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thesis entitled

"A Rheological Model Of Apple Flesh Failure During
The Magness-Taylor Puncture Test"

presented by

Sanghyup Jeong

has been accepted towards fulfillment
of the requirements for

M.S. degree in Agricultural Engineering

 

 

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A RHEOLOGICAL MODEL OF APPLE FLESH FAILURE DURING THE
MAGNESS-TAYLOR PUNCTURE TEST

By

Sanghyup Jeong

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1997

 

ABSTRACT

A RHEOLOGICAL MODEL OF APPLE FLESH FAILURE DURING THE
MAGNESS-TAYLOR PUNCTURE TEST

By

Sanghyup J eong

In an attempt to assess firmness, rheological behavior of apple flesh was studied by
developing a laminated cell layer model which can be used to emulate Magness-Taylor
puncture test.

Each layer of the model consisted of a compressive and a shear-tensile element.
Compressive component consisted of a Maxwell model with a fracture element. The
shear-tensile component consisted of an elastic element. The annular pumping effect was
also included in model. Layers were connected in series and each shear-tensile
component was grounded. Simulation was performed on this model with element
parameters and the postulated deformation sequence. The model depicted fairly well the
Magness-Taylor test results both quantitatively as well as qualitatively.

Nondestructive techniques using Hertz contact stress theory and acoustic impulse
technique (Armstrong, 1990) were used for estimating model parameters. These methods
were fairly accurate in predicting the model parameters. Also, a strong correlation with

the Magness-Taylor firmness reading was found.

 

ACKNOWLEDGMENTS

I would like to thank Dr. Aj it K. Srivastava for his direction, support, encouragement,
and patience. I also would like to thank the other members of my committee, Dr. Dan
Guyer and Dr. Randolph M. Beaudry for their suggestions and assistance. I thank Mr.
Dick Wolthius for his technical advice.

I also give my thanks to my parents for their financial and spiritual support for me.
All of the Paul Harris fellows of the Rotary Foundation deserve my heartfelt thanks for
their financial support for student like me.

I would like to thank all the colleagues of graduate office 9.

iii

TABLE OF CONTENTS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ACKNOWLEDGMENT ii:
LIST OF FIGURES . v:
CHAPTER 1
INTRODUCTION
1.1 Justification
1.2 Objectives
CHAPTER 2
REVIEW OF LITERATURE ‘
2.1 Rheological Models Representing the Textural
Characteristics of Food Materials 4
2.2 Physiological Considerations of Apple (
CHAPTER 3
THEORY i
3.1 Modeling Principles and General Assumptions 2
3.2 Modeling Compression Component 2
3.3 Modeling Shear-Tensile Component 15
3.4 Modeling Annular Pumping Component 7
3.5 Postulated Deformation Sequence 7]
3.6 Compression, Shear—Tensile, and Annular Pumping
Components allied Model 24
3.7 Parameter Determination Using Rubber “Thumb Test” ................................. 26
3.8 Parameter Determination Using Acoustic Impulse Technique ...................... 3(
CHAPTER 4
EXPERIMENTAL METHODS AND PROCEDURES 3]
4.1 Methods 3]
4.1.1 Compression Test 3]
4.1.2 Shear Test 34
4.1.3 Tensile Test 34
4.1.4 Magness-Taylor Puncture Test 34

 

4.1.5 Nondestructive Tests

4.1.5.1 Contact Pressure Measurement Using

 

 

 

 

 

 

 

 

 

 

 

 

 

Rubber “Thumb Test” 38
4.1.5.2 Elastic Modulus Measurement Using

the Acoustic Impulse Response 41

4.2 Materials 44

4.3 Computer Simulation of Laminated Cellular Model ...................................... 44
CHAPTER 5

RESULTS AND DISCUSSIONS 47

5.1 Results 47

5.1.1 Model Prediction and Magness-Taylor Puncture Test ..................... 47

5.1.2 Performance of Rubber “Thumb Test” 53

5.1.3 Performance of Acoustic Impulse Technique 59

5.2 Discussion 61

5.2.1 Quantitative Aspects of Model Prediction 61

5.2.2 Qualitative Aspects of Model Prediction 6]

5.2.3 Evaluation of Nondestructive Methods... .. 63

CONCLUSIONS 6%

SUGGESTIONS FOR FUTURE RESEARCH ..66

APPENDICES ......68

 

LIST OF REFERENCES 7m

 

LIST OF FIGURES

FIGURE 1 - Force-deformation relationship of compression test

 

 

 

 

 

 

 

 

 

for cylindrical apple flesh ............................................................ 9
FIGURE 2 - Compression model consisted of a Maxwell

and a fracture element 1 1
FIGURE 3 - Modeling concept of cylindrical apple flesh sample ................................... 12
FIGURE 4 - Modeling concept of shear-tensile component 16
FIGURE 5 - Annular pumping effect during mastication 18
FIGURE 6 - Model representing annular effect 19
FIGURE 7 - Postulated deformation sequence of Magness-Taylor puncture test .......... 23
FIGURE 8 - Final model of apple flesh for Magness-Taylor puncture test ..................... 25
FIGURE 9 - Hertz contact stress of two spheres 77
FIGURE 10 - Stress distribution of Hertz contact problem 79
FIGURE 11 - Sampling direction apple flesh for compression test ................................. 32
FIGURE 12 - Cutting guide for preparing cylindrical apple flesh ................................... 33
FIGURE 13 - Apparatus for shear test 35
FIGURE 14 - Specimen for tensile test 36
FIGURE 15 - Apple holding apparatus 37
FIGURE 16 - Location of the Magness—Taylor puncture test 39

 

vi

FIGURE 17 - Rubber thumb test

40

 

FIGURE 18 - Device for measuring the radius of curvature
(Radius of Curvature Meter) .....................

42

 

FIGURE 19 - Device for measuring acoustic response of apple ..........................

FIGURE 20 - Structure of the simulation program

............ 43

45

 

FIGURE 21 - Predicted versus measured first peak force

FIGURE 22 - Predicted versus measured second peak force

.48

49

 

FIGURE 23 - Predicted versus measured stiffness constant

FIGURE 24 - Comparison of model prediction with experiment .........................
FIGURE 25 - Predicted versus measured Magness-Taylor firmness

FIGURE 26 - Predicted versus measured compressive failure stress ...................

FIGURE 27 - Predicted versus measured shear failure stress

FIGURE 28 - Magness-Taylor firmness versus failure force of
rubber thumb test

FIGURE 29 - First peak force versus failure force ....................................

FIGURE 30 - Measured first peak force versus Magness-Taylor firmness

FIGURE 31 - Measured versus predicted modulus of elasticity by
using acoustic impulse

FIGURE 32 - Precision of model prediction

50

........... 51

.52

............ 54

55

56

........... 57

.58

60

6?

 

Chapter 1

INTRODUCTION

1.1 Justification

Fresh market apples are sorted by color, size, weight and fiminess. Apples classed by
their physical properties and texture are processed for the various apple products. The
texture of apples is an important quality attribute. Apple firmness is an indicator of
textural qualities. Boume (1982) defined fimmess as a texture characteristic during
mastication that displays moderate resistance to breaking. The Magness-Taylor pressure
test developed in 1925 to measure firmness, has been accepted as an industry standard.
The Magness-Taylor pressure test consists of forcing a cylindrical metal tip into the apple
flesh without skin and measuring the maximum force. The penetration depth is about 8
mm (5/16 in) and the diameter ofthe tip is approximately 11 mm (7/16 in) or 8 mm (5/16
in). The plunger tip is round and the penetration depth is marked on the plunger.

The destructive nature of the Magness-Taylor pressure test results in fruit loss which
contributes to economic loss for the apple industry. The firmness assessment is based on
sampling. Export markets require a better quality assessment of the product. A non-
destructive technique that can make it possible to test individual fruit would be beneficial.
The Magness-Taylor method relies on only one indicator to describe the textural quality
of the apple, the maximum force to masticate apple flesh. Other parameters such as

elastic modulus also contribute to texture.

2

An in-depth understanding of the Magness—Taylor test would be very helpful in
developing a nondestructive technique assessing fruit firmness to meet the needs of high

quality produce.

1.2 Objectives
The objectives of the research were
1. to develop a rheological model of apple flesh and to examine the capability of the

model for predicting the Magness-Taylor puncture test result.

2. to evaluate the potential of a rubber spherical indentor as a means of estimating the

compression and shear failure stresses of apple flesh.

3. to investigate the capability of the spherical indentor as a non-destructive technique to

measure apple firmness.

Chapter 2

REVIEW OF LITERATURE

2.1 Rheological Models Representing the Textural Characteristics of Food Materials

Much effort have been devoted to developing rheological models to describe
complex texture qualities of food materials. New rheological elements have been
suggested along with a combination of the conventional rheological elements e. g. spring
and dashpot. These models have been subjected to different types of loading conditions
and their responses have been compared to the experimental results. Maxwell and Kelvin
models which are the classical models in rheology have already been studied and
evaluated under compression, extension, creep, and relaxation tests. Maxwell and Kelvin
models are composed of a spring and a dashpot in a serial and in a parallel pattern,
respectively.

Peleg (1976) proposed a model system which was basically a parallel array of
generalized Maxwell body. He added two fracture elements which were suggested by
Drake (1971) to the model. The general elements of this model had an elastic stage and a
Maxwellian stage when the model worked as a Maxwell model until fracture. The
number of each stage and the parameters of the elements determine the pattern of
rheological behavior of a given material. This model can describe various rheological
behavior qualitatively.

Chen and Rosenberg (1977) suggested a nonlinear viscoelastic model which consisted

5

of Maxwell and Kelvin models containing an yield element. The model exhibited
Maxwellian behavior and then it showed the behavior of a four element Burgers model
which was a serial combination of a Maxwell and a Kelvin model afier the yield element
was activated. He indicated that the model was able to represent the behavior of
American cheese by adjusting model parameters.

Dickinson and Goulding (1980) tested various types of cheese and found that the
model suggested by Chen and Rosenberg (1977) could be used to fit individual
compression curve but the model was unable to predict general load deformation
behavior.

Johnson and et a1. (1981) modified the model suggested by Peleg (1976) by
incorporation of a contact and a fracture element. In this study the contact and the
fracture element were functions of time and temperature to describe the rheological
behavior of raw and cooked fish meat. They demonstrated that the model worked well to
describe the rheological behavior qualitatively.

McLaughlin (1987) had a different approach to develop a model describing apple
tissue failure phenomenon. Yield stress data for 800 cylindrical samples was studied.
Statistical test failed to reject (p=0.85) the hypothesis that the data followed a three
parameter Weibull distribution. This statistical model was suggested as an adequate
probability model for predicting the failure stress of apple flesh.

During the past decade most of the efforts were concentrated on any developing
property measurement techniques rather than developing a model having any physical

meaning.

2.2 Rheological Considerations of Apple

Much research has been conducted about the phenomenological and morphological
characteristics of the failure of fruits. Mechanical and structural characteristics of fruits
were observed and discussed. An understanding the nature of failure will help develop
appropriate models having physical meaning.

Peleg and et al. (1976) studied compressive failure patterns of several juicy fruits.
Compression tests were performed to the cylindrical samples by using an Instron
Universal Testing Machine. Fruits showed their characteristic failure patterns. Effect of
the juiciness and dimension of the sample were studied. In this research it was found that
structural characteristics, liquid content, and geometry of the sample affect the force—
deformation relationship.

Mohsenin (1977) studied the failure of food materials from the point view of solid
mechanics. Working with apple tissues he found that the shear resistance was a result of
the cementing agent (pectic substance) in the middle lamella holding together the cells in
the parenchyma tissue. He also studied the potential usage of the Hertz contact stress
theory to find failure parameters from the force-deformation relationship.

Pitt (1982) considered two different types of failure, cell wall rupture and cell
debonding. Sample was considered as the sum of a large number of cell layers normal to
the direction of the applied force. In case of constant rate strain due to the rupture of the
weakest cell of a layer, neighboring cells had higher stress level than before. If the stress
is higher than cell strength then failure occurs and this process propagates through the

layers of the sample. Due to this fractured transverse plane enzymatic browning occurred

7

in that cross section. This catastrophic failure was observed in the fresh apple tissue.

Lin and Pitt (1986) reported that turgor pressure and the strain rate affect failure
mode of fruit and vegetables and tissue strength.

Khan and Vincent (1990) observed that cells of apple flesh are arranged in radial
column and the cell size and shape changes along with the radial direction by using
scanning electron microscope, indicating that apple flesh should be considered as an
anisotropic material in the radial direction.

Khan and Vincent (1993) observed that if a radial cylindrical apple flesh sample was
subjected to a compressive force then it generally fractured by collapse of a single layer of
cells at right angle to the direction of force. Tangential sample failed in shear. This
phenomenon is due to the anisotropic property of apple parenchyma which was observed

by Khan and Vincent (1990).

Chapter 3

THEORY

3.1 Modeling Principles and General Assumptions

To develop a model representing Magness-Taylor puncture test it is necessary to
observe and analyze the mastication phenomenon. Basically Magness—Taylor puncture
test involves three major factors which are compression, shear-tension and annular
pumping effects. These factors will be combined into one system representing the apple
flesh afier being studied and modeled individually. Throughout this research several
simplifying assumptions were made. Even though the actual Magness-Taylor firmness
instrument has round tip the radius of curvature is large enough so that the plunger tip
was considered as flat. The second assumption was about the cylindrical apple flesh
sample. Actually the layer of the sample is curved because of its radial arrangement of
cells. However, the curvature was relatively large enough to be treated as flat because the

sample diameter was considerably less than that of the whole apple.

3.2 Modeling Compression Component
If several ideal conditions of the compression test are satisfied the saw-tooth shaped
force deformation relationship as shown in Figure 1 could be obtained. The first ideal

condition is to make perfect cylindrical apple flesh sample which means the flat cutting

FORCE [N]

 

140

120 ~—

100 —

804

60«

40 --

20-

P1 <~ P2

 

 

 

 

 

 

0.

0 0.5 1.0 1.5 2.0 2.5
DEFORMATION [mm]

FIGURE 1 - Force-deformation relationship of compression test
for cylindrical apple flesh

3.0

10

surface are normal to the direction of the compressive force. The second ideal condition
is lack of friction between cutting surface and the pressing die. The last ideal condition is
satisfied if the sample is obtained in the radial direction from the whole apple because of
the anisotropic characteristics of apple parenchyma studied by Khan and Vincent (1990).
In these ideal conditions sample shows two or three fractures caused by collapse of a
single layer of cells at right angles to the force (Figure 1). A simple model representing
this phenomenon was developed. This model was the building block of the final model.

The first compression region (b, Figure l) was represented by a Maxwell model and a
fracture element having 6c as its yield stress (Figure 2). The model was used to represent
a single layer of cells.

Mathematical expression for the model at constant strain rate is,

E
o=nV(1—e rl) , OSo<c5C

[1]

where o = Stress

r] = Viscosity

E = Elastic modulus

CC = Critical yielding stress
Time
V = Constant strain rate

99
||

Based on the research of Khan (1993) a cylindrical apple sample can be considered as
a system of stacks of a single cell layer. By connecting the model in a series pattern the
system of a cylindrical sample can be depicted physically. The model is shown in Figure
3. If apple flesh is assumed to be an ideal isotropic material in the radial direction oC
would be the same for each layer. However, it is expected that a limited variation would

exist from layer to layer in real life. Thus, if the model is subjected to compressive

11

l,

:3

to:

FIGURE 2 - Compression model consisted of a Maxwell and a fracture element

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force a layer containing the lowest yield stress will collapse first and so on. The fact
that the P2 is greater than the P1 in Figure 1 supports the above reasoning.

If the cylindrical apple flesh sample is subjected to a stress 0 (Figure 3) the total
deformation will be distributed to each cell layer. The layer having the weakest yield
stress will collapse first. The cylindrical apple flesh sample which has multi-layer of cells
can be represented by stacking the unit compression model (Figure 2). Elasticity and
viscosity of each layer were assumed to be the same. However each layer had different
critical yield stress.

At time t, the strain and the stress of every layer were equal because the compression
model in Figure 3 was a serial system until the stress reached the lowest critical yield

stress. The strain of unit layer was equal to the total strain divided by the number of cell

layers.
Thus,
olzoz- =oN=ou=o
_ _ __ _ _a
81-32- "-8N-8u-§
[2]

where on = Stress of unit layer

0 = Total stress
Su = Strain of unit layer
a = Total strain

N = Layer index
If the cylindrical apple flesh sample was considered as a simple combination of a

Maxwell model and a fracture element then,

=Zsu= [3]

14

Eq. [3] can be expressed as follows by using eq. [1]

N G" = 6 [4]

E

—5r ——r
nu(1-e ““) n(l-e “)

 

From eq. [4] the following relationships were obtained.

Eu=NE
nu:NTl [5]

Therefore the properties of unit layer, Eu and nu, can be calculated from eq. [5] if the
E and n were known. E and r] can be found from the force deformation relation of the
compression test by curve fitting using eq. [1]. These unit parameters will be used in the
final allied model.

After the first collapse system is undergoing inequilibrium state for a short period
until the system gets to equilibrium state. When the system gets to the equilibrium the
total number of layers is reduced by one. Because the transition period is too short, total
strain can be assumed to remain unchanged. Thus,

6 0
u.before : E Smaller : E [6]

before after

8

The total strains, before and after collapse of a layer, are assumed to be same due to the
short transition. Therefore,

N ' 8 = (N _ 1) - 8u,after [7]

u,before
The strain after the fracture is expressed as follows

E _ {(6 _ (8 before) + W} N 1
= - : 8before — [8]

8
u,a{ter E N _ 1

 

15

where f = thickness of a unit layer at time t
By using eq. [6], [7] and [8] the following equation is found

E — 0'
_ u,before before
Gafler _ Gbefore — N _ 1 [9]

By using eq. [9], e; in Figure 1 can be predicted. This fact supports that the suggested

compression model is reasonable.

3.3 Modeling Shear-tensile Component

Figure 4 shows the cross sectional deformation pattern of the apple flesh subjected to
compression by a cylindrical plunger. The strain of each layer decreased as the depth
increased. In Figure 4, layer shaped like a circular plate in a real situation modeled as a
two dimensional elastic element with the presence of a fracture element. A fracture
element represents the yield stress of a layer. In this case yielding involves tensile and
shear simultaneously. It is difficult to perform an ideal shearing test because of the
ductile characteristic of food material and the clearance between the shearing plunger and
guiding wall. Thus, the yield stress obtained from shearing test naturally contains tensile
and shear contribution. The yield stress from shearing can be used as the critical stress of
the fracture element. Also the angle or is important to determine the deformation rate of
shear-tensile component. The angle will vary within 0 to 90 degrees as the compression
goes on. If the angle is 90 degrees the deformation of shear-tensile component will be
the same as the sum of deformation rate of each layer below that shear-tensile component.
However, in a real situation the angle is less than 90 degrees and also it changes with

time. In this research the angle is assumed constant and the deformation rate of the shear-

16

 

 

 

APPLE
FLESH

 

 

 

 

mi l
a Elise?

SHEAR-TENSILE
COMPONENT

 

 

 

 

COMPRESSION

r COMPONENT
Fwd:

 

- —\\ {Ens/Wk +1:le

 

%—~—A/\/\» . l C?

l

T
WWW/WW%A

FIGURE 4 - Modeling concept of shear-tensile component

17

tensile component to the compression component was assumed 0.7.

3.4 Modeling Annular Pumping Component

Apple flesh contains about 80% of water by weight. Therefore, the squeezing action
of cylindrical probe produces juice. If the speed is high, then the resistance created by
juice is significant. The juice is expelled through the clearance in between probe and
apple flesh wall in Figure 5. The produced juice is pumped by pressure, Po, and this
pressure pushes the apple flesh wall to make clearance, c, in Figure 5.

A mechanical model was devised to imitate the phenomenon as depicted in Figure 6.
The model consisted of a piston and a cylinder which represent probe and apple flesh
wall respectively. A sliding block and a spring represents apple flesh wall pushed by
pressure P0. The cylinder is filled with apple juice entrapped air. As the piston moves
forward, pressure, P0, is produced which pushes the fluid through the clearance created by
the sliding block moving backward compressing the spring with a force F. Apple juice
flows at a high velocity through the clearance.

From the model displaced liquid inside the cylinder discharged through the clearance.

The steady flow-mass-conservation relation can be written as

thin : [Hour [10]
If the juice is assumed as an incompressible liquid, then the inlet and the outlet

volume should be the same so that eq. [10] can be replaced with

v.01in : v.010ut [1 l]

Patm

18

 

 

V//////// /////
/
Deformed é
Apple Flesh /
Wall 6
¢
//
APPLEFLESH

 

 

 

 

 

/////////////////

FIGURE 5 - Annular pumping effect during mastication

 

19

 

 

 

 

 

0:0

 

 

 

(A)

w
9
0
i
i

Q

/
l

 

\vw

 

 

 

 

 

 

 

 

l_
W

FIGURE 6 - Model representing annular effect

20

Ifthe piston moves with a constant velocity, the speed of the juice flowing through
the clearance can be calculated as follows.

UzVA—mzE [12]
AC 40

where U = Velocity of exiting apple juice
V = Velocity of the moving piston
c = Clearance
Am = Cross sectional area of the piston
Ac = Area of exit (= crtD)
D = Diameter of the piston

Bernoulli’s equation is used to determine pressure inside the cylinder.

P.(0—P. =%pu2 [13]
where Po(t) = Pressure inside the cylinder
Pa = Atmospheric pressure
p = Fluid density inside the cylinder
0 = Exiting speed of the liquid

The pressure or the stress acting on the moving block is,
c
Po=o=eE=EE [14]
where E is the original length

The clearance, c, can be expressed as following,

[P0 [15]

Using eq. [12], [13], and [15] following equation is obtained.

2 2 2
2——pVDE =0 [16]

P t3—PP
0() 80 32

Eq. [16] can be used to calculate P0.

21

3.5 Postulated Deformation Sequence

In compression test the displacement of a layer is equal to the total displacement
divided by the total number of layers because each layer is free to move. Therefore, the
displacement of each layer is all the same. For the Magness—Taylor test, however, total
displacement cannot be divided equally due to the restraint of each layer. Shear-tensile
resistance plays a role of those restraints. Thus, the distribution of the deformation of the
entire sample should be considered.

In this study it is assumed that the distribution of deformation of each layer follows
the geometric ratio. Therefore, the total displacement is the sum of the deformation of
each layer. It is expressed as,

D(t):dl(t)+d2(t)+----+dn(t) [17]

where D(t) = Total deformation at time t
and dn(t) = Displacement of the nth layer at time t

Because the deformation of each layer follows geometric series, eq. [17] can be
represented as follows,

D(t)=alt+a2t+a3t+~~+ant [18]
= alt +alrt +a1r2t+----+a]r""t

where an = Deformation rate of n th layer
t = Time
r = Geometric ratio(0<r<l)
If D(t) is constant strain rate then eq. [1 8] is
D(t)=Vt=(al +a1r+alr2 +--~+alr"")t [19]
where V = Speed of the cross-head

From eq. [19], a1 is expressed as

22

altar

By using a1 and r the deformation rate of each layer can be determined. In addition,

 

deformation history with time should be considered. Figure 7 shows the deformation
sequence based on the mastication phenomenon. The slope of the line OG represents the
speed of the cross head. Each layer is assumed to be deformed linearly according to its
defamation rate until the deformation gets to (1G which is the critical deformation for the
mechanical system failure of a layer. During the period, from t1 to t 2, deformation rate of
the first layer is increased rapidly due to collapse of mechanical structure until the
deformation of the first layer reaches d, which is the deformation of a layer showing no
more compression. At the same period (tl-tz) the other layers experience rapid relaxation
and they recover some amount of deformation to compensate the rapid compression of
the first layer. The period (tl-tz) can be considered as a non-equilibrium state. However,
at time t2 system turns to an equilibrium state. In the practical point of view, time span,
t1 and t2, can be neglected because the phenomenon of this period is so rapid.

After t2 the total number of layers is reduced by one because the first layer has already
been destroyed. Therefore, the deformation rate of each layer should be determined
again.

At t3 the deformation of the second layer reaches (1c and it is deformed to dt rapidly
until the time gets to t4. The other layers get into rapid relaxation.

This discrete pattern of deformation occurs throughout the destruction phenomenon of
apple flesh in the ideal condition. However this pattern of deformation is found three to

four times in the real life situation.

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3.6 Compression, Shear-tensile and Annular Pumping Component allied Model

Models of each component were combined to generate the combined force

deformation response. Figure 8 shows the allied model composed of the three models. A
in Figure 8 represents the compressive component which consisted of a Maxwell model
and a fracture element. B represents a shear-tensile component and every component is
grounded. C is an annular pumping component. During the early period of compression
flow of juice is not fully developed to produce resistance. S delays the activation timing
of the annular pumping component for a while. Then the postulated deformation
sequence is applied to the allied model to get the force response.

Castigliano’s theorem is used to calculate the force response of the system. This is
the simple method for the deflection problems. Castigliano’s theorem is that when forces
act on elastic systems subjected to small displacements the displacement corresponding to
any force, collinear with the force, is equal to the partial derivative of the total strain
energy with respect to that force. Using Castigliano’s theorem, energy of a system
consisting of non-linear elements is expressed as following.

5 n e.
E:jP-dt3=}_jjr‘,-dei [21]
0 i=1 0

where P = Resultant force

d5 = Differential total deformation
F] = Force of i th element

e] = Differential deformation of i th element
i = Layer index

n = Total number of layers

E = Energy

 

 

p—a

 

 

 

z --...
\\s

 

 

 

FIGURE 8 - Final model of apple flesh for Magness-Taylor puncture test

 

 

26

Each cell layer is elastic until it gets to failure and the each layer is subjected to very
small deflection. Thus the Castigliano’s theorem has no problem in the application for
this approach. Because the deformation is already known the force response of each layer
can be determined. Therefore the strain energy which is the force times of deformation
can be calculated for each layer at a certain time

The total strain energy calculated by the theorem is differentiated numerically with
total deformation to obtain the resultant force response which is the predicted Magness-

Taylor test result.

3.7 Parameter Determination Using Rubber “Thumb Test”

Stresses occur at the contact area when two bodies having curved surfaces are pressed
together. Hertz contact stress theory has been developed to describe the above situation.
Figure 9 shows two spheres contacting each other. By Hertz contact theory the radius of

contact area is

 

 

a=3\/_3_F__(1—v,2)/I~:,+(1—v22)/E,

 

[22]
8 l/dl +1/d2
where d1, d2 = Diameters of body 1 and 2
F = Force applied
v] , vz = Poisson ratio of body 1 and 2
E] , E2 = Modulus of elasticity of body 1 and 2
a = Radius of contact area
The maximum normal stress at the center of the contact area is
0z max = 1)max = 31:2 [23]
’ 2pa

Stresses in direction of x and y can be represented as functions of z.

27

FORCE

 

 

FORCE

FIGURE 9 - Hertz contact stress of two spheres

28

l

_ 1
0‘ =6 =—P 1~£tan l(l+m)———
x y max a z [ 22]
T 21+—
a
a2
—Pmax
oz: 2
1+2—
a2
3K—E

 

where m =
6K

K = Bulk modulus or incompressibility

And the shear stress can be calculated by using ox and oz as

where txy = Shear stress

Figure 10 shows the stress change for the distance below the surface i.e. along 2

[24]

[25]

[26]

direction. By using this relationship maximum compressive stress and the shear stress

can be calculated. The maximum shear stress is approximately 1/3 of the maximum

normal stress.

If body 1 is rubber sphere and the body 2 is apple then by pressing the two objects

until the apple goes over the elastic region the yield compressive and shear stress can be

predicted.

3.7 Parameter Determination Using Acoustic Impulse Technique

Elasticity of a resonating elastic sphere is defined as

29

.Eozoa 88:8 88: .«o souspmbmmw wmobm - 2 EDGE

m0<naDm Fog—.200 EOME mUZ<Fm5

«Nd

 

 

 

   
     

to."

 

md

 

\

mmobm Roam E=§§§

mmobm 38.52 825082

 

wag—nu Ow mmobm .mo 03mm

30

1/3 2 2/3
p (61: ) 2(1+ v)
E = I: Q2 f2 In2/3

where p = Density
v = Poisson’s ratio
9 = Normalized frequency
E = Modulus of elasticity
m = Mass
f = Frequency

The model includes apple mass, apple density, Poisson ratio, and normalized
frequency. There are three different kind of vibrating modes. The compressional mode

vibrating in the radial direction was assumed as the most predominate resonant frequency

by Armstrong (1989).

Chapter 4

EXPERIMENTAL METHODS AND PROCEDURES

4.1 Methods
4.1.1 Compression Test

Cylindrical apple flesh samples 20 mm in diameter and 12 mm in length were
prepared for the compression test. Cylindrical specimen was cut from fresh apples by
using a borer. The borer was pushed into the direction of center around equator in the
radial direction (Figure 11). Then the cylindrical sample was placed on the V-shaped
cutting guide (Figure 12) to get the sample having desired length and made ends flat and
normal to the direction of compression. A razor blade was used to cut the sample ends.

The sample was placed on platform of the Instron Universal Testing Machine and
was pressed with a flat die. The force signal was transmitted to the data acquisition
system. Cross-head speed was 0.00423 m/s (10 in/min). Mineral oil was added to both
ends of the cylindrical apple flesh specimen to reduce friction between the die and the
sample. The sampling rate of the data acquisition system was set to 100 Hz.

Actual force-deformation result was fitted using equation [1] and an optimization
program to determine elastic modulus and viscosity of the viscous element in the model.
The critical stress, Go, for the fiacture element is determined by P1 (Figure 1) divided by
the area of die. Elastic modulus, viscosity, and the critical stress will be used as

parameters of compression model.

31

 

32

APPLE

 

FIGURE 11 - Sampling direction of apple flesh for compression test

33

RAZOR BLADE

    

 

 

O

CUTTING GUIDE L/
o /
./
/

FIGURE 12 - Cutting guide for preparing cylindrical apple flesh

 

 

 

 

 

 

 

 

 

34

4.1.2 Shear test

Slices of apple flesh were prepared by using a slicer. A shearing device suggested by
Mohsenin and Goehlich in 1962 to determine shear strength of apple skin was used for
the test (Figure 13). The apparatus was installed on the platform of the Instron Universal
Testing Machine. The shear strength will be used as a critical stress of the fracture
element of shear-tensile model.

Strain rate was 0.00423 m/s (10 in/min). Force signal from the load cell was recorded

by data acquisition system at a sampling rate of 100 Hz.

4.1.3 Tensile Test

Slice of apple was obtained from the cheek of whole apple. Tensile specimen was
prepared from the slice of apple flesh (Figure 14). Length, L, and the width, W, were 20
mm and 9 mm, respectively. Thickness of the specimen, t, was measured using calipers.
The specimen was installed on the Instron Universal Testing Machine and tensile force
was applied until it failed. Tensile elasticity was calculated from the stress-strain

relationship. The elasticity will be used as a parameter of shear-tensile model.

4.1.4 Magness-Taylor Puncture Test

An apparatus as shown in Figure 15 was used to make the cutting surface of apple
normal to the direction of the force applied. Also this device was used to hold the apple.
The apparatus has cutting blade and guide to remove the skin of apple and to make the

surface flat and even. This device was placed on the platform of the Instron Universal

35

 

 

 

 

 

 

 

 

 

 

 

FORCE
A PLUNGER
A APPLE SLICE
=52;

 

 

 

FIGURE 13 - Apparatus for shear test

36

FORCE

 

 

 

 

FORCE

FIGURE 14 - Specimen for tensile test

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\ BLAD UID
~ H / r,
; l
I l 1
1 [ 1 lfi
[F A; Fm
\LBLADE Li i r—AA,
_}: I ,= U: E: ii
LE 1% a m
RUBBER l
I f FRAME
1 l /
1

WWW

 

FIGURE 15 - Ap 1e holdin a aratus

38
Testing Machine. A 11.11 mm (7/ 16 in) diameter probe with flat end was used to push

down into apple flesh. Cross-head speed was 0.0042 m/s (10 in/min).
The probe was pushed to a depth of 15 mm. The location for this test was
approximately on the equator as the probe was inserted in the radial direction (Figure 16).

The probe was lubricated with mineral oil to reduce friction.

4.1.5 Nondestructive Tests

Two nondestructive tests were studied in this research. One is rubber thumb test
which is developed in this study to predict the critical yield strengths of compression and
shear for the apple flesh. The other one is acoustic method which has been already
developed and evaluated by Armstrong in 1989. Through acoustic method elasticity of

apple flesh was estimated.

4.1.5.1 Contact Pressure Measurement using Rubber “Thumb Test”

A rubber indentor was used to measure contact stress using Hertz contact stress
theory. The rubber diameter of 26.8 mm diameter had an elastic modulus of 3.2 MPa and
a Poisson’s ratio of 0.62. The indentor was attached to a steel plunger using adhesive
(Figure 17). The pressure between the ball and apple was measured using a paper thin
Uniforce pressure sensor. This sensor had a range of 0 to 222 N ( 50 lbf ) and a circular
sensing area having 6.35 mm (0.25 in) diameter. The location for this test was on the

equator of apple. The radius of curvature of this point was measured in two directions.
One is in the direction of equator and the other is in the longitudinal direction. The

average value of the two measurements was used as the radius of curvature at that point.

39

I / PROBE
i
I
l / CUT SURFACE

 

 

 

 

 

 

 

FIGURE 16 - Location of the Magness-Taylor puncture test

CARBON PAPER
\

4O

SENSING AREA \

RUBBER BALL

UNIforce

r451

 

PRESSURE SENSOR

 

 

 

 

THINPAPER .

 

\ r

 

 

 

 

 

 

FIGURE 17 - Rubber thumb test

 

41

To measure the radii of curvature of convex body, an apparatus composed of a dial
indicator and two sharpened rods was used (Figure 18). Radii were calculated as
following

Radius = E + L32
8(BD) 2

[28]

Apple was held by a fixture as shown in Figure 15. Carbon paper and a sheet of paper
were used to get the contact area when the first “give” occurred. The term “give” means a
change of force response. The probe, pressure sensor, carbon paper, paper and apple
were arranged in the order as shown in Figure 17. The probe speed was 0.0021 m/s (5
in/min). The Instron Universal Testing Machine was manually stopped as quickly as

possible when the first failure of tissue was detected by hand. The “give” produced

vibration enough to be sensed by hand and it usually accompanied an audible sound.

4.1.5.2 Elastic Modulus Measurement using the Acoustic Impulse Response

An apparatus which was designed by Armstrong, et al. (1992) was used to determine
the elastic modulus of apple. The apparatus was composed of mass measuring sensor, an
actuator to swing an impulse hammer, and a microphone to measure the acoustic signal
(Figure 19). The device was connected to a data acquisition system and the signal was
converted automatically to the elastic modulus.

Every apple was tested using this device before they were tested by any destructive

testing methods. Impulse location was approximately at the equator of the apple.

4.2 Materials

42

 

 

 

/ OBJECT
18

FIGURE 18 Dev1ce for measuring the radius of curvature ( Radius of
Curvature Meter)

Flo

43

Emma .«o 85%»: cumsoom manage Sm oom>om -

2 mMDOE

 

 

 

 

 

7
m4<Om mm<2\

 

 

UH

 

”53:2;

 

 

 

 

Om

 

 

 

 

mmbefi/ A

 

 

 

Elm

\

n:Ome—Om

Er.

mammxx

 

 

 

 

 

 

/

mZOImOan~E

 

44

To have wide range of firmness, nine different cultivars were selected. Cultivars were
Red Delicious, Red Rome, Fuji, Granny Smith, Golden Delicious, Braebum, Ida Red,
Gala, and Jona Gold. A total of 45 apples were used for the experiment. Apples were
purchased from a local supermarket on the day of experiment and they were stored in a
refrigerator at 14° C.

Weight measurement, acoustic impulse method, and “rubber thumb” test were
performed on each apple prior to the destructive tests. Magness-Taylor puncture test,
compression, shear, and tensile test were carried out afier non-destructive tests were

conducted. Locations for tests were different from test to test .

4.3 Computer Simulation of Laminated Cellular Model

A computer program for simulation was written in C language. The major parts of
the program were the laminated cellular model, deformation sequence generator,
compressive and shear-tensile force calculator, and the Castigliano’s theorem. The block
diagram of the simulation program structure is in Figure 20.

The model parameters of this simulation come from the compression, shear, and
tensile test results. In this simulation 100 layer model represented a thickness,
approximately 20 mm of apple flesh sample. Geometric ratio, r, was set to 0.997. The
speed of testing tip was 0.00423 m/s (10 in/min) which was the same as that of the
experiment. During the infinitesimal time, deformation generator produced deformations
for every layer and the force of the components of each layer was calculated based on the
deformation information. Force was multiplied by infinitesimal deformation to obtain

infinitesimal energy and the energy was summed up throughout the simulation. After 5

45

 

     

 

Deformation Sequence

 

 

   

 

 

 

 

 
   
  

 

 

 

 

 

 

 

 

 

 

 

 

Parameters: Generator fl Parameters:

E, 11,60 E,O'c
Y Y 1
Compressive Shear-tensile 1‘;

Component Component 1

Compressive 1 Shear-tensile 1

Energy 1 Energy 1

L———>‘ Total Energy <—-——

 

 

 

 

 

 

 

 

‘ / - 7"-\\\
leferentiation/-

Total Force 1

 

 

 

 

Force from
Annular Pumping

 

 

 

Final Force-Deformation
Relationship

 

FIGURE 20 - Structure of the simulation program

46

seconds of simulation, numerical differentiation of energy for the deformation was
performed and it produced force-deformation relationship. To the force-deformation

result, annular pumping resistance was added gradually after the second peak force.

Chapter 5

RESULTS AND DISCUSSION

5.1 Results
5.1.1 Model Prediction And Magness-Taylor Puncture Test

From the force-deformation relationship of the Magness-Taylor puncture test the first
peak force was determined at a point showing significant drOp of force. Figure 21
illustrates the result of the comparison between predicted and measured first peak force of
Magness-Taylor test. The correlation coefficient was 0.76.

The measured second peak force of Magness-Taylor puncture test was compared with
that of model prediction. Figure 22 shows the correlation coefficient of 0.79 which is a
little higher than that of the first peak force shown in Figure 21. In some cases, the
second peak force could not be observed and those cases were not considered.

Even though the first peak forces are same different stiffness indicates different
texture of apple flesh. Figure 23 illustrates that the correlation coefficient was 0.83.
Stiffness constant was defined as the slope of the secant drawn from the origin to the first
peak of the force-deformation curve. Figure 24 is an example of the simulation result.

Magness-Taylor firmness predicted by the model was compared with that measured
by experiment. Figure 25 shows that the correlation coefficient is 0.82.

Even though the juice expelling effect produced constant resistance of 9.67 N which
was calculated by using the eq. [1 6] it took time until this resistance was fully developed.

47

Measured First peak of Magness-Taylor test [N]

120

100

80

60

40

20

48

Y = 1.02 X + 4.00
Correlation Coefficient=0.76

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Red
Delicious

Red
Rome

Fuji
Granny
Smith

Golden
Delicious
Braebum
Ida Red

Gala

Jona
Gold

—— Fitted

 

20 40 60 80 100
Predicted Flrst peak [N]

FIGURE 21 - Predicted versus measured first peak force

 

Measured 2nd Peak [N]

100

90

80

70

60

5O

40

30

20

1O

49

=0.83X+10.67

Correlation Coefficient=0.79

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1/ .

Red
Delicious

Red Rome
Fuji
Granny

Smith
Golden

Delicious
Braebum
Ida Red

Gala

Jona Gold

— Fitted

 

0 20 40 60 80 100 120
Predicted 2nd Peak [N]

FIGURE 22 - Predicted versus measured second peak force

 

Measured Stiffness Constant [Nlm]

60000

50000

40000

30000

20000

11 0000

50

Y=0.83X+3657

Correlation Coefficient=0.83

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Red
Delicious

Red
Rome

Fuji
Granny
Smith

Golden
Delicious
Braebum
Ida Red

Gala

Jona
Gold

—- Fitted

 

0

10000 20000 30000 40000 50000
Predicted Stiffness Constant [Nlm]

 

60000

FIGURE 23 - Predicted versus measured stiffiiess constant

r.-

 

FORCE[N]

51

WWfiimmv , wv,,flfi,, , .7

  
  
  

70 LL ,L,7,L, 7, ,
2nd Peak
Force
mT~M%“AAAA\>
Force , 1

30~

  

Stiffness

20 I " Constant

— Experiment

—Model Prediction

 

 

0 1 2 3 4
DEFORMATION [mm]

FIGURE 24 - Comparision of model prediction with experiment

"I

Model Predicted Magness Taylor Firmness [N]

120

100

80

60

40

20

Y = 0.7 X + 15.78
Correlation Coefficient=0.82

 

 

 

 

 

ii

 

 

 

 

 

 

 

 

Red
Delicious

Red Rome
Fuji
Granny

Smith
Golden

Delicious
Braebum
Ida Red

Gala

Jona Gold

 

 

 

 

 

Measured Magness Taylor Firmness [N]

— Fitted

 

 

 

FIGURE 25 - Predicted versus measured Magness Taylor F irrnness

"lf

53
The resistance increased linearly after the first peak until it reached a value of 9.67 N and

then it was fixed at 9.67 N. Because the viscous element was connected in parallel to the

model the resistance was just added to the result.

5.1.2 Performance of Rubber “Thumb Test”

The maximum normal stress at the center of the contact area between rubber ball and
the apple was calculated by using eq. [23]. Speed of the rubber thumb test was 0.00212
m/s (5 in/min). Figure 26 shows the correlation coefficient of 0.76.

Figure 27 illustrates the correlation coefficient of 0.64 between measured shear failure
stress and the predicted maximum shear stress. According to the Hertz contact stress
theory the maximum shear stress occurred below the contact surface and it was
approximately 1/ 3 of the maximum normal stress.

Magness-Taylor firmness was compared directly with the failure force which was
observed when the contact pressure dropped significantly. In this research this moment
of “give” was detected and the testing machine was stopped at that moment. Figure 28
shows a correlation coefficient of 0.9. In rare cases, no significant drop of the pressure
was observed due to tissue failure.

The first peak force showed a much higher correlation coefficient of 0.90 with the
failure force than that of the Magness-Taylor firmness (Figure 29). The high correlation
coefficient implies that the failure force represents the first peak force.

The relationship between the first peak force and the Magness-Taylor firmness was
observed in Figure 30. More than a half of the data is almost identical in the range of

error.

54

Y = 0.55 X + 35249

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Correlation Coefficient=0.76

5E+05

4E+05 .
w l
9:. i
a 4E+05 '
E 1
‘3 35+05
2
.2 35+05 1 1 .
o . I
.2 .
a .
9:9 2E+05
a
g .
8 ZE+05 1
B * 1
0
‘5 1 E+05
2
m

5E+04

0E+00

 

 

 

 

 

 

 

 

 

Red
Delicious

Red
Rome

Fuji

Granny
Smith

Golden
Delicious
Braebum
Ida Red
Gala

Jona
Gold

—— Fitted

 

 

0E+00 1E+05 2E+05 3E+05 4E+05 5E+05 6E+05 7E+05

Measured Compressive Failure Stress [Pa]

FIGURE 26 - Predicted versus measured compressive failure stress

 

Predicted Shear Failure Stress [Pa]

1 E+05

1E+05

1 E+05

8E+04

6E+04

4E+04

2E+04

0E+00

FIGURE 27 - Predicted versus measured shear failure stress

55

Y = 0.2 X + 40408

Correlation Coefficient=0.64

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

i l

 

 

 

 

Red
Delicious

Red
Rome

Fuji
Granny

Smith
Golden

Delicious
Braebum
Ida Red

Gala

Jona Gold

— Fitted

 

1

Measured Shear Failure Stress [Pa]

 

OE+00 5E+04 1E+05 2E+05 2E+05 3E+05 3E+05 4E+05

 

56

Y = 1.81 X-58.9
Correlation Coefficient=0.77
250

 

0 Red
Delicious

1

1 I Red
1 Rome
1 A Fuji
1 x Granny

Smith
150 -~

x Golden
Delicious .
e Braeburn:

100 «—
+ Ida Red

Magness-Taylor Firmness [N]

- Gala

50 —»
- Jona
Gold

— Fitted

 

 

 

 

 

 

Failure Force [N]

FIGURE 28 - Magness-Taylor firmness versus failure force of rubber thumb test

.«rr

Measured Failure Force [N]

250

200

150

100

50

57

Y = 2.44 X - 78.41
Correlation Coefficient=0.90

 

 

 

 

 

 

 

 

20 40 60 80 1 00

 

 

 

 

 

11-

 

 

Measured 1st Peak [N]

FIGURE 29— First peak force versus Filure Force

 

 

0 Red
Delicious

I Red
Rome

A Fuji
x Granny
Smith

at Golden
Delicious

0 Braebum
+ Ida Red
- Gala
- Jona

Gold
4— Fitted

 

 

 

 

lL

58

Y = 0.67 X + 12.83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Correlation Coefficient=0.78
1 .
e
100
1 O

z .
§ 80
e
u
x
(I
R
.. 60
.2
IL
3
a 401— __
fl
0
E

20

0

 

 

 

 

 

 

 

0 20 40 60 80 1 00

Measured Magness Taylor Firmness [N]

FIGURE 30 - Measured first peak force versus Magness-Taylor Firmness

qr

 

120

 

 

Red
Delicious

Red
Rome

Fuji
Granny

Smith
Golden

Delicious
Braebum
Ida Red
Gala

Jona Gold

—— Fitted

 

 

59

5.1.3 Performance of Acoustic Impulse Technique

Modulus of elasticity of apple tissue was predicted using eq. [27]. In the compression
mode, a Poisson’s ratio of 0.3 and the density of 800 kg/m3 were assumed for the
resonant sphere model. Measured modulus of elasticity was obtained from the
compression test of cylindrical apple flesh. From the compression test results initial
tangent modulus of elasticity was found. In the compression test cylindrical apple flesh
sample was bored in the radial direction which was different from the sampling direction
used by Armstrong (1989). Figure 31 illustrates 0.7 as the correlation coefficient between

the measured and predicted modulii of elasticity.

IL

Predicted Modulus of Elasticity [MPa]

60

Y = 0.0027 X + 2.43
Correlation Coefficient=0.7

 

___ ____1

 

 

 

 

 

 

 

 

 

944%

 

 

 

 

 

1 !

 

 

 

200 400 600 800 1000
Measured Modulus of Elasticity [MPa]

FIGURE 31 - Measured versus predicted modulus of elasticity

by using acoustic impulse

Red
Delicious

Red
Rome

Fuji
Granny
Smith

Golden
Delicious
Braebum
Ida Red

Gala

Jona
Gold

— Fitted

 

1200

I P

 

61
5.2 DISCUSSION

5.2.1 Quantitative Aspects of The Model Prediction

The laminated cell layer model showed fairly good correlation for the first peak force
and the second peak force prediction. The correlation coefficient of the second peak
(0.79) was little higher than that of the first peak force (0.76). Thus, the model
demonstrated its prediction capability for the first two peak forces. In addition, Figure 23
showed a strong correlation (0.83) in predicting stiffness constant which meant that the
model worked not just for the peak forces but also for the first slope of the force-
deformation relationship.

After the second peak it was hard to compare because unidentified disorder occurred
as the mastication progressed. However, the information about the early period of the
mastication period was enough to determine the texture of apple flesh.

In Figure 32, it was found that the percentages of the sample having less than 20%
error with its measured values were 51% for the first peak prediction, 78% for the second
peak prediction, 73% for the stiffness prediction, and 84% for the Magness-Taylor
firmness prediction. From the results explained above the laminated cell layer model was

considered as a good means to depict the Magness-Taylor puncture test quantitatively.

5.2.2 Qualitative Aspects of The Model Prediction

The characteristics of the force-deformation relationship was a saw-tooth shape which
inferred the significant change of force or the catastrophic destruction of material. The
model represented well this characteristics of the force-deformation relationship. Figure

23 shows the correlation coefficient of 0.83 for predicting the stiffness which indicates

62

ezerror AI

 

 

1st Peak Force

 

2nd Peak Force

   

 

 

 

 

“10% 920%
19% 22%
o e<10%
c2336 45%
0
10<¢<20% io<e<20%
32% 33%
Stiffness Constant Magness-Taylor Flnnness
e>20%
e>20% 16%

27%

e<lO%
57%

   

10<c<20%
16%

 

10<e<20%
29%

 

e<lO%
55%

 

FIGURE 32 - Precision of model prediction

1?

 

63
that the model has the capability to describe the different textural quality of two apples

having the same first peak force.

Until the second peak the juices expelling effect did not contribute significantly to the
total trend of force-deformation relationship because juices were not produced enough to
induce resistance and also because the penetration depth was so small.

Therefore, the model was considered to represent the early period of the Magness-

Taylor puncture test qualitatively.

5.2.3 Evaluation of Nondestructive Method

Rubber thumb test was considered a good method to provide model parameters such
as compressive, shear failure stress nondestructively. Figure 26 and 27 support the
possibility of the rubber thumb test. In addition, the method could be used to replace
Magness-Taylor puncture test. Figure 28 indicates that there was 0.77 of correlation
between the failure force and the Magness-Taylor firmness. This new method was not
perfectly nondestructive. Actually it made small bruise on the apple surface but it was
not significant. If the diameter of rubber ball was minimized up to some point the size of
bruise would be negligible. The first peak force was correlated to the failure force to
identify what the failure force in fact measured. Figure 29 shows correlation coefficient
of 0.9 which means that the rubber thumb test measures the first peak force efficiently
rather than the Magness-Taylor firmness.

The contact pressure was also measured using Uniforce pressure sensor and

thecorrelations with Magness-Taylor firmness and the failure force were investigated.

64

Ideally, contact pressure was expected to have good correlation with the failure force but
in fact it was not so. The reason for this was the characteristics of the pressure sensor. If
the film surface of pressure sensor was bent then it produced undesirable output. In the
experiment the contact surface was not flat so that the sensor output interfered with true
value. If a proper sensor for this purpose were available then the contact pressure would
also be expected to have good correlation with the failure force.

Acoustic impulse technique showed fairly good correlation of predicting the initial
modulus of elasticity. This technique was also considered to have the potential for

providing model parameters.

It

1.

CONCLUSIONS

Considering the results of this research following conclusions are drawn:
The laminated cell layer model developed in this research was considered to have
reasonable capability for depicting the Magness-Taylor puncture test results
quantitatively and also qualitatively. Correlation coefficients for predicting the first
peak was 0.76 and for the second peak it was 0.79. Also, the model predicted well

the stiffiiess constant with correlation coefficient of 0.83.

Rubber thumb test may be used to estimate model parameters. In this research this
method showed 0.76 and 0.64 of correlation for predicting the compressive and Shear
failure stress, respectively. Moreover, rubber thumb test was found to have strong

correlation of 0.9, with Magness-Taylor firmness.

Acoustic impulse technique may be used to estimate model parameters. This

technique showed correlation coefficient of 0.7 with the measured initial modulus of

elasticity.

65

1.

SUGGESTIONS FOR FUTURE RESEARCH

For future research the following ideas are suggested:
In preparing the cylindrical sample for compression test it is very critical to ensure
that the sample have two flat ends normal to the direction of the compression force. If
those ends are not normal to the compression force the shear failure comes first rather
than the collapse of the layer. It is also difficult to obtain correct mechanical

properties from the compression test if it is not flat.

There are several supplemental constants such as number of layers, geometric ratio,
ratio of stress recovery, ratio of increase of contact area and the initial length for
calculating the strain of shear-tensile component. Effects of these constants are

worthy of future study for better performance of the laminated cell layer model.

Bruise can be minimized by reducing the size of the rubber ball. The effect of size

reduction for the performance of the rubber thumb technique can be studied.

As the rubber ball was pressed onto the apple, sudden change of contact pressure
occurred which produced audible sound and vibration. By incorporating

accelerometer on the surface of apple this vibration can be sensed and testing machine

66

I:

67

can be stopped. Thus, it is possible to measure the contact diameter at the moment of

flesh failure.

5. The elasticity and the viscosity obtained by compression test can be studied to find a

relationship of these parameters to a textural quality.

"I'

APPENDICES

APPENDIX A

68

APPENDIX A

Table A1 - Magness-Taylor test results

 

 

 

 

 

 

 

 

 

 

 

1st Peak Force 2nd Peak Force Initial Slope Magness-Taylor
Obs. Predic. Obs. Predie. Obs. Predic. Obs. Predie.
N0. [N] [N1 [M [N] lN/ml [Wm] IN] IN]
1 56.23 48.9 50.06 47.9 31652 31209 56.49 48 88
2 48.12 72.5 59.80 77.5 34469 35660 60.06 91 01
3 52.29 58.1 57.41 64.7 30906 42853 62.80 64.94
4 53.16 45.1 " 54.4 30655 31359 59 99 69.44
5 60.12 55.1 67.61 64.0 36445 43365 74 70 69.78
6 58.24 51.1 67.56 57.9 33580 44690 82.92 68.06
7 72.50 58.0 70.53 68.8 46324 47261 77.88 70.19
8 50.37 53.1 52.21 57.5 32184 48218 56.41 59.49
9 58.85 48.2 52.41 58.2 39748 45549 66.33 58 22
10 49.40 34.3 50.72 38.7 44921 42656 54.92 53.03
11 55.28 68.0 79.83 84.3 48400 48697 79.83 87.60
12 59.56 56.5 72.96 64.5 37055 39259 74.27 71.54
13 71.59 69.6 75.93 77.6 38467 37351 75.93 77.64
14 56.85 69.3 79.57 68.5 48001 48132 90.47 71.56
15 79.89 70.3 82.25 73.4 34339 47429 83 17 73.44
16 67.15 65.6 72.67 73.3 38721 50022 106.54 87 84
17 51.77 48.6 56.23 58.9 34967 37026 83.28 58.91
18 61.22 48.6 75.40 56.7 35300 38305 92 21 67.66
19 56.75 52.2 62.92 54.5 31940 30101 65 41 54.57
20 56.90 54.4 79.48 58.8 35399 42868 104.30 71 92
21 53.59 41.4 46.90 43.3 30903 26434 53.59 45 64
22 44.12 49.5 45.82 59.7 24255 29226 46.22 59.72
23 56.35 50.5 46.77 53.1 30277 30607 57.01 53.08
24 50.60 33.0 41.14 36.2 24920 22906 50.60 38 22
25 30.28 35.1 38.42 41.1 20454 25142 39.08 41.65
26 77.35 65.0 60.15 69.9 48120 45126 77 35 75.83
27 107.21 84.9 79.25 102.1 58944 55716 107 21 102 15
28 67.86 63.4 80.33 70.0 53474 53498 80 33 69.97
29 103.50 78.2 " 89.7 54374 57713 103.50 100 55
30 97.10 70.3 97.10 79.2 57389 57289 97 10 90.58
31 44.64 59.8 46.87 53.7 36392 37183 56.72 62.68
32 45.51 48.2 41.97 51.4 35866 34528 50.37 51.42
33 43.13 41.1 44.70 43.9 29986 34706 47.20 47.58
34 46.81 48.6 48.78 51.3 33537 45952 51.54 51.32
35 40.07 38.6 50.31 47.3 35085 38008 51 36 47.27
36 63.82 48.9 50.17 50.0 29585 36127 63 82 59.65
37 62.18 48.3 " 55.2 26725 32570 62 18 55.15
38 57.06 53.0 57.32 59.1 30655 37948 57 71 59.17
39 74.15 54.7 53.93 58.1 41736 39166 74.15 63.87
40 60.16 52.1 57.80 57.5 37426 41032 62.39 57 52
41 44.52 44.6 49.25 51.4 33953 30081 49.25 51 37
42 41.48 41.2 45.55 41.0 29715 34761 48.44 43 92
43 44.77 41.4 46.74 44.9 32075 31555 47.53 44.87
44 42.17 42.8 44.80 46.7 31155 29758 47 29 46.68
45 56.75 50.6 52.68 47.9 31198 32318 57 80 50.62

 

 

 

* unobservable

 

69

Table A2 - Results of compression, shear, and tensile test

 

 

 

 

 

 

 

 

 

 

 

Compression Test Shear Test Tensile Test
E n 6c 6c 0. E

No. x10“ [Pa] x10“ [Pa s] [Pa] [Pa] [Pa] [Pa]
1 3.94 2.65 338438 114515 2219400
2 6.41 1.83 441721 299244 2893126
3 7.00 2.42 443736 185405 2661103
4 5.53 1.61 335967 248737 2019565
5 6.65 2.7 428455 228580 2603817
6 7.25 3.07 446245 191686 2186119
7 7.25 3.22 473311 219752 2644603
8 6.52 2.09 352807 181504 3603414
9 5.68 2.53 331709 176118 3262707
10 5.82 2.61 278642 248325 2382488
11 8.09 2.75 518319 312775 3038228
12 5.19 4.29 434385 224689 2365463
13 6.90 2.09 476922 242944 2669880
14 8.12 2.56 506877 201034 3140829
15 7.44 2.64 500491 212239 3262553
16 6.23 5.17 497526 300421 3204485
17 4.82 2.76 353833 189325 2495790
18 4.57 4.02 358053 235456 2556493
19 3.05 19.3 364249 160527 2106323
20 4.84 6.18 396447 288385 2878381
21 4.17 2.17 334104 102475 1488604
22 4.83 2.21 388122 145849 1718797
23 5.15 2.01 379075 130190 1910229
24 3.30 3.05 282443 89790 1113635
25 3.36 3.01 284230 112771 1423046
26 8.62 1.88 444801 211617 3227850
27 9.24 3.35 631107 293539 3545828
28 7.48 3.31 469624 200621 3437427
29 11.20 3.2 653307 318823 3034021
30 7.82 4.76 554547 293341 3415703
31 6.56 1.46 355620 177696 3085208
32 5.48 2.93 412565 120155 1748530
33 5.94 1.48 300310 129266 2268548
34 6.53 1.67 348930 1 11836 3514630
35 5.92 1.62 288335 132484 2438245
36 4.92 7.24 437958 155948 1687081
37 4.17 6.04 396105 159658 1794609
38 5.09 4.36 421764 146990 2176547
39 5.06 256 513378 165813 1578980
40 5.56 4.68 426326 168136 2231997
41 3.62 4.42 331139 146777 1916969
42 4.65 2.38 306164 116952 2252100
43 3.96 2.69 300994 134993 2116101
44 5.53 1.44 313349 123545 1938822
45 3.85 2.09 313121 130808 2625809

 

 

Table A3 - Rubber Thumb Test Results

70

 

Failure Force

Failure Pressure

Contact Diameter

 

 

 

No. [N] [Pa] [mm]
1 66.3 513727 12
2 65.8 513727 13
3 46.0 405574 11
4 48.3 459651 11
5 74.8 567804 13
6 66.2 513727 13
7 63.9 540765 13
8 42.3 405574 11
9 50.7 486689 11
10 43.8 405574 12
11 71.0 999740 12
12 63.4 896319 12
13 78.5 965266 13
14 65.4 965266 12
15 89.6 965266 14
16 83.9 999740 13
17 77.5 1034214 14
18 72.7 758424 14
19 51.0 792897 11

20 67.4 965266 13
21 29.0 344738 9
22 34.2 379212 10
23 29.1 448159 9
24 25.2 379212 9
25 28.4 344738 12
26 122.7 720816 16
27 201.8 655002 18
28 110.3 586055 13
29 201.3 620528 17
30 197.9 689476 17
31 26.6 344738 9
32 22.2 344738 9
33 27.0 344738 9
34 50.0 379212 13
35 28.6 413686 10
36 47.2 413686 11
37 43.8 344738 12
38 42.3 344738 11
39 59.3 448159 12
40 54.3 379212 12
41 53.0 379212 12
42 33.4 344738 9
43 25.9 306434 9
44 33.6 379212 10
45 63.5 379212 12

 

 

 

 

 

71

Table A4 - Elasticity measured by acoustic impulse technique

 

 

 

 

 

 

Elasticity
E
No. [MPa]

1 3.17
2 3.29
3 3.97
4 3.25
5 4.06
6 4.81
7 4.93
8 4.56
9 4.53
10 4.33
11 4.79
12 4.03
13 4.84
14 5.14
15 4.34
16 4.36
17 4.19
18 3.81
19 3.63
20 4.16
21 3.39
22 3

23 3.33
24 2.83
25 2.55
26 3.62
27 4.84
28 5.39
29 4.72
30 4.16
31 4.35
32 4.02
33 3.98
34 4.48
35 3.95
36 3.73
37 2.51
38 3.97
39 4.04
40 3.77
41 3.64
42 3.48
43 3.61
44 4.02
45 3.93

 

 

I}

APPENDIX B

I]?

72

APPENDIX B

Force—Deformation Plots of Magness-Taylor Puncture Test

General Information:

1. Material: 5 apples from 9 cultivars (total-=45 apples)

2. Explanation of file name: e. g. Y01_02

3. Numbering:

01-05:
06- 10:
ll -15:
16-20:
21 -25:
26-30:
31 -35:
36-40:
41 -45:

lst character (Y): No meaning

lst two digits (01): Sample No.

2nd two digits (02): Testing Code
02=Magness-Taylor Test
03 =C0mpression test
04=Shear Test
05 =Tensile Test

Red Delicious
Red Rome

Fuji

Granny Smith
Golden Delicious
Braebum

Ida Red

Gala

Jona Gold

* The above setups were applied to Magness-Taylor, compression, shear, and tensile test.
'1‘ In compression test, Maxwell model was fitted to the points in between A and B of

Figure C1.

Force [N]

60 .-

73

 

50 :

 

4o :

 

 

30 :

 

20 I

 

 

 

 

 

 

 

 

 

 

 

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

 

llllllll

 

.......
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Deformation [mm]

FIGURE Bl - Magness-Taylor puncture test result of Y01_02

iiiiiiiii

 

Force [N]

70 h

74

 

 

60

 

«r—
50 I
4.-
-1—

 

 

 

 

 

40

 

 

 

 

30

 

 

 

20 1:

 

10 f

 

 

 

 

 

 

 

 

 

1 1
l I |
1 1 , 1
! - 1 i
1 1 1 1
1 l
1
l 1
1 1
l
1 1
1
1
1
1_J llllllllllllllllll t iiiiiiiiiiiiiiii '1: 1 iiiiiii
lllllllllllllllllllllllllll [iITTIiIT-ltiilllllril. |1|I III|||ItlIII

FIGURE B2 - Magness-Taylor puncture test result of Y02_02

Deformation [mm]

 

 

Force [N]

70_

10 f:

75

 

 

60

 

so i:

<.\

 

4o :

 

30

 

 

20 ::

 

 

 

 

 

 

 

 

 

1111111111111111111111111111111111111111111111111111111111111

 

111111111

 

iiiiiiiiii
111111111111111111111111111111111111111111111111111111

Defamation [mm]

FIGURE B3 - Magness-Taylor puncture test result of Y03__02

111111111

 

Force [N]

70

76

 

 

60

 

50

 

40 :

 

30

 

20 j:

 

 

11111111111111111111111111111111111111111111111111111111

 

 

 

 

 

 

 

 

 

111111111111111111111111111111111111111111111111111111111111111111111111111111111

Deformation [mm]

FIGURE B4 - Magness-Taylor puncture test result of Y04_02

 

Force [N]

80 ._

77

 

7o

 

 

60

 

50

 

4o

 

30

 

20

 

 

 

 

 

 

 

 

 

11111111111111111111111111111111111111111111111111111111111111111

 

 

1111111111111111111111111111111111111111111111111111111111111111

Defamation [mm]

FIGURE B5 - Magness-Taylor puncture test result of Y05_02

I
111111111

 

78

 

90 __

 

 

60 ff

 

 

1

Force [N]

 

40 ff /

 

30:: 1

 

20 ff

 

 

 

 

 

 

 

 

 

 

 

 

Deformation [mm]

FIGURE B6 - Magness-Taylor puncture test result of Y06_02

Force [N]

80_

79

 

 

70

 

60

 

 

50

 

40 :

 

30

20

 

 

 

 

 

 

 

 

 

 

111111111111111111111111111111111111111111111111111111111

 

111111111

 

111111111
111111111111111111111111111111111111111111111111111111

Deformation [mm]

FIGURE B7 - Magness-Taylor puncture test result of Y07_02

111111111

 

Force [N]

60_

20

80

 

 

50 :

W‘W/

 

40 i:

30

 

 

 

1111111111111111111111111111111111111
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

 

 

111111111111111111111111111111111111

 

 

 

 

 

 

 

 

 

 

Deformation [mm]

FIGURE B8 - Magness-Taylor puncture test result of Y08_02

Force [N]

70 ,_

81

 

Ar

 

60

 

50

 

40

 

so ::

 

20 ::

 

10

 

 

 

11111111111111111111111111111111111111111111111111111111111111111111111

111111111

 

1111111111111111111111111111111111111111111111111111111111111111111111

 

 

 

 

 

Deformation [mm]

FIGURE B9 - Magness-Taylor puncture test result of Y09_02

 

 

Farce [N]

60'

82

 

 

so ::

40 :'

MW W

 

so ;:

 

20 :

 

 

 

 

11111111111111111111111111111111111111111111111111111111

 

 

 

 

 

 

 

111111111

 

..............
111111111111111111111111111111111111111111111111111111111111111111111

Defamation [mm]

FIGURE BIO - Magness-Taylor puncture test result of Y10_02

111111111

0 1 2 3 4 5 6 7 8

 

Force [N]

90_

83

 

 

80 ff

 

70 ff

 

60 f

50 ff

 

 

4o

 

30 f

20 if

 

 

 

 

 

 

 

 

 

 

 

11111111111111111111111111111111111111111111111111111111111111111

iiiiiiiii

 

11111111111111111111111111111111111111111111111111111111111111111111111

Deformation [mm]

FIGURE Bll - Magness-Taylor puncture test result of Y11_02

iiiiiiiii

 

Force [N]

80 ‘_

84

 

/1 W M. -A

 

7o

N \wr

 

60 ff

 

50

 

 

 

 

40 ff

 

30

20

 

 

 

 

 

 

 

 

 

 

 

 

111111111111111111111111111111111111111111111111111111111

11111111

 

111111111111111111111111111111111111111111111111111111111111

1 2 3 4 5 6 7 8

Deformation [mm]

FIGURE B12 - Magness-Taylor puncture test result of Y12_02

111111111

 

85

 

 

 

 

 

 

 

 

AAA/v\/\A AW»

 

 

 

 

 

 

 

 

 

 

pppppppppppppppppppppppp

 

 

 

 

 

_________________________
_______

 

 

 

 

 

 

 

..........
._.

 

 

»
11..

80

qqqqqqqqqqqqqqqqqq

_z_ 3.5“.

«««««««««

Defamation [mm]

FIGURE B13 - Magness-Taylor puncture test result of Y1 3_02

Farce [N]

100 0

86

 

 

90 ff

 

80 ff

 

70 if

 

60 f?

 

 

 

50 ff

 

40 ff

 

 

30 ff

 

20 ff

 

 

 

 

 

 

 

 

 

 

iiiiiiiii

 

111111111111111111111111111111111111111111

Defamation [mm]

FIGURE B14 - Magness-Taylor puncture test result of Y14_02

11111111111111111111111111111

 

Force [N]

90

80

70‘

60

50;

40 "

30 2'

10 ;_

87

 

lllllll
rTIIIIIIT

 

111.1111.
ITTrIII

 

LL11

L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20 f:

 

 

lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
----------

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Deformation [mm]

FIGURE B15 - Magness-Taylor puncture test result of Y15_02

lllllllllll
11111

 

Force [N]

110 ,_

88

 

 

100 if

90 ff

 

 

 

 

 

 

60 [1/ I
. /

 

40 if

30 if

 

 

20 if

 

 

 

 

 

 

 

 

 

 

111111111111111111111111111111111111

 

111111111111111111111111111111111111111111111
1111111111

111111111111111111111111111111111111111111

1 2 3 4 5 6 7 8

Deformation [mm]

FIGURE Bl6 - Magness-Taylor puncture test result of Y16_02

 

Force [N]

90 ,_

89

 

 

so if

 

70 ff

 

60 ff

 

 

50 ff

 

40 ff

 

30 f

20 ff

 

 

 

 

 

 

 

 

 

 

 

 

ml
.................................................................................
........................................................................ 11...”...

Deformation [mm]

FIGURE B17 - Magness-Taylor puncture test result of Y17_O2

 

Force [N]

100 0

90

 

 

90 ff

 

80 if

 

70 ff

 

60 ff

 

50 if

 

40 ff

 

30 ff

 

20 ff

 

 

10 ff

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5 6 7 8

......................
1111111111111111111111111111111111111111111111111111111111

Defamation [mm]

FIGURE B18 - Magness-Taylor puncture test result of Y18_02

 

Farce [N]

70 ..

91

 

 

60

 

50

 

 

4o :

 

 

30

 

20

 

 

 

 

 

 

 

 

 

 

................................................................................

 

111111111111111111111111111111111111111111111111111111111111111111111111111111

Defamation [mm]

FIGURE Bl9 - Magness-Taylor puncture test result of Y19_02

 

Force [N]

110 ,_

92

 

 

100 ff

 

oo ::

 

so 3E

 

70 if

 

60 if

50 ff

 

 

40 ff

 

30

 

20 if

 

10 ff

 

 

 

 

 

 

 

 

111111111111111111111111111111111111111111111111111111111111111111
x r

 

 

11111111111111111111111111111111111111111111111111111111

Defamation [mm]

FIGURE B20 - Magness-Taylor puncture test result of Y20_02

iiiiiiiii
111111111

 

Force [N]

60 0

93

 

 

50 :

 

40 I

30 :

 

20 :'

 

 

 

 

 

 

 

 

 

 

11111111111111111111111111111111111111111111111111111

 

0 1 2 3 4 5 6 7 8

 

Deformation [mm]

FIGURE B21 - Magness-Taylor puncture test result of Y21_02

 

Force [N]

50

4o 1'

20 ‘5

10‘

94

 

 

30 ”1

 

 

__i.¥m__-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11111111!'lll‘lllllllllllllllllllllLL‘l llllllllllllllllllllllll
........

 

1 2 3 4 5 6 7 8

Defamation [mm]

FIGURE B22 - Magness-Taylor puncture test result of Y22_O2

 

Force [N]

60 0

95

 

so ::

 

4o :

 

30 :

 

2o ::

 

 

 

 

 

 

 

 

 

 

 

11111111111111111111111111111111111111111111111111111111111111111111111111111111

 

1111111111111111111111111111111111111111111111111111111111111111111111111111111

Defamation [mm]

FIGURE B23 - Magness-Taylor puncture test result of Y23_02

 

96

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:rT-.

111 .. 111..

 

 

60

50 j:

.........

bbbbbbbbb
4 4 d .

Hza 3.6“.

hhhhhhhh
444444444

.........

Defamation [mm]

FIGURE B24 - Magness-Taylor puncture test result of Y24_02

Force [N]

40

97

 

 

 

 

 

30

 

 

 

 

 

20

 

 

3 1 1 1
1 1 1 1
1 1 ‘ 1
1 1

 

 

10

 

 

 

 

 

 

 

 

 

I I I 'lll"1 11'.
l-I--ruY l’»TYI.--I]IIIiui-I- .ITYYVI 11.1 VI.IV.-IIYITIIYI.11

Defamation [mm]

FIGURE B25 - Magness-Taylor puncture test result of Y25_02

 

Force [N]

80

98

 

[AAALL
..uyuu

 

70

 

60

 

 

50 f

 

4o

 

30

 

10 I

20 ff

 

‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘

 

 

J‘AAA‘AL—L ‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

FIGURE B26 - Magness-Taylor puncture test result of Y26_02

Force [N]

110

100

99

 

 

so ::

 

 

 

 

80 f?

 

70 ff

'V

 

60 if

so if

 

 

40 ff

 

30 if

 

20 if

 

 

 

.........

 

 

 

ttttttttttttttttttttttttttttt
rrrrrrrrrrrr

 

 

 

vvvvvvvvvvvvvvvvvvvvvv

.........................
vvvvvvvvvvvvvvvvvvvvvvvvvv

 

ttttttttt

 

Defamation [mm]

FIGURE B27 - Magness-Taylor puncture test result of Y27_02

........

 

 

100

 

 

 

WW If“

 

 

 

 

 

\M

 

 

 

 

V

 

fllll ll‘ [41‘ ““[L lir‘ l l

 

 

 

II I II" I

 

 

 

 

FFFFLVPIPIFF b».r—PFF»LV
—<au<~41€fi

 

 

 

 

 

bbbbbbbbbbb
..................

 

 

—
fififififififififi

—————
q —

 

 

0
9

.........

0 0 0
8 7 6

_z_ 83".

444444444

Deformation [mm]

FIGURE B28 - Magness-Taylor puncture test result of Y28_O2

100

 

..l'lll l‘lr

 

 

 

 

 

 

 

 

»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»

 

 

 

——————————————————

PPPPPP

lll'lll
IFIYIII|T III-1

 

 

 

 

 

 

.2. 3.5".

 

 

 

 

fififififififififififififififififififi

 

Deformation [mm]

FIGURE B28 - Magness-Taylor puncture test result of Y28_02

f-t

 

 

 

 

 

 

 

 

 

 

 

 

 

101

 

 

 

 

 

Deformation [mm]

 

 

 

 

 

qr—
4?-
ul—

hnhhbpphh b—PIPFFbrL ~__h—-—~. hpFPhFP-h hperPL_—
—«.4uq_u__ 1 .4414

 

 

 

 

 

 

 

100 f:

110 __

0 O 0 0 0 AU
9 8 7 6 5 4

_2_ echo".

 

 

FIGURE B29 - Magness-Taylor puncture test result of Y29_02

 

 

 

Force [N]

100 __

102

 

 

90 ff

 

80 ff

 

70 if

 

60 ff

 

50 ff

 

40 f

 

so if

 

20 ff

10 ii

 

 

.................................................................................

 

 

 

 

 

 

 

 

 

vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

Deformation [mm]

FIGURE B30 - Magness-Taylor puncture test result of Y30_02

 

Force [N]

60 fl

4o ""

20 I

10 '"

103

 

fr“

 

5o :

 

 

 

 

 

 

 

 

 

 

 

-.-
4—
4..
‘4—

 

 

 

 

 

 

 

 

 

 

 

 

.....
t—1.r.r|.i .r.r1|.ir .............................

Deformation [mm]

, FIGURE B31 - Magness-Taylor puncture test result of Y31_02

 

Force [N]

60

50

40

30 r-

20:

10

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

lllllllllll

 

1 2 3 4 5 6 7 8

Deformation [mm]

FIGURE B32 - Magness-Taylor puncture test result of Y32_02

 

Force [N]

50

105

 

 

4o ‘-

 

30 "

20 "

 

 

 

 

rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

 

 

 

 

 

 

 

 

 

 

...........................................................................

Deformation [mm]

FIGURE B33 - Magness-Taylor puncture test result of Y3 3_02

 

Force [N]

60

50

4o ”'

10'

106

 

 

1 L 1
T Tfi

 

 

 

 

3o

 

 

 

 

 

 

 

 

 

I ”But ___ _J,__k

 

20 j“

 

 

 

 

 

llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll

IIIIIIIII

 

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

 

 

 

 

 

Deformation [mm]

FIGURE B34 - Magness-Taylor puncture test result of Y34_O2

 

Force [N]

604

20 "

107

 

 

50:

4o :

 

 

 

30 ‘:

 

 

 

 

 

 

 

fill—FF"

 

1o "

 

 

 

111111111
I

 

 

 

llllllllllll
iiiiiiiiii

 

 

 

 

 

 

lllllllll
IT!

4

5

lllllllll
TY]

Deformation [mm]

lllllllll
e T

lllllllll
I I I

FIGURE B35 - Magness-Taylor puncture test result of Y3 5_02

11111111
T

 

 

Force [N]

108

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7o
60 l/
50 w f/X/JA‘VJAMNVJJ VV/
-~ I
40 l
l
E
l
30 x I
—~ I
” l
l
+- /
20
1o"
:" l I
0 ****** l . ,.;:;#+H+Hl#:;:::::: HHHH: HHHH: #:::::;:: mum;
1 2 3 4 5 6 8

Deformation [mm]

FIGURE B36 - Magness-Taylor puncture test result of Y3 6_02

 

“h

Force [N]

70 4.

109

 

 

60

 

50

 

 

40

 

30

 

20

 

 

 

 

11111111111111111111111111111111111111111111111111

 

 

 

 

 

 

 

..........
vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

Defamation [mm]

FIGURE B37 - Magness-Taylor puncture test result of Y37__02

 

Force [N]

60 q_

110

 

 

50

 

4o

 

3o :

 

20 f:

 

 

 

 

 

 

...........................................................
........................

 

 

 

 

 

vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

1 2 3 4 5 6 7 8

Deformation [mm]

FIGURE B38 - Magness-Taylor puncture test result of Y3 8_02

 

 

lll

 

 

* ilrliiw.‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PPPPPPP

hhhhhhhhh

bbbbbbbbb

.l‘IIII l.

 

 

 

 

---------

 

 

44444444

 

 

__________

 

 

 

hhhhhhhhhhhhhhhhhh
_________________

_z_ 83“.

. P
_________

 

 

uuuuuuuuu

 

Defamation [mm]

FIGURE B39 - Magness-Taylor puncture test result of Y3 9_02

112

 

 

 

 

 

 

 

 

 

 

 

_ w P
ddddddddd

 

________
-

 

 

 

 

 

 

 

 

 

 

 

 

_________

ppppppppp

 

__________

44444444

444444444

.2. 83".

 

 

Defamation [mm]

FIGURE B40 - Magness-Taylor puncture test result of Y40_02

Force [N]

50

30 "

20 ‘—

10 "

113

 

 

4o 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

111111111111111111111111111111111111111111111111111111
iiiiiiii

 

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

1 2 3 4 5 6 7 8

Defamation [mm]

FIGURE B41 - Magness-Taylor puncture test result of Y41_02

 

Force [N]

50

114

 

 

4o ‘—

 

30 4.

 

 

 

20 "

 

 

 

 

 

 

 

 

 

 

 

.........................................................

0 1 2 3 4 5 6 7 8

Deformation [mm]

FIGURE B42 - Magness-Taylor puncture test result of Y42_02

 

Force [N]

115

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 ‘k
W
f/m

40 WW
303? /
20 1:
1o;

0 1 2 3 4 5 6 7 8

Deformation [mm]

FIGURE B43 - Magness-Taylor puncture test result of Y43_02

 

Force [N]

116

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

so“
JNPAR/
40 A 1 ”\V/AAA/fi/f
30 I
20
1o
o_h.11115111HHHVHHH “HUMHHH“1.1,,”HHHfHHWIH? ,,,,, f”, 1:11:11}:
0 1 2 3 4 5 6 7 8

Deformation [mm]

FIGURE B44 - Magness-Taylor puncture test result of Y44_02

 

Force [N]

60_

117

 

 

50 :

 

4o

 

 

 

 

3o :

 

20 :

 

 

 

 

 

 

1111111111111111111111111111111111111111111111111111111111111111111111

 

 

 

 

 

Defamation [mm]

FIGURE B45 - Magness-Taylor puncture test result of Y45_02

 

 

APPENDIX C

 

118

APPENDIX C

Force-Deformation Plots of Compression Test and Curve Fitting

119

COMPRESSION TEST :Maxwell Model

Elasticity 3.36E+08 [Pa]
Viscosity 3.01E+08 [Pa‘s]
Yield stress 284230 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mAZ]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C1 - Compression test and curve fit for Y01_03

120

COMPRESSION TEST :Maxwell Model

 

 

 

 

 

 

 

 

 

 

Elasticity 6.41E+08 [Pa]
Viscosity 1.83E+08 [Pa's]
Yield stress 441721 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]
240 1
” Exp. ...........
22° :— ------ Fit ,,,,,,,,,,
200
180 U ,
160 t

 

 

140

120 //\

 

 

Force [N]

80 L / \./

100 .. / \ /’\

 

60

 

 

40 /

 

 

 

 

 

 

 

 

 

 

 

 

0 0.5 1 1.5 2

 

Defamation [mm]

2.5

3.5

 

FIGURE C2 - Compression test and curve fit for Y02_03

 

 

121

COMPRESSION TEST :Maxwell Model

Elasticity 7.00E+08 [Pa]
Viscosity 2.42E+08 [Pa‘s]
Yield stress 443736 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C3 - Compression test and curve fit for Y03_03

122

COMPRESSION TEST :Maxwell Model

 

 

 

 

 

 

 

 

 

 

 

Elasticity 5.53E+08 [Pa]
Viscosity 1.61E+08 [Pa‘s]
Yield stress 335967 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]
220 j
" Exp.
zoo «— ,,,,,, Fit """"""""""""""
180 ,,,,,,,,,,
160 r4 ‘1"
.1. I f
140 i, "
120

 

 

1oo / ’\\/
so

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E
O
2
O
u- / \
60 \
"' / KW”
40 // l
20
4b I
O ,L:# e e 4 T
-2o
.;
-40
0 0.5 1 1 .5 2 2.5 3 3.5

Defamation [mm]

 

 

 

FIGURE C4 - Compression test and curve fit for Y04_O3

123

COMPRESSION TEST :Maxwell Model

Elasticity 6.65E+08 [Pa]
Viscosity 2.7OE+08 [Pa‘s]
Yield stress 428455 [Pa]

Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

340
320
300
280
260
240
220
200
1 80
1 60
140
1 20

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C5 - Compression test and curve fit for Y05_03

124

COMPRESSION TEST :Maxwell Model

Elasticity 7.25E+08 [Pa]
Viscosity 3.07E+08 [Pa‘s]
Yield stress 446245 [Pa]

Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

380
360
340
320
300
280
260
240
220
200
1 80
1 60
140
1 20

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C6 - Compression test and curve fit for YO6_O3

125

COMPRESSION TEST :Maxwell Model

 

Elasticity 7.25E+08 [Pa]

Viscosity 3.22E+08 [Pa‘s]

Yield stress 473311 [Pa]

Velocity 0.00423 [m/s]

Contact area 0.000314 [m"2]
300

280
260
240
220
200
1 80
1 60
140
1 2O

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

 

Defamation [mm]

FIGURE C7 - Compression test and curve fit for Y07_O3

 

 

126

COMPRESSION TEST :Maxwell Model

Elasticity 6.52E+08 [Pa]
Viscosity 2.09E+08 [Pa*s]
Yield stress 352807 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C8 - Compression test and curve fit for Y08_03

127

COMPRESSION TEST :Maxwell Model

 

Elasticity 5.68E+08 [Pa]

Viscosity 2.53E+08 [Pa*s]

Yield stress 331709 [Pa]

Velocity 0.00423 [m/s]

Contact area 0.000314 [mA2]
300

280
260
240
220
200
1 80
1 60
1 4O
1 20

 

Farce [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C9 - Compression test and curve fit for Y09_O3

 

 

128

COMPRESSION TEST :Maxwell Model

Elasticity 5.82E+08 [Pa]
Viscosity 2.61E+08 [Pa‘s]
Yield stress 278642 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mAZ]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C10 - Compression test and curve fit for Y10_03

129

COMPRESSION TEST :Maxwell Model

 

 

 

 

 

 

 

 

 

 

 

Elasticity 8.0954418 [Pa]
Viscosity 2.75E+08 [Pa‘s]
Yield stress 518319 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

240 1

“ Exp. '

22° ‘H ------ Fit J:

200 , '

180

160 "

140

 

 

\
/ \\ / \/ “\e‘

Force [N]

 

100 /

 

60

 

 

 

20 /

 

 

 

 

 

 

 

 

 

 

 

0 0.5 1 1.5 2 2.5 3

Defamation [mm]

 

 

 

FIGURE C11 - Compression test and curve fit for Y11_O3

130

IOMPRESSION TEST :Maxwell Model

Llasticity 5.19E+08 [Pa]
'iscosity 4.29E+08 [Pa*s]
'ield stress 434385 [Pa]
’elocity 0.00423 [m/s]
Iontact area 0.000314 [mA2]

 

Force [N]

0 0.5 1 1.5 2 2.5 3

Defamation [mm]

 

3.5

 

 

FIGURE C12 - Compression test and curve fit for Y12_03

"I.

131

COMPRESSION TEST :Maxwell Model

Elasticity 6.90E+08 [Pa]
liscosity 2.09E+08 [Pa*s]
{ield stress 476922 [Pa]
lelocity 0.00423 [tn/s]
Iontact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

FIGURE C13 - Compression test and curve fit for Y13_03

132

COMPRESSION TEST :Maxwell Model

Elasticity 8.12E+08 [Pa]
Viscosity 2.56E+08 [Pa‘s]
Yield stress 506877 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

FIGURE C14 - Compression test and curve fit for Y14_03

133

IONIPRESSION TEST :Maxwell Model

Iasticity 7.44E+08 [Pa]
'iscosity 2.64E+08 [Pa*s]
'ield stress 500491 [Pa]
'elocity 0.00423 [m/s]
fontact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

FIGURE C15 - Compression test and curve fit for Y15_03

134

CONIPRESSION TEST :Maxwell Model

Elasticity 6.23E+08 [Pa]
Viscosity 5.17E+08 [Pa‘s]
Yield stress 497526 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

FIGURE C16 - Compression test and curve fit for Y16_03

135

COMPRESSION TEST :Maxwell Model

Elasticity 4.8ZE+08 [Pa]
Viscosity 2.76E+08 [Pa‘s]
Yield stress 353833 [Pa]
Velocity 0.00423 [m/s]
Sontact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

FIGURE C17 - Compression test and curve fit for Y17_03

 

136

COMPRESSION TEST :Maxwell Model

 

 

 

 

 

 

 

 

 

 

 

Elasticity 4.57E+08 [Pa]
Viscosity 4.02E+08 [Pa‘s]
Yield stress 358053 [Pa]
Velocity 0.00423 [tn/s]
Contact area 0.000314 [mAZ]
24o , a
1. Exp. 1
22° W ------ Fit
zoo "
180
160 .
14o : 4" A

 

 

’ I
J. l /\ / \
120 ' \

 

 

Farce [N]
\
<

<

100‘ /\ /

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4o //
20
o .,: . - - -
r I
-20 ’ 1
0 0.5 1 1.5 2 2.5 3
Defamation [mm]

 

 

FIGURE C18 - Compression test and curve fit for Y18_03

137

COlVIPRESSION TEST :Maxwell Model

Elasticity 3.05E+08 [Pa]
Viscosity 1.93E+09 [Pa‘s]
Yield stress 364249 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C19 - Compression test and curve fit for Y19_03

138

COMPRESSION TEST :Maxwell Model

Elasticity 4.84E+08 [Pa]
Viscosity 6.18E+08 [Pa‘s]
Yield stress 396447 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mAZ]

 

Force [N]

 

O 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C20 - Compression test and curve fit for Y20_03

139

CONIPRESSION TEST :Maxwell Model

Elasticity 4.17E+08 [Pa]
Viscosity 2.17E+08 [Pa‘s]
Yield stress 334104 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mAZ]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C21 - Compression test and curve fit for Y21_03

140

COMPRESSION TEST :Maxwell Model I

Elasticity 4.83E+08 [Pa]
Viscosity 2.21E+08 [Pa‘s]
Yield stress 388122 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mAZ]

 

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defomatlon [mm]

 

 

 

FIGURE C22 - Compression test and curve fit for Y22_03

141

COMPRESSION TEST :Maxwell Model

Elasticity 5.15E+08 [Pa]
Viscosity 2.01E+08 [Pa's]
Yield stress 379075 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C23 - Compression test and curve fit for Y23_03

“+4.:—

142

COMPRESSION TEST :Maxwell Model

Elasticity 3.30E+08 [Pa]
Viscosity 3.05E+08 [Pa*s]
Yield stress 282443 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C24 - Compression test and curve fit for Y24_03

143

COMPRESSION TEST :Maxwell Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Elasticity 3.36E+08 [Pa]
Viscosity 3.01E+08 [Pa*s]
Yield stress 284230 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]
24° 1 l I .I
*“ Exp. ‘ "
22° “ ------ Fit
200
h l 1
“’° ._ 1 " T
160 1
140
g 120 I
§ 1 I1, | 1
if 100 ‘. I
8° /\
50 .. / A\\\—-
0 / I W-\
40 /
20 45
O 4 T {’1 A ff L f T
-20 l
0 0.5 1 1.5 2 2.5 3 3.5
Defamation [mm]

 

 

 

FIGURE C25 - Compression test and curve fit for Y25_03

COMPRESSION TEST :Maxwell Model

Elasticity 8.62E+08 [Pa]
Viscosity 1.88E+08 [Pa*s]
Yield stress 444801 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C26 - Compression test and curve fit for Y26__03

145

COMPRESSION TEST :Maxweil Model

Elasticity 9.24E+08 [Pa]
Viscosity 3.35E+08 [Pa*s]
Yield stress 631107 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C27 - Compression test and curve fit for Y27_03

146

COMPRESSION TEST :Maxwell Model

Elasticity 7.48E+08 [Pa]
Viscosity 3.31E+08 [Pa*s]
Yield stress 469624 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C28 - Compression test and curve fit for Y28_03

147

COMPRESSION TEST :Maxwell Model

Elasticity 1.12E+09 [Pa]
Viscosity 3.20E+08 [Pa‘s]
Yield stress 653307 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

0 0.5 1 1.5 2 2.5 3

Defamation [mm]

 

 

3.5

 

FIGURE C29 - Compression test and curve fit for Y29_03

 

 

 

 

148

COMPRESSION TEST :Maxwell Model

Elasticity 7.82E+08 [Pa]
Viscosity 4.76E+08 [Pa*s]
Yield stress 554547 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C30 - Compression test and curve fit for Y30_03

149

COMPRESSION TEST :Maxwell Model

Elasticity 6.56E+08 [Pa]
Viscosity 1.46E+08 [Pa’s]
Yield stress 355620 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C31 - Compression test and curve fit for Y31_03

150

COMPRESSION TEST :Maxwell Model

Elasticity 5.48E+08 [Pa]
Viscosity 2.93E+08 [Pa‘s]
Yield stress 412565 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C32 - Compression test and curve fit for Y32_03

151

COMPRESSION TEST :Maxwell Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Elasticity 5.94E+08 [Pa]
Viscosity 1.48E+08 [Pa‘s]
Yield stress 300310 [Pa]
Velocity 0.00423 [In/s]
Contact area 0.000314 [mA2]
240 I
*1 Exp.
22° ._ ------ Fit
200
180 """""""""""""""
160
140 I
g 120 1 ,
a .. 1
2 I
O 100 L
“- l
40 /
2. /
it ', I
0 i": i c I i t t i .gL
‘ 1
-20 '
0 0.5 1 1.5 2 2.5 3 3.5
Defamation [mm]

 

 

 

FIGURE C33 - Compression test and curve fit for Y33_03

152

COMPRESSION TEST :Maxwell Model

Elasticity 6.53E+08 [Pa]
Viscosity 1.67E+08 [Pa's]
Yield stress 348930 [Pa]
Velocity 0.00423 [In/s]
Contact area 0.000314 [mAZ]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C34 - Compression test and curve fit for Y34_03

153

COMPRESSION TEST :Maxwell Model

Elasticity 5.92E+08 [Pa]
Viscosity 1.62E+08 [Pa*s]
Yield stress 288335 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C35 - Compression test and curve fit for Y35_03

 

154

COMPRESSION TEST :Maxwell Model

Elasticity 4.92E+08 [Pa]
Viscosity 7.24E+08 [Pa‘s]
Yield stress 437958 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C36 - Compression test and curve fit for Y3 6_03

155

COMPRESSION TEST :Maxwell Model

Elasticity 4.17E+08 [Pa]
Viscosity 6.04E+08 [Pa*s]
Yield stress 396105 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C37 - Compression test and curve fit for Y37_O3

 

 

156

COMPRESSION TEST :Maxwell Model

Elasticity 5.09E+08 [Pa]
Viscosity 4.36E+08 [Pa‘s]
Yield stress 421754 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C38 - Compression test and curve fit for Y3 8_03

157

COMPRESSION TEST :Maxwell Model

Elasticity 5.06E+08 [Pa]
Viscosity 2.56E+10 [Pa‘s]
Yield stress 513378 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Farce [N]

 

O 0.5 1 1.5 2 2.5 3

Defamation [mm]

 

3.5

 

FIGURE C39 - Compression test and curve fit for Y39_03

 

158

COMPRESSION TEST :Maxwell Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Elasticity 5.56E+08 [Pa]
Viscosity 4.685+08 [Pa‘s]
Yield stress 426326 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [WY]
240 I x
" Exp. '
22° ‘— ------ Fit
200 f
4. I1,
180 ,’
160
140 ;'
E 120 4
O t.
e / \
12 100
-_ / v N\
80 /
60
.. /
40
20 /
O .t' + g I T
-20 .
0 0.5 1 1.5 2 2.5 3 3.5
Defamation [mm]

 

 

FIGURE C40 - Compression test and curve fit for Y40_O3

 

 

 

 

 

159

COMPRESSION TEST :Maxwell Model

Elasticity 3.62E+08 [Pa]
Viscosity 4.42E+08 [Pa‘s]
Yield stress 331139 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mAZ]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C41 - Compression test and curve fit for Y41_03

 

 

160

COMPRESSION TEST :Maxwell Model

Elasticity 4.65E+08 [Pa]
Viscosity 2.38E+08 [Pa‘s]
Yield stress 306164 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C42 - Compression test and curve fit for Y42_03

161

COMPRESSION TEST :Maxwell Model

Elasticity 3.96E+08 [Pa]
Viscosity 2.69E+08 [Pa‘s]
Yield stress 300994 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [m"2]

 

Force [N]

0 0.5 1 1.5 2 2.5 3

Defamation [mm]

 

 

3.5

 

FIGURE C43 - Compression test and curve fit for Y43_03

 

162

COMPRESSION TEST :Maxwell Model

Elasticity 5.53E+08 [Pa]
Viscosity 1.44E+08 [Pa‘s]
Yield stress 313349 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

O 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C44 - Compression test and curve fit for Y44_03

163

COMPRESSION TEST :Maxweli Model

Elasticity 3.85E+08 [Pa]
Viscosity 2.09E+08 [Pa‘s]
Yield stress 313121 [Pa]
Velocity 0.00423 [m/s]
Contact area 0.000314 [mA2]

 

Force [N]

 

0 0.5 1 1.5 2 2.5 3 3.5 4

Defamation [mm]

 

 

 

FIGURE C45 - Compression test and curve fit for Y45_03

APPENDIX D

 

164

APPENDIX D

Force-Deformation Plots of Shear Test

 

165

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00218 [m] MT thick 0.0002 [m]
Sample area 0.00012 [m"2] —> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [m/s]
Yield stress 1145150 [Pa] Predicted:

Yield Strength 0.79 [N]

 

 

 

 

Force [N]
\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D1 - Shear test result for Y01_04

166

 

 

 

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00241 [m] MT thick 0.0002 [m]
Sample area 0.000132 [m"2] —> MT Area 6.91 E-06 [mA2]
Velocity 0.004233 [mls]
Yield stress 299244 [Pa] Predicted:
Yield Strength 2.07 [N]
60
50 //\\
4o / \
E
3 30
E / \
2. // \\
M
MM, \NWM~
1o
0

 

 

 

 

 

 

 

 

 

 

 

 

 

1 2 3 4 5

Defamation [mm]

 

FIGURE D2 - Shear test result for Y02_04

 

 

167

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00137 [m] MT thick 0.0002 [m]
Sample area 7.53E-05 [m"2] —> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [mls]
Yield stress 185405 [Pa] Predicted:
Yield Strengt 1.28 [N]
20 /
15
g \
3 10 —
:«2 ’ \M
W!
5 M
o
0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D3 - Shear test result for Y03__04

 

168

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.0021 [m] MT thick 0.0002 [m]
Sample area 0.000115 [m"2] —> MT Area 6.91E-06 [m‘2]
Velocity 0.004233 [mls]
Yield stress 248737 [Pa] Predicted:

Yield Strength 1.72 [N]

 

Farce [N]

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D4 - Shear test result for Y04_04

_. 1.5

 

 

 

169

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00197 [m] MT thick 0.0002 [m]
Sample area 0.000108 [m"2] —> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [m/s]
Yield stress 228580 [Pa] Predicted:

Yield Strength 1.58 [N]

 

40

 

35

. / \
.. / \
.. / \

 

 

 

 

Force [N]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D5 - Shear test result for Y05_04

53E

 

170

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00193 [m] MT thick 0.0002 [m]
Sample area 0.000106 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 191686 [Pa] Predicted:
Yield Strength 1.32 [N]
30
25 n

 

2. /

 

 

 

Farce [N]
a:
/

10

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D6 - Shear test result for YO6_O4

 

 

 

171

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00188 [m] MT thick 0.0002 [m]
Sample area 0.000103 [mA2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 219752 [Pa] Predicted:

Yield Strength 1.52 [N]

 

Force [N]

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D7 - Shear test result for Y07_04

 

172

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00194 [m] MT thick 0.0002 [m]
Sample area 0.000107 [mA2] » MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 181504 [Pa] Predicted:

Yield Strength 1.25 [N]

 

25

 

20

15 / WK HM.

 

 

 

Force [N]
8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D8 - Shear test result for Y08_04

173

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00164 [m] MT thick 0.0002 [m]
Sample area 9.01E-05 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [m/s]
Yield stress 176118 [Pa] Predicted:

Yield Strength 1.22 [N]

 

30

. A
.. l 1

 

 

 

 

 

 

 

 

Force [N]
6‘.
in

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O 1 2 3 4 5

Defamation [mm]

 

 

 

 

FIGURE D9 - Shear test result for Y09_04

 

 

174

 

 

 

 

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.0022 [m] MT thick 0.0002 [m]
Sample area 0.000121 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 248325 [Pa] Predicted:
Yield Strength 1.72 [N]
35
30
25 / \
_ 20 /
E
8 /
‘6
“' 15 I
\NV/VR
1o / W V‘ ‘vw.
m/
5
0

 

 

 

 

 

 

 

 

 

 

 

 

1 2 3 4 5

Defamation [mm]

 

FIGURE D10 - Shear test result for Y10__04

 

 

 

 

175

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00173 [m] MT thick 0.0002 [m]
Sample area 9.51 E-05 [m"2] —> MT Area 6.91E-06 [m02]
Velocity 0.004233 [mls]
Yield stress 312775 [Pa] Predicted:

Yield Strength 2.16 [N]

 

30
25 \

20

 

 

 

 

Force [N]
a:
\

 

 

WM

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D11 - Shear test result for Y11_04

Fr

 

176

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00256 [m] MT thick 0.0002 [m]
Sample area 0.000141 [m"2] —> MT Area 6.91E-06 [m‘2]
Velocity 0.004233 [mls]
Yield stress 224689 [Pa] Predicted:

Yield Strength 1.55 [N]

 

35

30 A

 

 

25

 

20

 

Force [N]
a:
\-
/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D12 - Shear test result for Y12_O4

 

177

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00277 [m] MT thick 0.0002 [m]
Sample area 0.000152 [m"2] —> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [mls]
Yield stress 242944 [Pa] Predicted:

Yield Strength 1.68 [N]

 

40

35 /\

 

 

30

 

25

 

 

Force [N]
N
O
/

 

 

’ \

\wf\

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D13 - Shear test result for Y13_04

 

 

178

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.0028 [m] MT thick 0.0002 [m]
Sample area 0.000154 [m"2] ——> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 201034 [Pa] Predicted:

Yield Strength 1.39 [N]

 

3., /A\

2. /\
.. \

 

 

 

 

Force [N]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D14 - Shear test result for Y14_04

 

 

179

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.0029 [m] MT thick 0.0002 [m]
Sample area 0.000159 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]

Yield stress

212239 [Pa] Predicted:
Yield Strength 1.47 [N]

 

Force [N]

40

35

25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 2 3 4 5

Defamation [mm]

 

FIGURE D15 - Shear test result for Y15_04

 

 

 

180

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00268 [m] MT thick 0.0002 [m]
Sample area 0.000147 [mA2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 300421 [Pa] Predicted:

Yield Strength 2.08 [N]

 

Force [N]

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D16 - Shear test result for Y16_04

 

181

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.0026 [m] MT thick 0.0002 [m]
Sample area 0.000143 [m"2] “—> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [m/s]
Yield stress 189325 [Pa] Predicted:

Yield Strength 1.31 [N]

 

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. /\
.. J \
1
10 t
5 W] \Mfmmmv

Defamation [mm]

 

 

FIGURE D17 - Shear test result for Y17_04

AI"

182

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00384 [m] MT thick 0.0002 [m]
Sample area 0.000211 [m"2] —> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [m/s]
Yield stress 235456 [Pa] Predicted:

Yield Strength 1.63 [N]

 

60

 

50

 

/"\

 

 

30

 

Force [N]

.., \
/ \

0 1 2 3 4 5

 

 

MWVv/W‘

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

 

FIGURE D18 - Shear test result for Yl 8_04

183

 

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.003 [m] MT thick 0.0002 [m]
Sample area 0.000165 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [m/s]
Yield stress 160527 [Pa] Predicted:

Yield Strength 1.11 [N]

3.00E+01

 

2.5OE+01 A

/\1

 

2.00E+01

 

1.50E+01

 

Farce [N]

1.00E+01

5.00E+00 \‘

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00E+OO l
O 1 2 3 4 5

 

Defamation [mm]

 

 

 

FIGURE D19 - Shear test result for Y19_04

 

184

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00221 [m] MT thick 0.0002 [m]
Sample area 0.000121 [m42] ~> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 288385 [Pa] Predicted:

Yield Strength 1.99 [N]

 

40

 

35

.. A
.. /\

 

 

 

 

Force [N]

 

 

 

/ \Www

0 WWWWA
0 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D20 - Shear test result for Y20_04

..J'I.

185

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00306 [m] MT thick 0.0002 [m]
Sample area 0.000168 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 102475 [Pa] Predicted:

Yield Strength 0.71 [N]

 

25

 

 

 

! 20
l
1
1

Force [N]

 

 

 

P/j WWWNMWl

0 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

 

FIGURE D21 - Shear test result for Y21_04

EAL

 

186

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00336 [m] MT thick 0.0002 [m]
Sample area 0.000185 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 145849 [Pa] Predicted:

Yield Strength 1.01 [N]

 

 

2. A

/\

 

 

 

Force [N]
a:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D22 - Shear test result for Y22_04

 

187

 

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00302 [m] MT thick 0.0002 [m]
Sample area 0.000166 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 130190 [Pa] Predicted:

Yield Strength 0.90 [N]

2.501901

 

2.00E+01 /\

 

 

1.50E+01

 

Farce [N]
/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 DOE-1'01 I \
5.005000
1 \
0.00E+00 ,
0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D23 - Shear test result for Y23_O4

 

 

 

188

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00292 [m] MT thick 0.0002 [m]
Sample area 0.00016 [mAZ] » MT Area 6.91E-06 [m42]
Velocity 0.004233 [m/s]
Yield stress 89790 [Pa] Predicted:
Yield Strength 0.62 [N]
15
1o
2

 

WMMMWW

0 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D24 - Shear test result for Y24_04

 

 

189

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00376 [m] MT thick 0.0002 [m]
Sample area 0.000207 [mA2] —> MT Area 6.91E—06 [m"2]
Velocity 0.004233 [mls]
Yield stress 112771 [Pa] Predicted:

Yield Strength 0.78 [N]

 

25

..i /1

 

 

 

 

Farce [N]

 

 

Wme/Wwv

0 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D25 - Shear test result for Y25_04

,.

 

190

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00248 [m] MT thick 0.0002 [m]
Sample area 0.000136 [m"2] 9 MT Area 6.91E-06 [m‘2]
Velocity 0.004233 [mls]
Yield stress 211617 [Pa] Predicted:

Yield Strength 1.46 [N]

 

30

. 1
25 /\

 

 

 

 

 

 

Force [N]
a:

 

 

\

i W
0 "‘~\,
0 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D26 - Shear test result for Y26_O4

at
l i A

 

191

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00263 [m] MT thick 0.0002 [m]
Sample area 0.000145 [m"2] » MT Area 6.91E-06 [mA2]
Velocity 0.004233 [m/s]
Yield stress 293539 [Pa] Predicted:

Yield Strength 2.03 [N]

 

Force [N]

 

0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D27 - Shear test result for Y27_O4

192

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00263 [m] MT thick 0.0002 [m]
Sample area 0.000145 [mA2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 200621 [Pa] Predicted:

Yield Strength 1.39 [N]

 

 

30

 

 

\

 

 

 

Farce [N]
a

 

 

 

 

 

 

 

 

 

 

 

 

 

1
‘ l \Wl.

Defamation [mm]

 

 

FIGURE D28 - Shear test result for Y28_04

Fa

193

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00251 [m] MT thick 0.0002 [m]
Sample area 0.000138 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [m/s]

Yield stress

318823 [Pa] Predicted:
Yield Strength 2.20 [N]

 

 

Force [N]

 

1 2 3 4 5

Defamation [mm]

 

 

FIGURE D29 - Shear test result for Y29_04

f.
A.

194

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.0024 [m] MT thick 0.0002 [m]
Sample area 0.000132 [m‘2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 293341 [Pa] Predicted:

Yield Strength 2.03 [N]

 

40

/\ .

::: 1 \
.. / l

 

 

 

 

 

Force [N]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

 

FIGURE D30 - Shear test result for Y30_04

?'

 

195

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00316 [m] MT thick 0.0002 [m]
Sample area 0.000174 [m"2] —> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [mls]
Yield stress 177696 [Pa] Predicted:
Yield Strength 1.23 [N]
35
30 A

 

 

/\

25

 

20

 

Farce [N]
6‘.
\
/

 

 

 

waWM—Mt

0 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

 

FIGURE D31 - Shear test result for Y31_04

 

196

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00318 [m] MT thick 0.0002 [m]
Sample area 0.000175 [m"2] ——> MT Area 6.91E-06 [mAZ]
Velocity 0.004233 [mls]
Yield stress 120155 [Pa] Predicted:

Yield Strength 0.83 [N]

 

25

 

A

 

 

 

Farce [N]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I
5
\R
WVWV‘WwW"
0 0 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D32 - Shear test result for Y32_04

 

197

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00285 [m] MT thick 0.0002 [m]
Sample area 0.000157 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 129266 [Pa] Predicted:
Yield Strength 0.89 [N]
25
20 A

 

 

Force [N]

 

 

\Mtjkww-

0 1 2 3 4 5

Defamation [mm]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FIGURE D33 - Shear test result for Y33_04

 
 

198

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00229 [m] MT thick 0.0002 [m]
Sample area 0.000126 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 111836 [Pa] Predicted:
Yield Strength 0.77 [N]
15
.o \
Z
5 / \
0
0 1 2 3 4 5
Defamation [mm]

 

 

 

FIGURE D34 - Shear test result for Y34_04

LL.

 

199

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00202 [m] MT thick 0.0002 [m]
Sample area 0.000111 [mA2] —> MT Area 6.91E-06 [mA2]
Velocity 0.004233 [mls]
Yield stress 132484 [Pa] Predicted:

Yield Strength 0.92 [N]

 

 

 

 

Force [N]

 

 

WWwW

0 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

 

FIGURE D35 - Shear test result for Y3 5_04

F.
LIL.

 

200

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.0024 [m] MT thick 0.0002 [m]
Sample area 0.000132 [mA2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 155948 [Pa] Predicted:
Yield Strength 1.08 [N]
25
20 '\
15
Z

 

 

/ MWWWW

O 1 2 3 4 5

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D36 - Shear test result for Y3 6_04

 

201

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.0024 [m] MT thick 0.0002 [m]
Sample area 0.000132 [mA2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [m/s]
Yield stress 159658 [Pa] Predicted:
Yield Strength 1.10 [N]
25
15 r
E

 

 

 

 

 

 

 

 

 

 

 

 

 

0 1 2 3 4 5

 

Defamation [mm]

 

 

FIGURE D37 - Shear test result for Y37_04

 
 

 

 

202

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00223 [m] MT thick 0.0002 [m]
Sample area 0.000123 [mA2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 146990 [Pa] Predicted:
Yield Strength 1.02 [N]
20
15
‘1
E
8 1° 1
“8- 1
. \

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D38 - Shear test result for Y3 8_04

 
 

203

 

 

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.0021 [m] MT thick 0.0002 [m]
Sample area 0.000115 [mA2] —> MT Area 6.91E-06 [m42] ‘
Velocity 0.004233 [mls]
Yield stress 165813 [Pa] Predicted:
Yield Strength 1.15 [N]
20 '
.5 1
I
I
_ 1
a 1
g 10 fl — — — — ‘1
S

 

 

 

 

 

 

 

 

 

 

 

 

0 \LW/Lr/MAA ,5. Id

0 1 2 3 4 5

 

 

Defamation [mm]

 

 

FIGURE D39 - Shear test result for Y39_04

‘1. ‘

204

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00154 [m] MT thick 0.0002 [m]
Sample area 8.46E-05 [m"2] —> MT Area 6.91E—06 [m"2]
Velocity 0.004233 [mls]
Yield stress 168136 [Pa] Predicted:

Yield Strength 1.16 [N]

 

 

n—y—np

 

 

Force [N]

 

 

 

 

 

 

 

 

 

 

 

 

Defamation [mm]

 

 

FIGURE D40 - Shear test result for Y40_04

 

205

 

SHEAR TEST

MT Dia. 0.011 [m]
"Thickness 0.00214 [m] MT thick 0.0002 [m]
Sample area 0.000118 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 146777 [Pa] Predicted:

Yield Strength 1.01 [N]

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.1 41 . ° ’
57 \ L—m
.. i l Mimi/WWW

Defamation [mm]

 

 

FIGURE D41 - Shear test result for Y41_04

   

 

206

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00237 [m] MT thick 0.0002 [m]
Sample area 0.00013 [m42] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [m/s]
Yield stress 116952 [Pa] Predicted:
Yield Strength 0.81 [N]
20
15 -\ 4
E
3 10
E

 

 

 

 

 

 

 

 

 

 

 

 

'\/\/‘ MAM/WW1

0 1 2 3 4 5

 

Defamation [mm]

 

 

FIGURE D42 - Shear test result for Y42_04

 

 

207

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00262 [m] MT thick 0.0002 [m]
Sample area 0.000144 [mA2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 134993 [Pa] Predicted:
Yield Strength 0.93 [N]
25
.0 r1 1

 

/

 

Force [N]

 

. / Wm

 

 

 

 

 

 

 

 

 

 

 

 

 

O 1 2 3 4 5

Defamation [mm]

 

 

FIGURE D43 - Shear test result for Y43_04

fix,“

208

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SHEAR TEST
MT Dia. 0.011 [m]
Thickness 0.00256 [m] MT thick 0.0002 [m]
Sample area 0.000141 [m"2] ~—*> MT Area 6.91E-06 [mAZ]
Velocity 0.004233 [mls]
Yield stress 123545 [Pa] Predicted:
Yield Strength 0.85 [N]
20
15
l
1 z
1 g 10
12
l 5 / . \
1 l \J\/
0
0 1 2 3 4 5

Defamation [mm]

FIGURE D44 - Shear test result for Y44_O4

 

209

SHEAR TEST

MT Dia. 0.011 [m]
Thickness 0.00229 [m] MT thick 0.0002 [m]
Sample area 0.000126 [m"2] —> MT Area 6.91E-06 [m"2]
Velocity 0.004233 [mls]
Yield stress 130808 [Pa] Predicted:

Yield Strength 0.90 [N]

 

 

 

 

 

Force [N]
8

 

 

WWMMWW‘

 

 

 

 

 

 

 

 

 

 

 

_L ‘——. . —-"i4.4 4

2 3 4 5

Defamation [mm]

 

FIGURE D45 - Shear test result for Y45_04

r-
LL

APPENDIX E

210

APPENDIX E

Stress-Strain Plots of Tensile Test

211

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TENSILE TEST
Sample Thickness 0.00206 [m] Elasticity 2219400 [Pa]
Width 0.009 [m]
Area 1.9E-05 [m"2]
Length 0.02 [m]
3.0E+06
2.5E+06 //
2.0E+06 . //
1.5E+06 - M
"’ 1.0E+06 ' A I" 1»,
5.0E+06 (j
0.0E+06 111 feg 1:1/\/\/\/\0/\::
-5.0E+06 .
o 0.02 0.04 0.06 0.08 0.1 0.12 0.14

 

Strain [mlrn]

 

FIGURE E1 - Tensile test result for Y01_05

 

 

212

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TENSILE TEST
Sample Thickness 0.00208 [m] Elasticity 2893126 [Pa]
Width 0.009 [m]
Area 1.9E-05 [m"2]
Length 0.02 [m]
4.0E+06
3.5E+06 /
3.0E+06 //
2.5E+06 /
/
7.. 2.0E+06 ' A n/
a. /f/ f
5% 1.5E+06 ’ /\/nv//
1.0E+06 - f,//
5.0E+06 /\/: /\/V\/VA\/\/\/
0.0E+06 .4
-5.0E+06
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

FIGURE E2 - Tensile test result for Y02_05

Us.

 

 

213

TENSILE TEST

Sample

Thickness 0.00191 [m] Elasticity 2661102 [Pa]
Width 0.009 [m]

Are

a 1.7E-05 [mA2]

Length 0.02 [m]

 

Stress [Pa]

 

3.5E+06

3.0E+06

2.5E+06

2.0E+06

1.5E+06

1 .0E+06

5.0E+06 ’

0.0E+06

-5.0E+06 ’

-1 .0E+06

 

 

 

 

 

 

 

[ivy/11..

 

 

 

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlm]

 

FIGURE E3 - Tensile test result for Y03_05

 

214

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TENSILE TEST
Sample Thickness 0.00261 [:11] Elasticity 2019565 [Pa]
Width 0.009 [m]
Area 2.3E-05 [m"2]
Length 0.02 [m]
3.0E+06
2.5E+06 _ //
2.0E+06 - /
- ll
4 1.5E+06 A
t . V
(I)
1.0E+06 . //\.
1. 1W1
0.0E+06 i f + 1 .
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

 

Strain [mlrn]

 

FIGURE E4 - Tensile test result for Y04_05

0...“!
L

AI"

 

215

TENSILE TEST

Sample Thickness 0.00178 [m] Elasticity 2603817 [Pa]
Width 0.009 [111]
Area 1.6E-05 [m"2]
Length 0.02 [m]

 

3.5E+06

 

J.
3.0E+06 ” /

2.5E+06

 

 

2.0E+06
1.5E+06 ’ffl),
1.0E+06 D
5.0E+O6 : [\[7fl/
0.OE+06334.+1 +1: t1+ 1 1 ctr 1%i/t/ii

-5.0E+06 0

 

 

Stress [Pa]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-1.0E+06 ”
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlrn]

 

 

 

FIGURE E5 - Tensile test result for Y05_05

 

216

 

 

 

TENSILE TEST
Sample Thickness 0.00264 [In] Elasticity 2186119 [Pa]
Width 0.009 [m]
Area 2.38E-05 [mA2]
Length 0.02 [m]
3.0E+06
2.5E+06 v v

\

 

 

2.05.06 /
1.55.06 : MAJ/l

10906 N/ /
5.0E+06 AV/\,/
0.0E+06 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [/. 1 1

-5.0E+06
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlrn]

 

Stress [Pa]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FIGURE E6 - Tensile test result for Y06_05

TENSILE TEST

Sample

Thickness
Width

Area

Length

217

0.00273 [m]
0.009 [m]
2.46E-05 [mAZ]

0.02 [m]

Elasticity 2644603 [Pa]

 

Stress [Pa]

 

-5.0E+06

3.58-1-06

 

 

3.0E+06

 

2.55-+06

 

2.0E+06

 

 

1.5E+06 '

1W

 

 

1 .OE+06

5.0E+06

 

0.0E+06 1 1 1

1
1

1/

 

 

 

 

 

 

.l
1 UV

 

 

 

 

0.02

0.04 0.06

strain [mlrn]

0.08

0.1

0.12

0.14

 

FIGURE E7 - Tensile test result for Y07_05

 

218

 

 

 

TENSILE TEST
Sample Thickness 0.0027 [111] Elasticity 3603414 [Pa]
Width 0.009 [m]
Area 2.43E-05 [mAZ]
Length 0.02 [111]
5.0506 ..
4.5506 /

Stress [Pa]

 

 

4.0506 " /

3.5506 0 /

3.0506 " /
2.5506 " /

2.0506 " M

 

 

 

 

1.5506 0 ,
1.0506 ” /

5.0E+06 /

 

 

 

 

 

 

 

 

 

 

 

 

0.0E+0611+111 ‘11111‘1' 111

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

FIGURE E8 - Tensile test result for Y08_05

 

TENSILE TEST

Sample

Thickness
Width
Area
Length

0.00253 [m]
0.009 [m]
2.28E-05 [mA2]

0.02 [m]

219

Elasticity 3262707 [Pa]

 

Stress [Pa]

 

4.5E+06 >
4.0506
3.5506
3.0506 :
2.5506
2.0506
1.5506 '

1.0506 .

5.0E+06

0.0E+06

 

 

 

 

 

 

 

i/

y/,

 

j?”

 

 

 

 

 

 

 

AA
,\/V\

 

 

 

 

0 0.02 0.04

0.06 0.08
Strain [mlrn]

0.1

 

FIGURE E9 - Tensile test result for Y09_05

 

TENSILE TEST

Sample

Thickness
Width

Area

Length

0.00272 [m]
0.009 [m]
24513-05 [In/‘2]

0.02 [m]

220

Elasticity 2382488 [Pa]

 

Stress [Pa]

 

-5.0E+06

3.5E+06

 

 

3.0E+06

 

2.5E+06

2.0E+06

 

1 .5E+O6

 

 

1 .0E+06

5.0E+06

 

0.0E+06

1Mwl

 

 

 

 

V'fi

 

 

 

 

 

 

0.04

0.06 0.08 0.1
Strain [mlm]

 

FIGURE E10 - Tensile test result for Y10_05

 

221

 

 

 

TENSILE TEST
Sample Thickness 0.00207 [m] Elasticity 3038228 [Pa]
Width 0.009 [in]
Area 1.86E-05 [mAZ]
Length 0.02 [m]
4.0506
. //
3.0E+06 A “/V

Stress [Pa]

 

I V
: / .
2...... : Jfi/W V

 

 

/J
.e/
/

 

 

 

 

 

 

 

 

 

 

 

 

0.0506 MFA—f .
-1.0E+06
-2.0E+06
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

FIGURE E11 - Tensile test result for Y11_05

222

 

 

TENSILE TEST
Sample Thickness 0.00276 [m] Elasticity 2365463 [Pa]
Width 0.009 [m]
Area 2.48E-05 [mA2]
Length 0.02 [111]
3.5506

 

3.0E+06

2.5E+06 . /

2.0E+06 .v/\/-
I ffd/

1.5E+06 . /A

1.0506 . fl /

5.0506 If,

0.OE+06111111111111111111/\./11

 

 

 

Stress [Pa]

 

 

 

 

 

 

 

 

 

 

 

-5.0E+06 -
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlrn]

 

 

 

 

FIGURE E12 - Tensile test result for Y12_05

 

223

 

 

TENSILE TEST
Sample Thickness 0.00314 [m] Elasticity 2669880 [Pa]
Width 0.009 [m]
Area 2.83E-05 [mA2]
Length 0.02 [m]
3.5E+06

 

1. /
3.0E+06

...... 3 </”
.1/
.M’

 

 

 

Stress [Pa]

 

1 .OE+06

 

 

 

 

 

 

 

 

 

 

 

5.0E+06 A 1.]
0.0E+06 1 1 1 - 1 . 5
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [hum]

 

 

 

FIGURE E13 - Tensile test result for Y13_05

224

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TENSILE TEST
Sample Thickness 0.00261 [m] Elasticity 3140829 [Pa]
Width 0.009 [m]
Area 2.35E-05 [mAZ]
Length 0.02 [m]
4.0E+06 /
3.5506 F //
3.0506 //
2.5506 ’
E 2.0506 _ fly
1% 1.5506 - ,/
1.0E+06 WW
5.0E+06 A)
0.0506 AVAVAJL/
5.05106
0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

FIGURE E14 - Tensile test result for Y14_05

 

 

 

225

 

TENSILE TEST
Sample Thickness 0.00288 [m] Elasticity 3262553 [Pa]
Width 0.009 [m]
Area 2.59E-05 [mAZ]
Length 0.02 [m]
4.5506

Sness [Pa]

 

4.0E+06

3.5E+06

3.0E+06

2.5E+06

2.0E+06

1 .5E+06

1 .0E+06

5.0E+06

0.0E+06

0.04

 

0.06 0.08
Strain [mlrn]

0.1

 

FIGURE E15 - Tensile test result for Y15_05

 

 

226

 

TENSILE TEST
Sample Thickness 0.0024 [m] Elasticity 3204485 [Pa]
Width 0.009 [m]
Area 2.16E-05 [mAZ]
Length 0.02 [m]
4.5E+06

Stress [Pa]

 

4.0E+06

3.5E+06

3.0E+06

2.5E+06

2.0E+06

1.5E+06

1 .0E+06

5.0E+06

0.0E+06

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

FIGURE E16 - Tensile test result for Y16_05

 

227

TENSILE TEST

Sample Thickness 0.00153 [m] Elasticity 2495790 [Pa]
Width 0.009 [m]
Area 1.38E-05 [m"2]
Length 0.02 [m]

 

3.5E+06

 

3.0E+06 '

 

 

2.5506 ’

2.0506 , / V ,
1.5506 AUAVM

1.0506 {VA [\j
5.0506 A}

0.0E+06 111 111 +151 4—51 5 11 A 1 l

 

 

Stress [Pa]

 

 

 

 

 

-5.0E+06 '

 

 

 

 

 

 

 

 

-1.0E+06 '
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlrn]

 

 

 

 

FIGURE E17 - Tensile test result for Y17_05

 

228

 

 

TENSILE TEST
Sample Thickness 0.00193 [m] Elasticity 2556493 [Pa]
Width 0.009 [m]
Area 1.74E—05 [mA2]
Length 0.02 [m]
3.5E+06
3.0506 - //

 

1W
..MV
WY
JV
5.0506 k [1 WV A

0.OE+061'r1111111111111111/..11

 

 

 

 

Stress [Pa]

 

 

 

 

 

 

 

 

 

 

 

 

-5.0E+06

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

 

FIGURE E18 - Tensile test result for Y18_05

229

 

 

TENSILE TEST
Sample Thickness 0.00307 [m] Elasticity 2106323 [Pa]
Width 0.009 [m]
Area 2.76E-05 [mAZ]
Length 0.02 [m]
3.0E+06

 

2.SE+06

 

2.0E+06

 

1 .5E+06

 

 

1.0E+06

Stress [Pa]

 

5.0E+06

 

0.0E+06

 

 

-5.0E+06

 

 

 

 

 

 

 

 

 

-1.0E+06

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

 

FIGURE E19 — Tensile test result for Y19_05

230

 

TENSILE TEST
Sample Thickness 0.00262 [m] Elasticity 2878381 [Pa]
Width 0.009 [m]
Area 2.36E—05 [mA2]
Length 0.02 [in]
4.5506

4.0E+06

3.5E+06

3.0E+06

 

2.5E+06

2.0E+06

Stress [Pa]

1.5E+06

1 .0E+06

5.0E+06

0.0E+06

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlm]

 

 

 

FIGURE E20 - Tensile test result for Y20_05

231

TENSILE TEST

Sample

Thickness 0.00255 [m]
Width 0.009 [m]
Area 2.3E-05 [mAZ]
Length 0.02 [m]

Elasticity 1488604 [Pa]

 

Stress [Pa]

 

-5.0E+06

 

2.5E+06

 

2.0E+06

 

1 .5E+06

1 .0E+06

 

 

5.0E+06 — flu, v

 

0.0E+06 V1 '

 

 

 

 

 

. . 11.11/iv“

 

 

 

 

0 0.02 0.04 0.06 0.08

Strain [mlrn]

0.1 0.12 0.14

 

 

FIGURE E21 - Tensile test result for Y21_05

232

 

 

 

TENSILE TEST
Sample Thickness 0.0032 [m] Elasticity 1718797 [Pa]
Width 0.009 [m]
Area 2.88E—05 [mAZ]
Length 0.02 [In]
2.5506
2.0E+06 . //
1.5506 . /

Stress [Pa]

 

~5.0E+06

 

 

1.0506 Mid

 

5.0E+06 fl

0.0E+0611.111.T
V

 

1.11M

 

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08

Strain [mlm]

0.1

 

FIGURE E22 - Tensile test result for Y22_05

 

 

233

TENSILE TEST

Sample Thickness 0.0028 [m] Elasticity 1910229 [Pa]
Width 0.009 [m]
Area 2.52E-05 [mA2]
Length 0.02 [m]

 

Stress [Pa]

 

-5.0E+06

 

3.0E+06

2.5506 /

2.0E+06 1.
. /

1.5506 /\~l

1.0E+06 A/

 

 

 

 

 

5.0E+06

ODE-906.11111111111er1+11\1/_1\/1\

 

 

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

FIGURE E23 - Tensile test result for Y23_05

234

TENSILE TEST

Sample

Thickness 0.00324 [m]
Width 0.009 [m]
Area 2.92E-05 [m"2]
Length 0.02 [m]

Elasticity 1113635 [Pa]

 

Stress [Pa]

 

1.6E+06 .
1.4E+06 _
1.2E+06
1.0E+06
8.0E+06 :
6.0E+06 .

4.0E+06

2.0E+06

0.0E+06

 

 

 

 

E>

 

 

.WV

 

 

 

 

 

 

 

 

 

Strain [mlrn]

11
W 1 -
11 1 WJVV

 

 

 

 

 

FIGURE E24 - Tensile test result for Y24_05

 

 

235

 

TENSILE TEST
Sample Thickness 0.00292 [m] Elasticity 1423046 [Pa]
Width 0.009 [m]
Area 2.63E-05 [mAZ]
Length 0.02 [m]
2.0E+06

Stress [Pa]

 

-5.0E+06

 

 

1.5E+06 /

 

1.0E+06 V" V
5.0E+06 . /\//

1
0.0E+0611—11111111111./\1'*r/\1/\111

 

 

 

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlm]

 

 

FIGURE E25 - Tensile test result for Y25_05

236

 

TENSILE TEST
Sample Thickness 0.00248 [m] Elasticity 3227850 [Pa]
Width 0.009 [111]
Area 2.23E-05 [mA2]
Length 0.02 [m]
5.0E+06

Stress [Pa]

 

-5.0E+06

4.5E+06

4.0E+06

3.5E+06

3.0E+06

2.5E+06

2.0E+06

1 .5E+06

1.0E+06

5.0E+06

0.0E+06

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlm]

 

FIGURE E26 - Tensile test result for Y26_05

 

237

 

 

 

TENSILE TEST
Sample Thickness 0.00274 [m] Elasticity 3545828 [Pa]
Width 0.009 [m]
Area 2.47E—05 [mA2]
Length 0.02 [m]
5.0E+06 /
4.0506 . /

Stress [Pa]

 

 

R

3,
3.0506 / 7

 

2.0E+06 W

1 .0E+06

 

Kc

 

 

 

 

 

 

 

 

 

 

 

0.0E+06 1 1 1 1 1 1 if 1 1 1 ”W
-1.0E+06
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlrn]

 

 

FIGURE E27 - Tensile test result for Y27_05

 

238

 

 

 

 

 

TENSILE TEST
Sample Thickness 0.00259 [m] Elasticity 3437427 [Pa]
Width 0.009 [111]
Area 2.33E—05 [m"2]
Length 0.02 [m]
5.0506
4.0506 — //
3.0506
. /
3 2.0506
3 - /
(D

 

-1 .0E+06

 

1.0E+06 /

 

 

0.0E+06 1 1 1 1 1 1 5+ . 1 1

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlrn]

 

 

FIGURE E28 - Tensile test result for Y28_05

239

TENSILE TEST

Sample Thickness 0.0024 [in] Elasticity 3034021 [Pa]
Width 0.009 [111]
Area 2.16E-05 [mAZ]
Length 0.02 [m]

 

Stress [Pa]

 

5.0E+06

 

 

4.0E+06 /

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.0E+06
.. /
1.0E+06 /V//.\/—/
°'°E*°6_"""""’T*\'/V'\/\
-1.0E+06
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Straln[mlm]

 

FIGURE E29 - Tensile test result for Y29_05

 

240

TENSILE TEST

Sample Thickness 0.00202 [m] Elasticity 3415703 [Pa]
Width 0.009 [m]
Area 1.82E-05 [mAZ]
Length 0.02 [m]

 

Stress [Pa]

 

 

5.0E+06

4.0E+06 //
3.0E+06 /

2.0E+06 /l/

/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0E+06 . [V

0.0E+061-51111 5.555.- .5 WW
’ J\/\/‘

—1.0E+06 ' /\/J

-2.0E+06 _
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlrn]

 

FIGURE E30 - Tensile test result for Y30_05

 

 

241

 

TENSILE TEST
Sample Thickness 0.0019 [m] Elasticity 3085208 [Pa]
Width 0.009 [111]
Area 1.71E-05 [m"2]
Length 0.02 [m]
4.5506

Stress [Pa]

 

4.0E+06

3.5E+06

3.0E+06

2.5E+06

2.0E+06

1 .5E+06

1.0E+06

5.0E+06

0.0E+06

0.04

 

0.06 0.08
Strain [mlrn]

0.1

 

FIGURE E31 - Tensile test result for Y31_05

 

 

 

242

 

TENSILE TEST
Sample Thickness 0.00305 [m] Elasticity 1748530 [Pa]
Width 0.009 [m]
Area 2.75E—05 [m"2]
Length 0.02 [m]
2.5E+06

 

/

 

2.0506 /

1.5E+06

1.0E+06 ’ \V

5.0E+06
/

 

 

Stress [Pa]

 

0.0E+06

 

 

-5.0E+06

 

 

 

 

 

 

 

 

 

-1.0E+06
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlm]

 

 

 

 

FIGURE E32 - Tensile test result for Y32_05

243

 

 

 

TENSILE TEST
Sample Thickness 0.00228 [m] Elasticity 2268548 [Pa]
Width 0.009 [m]
Area 2.05E-05 [mA2]
Length 0.02 [m]
3.5506
3.0506 ' /

2.5506 /
2.0506 _ /

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E I /
1.5E+06 A
i Mf/l/
m
1.05106 N / L
5...... ff/ W
0.0E+06 1 1 1 1 1 1 1 1 5 1 . : WV VIA/\VA AVAV/\
-5.0E+06
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Strain [mlrn]

 

 

 

FIGURE E33 - Tensile test result for Y3 3_05

244

TENSILE TEST

Sample

Thickness 0.00267 [m]
Width 0.009 [111]
Area 2.4E-05 [mAZ]
Length 0.02 [m]

»_———--.——-u-vu-—

Elasticity 3514630 [Pa]

 

Stress [Pa]

 

‘1
-1 .0E+06

 

5.0E+06

4.0E+06

/

 

3.0E+06

 

/

 

2.0E+06 /

 

1 .0E+06

Amp—RA

. , r AAVAV/

 

41-
ooe+oe
. V_7I 1_V‘T
a»

 

 

 

l
I _T I 1 V V

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08 0.1

Straln [mlrn]

0.12

0.14

 

FIGURE E34 - Tensile test result for Y34_05

 

   

245

 

 

TENSILE TEST
Sample Thickness 0.00272 [m] Elasticity 2438245 [Pa]
Width 0.009 [m]
Area 2.45E—05 [mA2]
Length 0.02 [m]
3.5E+06

Stress [Pa]

 

-5.0E+06

 

3.0E+06 /

2.5E+06 , ,/ g
h / l

2.0E+06 ,

1.5E+06 fl'/

1.0E+06

5.0E+06 P/

0.0E+06 1 1 1 1 1 1 ' 1 .1 w [\V/VJV\/\VIV\VIL\VAVM

 

 

 

7

 

 

 

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Straln [mlrn]

 

 

FIGURE E35 - Tensile test result for Y3 5_05

_... ~--__ ,

 

 

 

246

TENSILE TEST

Sample Thickness 0.00209 [m] Elasticity 1687081 [Pa]
Width 0.009 [111]
Area 1.88E-05 [mA2]
Length 0.02 [m]

 

 

2.5E+06

2.0906 /,
<1

1.5E+06 /

1.0906 \ APA /

5.OE'I*()6L V/
0.0E+06l111111411 AAAAAA

. . . ..A
WVUVWWV

/

 

 

 

 

Stress [Pa]

 

 

 

 

 

1: l

 

 

 

 

 

 

 

 

-5.0E+06

 

Straln [mlrn]

 

0 0.02 0.04 0.06 0.08 0.1 0.12 O. 14

 

 

FIGURE E36 - Tensile test result for Y36_05

247

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TENSILE TEST
Sample Thickness 0.00273 [m] Elasticity 1794603 [Pa]
Width 0.009 [m]
Area 2.46E-05 [mA2]
Length 0.02 [m]
3.0E+06
2.5906 ' /
2.0E+06 . //
'a‘ 1.5906 WA /
E.
1 f /
1.0906 , n/AV /1
5.0906 1 /
/ \/\f\/J\/\/\/\
0.0E+06 1 V/\Cf 19' 1 ~19 1 1 /\/1\/1\/
-5.0906
0.02 0.04 0.06 0.08 0.1 0.12 0.14
Strain [mlm]

 

 

 

FIGURE E37 - Tensile test result for Y37_05

 

 

248

 

TENSILE TEST
Sample Thickness 0.00282 [m] Elasticity 2176547 [Pa]
Width 0.009 [m]
Area 2.54E-05 [mAZ]
Length 0.02 [m]
3.5E+06
3.0E+06 4? /j
2.5E+06 0 //
2.0906 0 //
g .55... fl //
(I) :r /
+ “ A
1.05 06 0 /\/\/r, /
5.0906 ”(V //
:1
0.0E+06 ”A 1 1 4 A A1" "1 1Av/MAA/Hv/\1fr\w
.. . W V vw V V V
5.0906 l
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Stralnlmlm]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FIGURE E38 - Tensile test result for Y3 8_05

 

 

249

 

TENSILE TEST
Sample Thickness 0.00272 [m] Elasticity 1578980 [Pa]
Width 0.009 [m]
Area 2.45E-05 [m"2]
Length 0.02 [m]
2.5906

 

2.0906 /

/

 

 

 

1.5906 //
1.0906 - /‘ /

H /

 

Stress [Pa]

 

 

 

 

 

 

 

 

 

 

-5.0E+06 l l

 

Strain [mlrn]

 

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

 

 

FIGURE E39 — Tensile test result for Y39_05

 

250

 

 

 

 

TENSILE TEST
Sample Thickness 0.00225 [m] Elasticity 2231997 [Pa]
Width 0.009 [m]
Area 2.03E-05 [m"2]
Length 0.02 [m]
3.5906
3.0906 //
2.5906 - /

Stress [Pa]

 

-5.0E+06

 

2.0E+06 /

 

1.5E+06
/

1.0E+06

 

 

/

 

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08
Straln [mlrn]

0.1

0.12

0.14

 

FIGURE E40 - Tensile test result for Y40_05

 

251

TENSILE TEST

Sample Thickness 0.00234 [m] Elasticity 1916969 [Pa]
Width 0.009 [m]
Area 2.11E-05 [mAZ]
Length 0.02 [m]

 

 

3.0906
2.5906 /

/
M... ’\/[l //
VA//
M/
M... MWU/hu/IVA .m

U'V

 

 

 

 

Stress [Pa]

 

 

 

 

 

 

 

 

 

 

 

 

-5.0E+06
0 0.02 0.04 ' 0.06 0.08 0.1 0.12 0.14

Straln [mlrn]

 

 

 

FIGURE E41 - Tensile test result for Y4l_05

252

 

 

 

TENSILE TEST
Sample Thickness 0.00241 [m] Elasticity 2252100 [Pa]
Width 0.009 [111]
Area 2.17E-05 [mA2]
Length 0.02 [m]
3.5906
3.0906 ’ //
2.5906 ’ /

Stress [Pa]

 

-5.0E+06

-1.0E+06 -

 

2.0906 F /

 

1.5906 ’ /

 

 

1.0906 F . .. /

 

 

5.0E+06> V ,

0.0E+06b111.~11\-1111k

 

VVNM

fW/Ab

 

 

 

 

 

 

 

 

 

 

0 0.02 0.04 0.06 0.08
Straln [mlrn]

0.1

0.12 0.14

 

FIGURE E42 - Tensile test result for Y42_05

 

253
TENSILE TEST

Sample Thickness 0.00289 [m]

Elasticity 2116101 [Pa]

 

 

 

Width 0.009 [111]
Area 2.6E-05 [mAz]
Length 0.02 [m]
3.0E+06
2.5E+06 . //

 

2.0E+06 /

 

1.5906 /

Stress [Pa]
>
>
\
\

1 .0E+06

 

 

 

0.0E+06111111111'r1

5.0E+06 / ‘
“J Wm

 

 

 

 

 

 

-5.0E+06

 

 

 

 

0 0.02 0.04 0.06 0.08
Straln [mlrn]

 

0.1

 

FIGURE E43 - Tensile test result for Y43_05

 

253

 

 

 

 

TENSILE TEST
Sample Thickness 0.00289 [m] Elasticity 2116101 [Pa]
Width 0.009 [111]
Area 2.6E-05 [mAZ]
Length 0.02 [111]
3.0906
2.5E+06 ' //
2.0E+06 i /

Stress [Pa]

 

-5.0E+06

1.5906 /

 

 

1 .0E+06

 

 

5.0E+06 JJ / ‘
; Wm

 

0,0E+06111 1111111111

 

 

 

 

 

 

 

 

 

o 0.02 0.04 0.06 0.08
Strain [mlm]

0.1

0.14

 

FIGURE E43 - Tensile test result for Y43_05

 

 
 

254

TENSILE TEST

Sample Thickness 0.00269 [111]
Width 0.009 [m]
Area 2.42E—05 [mA2]
Length 0.02 [m]

Elasticity 1938822 [Pa]

 

3.0E+06

 

2.5E+06

 

 

2.0E+06

1 .5E+06

/

 

1.0E+06

Stress [Pa]
>
‘7
/
>

/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Straln [mlrn]

fl -
5.0906 /\// \
0.0E+06 1 1 1 1 1 1 1 111/'\/\./1\)/\1r/1\ 1 1 W
. V V V v
-5.0E+06 l
0 0.02 0.04 0.06 0.08 0.1 0.12

 

FIGURE E44 - Tensile test result for Y44_05

 

255

TENSILE TEST

Sample Thickness 0.00266 [m] Elasticity 2625809 [Pa]
Width 0.009 [m]
Area 2.39E-05 [m"2]
Length 0.02 [m]

 

4.0E+06

3.5906 ' /

 

 

3.0E+06 * /

 

2.5E+06 /

 

 

2.0906 /

1.5906 ; AMW

1 .0E+06 /

NV \

0.0E+06111 .1. ..1.-\f\[\nA../\.
VVVVVV

Stress [Pa]

 

 

 

 

 

 

 

 

 

 

 

 

-5.0E+06 ’
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Straln [mlm]

 

 

 

 

FIGURE E45 - Tensile test result for Y45_05

 

APPENDIX F

 

 

36

APPENDIX F

Computer Simulation Program

 

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define V1 1 /* 1 in/min */
#define V10 10 /* 10 in/min */
#define r 0.997

#define N 100.0

/* # of layers for grand simulation */

#define lambda 1

#define alpha 3.0

#define freq 100.0 /* sampling rate [Hz]*/
#define Th 0.0002 /* Thickness of unit layer */
#define Area 3.14*pow(0.011,2)/4 /* Area of the
plunger */

#define Area2 3.14*0.011*Th

double Vchl, Vchlo;

float F[500],
iFC[500],iFS[500],FC[500],pFC[500],FS[500],U[500],iF[500],FC
omp[500],Fshear[500];

float dtot[500], Frac;

float D_max;

double d_max, f_max;

double kf_s, kd_s,pc,mo;

float Fvisco=9;
int m, mt;

float ip[45][6]={ {2.36, 1.59, 338438, 0 79, 2219400,
0.42},

{3.85, 1 10, 441721, 2.07, 2893126, 0.33},
{4.20, 1.45, 443736, 1.28, 2661103, 0.40}

 

 

PMPMAAAAAAAAAAAAAAAAAAAAAAAA
ONIbUTUTNl—‘WNNNHNNWih-ibih-LUthWWI-bibww

PM
14>.

AAAF’HAF‘HAAAAAAAAA
NWNNNWWWNNWWWWW

.32, 0.97,
.99, 1.62,
.35, 1.84,
.35, 1.93,
.91, 1 25,
.41, 1 52,
.49, 1.57,
.85, 1.65,
.11, 2.57,
.14, 1 25,
.87, 1.54,
.46, 1 58,
.74, 3.10,
.89, 1.66,
.74, 2.41,
.83, 11.6,
.90, 3.71,
.50, 1.30,
.90, 1.33,
.09, 1.21,
.98, 1.83,
.02, 1.81,
.17, 1.13,
.54, 2.01,
.49, 1.99,
.72, 1.92,
.69, 2.86,
.94, 0.88,
.29, 1.76,
.56, 0.89,
.92, 1.00,
.55, 0.97,
.95, 4.34,
.50, 3 62,
.05, 2.62,
.04, 154 ,
.34, 2.81,
.17, 2.65,
.79, 1.43,
.38, 1 61,
.32, 0.86,
.31, 1 25,

335967,
428455,
446245,
473311,
352807,
331709,
278642,
518319,
434385,
476922,
506877,
500491,
497526,
353833,
358053,
364249,
396447,
334104,
388122,
379075,
282443,
284230,
444801,
631107,
469624,
653307,
554547,
355620,
412565,
300310,
348930,
288335,
437958,
396105,
421764,
513378,
426326,
331139,
306164,
300994,
313349,
313121,

};

N

N H m H o o o H o N H H H N H H H H N H H H H H H H

OOOOHHHI—‘l—‘l—‘OOOOH

72,
58,
32,
52,
25,
22,
72,
16,
55,
68,
39,
47,
08,
31,
63,
ll,
00,
71,
01,
90,
62,
78,
46,
O3,
39,
20,

.03,

.23,
.83,
.89,
.77,

92,
08,

.10,

02,

.15,
.16,

01,

.81,

93,
85,
90,

2019565,
2603817,
2186119,
2644603,
3603414,
3262707,
2382488,
3038228,
2365463,
2669880,
3140829,
3262553,
3204485,
2495790,
2556493,
2106323,
2878381,
1488604,
1718797,
1910229,
1113635,
1423046,
3227850,
3545828,
3437427,
3034021,
3415703,
3085208,
1748530,
2268548,
3514630,
2438245,
1687081,
1794609,
2176547,
1578980,
2231997,
1916969,
2252100,
2116101,
1938822,
2625809,

O

OOOOOOOOOOOOOOO_

OOOOOOOOOOOOOOOOOOOOOOOOOO

7'51"

 

258

void main(void)

{
int x, i, j, k, c, h,z,q,qc,y[30],s[3],minj;
float pd[150],pt,A,tt,sFC,sFS,ppt,max,min,Fv;

float a[lSO], as[150], t, dl, d[150];

float ds[150],dss,dds,dx,temp,pop,force,pc;

float Eu,Nu,SIGMAC,F_max,Es1,ct;

char
*fn[45]={"m:\\m01","m:\\m02","m:\\m03","m:\\m04","m:\\m05",

"m:\\m06","m:\\m07","m:\\m08","m:\\m09","m:\\m10",

"m:\\mll","m:\\m12","m:\\ml3","m:\\ml4","m:\\m15",'m:\\m16",
"m:\\m17","m:\\ml8","m:\\m19","m:\\m20","m:\\m21",'m:\\m22",
"m:\\m23","m:\\m24","m:\\m25","m:\\m26","m:\\m27","m:\\m28",
"m:\\m29","m:\\m30","m:\\m31","m:\\m32","m:\\m33","m:\\m34",
"m:\\m35","m:\\m36","m:\\m37","m:\\m38","m:\\m39","m:\\m40",
"m:\\m41","m:\\m42","m:\\m43","m:\\m44","m:\\m45"};

FILE *destin, *M_T;

Vchl=Vl*0.0254/60;
VCth=VlO*0.0254/60;

M_T=fopen("m:\\MagT","wt");

for(x=0;x<=44;x++) {

Eu=ip[x][0]*pow(10,10);

Nu=ip[x][1]*pow(10,10);
SIGMAc=ip [x] [2];
F_max=ip[x][3];
Es1=ip[x][4];
ct=ip[x][5];

destin=fopen(fn[x],"wt");

q=li

FV=O;
a[l]=(l-r)*Vcth/(l—powl(r,N));

for(i=0;i<=l49;i++) {

2”

dsli]=0.0;

}

Frac=SIGMAc*Area;
dx=Vch10*(l/freq);

Ppt=0;
Pt=0;
C=l;

for(i=0;i<=499;i++) {
iFCli]=0;
iFSlil=0;
Ulil=0;
pFCli]=O;

}

for(i=0;i<=N;i++) {
pd[i]=0;

}

as [1] =61 [1];
for(j=2;j<=N;j++) {
a[j]=a[j-l]*r;

aS[j]=a[j];

}

for(i=0;i<=499;i++) {
t=i*(l/freq); /* time */
dtot[i]=t*Vch10;

for(j=l;j<=N;j++) {
d[j]=pd[j]+a[j]*(t-pt);
}
for(j=c;j<=N;j++) {
/* tt=(dtot[i]-A*(c-l))/Vch10;*/

FC[j]=Area*a[j]*Nu*(l—1/exp(Eu*((t—pt)+0.6*ppt)/Nu));
if(j==c) FC[j]=Area*a[j]*(Nu*(1-0.06*c))*(1-
l/exp(Eu*((t-pt)+0.6*ppt)/(Nu*(l-0.06*c))));

260

if(c== ) FC[j]=Area*a[j]*Nu*(1—1/exp(Eu*t/Nu));
if(FC[j]>=(Frac*(l+0.03*(c—1))))
y[c]=i;
for(k=c+1;k<=N;k++) {
pFC[k]=FC[k];

Pt=t;

if(c==1) ppt=t;
C+=l;
FC[j]=O;

d[j]=Th;
A=Th;
pdljl=Ai

if((N—c+1)== ) goto SSS;
a[c]=(1-r)*Vch10*(l-0.09*c)/(l—powl(r,(N—c+l)));
for(k=(c+l);k<=N;k++) {
a[k]=a[k-l]*r;

for(k=c;k<=N;k++) {
pd[k]=a[k]*(dtot[i]—A*(C-l))/Vch10;
d [k] =pd [k] ;
}

goto FFF;
}

}

FFF:

ch=0;
for(j=l;j<=N;j++) {
sFC=sFC+FC[j]*(a[j]*(1/freq));

iFC[i]=iFC[i-l]+SFC;
if(i== ) iFC[i]=SFC;

a[0]=Vch10;
as[0]=a[0];

SFS=O;

z=l;
for(j=q;j<=N;j++) {

261

dSS=0;
ddS=O;
for(k=j;k<=N;k++) {
if(i== ) Z=0;
dss+=a[k]*(l/freq)*z;
dds+=a[k]*(l/freq)*z;
}
if(qc!=q) { mo=0.6; }
else { mo=1;}
ds[j]=ds[j]*mo+dds;

force=(Esl*(ds[j]*0.7)/0.025)*Area2;
if(force>F_max) q+=1;
sFS=sFS+dss*force;
}
PC=C;
iFS[O]=O;
if(i>0) iFS[i]=iFS[i-l]+sFS;

U[i] =iFC [i] +iFS [i] ;

F[0]=O;

min=200;
for(j=y[l];j<=Y[2];j++) {
if(Flj]<min) {
minj=j;
min=F[j];
}
}
for(i=l;i<=498;i++) {
Fcomp[i]=(iFC[i+1]-iFC[i—l])/(2*dx);
Fshear[i]=(iFS[i+l]-iFS[i-1])/(2*dx)i
if(i>=minj) {
h=l;

Fv=h*(i-minj)*(1/freq)*Fvisco/(minj*0.01);

if(Fv>=Fvisco) Fv=Fvisco;

}

. -_.-——u I.

 

 

 

i.)

262

F[i]=(U[i+l]—U[i-1])/(2*dx)+Fv;
fprintf(destin,"%f %f %f %f
%f\n",i*(1/freq),iFC[i],iFS[i],U[i],F[i]);

}

for(i=l;i<=2;i++) {
max=0;
for(j=(y[i]—10);j<=(y[i]+10);j++) {
if(F[j]>max) {

max=F[j];
s[i]=j;
}
1 1
} {1
max=0; .
for(i=l;i<=l89;i++) { /* 189: Depth of MT [8 mm]*/

if(F[i]>maX) {
max=F[i];
mt=i;

}

fprintf(M_T,"%d %g %g %g %d
%g\n",x+l,F[s[l]],F[s[2]],F[s[l]]/(s[l]*0.0l*Vcth),mt,F[mt]
);

fclose(destin);
printf("%2d\n",x+l);

}

fclose(M_T);

}

 

* This program was written by using C language.

LIST OF REFERENCES

 

263

LIST OF REFERENCES

Armstrong, RR. 1989. Measurement of apple firmness using the acoustic impulse
response. Ph. D. Dissertation. Michigan State University, East Lansing, MI.

Armstrong, RR. and GK. Brown. 1992. Non-destructive firmness measurement of
apple. ASAE Paper No. 936023. St. Joseph, Mich.:ASAE.

Bourne, MC. 1982. Considerations of a general rheological model for the mechanical
behavior of viscoelastic solid food materials. J. of Texture Studies 7:243-255.

Chen, Y. and J. Rosenberg. 1977. Nonlinear viscoelastic model containing a yield
element for modeling a food material. J. of Texture Studies 8:477-485.

Crandall, S.H., N.C. Dahl, and T.J. Lardner. 1978. An Introduction to the Mechanics of
Solids. New York: McGraw-Hill Book Co.

Dickinson, E. and LC. Goulding. 1980. Yield behavior of crumbly English cheeses in
compression. J. of Texture Studies 11:51-63.

Drake, B. 1971. A quasi-rheological model element for fracture. J. of Texture Studies
2:365-372.

Johnson, E.A., M. Peleg, R.A. Segars, and J .G. Kapsalis. 1981. A generalized
phenomenological rheological model for fish flesh. J. of Texture Studies 12:413-425.

Khan, AA. and J .F.V. Vincent. 1990. Anisotropy of apple parenchyma. J. Sci. Food and
Agric. 52:455-466.

264

Khan, AA. and J .F.V. Vincent. 1993. Compressive stiffness and fracture properties of
apple and potato parenchyma. J. of Texture Studies 24:423-435.

Lin, T. and RE. Pitt. 1986. Rheology of apple and potato tissue as affected by cell turgor
pressure. J. of Texture Studies 17:291-313.

McLaughlin, N.B. 1987. Statistical models for failure of apple tissue under constant-
strain-rate loading. J. of Texture Studies 18:173-186.

Mohsenin, N.N. 1977. Characterization and failure in solid foods with particular
reference to fruits and vegetables. J. of Texture Studies 8:169-193.

Mohsenin, N.N. and H. Gohlich. 1962. Techniques for determination of mechanical
properties of fruits and vegetables as related to design and development of harvesting and
processing machinery. J. of Agricultural Engineering Research 7:300-315.

Mohsenin, N.N. 1986. Physical Properties of Plant and Animal Materials. New York:
Gordon and Breach Science Publishers.
Peleg, M. 1976. Consideration of general rheological model for the mechanical behavior

of viscoelastic solid food materials. J. of Texture Studies 72243-255.

Peleg, M. 1976. Compressive failure patterns of some juicy fruits. J. of Food Sci.
41:1320-1324.

Pitt, RE. 1982. Models for the rheology and statistical strength of uniformly stressed
vegetative tissue. Transaction of ASAE 1776-1784.

Shigley, J .E. and CR. Mischke. 1984. Mechanical Engineering Design. New York:
McGraw-Hill Book Co.

White, RM. 1986. Fluid Mechanics. New York: McGraw-Hill Book Co.

 

 

"71111111111111.1111