Simulation and Modelling ofInjection Molded ComponentsFiber Reinforced Polymers in Powertrain Mounts

Simulering och modellering av formsprutade komponenterPolymera kompositer i motorupphängning

Hanna Jakobsson

Faculty of Health, Science and Technology

Degree project for Master of Science in Engineering, Mechanical Engineering

30 hp

Supervisor: Mohamed Sadek

Examinator: Jens Bergström

2020-07-02

AbstractPowertrain mounts’ purpose is to mount the engine and the gearbox in the car. Be-sides that, it isolate the body from the powertrain movements and road excitation.The most common material in powertrain mounts bracket is aluminum but lately,fibre reinforced polymer (FRP) has been acting as a substitute for the aluminum.The major drive forces for the change is the possibility to decrease the weight andimprove the attribute noise, vibrations and harshness (NVH). The main objectiveof this study was to compare aluminum and FRP in order to find advantages anddisadvantages for use in a powertrain mount bracket. FRP’s have in earlier inves-tigations at Volvo Cars been assumed to be isotropic, although it is orthotropicdue to fiber orientation. Hence, a comparison between isotropic and orthotropicmaterial properties for the powertrain mount bracket was conducted. There was noestablished method for modelling orthotropic materials available at the powertrainmount department, so a suggestion of a work process was presented in this thesis.Information regarding FRP, as well as a comparison to aluminum was presented ina literature study. The different materials and material models were compared inseries of stress-strain and eigenmode FEM analyses.

The results from the stress-strain analyses evinced that the design for the aluminumbracket can withstand the loads without exceeding the design limit. In the FRPbracket with orthotropic material properties, the design limit was exceeded for theload cases with the highest load. The results from the stress-strain and eigenmodeanalyses of the isotropic and orthotropic material models showed significant differ-ences. According to the isotropic material model, the bracket could withstand theloads, and the eigenfrequencies was 25-30% higher compared to the orthotropic ma-terial model.

The conclusions drawn from this study was that FRP’s may be an advantageousmaterial for the powertrain mount bracket, compared to aluminum. The FRP’sbracket will decrease the cost, weight, and carbon footprint as well as improve theNVH. However, difficulties of using FRP’s have been observed and need to be furtherinvestigated. The main difficulties identified are creep, fatigue, moisture absorption,and aging. This study has also proved that orthotropic material properties must beincluded in order to understand the material behavior and find critical areas.

Keywords: Material modelling, polymer composites, FRP, orthotropic, powertrainmount, vehicle engineering, Digimat

ii

SammanfattningSyftet för motorupphängning är att fästa motorn och växellådan i bilen. Utöverdet, bidrar motorupphängningen till att isolera bilen från rörelse och vibrationerorsakade av motorn. Det vanligaste materialet för motorupphängningsfästen är alu-minium, men den senaste tiden så har aluminiumet börjat ersättas av polymerakompositer. De största drivkrafterna för att imlementera polymera kompositer ärminskad vikt samt förbättrad noise, vibration och harshness (NVH). Det huvudsak-liga målet för studien var att identifiera för- och nackdelar med att ersätta aluminiummed en polymer komposit. Formsprutade polymera kompositer har i tidigare under-sökningar antagits vara isotropiska, trots att de är anisotropiska på grund av fiberor-ienteringen. Därmed så utfördes en jämförelse mellan isotropiska och anisotropiskamaterialegenskaper i fästet. Avdelningen för motorupphängning hade ingen metodför att modellera anisotropiska material och således har ett förslag på en metod pre-senterats i uppsatsen. Information angående polymera kompositer samt jämförelsermot aluminium presenterades i en litteraturstudie. De olika materialen och mate-rialmodellerna jämfördes i form av spänningsanalyser och egenmodsanalyser medhjälp av FEA .

Resultaten från spänningsanalyserna visar på att fästet i aluminium klarar av depålagda krafterna utan att överstiga den maximala tillåtna töjningen. Töjningarnai det fäste med ortotropiska egenskaper av polymera kompositer överstiger, för destörsta krafterna, den maximala tillåtna töjningen. Resultaten från jämförelsen mel-lan isotropisk och ortotropisk materialmodell visar på signifikanta skillnader i bådespänningsanalysen och egenmodsanalysen. Enligt den isotropiska materialmodellenså översteg inte töjningarna den maximala tillåtna töjningen i något lastfall. Egen-modsanalyserna visade att egenfrekvenserna var 25–30% högre för den isotropiskamaterialmodellen.

Slutsatserna från studien var att polymera kompositer kan vara ett fördelaktigtmaterial för fästen i motorupphängningen i jämförelse med aluminium. Polymerakompositer kommer att bidra till en lägre kostnad, vikt och koldioxidavtryck, samtförbättrad NVH. Däremot så har det identifierats möjliga hinder för polymera kom-positer. The största hinder som identifierats är kryp, utmattning, fukt samt åldring.I studien har det även bevisats att för att förstå och upptäcka kritiska områden ien formsprutad komponent, så bör anisotropiska materialegenskaper användas.

Nyckelord: Material modellering, polymera kompositer, ortotropisk, motorupphäng-nig, Digimat

iv

AcknowledgementsThis Master Thesis in Mechanical Engineering was performed at the PowertrainMount department at Volvo Cars during the spring of 2020.

I would like to express my very great appreciation to my supervisor Daniel Högbergat Volvo Cars for his support and help through the thesis. I also would like tothank Sreedhar Venkatesan and Henrik Åkesson for their help with the FE softwareand their valuable inputs to my research. I also want to extend my gratitude to allemployees at Powertrain Mount for welcoming me to the group.

A special thanks to Mohamed Sadek, my supervisor at Karlstad University, for hisguidelines, support, and constructive criticism throughout the project.

Hanna Jakobsson, Gothenburg, May 2020

vi

Abbreviations

FRP Fiber reinforced polymerNVH Noise, vibrations and harshnessPA66-GF35 Polyamide 66 reinforced with 35 wt% glass fiberFEA Finite element analysisRVE Representative volume elementsMFH Mean field homogenizationCAE Computer aided engineeringICE Internal combustion engineBEV Battery electric vehicleDOF Degree of freedom

viii

Contents

List of Figures xi

List of Tables xiii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theory 42.1 Powertrain Mounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Polymer Composites . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Fiber Content . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.2 Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . 62.2.3 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.4 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.5 Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.6 Damping Characteristics . . . . . . . . . . . . . . . . . . . . . 102.2.7 Moisture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Injection Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3.1 Fiber Orientation . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.2 Weld Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.3 Residual Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Material Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 Digimat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5.1 Digimat MF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.2 Digimat MX . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.3 Digimat MAP . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.5.4 Digimat CAE . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.6 Sustainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.7 Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . . . 24

ix

Contents

3 Methods 263.1 Material Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Validation of Digimat-Abaqus Interface . . . . . . . . . . . . . . . . . 27

3.2.1 Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 273.2.3 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Component Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.2 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . 303.3.3 Stress-strain Analysis . . . . . . . . . . . . . . . . . . . . . . . 313.3.4 Eigenmode Analysis . . . . . . . . . . . . . . . . . . . . . . . 32

4 Results 334.1 Validation of Digimat-Abaqus Interface . . . . . . . . . . . . . . . . . 334.2 Component Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2.1 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.2 Stress-strain Analysis . . . . . . . . . . . . . . . . . . . . . . . 374.2.3 Eigenmode Analysis . . . . . . . . . . . . . . . . . . . . . . . 39

5 Discussion 405.1 Material Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.2 Material Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.3 Material in Bracket . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

6 Conclusions 44

7 Future Work 45

x

List of Figures

2.1 Stress-strain curves under tensile test for PA66 and glass fiber rein-forced PA66. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Stress-strain behavior of PA66-GF35 at various temperatures. . . . . 72.3 Typical creep behaviour for a viscoelastic material for a constant load. 92.4 Temperature and load effects for creep behaviour. . . . . . . . . . . . 92.5 The relationship between the complex modulus, loss modulus, storage

modulus and tan δ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.6 Material damping behaviour of PA66-GF50 and aluminum. . . . . . . 132.7 Skin-shell-core structure. . . . . . . . . . . . . . . . . . . . . . . . . . 152.8 Flow chart for creating a orthotropic material model. . . . . . . . . . 192.9 Global error indicator for a11 where the pink staples are from the

donor mesh and the grey staples are from the receiving mesh. . . . . 20

3.1 Modification of orientation tensor. . . . . . . . . . . . . . . . . . . . . 273.2 Boundary conditions for the different load cases for the cube. . . . . . 283.3 An schematic illustration of the bracket assembly. . . . . . . . . . . . 293.4 Stress-strain curve for Zytel®70G35HSLRA4 BK267 at 23◦C. . . . . . 313.5 Stress-strain curve for Zytel®70G35HSLRA4 BK267 at 60◦C. . . . . . 31

4.1 Stress-strain relationship from tension test in the fiber orientation. . . 334.2 Stress-strain relationship from tension test normal to the fiber direction. 344.3 Stress-strain relationship from shear test. . . . . . . . . . . . . . . . . 344.4 Global error for a11. Receiver mesh 1 and receiver mesh 2 are achieved

with mapping technique integration point/node to integration pointand element to integration point, respectively. . . . . . . . . . . . . . 35

4.5 Global error for a22. Receiver mesh 1 and receiver mesh 2 are achievedwith mapping technique integration point/node to integration pointand element to integration point, respectively. . . . . . . . . . . . . . 36

4.6 Global error for a33. Receiver mesh 1 and receiver mesh 2 are achievedwith mapping technique integration point/node to integration pointand element to integration point, respectively . . . . . . . . . . . . . 36

xi

List of Figures

4.7 Maximal principal strain for the FRP bracket for load in negativez-direction at 23◦C. The location is at the transition between the ribsand one of the front screw holes on the bottom surface. . . . . . . . . 37

4.8 Maximal principal strain for the FRP bracket for load in negativez-direction at 60◦C. The location is at the transition between the ribsand one of the front screw holes on the bottom surface. . . . . . . . . 38

4.9 Maximal principal strain for the FRP bracket for load in positive z-direction at 60◦C. The location is at the transition between the ribsand one of the front screw holes on the bottom surface. . . . . . . . . 38

4.10 Maximal principal strain for the aluminium bracket for load in neg-ative z-direction at 23◦C. The location is the bottom surface of therear screw hole in the bracket. The maximum strain is 0.3%. . . . . 39

xii

List of Tables

2.1 Fatigue strength at 107 cycles for different materials . . . . . . . . . . 72.2 Acoustic velocity at 23◦C. . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Comparison of aluminium and FRP’s for an engine mount application

from a sustainability point of view. . . . . . . . . . . . . . . . . . . . 222.4 The total weight for the two bracket designs . . . . . . . . . . . . . . 222.5 Carbon footprint of different material . . . . . . . . . . . . . . . . . . 23

3.1 The proportion between the applied loads . . . . . . . . . . . . . . . 323.2 Maximum allowed percent of strain according to the design limit . . . 32

4.1 Frecuency for three first eigenmodes for the bracket . . . . . . . . . . 39

xiii

1Introduction

The introduction introduces the reader to the background of the thesis. It alsopresents the objectives and delimitations.

1.1 BackgroundPowertrain mounts’ purpose is to mount the engine and the gearbox in the car. Be-sides that, it isolates the body from the powertrain movements and vibrations. Thematerial for the powertrain mounts in cars has over the years been dominated byaluminum alloys, but during the recent years, powertrain mounts in fiber-reinforcedpolymers (FRP’s) have been introduced to the market. The FRP’s mounts have beenproven to reduce the weight and improve noise, vibrations, and harshness (NVH) [1].

In the designs at Volvo Cars, mounts made of FRP’s have not been an option inthe combustion engine powertrain mounts due to high temperatures. Although, inrecent years electrical vehicles have managed to penetrate the market and the futureusage is expected to increase. The electrical engine generates lower temperatureswhich imply that the FRP could be a feasible material for the powertrain mountsat Volvo Cars. Therefore, the purpose of this master thesis is to investigate thepossibility to replace the current aluminum bracket in the powertrain mounts withan FRP bracket.

Volvo Cars has started an investigation regarding FRP’s in powertrain mount brackettogether with a supplier, where the supplier has provided a suitable design and ma-terial selection for injection molding. The material suggested by the supplier waspolyamide 66 reinforced with 35wt% glass fiber (PA66-GF35).

Previous studies executed at Volvo Cars have resulted in the cost of the FRP com-ponents have turned out to be higher than the current material, which has stoppedthe investigation. In these studies, the material has been assumed to be isotropicalthough it does not reflect the reality and therefore the components have for many

1

1. Introduction

cases been over-dimensioned. Instead, if the orthotropic behavior of the FRP is in-cluded in the investigation, a better understanding of the material can be obtained.Thus, the weaker and stronger regions depending on fiber orientation could be foundin components and by that, designs can be optimized for the loads. Until today, thepowertrain mount department has not been working with orthotropic materials anddoes not have an established workflow for simulations which includes orthotropicproperties. Thus, there exist possibilities of weight reductions and improved NVH,if the knowledge can be enhanced.

1.2 Purpose and ObjectivesThe purpose of this thesis is to provide documentation regarding implantation ofFRP’s in the powertrain mount and the possible difficulties it may imply. Thus,this thesis serves to act as a basis for orthotropic material modelling and FRP’s ingeneral. To get more accurate results for calculations in the FRP bracket, a materialmodel that includes the orthotropic behavior in injection molded components mustbe provided. In addition, the experience with FRP’s for this application is small andan overall investigation of FRP’s is needed to identify obstacles and problems thatmight be facing later in the process as well as advantages the FRP’s can provide.Therefore, the objectives for the thesis are to;

• Deliver a literature study including the behavior of FRP’s.• Suggest a method for creating an orthotropic material model depending on

the fiber orientation.• Identify advantages and disadvantages with FRP’s compared to aluminum.• Analyze the effects of assuming isotropic material model compared to the or-

thotropic material model by performing static stress-strain analyses and eigen-frequency analyses.

• Compare the results from stress-strain analyses and eigenfrequency analysesfor the aluminum bracket with the FRP bracket.

1.3 DelimitationsThe purpose of the thesis is to provide documentation regarding FRP’s in the pow-ertrain mount and the possible difficulties it can imply as well as provide suggestionsfor a potential work process for modeling injection molded components. Thereforethe following delimitations have been made;

• No physical testing will be performed to verify the results.

2

1. Introduction

• The material selection will not be included since the material has already beensuggested by the supplier.

• No design improvement will be suggested.• The moldflow analysis will be performed by another department and will not

be investigated.

3

2Theory

The theory chapter provides the reader with general information about powertrainmount and information about FRP’s. The information and material properties re-garding FRP’s are set in proportion to aluminum to be able to identify advantagesand disadvantages. Further, since the manufacturing process for FRP bracket isinjection molding, a section regarding injection molding and the effect it provides tothe final component is included. In addition to the technical information, a sustain-ability perspective of the two materials are investigated.

2.1 Powertrain MountsThe powertrain mounts’ purposes are to mount the engine and the gearbox and toisolate the body from the powertrain movements and vibrations. The powertrainmounts are important in order to provide a good driving experience, without noiseand vibrations caused by the engine. There are also some limitations for powertrainmounts such as keeping the powertrain mounts within the allowed packaging space,respecting crash and safety requirements, keeping function and efficiency during ve-hicle lifetime, and allowing assembly and serviceability. When designing the mountsthere exists a trade-off between different properties. The main attributes to balanceare NVH, which demand soft mounts to damp the vibrations, and the attributeswhich demand as high stiffness, like drivability, durability and ride [2].

The current aluminum alloy in the bracket investigated in this thesis is EN AC-44300and the material suggestion for FRP given from supplier is polyamide 66 reinforcedwith 35wt% glass fiber (PA66-GF35). Glass reinforced PA66 is commonly used forunder the bonnet applications, and as a substitute for metal. It is an advantageousmaterial due to a great balance between mechanical properties and cost as well ashigh thermal stability, chemical resistance and creep resistance [3]. To be able tocarry the pretension load applied in the screws in the bracket, inserts are needed inthe FRP bracket. The suggested material of the inserts is aluminum.

4

2. Theory

2.2 Polymer CompositesPolymer composites are well-known for their low weight-to-stiffness ratio and aretherefore a commonly used material group for lightweight structures. In addition,the polymer composite also provides high resistance to impact and wear, good damp-ing characteristics, and high durability. This combination of properties makes thepolymer composite a suitable option as a replacement to traditional materials asmetals [4].

Replacing metal with FRP is followed by new challenges since FRP’s has anisotropicbehavior and is viscoelastic even at low temperatures. The behavior and proper-ties are rather complex compared to substitutes as metals and thus, the followingchapters aim to provide a deeper understanding of the parameters affecting theperformance of FRP’s.

2.2.1 Fiber Content

The fiber content strongly affects the mechanical properties of FRP’s. By increas-ing the fiber content, higher stiffness, and tensile strength are achieved while theductility is greatly decreased. This behaviour is illustrated in Figure 2.1 [5].

Figure 2.1: Stress-strain curves under tensile test for PA66 and glass fiber rein-forced PA66 [5].

The maximum effect from fiber reinforcement is found at 40-50% fiber content.Above this level, the elastic deformation is very low and thus the material will notsatisfy the demands of most structural material applications [6].

5

2. Theory

Taha et al. [6] have investigated how the tensile strength and tensile modulus areaffected by the fiber content in a PP-GF composite. The fiber content was varied be-tween 0-40wt% since these are the grades mostly used. The results of the study haveproved that stiffness and strength are increased with increased fiber content. Withincreased fiber content, the stiffness increases linearly. The tensile strength, how-ever, increases with a lower rate at higher fiber contents. The conclusion from thisobservation has been that other factors than fiber content are affecting the strengthas well. One factor that could affect the tensile strength, according to Taha et al. [6],is how strong the fiber-matrix cohesion is. This factor does not affect the stiffnesssince the stiffness is measured at low strains and is not associated with interfacialfailure. Additionally, higher fiber content make the fibers more likely to damage eachother during the injection molding process. Therefore, a lower mean fiber lengthwill be presented which decreases the aspect ratio of the fibers (length/diameter) [7].

2.2.2 Temperature Effects

Compared to metals, the mechanical properties of polymer composites are highlydependent of temperatures. Thermoplastics composites are much more sensitiveto high temperatures than thermosetting composites. For amorphous polymers,Young’s modulus are drastically decreased at the glass transition temperature andfor partially crystalline polymers the reduction occurs slowly over a larger tempera-ture interval. The glass transition temperature Tg is dependent on the heating rateand is not a fixed value. A low heating rate will decrease Tg as well as a high heatingrate increases Tg [8].

The temperature effects on mechanical properties are strongly affected by the poly-mer matrix and the fiber content. Increased fiber content will enhance the temper-ature resistance. All polymer composites have decreased strength and stiffness andincreased strain at elevated temperatures. This behaviour is illustrated in Figure2.2 [9].

Aluminum is less heat-sensitive compared to FRP’s which could be indicated withmaximum service temperature stated in CES EduPack. The maximum service tem-perature is the highest temperature the material can withstand for an extendedperiod of time without causing significant problems due to e.g. chemical change,loss of strength, oxidation, excessive creep, or other properties that are primary inapplications. The maximum service temperature for EN AC-44300 is 170-200◦C andfor PA66 the temperature is between 90-130◦C [10].

6

2. Theory

Figure 2.2: Stress-strain behavior of PA66-GF35 at various temperatures [9].

2.2.3 Fatigue

The engine mounts are exposed to lots of vibrations during their lifetime and thus,fatigue can be a risk factor. During cyclic loading, failure may occur at significantlylower loads than under static loading conditions [11]. In previous bracket designs,fatigue has not been a large problem and the brackets have only been optimized anddesigned for extreme load cases. According to material data obtained from CESEduPack [10] polymer composites have lower fatigue strength than EN AC-44300 at107 cycles, see Table 2.1. Due to lower fatigue strength in the polymer composites,fatigue behavior must be investigated in order to secure that the fatigue strength ishigh enough.

Table 2.1: Fatigue strength at 107 cycles for different materials [10]

Material Fatigue strength (MPa)

PA66-GF50 67.1-74.1PA66-GF30-33 56.5-62.5PA6-GF50 58.5-64.6EN AC-44300 81-94

The design and material affect the fatigue strength. For polymers and polymercomposites, the fatigue strength is decreased at weld lines, by fiber agglomerationsor by the presence of notches. For polymers, the load level, load frequency, andthe test temperature strongly affect the mechanical behavior due to the facts that

7

2. Theory

polymers have low heat conductivity and high damping. During cyclic loading, en-ergy will be absorbed by the material and dampen the vibrations. Due to the lowheating conductivity and the high damping of polymer materials, the temperatureis increased to high levels without reaching an equilibrium plateau before fracture.This fracture mechanism is called thermal fracture [11]. The other fracture mech-anism common in polymer composites is mechanical fracture which is indicated bycrack initiation and propagation, where the cracks propagate along the fibers [12].Bellenger et. al. [12] have investigated the fatigue behavior of glass-reinforced PA66and by applying different strains at two different frequencies, 2 Hz and 10 Hz. Atthe lower frequency, the matrix remains in the glassy state and the fracture is onlymechanical. When the frequency is increased to 10 Hz, both thermal and mechani-cal fracture occurs since the temperature is elevated to 160◦C on the surface of thesample. For 10 Hz the matrix is in the rubbery state and the fracture is ductile.

While thermal fracture is common during cyclic loading of polymers, mechanicalfracture mechanism will occur for metals, even at higher frequencies. Further forpolymers, already at room temperature creep and stress relaxation must be takeninto account which is not required for metals [11].

2.2.4 Creep

When a polymer is exposed to a stress, the strain will increase slowly but not con-stant over time, which is called creep. The reason for this phenomenon is due tomolecular rearrangement in the polymer. When the stress is removed the strain goback since the molecular want to return to their initial position, due to the materialsviscoelastic behaviour. [13].

The creep goes through different stages, as illustrated in Figure 2.3. First, an initialelastic strain occurs when the constant load is applied which thereafter are followedby the three stages; primary creep, secondary creep, and tertiary creep. The primarystage has a decreasing rate which indicates that the strain rate is decreasing untilthe strain rate is constant and that’s when the second stage begins. The secondstage is called the steady state stage due to the constant strain rate. In the thirdand last stage, the strain rate is increasing very rapidly and rupture will occur. Dueto the high strain rate, necking or another failure will take place in the material.The necking will result in very high local stresses giving an even faster increase ofstrain rate [14].

8

2. Theory

Figure 2.3: Typical creep behaviour for a viscoelastic material for a constant load[14].

Creep is a function of time, temperature, applied load, and material properties.Increased load and increased temperature have the same effect on creep and asillustrated in Figure 2.4 [14].

Figure 2.4: Temperature and load effects for creep behaviour [14].

Creep is observed in metals as well but there are three principal differences betweenmetallic creep and polymeric creep. In metals, the creep is only significant at hightemperatures, it is not linearly viscoelastic and it does not recover. For the power-train mounts in an electric powertrain, the temperatures are not considered as high

9

2. Theory

for metals and therefore creep could be neglected in the aluminum bracket. Forpolymers the creep is significant for all temperatures above -200◦C and needs to beconsidered in the FRP bracket [13].

2.2.5 Aging

The material properties of polymers will be changed over time, which is calledaging. Polymer aging can be divided into four groups; physical aging, chemicalaging, thermal aging, and photochemical aging [15].

• Physical aging is the most common type of aging in polymers. After the injec-tion molding, the polymer is cooled down rapidly, and thereby, the materialwill reach thermal equilibrium before thermodynamic equilibrium is obtained.Since thermodynamic equilibrium is not reached, the molecules within thepolymer will reorganize in order to lower their energy. The effects of physicalaging are often reduced volume and increased stiffness.

• Chemical aging is due to cross-linking in thermosetting polymers. Duringcross-linking the molecules become larger and the mobility decreases whichdecreases ductility.

• Thermal aging is due to elevated temperatures which can accelerate the phys-ical and chemical aging.

• Photochemical aging is also called photo-oxidation as it occurs due to UV-radiation in the presence of oxygen. The reaction will lead to degradation ofsurface since a brittle layer will be formed.

2.2.6 Damping Characteristics

Damping capacity is the definition of a mechanical system’s capacity to reduce theintensity of vibrations. The reduction of vibration magnitude is due the dissipationof the vibration energy into other forms of energies [16]. A high damping capacitywill give improved NVH since more vibrations and noises will be canceled withinthe bracket, and thus, not be able to affect the rest of the vehicle. The dynamicmodulus E∗ in Equation 2.1, also called complex modulus, is used for measuringdamping. It consists an imaginary and a real part [17].

E∗ = E ′ + iE ′′ (2.1)

Where E ′ is the storage modulus which is the capacity to store potential energyand release it during deformation. E ′′ is the loss modulus which is associated withthe ability to dissipate energy into heat during deformation. The fraction of theseparameters will give tan δ, see Equation 2.2, which is a material parameter that

10

2. Theory

could be obtained from data sheets or experimentally [17]. The polymers’ dampingcapacity depends on the structure of the polymer. Amorphous polymers have lessdamping capacity compared to crystalline polymers [10]. The maximal dampingcapacity for a polymer is obtained at Tg [8].

tan δ = E ′′

E ′(2.2)

Figure 2.5 illustrate the relationship between the complex modulus, loss modulus,storage modulus and tan δ.

Figure 2.5: The relationship between the complex modulus, loss modulus, storagemodulus and tan δ.

Another property that is important for NVH is the acoustic velocity, see Equation2.3, which is the property for the speed of longitudinal sound waves in a solidmaterial. In order to minimize the noise in the car, the acoustic velocity should beas low as possible since this indicates that the material absorbs sounds, rather thantransporting it. The acoustic velocity is defined as [10]:

Acoustic velocity =(E

ρ

)0.5

(2.3)

Where(E

ρ

)is the specific stiffness.

In Table 2.2 the acoustic velocity is stated for different polymers, polymer compos-ites, and aluminum.

11

2. Theory

Table 2.2: Acoustic velocity at 23◦C [10]

Morphology Acoustic velocity (m/s)

PA66 semi-crystalline 1080-1210PA66-GF30-33 2110-2370ABS amorphous 1450-1580ABS-GF30 2290-2540EN AC-44300 metal 5230-5350

The mechanisms for damping in FRP’s differ from the mechanisms observed in met-als. The energy dissipation in a polymer composite depends on several mechanisms.The damping mechanisms for composites described by Chandra et al. [18] are:

• Viscoelastic behavior of matrix and/or fiber. The major contribution to damp-ing in the composite is due to the matrix but some fibers could contribute tothe damping.

• Damping due to interphase. Interphase is the volume of material affectedby the interaction between the fibers and the matrix [19]. In this regionthe chemistry, polymer chain mobility, degree of cure, and crystallinity variescompared to the bulk matrix.

• Damping due to damage. The damage could be divided into two categories.Frictional damping since the fibers and matrix may slip in unbounded areasor damping due to energy dissipation in terms of matrix cracks, broken fibers,etc.

• Viscoplastic damping. This mechanism is especially related to thermoplasticscomposites exposed to high-stress levels or large-amplitude vibrations. Underthese conditions, high stresses and strains will occur between the fibers whichlead to non-linear damping.

• Thermoeleastic damping. Arises due to temperature differences between thecompressed regions and regions exposed to tension. The compressed regionshave a higher temperature than the extended areas and thus a cyclic heatflow will be generated due to thermal equilibrium. This mechanism is moresignificant in metal composites than in polymer composites.

In a study regarding a torque reaction mount for a powertrain mount, physicaltesting of damping characteristics have been performed. The results of the studyhave confirmed that glass fiber reinforced PA66 significantly dampens vibrationsmore efficiently than aluminum. The results from the study is presented in Figure2.6 [20].

12

2. Theory

Figure 2.6: Material damping behaviour of PA66-GF50 and aluminum [20].

2.2.7 Moisture

Most polymers are absorbing water from the environment during standard atmo-spheric conditions but the capacity differs between different materials. When waterfrom the surrounding is absorbed by the polymer, the water will act as a plasticizerand decrease the strength and glass transition temperature of the polymer. Besidesthe plasticizing effect, the moisture absorption will generate dimensional changes,like swelling of the polymer part. This process is reversible but the absorbed wa-ter may cause aging of the polymer which is irreversible and will give permanentchanges in properties [21].

Plenty of factors are affecting the water absorption in a polymer and must be in-cluded in an absorption analysis. Some factors affecting water absorption accordingto Omnexus [21] are;

• Type of polymer• Type and amount of fillers, reinforcement and additives• Exposing time• Relative temperature and humidity in the environment.

2.3 Injection MoldingInjection molding is a cost-efficient manufacturing process for complex designs atmedium to high volumes. There are changes in the material properties caused bythe manufacturing process that must be taken into consideration during calculationsof injection-molded parts [13]. These aspects will be presented in this section.

13

2. Theory

2.3.1 Fiber Orientation

The fiber orientation in a composite strongly affects the material properties and com-posites have orthotropic properties where the stiffness is higher in fiber orientationand lower in the normal direction. The material properties from injection moldedparts are often wrongly assumed to be isotropic, for simplicity. This might resultin incorrect results for executed calculations. One way to predict the fiber orienta-tion in injection molded parts is by performing a moldflow analysis by using toolslike Autodesk Moldflow Insight. The fiber orientation obtained can be described bya symmetric orientation tensor aij, showed in Equation 2.4, which represents theprobability distribution of finding fibers in a 3D space.

aij =

a11 a12 a13

a22 a23

a33

(2.4)

The general constrains of the orientation tensor is;• 0 ≤ aii ≤ 1• ∑3

i=1 aii = 1• aij = aji

• −0.5 ≤ aij ≤ 0.5 for i 6= j

The diagonal values in the orientation tensor describe the intensity of the fiber ori-entation in the respective axis in which they are associated with. Some examples oforientation tensor for special cases are presented below.

• When all fibers are oriented in the first principal direction the orientation areindicated by:

aij =

1 0 0

0 00

• When the fibers are randomly oriented in the 2D plane of the first and secondprincipal direction the orientation are indicated by:

aij =

12 0 0

12 0

0

14

2. Theory

• When the fibers are randomly oriented in the 3D space the orientation areindicated by:

aij =

13 0 0

13 0

13

The orientation will vary within the material and therefore, the tensor is valid onlyfor a point in the material. In general, a skin-shell-core structure is formed duringinjection molding, see example in Figure 2.7. In the skin-layer, which usually arevery thin, the fibers are almost random oriented since the melt solidifies fast andfibers get stuck in their position. In the shell layer the fibers are oriented in theflow direction due to shear flow. In the core layer, there is a stretching flow whichorients the fibers perpendicular to the flow direction [22].

Figure 2.7: Skin-shell-core structure [23].

Other parameters that influence the fiber orientation are;• Fiber content: During the injection molding process, the fibers are forced to

align in the flow direction. When the fiber content is low in the mold, thefibers can rotate and change their orientation. At higher fiber content thedistance between the fibers may be smaller than the actual fiber length andfiber rotation can be hindered by surrounding fibers. [6]

• Design of the mould: Depending on where the gates, runners, and coolingchannels are placed, the fiber orientation will differ [24]. Thus, the design ofthe mold must be defined before calculations are executed since the materialproperties are strongly influenced by fiber orientation.

• Filling speed: Increased filling speed give a smaller degree of total fiber orien-tation [24].

15

2. Theory

In order to get accurate and, through that, useful data from calculations the materialmodel used is very important. Carlsson [25] have investigated how the deflectionof a battery tray was changed depending on which stiffness that was used. Thematerial models investigated were:

a) an isotropic material model based on Young’s modulus from the datasheet.b) an isotropic material model based on the Young’s modulus that was obtained

in a simulated tensile test.c) an isotropic material model based on Young’s modulus for random fiber ori-

entation.d) orthotropic material model based on the Young’s modulus obtained fromMold-

Flow for the battery tray.

The results presented in the study have shown that case b) only has 2% largerdeflection compared to a), and that c) and d) have 7% and 8% larger deflection,respectively [25]. The conclusions that can be drawn from the study are that assum-ing randomly oriented fiber orientation gives a much more accurate value comparedto using Young’s modulus from the datasheet.

2.3.2 Weld Lines

Another defect caused by injection molding is weld lines. Weld lines occur when twomold flows meet. At the finished part these lines are visible and could also causedecreased strength which could lead to failure. The reason for weld lines to occuris that the polymer melt flow is divided due to the existence of cores, pins, andmultiple gates [26].

2.3.3 Residual Stresses

Injection-molded parts will contain internal stresses caused by the manufacturingprocess, these stresses are called residual stresses. The stresses are distributed in twocategories, flow-induced stresses, and thermal-induced stresses. The flow-inducedstresses originate from the filling and post-filling stage and are due to the orientationof the polymer chains. The thermal-induced stresses originate from the coolingstage. During the cooling process, the outer layer cools faster than the inner coresince almost all heat removal occurs on the outer surface. This creates compressionstresses on the surface and tensile stresses within the core. The residual stresses areaffecting the parts in the same way as applied stresses. This may result in warpageand shrinkage of the produced part [27].

16

2. Theory

2.4 Material ModelsInjection-molded composites have anisotropic behavior due to fiber orientation. Inorder to find out how the material model is affecting the results, different modelsmust be tested and compared for the FRP bracket. The stiffness tensor is used forpredicting the elastic behavior of materials. The stiffness tensor is characterized inthe generalized Hooke’s law and formulated by the equation:

σij = cijklεkl ⇐⇒ εij = sijklσkl (2.5)

where cijkl is the stiffness tensor and sijkl is the compliance tensor. The tensors is ofrank 4 and therefore include 81 constants. Due to symmetry in stress, strain, andquadratic-form strain energy density, the number of constants is reduced. The mostgeneral anisotropic homogeneous material model has 21 elastic constants. The twomaterial models included in this study was orthotropic and isotropic which due tosymmetry around different axis has fewer elastic constants. The standard model formaterial properties in most engineering materials is isotropic properties. Isotropicindicates that the material properties are invariance to arbitrary transformation.For an isotropic material, there are only 2 independent elastic constants [28]. Thecompliance matrix for the isotropic material is characterized by

S =

1E

−νE

−νE

0 0 0

−νE

1E

−νE

0 0 0

−νE

−νE

1E

0 0 0

1G

0 0

symm1G

0

1G

(2.6)

where G = E

2(1 + ν) .

Since the material properties in the injection-molded bracket are dependent on thefiber orientation the isotropic material properties are incorrect and anisotropic ma-terial properties must be used. Due to the fiber orientation, the material propertieswill be orthotropic [29]. An orthotropic material has invariance to rotation aroundx-,y- and z-axis which gives 9 independent constants, i.e. elastic material con-

17

2. Theory

stants [28]. The compliance matrix for the orthotropic material is characterizedby

S =

1E1

−ν21

E2

−ν31

E30 0 0

−ν12

E1

1E2

−ν32

E30 0 0

−ν13

E1

−ν23

E2

1E3

0 0 0

1G12

0 0

symm1G13

0

1G23

(2.7)

where −ν21

E2= −ν12

E1, −ν31

E3= −ν13

E1, −ν23

E2= −ν32

E3.

2.5 DigimatDigimat is composite material modelling software. Digimat enables to create mate-rial models for different kinds of composites, for instance, short fibers, long fibers,UD, and woven. The material models can be used to analyze crash, durability, NVH,fatigue as well as strength and stiffness performance. In the modelling platform, itis also possible to include effects from the manufacturing process, e.g. fiber orienta-tion, weld lines, and residual stresses. The results from Digimat can be coupled todifferent kinds of FEA softwares, for instance, Abaqus/Standard which was used assolver for this thesis [30]. Digimat consists of several tools and the main ones relatedto the thesis are described in this section. A flow chart presenting the interactionwith Moldflow and FEA is illustrated in 2.8.

18

2. Theory

Figure 2.8: Flow chart for creating a orthotropic material model.

2.5.1 Digimat MF

Digimat MF is a homogenization tool that computes the macroscopic properties ofcomposite material. The materials are modelled by modelling each phase separatelyand to fulfill the microstructure additional information such as fiber fraction, fiberorientation, and aspect ratio is added. The connection from micro to macro scale isbased on the principle of representative volume elements (RVE). The RVE needs tobe small enough at the macro-scale so it can be assumed to be homogeneous but atthe micro-scale, the size has to be sufficiently large to represent the heterogeneousmicrostructure. In Digimat there are two available homogenization methods, mean-field homogenization (MFH) and direct finite element analysis of RVE at micro-scale.Direct finite element analysis of RVE at micro-scale is a very accurate method butMFH is in many cases preferable to avoid problems for non-linear models such ashigh CPU-time and memory issues. There are two methods for MFH available,Mori-Tanaka and double inclusion. Mori-Tanaka is used in almost all cases, but forvery high fiber mass fractions double inclusion can be more accurate [30].

In Digimat MF it is possible to create materials and correlate with experimentaldata by reverse engineering. In this study materials given from material suppliersin the Digimat MX tool were used without making any adjustments, and creatingmaterial will not be further investigated.

19

2. Theory

2.5.2 Digimat MX

Digimat MX is a tool to store anisotropic measurements and related material models.The materials available are given from material suppliers, Digimat, as well as it ispossible to create your own materials in Digimat MF and import it to DigimatMX. Material models available have various complexity but material behaviors thatcould be selected are elastic, plastic, elastic-plastic, elastic-viscoplastic, viscoelastic-viscoplastic. It is also possible to include failure and temperature dependence intothe material models [30].

2.5.3 Digimat MAP

Digimat MAP is a tool used to map information between different meshes, typicallyfrom a manufacturing mesh (donor mesh) to an FEA mesh (receiving mesh). It ispossible to map different information e.g. fiber orientation, residual stresses, initialtemperatures, weld lines, and porosity. In this thesis, the manufacturing processis injection molding and the information mapped from the injection molding isfiber orientation. There are different techniques of mapping and the default andrecommended one according to Digimat is integration point/node to integration pointand the second most recommended method is element to integration point. Whenmapping information between meshes the global error between the meshes can beobtained. The global error indicator is a histogram viewer that compares the relativenumber of elements with a certain value of aij in the donor and receiving mesh. Thevalues of aij is the probability that the fibers are oriented in the direction, where 0indicates no fibers will be in the direction and 1 indicates all fibers will be orientedin the direction [30]. An example of a plot from the global error indicator for a11 ispresented in Figure 2.9.

Figure 2.9: Global error indicator for a11 where the pink staples are from the donormesh and the grey staples are from the receiving mesh.

20

2. Theory

2.5.4 Digimat CAE

Digimat CAE is a tool to couple the material data created in Digimat to the finalperformance in the composite structural parts. There are three different couplingprocesses available [30];

• Macro - Gives a linear behavior of the material and could therefore be used forlinear materials only. The solution processes provide results for the compositeonly.

• Hybrid - The recommended solution for most analyses. In the method, homog-enized material properties are pre-calculated in Digimat before FEA analysis.The homogenized material properties are called hybrid parameters and arestored in a material file that is connected to the job while running simulation.It provides results on the composite level only.

• Micro - The solution is the most accurate one since the results for each phaseis calculated for each iteration during FEA. At each iteration, homogenizationis performed to calculate the composite material properties and results forthe composite. Since the homogenization is executed in every increment thissolution method is time-consuming. This method enables results for eachphase in the composite as well as for composite level and can be used for bothnon-linear and linear materials.

2.6 SustainabilityVolvo Cars’ purpose is to provide freedom to move in a personal, sustainable, andsafe way. Volvo Cars invest a lot of effort within the area of sustainability. The long-term vision is that sustainability should be associated with the Volvo Car brand,like safety is today. The climate road map formulated by Volvo Cars is one ofthe most ambitious plans within the automotive industry. Volvo Car’s long-termgoal is to be climate neutral by 2040 and a short-term goal is to reduce the CO2-emission with 40% by 2025. In order to achieve the above targets, electrificationis not enough, more actions need to be executed. Volvo Cars must reduce theirCO2-emission by making changes in areas, such as, selection of raw materials (sec-ondary and renewable materials), supply chain (renewable energy, transportation,etc.) and manufacturing processes (high material utilization, energy effective). Inthe area of materials, Volvo Cars has an ambition that at least 25 % of the plasticused in the cars launched after 2025 should be based on recycled plastics or bio-based plastics [31].

The aspects mentioned above must be taken into consideration during the prod-

21

2. Theory

uct development stage and should therefore be combined with the other technicalrequirements, like weight, noise, and vibrations, when evaluating different designoptions. For the front bracket, the current material is aluminum with 30% recycledcontent. In this work, this standard option is being compared to using PA66-GF. Ageneral comparison between aluminum and the materials used in FRP’s is shown inTable 2.3.

Table 2.3: Comparison of aluminium and FRP’s for a engine mount applicationfrom a sustainability point of view [10,32]

Aluminium Plastics Glass

CO2 eq. −− /− + +Recycled content +/++ − −Recyclable ++ − −−Weight − + +Bio-based N/A ++ N/A

A major advantage of using FRP’s compared to aluminum is weight reduction, whichis one of the driving forces to implement FRP’s in the powertrain mount. It shouldnot be forgotten that weight is a key sustainability area in the automotive sectorsince it impacts fuel consumption (ICE) and driving range (BEVs). Table 2.4 showsthat a weight reduction of about 40 % is obtained by substituting the aluminumbracket with the plastic bracket. The total weight measured is the sum of the weightfrom the inserts and the weight from the bracket.

Table 2.4: The total weight for the two bracket designs

Aluminum Bracket FRP Bracket

Bracket [g] 677.6 359.7Inserts [g] N/A 54.9Total [g] 677.6 414.6

There are two challenges with using FRP’s in this specific application. First, it isthe difficulties of incorporating recycled material into a polymer blend, since high-quality material is needed in order to withstand high loads for long periods of time.Second, FRP’s is more difficult to recycle at end-of-life unless the component canbe separated from the vehicle before crushing. Adding additional primary plasticsas a substitute for aluminum could be argued to serve in contradiction to the 25%recycled plastic goal. One option could be to use bio-based plastics in the FRP

22

2. Theory

since bio-based plastics fall within the recycled material target. It is a materialcategory Volvo Cars would like to increase in the vehicle. Bio-based materials havesimilar properties as primary fossil-based polymers and can therefore be used inapplications which demand high quality. Bio-based polymers have less environmen-tal impact since the source of origin is from nature instead of fossil-based oil. Onaverage bio-based polyamides have a 50% lower carbon footprint compared to theirfossil-based counterparts [33]. The natural source can, for example, be castor oilextracted from castor seeds [34]. Today bio-based polymers generally have a higherprice than fossil-oil-based polymers so there must be a trade-off in which aspecthas a higher priority. However, according to European Bioplastics [35] the price forbio-based polymers will be comparable with the fossil-based plastic in the futuresince the oil-price is expected to increase over time as well as the rising demandfor bio-based polymers and increasing production volume will give more efficientproduction processes and therefore decrease the price [35, 36].

The largest disadvantage of using aluminum is the high emissions of CO2 eq. perkg of material. The CO2 footprint varies greatly depending on where in the worldthe production occurs, since the carbon footprint of electricity varies greatly andthe carbon footprint of aluminum is highly tied to electricity [37, 38]. In China,where a large part of the aluminum production is located, the CO2 eq. emissionsper kg material produced are about 20 kg since the electricity comes from coal. InEurope, the average emissions of CO2 eq. per kg of material is around 7 kg, sincemore renewable and nuclear energy is used [39]. On the other hand, 30%wt of thealuminum used in the bracket is recycled, leading to a decrease in CO2 eq. emission.The emissions are about 95% lower for recycled aluminum compared to primary [40].Even though recycled aluminum is used in the bracket, the FRP design still has alower carbon footprint, see Table 2.5.

Table 2.5: Carbon footprint of different material [39–41]

kg CO2 eq.

Aluminum China with 30% recycled 9.6Aluminum EU 30% recycled 3.5PA66-30%GF 1.0

23

2. Theory

2.7 Advantages and DisadvantagesFrom the literature study, both advantages and disadvantages of replacing the alu-minum bracket with a polymer composite bracket have been identified. The advan-tages and disadvantages are listed below.

Advantages• Corrosion and chemical resistance - By substituting the aluminum to PA66-GF

the risk for corrosion is eliminated and the chemical resistance is increased.• NVH - According to studies and information from other car brands, the NVH

is improved for PA66 with glass fibers compared to aluminum which will bebeneficial.

• Sustainability - The environmental impact from the FRP bracket is lower thanfor the aluminum bracket due to the reduced weight of the component andsmaller carbon footprint.

• Weight - the weight reduction about 40%. This value might change since it isnot in the final designs but a clear weight reduction is expected.

• Price - The total cost for the FRP bracket is decreased with ∼10% comparedto the aluminum bracket.

Disadvantages• Knowledge and experience - This is an important factor to include. Aluminum

has been used for a long time in similar applications and the knowledge andexperiences are high. The testing and validation are established as well as cal-culation methods. For the FRP bracket, new methods for testing, validation,and calculations must be established.

• Fatigue - The fatigue strength for FRP’s are lower than aluminium. Addition-ally, the fatigue strength is strongly affected by frequency since the tempera-ture in the polymer is increased rapidly at higher frequencies.

• Creep - The plastic in FRP’s is time-dependent and therefore creep will occurand must be taken into account during calculations.

• Aging - Aging changes the properties of the FRP and is, therefore, affectingthe performance in the bracket. A method to include these effects must beestablished.

• Moisture - The moisture absorption is strongly affecting the mechanical prop-erties since the absorbed water acts as a plasticizer in the plastic. Thereforeit is very complex to model and verify that the bracket has sufficient perfor-mance in every condition, from the dry and cold winters in the north to thehigh humidity and heat around the equator.

24

2. Theory

• Dimensional changes - The FRP bracket has a higher sensitivity in dimensionalchanges. The dimensions may change due to heat, creep, or moisture.

• Anisotropic behavior - The injection molded FRP’s are orthotropic which im-plies a more complex material model where the fiber orientation must be in-cluded. Aluminum is isotropic and the traditional material modelling can beused.

.

25

3Methods

This chapter aims to describe the analyses performed, the different material modelused for the FRP brackets, as well as the work process to create a material modeldependent on fiber orientation.

3.1 Material ModellingTo create a material dependent on the fiber orientation, additional steps comparedto traditional isotropic material must be performed. These added steps, which wereperformed, to provide the orthotropic material will be described in this section. Aflow chart of the included steps was presented in previous section, see Figure 2.8.

The first step was to predict the fiber orientation from the injection molding process.The analysis of the moldflow was executed in Autodesk Moldflow Insight. The out-put given from the moldflow simulation was the mesh used for moldflow simulations,and an orientation file including orientation tensors for every element, as describedin Section 2.3.1. This mesh is referred to as the donor mesh and the mesh providedin the FEA software is referred to as the receiver mesh. To transfer the informationregarding fiber orientation to the FEA mesh the tool Digimat MAP in the softwareDigimat version 2019.1 was used. The donor mesh, receiver mesh, and the orienta-tion tensor were imported in Digimat MAP to perform the mapping. As describedin Section 2.5.3 there are different mapping techniques available and a comparisonof two most recommenced methods, integration point/node to integration point, andelement to integration point were performed. The comparison aimed to find themethod with the smallest global error and the most accurate mapping of the fiberorientation. From the mapping, a file containing the orientation tensor for the FEAmesh was provided.

To create material properties dependent on the fiber orientation Digimat CAE wasused. The material obtained from the supplier was exported from Digimat MX.The material model used in this thesis was elastic-plastic. The material used was

26

3. Methods

homogenized by MFH, using the Mori-Tanaka model which is based on approxima-tions of Eshelby’s solution. The hybrid solution is used since it is the recommendedsolution according to Digimat and was assumed to be sufficient for the analysesperformed. It was assumed to be sufficient since the analyses were executed on acomposite level and results from separate phases were not needed. The interface se-lected was Abaqus/Standard. The fiber orientation for the FEA created in DigimatMAP was imported to the material analysis in Digimat CAE, and then the analysiswas executed. By running the analysis the material data and hybrid parameterswere obtained and afterward included in the FEA input file.

3.2 Validation of Digimat-Abaqus InterfaceIn order to validate the coupling from Digimat to Abaqus a study of a simple cubewas executed. From the material data equipped from the supplier, stress-straingraphs could be produced in Digimat. The curves available was tension stress andstrain in the fiber direction and normal to the fiber direction as well as stress andstrain for shear.

3.2.1 Process

The orientation file created in Moldflow was modified in order to orient all fibers inthe same direction, the x-direction. The two different orientations for the file areillustrated in Figure 3.1. The mapping and coupling between Digimat and Abaquswere executed as described earlier.

Figure 3.1: Modification of orientation tensor.

3.2.2 Boundary Conditions

Three different analyses were conducted to validate the material behavior. Theboundary conditions for the three load cases are described in the following list and

27

3. Methods

illustrated in Figure 3.2.• Tension in x-direction

– DOF 1-6 locked on one of the x-surfaces.– DOF 2 and 3 locked on the opposite surface in x-direction.– Displacement in DOF 1 on the same surface as in previous item.

• Shear in xz-direction– DOF 1-6 locked on one of x-surface.– DOF 1 and 2 locked on the opposite surface in x-direction.– Displacement in DOF 3 on the same surface as previous item.

• Tension in z-direction– DOF 1-6 locked on one of z-surface.– DOF 1 and 2 locked on the opposite surface in z-direction.– Displacement in DOF 2 on the same surface as in previous item.

(a) Tension in x-direction (b) Shear in xz-direction

(c) Tension in z-direction

Figure 3.2: Boundary conditions for the different load cases for the cube.

28

3. Methods

3.2.3 Validation

The material model was validated by comparing the graphs for stress-strain createdin Digimat with the stress-strain graphs created by plotting the stress-strain values.The stress and strain values were obtained from the center of the cube.

3.3 Component StudyThe components compared in this study were one aluminum bracket and one FRPbracket. The detailed designs of the brackets were different due to the variousmanufacturing methods, but the overall design was the same as well as the attach-ment points. For the FRP bracket, two different material models were compared toidentify the impact of the fiber orientation. A schematic image of the assembly isillustrated in Figure 3.3. In the FRP bracket, aluminum inserts are placed in thescrew holes to make the bracket able to carry the pretension loads. The bracket is,together with the intermediate bracket, attached with screws to the subframe.

Figure 3.3: An schematic illustration of the bracket assembly.

The bushing was removed for the analyses, and to be able to apply the loads inthe bushing, a distributed coupling constrain was created in ANSA. A distributedcoupling constrain creates a reference node, connecting all the nodes in the selectedsurface. The loads can then be applied on the single node, instead of on the wholesurface. The analyses performed for the powertrain mount bracket were static stress-strain analyses and an eigenfrequency analysis.

29

3. Methods

The three different cases that the analyses are performed for are;• The aluminum design with elastic-plastic material properties.• The FRP design with orthotropic elastic-plastic material properties.• The FRP design with isotropic elastic-plastic material properties.

3.3.1 Pre-processing

The geometry was pre-processed in ANSA version 2019.1.1. It was meshed withsolid tetrahedral and mesh quality analysis was run to detect and correct disorderedelements. To prepare the model for the two different analyses, sections and stepswere created, material assigned, contacts created as well as boundary conditionsapplied.

• The boundary condition applied was DOF 1-6 was locked on the intermediatebracket on the surface which faces the subframe.

• The contact condition used for contact between the bracket and the interme-diate bracket as well as between screw heads and the bracket was surface tosurface contact with friction.

• The contact condition between the treads and screws as well as between theinserts and bracket was tie.

• Pretension was applied to the screws.

3.3.2 Material Properties

The materials used for the analyses were the aluminum alloy EN AC-44300 and thepolymer composite PA66-GF35. The supplier for the polymer composite is DuPontand the grade name is Zytel®70G35HSLRA4 BK267. The stress and strain curvesfor the isotropic and orthotropic material model at 23◦C are presented in Figure 3.4and the curves for 60◦C are presented in Figure 3.5. The stress and strain values forthe isotropic material model are obtained from CampusPlastics website [9], and forthe orthotropic material model, the values are derived from the Digimat materialmodel.

30

3. Methods

Figure 3.4: Stress-strain curve for Zytel®70G35HSLRA4 BK267 at 23◦C.

Figure 3.5: Stress-strain curve for Zytel®70G35HSLRA4 BK267 at 60◦C.

3.3.3 Stress-strain Analysis

The static stress-strain analysis was executed for the three cases for the bracket de-scribed previously. The results were compared in order to analyze the strain levelsfor the three cases. Thereafter, conclusions were drawn about how the orthotropicmaterial model affects the component as well as how well the FRP performed incomparison to aluminum. The analyses were performed for two different tempera-tures, 23◦C and 60◦C. The loads in the analyses were applied in the reference nodefor the distributed coupling as described earlier. Six different load cases were inves-tigated and in each load case, one unidirectional positive/negative load was appliedin the reference node. The proportion between the loads are listed in Table 3.1. Theloads which the bracket is optimized for are results from tests of drive events suchas, including dropping the clutch, driving over a curb, and driving at bumpy roads.

31

3. Methods

Table 3.1: The proportion between the applied loads

Positive Negative

x 1.4 −1.4y 1 −1z 2.3 −3.4

To be able to measure if the strength is sufficient and the bracket is able to carry theload without failure a design limit was determined. The design limit was assumed tobe 50% of strain at break. Since the orthotropic material has different strain levelsdepending on orientation, see Figures 3.4 and 3.5, the lowest strain value which is inparallel with fiber orientation was used. Since aluminum is less heat sensitive thanplastics, the strain at break at 60◦C was assumed to be equal to the strain at breakat room temperature.

Table 3.2: Maximum allowed percent of strain according to the design limit

Isotropic Orthotropic Aluminium

23◦C 2.40% 2.24% 0.5%60◦C 3.27% 2.70% 0.5%

3.3.4 Eigenmode Analysis

It is important to analyze the eigenfrequencies of assemblies in order to avoid havingfrequencies too close to the frequencies of the engine. If other assemblies haveeigenfrequencies close to the engines the noise and vibrations caused by the engineare amplified which may result in undesirable noise or damage of the component.In this study, the first three modes are analyzed in order to compare the differencebetween the material models as well as between FRP and aluminum. The analyseswere executed using the Lanczos method in Abaqus.

32

4Results

In this chapter the results of the numerical study are presented. The results includethe material model process and validation as well as results from simulations of thecomponent. The siumlations for the component are eigenmode analyses and staticstress-strain analyses.

4.1 Validation of Digimat-Abaqus InterfaceThe stress-strain results from Abaqus for tension in the direction parallel to fiberorientation for the cube, as well as the stress-strain values obtained in Digimat forthe parallel direction are presented in Figure 4.1.

Figure 4.1: Stress-strain relationship from tension test in the fiber orientation.

The stress-strain results from Abaqus for tension in the direction normal to the fiberorientation for the cube, as well as the stress-strain values obtained in Digimat forthe transverse direction are presented in Figure 4.2.

33

4. Results

Figure 4.2: Stress-strain relationship from tension test normal to the fiber direction.

The stress-strain results for the shear test for the cube in Abaqus, as well as thestress-strain values obtained for shear in Digimat, are presented in Figure 4.3.

Figure 4.3: Stress-strain relationship from shear test.

As presented in Figures 4.1-4.3 of the stress-strain behavior of the material, theresults from Abaqus obtained for the unidirectional cube agrees with the Digimatmaterial output. The shear and tension parallel to fiber direction are almost identicalfor all values while the tension normal to the fiber direction showed deviations athigher strains. The results from the analyses imply that the interface Digimat-Abaqus is sufficient and that the method can be applied for the powertrain mountbracket.

34

4. Results

4.2 Component StudyThis chapter presents the results of the simulations for the bracket with the twodifferent material models for FRP’s as well as the simulations of the aluminumbracket. Additionally, results from investigations regarding mapping techniques forthe bracket are presented.

4.2.1 Mapping

The mapping from the donor mesh to the receiver mesh was for the bracket executedwith two different techniques; integration point/node to integration point, and ele-ment to integration point. The global errors of a11, a22 and a33 of the two methodsare presented in Figure 4.4-4.6. With the global error indicator, it is proven thatthe mapping quality is equivalent but there is small evidence that receiving mesh 1has slightly more equal distribution of oriented element as the donor mesh. Conse-quently, the mapping technique integration point/node to integration point was usedin the component study.

Figure 4.4: Global error for a11. Receiver mesh 1 and receiver mesh 2 are achievedwith mapping technique integration point/node to integration point and element tointegration point, respectively.

35

4. Results

Figure 4.5: Global error for a22. Receiver mesh 1 and receiver mesh 2 are achievedwith mapping technique integration point/node to integration point and element tointegration point, respectively.

Figure 4.6: Global error for a33. Receiver mesh 1 and receiver mesh 2 are achievedwith mapping technique integration point/node to integration point and element tointegration point, respectively

36

4. Results

4.2.2 Stress-strain Analysis

The maximal principal strain was analyzed and compared to the design limit. Theoverall results indicate that the strain peeks in the transition between the ribs andthe screw holes while the aluminum bracket has its peeks at the edges of the screwholes. The strain levels in the aluminum bracket and the FRP bracket with theisotropic material model were below the design limit for all load cases. Since thestrain levels for the FRP bracket with isotropic material properties were below thedesign limit, the limit for the strain was set equal to the orthotropic design limit.Due to this change, the strain levels were easier to compare.

The strain levels in the FRP bracket with the orthotropic material model are abovethe design limit in one load case at 23◦C and two load cases at 60◦C. The criticaldirection is the z-direction which is the direction with the highest applied load. Thestrain results obtained with Abaqus for these three cases are presented in Figure4.7- 4.9.

(a) Orthotropic (b) Isotropic

Figure 4.7: Maximal principal strain for the FRP bracket for load in negative z-direction at 23◦C. The location is at the transition between the ribs and one of thefront screw holes on the bottom surface.

37

4. Results

(a) Orthotropic (b) Isotropic

Figure 4.8: Maximal principal strain for the FRP bracket for load in negative z-direction at 60◦C. The location is at the transition between the ribs and one of thefront screw holes on the bottom surface.

(a) Orthotropic (b) Isotropic

Figure 4.9: Maximal principal strain for the FRP bracket for load in positive z-direction at 60◦C. The location is at the transition between the ribs and one of thefront screw holes on the bottom surface.

38

4. Results

Figure 4.10: Maximal principal strain for the aluminium bracket for load in nega-tive z-direction at 23◦C. The location is the bottom surface of the rear screw hole inthe bracket. The maximum strain is 0.3%.

4.2.3 Eigenmode Analysis

The eigenmode analysis was executed for the aluminum bracket and for the FRPbracket with the two different material models. The frequency of the three firsteigenmodes is presented in Table 4.1.

Table 4.1: Frecuency for three first eigenmodes for the bracket

Isotropic Orthotropic Aluminium

Mode 1 847 Hz 633 Hz 1264 HzMode 2 1061 Hz 787 Hz 1760 HzMode 3 1545 Hz 1084 Hz 3080 Hz

39

5Discussion

This chapter includes discussion regarding the results of the numerical simulationsas well as information obtained in the theory chapter. The discussion also providespossible errors in the modelling of orthotropic materials.

5.1 Material ModellingOne of the objectives of this study was to suggest a method to create a materialmodel depending on the fiber orientation. A method has been suggested but theprocess to create an orthotropic material model is complex and includes several stepswhere errors might occur. The first step in the process is to perform a moldflowsimulation. In the moldflow simulations, it is very important that assumptions aremade correctly and one example is the position of the inlet/inlets. If the position ofthe inlets is modified later in the process, the fiber orientations and weld lines willbe affected [24]. Consequently, simulations performed earlier will be incorrectly andeverything must be redone. Additionally, the fiber orientation provided in moldflowsimulations is not correlated with real moldflow results so the results may vary fromthe actuality.

The second step is to map the fiber orientation as described in Section 2.5.3. Thereare different mapping techniques that will provide various errors when transferringthe fiber orientation between the donor mesh and receiving mesh [30]. To reduce theerror between the meshes, the same mesh could be used for moldflow simulationsand FEA simulation. The risk with using the same mesh for the two separatedsimulations is that the optimal mesh for moldflow is not the optimal mesh for FEA,which may deteriorate the overall results [42]. A better suggestion to decrease theerror could be to reduce the size of the elements in the FEA mesh which will give amore similar mesh. The size of the elements close to the surface is extra important inorder to include the skin-shell-core effect since the skin and shell layers are thin [23],as described deeper in Section 2.3.1. In this study, the element size was uniform inthe whole component as well as the difference between donor and receiving mesh

40

5. Discussion

was quite large. Due to time-limitations, simulations with different kind of mesheswas not executed.

The third step is to connect the fiber orientation to the material and create theorthotropic material to use for the analyses. In this study, the hybrid solution wasused which is the recommenced solution according to Digimat. By analyzing ear-lier studies [43, 44], where Digimat has been used, no remarks that imply that thehybrid solution is insufficient have been found and therefore this step is assumed tonot include errors that significantly affect the results.

Overall, the method investigated in this thesis has potential to be used for cal-culations at the powertrain mount department. However, the method should bevalidated with experimental testing in order to secure the accuracy.

5.2 Material ModelsThe objectives for this thesis included analyzing and comparing the two differentmaterial models, an isotropic which is the traditional way to model injection moldedpolymer composite components, and an orthotropic material model. Several differ-ences have been identified and have been discussed in this subsection.

As seen in Figure 4.7-4.9 the strain levels are higher for the orthotropic materialmodel which agrees with Carlssons [25] study that the material properties for theisotropic material are overestimated. As seen in the stress-strain curves presented inFigure 3.4 and 3.5 the isotropic material behavior closely matches the properties inthe fiber orientation and will therefore provide a stronger component than it really is.

By analyzing the fiber orientation in the areas with the maximal strains, it is proventhat the fiber orientation does not agree with the parallel direction which the designlimit was based on. The diagonal values in the orientation tensor for an elementin the region with highest strains are a11 = 0.62, a22 = 0.15 and a33 = 0.23.Therefore, to be able to take advantage of the fiber orientation, a better designlimit must be developed. To improve the design limit it is recommended to performdifferent physical testing and try to find a relationship. Another method could be toidentify critical areas, investigate the orientation in the areas, and draw conclusionson whether the strength is enough compared to the properties for the orientation.The problem with this method is that it is time-consuming since several areas mightbe critical.

41

5. Discussion

Another advantage of the orthotropic material model is that the weld lines can beincluded [30]. In the bracket for this study, the weld lines were not placed in a crit-ical area and therefore this was not a problem. For other components, the locationof weld lines could be in a critical region and if the isotropic material model is used,there are possible risks that a weld line will not be noticed during simulations.

The frequencies for the eigenmodes for the two material models differ between 25-30% which is a large difference and indicates that the fiber orientation stronglyaffects the frequencies and must be included in the eigenmodes analysis. However,the values obtained for the eigenfrequencies in this study are different from thoseobtained in the vehicle since additional parts in the powertrain mounts will con-tribute with stiffness to the mounting assembly. The overall stiffness for the bracketis overestimated in the isotropic material model since the constant Young’s modu-lus is at the same level as in the fiber orientation, the strongest direction, in theorthotropic material.

The residual stresses were not included in the analyses and by including these stressesthe difference in results may have been even larger since the residual stresses are af-fecting the parts in the same way as applied stresses [27]. By analyzing the residualstresses, warping, and shrinking of the component might have been observed.

By analyzing the results of the two material models it is definitely proven thatassuming isotropic properties have a large impact on final results. By including thefiber orientation and use orthotropic material properties, the results from simulationsare more likely to agree with physical testing. This will lead to time savings andcost reduction since problems can be identified and solved already in the early designphase and therefore avoided to be faced during physical verification.

5.3 Material in BracketSince the current material in the powertrain mount bracket is aluminum, one of theobjective was to compare the aluminum alloy EN AC-44300 and the FRP PA66-GF35. However, the results from the stress-strain analyses and the eigenmode anal-yses have been difficult to compare due to different designs. The design for the FRPbracket is currently in an earlier stage than the design for the aluminum bracket.The FRP-results discussed in this section are referring to the orthotropic materialmodel since it is assumed to have higher reliability than the isotropic material model.

42

5. Discussion

When comparing the locations for maximum strain in the aluminum bracket withthe FRP bracket, the locations differ. The aluminum bracket has its maximumstrains located around the screw holes, where the screws are in contact with thebracket, and the maximum strain levels for the FRP brackets are located on thebottom side of the bracket in the radius between the ribs and the screw hole. Inaddition to this, the aluminum bracket has a higher margin of safety against failure.In the aluminum bracket, the stress-strain levels are only increased slightly com-pared between pretension applied only and when loads are applied as well. This,in combination with the low strain levels, indicates that the aluminum bracket isover-dimension against the static loads. The design optimization of the aluminumbracket is based on the requirements from NVH. As discussed in Section 5.2, thestrain levels in the FRP bracket exceeds the design limit, but since the fiber orienta-tion in the critical areas is less oriented than assumed in the design limit, the areasmay still have sufficient strength.

There is a large difference in frequencies for the first eigenmodes between the twomaterials. These large differences were expected due to various designs as well as thehigher stiffness in the aluminum [10]. The comparison of the frequencies is thereforedeficient. However, the overall stiffness in the aluminum bracket is higher which isbeneficial for the application. On the other hand, the damping in the FRP bracketis higher [20], and therefore vibrations could be canceled more efficiently within thebracket and less stiffness would be needed. Depending on how large the dampingeffect from the viscoelastic-viscoplastic behavior is, the stiffness could still be suffi-cient. Further investigations regarding damping are needed to be able to confirm orreject this statement.

43

6Conclusions

This thesis included investigations regarding FRP as a substitute for aluminum ina powertrain mount bracket. Comparisons in terms of stress-strain analyses and aneigenfrequency analysis was executed, as well as a literature study of FRP’s. Fur-ther for the FRP’s, the stress-strain analysis, as well as the eigenfrequency analysis,was performed with both isotropic and orthotropic material properties. In order toperform the analysis with orthotropic material properties, a method to provide anorthotropic material model was suggested.

The conclusions drawn from the investigations are that;• FRP’s has the potential to serve as a substitute for aluminum in the bracket,

but further investigations are needed.• The main advantages of FRP’s are decreased weight, cost, and carbon footprint

as well as improved NVH.• The main disadvantages of FRP’s are the complex material behavior as well

as lack of knowledge and experience for FRP’s compared to aluminum.• The isotropic material model for FRP’s has higher overall strength and stiffness

compared to the orthotropic material model.• The orthotropic material model for FRP’s is more likely to agree with exper-

imental testing than the isotropic material model.• A better design limit which includes the orthotropic behavior must be devel-

oped.

44

7Future Work

In order to implement FRP’s in the brackets in powertrain mount, several additionalinvestigations are needed. The investigation of orthotropic material must be furtherdeveloped. Validation of the method to create an orthotropic material model mustbe validated and a suggestion is to perform physical testing. A major factor thatmust be developed to fulfill the method is a better design limit which takes the fiberorientation into account. Another factor to improve in the process is the mapping.The element size should be smaller for the receiving mesh in order to decrease theloss of information regarding i.e. the ’skin-shell-core’ structure.

The residual stress was not included in this study and thus it is not clear how largethe effect of these stresses is. Thereby, additionally, analysis including the residualstresses should be performed.

The study performed is only regarding the static strength of FRP’s and thereforethe material model is elastic-plastic. A material model that includes viscoelastic-viscoplastic behavior must be developed to be able to investigate i.e creep, fatigue,and damping of the component.

Suggestions for further work is to develop a design limit to orthotropic materialmodels, validate the work processes provided as well as to provide methods forcreep, fatigue, and damping. It is also important to perform investigations on howto include the effects of moisture and aging.

45

Bibliography

[1] Jacob A. Daimler replaces aluminium engine support with composite in Merced-ers GL Class. Materials Today [Internet]. 6 March 2013 [cited 2020 March 13];Available from: https://www.materialstoday.com/composite-applications/news/daimler-replaces-aluminium-engine-support-with/.

[2] Klars H. Powertrain Mounts System School. Unpublished. 2019.

[3] Invista. A Perfect Balance of Properties [Internet]. Invista; c 2019 [date un-known; cited 2020-04-23]. Available from: https://www.invista.com/pa66.

[4] Rajak D.K, Pagar D.D, Menezes L.P, Linul. Fiber-Reinforced PolymerComposites: Manufacturing, Properties, and Applications. Polymers. 2019;11(10):1667. doi: 10.3390/polym11101667.

[5] Chebbi E, Mars J, Dammark. Fatigue Behaviour of Short Glass Fiber Re-inforced Polyamide 66: Experimental Study and Fatigue Damage Mod-elling. Periodica Polytechnica Mechanical Engineering. 2016;60(4):247-255. doi:10.3311/PPme.9054.

[6] Taha I, Abdin F.Y. Modeling of strength and stiffness of short randomly ori-ented glass fiber-polypropylene composite. Journal of Composite Materials.2011;45(17):1805-1821. doi: 10.1177/0021998310389089.

[7] Thomason L.J. Micromechanical parameters from macromechanical measure-ments on glass reinforced polyamide 6,6. Composites Science and Technology.2001;61(14):2007-2016. doi: 10.1016/S0266-3538(01)00062-8.

[8] Klason C, Kubát J. Plaster - Materialval och Materialdata. Stockholm: Indus-trilitteratur; 2006.

[9] CAMPUS. Zytel 70G35HSLRA4 BK267 [Internet]. Frankfurt am Main:CAMPUS; 2020 [updated date unknown; cited 2020-02-28]. Availablefrom: https://www.campusplastics.com/campus/en/datasheet/Zytel%C2%AE+70G35HSLRA4+BK267/DuPont/52/809327f4/SI?pos=62.

46

Bibliography

[10] CES_EduPack_software, 2019. Granta Design Limited. www.grantadesign.com: Cambridge, UK.

[11] Grellmann W, Bierögel C. Polymer Solids and Polymer Melts–Mechanical andThermomechanical Properties of Polymers. Springer-Verlag Berlin and Heidel-berg GmbH Co. K; 2014. Chapter 4.5, Fatigue loading of plastics; 281-286. doi:10.1007/978-3-642-55166-6_47.

[12] Bellenger V, Tcharkhtchi A, Castaing P. Thermal and mechanical fa-tigue of a PA66/glass fibers composite material. Comptes Rendus Chimie.2006;28(10):1348-1352. doi: 10.1016/j.ijfatigue.2006.02.031.

[13] McCrum N.G, Buckley C.P, Bucknall C.B. Principles of Polymer Engineering.Oxford: Oxford University Press; 1996.

[14] McKeen W.L. Effect of Creep and other Time Related Factors on Plastics andElastomers. 3 ed. Norwich: William Andrew; 2014.

[15] White R.J. Polymer ageing: physics, chemistry or engineering? Timeto reflect. Comptes Rendus Chimie. 2006;9(11-12):1396-1408. doi:10.1016/j.crci.2006.07.008.

[16] Rivin I.E. Stiffness, Damping in Mechanical Design. New York, and Inc; 1999Basel: Marcel Dekker.

[17] Fayed S, Göken J, Schäfer H, Enzenauer J. A Study on the Correlation betweenWood Moisture and the Damping Behaviour of the Tonewood Spruce. ActaPhysica Polonica A. 2018;133(5). doi: 10.12693/APhysPolA.133.1241.

[18] Chandra R, Singh S P, Gupta K. Damping studies in fiber-reinforced composites- a review. Indian Institute of Technology. New Delhi; 1999.

[19] Jesson A.D, Watts F.J. The Interface and Interphase in Polymer Matrix Com-posites: Effect on Mechanical Properties and Methods for Identification. Poly-mer Reviews. 2012;52(3):321-354. doi: 10.1080/15583724.2012.710288.

[20] Bykowski S, Karkosch H, Schneider D, ContiTech, Klink H, Lambi M.N. HighPerformance Plastic Component for Engine Mount Application. 2008.

[21] Omnexus. Water Absorption 24 hours [Internet] c 2020 [updated date un-known; cited 2020-02-26]. Available from: https://omnexus.specialchem.com/polymer-properties/properties/water-absorption-24-hours.

[22] Bernasconi A, Cosmi F, Dreossi D. Local anisotropy analysis of injectionmolded fibre reinforced polymer composites. Composite Science and Technol-ogy. 2008;68(12):2574-2581. doi: 10.1016/j.compscitech.2008.05.022.

47

Bibliography

[23] Rolland H, Saintier N, Robert G. Fatigue Mechanisms Description in ShortGlass Fibre Reinforced Thermoplastic By Microtomographic Obeservartions.2015.

[24] Shaharuddin S.I.S, Salit S.M, Zaindudin S.E. A review of the effect of mould-ing parameters on the performance of polymeric composite injection moulding.Turkish J. Eng. Env. Sci. 2006;30:23-34.

[25] Carlsson J. Coupling of Injection Moulding process to stress analysis ofshort fibre composite structures [master’s thesis on the Internet]. Gothenburg.Chalmers University of Technology. 2012 [cited 2020 March 7]. Available from:https://hdl.handle.net/20.500.12380/160322.

[26] Advani G.S, Hsiao K-T. Manufacturing Techniques for Polymer Matrix Com-posites (PMCs). Philadelphia, Pennsylvania: Woodhead Publishing; 2012.

[27] Guevara-Morales A, Figueroa-López U. Residual stresses in injection moldedproducts. Journal of Materials Science. 2014;46:4399-4415. doi: 10.1007/s10853-014-8170-y.

[28] Gudmundson P. Material Mechanics. Stockholm: Department of Solid Mechan-ics, KTH Engineering Sciences; 2006.

[29] Kulkarni A, Aswini N, Dandekar R. C, Makhe S. Modeling of short fiber rein-forced injection moulded composite. IOP Conf. Ser.: Material. Sci. Eng. 2012;40. doi: 10.1088/1757-899X/40/1/012025.

[30] e-Xstream Engineering. Digimat user’s manual 2019.1. Mont-Saint-Guibert.2019.

[31] Volvo Car Corporation. Sustainability [Internet]. Volvo Car Corpora-tion; 2020[cited 2020-03-04]. Available from: https://group.volvocars.com/sustainability.

[32] Interview with L. Petersson, Senior Expert in Environmental Strategy at VolvoCars. 2020-02-28, Gothenburg.

[33] Brehmer B. Biopolyamides: Durable and Eco-Friendly. Kunststoffe interna-tional. 2012; 2012(3): 39-41.

[34] Bio-based News. New grades of polyamide based on naturally oc-curring feedstocks [Internet]. Bio-based News; 2011 [Updated 2011-06-14; cited 2020-03-05]. Available from: http://news.bio-based.eu/new-grades-of-polyamide-based-on-naturally-occurring-feedstocks/.

48

Bibliography

[35] European Bioplastics. Are bioplastics more expensive then conventional plas-tics? [Internet]. Berlin: European Bioplastics; 2016 [uppdated 2016-03-02; cited2020-03-03] Available from: https://www.european-bioplastics.org/faq-items/how-are-costs-for-bioplastics-developing/.

[36] Knoema. Crude Oil Price Forecast: 2020, 2021 and LongTerm to 2030 [Internet]. Knoema; 2020 [updated 2020-04-22;cited 2020-04-28]. Available from: https://knoema.com/yxptpab/crude-oil-price-forecast-2020-2021-and-long-term-to-2030.

[37] U.S Energy Information Administration. Chinese coal-fired electricity gener-ation expected to flatten as mix shifts to renewables [Internet]. WashingtonDC: U.S. Energy Information Administration; 2017 [updated 2017-09-27; cited2020-03-04]. Available from: https://www.eia.gov/todayinenergy/detail.php?id=33092.

[38] Renewables ‘dominate’ European energy mix in 2019. reNEWS [Internet]. 14January 2020 [cited 2020-03-04]; Available from: https://renews.biz/57378/renewables-dominate-european-energy-mix-in-2019/.

[39] European Aluminium. Vision 2050 - European aluminium’s contribution to theEU’s med-century low-carbon roadmap. Brussels: European Aluminium; 2019.[cited 2020 April 29]. Available from https://www.european-aluminium.eu/media/2552/sample_executive-summary-vision-2050_web_pages_20190408.pdf.

[40] Alupro. Why is recycling aluminium so important? [Internet]. Redditch:Alupro; date unkown [cited 2020-05-05]. Available from: https://alupro.org.uk/consumers/why-is-recycling-aluminium-so-important/.

[41] Emissionsfaktorer i GHG-rappotering. Internal Report VCC. 2019.

[42] Andreasson E, Persson L, Jacobsson H, Nordgren J. Integrating Moldflow andAbaqus in the Package Simulation Workflow. 2013.

[43] Lindhult, J-A. Ljungberg M. Fatigue analysis of anisotropic short fibre rein-forced polymers - by use of Digimat and nCode DesignLife [master’s thesis onthe Internet]. Gothenburg. Chalmers University of Technology. 2015 [cited 2020April 7]. Available from: https://hdl.handle.net/20.500.12380/218633.

[44] Landervik M, Jergeus J. Digimat Material Model for Short Fiber ReinforcedPlastics at Volvo Car Corporation. 2015.

49