – Original Draft, Writing – Review & Editing, Visualization, Supervision, Project

administration

H.-G. Schweiger: Resources, Writing – Review & Editing, Project administration,

Funding acquisition

B Accuracy Analysis

118

B. Accuracy Analysis

B.1. Crush Testing Approach for Flat Plate Fibrous Materials

In order to reproduce the material behavior accurately by means of the measured

data, the uncertainty of the measuring equipment needs to be calculated. Temperature and

creep errors can be ignored due to a constant temperature condition during the test and a

steady increase of the applied crushing stroke. The linear scaling uncertainty of the force

sensors, as well as of the measuring amplifier and an offset component, given in the manufacturer's datasheet, results in a maximum uncertainty of ±16 N for the measured

force. The summation of the shift of one-step, which can occur, the interpolation deviation

of a signal period and a position deviation over the measuring path of the linear encoder

leads to an uncertainty of ±0.0092 mm for the measured stroke. Calculating the uncertainty for the energy dE,

𝑑𝑑𝐸𝐸 = �𝜕𝜕𝐸𝐸𝜕𝜕𝐹𝐹∗ 𝑑𝑑𝐹𝐹�+ �𝜕𝜕𝐸𝐸

𝜕𝜕𝑠𝑠∗ 𝑑𝑑𝑑𝑑�

𝑑𝑑𝐸𝐸 = |𝑑𝑑𝑚𝑚𝑎𝑎𝑥𝑥 ∗ 𝑑𝑑𝐹𝐹| + |𝐹𝐹𝑚𝑚𝑎𝑎𝑥𝑥 ∗ 𝑑𝑑𝑑𝑑| , (B.1-1)

for the maximal measured values leads to the estimation of the maximum possible

uncertainty of the calculated energy. These uncertainties are between 1.3 J and 1.9 J. In

comparison with the standard deviation SD of the measured force distribution summarized

in Table B.1-1, the estimated maximum uncertainty has no significant influence on the

calculated energy of the measured force. Keeping in mind that the error values given in Table B.1-1 are calculated for the worst possible scenario, the actual uncertainty should be

even smaller. Due to the differential calculation of the edge energy, systematic uncertainties

given by the test rig negate each other.

Table B.1-1: Summary of the mean values, the standard deviation, and the total uncertainty for the calculated energy of all used materials.

Material w / mm 𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆)

/kN

SD of 𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆)

/ kN

CV of 𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆)

/ % dE / J

CV of dE / %

PW(90/0/90/0�)S 23.6 6.34 1.46 23.0 1.4 0.3 36.0 7.82 2.16 27.7 1.4 0.2 48.2 9.43 2.99 31.7 1.5 0.2

LDF 23.6 1.28 0.39 30.3 1.3 1.3 48.2 2.08 0.42 20.0 1.3 0.8

MDF 23.6 2.30 0.55 23.7 1.3 0.7

B Accuracy Analysis

119

48.2 3.52 0.75 21.2 1.3 0.5

PW(90/0/90)S 23.6 3.33 0.49 14.6 1.3 0.5 48.2 5.33 1.01 18.9 1.4 0.3

DCFC 23.6 5.77 1.37 23.7 1.8 0.3 36.0 7.21 1.73 24.0 1.8 0.2 48.2 8.74 2.29 26.2 1.9 0.2

B.2. Crush Characteristics of Flat Plate Discontinuous Carbon Composites

For the measurement data to be valid and meaningful, the uncertainty of the

measurement devices must be determined. Due to laboratory conditions during the experiments, temperature errors can be ignored. Also, creep errors can be neglected due to

a steady increase in the crushing stroke. In static testing, a maximum uncertainty of ±16 N

is induced by the used force sensors and the measuring amplifier due to linear scaling error

and offset error. For the measured stroke, a maximum uncertainty of ±0.0092 mm is

represented in the measurements. Due to the linear encoder and measuring amplifier, this uncertainty is composed of the shift in one step, the deviation of interpolation in a signal

period, and a position deviation. In dynamic testing, the used hardware is calibrated,

resulting in the following uncertainties. The linear scaling uncertainty of the force sensors

is ±200 N. The maximum uncertainty of the high-speed laser sensors is ±0.05 mm. The uncertainty of the measuring amplifier for dynamic testing can be neglected since it is less

than 0.2% of that of the sensors. The plate thickness and the crushing widths are measured

with a Vernier caliper, which implies an uncertainty of ±0.01 mm. The density of the plates

is measured using the hydrostatic balance principle. Therefore, the uncertainty of the

configurations varies between ±1.09 kg/m³ and ±3.32 kg/m³.

The calculation of the uncertainty of the specific energy absorption value dSEAM,

𝑑𝑑𝑆𝑆𝐸𝐸𝑑𝑑𝑀𝑀 = �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝐹𝐹

∗ 𝑑𝑑𝐹𝐹�+ �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝑠𝑠

∗ 𝑑𝑑𝑑𝑑� + �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝑡𝑡

∗ 𝑑𝑑𝑑𝑑� + �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝜌𝜌

∗ 𝑑𝑑𝑑𝑑� + �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝑤𝑤

∗ 𝑑𝑑𝑤𝑤�;

𝑑𝑑𝑆𝑆𝐸𝐸𝑑𝑑𝑀𝑀 = � 1𝑡𝑡𝜌𝜌𝑤𝑤

∗ 𝑑𝑑𝐹𝐹� + |0 ∗ 𝑑𝑑𝑑𝑑| + � 𝐹𝐹�

𝑡𝑡2𝜌𝜌𝑤𝑤∗ 𝑑𝑑𝑑𝑑� + � 𝐹𝐹�

𝑡𝑡𝜌𝜌2𝑤𝑤∗ 𝑑𝑑𝑑𝑑� + � 𝐹𝐹�

𝑡𝑡𝜌𝜌𝑤𝑤2∗ 𝑑𝑑𝑤𝑤�, (B.2-1)

leads to the estimated possible uncertainty of the calculated SEAM for the configurations.

These uncertainties range between 0.2 kJ/kg and 0.6 kJ/kg in static testing and between

0.5 kJ/kg and 2.7 kJ/kg in dynamic testing. Comparing the uncertainty dSEAM with the standard deviation (SD) of the average force value 𝐹𝐹�, given in Table B.2-1, the uncertainty

B Accuracy Analysis

120

has no substantial effect on the SEAM. These uncertainties are also valid for the SEAC. In

addition, due to the calculation of the components similar to those of the linear regression,

systematic uncertainties caused by the testing setup refute each other.

Table B.2-1: Overview of the uncertainty of each configuration.

B Accuracy Analysis

121

B.3. Insight into Crush Performance Comparison of Composite Profiles and Flat Plates

In order to provide valid and meaningful measurement data, the accuracy of the data

must be verified considering the uncertainty of the measurement devices. Temperature

errors can be ignored due to laboratory conditions during the experiments. Since the test

conditions are quasi-static and therefore a steady increase of the crushing stroke, creep

errors can also be neglected. The maximum uncertainty of the force sensors and the measuring amplifier due to linear scaling error and offset error dF is ±16 N. The linear

encoder can have a maximum uncertainty ds of ±0.0092 mm for the measured stroke. This

uncertainty is a combination of the shift of one step, the interpolation deviation of a signal

period, and a position deviation of the linear encoder and the utilized measuring amplifier.

The specimen dimensions and cross-section are determined via digital image processing with a resolution of 0.005 mm. A minimal amount of 5 pixels are necessary to provide

sustainable edge detection. The estimated uncertainty dA for determining the cross-

sectional area is ±0.0008 mm² ((resolution * amount of pixel for edge detection)² * safety

factor of 2). The density of the plates is measured based on the hydrostatic equilibrium

principle using a Kern PCB 3500-2 as a precision equilibrium measuring device. The CTR2000 temperature measuring device is used to measure temperature. The uncertainty

of the density dρ varies between ±0.4 kg/m³ and ±33.5 kg/m³ depending on the

corresponding configuration. The detailed values for each configuration are listed in Table

B.3-1. The calculation of the uncertainty of the specific energy absorption value dSEAM,

𝑑𝑑SEAM = �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝐹𝐹

∗ 𝑑𝑑𝐹𝐹�+ �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝑠𝑠

∗ 𝑑𝑑𝑑𝑑� + �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝜕𝜕

∗ 𝑑𝑑𝑑𝑑� + �𝜕𝜕𝑆𝑆𝐸𝐸𝜕𝜕𝜕𝜕𝜌𝜌

∗ 𝑑𝑑𝑑𝑑�;

𝑑𝑑SEAM = �𝑑𝑑𝐹𝐹𝜌𝜌𝜕𝜕� + |0| + �𝐹𝐹�𝑑𝑑𝜕𝜕

𝜕𝜕2𝜌𝜌� + �𝐹𝐹�𝑑𝑑𝜌𝜌

𝜌𝜌2𝜕𝜕�, (B.3-1)

leads to the maximum possible uncertainty of the calculated SEAM for the configurations.

For the angle-shaped profiles, the uncertainty ranges from 0.4% to 1.9%. The other

configurations have an uncertainty of less than 0.3%. All values for the CV of dSEAM are

listed in Table B.3-1. In comparison between the CV of the uncertainty and the CV of the average force, the uncertainty has a negligible influence on the calculated SEAM. These

uncertainties are also valid for the SEAC. In addition, systematic uncertainties given by the

test rig negate each other due to the calculation of the components as of the linear

regression.

B Accuracy Analysis

122

Table B.3-1: Overview of the uncertainty of each configuration.

Config. Area

A / mm²

Density ρ / kg/m³

dρ / kg/m³

𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆)

/ kN

CV of 𝐹𝐹�(𝑆𝑆𝐶𝐶𝑆𝑆) / %

SEAM / kJ/kg

CV of dSEAM / %

A17175 137.5 1879.7 33.5 10.14 12.9 39.2 1.9 A27275 234.1 1877.5 18.6 14.30 13.4 32.5 1.1 A37375 333.2 1883.9 13.6 18.78 14.4 29.9 0.8 A47475 432.2 1883.8 10.4 22.73 15.4 27.9 0.6 A57575 540.1 1887.7 8.7 27.23 18.2 26.7 0.5 A67675 627.5 1887.4 7.3 30.91 13.1 26.1 0.4

C40125 265.0 1876.0 1.6 19.85 15.9 39.9 0.2 C50175 356.8 1893.0 1.1 23.80 14.9 35.2 0.1 C40265 396.6 1880.8 1.3 25.71 8.5 34.5 0.1 C60225 454.3 1882.2 0.9 28.03 16.1 32.8 0.1 C50315 498.6 1887.6 1.1 29.79 11.6 31.7 0.1 C60365 602.8 1879.3 0.7 34.45 9.5 30.4 0.1

S40405 682.8 1883.8 0.6 46.71 7.5 36.3 0.1 S50505 880.5 1883.5 0.6 55.16 6.8 33.3 0.1 S60605 1074.2 1886.4 0.4 63.66 5.3 31.4 0.0

F245 118.7 1882.3 1.8 9.81 10.8 43.9 0.3 F365 181.8 1882.2 1.9 12.50 12.0 36.5 0.2 F485 240.9 1888.5 1.8 15.02 13.9 33.0 0.2

T20143 162.7 1887.2 2.7 12.58 7.5 41.0 0.3 T28223 243.3 1885.0 1.8 20.72 6.8 45.2 0.2 T30243 259.5 1888.0 1.7 22.61 10.1 46.2 0.2 T32263 275.2 1885.7 1.6 25.96 9.7 50.0 0.1

F243 74.1 1880.2 1.0 5.65 8.7 40.6 0.3 F363 111.7 1882.2 1.0 7.06 15.2 33.6 0.3 F483 149.3 1881.4 1.1 8.44 16.6 30.1 0.2

Characterizing the Crush Performance of Composite Flat ...

Documents

Transcript of Characterizing the Crush Performance of Composite Flat ...