PLA COMPOSITE AFTER ENDURING A RADIAL BENDING ...

Gabriel Camilo Vásquez Gutiérrez | Edgar A. Marañón

UNIVERSIDAD

DE LOS

ANDES

A STUDY OF THE ELASTIC RECOVERY OF MANICARIA SACCIFERA/ PLA COMPOSITE AFTER ENDURING A RADIAL BENDING CONFORMATION

PROCESS

A STUDY OF THE ELASTIC RECOVERY OF MANICARIA

SACCIFERA/ PLA COMPOSITE AFTER ENDURING A RADIAL

BENDING CONFORMATION PROCESS

Author

Gabriel Camilo Vásquez Gutiérrez

201024131

Graduation Project Advisor

Edgar A. Marañón

Bogotá - Colombia

Special Regards…

I want to thank my parents for their support, for coming with me this long way and to the end. I want to thank professor Marañon for being a great mentor and believing in me and my ideas. I want to thank Alicia Porras for all the companionship and advice given to make this possible. And last, but not least, I want to thank God for giving me the opportunity and the strength of achieving this goal in my life.

CONTENT TABLE ................................................................................................................................................................. 0

1. INTRODUCTION .................................................................................................................. 1

2. JUSTIFICATION................................................................................................................... 2

3. OBJECTIVES ....................................................................................................................... 3

Main........................................................................................................................................................... 3

Secondary .................................................................................................................................................. 3

4. STATE OF THE ART ........................................................................................................... 3

Manufacturing Process and Specifications ............................................................................................... 6

Thermal Characterization .......................................................................................................................... 8

Mechanical Properties............................................................................................................................... 9

The ICAD Concept .................................................................................................................................... 10

5. METHODOLOGY ............................................................................................................... 11

Case of Study ........................................................................................................................................... 11

Experimental Protocol ............................................................................................................................. 13

Experimental Instrumentation ................................................................................................................ 15

Data Definition ........................................................................................................................................ 22

Data Retrieving ........................................................................................................................................ 23

Other Data Parameters ........................................................................................................................... 25

Data Analysis Method ............................................................................................................................. 26

7. RESULTS .......................................................................................................................... 29

Main Results Tables ................................................................................................................................... 0

Main Results - Graphs ............................................................................................................................... 3

8. ANALYSIS............................................................................................................................ 0

Estimation Equations ................................................................................................................................. 5

9. CONCLUSIONS ................................................................................................................... 8

10. RECOMMENDATIONS AND FUTURE WORK ................................................................. 8

11. REFERENCES ................................................................................................................. 9

FIGURES & TABLES INDEX

Figure 1: Manicaria Saccifera distribution in America ................................................................................................... 2

Figure 2:Classification of composites on raw materials and processing techniques ...................................................... 4

Figure 3: Manicaria Saccifera Palm and Component Illustrations ................................................................................. 5

Figure 4: Raw materials to fabricate MS/PLA Laminae ................................................................................................. 6

Figure 5: Preprocessing steps to manufacture the MS/PLA Compound ......................................................................... 6

Figure 6: Processing the lamina of MS/PLA ................................................................................................................... 7

Figure 7: MS/PLA Finished Lamina ................................................................................................................................. 8

Figure 8: Main Coupon Configuration Patterns ............................................................................................................. 9

Figure 9: ICAD Concept ................................................................................................................................................. 10

Figure 10: ICAD sketched modus operandi ................................................................................................................... 10

Figure 11: ICAD Blue Print 1 ......................................................................................................................................... 11



Figure 14: Length Angle & Radius Convention ............................................................................................................. 12

Figure 15: Sketch of the general experimental protocol .............................................................................................. 13

Figure 16:Scope of the general Process........................................................................................................................ 13

Figure 17:INSTRON Cat. 2716-010 ............................................................................................................................... 14

Figure 18: Instruments used (among others) IR Thermometer (left), Oven (center) and thermocouple for

temperature control of the oven (right) ....................................................................................................................... 15

Figure 19: Bulk bar cross section; 1m length ................................................................................................................ 16

Figure 20: Coupon sizes ................................................................................................................................................ 22

Figure 21: Sketch of the measure method ................................................................................................................... 23

Figure 22: Coupon Mark Convention Example: Right – 60°C, Configuration 1, 1 Cluster, Parallel, Coupon 1 Left –

100°C, Configuration 3, 2 Clusters, Perpendicular, Coupon 1 ...................................................................................... 23

Figure 23: Demonstration of the measurements ......................................................................................................... 24

Figure 24: Radius geometrical relationship .................................................................................................................. 24

Figure 25: Trapezoid Rule - Integral Approximation Method ....................................................................................... 25

Figure 26: Simply supported beam deflection sketch ................................................................................................... 25

Figure 27: Examples of invalid coupon data ................................................................................................................ 28

Figure 28: Color Convention for Coupon Superficial Analysis ....................................................................................... 29

Figure 29: Picture of Coupon Results............................................................................................................................ 29

Figure 30: Color Pattern on Temperatures ..................................................................................................................... 0

Figure 31: Sketch of the behavior of the material under the hot-press method ............................................................ 1

Table 1: PLA Thermal Properties ........................................................................................................................................................ 8

Table 2: Specific Mechanical Properties of PLA and MS/PLA Composite ............................................................................................ 9

Table 3: Measured and selected values for experimental coupons .................................................................................................. 12

Table 4: General Process step by step .............................................................................................................................................. 14

Table 5: Experimental reference variables ....................................................................................................................................... 15

Table 6: Selected Experimental Conditions ....................................................................................................................................... 16

Table 7: Variable Combination Datasheet for each Configuration ................................................................................................... 22

Table 8: Coupon numbers and Lot distribution ................................................................................................................................. 22

Table 9: Pi theorem Variables........................................................................................................................................................... 26

Table 10: Repeated Variables Selected............................................................................................................................................. 26

Table 11: Terms for each Combination Group .................................................................................................................................. 28

Table 12: Datasheet 1 - General Geometrical Properties and Radii Changes ..................................................................................... 0

Table 13: Datasheet 2 – Complete Data Compilation for the Pi Variables – 60°C Coupons ............................................................... 0

Table 14: Datasheet 3 - Complete Data Compilation for the Pi Variables – 100°C Coupons .............................................................. 1

Table 15: Datasheet 4 - Complete Data Compilation for the Pi Variables – 150°C Coupon ................................................................ 2

Table 16: P1 Estimation Equations Summary ..................................................................................................................................... 5



Blue Print 1: Configuration 1 - Female Mold .................................................................................................................................... 17

Blue Print 2: Configuration 1 - Male Mold 1 Cluster ......................................................................................................................... 17

Blue Print 3: Configuration 1 - Male Mold 2 Clusters ....................................................................................................................... 18


Blue Print 5: Configuration 2 - Male Mold 1 Cluster ......................................................................................................................... 19



Blue Print 8: Configuration 3 - Male Mold 1 Cluster ........................................................................................................................ 20


Graph 1: P1 -Full Pi Terms - Pi Group 1 – Parallel - Logarithmic Function Adjustment ....................................................................... 3

Graph 2: P1 - Full Pi Terms - Pi Group 1 – Perpendicular - Logarithmic Function Adjustment ............................................................ 3

Graph 3: P1 - Full Pi Terms - Pi Group 2 – Parallel - Logarithmic Function Adjustment ...................................................................... 4






Graph 9: P1 - No Pi 1 Term - Pi Group 1 – Parallel - Power Function Adjustment .............................................................................. 7

Graph 10: P1 - No Pi 1 Term - Pi Group 1 – Perpendicular - Power Function Adjustment .................................................................. 7

Graph 11: P1 - No Pi 1 Term - Pi Group 2 – Parallel - Power Function Adjustment ............................................................................ 8


Graph 13: P1 - No Pi 1 Term - Pi Group 3 – Parallel - Power Function Adjustment ............................................................................ 9


Graph 15: P1 - No Pi 1 Term - Pi Group 4 – Parallel - Power Function Adjustment .......................................................................... 10

Graph 16: P1 - No Pi 1 Term - Pi Group 4 – Perpendicular - Logarithmic Power Adjustment ........................................................... 10


Graph 18: P2 - No Pi 1 Term - Pi Group 1 – Perpendicular - Power Function Adjustment ................................................................ 11















Graph 33: P1 Measure Estimation Function - Parallel Orientation ..................................................................................................... 2

Graph 34: P1 Measure Estimation Function - Perpendicular Orientation........................................................................................... 2





ABREVIATIONS AND SYMBOLS

ICAD (Infant Carrier Assistant Device)

MS (Manicaria Saccifera)

PLA (Poly Lactic Acid)

MS/PLA cluster (Arrange of PLA – MS – MS – PLA)

Radius (λ)

Length Angle (β)

Pre-Heating Temperature (φ)

Compression Extension (μ)

Push Force (σ)

Cooling time (ζ)

Delta First Measure (∆1)

Delta Second Measure (∆2)

Delta Third Measure (∆3)

Specific Length (𝐿𝑜)

Initial Radius (𝑅𝑜)

Final Radius (𝑅𝑓)

Thickness (𝐻)

Width (𝑤)

Sagitta (𝑆)

Inertia (𝐼)

Conforming Time (𝑡𝑐)

Compression Time (𝑡𝑚)

Mass (𝑚)

Young (Elasticity) Modulus (𝐸)

Work (𝑈)

ABSTRACT

MS/PLA composite laminae a material that integrates a polymeric matrix and the natural fiber of

Cabecinegro palm, which has been proven to have good mechanical properties and promising

industrial applications. To be able to use it on an actual commercial or industrial application, tests

must be carried on to examine its behavior under different conditions, and more importantly, study

how it can be formed into final products through various kinds of processes.

This project studies how the MS/PLA composite laminae react to conformation process by hot-

pressing it under certain temperature, velocity and force conditions, in order to characterize its

elastic recuperation and try to predict statistically the final radius that will take after enduring the

process. Given the fact that there is no specialized literature that states a standard for this kind of

test, a method was developed to attend this need. Molds were specially designed, taking the

dimensions and geometries from the ICAD concept (particular product), from which the results will

be drawn to fit similar shapes. Coupons were designed too to fit the molds and to represent a wide

population, so that the conclusions that might come out are robust and well supported.

To analyze the complete set of information that came out from testing all the coupons, the

Buckingham Pi Theorem was used, including all the variables that were encountered that had any

relation on the procedure, that were measurable or could be controlled. With this analysis, the

data was compiled on graphs and the best describing function of the dispersion could be found,

describing a model that envelopes a range of parameters and concludes about some others that

can be the base line to find the optimal solution to apply this method.

1. INTRODUCTION

The study and development of new materials takes place continuously on the industry and

research fields, where the need to create better parts or products to a given application drives the

efforts to experiment with resources though rather odd for engineering purposes in other times.

Manicaria Saccifera (MS), also known as Palma Cabecinegro, is a palm tree found on the Pacific

Low Lands in Colombia (among other locations) that counts many uses1, is increasingly

demanded for its artisanal handcrafts uses and recently, for its engineering applications as a

composite natural fiber.

As stated before, more demanding applications require better performing materials, and

composite materials are continuously studied to not just improve their performance and have a

whole lot of applications in aircraft, military and spacecraft specialized uses2, but to actually make

them able to be produced industrially and available massively, other fabrication methods and

manufacturing techniques must be taken in place to know the drawbacks and benefits they might

bring to the final outcome on the final product.

One of these thriving new materials that is being recently studied is the product composite of the

novel natural fabric extracted from the penducular bract of the Manicaria Saccifera palm as a

reinforcement and Poly-Lactic Acid (PLA) sheets serving as matrix to it3 . This composite has been

studied on standard conditions targeting to find optimal conditions on laminated coupons,

attending to various factors and conditions that include chemical treatment concentrations and

times, compression molding temperature, pressure and time and fiber orientation and weight

ratio4; based mainly on the findings of this study and supporting literature on the topic, the goal of

this project is to replicate the conditions of an optimally constructed lamina that will serve as raw

material to a posterior manufacturing process: Heated Conforming5.

Although conformation processes are widely used across many industries, composite materials

are not well known for their flexibility under this particular method, in fact, natural fibers tend to be

even more challenging due to their maximum permitted working temperatures in order to keep

them from degrading6 and they don’t tend to be as ductile as pure polymers; never the less, once

the limitations have been overcome, mass produced laminae might be utilized as prime material

to fabricate other specialized goods that include more complex shapes and retain most of the

physical and mechanical properties exhibited under laboratory conditions.

For this analysis, the ICAD (Infant Carrier Assistant Device)7 concept will be taken as the template

that will guide the forms, shapes and sizes of the experimental procedures, from which the

conclusions will be drawn, following a specific examination pattern to extrapolate the results to

imply possible use of these procedures on similar products based on the MS.

1 (Renteria, 2011) 2 (Mallick, 2008), Ch. 1 3 (A. Porras, 2016) 4 (A. Porras, 2016) 5 (LEONG, 2014) 6 (LEONG, 2014), Ch. 8.2 7

2. JUSTIFICATION

The progress and study of these kinds of materials that utilize natural resources in such a direct

way has impacts in many levels that range from obvious environmental matters, to some that are

much more difficult to measure, like anthropological ones. MS is for instance one of the most used

on the pacific lowlands in Colombia, not just for the bracts but for other parts of the tree8; In fact,

this specie has been used historically for food, construction, artisanal and even medicinal

purposes in the region it’s found, meaning it has great importance between its population and of

course, its economy.

Correctly improving the usage of this resource might be a good way to bring benefits both

engineering and economical wise, which means the people involved on the supply chain can be

benefited too, by creating more demand on the raw materials, more jobs and more invest capital

on the topic, bringing development to a region that is far behind its full potential.

It is also important to highlight the importance of sustainable harvesting. Taking into account that

this palm has a very specific habitat and that there are no current “crop sites” the correct handling

and extraction of the materials is vital. The tree takes around two years to completely grow as an

adult and can give away material each three months; it requires relatively low soil qualities and

grows on swampy areas that get flooded regularly9. This information can serve as reference to an

overall view of how could an eventual arranged crop be made, which could facilitate mass

production and protect the species from over usage and harming the environment.

Covering all of these matters, the new findings that can bring this study and further studies on the

subject, can be one of the cornerstones that support a bigger and better ways to take advantage

of the natural resources given to this particularly diverse region and others that might too harvest

it, using state of art engineering and pushing beyond conventional methods by introducing a new

competent sustainable material.

Figure 1: Manicaria Saccifera distribution in America10

8 (Renteria, 2011) 9 (Artesanias de Colombia, n.d.) 10 (Renteria, 2011), Ch. 2

3. OBJECTIVES

Main To study the conforming process by hot pressing Manicaria Saccifera/PLA laminae on rounded

shapes taken from the ICAD concept and determine the effects temperature, force, and time,

elasticity modulus and work, in addition to the specific characteristics of the laminae such as

thickness, length, width and fabric orientation, have on the output radius that can be formed.

Secondary Identify the main radii associated with the ICAD concept

Create a protocol to test the different configurations

Evaluate the finishing features after the process and how affected they are with it

Measure the material´s capacity of keeping the given mold shape

Examine the delamination that may occur on the coupons

Determine the factors that drive the conformation process on the material

Analyze the experimental results to check behavior tendencies and correlations

Draw conclusions that generalize may serve future investigations on the topic

4. STATE OF THE ART

The capacity to transform raw materials to finished products in the most efficient way, while

procuring optimal performance and replicability is one of the main concerns in modern production

industries. Regarding conforming processes, many studies have been carried on and the results

have been implemented worldwide, focusing most efforts on metallic materials for hundreds and

even thousands of years. On the other hand, composite materials have other sort of properties

that make them different to work with and taking into account their relatively novelty – the first

engineering composites date from around mid-20th century and the space era11 – the development

and understanding level has come a long way but is still a vast topic to explore.

Between the many kinds of composite materials, from which the most commonly known is perhaps the glass fiber for being one of the primogenitors of this family of materials, there are currently hundreds of possibilities parting from the mere definition of a composite material, meaning that the limit is somewhere between the plausibility of combining a matrix with a reinforcement material; here, on the reinforcement material category, is where the natural fibers come. Quoting J. Summer scales and S. Grove from Plymouth University (UK)

“Natural fibers may be sourced from animals (e.g. hair, silk, wool), minerals (e.g. asbestos, basalt) or plants (e.g. leaf, seed, stem). … Plant fibers can be categorized according to where

they are located in the plant. The principal divisions are bast (from the stem, e.g. flax, hemp and nettle in temperate zones or jute and kenaf in tropical zones), leaf (e.g. abaca, pineapple or

sisal), grasses (e.g. bamboo, miscanthus or wheat straw), seeds (e.g. coir or cotton) or wood fibers. All these fibers find application as the reinforcement for composites 12”

11 (Overview, 2002) 12 (GROVE)

Natural fiber reinforced matrix composites are now a day a study subject that is opening its way

on the processing and manufacturing industries, making these new generation materials more

desirable on different applications. Even though there are a wide lot of plants to choose from, most

research has been published on few fiber types which include flax, sisal, jute, hemp, bamboo,

kenaf and ramie, testing their physical/chemical properties and performance.

Figure 2:Classification of composites on raw materials and processing techniques13

13 (Sanjay K. Mazumdar, 2002), Fig. 1.5 & 2.1

Beyond the fabric type, the matrix material selected to accompany the set of properties is also a

main concern. In order for them to “fit together” to form a competent composite material, they have

to bond correctly, meaning that they have to be physically and chemically compatible – or endure

a treatment that make it so. Figure 3 shows the difference on the processing methods depending

on the nature of the matrix, whether it’s a thermoset (materials once cured cannot be re melted or

reformed) or a thermoplastic (ductile and tougher than thermosets and can be melted by heating

and solidified by cooling). As can be seen, manufacturing processes considerably change in

function of the matrix, the length of the fabric and the point the raw material is taken.

Figure 3: Manicaria Saccifera Palm and Component Illustrations14

The subject of study regarding this project is as stated before, a compound material made up by

the woven fabric obtained from the bracts of the palm tree known as Manicaria Saccifera and PLA

sheets, arranged in a certain configuration and hot pressed to form laminae with wood like

consistency and looks, but with very specific and high value engineering capabilities. Figure 4

shows the palm tree on its habitat and the components that can be taken from it to form into

various artisanal goods; the bract is shown on the right enclosed on the red frame. Figure 5 on

the other hand, shows the raw material ready to go through the manufacturing process – PLA is

extruded from pellets to rolled sheets of a given thickness and the MS fabrics are cut into the

dimensions needed to make the materials fit together.

14 (Palmpedia, 2016)

Figure 4: Raw materials to fabricate MS/PLA Laminae

As has already been pointed out, this specific compound material has not been widely studied,

which means that literature regarding ways to work with it is very limited. Founded on this, the

main source of knowledge to stablish ground base will be the previous works and foundlings on

the topic developed by A. Porras, A. Maranon and I.A. Ashcroft on their joint investigation papers

on the matter15. Between the many discoveries made on the subject, what needs to be highlighted

to reach the end of this investigation are the manufacturing process and specifications to reach

optimal conditions, the thermal characterization and properties and the expected mechanical

properties to conduct a comparative analysis.

Manufacturing Process and Specifications The fabrication process can be deconstructed on a step chain with little variations depending on

the wanted outcome thickness of the lamina. The preprocessing process is depicted on Figure 6;

these steps are crucial to make sure the final outcome is of the quality expected.

Figure 5: Preprocessing steps to manufacture the MS/PLA Compound

15 (A. Porras, 2016)

Step 1 consists on dimensioning both materials to an adjusted size, making rectangular sheets

with equal X & Y lengths as good as possible – MS fabric may be difficult to work with, for its

nature is not completely rectangular. After enough material has been sorted out, the sheets must

be dried to take away the humidity of both the MS and PLA; this is done by arranging the sheets

(separately!) as shown in step 2, where the aluminum sheets serve as separators to each layer

and the steel plates seal the arrangement into two flat surfaces evenly. Step 3 consists on the

drying course; the ‘sandwich’ prepared on step 2 is taken to a preheated oven at 110°C for at least

an hour. This complete preprocessing layout will result on the flattened and fully ready raw

materials to start the actual hot pressing process

.

Figure 6: Processing the lamina of MS/PLA

Figure 7 shows the continuation leading to the final processing stage. On the first place, the dried

sheets of PLA and MS are arranged as shown in step 1, making layers on the following order:

PLA – MS – MS – PLA. The patter is that that will always leave two layers of MS together and

between two layers of PLA, and will always start and end with this last one, for future reference

and ease one of these arrangements will be called a MS/PLA cluster. The Teflon layers are used

to avoid sticking the polymer to the pressing surface and again, the metal plates are used to make

even both contact surfaces.

The new ‘sandwich’ is now taken to a preheated hot press machine at 190°C, laying it evenly

distributed under its surfaces. Before fully pressing, a venting procedure must be made; step 2

illustrates it, the plates are closed and a pressure Po – No bigger than 2000psi (1.38 ∙ 107Pa)- is

applied for around 30 seconds and then loosened, repeating this at least 6 times per MS/PLA

cluster. Once the venting is done, the actual compression can begin; step 3 shows the pressing

machine impressing force evenly on both surfaces to create a pressure P between 7500psi (5.17∙

107Pa) and 8000psi (5.51∙ 107Pa) for 8 minutes at the same constant temperature. After keeping

these conditions, the press must be cooled down but the pressure must be kept still until the

temperature reaches at least 40°C.

Following methodically this steps, the outcome will be a lamina that can be now be used for plank

like purposes. It must be lightly machined to make the borders even and clean cut to any given

size required. Figure 8 shows a photograph of the final outcome.

Figure 7: MS/PLA Finished Lamina

Thermal Characterization The main thermal concerns regarding the material on the further process to be studied are linked

to the maximum working temperatures to prevent degradation of any of the components and the

lower limit to start the study. The findings given by the studies consulted show that linked to the

100°C limit is a loss of weight due to the evaporation of the moisture absorbed by the lamina and

at 220°C the degradation of the natural fiber starts to occur by the decomposition of hemicellulose.

On the other hand, the PLA has other set of thermal properties that must be checked out to stablish

a proper working window of temperatures. Figure 9 conceals these properties.

The conclusion regarding the combination of these materials is a quoted “…the degradation of the

MS/PLA composite started at lower temperature than the PLA but at higher temperature than MS

fabric, an important issue to identify the processing limits and operating temperatures of the

composite”16 which means that the process temperature being seek must be between these

values.

Table 1: PLA Thermal Properties17

16 (A. Porras, 2016), Ch. 3.1 Thermal Properties 17 (Material Property Data, 2016)

For instance, the melting point of the matrix polymer is above 110°C, but as the objective of the

study is to deform to a given shape rather than completely deconstruct the laminae, a more

interesting property might be the deflection temperature, defined as “the temperature at which a

standard test bar deflects a specified distance under a load” by the ASTM D648, ISO 7518. As can

be seen in Figure 9, the 50°C is a lower limit to begin with, and given the fact that the compound

enhances the final thermal properties, the expected working temperature must be above this one.

Mechanical Properties Given that the material studied is a highly non-isotropic material due to the dependence of the

orientation of the fibers, this characteristic is fundamental to the characterization made to any

coupon on tensile and flexure analysis.

Figure 8: Main Coupon Configuration Patterns

As shown in figure 10, there will be considered two main configurations of the fabric, both coming

from the same unidirectional pattern lamina. The parallel configuration takes the fabric along and

uses longer stripes while the perpendicular cuts through them. The expectation is to find a

substantial difference between both configurations, which can mean better outcomes for a given

operation or process.

As a reference of values, the following table shows the specific mechanical properties of PLA and

MS/PLA composite:

Table 2: Specific Mechanical Properties of PLA and MS/PLA Composite19

18 (ASTM International, 2016) 19 (Ashcroft, 2016), Ch. 3.2 (Table 3)

The ICAD Concept To aim the investigation process to a real application, the shapes and dimensions will be taken

from a product that consists on simple forms with gentle flexing radii and multiple individual values

to choose from.

Figure 9: ICAD Concept

“Infant Carrier Assistant Device "ICAD" is a tool used to carry infants from zero to six months

ideally. Use a geometry that adapts ergonomics information, proportions and dimensions of the

human being and especially babies’ data found in studies conducted by WHO. ICAD is composed

of two main parts that interact with two types of target individuals: first the loaded individual (the

infant) and on the other the individual load (adult). Minor components operate such that provide

comfort and safety during use, supplemented by one particular use that mitigates any possibility

of accidents.”20

The ICAD concept was developed by the author of this paper and will serve as the referent to the

conclusions of the capabilities of the material studied to eventually extrapolate these results to

other similarly shaped products that can be made from MS/PLA composite lamina.

Figure 10: ICAD sketched modus operandi21

Figure 11 shows the way the ICAD concept works, serving as a surface to lean on newborn babies

to protect them from mishandling and all the risks that it implies.

20 (Colombia Patent No. Dispositivo Asistente de Manipulación de Infantes “ICAD” (Patent Pending), 2016) 21 (Colombia Patent No. Dispositivo Asistente de Manipulación de Infantes “ICAD” (Patent Pending), 2016) – Figure #8 from patent

5. METHODOLOGY

Case of Study To have a reference frame to enclose the problem to a discrete result, the shapes and sizes will

be extracted from the mentioned ICAD concept; the curves will be measured in both their radius

(λ) and length angle (β) directly from the blue prints taken from the patent of the concept, selecting

the most important ones to characterize the general process.

Figure 11: ICAD Blue Print 1



Figure 14: Length Angle & Radius Convention

By observing and analyzing figures 12, 13 and 14, there are several curves, but the three selected

capture the essence of the concept and approaching them can better give understanding to how

to construct it. Table 3 down below condensates the information taken from the figures above:

Configuration Radius [mm] (λ) Length Angle [degrees] (β)

Measured Coupon Measure Coupon

1 290,3 300 20,3 20

2 158,6 150 42,4 45

3 42 40 95,8 90

Table 3: Measured and selected values for experimental coupons

The values measured won’t be the ones used to fabricate the experiment; the coupon values are

rounded numbers that can be more easily made and measured after, serving the same purpose

on descriptive terms and giving a more general idea of the process.

Experimental Protocol Given the fact that there is no specialized literature (till date) for the specific process to be tested,

an experimental protocol must be developed to come to replicable and reliable conclusions. Using

the convention described in figure 15 – the same used in table 3 – a set of specially designed test

molds will be made to create laminae that match these forms.

Figure 15: Sketch of the general experimental protocol

The experiment for each of the configurations will consist mainly of the elements listed on figure

16: a male mold and a female mold that fit together will push down a lamina at given conditions

that will be controlled and measured to assure constant output and consistent results. The bent

area refers to the actual contact surface that will interact with the mold in each side. A bent plank

with a particular length angle and radius will be taken out. Considering that there will be several

other variables that must be taken into account, a detailed general step by step process will be

described and then the specific conditions will be named.

General Process

The composite lamina obtained from the MS/PLA can be formed into flexed radius shapes as

shown in Figure 16, by means of heating to a certain temperature the lamina, sequentially pressing

it on a male-female mold and letting it cool down to room temperature, all of this maintaining most

of the mechanical properties and not compromising the surface finish.

After the conformation process, said laminae will suffer an elastic recuperation which comes from

some of the energy that is given to it, and the elastic recuperation will continue for a given time

until the energy that was not absorbed on plastic deformation is totally expended.

Figure 16:Scope of the general Process

The process will be taken on a standard test machine capable of measuring both input force and

displacement speed. In this case, an INSTRON Cat. #2716-010 (Max Load 5kN) will be utilized,

knowing that the competences given by it will match what will be expected to find and needed.

Figure 17 shows an image of the machine (left) and a close up of the claws (right).

Figure 17:INSTRON Cat. 2716-010

Step Description

1 Coupon shaping The coupon laminae must be cut to match the mold size

2 Mold placing In the case of using an INSTRON-like machine, the female mold is fastened on the down claw and the male on the upper one, making sure that the movement will end on both parts meeting on the expected position as good as possible

3 Preheating The lamina must be preheated to a given temperature (φ)

4 Laying Up The lamina is put on top of the female mold on a given direction guided by a slot designed for this purpose

5 Pressure Stage The male mold is taken down at a given Compression Extension (μ) and stops until it reaches a given push force (σ), keeping this condition until a cooling time (ζ) elapses.

6 Take-out The male mold is raised up and the lamina is taken out of the mold

7 First Analysis General superficial analysis is carried on and the first radius data registration is taken

8 Stand-by Time The coupons are taken away and stored on standard room conditions until the next measure time comes

9 Intermediate Time measure

The radii changes are measured on the same manner as on the first analysis, and compared

10 Second Stand-by The coupons must be kept another time lapse on standard room conditions (equal to the first)

11 Final Measure The new displacement is registered on the same datasheet

12 Future Observations

After the final measure, the elastic recuperation is expected to be too small to be able to measure useful data on the same time lapses; Never the less, the coupons might be observed and if present, take relevant data on a longer period.

Table 4: General Process step by step

Experimental Variables

As shown above on the general process description, there are some “given” factors; these factors

are the variables that will change in order to find optimal conditions for a given pattern or

configuration. To make possible the analysis, the magnitude of the variables must be quoted at

least on one end (max or min) and be linked to a reference value. The next table lists and contrasts

these parameters to be combined and tested.

Parameter Min Value Max Value Reference

Preheat temperature (φ) 50°C 200°C Reference Tables


5 mm/min 100 mm/min Experimental

Push Force (σ) 100 N 2000 N Experimental

Cooling Time (ζ) 1 min 5 min Experimental

Others

Fiber Direction Parallel or Perpendicular oriented

MS/PLA cluster Number 1 or 2 clusters (different thickness) Table 5: Experimental reference variables

Experimental Instrumentation The experimentation process requires mainly two machines and the molds; other minor tools will

be also needed to control the parameters involved. The specifications of the machines and tools

used will be listed ahead by the side of the blue prints of the molds designed:

Press: INSTRON Cat. #2716-010 (Max Load 5kN)

Oven: INSTRON 3111 Temperature Chamber (OMEGA Thermometer Model CL25)

Caliper: Mitutoyo Digital Vernier Caliper (±0.01mm)

Thermometer: Fluke 62 Mini Thermometer - IR Thermometer (±0.1°C)

Chronometer: Casio HS-3V Hand Held 7-digit Stopwatch (±0.01s)

Scale: Diamondo66 pocket Balance (±0.1g)

Figure 18: Instruments used (among others) IR Thermometer (left), Oven (center) and thermocouple for temperature control of the oven (right)

After making some previous testing on the laboratory by with additional test coupons, the

experimental variables were set according to the given conditions appreciated and the capabilities

of the instrumentation that was available to work with. By setting a default configuration, the

experimental conditions wouldn’t vary and the results will be comparable, eliminating parameters

on the analysis. Table 6 shows the selected conditions for the experiment.

Parameter Selected Condition(s)

Preheat temperature (φ) 60°C – 100°C – 150°C


50 mm/min

Push Force (σ) 1000 N

Cooling Time (ζ) 2min – 2:30min – 3min

Fiber Direction Parallel or Perpendicular oriented

MS/PLA cluster Number 1 or 2 clusters (different thickness) Table 6: Selected Experimental Conditions

For the condition of preheat temperature, the points were selected to have a wide range of

temperature that went from the lower reference given, to as close as the highest temperature that

the instruments could achieve. On the other hand, the cooling times are directly taken from the

measure made on the lab of how much will take the coupon take to reach room temperature on

each case respectively. Compression Extension (μ) was set on an intermediate value that could

be fast enough to bend the coupons without losing to much heat while it went all the way down

and not too fast so the material would have time to move freely. A push force (σ) of 1000N was

decided after seeing the force range needed was around 100N to 800N.

Mold design Process

To fabricate the molds, the main concern was that the conditions that the coupons would endure

wouldn’t affect their integrity in any way, meaning principally temperature and force. Under this

consideration and looking for a material of easy access and machinability, that was cheap all at

once, common commercial aluminum (6061) was chosen. Using the radii and angle from table 3

(coupon), the molds were designed in a fashion that all of them could be made out on a similar

scale, facilitating the fabrication raw material access and the coupon size distribution. Also, to give

a starting point of design, the dimensions of the claws of the press machine and the other

instrumentation were compiled to give minimums and maximums to the outcome. With this

information, the molds were designed for each case of study (mold blue prints). To make them, a

bulk bar of extruded aluminum of square cross section as shown in figure 19 was taken and cut

into parts so that each would match a mold piece.

Figure 19: Bulk bar cross section; 1m length

A Computer Numerical Control (CNC) machine was then used to fabricate the forms to make more

efficiently and precise the product, making each part in two stages – curve and clamping area.

Mold Blue Prints

The molds were fully designed from the parameters taken from the reference product – ICAD

Concept – and adapted to create a simple yet functional tool. As stated in Table 3, there are three

configurations that will be tested, from which each need two male molds radius depending on the

number of clusters that will translate into a thicker lamina and therefore a smaller inner value. Blue

prints 1, 2 and 3 correspond to the first configuration, which will serve as reference to the biggest

radius and the narrowest length angle. Blue prints 4, 5 and 6 are for the medium reference and 7,

8 and 9 for the smallest flex radius but biggest length angle.

Blue Print 1: Configuration 1 - Female Mold

Blue Print 2: Configuration 1 - Male Mold 1 Cluster

Blue Print 3: Configuration 1 - Male Mold 2 Clusters


Data Definition For each configuration, the steps enounced on table 4 must be carried on. Table 7 on the other

hand, shows all the iterations that will be made to come to the results that will be compiled and

analyzed; Coupons will be cut into parallel and perpendicular fiber orientation on two-layer

thickness given by cluster number. These four combinations will be then tested on three different

instances of the variable that concerns the most: temperature. The preheat temperature (60°C,

100°C & 150°C) will be changed for each configuration, using three different values to evaluate

the influence of higher or lower temperatures on the samples tested.

Preheat temperature (φ) 60°C 100°C 150°C

Parallel 1 cluster

2 clusters

Perpendicular 1 cluster

2 clusters

Table 7: Variable Combination Datasheet for each Configuration

With this stablished, the whole test parameters are enclosed and the number of coupons can be determined.

Given that there are 12 combinations for the main parameters and 3 configurations, 36 coupons must be

made to get a complete lot, but in order to get better insight, 3 complete lots will be tested to give a total of

108 coupons distributed as shown in Table 8.

Quantity 13cm Conf. 1

13cm Conf. 2

8cm Conf. 3

Parallel 1 cluster 27 9 9 9

2 clusters 27 9 9 9

Perpendicular 1 cluster 27 9 9 9

2 clusters 27 9 9 9 Table 8: Coupon numbers and Lot distribution

As was already stated, the thickness of the planks depends on the number of clusters; in the case

of study, one cluster come to be approximately 3mm thick and two around 5mm. The length is the

same for configurations 1 and 2, but configuration 3 uses a shorter coupon. The last side

corresponding to the width is the same for all of the coupons. Figure 17 illustrates the coupons,

which in total must be of four different dimensions: 130X40X3 [mm], 130X40X5 [mm], 80X40X3

[mm] and 80X40X5 [mm].

Figure 20: Coupon sizes

Once the process for all the bends is completed, the characteristics to be looked at will be:

1. Depth Difference

2. Failure (break)

3. Delamination Presence

4. Other damages/conditions

Data Retrieving

To facilitate the big amount of data that must be taken from each coupon, and to make a

systematic comparison of the sequential measurements that must be taken on the course of

several days, the method that will be used to compile this information will be on a millimetric grid

paper as shown on figure 20.

Figure 21: Sketch of the measure method

The information taken for each coupon will be as follows: the first delta will be taken right away

when the coupon is taken out of the mold, marking the initial elastic recuperation that occurs. The

second delta will be taken a week after the experiment was carried on – this time was set by

observing the coupons progression on the first week and noticing a day interval was too short,

making the next whole standard unit the base line of the second and final measurement. The way

the measurement is taken, is by first drawing the initial template for each mold using the male

molds, considering that the radii will change too with the thickness (black line). Now, when the

coupon is just out of the machine, it must be marked as shown on Figure 21, fixing a point (middle

point) that will be the reference for all the measurements. The Test temperature is the first value,

and it distinguish between the 3 main sets 60°C, 100°C and 150°C. The configuration number

defines whether the coupon is part of the 300mm (configuration 1) 150mm (configuration 2) or the

40mm (configuration 3) female mold. The cluster number (in black), identify this feature and was

marked previously on the fabrication process of each coupon. The orientation is not marked

because it is clearly seen on the fiber patterns. Finally, the coupon number serves to identify the

specific dataset of said lot.

Figure 22: Coupon Mark Convention Example:

Right – 60°C, Configuration 1, 1 Cluster, Parallel, Coupon 1 Left – 100°C, Configuration 3, 2 Clusters, Perpendicular, Coupon 1

With the coupon properly identified, it is put on top of the millimetric grid paper in a way that the

trace marks are just visible and the middle point mark is in aligned with the middle point line as

seen in figure 22 below. It’s important to highlight that the concave face is the one that must be

traced, because this is the one facing the male mold and in consequence, the radius of interest.

To make the markings as good as possible, a propelling 0.5mm pencil was used. To distinguish

between the time lapses, the convention taken was: 1st continuous line, 2nd intermittent line and

3tha dot on the middle point line.

Figure 23: Demonstration of the measurements

To calculate the radius of the coupons on each point of measurement, the geometrical relationship

given on figure 23 will be used, defining it on terms of the Length and the Sagitta, both derived

from the conditions of the experiment and the coupon itself.

Figure 24: Radius geometrical relationship

The results that come from this geometrical analysis are half the data that will be taken from the

experiment. The INSTRON machine on the other hand, has the capability of catching all the

information regarding time, displacement and force while doing the test on each coupon, meaning

that the energy input can be calculated as work, the time it takes to do such work and general

information of the process while it holds the load. To retrieve the quantity of work for each case, a

simple discrete integral shown in figure 23 was utilized. The interval was defined between the start

of the displacement and the value where the force equals the load force stablished (1000N) so

that all the values may be comparable.

Figure 25: Trapezoid Rule - Integral Approximation Method22

To try to make a more robust observation, another information will be extracted from each dataset.

The instant Force and the instant displacement of one of the initial values (the 6th entry will be

taken on the 1st configuration – smallest run) and 10th entry on the 2nd and 3th configurations.

These two values will be used to roughly estimate the elasticity modulus for each coupon

individually, providing yet another parameter to compare the results. This calculation will be made

with the equation provided on figure 24. To obtain this value, all the dimensions of each coupon

must be defined to get the Inertia. By tabulating this data, the numerical analysis can begin.

Figure 26: Simply supported beam deflection sketch23

Other Data Parameters Something important that was not taken into account was the difficulty that the manufacturing

process of the coupons might signify. The fiber material that was available to make the laminae

for this project was not as homogenous as it can get – usually by chemical treatment- which means

that the layers that conformed each cluster vary as well, giving in many occasions diverse

thicknesses on same cluster number coupons. The PLA sheets weren’t homogenous as well,

adding another differential on this dimension. Because of this, the thickness of each coupon was

measured and registered as a variable parameter that might influence the results. On the other

transversal axis, the width wasn’t homogenous either; to get the designed width, the coupons were

cut slightly longer on this dimension and then put together on a milling machine to get a straighter

and uniform finish. Never the less, as not all the coupons could be put at the same time, the width

varied too to some degree, making this parameter another one to put on the variable table. As the

volume changed, the mass would be as well something that will not be the same on every coupon,

and that is why it must be measured too. Having all this clear, all the variable parameters can be

considered and the common ones can be set as default, giving the baseline to find if there are

correlations and how they affect the outcome.

22 (Pauls Online Notes, 2016) 23 (Hibbeler, 2013)

Data Analysis Method The challenge that surrounds this problem is mostly held on the amount of variables that may or

not affect the outputs. To come to a conclusion that consider the effect on a comparable manner,

the parameters must be somehow normalized in a way that their interactions make sense on a

physical and numerical scale. For this end, the method selected is to carry on a dimensionless

analysis by means of the Buckingham Pi Theorem24.

The analysis starts by stating the variables that may concern the experiment that vary and were

measured. For the process in study, the following table states those variables:

Variable Convention Unit (SI) Dimension

Specific Length 𝐿𝑜 𝑚 L

Initial Radius (mold radius) 𝑅𝑜 𝑚 L

Final Radius (T0 Radius) 𝑅𝑓 𝑚 L

Thickness 𝐻 𝑚 L

Width 𝑤 𝑚 L

Conforming Time 𝑡𝑐 𝑠 T

Compression Time 𝑡𝑚 𝑠 T

Mass 𝑚 𝑘𝑔 M

Young (Elasticity) Modulus 𝐸 𝑘𝑔/𝑚𝑠2 M*L-1*T-2

Work 𝑈 𝑘𝑔𝑚2/𝑠2 M*L2*T-2 Table 9: Pi theorem Variables

Table 9 condenses all the variable inputs of the general function; Anyhow, the variable that interest

the problem the most is the final radius (R_f), because by making an accurate prediction of the

outcome by means of the other quoted characteristics, a model for a confirmation process might

be developed to check the viability of the use of conforming this material by hot pressing it. Now,

with this in mind, the functional equation will be:

𝑓(𝑅𝑓 , 𝑅𝑜, 𝐿𝑜, 𝐻, 𝑤, 𝑡𝑐 , 𝑡𝑚, 𝑚, 𝐸, 𝑈)

The next step to this process is to determine which of the parameters might serve as repeated

variables. As R_f is the interest value, it is discarded as one of these values, leaving several

combinations with the other 9 on the table. Never the less, the dimensions of several of these

variables are the same, meaning that the useful combinations left are fewer. For the analysis, the

next set of combinations is to be examined:

Repeated Variables

𝐸 𝑚 𝑡𝑐

𝑈 𝑚 𝑡𝑐

𝐸 𝑈 𝑡𝑐

𝐸 𝑈 𝑚 𝑈 𝐿 𝑡𝑐

𝑈 𝐿 𝑚

𝐸 𝐿 𝑡𝑐

𝐸 𝐿 𝑚 Table 10: Repeated Variables Selected

24 (Wylie, 2011)

The combinations taken are developed on table 11, where the pi terms are written for each case.

An important observation of the pi terms is given on the right column of the same table: the number

of pi terms that count with just one dimension (ex. Group 1 has Pi_7, which has time only as a

dimension among the variables). This number tells something about the combination possibilities

and the complexity that will come out of it, meaning that the more pi numbers with just 1 dimension

on the group, the less interesting will it be for the dimension analysis. For this reason, the groups

that will concern this attempt to correlate the variables will be 1, 2, 3 and 4.

Group Repeated Variables

𝜋 Terms #𝜋 with 1 dim

1 𝐸 𝑚 𝑡𝑐 𝜋1 =

𝑅𝑓𝐸𝑡𝑐2

𝑚 ; 𝜋2 =

𝐿𝐸𝑡𝑐2

𝑚 ; 𝜋3 =

𝑅𝑜𝐸𝑡𝑐2

𝑚 ; 𝜋4 =

𝐻𝐸𝑡𝑐2

𝑚

𝜋5 =𝑤𝐸𝑡𝑐

2

𝑚 ; 𝜋6 =

𝑈𝐸2𝑡𝑐6

𝑚3 ; 𝜋7 =

𝑡𝑐

𝑡𝑝

1

2 𝑈 𝑚 𝑡𝑐 𝜋1 =

𝑅𝑓2𝑚

𝑡𝑐2𝑈

; 𝜋2 =𝐿2𝑚

𝑡𝑐2𝑈

; 𝜋3 =𝑅𝑜

2𝑚

𝑡𝑐2𝑈

; 𝜋4 =𝐻2𝑚

𝑡𝑐2𝑈

𝜋5 =𝑤2𝑚

𝑡𝑐2𝑈

; 𝜋6 =𝐸√𝑈𝑡𝑐

3

𝑚32

; 𝜋7 =𝑡𝑐

𝑡𝑝

1

3 𝐸 𝑈 𝑡𝑐 𝜋1 =

𝑅𝑓3𝐸

𝑈 ; 𝜋2 =

𝐿3𝐸

𝑈 ; 𝜋3 =

𝑅𝑜3𝐸

𝑈 ; 𝜋4 =

𝑤3𝐸

𝑈

𝜋5 =𝐻3𝐸

𝑈 ; 𝜋6 =

𝑚

𝐸23 𝑈

13𝑡𝑐

2

; 𝜋7 =𝑡𝑐

𝑡𝑝

1

4 𝐸 𝑈 𝑚 𝜋1 =

𝑅𝑓3𝐸

𝑈 ; 𝜋2 =

𝐿3𝐸

𝑈 ; 𝜋3 =

𝑅𝑜3𝐸

𝑈 ; 𝜋4 =

𝑤3𝐸

𝑈

𝜋5 =𝐻3𝐸

𝑈 ; 𝜋6 =

𝑡𝑐3𝐸√𝑈

𝑚32

; 𝜋6 =𝑡𝑝

3𝐸√𝑈

𝑚32

0

5 𝑈 𝐿 𝑡𝑐 𝜋1 =

𝑅𝑓

𝐿 ; 𝜋2 =

𝑚𝐿2

𝑈𝑡𝑐2

; 𝜋3 =𝐸𝐿3

𝑈 ; 𝜋4 =

𝐿

𝑅𝑜

𝜋5 =𝐿

𝐻 ; 𝜋6 =

𝐿

𝑤 ; 𝜋7 =

𝑡𝑐

𝑡𝑝

5

6 𝑈 𝐿 𝑚 𝜋1 =

𝑅𝑓

𝐿 ; 𝜋2 =

𝐿

𝑅𝑜 ; 𝜋3 =

𝐿

𝐻 ; 𝜋4 =

𝐿

𝑤

𝜋5𝐸𝐿3

𝑈 ; 𝜋6 =

𝑡𝑐√𝑈

𝐿√𝑚 ; 𝜋7 =

𝑡𝑝√𝑈

𝐿√𝑚

4

7 𝐸 𝐿 𝑡𝑐 𝜋1 =

𝑅𝑓

𝐿 ; 𝜋2 =

𝐿

𝑅𝑜 ; 𝜋3 =

𝐿

𝐻 ; 𝜋4 =

𝐿

𝑤

𝜋5 =𝑡𝑐

𝑡𝑝 ; 𝜋6 =

𝑚

𝐸𝐿𝑡𝑐2

; 𝜋7 =𝑈

𝐸𝐿3

5

8 𝐸 𝐿 𝑚 𝜋1 =

𝑅𝑓

𝐿 ; 𝜋2 =

𝐿

𝑅𝑜 ; 𝜋3 =

𝐿

𝐻 ; 𝜋4 =

𝐿

𝑤

𝜋5 =𝑈

𝐸𝐿3 ; 𝜋6 =

𝑡𝑝2𝐸𝐿

𝑚 ; 𝜋7 =

𝑡𝑐2𝐸𝐿

𝑚

4

Table 11: Terms for each Combination Group

With the definition of the Pi Groups and the Pi terms on each one, the equations that relate the

variable of interest can be finally defined for each of the groups as follow:

Group 1

o Full Pi terms 𝑅𝑓 = 𝑓1 (𝐿

𝑅𝑜

𝐻

𝑤

𝑈𝐸𝑡𝑐4

𝑚2

𝑡𝑐

𝑡𝑝)

o No Pi 1 Term 𝑅𝑓𝐸𝑡𝑐

𝑚= 𝑓1 (

𝐿

𝑅𝑜

𝐻

𝑤

𝑈𝐸𝑡𝑐6

𝑚3

𝑡𝑐

𝑡𝑝)

Group 2

o Full Pi terms 𝑅𝑓 = 𝑓2 (√𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝑡𝑐

𝑡𝑝 √𝑈𝑚

𝐸𝑡𝑐) = 𝑓2 (

𝐿

𝑅𝑜

𝐻

𝑤 √

𝑡𝑐

𝑡𝑝 √𝑈𝑚

𝐸𝑡𝑐)

o No Pi 1 Term 𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 𝑓2 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝)

Group 3

o Full Pi terms 𝑅𝑓 = 𝑓3 (√𝐿3

𝑅𝑜3

𝐻3

𝑤3 𝑈

23 𝑚

𝐸53𝑡𝑐

2

𝑡𝑐

𝑡𝑝

3

) = 𝑓3 (𝐿

𝑅𝑜

𝐻

𝑤√

𝑈23 𝑚

𝐸53𝑡𝑐

2

𝑡𝑐

𝑡𝑝

3

)


3𝐸

𝑈= 𝑓3 (

𝐿3

𝑅𝑜3

𝐻3

𝑤3

𝑚

𝐸23𝑈

13 𝑡𝑐

2

𝑡𝑐

𝑡𝑝)

Group 4

o Full Pi terms 𝑅𝑓 = 𝑓4 (√𝑈

𝐸

𝐿3

𝑅𝑜3

𝐻3

𝑤3

𝑡𝑐3

𝑡𝑝3

3) = 𝑓4 (

𝐿

𝑅𝑜

𝐻

𝑤

𝑡𝑐

𝑡𝑝√

𝑈

𝐸

3)


3𝐸

𝑈= 𝑓4 (

𝐿3

𝑅𝑜3

𝐻3

𝑤3

𝑡𝑐3𝑡𝑝

3𝐸2𝑈

𝑚3 )

With one of these relationships and functions, the analysis may converge to a solution by

projecting a correlation described by a function for a give lot of data. The results won’t be mixed

all together for the 108 coupons, but they will be separated by two criteria, work temperature and

fiber orientation, giving a total of 6 groups with a maximum of points spread of 18 each. The

maximum is given by the fact that there may be less on any of the sets, because some of the

coupons were damaged in such a way that make their information not useful, some because they

delaminated and on the worse cases, because they broke. The information will be tabulated, but

for the main calculations, they will be left out to avoid noise on the results.

Figure 27: Examples of invalid coupon data

7. RESULTS After the extensive labor of testing the coupons for each configuration, the information extracted

can be found in tables 12, 13, 14 and 15. The table 12 contains the data that concerned the

general properties for each coupon: Mass, width and thickness, deriving the inertia from the last

two. On the bottom part of the same table, is the register of the radii calculated from the height

differences for each time delta (in mm), being P0 the reference mold radius, and P1, P2 and P3

the sequential measurements. Additionally, each set has the average value from the concerning

data, and right bellow is the percentual difference from for each average in comparison to the one

that came before it. From this table is also important to highlight the color convention, which

translates as shown in figure 27.

Figure 28: Color Convention for Coupon Superficial Analysis

On the other hand, tables 13, 14 and 15 show the data collected and calculated for each of the

variables that were considered to make the Pi theorem analysis. The information was reset to the

standard international system units (m-kg-s) to normalize them and make sure all the subsequent

calculations won’t be at some point mistaken by a magnitude factor. Similar as with the table 12,

the coupons that were checked as broken or delaminated are highlighted too, utilizing just red for

both; blue marked instances are part of other set of discarded data, but rather than for being

notoriously defective, by having evident deviation from the other couple of values that go by their

side. Figure 28 shows a picture of the probes in order from left to right lowest temperature to

highest, and bottom to top smallest to biggest conformation radius. Each iteration is piled up one

on top of the other; in this manner were kept the coupons for the waiting times, keeping the room

with closed blinds (away from direct sunlight) and making sure no environmental factor may

interfere with the measurements.

Figure 29: Picture of Coupon Results

Main Results Tables

Table 12: Datasheet 1 - General Geometrical Properties and Radii Changes

Probe Mass Configuration

Mass

(g)

Withd

(mm)

Thickness

(mm)

Inertia

(mm^4)Mass (g)

Withd

(mm)

Thickness

(mm)

Inertia

(mm^4)

Mass

(g)

Withd

(mm)

Thickness

(mm)

Inertia

(mm^4)

Mass

(g)

Withd

(mm)

Thickness

(mm)

Inertia

(mm^4)

Mass

(g)

Withd

(mm)

Thickness

(mm)

Inertia

(mm^4)

Mass

(g)

Withd

(mm)

Thickness

(mm)

Inertia

(mm^4)

1 6.4 3.6 2 0.002400 10 3.4 2.4 0.003917 7.9 3.5 1.7 0.001433 13.8 3.5 3 0.007875 8.9 3.3 2 0.002200 14.9 3.6 3.1 0.008937

2 6.5 3.6 2 0.002400 9.8 3.4 3.2 0.009284 8.7 3.5 1.8 0.001701 14.3 3.5 2.9 0.007113 5.1 3.3 1.6 0.001126 14.3 3.6 3.2 0.009830

3 6.3 3.6 1.9 0.002058 5.1 3.4 2.5 0.004427 7.5 3.5 1.5 0.000984 14.5 3.5 2.7 0.005741 9.9 3.3 2.5 0.004297 11.9 3.6 2.6 0.005273

1 5 3.6 1.8 0.001750 8.6 3.6 3.1 0.008937 5.3 3.1 1.7 0.001269 15.3 3.6 3 0.008100 5.5 3.1 1.5 0.000872 15.4 3.5 3 0.007875

2 6 3.6 2.1 0.002778 8.7 3.6 2.9 0.007317 9 3.1 2.1 0.002392 15.1 3.6 3.3 0.010781 5.3 3.1 1.7 0.001269 26.7 3.5 5.4 0.045927

3 6.3 3.6 1.8 0.001750 7.8 3.6 2.6 0.005273 NA 0 0.000000 15.4 3.6 3.3 0.010781 6.5 3.3 1.5 0.000928 28.6 3.5 5.8 0.05690767

1 6.5 3.4 2 0.002267 8.9 3.3 2.9 0.006707 5.9 3.3 1.9 0.001886 15.1 3.6 3.4 0.011791 6.6 3.3 1.7 0.001351 13.6 3.6 3.1 0.008937

2 6.8 3.4 2.2 0.003017 9.5 3.3 3.1 0.008193 12.2 3.3 3 0.007425 9.4 3.6 3.4 0.011791 6.3 3.3 1.9 0.001886 15.2 3.6 3.2 0.009830

3 5.8 3.4 2.7 0.005577 7.8 3.3 3.1 0.008193 8.8 3.3 1.6 0.001126 12.9 3.3 2.9 0.006707 8.4 3.3 2 0.002200 10.6 3.3 2.5 0.004297

1 6.4 3.3 2.6 0.004833 11.3 3.3 4.3 0.021864 9.3 3.1 2 0.002067 14.7 3.5 3.2 0.009557 5.3 3.1 1.7 0.001269 238 3.4 4.7 0.029417

2 4.1 3.3 1.9 0.001886 10.5 3.3 4.1 0.018953 5.3 3.1 1.7 0.001269 28.4 3.5 6 0.063000 9.3 3.1 2.1 0.002392 15 3.4 3 0.007650

3 4.3 3.3 1.9 0.001886 10.9 3.3 4.3 0.021864 6.2 3.1 1.6 0.001058 22.6 3.5 4.3 0.023190 5.1 3.1 1.6 0.001058 25.6 3.4 5.2 0.03983893

1 7.1 3.5 2.5 0.004557 9.9 3.3 3.5 0.011791 6.2 3.1 1.6 0.001058 15 3.5 3 0.007875 6.2 3.3 1.7 0.001351 12.7 3.6 2.9 0.007317

2 5.5 3.5 2.9 0.007113 5.1 3.3 2.5 0.004297 8.7 3.1 1.8 0.001507 13.9 3.5 3 0.007875 10.9 3.3 2.6 0.004833 10.2 3.6 2.3 0.003650

3 4.4 3.3 1.5 0.000928 9.5 3.3 3.2 0.009011 5.8 3.1 1.5 0.000872 15.8 3.3 2.9 0.006707 5.5 3.3 1.5 0.000928 11.6 3.6 2.5 0.004688

1 6.5 3.3 2.3 0.003346 10.2 3.3 3.5 0.011791 5.7 3.1 1.4 0.000709 15.4 3.5 3.1 0.008689 10.2 3.5 2 0.002333 21.9 3.6 4.4 0.025555

2 4.8 3.3 2 0.002200 9.4 3.3 3 0.007425 8.7 3.1 2 0.002067 27.8 3.5 5.6 0.051221 10 3.5 2 0.002333 23.7 3.6 4.7 0.031147

3 4.3 3.3 1.8 0.001604 9.7 3.3 3.7 0.013930 9.3 3.1 2.2 0.002751 27.7 3.5 5.8 0.056908 10 3.5 2 0.002333 28 3.6 6 0.0648

60C

Parallel

Perpendicular

100C

Parallel

Perpendicular

150C

Parallel

Perpendicular

R300-R295R40-R37 R40-R35 R150-R147 R150-R145 R300-R297

Temperatura Configuration

60°C PROBE P0 P1 P2 P3 P0 P1 P2 P3 P0 P1 P2 P3 P0 P1 P2 P3 P0 P1 P2 P3 P0 P1 P2 P3

1 37.00 94.40 120.98 141.25 35.00 46.78 64.09 68.76 147.00 610.92 2322.16 7797.87 145.00 876.54 1862.07 1862.07 297.00 1171.47 1171.47 2035.97 295.01 510.08 624.97 1140.49

2 37.00 120.98 449.21 1002.98 35.00 56.69 68.76 80.92 147.00 610.92 1364.57 2322.16 145.00 876.54 1862.07 4260.83 297.00 822.62 822.62 2035.97 295.01 807.25 1140.49 1944.11

3 37.00 120.98 289.76 1002.98 35.00 35.00 35.00 35.00 147.00 394.59 516.28 610.92 145.00 573.86 1862.07 1862.07 297.00 1171.47 1171.47 7786.11 295.01 1944.11 6594.00 -4735.97

AVERAGE 37.00 112.12 286.65 715.74 35.00 51.73 66.42 74.84 147.00 538.81 1401.00 3576.98 145.00 775.65 1862.07 2661.66 297.00 1055.18 1055.18 3952.68 295.01 658.66 882.73 1542.30

1.00 67.00% 60.89% 59.95% 1.00 32.35% 22.12% 11.24% 1.00 72.72% 61.54% 60.83% 1.00 81.31% 58.35% 30.04% 1.00 71.85% 0.00% 73.30% 1.00 55.21% 25.38% 42.77%

1 37.00 66.61 77.84 77.84 35.00 43.35 46.78 48.81 147.00 353.19 966.47 1364.57 145.00 489.63 876.54 1191.71 297.00 822.62 822.62 1171.47 295.01 510.08 624.97 624.97

2 37.00 58.55 71.73 71.73 35.00 41.90 46.78 48.81 147.00 394.59 966.47 1364.57 145.00 340.64 573.86 876.54 297.00 634.13 634.13 822.62 295.01 373.42 373.42 431.06

3 37.00 66.61 77.84 77.84 35.00 43.35 48.81 51.10 147.00 147.00 147.00 147.00 145.00 340.64 1191.71 1862.07 297.00 516.14 516.14 822.62 295.01 510.08 624.97 807.25

AVERAGE 37.00 63.92 75.80 75.80 35.00 42.63 46.78 48.81 147.00 373.89 966.47 1364.57 145.00 390.31 880.70 1310.11 297.00 657.63 657.63 938.90 295.01 464.52 541.12 621.09

1.00 42.12% 15.67% 0.00% 1.00 17.90% 8.87% 4.16% 147.00 60.68% 61.31% 29.17% 1.00 62.85% 55.68% 32.78% 1.00 54.84% 0.00% 29.96% 1.00 36.49% 14.16% 12.88%



1 37.00 58.55 71.73 77.84 35.00 51.10 64.09 68.76 147.00 447.20 447.20 447.20 145.00 283.71 340.64 340.64 297.00 822.62 822.62 822.62 295.01 624.97 624.97 807.25

2 37.00 66.61 94.40 94.40 35.00 51.10 64.09 68.76 147.00 353.19 610.92 748.45 145.00 427.13 427.13 489.63 297.00 516.14 822.62 1171.47 295.01 510.08 624.97 624.97

3 37.00 85.25 105.95 120.98 35.00 48.81 53.71 56.69 147.00 394.59 516.28 516.28 145.00 283.71 340.64 427.13 297.00 516.14 516.14 822.62 295.01 1140.49 1140.49 1944.11

AVERAGE 37.00 70.14 90.69 97.74 35.00 50.34 60.63 64.73 147.00 398.33 524.80 570.64 145.00 331.51 369.47 419.13 297.00 618.30 720.46 938.90 295.01 758.51 796.81 1125.44

1.00 47.25% 22.67% 7.21% 1.00 30.47% 16.98% 6.33% 1.00 63.09% 24.10% 8.03% 1.00 56.26% 10.27% 11.85% 1.00 51.97% 14.18% 23.27% 1.00 61.11% 4.81% 29.20%

1 37.00 71.73 85.25 94.40 35.00 43.35 46.78 48.81 147.00 194.11 218.21 249.65 145.00 213.52 261.98 261.98 297.00 376.63 435.37 516.14 295.01 510.08 510.08 624.97

2 37.00 77.84 94.40 105.95 35.00 41.90 46.78 48.81 147.00 353.19 394.59 447.20 145.00 190.44 213.52 213.52 297.00 376.63 376.63 516.14 295.01 431.06 510.08 624.97

3 37.00 66.61 94.40 105.95 35.00 43.35 44.97 44.97 147.00 232.82 394.59 447.20 145.00 190.44 227.45 227.45 297.00 332.02 376.63 516.14 295.01 510.08 624.97 624.97

AVERAGE 37.00 72.06 91.35 102.10 35.00 42.87 46.17 47.53 147.00 260.04 335.80 381.35 145.00 198.13 234.32 234.32 297.00 361.76 396.21 516.14 295.01 483.74 548.37 624.97

1.00 48.66% 21.12% 10.53% 1.00 18.36% 7.16% 2.85% 1.00 43.47% 22.56% 11.95% 1.00 26.82% 15.44% 0.00% 1.00 17.90% 8.69% 23.24% 1.00 39.01% 11.79% 12.26%



1 37.00 50.06 66.61 71.73 35.00 40.60 43.35 43.35 147.00 447.20 516.28 610.92 145.00 283.71 340.64 378.93 634.13 1171.47 2035.97 295.01 624.97 807.25 807.25

2 37.00 55.33 66.61 71.73 35.00 46.78 51.10 51.10 147.00 292.27 447.20 516.28 145.00 227.45 309.51 340.64 297.00 516.14 7786.11 -4266.80 295.01 1944.11 1944.11 1944.11

3 37.00 71.73 94.40 120.98 35.00 40.60 46.78 46.78 147.00 353.19 447.20 516.28 145.00 201.28 261.98 340.64 297.00 1171.47 7786.11 -4266.80 295.01 807.25 1944.11 1944.11

AVERAGE 37.00 59.04 75.87 88.14 35.00 42.66 47.08 47.08 147.00 364.22 470.23 547.82 145.00 237.48 304.04 353.41 297.00 773.91 5581.23 -2165.88 295.01 1125.44 1565.16 1565.16

1.00 37.33% 22.19% 13.92% 1.00 17.96% 9.39% 0.00% 1.00 59.64% 22.54% 14.16% 1.00 38.94% 21.89% 13.97% 1.00 61.62% 86.13% 357.69% 1.00 73.79% 28.09% 0.00%

1 37.00 47.88 58.55 66.61 35.00 39.42 41.90 41.90 147.00 184.06 136.40 104.65 145.00 157.27 164.33 172.13 297.00 332.02 332.02 376.63 295.01 373.42 373.42 373.42

2 37.00 52.52 62.27 66.61 35.00 44.97 44.97 44.97 147.00 175.07 175.07 184.06 145.00 150.86 150.86 157.27 297.00 516.14 822.62 822.62 295.01 373.42 431.06 431.06

3 37.00 52.52 62.27 66.61 35.00 39.42 43.35 43.35 147.00 159.68 194.11 218.21 145.00 157.27 157.27 164.33 297.00 297.00 297.00 297.00 295.01 431.06 510.08 510.08

AVERAGE 37.00 50.98 61.03 66.61 35.00 41.27 43.41 43.41 147.00 172.94 168.53 168.97 145.00 155.14 157.49 164.58 297.00 381.72 483.88 498.75 295.01 392.63 438.18 438.18

R40-R37 R40-R35 R150-R147 R150-R145 R300-R297 R300-R295

R300-R295

Parallel

Perpendicular

Geo

met

rica

l Pro

gres

s -

Rad

ius

R40-R37 R40-R35 R150-R147 R150-R145 R300-R297

R150-R145 R300-R297 R300-R295

Parallel

Perpendicular

Parallel

Perpendicular

R40-R37 R40-R35 R150-R147

Table 13: Datasheet 2 – Complete Data Compilation for the Pi Variables – 60°C Coupons

Compression

Time (s)

Conformation

Time (s)

Measure Time

(s)

Young Modulus

(Pa)Work (J)

T T T (kg/m*s^2) (k*m^2/s^2)

Probe # DatoR_f (mm) R_f (m) R_o (mm) R_o (m) L (mm) L (m) H (mm) H (m) w (mm) w (m) t_p t_c t_m m (g) kg (kg) E U

1 1 94.40 0.094399 37.00 0.037 57.00 0.057 2.0 0.00200 3.6 0.0036 120 12.422 120.00 6.40 0.0064 2.72E+10 1.16

2 2 120.98 0.120976 37.00 0.037 57.00 0.057 2.0 0.00200 3.6 0.0036 120 12.116 120.00 6.50 0.0065 3.13E+10 1.29

3 3 120.98 0.120976 37.00 0.037 57.00 0.057 1.9 0.00190 3.6 0.0036 120 12.306 120.00 6.30 0.0063 2.70E+10 1.00

1 4 66.61 0.066610 37.00 0.037 57.00 0.057 1.8 0.00180 3.6 0.0036 120 11.904 120.00 5.00 0.0050 2.47E+10 0.42

2 5 58.55 0.058547 37.00 0.037 57.00 0.057 2.1 0.00210 3.6 0.0036 120 12.004 120.00 6.00 0.0060 1.10E+10 0.45

3 6 66.61 0.066610 37.00 0.037 57.00 0.057 1.8 0.00180 3.6 0.0036 120 12.128 120.00 6.30 0.0063 1.11E+10 0.60

1 7 46.78 0.046776 35.00 0.035 57.00 0.057 2.4 0.00240 3.4 0.0034 120 12.004 120.00 10.00 0.0100 6.20E+10 3.43

2 8 56.69 0.056689 35.00 0.035 57.00 0.057 3.2 0.00320 3.4 0.0034 120 11.506 120.00 9.80 0.0098 2.69E+10 3.25

3 9 35.00 0.034998 35.00 0.035 57.00 0.057 2.5 0.00250 3.4 0.0034 120 12.766 120.00 5.10 0.0051 #DIV/0! 1.12

1 10 43.35 0.043351 35.00 0.035 57.00 0.057 3.1 0.00310 3.6 0.0036 120 12.400 120.00 8.60 0.0086 7.01E+09 0.89

2 11 41.90 0.041902 35.00 0.035 57.00 0.057 2.9 0.00290 3.6 0.0036 120 12.438 120.00 8.70 0.0087 5.83E+09 0.72

3 12 43.35 0.043351 35.00 0.035 57.00 0.057 2.6 0.00260 3.6 0.0036 120 12.126 120.00 7.80 0.0078 3.42E+09 0.67

1 13 610.92 0.610915 147.00 0.147 115.00 0.115 1.7 0.00170 3.5 0.0035 120 14.102 120.00 7.90 0.0079 2.12E+10 0.43

2 14 610.92 0.610915 147.00 0.147 115.00 0.115 1.8 0.00180 3.5 0.0035 120 12.926 120.00 8.70 0.0087 1.79E+10 0.31

3 15 394.59 0.394586 147.00 0.147 115.00 0.115 1.5 0.00150 3.5 0.0035 120 120.00 7.50 0.0075 #DIV/0! Damaged

1 16 353.19 0.353189 147.00 0.147 115.00 0.115 1.7 0.00170 3.1 0.0031 120 11.004 120.00 5.30 0.0053 4.27E+09 0.32

2 17 394.59 0.394586 147.00 0.147 115.00 0.115 2.1 0.00210 3.1 0.0031 120 9.832 120.00 9.00 0.0090 2.18E+10 0.32

3 18 147.00 0.147004 147.00 0.147 115.00 0.115 0.0 0.00000 0.0 0.0000 120 120.00 NA #VALUE! #DIV/0! NA

1 19 876.54 0.876540 145.00 0.145 115.00 0.115 3.0 0.00300 3.5 0.0035 120 13.624 120.00 13.80 0.0138 2.40E+10 1.02

2 20 876.54 0.876540 145.00 0.145 115.00 0.115 2.9 0.00290 3.5 0.0035 120 11.090 120.00 14.30 0.0143 4.92E+10 1.00

3 21 573.86 0.573856 145.00 0.145 115.00 0.115 2.7 0.00270 3.5 0.0035 120 11.644 120.00 14.50 0.0145 4.90E+10 0.82

1 22 489.63 0.489629 145.00 0.145 115.00 0.115 3.0 0.00300 3.6 0.0036 120 11.004 120.00 15.30 0.0153 2.16E+10 0.59

2 23 340.64 0.340645 145.00 0.145 115.00 0.115 3.3 0.00330 3.6 0.0036 120 10.500 120.00 15.10 0.0151 9.06E+09 0.83

3 24340.64 0.340645 145.00 0.145 115.00 0.115 3.3 0.00330 3.6 0.0036 120 11.450 120.00 15.40 0.0154 1.60E+10 0.50

1 25 1171.47 1.171468 297.00 0.297 105.00 0.105 2.0 0.00200 3.3 0.0033 120 3.902 120.00 8.90 0.0089 1.32E+10 0.22

2 26 822.62 0.822618 297.00 0.297 105.00 0.105 1.6 0.00160 3.3 0.0033 120 3.372 120.00 5.10 0.0051 6.51E+10 0.23

3 27 1171.47 1.171468 297.00 0.297 105.00 0.105 2.5 0.00250 3.3 0.0033 120 3.008 120.00 9.90 0.0099 7.50E+10 0.27

1 28 822.62 0.822618 297.00 0.297 105.00 0.105 1.5 0.00150 3.1 0.0031 120 3.780 120.00 5.50 0.0055 1.13E+10 0.22

2 29 634.13 0.634127 297.00 0.297 105.00 0.105 1.7 0.00170 3.1 0.0031 120 3.506 120.00 5.30 0.0053 1.22E+10 0.22

3 30 516.14 0.516141 297.00 0.297 105.00 0.105 1.5 0.00150 3.3 0.0033 120 3.540 120.00 6.50 0.0065 1.25E+10 0.43

1 31 510.08 0.510075 295.00 0.295 105.00 0.105 3.1 0.00310 3.6 0.0036 120 3.904 120.00 14.90 0.0149 1.99E+10 0.28

2 32 807.25 0.807247 295.00 0.295 105.00 0.105 3.2 0.00320 3.6 0.0036 120 3.964 120.00 14.30 0.0143 1.57E+10 0.33

3 33 1944.11 1.944113 295.00 0.295 105.00 0.105 2.6 0.00260 3.6 0.0036 120 4.034 120.00 11.90 0.0119 2.63E+10 0.52

1 34 510.08 0.510075 295.00 0.295 105.00 0.105 3.0 0.00300 3.5 0.0035 120 3.004 120.00 15.40 0.0154 1.20E+10 0.24

2 35

373.42 0.373417 295.00 0.295 105.00 0.105 5.4 0.00540 3.5 0.0035 120 2.500 120.00 26.70 0.0267 9.38E+09 0.26

3 36 510.08 0.510075 295.00 0.295 105.00 0.105 5.8 0.00580 3.5 0.0035 120 3.004 120.00 28.60 0.0286 1.18E+10 0.33

Temperature 60°C

Pa

ralle

lP

erp

en

di

cula

rP

ara

llel

Pe

rpe

nd

i

cula

rP

ara

llel

Pe

rpe

nd

i

cula

rP

ara

llel

Pe

rpe

nd

icu

l

ar

1 C

lust

er

2 C

lust

er

1 C

lust

er

2 C

lust

er

1 C

lust

er

2 C

lust

er

Co

nfi

gu

rati

on

3 (

40

mm

)C

on

fig

ura

tio

n 2

(1

50

mm

)C

on

fig

ura

tio

n 1

(3

00

mm

)

Pa

ralle

lP

erp

en

di

cula

rP

ara

llel

Pe

rpe

nd

icu

lar

Mass (kg)

M

Mold Radius

L

Final Radius

L

Specific Length

L

Thickness

L

Width

L

Table 14: Datasheet 3 - Complete Data Compilation for the Pi Variables – 100°C Coupons

Probe # DatoR_f (mm) R_f (m) R_o (mm) R_o (m) L (mm) L (m) T (mm) T (m) w (mm) w (m) t_p t_c t_m m E

1 1 58.55 0.058547 37.00 0.037 57.00 0.057 2.0 0.00200 3.4 0.0034 150 11.966 120.00 6.50 0.01 1.19E+10 0.69

2 2 66.61 0.066610 37.00 0.037 57.00 0.057 2.2 0.00220 3.4 0.0034 150 12.988 120.00 6.80 0.01 1.31E+10 0.87

3 3 85.25 0.085251 37.00 0.037 57.00 0.057 2.7 0.00270 3.4 0.0034 150 12.342. 120.00 5.80 0.01 1.16E+10 1.09

1 4 71.73 0.071729 37.00 0.037 57.00 0.057 2.6 0.00260 3.3 0.0033 150 12.518 120.00 6.40 0.01 9.02E+08 0.31

2 5 77.84 0.077841 37.00 0.037 57.00 0.057 1.9 0.00190 3.3 0.0033 150 12.856 120.00 4.10 0.00 1.26E+09 0.26

3 6 66.61 0.066610 37.00 0.037 57.00 0.057 1.9 0.00190 3.3 0.0033 150 12.120 120.00 4.30 0.00 2.94E+09 0.31

1 7 51.10 0.051104 35.00 0.035 57.00 0.057 2.9 0.00290 3.3 0.0033 150 11.818 120.00 8.90 0.01 2.44E+10 2.31

2 8 51.10 0.051104 35.00 0.035 57.00 0.057 3.1 0.00310 3.3 0.0033 150 11.908 120.00 9.50 0.01 2.44E+10 2.63

3 948.81 0.048809 35.00 0.035 57.00 0.057 3.1 0.00310 3.3 0.0033 150 11.732 120.00 7.80 0.01 2.17E+10 2.41

1 10 43.35 0.043351 35.00 0.035 57.00 0.057 4.3 0.00430 3.3 0.0033 150 11.876 120.00 11.30 0.01 1.36E+09 0.55

2 11 41.90 0.041902 35.00 0.035 57.00 0.057 4.1 0.00410 3.3 0.0033 150 11.960 120.00 10.50 0.01 1.62E+09 0.55

3 12 43.35 0.043351 35.00 0.035 57.00 0.057 4.3 0.00430 3.3 0.0033 150 11.876 120.00 10.90 0.01 1.36E+09 0.55

1 13 447.20 0.447202 147.00 0.147 115.00 0.115 1.9 0.00190 3.3 0.0033 150 11.828 120.00 5.90 0.01 1.73E+10 0.28

2 14 353.19 0.353189 147.00 0.147 115.00 0.115 3.0 0.00300 3.3 0.0033 150 11.048 120.00 12.20 0.01 2.81E+10 0.89

3 15 394.59 0.394586 147.00 0.147 115.00 0.115 1.6 0.00160 3.3 0.0033 150 11.604 120.00 8.80 0.01 4.14E+10 0.35

1 16 194.11 0.194109 147.00 0.147 115.00 0.115 2.0 0.00200 3.1 0.0031 150 10.004 120.00 9.30 0.01 8.40E+09 0.22

2 17 353.19 0.353189 147.00 0.147 115.00 0.115 1.7 0.00170 3.1 0.0031 150 10.050 120.00 5.30 0.01 5.13E+09 0.40

3 18 232.82 0.232825 147.00 0.147 115.00 0.115 1.6 0.00160 3.1 0.0031 150 8.190 120.00 6.20 0.01 7.18E+09 0.22

1 19 283.71 0.283706 145.00 0.145 115.00 0.115 3.4 0.00340 3.6 0.0036 150 11.188 120.00 15.10 0.02 1.76E+10 0.68

2 20 427.13 0.427130 145.00 0.145 115.00 0.115 3.4 0.00340 3.6 0.0036 150 11.846 120.00 9.40 0.01 1.34E+10 0.55

3 21

283.71 0.283706 145.00 0.145 115.00 0.115 2.9 0.00290 3.3 0.0033 150 11.932 120.00 12.90 0.01 1.50E+10 0.42

1 22 213.52 0.213519 145.00 0.145 115.00 0.115 3.2 0.00320 3.5 0.0035 150 11.870 120.00 14.70 0.01 2.27E+09 0.26

2 23 190.44 0.190439 145.00 0.145 115.00 0.115 6.0 0.00600 3.5 0.0035 150 12.036 120.00 28.40 0.03 4.75E+09 1.01

3 24 190.44 0.190439 145.00 0.145 115.00 0.115 4.3 0.00430 3.5 0.0035 150 12.162 120.00 22.60 0.02 5.29E+09 0.54

1 25 822.62 0.822618 297.00 0.297 105.00 0.105 1.7 0.00170 3.3 0.0033 150 3.060 120.00 6.60 0.01 5.14E+10 0.37

2 26 516.14 0.516141 297.00 0.297 105.00 0.105 1.9 0.00190 3.3 0.0033 150 3.786 120.00 6.30 0.01 2.56E+10 0.23

3 27 516.14 0.516141 297.00 0.297 105.00 0.105 2.0 0.00200 3.3 0.0033 150 3.932 120.00 8.40 0.01 1.14E+10 0.01

1 28 376.63 0.376635 297.00 0.297 105.00 0.105 1.7 0.00170 3.1 0.0031 150 3.356 120.00 5.30 0.01 1.52E+09 0.21

2 29 376.63 0.376635 297.00 0.297 105.00 0.105 2.1 0.00210 3.1 0.0031 150 3.000 120.00 9.30 0.01 2.42E+08 0.21

3 30 332.02 0.332020 297.00 0.297 105.00 0.105 1.6 0.00160 3.1 0.0031 150 2.230 120.00 5.10 0.01 1.46E+10 0.22

1 31 624.97 0.624973 295.00 0.295 105.00 0.105 3.1 0.00310 3.6 0.0036 150 3.826 120.00 13.60 0.01 1.36E+10 0.26

2 32

510.08 0.510075 295.00 0.295 105.00 0.105 3.2 0.00320 3.6 0.0036 150 3.870 120.00 15.20 0.02 1.31E+10 0.26

3 33 1140.49 1.140493 295.00 0.295 105.00 0.105 2.5 0.00250 3.3 0.0033 150 3.660 120.00 10.60 0.01 4.71E+10 0.33

1 34 510.08 0.510075 295.00 0.295 105.00 0.105 4.7 0.00470 3.4 0.0034 150 4.260 120.00 238.00 0.24 2.75E+09 0.28

2 35 431.06 0.431061 295.00 0.295 105.00 0.105 3.0 0.00300 3.4 0.0034 150 3.342 120.00 15.00 0.02 4.04E+09 0.22

3 36 510.08 0.510075 295.00 0.295 105.00 0.105 5.2 0.00520 3.4 0.0034 150 3.530 120.00 25.60 0.03 6.88E+09 0.60

Co

nfi

gu

rati

on

2 (

15

0m

m)

1 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

2 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

Co

nfi

gu

rati

on

1 (

30

0m

m)

1 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

2 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

Temperature 100°C

Co

nfi

gu

rati

on

3 (

40

mm

)

1 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

2 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

Table 15: Datasheet 4 - Complete Data Compilation for the Pi Variables – 150°C Coupon

Probe # DatoR_f (mm) R_f (m) R_o (mm) R_o (m) L (mm) L (m) T (mm) T (m) w (mm) w (m) t_p t_c t_m m E U

1 1 50.06 0.050059 37.00 0.037 57.00 0.057 2.5 0.00250 3.5 0.0035 180 12.054 120.00 7.10 0.01 6.99E+09 1.04

2 2 55.33 0.055328 37.00 0.037 57.00 0.057 2.9 0.00290 3.5 0.0035 180 12.554 120.00 5.50 0.01 2.16E+09 0.73

3 3 71.73 0.071729 37.00 0.037 57.00 0.057 1.5 0.00150 3.3 0.0033 180 13.290 120.00 4.40 0.00 1.05E+10 0.46

1 4 47.88 0.047884 37.00 0.037 57.00 0.057 2.3 0.00230 3.3 0.0033 180 10.356 120.00 6.50 0.01 9.48E+08 243.00

2 5 52.52 0.052522 37.00 0.037 57.00 0.057 2.0 0.00200 3.3 0.0033 180 11.770 120.00 4.80 0.00 9.39E+08 0.25

3 6

52.52 0.052522 37.00 0.037 57.00 0.057 1.8 0.00180 3.3 0.0033 180 11.628 120.00 4.30 0.00 1.07E+09 0.34

1 7 40.60 0.040599 35.00 0.035 57.00 0.057 3.5 0.00350 3.3 0.0033 180 11.896 120.00 9.90 0.01 7.87E+09 1.21

2 8 46.78 0.046776 35.00 0.035 57.00 0.057 2.5 0.00250 3.3 0.0033 180 12.614 120.00 5.10 0.01 1.50E+10 1.25

3 9 40.60 0.040599 35.00 0.035 57.00 0.057 3.2 0.00320 3.3 0.0033 180 11.636 120.00 9.50 0.01 1.14E+10 1.55

1 10 39.42 0.039422 35.00 0.035 57.00 0.057 3.5 0.00350 3.3 0.0033 180 11.560 120.00 10.20 0.01 1.36E+09 0.65

2 11 44.97 0.044967 35.00 0.035 57.00 0.057 3.0 0.00300 3.3 0.0033 180 11.694 120.00 9.40 0.01 2.99E+09 0.48

3 12 39.42 0.039422 35.00 0.035 57.00 0.057 3.7 0.00370 3.3 0.0033 180 12.498 120.00 9.70 0.01 5.31E+08 0.08

1 13 447.20 0.447202 147.00 0.147 115.00 0.115 1.6 0.00160 3.1 0.0031 180 13.218 120.00 6.20 0.01 1.23E+10 0.29

2 14 292.27 0.292269 147.00 0.147 115.00 0.115 1.8 0.00180 3.1 0.0031 180 12.436 120.00 8.70 0.01 1.87E+10 0.29

3 15 353.19 0.353189 147.00 0.147 115.00 0.115 1.5 0.00150 3.1 0.0031 180 12.486 120.00 5.80 0.01 2.86E+10 0.27

1 16 184.06 0.184059 147.00 0.147 115.00 0.115 1.4 0.00140 3.1 0.0031 180 10.594 120.00 5.70 0.01 3.06E+09 0.33

2 17 175.07 0.175071 147.00 0.147 115.00 0.115 2.0 0.00200 3.1 0.0031 180 6.826 120.00 8.70 0.01 4.60E+08 0.22

3 18 159.68 0.159681 147.00 0.147 115.00 0.115 2.2 0.00220 3.1 0.0031 180 7.430 120.00 9.30 0.01 3.69E+08 0.21

1 19283.71 0.283706 145.00 0.145 115.00 0.115 3.0 0.00300 3.5 0.0035 180 11.268 120.00 15.00 0.02 1.82E+10 0.51

2 20 227.45 0.227452 145.00 0.145 115.00 0.115 3.0 0.00300 3.5 0.0035 180 11.634 120.00 13.90 0.01 2.26E+10 0.65

3 21 201.28 0.201276 145.00 0.145 115.00 0.115 2.9 0.00290 3.3 0.0033 180 11.078 120.00 15.80 0.02 1.96E+10 0.65

1 22 157.27 0.157274 145.00 0.145 115.00 0.115 3.1 0.00310 3.5 0.0035 180 10.792 120.00 15.40 0.02 2.00E+08 0.23

2 23 150.86 0.150858 145.00 0.145 115.00 0.115 5.6 0.00560 3.5 0.0035 180 8.174 120.00 27.80 0.03 2.48E+09 0.41

3 24 157.27 0.157274 145.00 0.145 115.00 0.115 5.8 0.00580 3.5 0.0035 180 7.430 120.00 27.70 0.03 2.02E+09 0.29

1 25 634.13 0.634127 297.00 0.297 105.00 0.105 1.7 0.00170 3.3 0.0033 180 4.658 120.00 6.20 0.01 5.71E+09 0.25

2 26 516.14 0.516141 297.00 0.297 105.00 0.105 2.6 0.00260 3.3 0.0033 180 3.768 120.00 10.90 0.01 6.39E+09 0.24

3 27 1171.47 1.171468 297.00 0.297 105.00 0.105 1.5 0.00150 3.3 0.0033 180 4.710 120.00 5.50 0.01 6.24E+09 0.24

1 28 332.02 0.332020 297.00 0.297 105.00 0.105 2.0 0.00200 3.5 0.0035 180 4.198 120.00 10.20 0.01 1.24E+09 0.23

2 29 516.14 0.516141 297.00 0.297 105.00 0.105 2.0 0.00200 3.5 0.0035 180 2.690 120.00 10.00 0.01 6.62E+08 0.25

3 30 297.00 0.296999 297.00 0.297 105.00 0.105 1.6 0.00160 3.5 0.0035 180 5.984 120.00 10.00 0.01 4.96E+09 0.26

1 31 624.97 0.624973 295.00 0.295 105.00 0.105 2.9 0.00290 3.6 0.0036 180 5.416 120.00 12.70 0.01 5.80E+09 0.25

2 32 1944.11 1.944113 295.00 0.295 105.00 0.105 2.3 0.00230 3.6 0.0036 180 5.606 120.00 10.20 0.01 1.27E+10 0.38

3 33 807.25 0.807247 295.00 0.295 105.00 0.105 2.5 0.00250 3.6 0.0036 180 4.778 120.00 11.60 0.01 8.23E+09 0.27

1 34 373.42 0.373417 295.00 0.295 105.00 0.105 4.4 0.00440 3.6 0.0036 180 2.108 120.00 21.90 0.02 2.95E+10 0.35

2 35 373.42 0.373417 295.00 0.295 105.00 0.105 4.7 0.00470 3.6 0.0036 180 2.288 120.00 23.70 0.02 7.00E+09 0.23

3 36 431.06 0.431061 295.00 0.295 105.00 0.105 6.0 0.00600 3.6 0.0036 180 2.534 120.00 28.00 0.03 3.54E+09 0.51

Co

nfi

gu

rati

on

1 (

30

0m

m)

1 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

2 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

Temperature 150°C

Co

nfi

gu

rati

on

3 (

40

mm

)

1 C

lust

er

Pa

ralle

lP

erp

en

dic

ula

r

2 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

Co

nfi

gu

rati

on

2 (

15

0m

m)

Pa

ralle

lP

erp

en

di

cu

lar

1 C

lust

er

Pa

ralle

lP

erp

en

di

cu

lar

2 C

lust

er

Main Results - Graphs

Graph 1: P1 -Full Pi Terms - Pi Group 1 – Parallel - Logarithmic Function Adjustment

Graph 2: P1 - Full Pi Terms - Pi Group 1 – Perpendicular - Logarithmic Function Adjustment

Graph 3: P1 - Full Pi Terms - Pi Group 2 – Parallel - Logarithmic Function Adjustment


Graph 9: P1 - No Pi 1 Term - Pi Group 1 – Parallel - Power Function Adjustment

Graph 10: P1 - No Pi 1 Term - Pi Group 1 – Perpendicular - Power Function Adjustment


Graph 16: P1 - No Pi 1 Term - Pi Group 4 – Perpendicular - Logarithmic Power Adjustment

8. ANALYSIS

To start giving insight on the results, the information must be described step by step. Table 12

shows the discrete information of geometry and mass for each coupon, in addition of the radius

progress on each time of measure. Even though this information supports the whole analysis, it

doesn’t say much when looking at each individual point; never the less, the information that is

relevant has to do with the color convention, which clearly gives away a pattern linked to the

temperature: 60°C coupons suffered several notorious superficial damages and had the most

broken coupons. The 150°C seemed to have another kind of problem; the delamination rate was

considerably higher than on the other two experimental conditions and the damaged coupon

number added to these almost add up to half of the tests carried on. On the other hand, the 100°C

testing have the least problems regarding damage, with only two coupons that delaminated.

This particular behavior, with such consistent pattern, point out to say that temperature, as

expected, is a main concern on the fabrication process. Even though these results are not

completely conclusive because of the considerably big gap between testing temperatures, it can

be observed that the optimal operation point must be around the 100°C. The explanation for why

the bottom and upper limit didn´t work as well might be probably because the temperature was

too close to the inferior limit and didn´t gave the material enough thermal energy to deflect

optimally, causing it to resist more to a plastic deformation and ultimately yielding in some cases;

the upper limit problem must be in contrast, the opposite, giving the coupon an excess of thermal

energy that might have de constructed the material and created a bi phase outcome and thus, the

delamination and superficial damage.

Figure 30: Color Pattern on Temperatures

On hindsight, the best data lot to estimate the behavior of the material under this set of conditions

will be the 100°C lot. Tables 13, 14 and 15 show this as well; on these tables is the information of

each variable that was taken into account on the Pi theorem analysis, displayed in order to create

an easy to handle database. Both colors on these tables indicate that the information of that

coupon won´t be used, red for visible damage and blue for information that is way too off compared

to the average observed on their particular condition. Because of this, the most reliable results

must be linked to the middle temperature, while the upper one may not have enough data to come

to an accurate conclusion.

The graphs presented are the visual description of the calculations made with the equations

described previously. Each of the graphs show the same kind of information: Fist of all, the Pi

Group they belong to right next to the orientation. The y-axis states whether or not the R_f variable

is been set or if it is the whole Pi 1 term. All the temperatures are graphed for each iteration for

comparison purposes, and each temperature has its own function that best describe its behavior.

The precision of each function is given in terms of the R2 factor, meaning that the closer it is to 1,

the more precise the experimental data came to the actual curve. It can be seen that the magnitude

of the graphs is not homogenous, but this doesn’t affect the selection criteria because the baseline

to compare which dataset compiles better the correlation information is the R2 factor.

After scoping in detail all the combinations and examining the tendencies that better fit on each

case, it came clear some things. First, the function that best takes the data while comparing R_f

to all the other Pi terms is a logarithmic function, while putting the whole Pi 1 term on the y-axis is

always tending to go as a power function. Second, as expected, the tendencies that adjust the

best were the ones on the 100°C mark with the best R2 factor in most regressions. Finally, the

form that better adjust all the data for each case is to use the Pi 1 term on the y-axis in function of

the other six, which gives the following information:

Graphs 33 to 38 illustrate the selected relations: The data best adjusted, even through the different

time R_f values, was the second Pi Group with Pi 1 Term in function of the other Pi terms. Graphs

33 and 34 show the first R_f embedded in the Pi 1 term value, meaning these graphs show the

estimated behavior of the radius of the lamina (given the stated parameters) for when it is just

taken out of the machine. Graphs 35 and 36 show this same situation for the radius value on P2

(one week after the conformation process) and P3 (2 weeks after the conformation process).

The different values calculated on the different time lapses are important for the analysis because

by being consistent, the equations that are said to describe each case gains more value. Never

the less, the set of equations that will matter the most on a manufacturing level will be the ones

on the time 3, P3. The final radius R_f on the second week mark is more important because this

is the moment when most of the stored elastic energy seems to have dispersed and the actual

shape that will hold the lamina can be observed and utilized. This means that it was found that the

material has a very slow elastic recuperation to achieve its final form, which implies that a

fabrication method for it must include this holding period to get to the curvature needed.

Figure 31: Sketch of the behavior of the material under the hot-press method

Graph 33: P1 Measure Estimation Function - Parallel Orientation

Graph 34: P1 Measure Estimation Function - Perpendicular Orientation

Estimation Equations

To wrap up all the information that has been got, and conceal it in a set of more useful shape,

tables 16, 17 and 18 gather it together. Each table has the given graph function found and uses

the equalities to put it on terms of the actual variables that form the expression (equations in bold

letter) for each temperature and fiber orientation. It’s to be noted that most of the information

seems to be reliable by having a R2 considerably good, except for the case of 150°C on a

perpendicular configuration consistently; this might be justified, as stated before, because of the

lack of useful information for it and the little homogenous nature of the probes afterwards too. In

comparison, the temperature that concern this analysis the most is 100°C, which has a surprisingly

good approximation factor to the function that describes it, averaging more than 93% on the

parallel orientation and 82% on the perpendicular one, values that on an experimental reach are

good to assume that the variables do have a clear relationship that converge on the outcome of

the final radius.

Detailing the equations shown on the following tables, the final radius is given squared, in terms

of the compression time squared, the work input and divided by the mass (variables that keep a

degree of dimension), while this number will be multiplied by the dimensionless term sealed on

the parenthesis that does include the other part of the variables that describe the lamina to be

bent I this fashion.

P1 𝑓2 = (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝)

T° Parallel Perpendicular

Function (𝑦 =𝑅𝑓

2𝑚

𝑡𝑐2𝑈

; 𝑓2 = 𝑥) R2


2𝑚

𝑡𝑐2𝑈

; 𝑓2 = 𝑥) R2

60°

𝑦 = 5𝐸 + 13𝑥−1.564 (0.8867) 𝑦 = 5𝐸 + 13𝑥−1.639 (0.8882)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 5𝐸 + 13 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.564

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 5𝐸 + 13 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.639

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟓𝑬 + 𝟏𝟑 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟓𝟔𝟒

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟓𝑬 + 𝟏𝟑 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟔𝟑𝟗

]

100°

𝑦 = 2𝐸 + 12𝑥−1.503 (0.9527) 𝑦 = 4𝐸 + 7𝑥−1.185 (0.8469)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 2𝐸 + 12 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.503

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 4𝐸 + 7 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.185

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟐𝑬 + 𝟏𝟐 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟓𝟎𝟑

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟒𝑬 + 𝟕 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟏𝟖𝟓

]

150°

𝑦 = 7𝐸 + 10𝑥−1.431 (0.8636) 𝑦 = 1𝐸 + 7𝑥−1.154 (0.5714)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 7𝐸 + 10 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.431

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 1𝐸 + 7 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.154

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟕𝑬 + 𝟏𝟎 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟒𝟑𝟏

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟏𝑬 + 𝟕 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟏𝟓𝟒

]

Table 16: P1 Estimation Equations Summary

P2 𝑓2 = (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝)



2𝑚

𝑡𝑐2𝑈

; 𝑓2 = 𝑥) R2


2𝑚

𝑡𝑐2𝑈

; 𝑓2 = 𝑥) R2

60°

𝑦 = 2𝐸 + 13𝑥−1.486 (0.7888) 𝑦 = 1𝐸 + 13𝑥−1.576 (0.8129)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 2𝐸 + 13 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.486

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 1𝐸 + 13 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.576

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟐𝑬 + 𝟏𝟑 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟒𝟖𝟔

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟏𝑬 + 𝟏𝟑 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟓𝟕𝟔

]

100°

𝑦 = 7𝐸 + 11𝑥−1.45 (0.9356) 𝑦 = 3𝐸 + 7𝑥−1.163 (0.8225)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 7𝐸 + 11 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.45

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 3𝐸 + 7 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.163

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟕𝑬 + 𝟏𝟏 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟒𝟓

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟑𝑬 + 𝟕 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟏𝟔𝟑

]

150°

𝑦 = 3𝐸 + 11𝑥−1.452 (0.7926) 𝑦 = 7𝐸 + 7𝑥−1.225 (0.6033)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 3𝐸 + 11 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.452

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 7𝐸 + 7 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.225

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟑𝑬 + 𝟏𝟏 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟒𝟓𝟐

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟕𝑬 + 𝟕 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟐𝟐𝟓

]


P3 𝑓2 = (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝)



2𝑚

𝑡𝑐2𝑈

; 𝑓2 = 𝑥) R2


2𝑚

𝑡𝑐2𝑈

; 𝑓2 = 𝑥) R2

60°

𝑦 = 9𝐸 + 14𝑥−1.626 (0.8876) 𝑦 = 4𝐸 + 14𝑥−1.689 (0.7869)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 9𝐸 + 14 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.626

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 4𝐸 + 14 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.689

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟗𝑬 + 𝟏𝟒 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟔𝟐𝟔

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟒𝑬 + 𝟏𝟒 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟔𝟖𝟗

]

100°

𝑦 = 4𝐸 + 12𝑥−1.509 (0.9377) 𝑦 = 9𝐸 + 7𝑥−1.201 (.8365)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 4𝐸 + 12 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.509

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 9𝐸 + 7 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.201

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟒𝑬 + 𝟏𝟐 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟓𝟎𝟗

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟗𝑬 + 𝟕 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟐𝟎𝟏

]

150°

𝑦 = 5𝐸 + 12𝑥−1.56 (0.819) 𝑦 = 1𝐸 + 8𝑥−1.241 (0.6184)

𝑅𝑓2𝑚

𝑡𝑐2𝑈

= 5𝐸 + 12 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.56

𝑅𝑓

2𝑚

𝑡𝑐2𝑈

= 1𝐸 + 8 (𝐿2

𝑅𝑜2

𝐻2

𝑤2

𝐸√𝑈𝑡𝑐

𝑚32

𝑡𝑐

𝑡𝑝

)

−1.241

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟓𝑬 + 𝟏𝟐 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟓𝟔

] 𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟏𝑬 + 𝟖 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑

)

−𝟏.𝟐𝟒𝟏

]


By keeping in mind the fact that the main concern and the final aim of this investigation is to figure

out a way to predict the output radius to the hot-pressing technic on the given material, the result

that most interests will be the one that optimize the energy consumption and gives a more

consistent result, by also maintaining the material properties and superficial characteristics. That

is why the clear relationship equation of interest will be at 100°C on the third measure time, P3,

for both parallel and perpendicular configurations.

𝑷𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝑶𝒓𝒊𝒆𝒏𝒕𝒂𝒕𝒊𝒐𝒏:

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟒𝑬 + 𝟏𝟐 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑)

−𝟏.𝟓𝟎𝟗

] (~𝟗𝟒%)

𝑷𝒆𝒓𝒑𝒆𝒏𝒅𝒊𝒄𝒖𝒍𝒂𝒓 𝑶𝒓𝒊𝒆𝒏𝒕𝒂𝒕𝒊𝒐𝒏:

𝑹𝒇𝟐 =

𝒕𝒄𝟐𝑼

𝒎[𝟗𝑬 + 𝟕 (

𝑳𝟐

𝑹𝒐𝟐

𝑯𝟐

𝒘𝟐

𝑬√𝑼𝒕𝒄

𝒎𝟑𝟐

𝒕𝒄

𝒕𝒑)

−𝟏.𝟐𝟎𝟏

] (~𝟖𝟒%)

It’s clear that the perpendicular orientation is consistently more difficult to normalize under a global

function, even though it has an acceptable way to predict it; this difference might have to do with

the orthotropy and the way the fibers interact with each other on both configurations, perhaps

being less predictable on a perpendicular order. Never the less, the equations above are a very

powerful argument to state that the MS/PLA composite lamia is a material that can be used on

certain applications with a good degree of certainty, for it can assure (if done properly) a consistent

final product. Also, speaking of the hot-pressing technique, the difficulties that one as a designer

might encounter might be the limitations in time and mold fabrication; if these two factors can be

overcome, the conformation of this material through this particular method is plausible and

measurable, and thus, applicable in a certain range of radii, being necessary to perform further

investigations to corroborate the actual smallest and biggest radius that may be constructed under

this model.

9. CONCLUSIONS

It has been found that the MS/PLA composite is effectively conformable by a hot-pressing

technique to achieve certain radii range, having a consistent behavior with functions that

accurately describe the final radius in terms of the initial radius (mold radius), the specific length,

the thickness of the lamina, its width and mass, in addition to the fabrication variables of

conforming time, compression time, elasticity modulus and work input.

The optimal conforming temperature is somewhere around the 100°C, which gives the most

dependable results while keeping the lamina intact on the superficial level and seemingly (not

confirmed under lab conditions) on the general mechanical properties. In any case, the actual

optimal temperature must be found through further studies based on this premise.

The Fiber orientation appears to have an important effect on how predictable is the final radius,

due to the highly orthotropy that this implies; the perpendicular configuration is, although good,

considerably less precise than its parallel counterpart. It’s important to highlight too that these

results are consistent on a radius range and to be confirmed on a bigger scale or as a model that

can capture an absolute material behavior, it must be further tested.

By using the Buckingham Pi Theorem, the variables that were considered for the analysis could

be utilized to create a function that effectively describe and predicts the radius of a given lamina

under given conditions on different lapses of time, and more importantly, on the final stage of its

shape, estimated to be around 15 days after the conforming process took place.

With the equations defined, a further study on how to create a method and molds for certain

curvatures might be developed, testing these findings and refining the curves to create a better

know-how on fabrication systems for the MS/PLA composite laminae in engineering applications.

10. RECOMMENDATIONS AND FUTURE WORK The work above presented has tried to be faithful to the proceedings it states up to the reach of

the tools and the materials that were available to do so. Never the less, there are certain points to

consider if further investigation is to be made on this topic or any related to this material. As the

laminae fabrication method rely heavily on the expertise of whom makes it, its recommended to

have knowledge beyond basics to make the actual coupon lot, trying to make the product as

homogenous as possible. Also, the materials to make the laminae should be better selected to

make sure the quality of the fibers are systematically similar and the PLA sheet thickness is

standardized, thus having a more predictable thickness and homogenous fiber distribution.

The post processing of the laminae to come to the coupons is very important too. Trying to make

them as consistent in width as possible might eliminate a variable from the set and leave the

outcome with a more consistent result. The temperature control that was used was not very

accurate, and its loading capacity was very small, leading to difficulties on the experiment, so it is

recommended to use a bigger and more capable oven for the preheating stage. Finally, a last

recommendation will be to use more precise instruments in general, but mostly on the geometrical

retrieving part, given the small differences that might be negligent on the reference frame that was

taken; this way, this phenomenon might be better understood and modeled.

11. REFERENCES A. Porras, A. M. (2016). Optimal Tensile Properties of a Manicaria/Based Biocomposite by the Taguchi

Method. Bogota: ELSEVIER.

Artesanias de Colombia. (n.d.). www.artesaniasdecolombia.com. Retrieved 08 22, 2016, from

http://www.artesaniasdecolombia.com.co/PortalAC/C_sector/cabecinegro_182

Ashcroft, A. P. (2016). Thermo Mechanical characterization of Manicaria Saccifera natural fabric

reinforced poly lactic acid Composite Lamina. Bogota: ELSEVIER.

ASTM International. (2016, 09 10). astm.org. Retrieved from Standard Test Method for Deflection

Temperature of Plastics Under Flexural Load in the Edgewise Position:

https://www.astm.org/Standards/D648.htm

Gabriel Vasquez, G. S. (2016). Colombia Patent No. Dispositivo Asistente de Manipulación de Infantes

“ICAD” (Patent Pending).

GROVE, J. S. (n.d.). Manufacturing Methods for Natural Fibre Composites. Plymouth, UK: Plymouth

University.

Hibbeler, R. (2013). Mechanics Of Materials. Upper Saddle River, NJ: Prentice Hall.

LEONG, Y. W. (2014). Compression and injection molding. Kyoto: WoodHEad Publishing Limited.

Mallick, P. (2008). Fiber-Reinforced Composites. Boca Raton, Fl: Taylor & Francis Group.

Material Property Data. (2016, 09 08). Matweb.com. Retrieved from Overview of materials for Polylactic

Acid (PLA) Biopolymer :

http://www.matweb.com/search/DataSheet.aspx?MatGUID=ab96a4c0655c4018a8785ac4031b92

78&ckck=1

Overview, T. P.-V. (2002, 10 19). authors.library.caltech.edu. Retrieved 08 24, 2016, from History of

Recent Science and Technology:

http://authors.library.caltech.edu/5456/1/hrst.mit.edu/hrs/materials/public/composites/Composites_

Overview.htm

Palmpedia. (2016, 09 08). palmpedia.net. Retrieved from Manicaria saccifera:

http://www.palmpedia.net/wiki/Manicaria_saccifera

Pauls Online Notes. (2016, 11 22). http://tutorial.math.lamar.edu/. Retrieved from Approximating Definite

Integrals: http://tutorial.math.lamar.edu/Classes/CalcII/ApproximatingDefIntegrals.aspx

Renteria, E. D. (2011). Etnobotanica de las Palmas en las Tierras Bajas del Pacifico Colombiano, con

Enfasis en la Palma Cabecinegro. Bogota: Universidad Nacional de Colombia.

Sanjay K. Mazumdar, P. (2002). Composites Manufacturing. Materials, Product and Process Engineering.

Boca Raton, FL: CRC Press.

Wylie, V. L. (2011). Mec[anica de los Fluidos. Bogota: McGraw Hill.

PLA COMPOSITE AFTER ENDURING A RADIAL BENDING ...

Documents

Transcript of PLA COMPOSITE AFTER ENDURING A RADIAL BENDING ...