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This is to certify that the

thesis entitled

Development Of A Mechanical Probe For NonDestructive
Apple Firmness Evaluation

presented by

Hussain A. Ababneh

has been accepted towards fulfillment
of the requirements for

Doctoral degnx3h1Agricultural Engineering

Major professor

 

 

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DEVELOPMENT OF A MECHANICAL PROBE FOR NONDESTRUCTIVE

APPLE FIRMNESS EVALUATION

By

Hussain Ahmad Amin Ababneh

A DISSERTATION

Submitted to
Michigan State University

in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

2002

ABSTRACT
DEVELOPMENT OF A MECHANICAL PROBE FOR NODESTRUCTIVE

APPLE F IRMNESS EVALUATION

By

Hussain Ahmad Amin Ababneh

Fruit ﬁrmness is an important quality attribute of apples. It is
important for consumer satisfaction, proper fruit storage, and shelf life.
Therefore, it is considered a crucial parameter in the postharvest system. The
Magness-Taylor pressure tester is widely accepted in the fruit industry for
ﬁrmness measurement. However, it is destructive since it requires penetration
of steel probe into the fruit ﬂesh. The overall objective of this study was to
develop a ﬁrmness tester that would be consistent with the Magness-Taylor
measurement without causing fruit damage.

Since ﬁrmness is a measure of apple tissue strength in resisting probe
penetration, the measurement of the bioyield strength of tissue was used to
predict apple ﬁrmness. A mechanical probe composed of a cylindrical steel
probe with rubber bonded at the end was pressed against fruit skin at a quasi-
static rate, applying quasi-uniform pressure on the constant contact area. The
Instron machine was used to detect the load drop due to the tissue failure.

A ﬁnite element (FE) mode] of the apple-probe contact was used to

analyze the effect of various parameters on the contact stress distribution. It

provided guidelines for designing the probe to produce a quasi-uniform stress
distribution.

Based on the FE results, six probes were built and evaluated
experimentally. The probes were pressed against the fruit at a constant speed.
The Instron testing machine was programmed to stop when a small drop in the
contact force was suddenly detected due to tissue bioyielding. The force at
the bioyield point was well correlated to the MT ﬁrmness measurement.

The 1/4” diameter probe with 1/8” rubber thickness was found to be
the optimal probe. It was repeatable, produced minimum damage, and had the
maximum correlation coefﬁcient with the MT ﬁrmness measurement of 0.853
in comparison with the 0.919 of the MT ﬁrmness measurements on apposite

sides of the fruit.

DEDICATION t

 

This dissertation is dedicated to my wife Nabila Alomari, my daughter Judy,

and son Hamzah to the memory of the time when we started our family.

 

iv

ACKNOWLEDGMENTS

I would like to express my sincere gratitude to my admirable major
professor, the Chairman of the Agricultural Engineering Department Prof.
Ajit K. Srivastava for his guidance, suggestions and ﬁnancial support. His
wonderful scheme of technical analysis attracts my interest and made me
delighted that he accepted me as a graduate student, and he would remain

my academic example.

I am grateful to Dr. Renfu Lu my co-major professor, Agricultural
Engineering Department -—USDA for his assistance in the ﬁnite element

study, experimental design and providing with the fruit samples.

My deepest thanks to Dr. Daniel E. Guyer, Agricultural Engineering
Department for his serving as a member of my committee and providing
valuable suggestions about the possible factors that might affect the bioyield

test measurements.

I extend thanks for Dr. Randolph Beaudry, Department of Horticulture,
who assisted me in recognizing the postharvest system and the biological

structure of fruits.

I want also to extend my appreciation to Dr. Clark J. Radcliffe ,

Department of Mechanical Engineering, for his serving in my committee

and providing valuable suggestions about the contact problem and the

prospective online application of the probe in apple sorting.

Finally, I am thankful for Richard Wolthuis and Steve Marquie,
Agricultural Engineering Department for their technical assistance in

experimental construction and data acquisition.

vi

TABLE OF CONTENTS

Abstract ..................................................................................... ii

Dedication ................................................................................ iv

Acknowledgement ...................................................................... v

Table of Contents ...................................................................... vii

Table of Figures ........................................................................ xi

List of Tables ........................................................................... xiv
Chapter 1

Introduction ................................................................................ 1

1.1 Introduction ...................................................................... 1

1.2 The Standard Firmness Test ............................................... 2

1.3 Objectives ...................................................................... 5
Chapter 2

Literature Review ......................................................................... 6

2.1 Acoustic and Impact Tests ................................................... 6

2.2 Quasi-Static Loading .......................................................... 7

2.3 The behavior of Apple Material ............................................ 10

2.4 Failure Criteria .................................................................. 13

2.5 Finite Element Studies ........................................................ 14

2.6 Summary ......................................................................... 14
Chapter 3

Theory of Contact between Bodies ................................................ 16

3.1 Hertz Contact Theory ....................................................... 17

3.2 Assumptions for Apple-Probe Contact .................................. 18

3.3 Analysis ......................................................................... 19

3.3.1 Concentrated Normal Force ........................................ 23

3.3.2 General Axi-Symmetric Pressure Distribution .................. 25

vii

3.3.2.1 Uniform Pressure (n=0) ....................................... 26

3.3.2.2 Uniform Normal Displacement (n= -‘/2) ................... 30

3.3.2.3 Hertz Pressure (n=+‘/2) ....................................... 31

3.3.3 Normal Stress at Any Point ......................................... 35

3.3.4 The Viscoelestic Contact ............................................ 35

3.3.5 Onset of Bioyield ...................................................... 37

3.4 Summary ........................................................................ 40
Chapter 4

Finite Element Simulation of the Contact Problem ............................ 42

4.1 The Concept of the Finite Element Method ........................... 43

4.2 Probe Design Considerations ............................................. 45

4.3 Objectives ...................................................................... 47

4.4 The Finite Element Model .................................................. 48

4.5 Results and Discussion ..................................................... 53

4.5.1 Validation of the Finite Element Solution ........................ 53

4.5.2 Development of Bioyield Failure Criterion ....................... 56

4.5.3 Effects of Probe and Fruit Parameters ........................... 68

4.5.3.1 Rubber Elastic Modulus ....................................... 68

4.5.3.2 Probe Diameter ................................................. 70

4.5.3.3 Rubber Tip Thickness ......................................... 71

4.5.3.4 Probe Edge Fillet Radius ..................................... 71

4.5.3.5 Apple Size ........................................................ 73

4.5.3.6 Apple Skin ........................................................ 76

4.5.3.7 Friction ............................................................ 77

4.6 Summary and Conclusions ................................................ 78
Chapter 5

Experimental Evaluation ............................................................. 80

5.1 Introduction .................................................................... 80

viii

5.2 Objectives ....................................................................... 80

5.3 Materials and Methodology ................................................ 81

5.3.1 Measuring Apple Material Properties ............................. 83

5.3.1.1 The Compression Test ......................................... 83

5.3.1.2 The Stress Relaxation Test ................................... 85

5.3.2 The MT Firmness Test and The Bioyield Test ................. 85

5.3.2.1 The Magness-Taylor Firmness Test ....................... 85

5.3.2.2 The Bioyield Point Test ....................................... 87

5.3.2.3 The Mechanical Probes .................................... 88

5.3.3 Testing Procedure ................................................... 90

5.4 Results and Discussion ..................................................... 92

5.4.1 Typical Bioyield Test .................................................. 92

5.4.2 The Modulus of Elasticity ............................................. 94

5.4.3 The Stress Relaxation Function .................................... 94

5.4.4 The Bioyield Point Test and Firmness Prediction .............. 98

5.4.4.1 Regression Analysis ......................................... 100

5.4.4.2 The Small-Thick Probe ...................................... 105

5.5 Summary and Conclusions ............................................... 119
Chapter 6

Overall Summary, Conclusions and Recommendations .................... 122

6.1 Summary ...................................................................... 122

6.2 Conclusions .................................................................. 124

6.3 Recommendations ......................................................... 125

References ............................................................................. 126

Appendices ............................................................................. 132

Appendix A. The Testing Codes ............................................. 133

A.1 The Relaxation Testing Code ....................................... 134

A2 The Bioyield Point Testing Code ................................... 136

ix

Appendix B. The Bioyield Test Results .................................... 138

B1 Golden Delicious ....................................................... 139
8.2 Red Delicious ............................................................ 143
B3 Fuji ......................................................................... 147
8.4 Gala ........................................................................ 151

TABLE OF FIGURES

Esme liege
3.1 Coordinate system for the contact problem .................................... 17
3.2 Hertz contact of two convex bodies showing the principal axes ............ 21
3.3 Concentrated force acting at the surface of a half-space ................... 24
3.4 General axi-symmetric pressure distribution .................................. 26
3.5 Integration of the effect of pressure applied over a circular

3.6

area at point B(r, 0) located: (a) Inside the circle [r<a]
(b) Outside the circle [r>a] ...................................................... 27
Rigid cylindrical die loaded against half-space (Boussinesq problem) ....30

3.7 Comparison of stress distributions at the surface and along the axis

3.8

3.9
4.1
4.2

of symmetry due to (left) uniform pressure and (right) Hertz
pressure on a circular area of radius a (Johnson 1985) ...................... 34

Variation of the pressure distribution against dimensionless

radius at particular times (Lee and Radok, 1960) ........................... 37
von Mises failure criterion in two-dimensional body .......................... 40
Probe geometry ................................................................... 46

Comparison of apple bioyield test by a cylindrical steel probe

with and without rubber tip .................................................... 47

4.3 The ﬁnite element model showing the model components, the

boundary condition, and the path AB in the zoomed view of

the contact area .................................................................. 52
4.4 Uniaxial compression of cylindrical samples of apple and rubber,
the horizontal and vertical lines identify the linear .......................... 54
4.5 Comparison of the F D-curve of experimental and FE simulation
results of a particular apple ..................................................... 56
4.6 Displacement in the axial direction (mm) .................................... 62
4.7 Component of stress in the axial direction , ox (MPa) ......................... 63

4.8 Shear stress concentration under the outer edge (MPa) 64

xi

4.9 Axial component of total strain (811) ........................................... 65

4.10 Total strain energy density (J/cm3) .............................................. 66

4.11 Equivalent von Mises Stress, the white line indicates the locus

of local maximum stress ........................................................ 67
4.12 Effect of rubber modulus of elasticity on the normal

stress distribution ................................................................ 69
4.13 Effect of probe diameter on the normal contact stress distribution ....... 70

4.14 Effect of rubber tip thickness on the normal contact stress

distribution ....................................................................... 72
4.15 Effect of ﬁllet radius on the normal contact stress distribution ........... 72
4.16 Effect of fruit size on the normal contact stress distribution .............. 75

4.17 Effect of skin modulus of elasticity on the normal contact

stress distribution ............................................................... 75
4.18 Effect of skin thickness on the normal contact stress distribution ........ 77
4.19 Effect of friction on the compression and shear stress distributions . ...78

5.1 The bioyield point test setup using the Instron Universal

Testing Machine .................................................................. 82
5.2 Preparation of the cylindrical sample .......................................... 84
5.3 Compression test or relaxation test of the sample between

two parallel plates ............................................................... 84
5.4 The Magness-Taylor ﬁrmness test .............................................. 86
5.5 The mechanical probes used in the bioyield test .............................. 89

5.6 Locations of the MT ﬁrmness and bioyield tests at opposite
5.7 Locations of the MT ﬁrmness and bioyield tests at opposite sides
of the fruit. The circular areas are reserved for the MT tests, and
the bioyield tests are conducted at the spots marked by (x) using
the probe abbreviated next to the mark .......................................... 91
5.8 Typical force-deformation relationship of the bioyield test
generated by the small-thick probe ............................................. 93

xii

5.8 The generalized Maxwell model of two simple elements .................... 96

5.9 The stress relaxation curve of apple material ................................ 97

5.10 Correlation of the MT ﬁrmness with the force at the bioyield point

5.11

5.12

5.13

5.14

5.15

5.16

5.17

5.18

5.19

5.20

5.21

measured by the small-thick probe (SK) .................................... 107
Correlation of the MT ﬁrmness with the force at the bioyield point
measured by the medium-thick probe (MK) ................................. 108
Correlation of the MT ﬁrmness with the force at the bioyield point
measured by the large-thick probe (LK) ................................. 109
Correlation of the MT ﬁrmness with the force at the bioyield point
measured by the small thin probe (SN) .................................... 110
Correlation of the MT ﬁrmness with the force at the bioyield point
measured by the medium-thin probe (MN) .............................. 111
Correlation of the MT ﬁrmness with the force at the bioyield point
measured by the large-thin probe (LN) ...................................... 112
Comparison of the MT ﬁrmness measurements at opposite sides
of the fruit of four apple varieties ............................................ 113
Correlation of the MT ﬁrmness with the stress at the bioyield point
measured by three probe diameters (1/4, 3/8, and 7/ 16 inch), with
constant rubber thickness to diameter ratio of 1/2 ........................... 114
Correlation of the MT ﬁrmness with the stress at the bioyield point
measured by three probe diameters (1/4, 3/8, and 7/16 inch), with
constant rubber thickness to diameter ratio of ‘A ........................... 115
Variation of the deformation required for tissue bioyield with

the diameter of the probe for thin and thick rubber tips .................. 116
Scatter plot of MT ﬁrmness versus the bioyield force measured by the
small-thick (SK-probe), showing the prediction interval (PI) and
conﬁdence interval (CI), based on 95% conﬁdence level, after
eliminating 2% outlier data with the highest standardized residuals ....117
Correlation of bioyield force measurements of the small-thick

(SK) probe and the medium-thick (MK) probe ............................ 118

xiii

LIST OF TABLES

 

Table Page
5.1 Dimensions and abbreviations of the probes ................................ 89

5.2 The correlation coefﬁcient (r) between the Magness-Taylor
ﬁrmness and force, deformation, slope or energy at the

bioyield point ................................................................... 102

xiv

Chapter 1

Introduction

1.1 Introduction

F irrnness is an important attribute for evaluating the quality of fruit; it is
directly associated with fruit growth, maturity, the resistance for bruising, the
potential for good storability, shelf life and the acceptability by the consumer.
Therefore, it is of critical importance and interest for fruit growers, handlers,
quality controllers and retailers. In general, ﬁrmness of climacteric fruit,
including apples, decreases gradually with maturity and decreases rapidly after
the onset of the climacteric rise where the respiration has a peak rate (Seymour et
aL,1993)

Growers use the number of days after bloom as an estimator of fruit
ﬁrmness, but this is a subjective measure, since fruit ﬁrmness varies within the
same tree, and it might be inﬂuenced by a diversity of features. Among them are
the environmental conditions during the growing season and the storage
conditions after harvest, the cultural practices, the apple cultivar and variety, the
use of plant growth regulators and calcium content (Watkins et al., 1980).

The dependence of fruit quality preharvest factors is complex and not
well understood (Shewfelt and Prussia, 1992). Fruit ﬁrmness in the postharvest
stage is also inﬂuenced by several handling techniques and storage conditions.

Fruit growers, processors, and retailers compete to supply and maintain
certain standards of quality to meet the consumer’s demands, which is the

ultimate objective of the fresh fruit industry. Therefore, it is advantageous to be

able to pack the fruit at a stage of maturity that will ensure adequate maturity,
satisfactory and consistent quality as the product reaches the terminal market.

Fresh apples must be handled properly to retain high quality so as to meet
the high standards of the domestic and export markets. Postharvest sorting is of
critical importance in the fruit industry. The consumers prefer a high quality
fruit that is ﬁrm, has a smooth, clean skin and a good color. Human senses are
commonly used to evaluate fruit quality. For example, consumer might inspect
apple ﬁrmness by holding it in the palm of the hand and listening to the sound
pitch generated from thumping the fruit. However, instrumental measurement of
ﬁrmness is more objective than sensory evaluation, and is, therefore, preferred.

A novel approach is used in this study; the ﬁrmness of the fruit is
estimated by measuring the bioyield strength. The test must not result in
degrading of the fruit. The bruise allowance for Extra Fancy apple grade is 3.2
m (1/8 inch) in depth and 15.9 mm (5/8 inch) in equivalent diameter (The
USDA Shipping Point Instructions, 1976). Canadian standards for the Extra
Fancy grade requires apples to be free from individual bruises that exceed 19
mm (3/4 inch) in diameter or an aggregate area of bruises per apple greater than

25 mm (1 inch) in diameter (Canada Extra Fancy Grade Standards, 2001).

1.2 The Standard Firmness Test

Instruments and techniques for evaluating the textural properties of fruits
are important in grading, quality control, and in predicting the mechanical

behavior of the product during certain handling and storage conditions.

The most widely used instrument for evaluating the ﬁrmness of fruits is
the Magness-Taylor (MT) pressure tester, which was developed in 1925 and still
is accepted as the standard measure of ﬁrmness in the fruit industry. The test is
composed of a cylindrical steel probe with a rounded tip; the probe is pressed
into the peel fruit ﬂesh to a certain depth. The maximum force required to
penetrate the probe is considered as the ﬁrmness index of the fruit. Because of
its destructive nature, the use of MT test is limited to fruit sampling and is
inappropriate for sorting each individual fruit.

There are variant forms of MT testers available, for example:
1. The hand—held Effe-gi instruments (Abbott et al., 1976).
2. The foot pedal modiﬁcation of the hand-held instrument (Shewfelt, et al.,
1987)

3. The mechanized Instron test.

The MT pressure tester is simple, low cost, and portable. However, it has
the following disadvantages:

l) The test is of destructive nature in that the fruit being peeled and

penetrated.

2) Penetration into the fruit involves a complex loading process, which

makes it virtually impossible to simulate analytically.

3) MT ﬁrmness measurements may vary signiﬁcantly with operator,

owing to the viscoelastic behavior of ﬂesh material, which is sensitive

to strain rate or loading speed.

Elastic parameters of the quasi-static force / deformation compression
curve of fruit were often considered as satisfactory indicators of fruit
ﬁrmness. These parameters are based on the quasi-static compression of fruit
in the elastic range, and are therefore related to the modulus of elasticity
rather than ﬁrmness. Our preliminary experiments conﬁrmed the conclusions
of Boume (1966) that MT ﬁrmness is best correlated with the shear strength
and the bioyield compression strength. However, the measurement of shear
strength requires relative deformation, for example cutting of fruit ﬂesh,
which would cause fruit destruction. Thus, the hypothesis of this study was
to use the bioyield compression strength as a parameter for apple ﬁrmness
prediction.

The bioyield point of biological materials is analogous to the yield point
of engineering materials (Mohsenin 1986). Bioyielding is due to cell rupture.
However, the damage due to the bioyield point measurement is minimal and
the bruise depth is less than 2 mm (1/ 16 inch) under the skin. Therefore,
Mohsenin et al. (1965) considered the bioyield approach as a practicable
nondestructive technique for fruit ﬁrmness evaluation.

Grading of apples based on this concept could be accomplished without
requiring that each apple reach the bioyield point. As such, good, ﬁrm apples
can be judged by their capacity to withstand a threshold value of load without

demonstrating a bioyield point.

1.3 Objectives

The objective of this study was to develop a nondestructive or a minimally

destructive mechanical probe to evaluate apple ﬁrmness. The probe is used to

detect the bioyield strength, which is considered an important textural property

that relates to fruit ﬁrmness.

The speciﬁc objectives of the research reported in this dissertation were:

1)

2)

3)

4)

5)

To establish an experimental technique for determining the bioyield
point nondestructively.

To apply the ﬁnite element method to investigate the effect of the
various parameters on the evaluation of the bioyield strength of fruit
material.

To design an optimal mechanical probe for nondestructive or minimally
destructive evaluation of ﬁrmness.

To examine different failure criteria in order to specify the most suitable
criterion, this could predict apple tissue failure in the bioyield test by
comparing with the criterion at failure of a uniaxial sample with the
corresponding value, obtained by the ﬁnite element solution of the same
apple.

To use the designed mechanical probes and experimentally evaluate
their ability to measure the bioyield point and predict the standard MT

ﬁrmness test measurements.

Chapter 2

Literature Review

Nondestructive fruit ﬁrmness evaluation has been a subject of interest to
researchers for many years. Several methods have been investigated for the
nondestructive evaluation of apple ﬁrmness. These methods are based on quasi-
static loading, sonic vibration, and impact response. Most of the nondestructive
methods measure elastic properties and relate them to the ﬁrmness of the fruit.
The modulus of elasticity is a measure of material capacity to store energy as it
undergoes a given elastic deformation. The material will recover the original
shape when the load is released. F irmness is a measure of produce resistance to
puncture in which material undergoes permanent plastic deformation, and tissue

failure takes place past the bioyield point.

2.1 Acoustic and Impact Tests

When an impulse strikes an apple, it displays a series of resonant

frequencies. The stiffness index f 2m”

, where f and m are the second resonant
frequency and mass of the fruit, respectively, was the best related to the
Magness-Taylor ﬁrmness of the fruit (Abbott et al., 1968, 1992, 1994, 1995;
Armstrong et al., 1990, 1997; and Chen et al., 1993, 1996). On the other hand,
the analysis of the fruit impact with a rigid surface produced the impact index

F/tz, which was the best related to the ﬁrmness measurement. F and t are the

peak impact force and time to reach that peak, respectively (Delwiche et al.,

1987, 1989, and 1996). Unfortunately, both of the sonic and impact indices were
unsatisfactorily correlated with MT ﬁrmness. Conceptually, the sonic and
impact indices are estimators of the fruit modulus of elasticity rather than
ﬁrmness (Armstrong et al., 1990).

In studying a probe-type impact sensor, Delwiche et al. (1996) had
attributed the lack of agreement with the conventional penetrometer ﬁrmness to
the reason that each instrument was measuring a distinct physical property. They
concluded that the “nondestructive measurements of fruit tissue strength will

never be highly correlated with the penetrometer measurements. "

2.2 Quasi-Static Loading

Fruit material exhibits viscoelastic behavior under dynamic mechanical
loading such that the response depends on the amount of load as well as on the
rate of loading. Many nondestructive methods for ﬁrmness evaluation oﬁen
assume that apple material has elastic behavior, which is independent of the
loading rate.

For practical purposes, elasticity at small deformations was considered a
reasonable indicator of fruit ﬁrmness. Abbott et al. (1995) used fruit stiffness
rather than failure strength as a measure of fruit texture. Timm et al. (1993) built
a portable data-acquisition instrument to evaluate ﬁrmness of cherries and berries
in terms of the mean chord stiffness computed from a force-deformation curve.
Perry (1977) applied air pressure on small areas on the opposite sides of peaches,

the produced deformation was used to characterize fruit ﬁrmness.

A majority of the previous quasi-static applications were based on the
force-deformation curve in the elastic range. They measure either the
deformation of the intact fruit caused by a predetermined force or the force
required to cause a predetermined deformation and relate the measurement to
fruit ﬁrmness.

In an attempt to limit fruit destruction, Schomer and Olsen (1962)
developed an instrument called the ‘mechanical thumb’. They had replaced the
probe of the MT tester with a cylindrical plunger of 1/2 inch (12.7 mm) diameter
and a spherical head. The mechanical thumb was nondestructive in that the
intact fruit could be tested without removing the skin. It resulted in a small
bruise on fruit skin, since it created an indentation depth of 0.05-inch (1.4-mm).
However, the nature of the contact area variations during loading was unknown,
hence the measured force was not very informative. Mattus (1965) questioned
the validity of this test for MT estimation and concluded that it had overrated
large and soft fruit, underrated hard and small fruit, and was variety-dependent.

The measurement of the amount of deformation when the fruit is
subjected to a known load is a second option for quasi-static ﬁrmness
assessment. Fridley (1969) and Fridley et al. (1977) applied preset loads to a
plunger and a ball, respectively. Mehlschau et al. (1981) had developed a
nondestructive deformeter that detected the deformation created by two steel
balls acting on opposite sides of pear fruit. In comparing several probe
geometries, Wilkus (1980) concluded that the ﬂat probe was more appropriate

for apple ﬁrmness measurement than spherical or conical probes. Mizrach et al.

(1992) developed a mechanical thumb to sense the ﬁrmness of oranges and
tomatoes. An adjustable, spring-loaded 3-mm (1/8-inch)-diameter pin was
operated in a Go-No-Go mode to discriminate between ﬁrm and soft fruit. The
pin was also applied on a continuous basis by measuring the deﬂection of the
elastic cantilever beam to discriminate between hard-green, ﬁrm-red and soft-red
tomatoes. Dobrzanski and Rybczynski (1999) used the same pin for strain
measurement to assess slight changes in apple ﬁrmness. The 3-mm plunger was
reported as too small and induced a bruise when the contact stress exceeds the
bioyield strength. Also, the elastic modulus rather than the strain had better
relationship with fruit ﬁrmness.

The soft touch sensor, HIT-Counter (stands for Hardness, Immaturity and
Texture) was commercialized in Japan since 1989 (Takao and Ohmori 1994).
The sensor integrates the time interval required for a plunger to pass across a
speciﬁed load increment within the elastic range. The sensor was used for online
fruit sorting; the correlation coefﬁcient with the conventional ﬁrmness was as
high as 0.927 for kiwifruit. Later, a small portable version called the Handy HIT
was developed (Takao and Ohmori 1994). The sensor was able to evaluate the
ﬁrmness of Japanese persimmon, a type of oranges (Yakushiji et al., 1995).

Within a certain range of strain, the apple can be deformed without any
permanent deformation. A small penetrometer for quasi-nondestructive
measurement of apple ﬁrmness at a very slow compression rate had no
signiﬁcant distortion for deformations below the point of inﬂection, nearly 0.3

mm (0.01 inch) in the case of apples (Fekete, 1994).

2.3 The Behavior of Apple Material

The bioyield point is believed to be closely related to the MT ﬁrmness,
which could also cause permanent deﬂection or damage to the fruit. At the
bioyield point, cell rupture occurs so that browning and discoloration are
initiated. However, the damage to the tissue is small, and the bruise depth is less
than 2 mm (1/16 inch) under the skin. Mohsenin and co-workers (1965) had
considered the bioyield point measurement a feasible nondestructive method for
fruit ﬁrmness evaluation. A % inch (6.4 mm) diameter ﬂat-ended steel plunger
was driven at a speed of 0.6 inch/min (15.2 mm/min) against the fruit skin until
the bioyield point was detected at about 0.04 inch (1.0 mm) of deformation. The
study was focused on the variations of the bioyield strength and the
corresponding deformation with time during maturation and ripening. The
decrease of the bioyield force with time was reported to represent the decrease of
fruit ﬁrmness, but the relation between the bioyield strength and the ﬁrmness
was not investigated.

The compression force at the bioyield point is predominant in the MT
test. The primary step of the penetration process is bioyielding; however, the
penetration physics is not well understood and a comprehensive analysis is not
available to the best of the author’s knowledge. During penetration the material
is sheared and compressed simultaneously. Boume (1966) considered the shear
strength and the compressive strength as the major parameters that are involved

in the penetration process, and hence in the MT test. The total force required for

10

penetration was expressed as a rectilinear combination of the compression and

the shear coefﬁcients, equation (2.1):

F=KCA+KSP+C (2.1)

where F: measured force (kg), Kc: compression coefﬁcient of the material
being tested (kg/cmz), Ks: shear coefﬁcient of the material being tested (kg/cm),
A= area of punch (cmz), P= perimeter of the punch (cm), and C: constant (kg).

The coefﬁcients Kc, Ks and the constant C are dependent on the nature
of the tested material. The constant C that usually has a negative value was
thought to account for the inﬂuenced zone around the puncture and other
uncertain minor parameters. Tensile and pumping effects were introduced as
minor parameters that counteract the MT puncture force (Jeong, 1997). A radial
tensile force pulling the surrounding zone is implicated with the shearing
process, and the curved tip of the puncture promotes the tensile force. The
pumping effect, on the other hand, is due to the piston action of the puncture that
expels the juice throughout the annular clearance around the puncture sides. The
compression of a cylindrical sample was modeled by a series of Maxwell units
with a fracture element; each unit represents a single layer of the apple sample.
The layers were believed to bioyield sequentially with compression, which
explained the saw-tooth force deformation relationship (J eong, 1997).

According to the trend of the penetration force following the yield point,
Boume (1980) classiﬁed the curves into three possible groups: increasing, almost

remaining constant and decreasing. Fresh apples exhibited a rapid increase of

11

force with deformation after the bioyield point, whereas the cold stored apples
had roughly constant force over a considerable deﬂection after the bioyield point,
and the curve looked like a plateau. On the other hand, the apples stored at
elevated temperatures exhibited a sharp drop of penetration force after the
bioyield point. In the ﬁrst two groups the penetration depth could be controlled
but not in the group of decreasing force (Boume, 1980). There was no physical
reasoning reported behind these differences of the trends.

Air space makes up about 25% of the mature fruit volume; air is
produced by cell separation that occurs during apple growth. The air spaces tend
to form radial canals through the cortex and they continue to increase during
storage and ripening (Seymour et al., 1993). This increase in air space may
contribute to the decline in ﬂesh ﬁrmness during storage and ripening.

Chen et al. (1996) concluded that the MT test is more sensitive to
viscous properties than elastic properties. The viscoelastic characteristics of fruit
material are signiﬁcantly divergent from those of engineering material in which
Hooke’s law holds for the elastic range. The contact problem of fruit material is,
consequently, deviant from the classical Hertz contact theory. Fridley et al.
(1968, 1977) reported that the forces required to deform whole pears and peaches
with a cylindrical plunger or a ﬂat plate were signiﬁcantly below those predicted
by Hertz contact theory. This difference was due to the relaxation of fruit
material upon compression. Likewise, Hertz contact model overestimated the
bruise diameter due to apple impact with a hard ﬂat surface. Also, the plastic

theory that considers the permanent deformation after the bioyield point,

12

generally, underestimates the bruise diameter. However, experimental
adjustment of Hertz contact theory by considering the effect of loading rate of
the viscoelastic apple material has given more accurate estimation of the bruise
size (Siyami et al. 1988).

The applied compression force by a sensor on an elastic body is
proportional to the local deformation raised to the power of 3/2 (Fridley et al.,
1968), as predicted by the classical Hertz contact theory. However, due to stress
relaxation of fruit material the power is less than 3/2. A range of 0.9-1.4 was

reported by Chemg (1999), which varies with fruit growth and storage period.

2.4 Failure Criteria

Many researchers have studied the failure criteria of fruits. The
maximum shear stress was believed to cause failure of apple samples (Miles and
Rehkugler, 1973). Experimental results of De Baerdemaeker (1975) supported
the maximum shear stress theory. Failure was initiated at a depth of less than
one third the contact diameter in ﬂat plate compression for pears and peaches
(Fridley et al., 1968). The maximum shear stress in an elastic material is located
at a depth of about one half the contact diameter. In contrast to the maximum
shear stress theory, Segerlind and Fabbro (1978) reported that apples fail when
the normal strain exceeds a critical value. This critical value was in the range of

0.10—0.15 strain.

13

2.5 Finite Element Studies

The contact problem of biomaterials has been studied using the ﬁnite
element method. Sherif (1976) applied the ﬁnite element technique to
investigate the stress distribution in diametrically loaded cylindrical samples of
apples, peaches and potatoes. The material was assumed homogenous, isotropic
and elastic, the apple samples failed at the maximum shear strength. Rumsey
and F ridley (1977) analyzed the contact problem of a viscoelastic spherical body
with an exponential decaying shear modulus and a constant elastic bulk modulus.
They found that there was good agreement between the analytical and the ﬁnite
element solutions. De Baerdemaeker (1975) considered apple material with time
dependent bulk modulus and shear modulus in studying the creep and the contact
problem of spherical samples of Red Delicious with a ﬂat plate. He supported
the theory of distortion energy over the maximum shear stress theory to account
for the failure pattern. The relaxation functions were found to be sensitive to the
loading rate. De Baerdemaeker and Segerlind (1976) developed a procedure to
determine the viscoelastic properties - the coefﬁcients and exponents of the

exponential series - using the generalized Maxwell model for apple samples.

2.6 Finite Element Studies

The dynamic techniques were more sensitive to the elastic properties of
the fruit material rather than the ﬁrmness. In attempting to achieve a
nondestructive testing, the quasi-static studies were primarily restricted to the

inspection of the force-deformation relationship in the linear range prior to the

14

bioyield point. Therefore, the measurements could be considered as different
approaches to estimate the elastic properties rather than the tissue strength. The
later property is the dominant property in determining the maximum force, which
the fruit tissue is able to withstand before failure under the MT probe. Therefore,
creating a failure of fruit tissue is necessary to evaluate the apple material
strength and eventually the ﬁrmness. However, minimizing the damage in the
measurement of tissue strength is the challenge for developing a new successful

ﬁrmness sensor.

15

Chapter3

Theory of Contact between Bodies

The proposed method for evaluating the apple ﬁrmness is based on
contacting the apple fruit with a probe. The understanding of classical contact
theory is necessary for designing a new probe that would be appropriate to detect

the strength of apple material while causing minimum damage.

When two solid bodies are brought into contact, they touch each other at
a single point or occasionally along a line. This general case of contact, where
no perfect ﬁt is accessible between the two surfaces prior to deformation, is
known as a non-conforming contact. As load is applied on the bodies, the high
stress concentration at the contact point causes deformation in the two surfaces at
the neighborhood of the initial contact point. Therefore, it results in a small ﬁnite
area of contact. The order of magnitude of the contact area and the deformation
are very small compared to the dimensions of the bodies. This chapter looks into
the classical Hertz contact theory, and investigates the Boussinesq die contact
and the contact due to a uniform pressure, which is applied throughout this study.
The divergence of the contact with viscoelastic material from contact with elastic
material is presented. Finally, some criteria for the onset of material yield are

stated.

16

3.1 Hertz Contact Theory

When two non-conforming bodies are pressed against each other, they
touch at a single point, as the load is applied, the surfaces in the vicinity of the
contact point start to deform and a ﬁnite area of contact is developed. The Hertz
theory investigates the contact process of two elastic bodies to predict the shape,
deformation of the contact region, the way in which bodies respond as load

progresses, and speciﬁes stress distribution that is generated at the interface.

The Hertz theory is based on the fact that the deformation and dimensions
of the contact area are sufﬁciently small compared to the dimensions of the

contact bodies, such that each body is considered a semi-inﬁnite half space.

In analyzing the contact problem of axi-symmetric bodies, it is
advantageous to use cylindrical polar coordinate systems. The origin “0" is

chosen as the ﬁrst point of contact (Fig. 3.1), and the axis 02 is the common

Common
normal

‘(

 

Fig. 3.1 Coordinate system for the contact problem

17

 

normal to the contact surfaces. The coordinate r is the radial distance from the

axis 02, and His the angle between r and a certain reference axis 0x.

3.2 Assumptions for Apple-Probe Contact

The intended apple ﬁrmness test used a cylindrical probe with a rubber
tip contacting the apple. The probe is pressed against the fruit surface until the
bioyield stress is achieved underneath the contact area. In developing his
classical contact theory Hertz had made some assumptions. Before analyzing the
contact problem, it is necessary to discuss the extent to which Hertz’s
assumptions are valid in the intended contact problem between the apple and the
probe. Hertz assumptions include:

1. The materials of the contact bodies are homogeneous. This is valid for the probe
material, which is made of steel and rubber, while for apple, as a biological
material this condition does not hold.

2. The applied load is static. The rate of compression process (0.5 inch/min) is
slow enough such that the inertia forces are insigniﬁcant and can be neglected.

3. The contacting bodies are elastic. Again this is not an exact condition for apple
material, since the viscous behavior is anticipated to be more signiﬁcant with
time. However, the duration of the test is small compared with the smallest time
constant of average apple relaxation function. The later was found
experimentally to be 2.27 seconds (see Chapter 5).

4. The contacting bodies are semi-inﬁnite. Apple bioyield stress is moderately

small, and the test is conducted over a small area such that the stress vanishes at

18

the opposite side of the contact area, as found by the ﬁnite element simulation,
(See Fig. 4.7). Hence an apple can be considered a semi-inﬁnite body.

5. The radii of curvature of the contacting surfaces are very large compared to the
radius of the contact area. For a cylindrical probe, the radius is small compared to
the radii of curvature of the contact surfaces, the probe cross-sectional area is
assumed to be the upper limit for the contact area (neglecting the radial expansion of
the rubber tip). Hertz designated a threshold of 10 for the ratio of the radius of
curvature of the contact surface. to the contact radius for his equations to be
applicable. This ratio is achieved for probe diameter less than 3/8 inch in contact
with an average apple fruit.

6. The surfaces in contact are sufﬁciently smooth, such that no radial friction forces are
encountered as the loading progresses. The rubber is expected to have a high
friction coefﬁcient with the skin, however, the relative radial movement is negligibly

small.

3.3 Analysis

The contact situation of two bodies is shown in Fig. 3.2. Throughout the
analysis we use the subscripts l and 2 to refer to the two contact bodies. The

proﬁle of the original surface can be described by:
Zr =fl(X,y)=AIX2 'IhBry2 +Crxy+ (3.1)

Due to the small order of magnitude of x and y within the contact area,

the higher order terms are neglected. The third term (C zxy), .on the other hand,

19_

would vanish by choosing the orientation of the coordinate system to coincide
with the principal axes. The principal axes x1 and y, shown in Fig. 3.2 are in the
direction of the projection of the planes that contain the principal radii on the
common tangent plane of those planes, which contains the principal radii of

curvature as below. Then equation 3.1 becomes:

 

_ 2 2 (3.1)
2 — — x + y
' 2R: 1 2R," 1
where R'1 and R"1 are the principal radii of curvature of body 1 at the origin.
Similarly the surface proﬁle of the second body may be described by:
1 1
z. = — -—,x3 + —.-y: (3.3)
2R2 2R2

A similar approach can be used to express the separation between the surfaces

(h=zl-zz), such that:

h = sz + By2 = if + 2:?" y2 (3'4)

 

where R ’and R ” are the principal relative radii of curvature.
The requirement for eliminating the xy-term in Eq. 3.4 implies the following

expressions for the constants A and B (refer to Johnson (1985) for more details).

(A+B)=l(—1—+1)=l --1—+-1—+—1—+1
2 R' R" 2 R; R," R; R,"

and (3-5)

 

 

 

 

20

mm):

where or is the angle between the principal axis x, and x2 (Fig. 3.2). The contour
of points which has constant separation h in Eq. 3.4 is an ellipse with axis ratio

equal to (B/A) ”2=(R 7R ’9 ”2.

 

/\ Plane of

/ \\ R2

"///// “ .

 

 

Fig. 3. 2 Hertz contact of two convex bodies, showing the principal axes.
If the two bodies are assumed solids of revolution (axi-symmetric), then,
the angle a=0, R 7=R ';=R,, and R 3=R ’3=R2, hence A=B='/2(1/R,+1/R2).

Therefore, the contours of constant separation are always circles.

When a normal load is applied, the boundary condition of no interference
between the points on the two contact surfaces together with the linear elastic
behavior of the materials, suggests that the mean contact pressure within the

contact area (pm) be:

p cc “(l/R1 + l/Rzl (3,6)
m l/E. + 1/152

 

21

where E is the material modulus of elasticity.

Hertz proposed a pressure distribution that satisﬁes the above conditions

.0 = fix/1- "2/02 (3'7)

The expressions of the contact radius (a), the approach distance of two

as follows:

points far away on the two bodies (5) and the maximum pressure at the center

(p0) are given by:

a=[ﬂ)m, 522i: it: ”3, p ziz 2P2 V3 (3.8)
45’ R 16 RE" 0 2;: a2 78122

where 1/R=1/R1+1/R2 is the relative curvature, P: is the applied force, a: is the

contact radius and E I is given by:

 

 

1 l-V,2 1—1/22
.= +——-
E E, E,

Although the Hertz stress distribution has no stress concentration at the
boundary of the contact area, it has a peak at the center. Thus, if a spherical
probe were used in apple testing to determine the bioyield strength, the failure of
apple tissue would initiate at the center and extend outwards gradually in the
radial direction. Furthermore, the continuous variations of the contact radius, the
approach distance, and stress with loading make it unfeasible to detect a certain

value that is clearly indicative of bioyield strength.

22

Finney (1963) suggested a rigid cylindrical probe for testing fruits and
vegetables to determine their mechanical properties. Prior to the full contact, a
cylindrical probe has to pass through a preparatory stage that is initiated from the
onset of contact, and terminated as the entire probe end area becomes in contact
with the fruit. Throughout the preparatory stage, the contact area is increasing
continuously, in a way similar to Hertz contact, in which the probe end is seen as
a ﬂat plate. Once full contact is achieved, the contact area almost remains
constant. As load increases in this stage, the stress concentrates at the outer
edge. If the cylindrical probe is rigid, the trend of stress distribution shifts from
Hertz distribution (elliptic concave down), to Boussinesq distribution of rigid
dies (concave up) as shown in Fig. 3.4. The inﬁnite stress at the outer edge
would be of destructive nature and should be eliminated. Introducing a rubber
tip at the end of the probe would not only eliminate this stress concentration, but
also distribute the stress over the entire contact area, resulting in quasi-uniform

stress distribution.

A thorough understanding of the contact situation would be achieved
when the components of stress and deformation due to the applied load at the
contact area can be recognized. Since most of the material behavior can be
approximated by linear functions at small deformations, the superposition
principle is applicable. For elastic materials, this technique can be used when the
components of displacement and stress produced by a concentrated force are

known, and then integrated over the entire loading area.

23

3.3.1 Concentrated Normal Force

The classical approach, which is based on the theory of potential,
developed by Boussinesq and Cerruti, enabled the ﬁnding of the stresses and
displacements due to load at the surface. Using that approach, Timoshenko and
Goodier (1951) introduced a stress function to deduce the components of stress
and displacements due to a concentrated force P acting on an axi-symmetric

elastic half—space (Fig. 3.3).

 

 

)r

 

 

Fig. 3.3 Concentrated force acting at the surface of a half-space
The problem is axi-symmetric, using cylindrical coordinates (r, 62 z), the
solution is independent of (9, and the 1,6; and m are zero, the remaining stress

components are:

 

 

0' P (1 2V 1 Z Z
a — —_ T — " T 3.9
2” r2 r \lr +2:2 (r2 +22)3'/2 ( )
3P 23 3P r2“2
0' = -—— , r = ——

Since at any point o;/r,.,. = z/r in the above equations, therefore, they

concluded that the horizontal component of the resultant stress at any point on

the surface of the sphere of diameter d is constant and equal to 3P/272d 2.

The components of displacement in the vertical and radial directions are:

= P (1+V)22 + 2(1-v2)
2 27d; (r2 + 22)” Vrz + z2 (3.10)

(l — 2V)(1 + V)P z _ 1 1 zr2

r 2715’ Vrz + 22 + 1" 2" (r2 + 22)3/2

 

 

 

 

3.3.2 General Axi-Symmetric Pressure Distribution

An axi-symmetn'cal pressure distribution applied by a probe over a circular
interface area with elastic half-space is to be analyzed in this section. The

pressure distribution takes the general form:
2 I?
r
p = Po[1 — 7) (3.11)

where P0 is the pressure at the center of the contact area, and the exponent n is
any real number. Fig. 3.4 shows pressure distributions for selected values of the

parameter n.

25

- - -1/2 Boussinesq
—0 (Uniform)

- +1/2 (Hertz)
—+1

 

 

 

 

 

 

0
-1 -0.5 0 0.5 1
rla

Fig. 3.4 General axi-symmetric pressure distribution

Three particular values of the parameter n are of classical importance and
will be discussed in detail. These are n=0, -1/2, and +1/2. For n=0 the pressure
distribution is uniform; at n= -I/2 the distribution corresponds to the case of
loading by absolutely rigid die which is known as Boussinesq problem. The
pressure distribution is elliptical when n=+1/2, which is associated with the

Hertz contact.

3.3.2.1 Uniform Pressure (n=0)
When a uniform load is applied over a circular area of radius a at the
apple surface, the displacements in the vertical and radial directions are found by

integrating equations 3.10 over the circle as shown in Fig. 3.5 (Johnson 1985).

26

o /n(r. 0)

“I

 

«'3

 

 

 

(b)

Fig. 3.5 Integration of the effect of pressure applied over a circular area
at point B(r, 0) located: (a) Inside the circle [r<a] (b) Outside
the circle [r>a]

The displacement in the vertical direction is:

'2a2(1—v2)P0

 

E(r/a) r<a

“2 :4 (3.12)
2 2
2a (jg—V )Por{E(a/r)—(l—a2/r2)K(a/r)} r>a

 

 

l

27

where E (m) is the complete elliptic integral of the second kind of modulus m,

and K (m) is the complete elliptic integral of the ﬁrst kind, deﬁned as:

Ir/2
E(m) = J‘(1 — m2 sin2 ¢)|/2d¢
(3.13)

0
7r/2
K(m) = [(1— m2 sin2 ¢)'”2d¢
0

The maximum vertical displacement occurs at the center [E (0)=/v’2], and
drops gradually with radial distance to a minimum value at the boundary edge
[E(I)=1]. Outside the contact area, it continues to drop asymptotically with
distance.

The radial displacement at the solid surface is:

—(1—2V)(1+V)P0r/2E rs a
u, = (3.14)
—(1—2V)(1+V)P0a2/2rE r> a

Since the total load is P= Ponaz, the radial displacement in Eq. 3.14 is
identical to that generated by an equivalent concentrated force applied at the
center (Eq. 3.10 for z=0). Using the superposition principle, Johnson (1985)

concluded that the radial displacement depends only on the total load, and is

independent of the nature of stress distribution as long as it is axi-symmetric.

28

As far as the components of stress are concerned, they can be found by
integrating Eq. 3.9 over the entire circle, the ﬁnal forms of stress components

along the Oz-axis (Timoshenko & Goodier, 1951) are:

oz=Po—l+ Z3 ,2}
(a2+zz)J

o = 0'9 =329—[— (1+2v)+

 

(3.15)
2(1 + v)z _ Z3

/2
\la2+z2 (a2+zz)3

 

Then by using the Mohr’s circle, the principal shearing stress at any point

along the z-axis occurs at 45 degrees to the z—axis, and its magnitude is 1/2|cr9—crz|

given by:

P0 1— 2v 2 i z (3.16)
2

 

 

 

2'1:

 

 

The maximum value of the principal shear stress is:

rm, 2 P°[1—2v +:—(1+v)\ﬁ(l+v):|

 

 

2 2

at z=a\/2(1+v)
7—2v

 

 

29

3.3.2.2 Uniform Normal Displacement (n=-1/2)
When an absolutely rigid, frictionless cylindrical probe is pressed against
an elastic half space, this case is known as the ﬂat die Boussinesq problem (Fig.
3.6). The vertical displacement uz is uniform inside the contact circle, and the

contact stress can be found by substituting n=-1/2 in Eq. 3.10.

 

P0
p: (3.17)
x/I—rZ/az

where a is the radius of the probe, and P0 is the stress at the center, which is

equal to half the average contact stress.

\\1\\\\‘1

All

 

 

 

 

 

 

Fig. 3.6 Rigid cylindrical die loaded against half-space
(Boussinesq problem)

The vertical displacement at the surface is constant within the contact

area. However, it decreases with distance from the origin outside, such that:

fn(1—v2)Poa/E rSa

u, =i 2 (3.18)
2-(1——-—v—)-Poa sin-1(a/r) r>a

 

L

30

Note that for a given value of Po, the deﬂection at the contact area

increases linearly with the probe radius (a). On the other hand, the normal stress

has theoretically an inﬁnite value at any point on the boundary (r=a), and drops

to zero outside, resulting in an inﬁnite stress gradient. If used for apple testing,

this probe would cause damage to apple tissue, therefore, hard probes should be

excluded.

3.3.2.3 Hertz Pressure (n=+1/2)

The case of n=1/2 corresponds to contact between two axi-symmetric

frictionless bodies, where the pressure distribution is elliptical as stated in Eq.

3.7 earlier as:

 

1v=1".\/1-r2/a2

The displacement and stress components in the vertical and radial

directions, again, can be obtained by integrating the load over the circular contact

area. The ﬁnal form of the vertical displacement at the surface (z=0) as stated by

 

 

 

Johnson (1985) is:
I—Evz 4}:(a2_r2) rSa
a
u, =< (3.19)
2
B {(2. _.2)..,.,(./.)..2(./.x,32.))
k E 2a

31

The radial displacement u, is given by:

 

 

' (1—2v)(1+v) a2P , , .2
— ° 1— I—r a rSa
3E r { ( / )3}
u, =< (3.20)
(1—2v)(1+v) a2}:
— r>a
( 3E r

 

The radial displacement outside the contact circle is related to the total force, in
this case P= 2P0/ta2/3. Thus u, is 2/3 that of the uniform pressure (P0).

The stress components at the surface (z=0) are:

l1—2v a2
2
o./P 3 r

 

{I—(I—r2/a2)w}—(I—r2/a2)/2r S a

 

. (1 — 2v )a" /3r2 r > a (321)

 

' __ 2
-1 321/3,{1..(1_.2/azy/2}-2.(1_.2/.2)Wrs.
09/13. :1 (3.22)

K—(1—2V)a‘7/3r2 r>a

 

At any point on the surface outside the contact area, the radial stress (6,)

and the circumferential stress (0'9) have the same magnitude. However, the
former is tensile and the later is compression. The maximum tensile stress of a

value 6mm = P0 (1-2 V)/3, occurs at r=a. This stress is the absolute maximum

32

tensile stress throughout the whole body, which may cause failure when the body
material is brittle.
Along the axis 02, the stress components oz, 09, and or are principal stresses,
thus the principal shear is I]: 1/2 loz-ogl, thus:
—1
O'Z/P0 = —(1 + zz/az)

1 (3. 23)
(rt/P0 = (re/Po = —(1 + v){1-(z/a)tan“(a/z)}+%(l+ zz/az)

 

Tr/Po = {l — (z/a)tan"(a/z)} — i- (1 + zz/az)l

The stress components at the solid surface and along the symmetrical axis
are illustrated for the case of uniform pressure and compared with Hertz pressure
distribution acting on a circular area of a half space elastic material with v=0.3.

The maximum shear stresses are:

(7141111503312) at z=0.64a (Uniform)
(7,)max=0.311% at z=0.57a (Hertz)

33

1.5-

 

 

 

 

 

 

02/?
00/?
$0
0.5 ~
0./p ‘. ‘, a
%m ‘*

Uniform pressure p

-no —qs o . —qs -no —L5

 

 

 

 

Fig. 3.7 Comparison of stress distributions at the surface and along the axis of
symmetry due to (left) uniform pressure and (right) Hertz pressure on
a circular area of radius a (Johnson 1985)

34

3.3.3 Normal Stress at Any Point
The formulas in the previous discussion are restricted to a point located
either on the surface of a solid or along the axis of symmetry (z-axis). The stress
at an interior point B(r, 2) throughout the solid can be treated similarly by
superimposing the solution due to the concentrated force over the entire circular

area shown in Fig. 3.5. The ﬁnal result for the normal stress is:

 

 

 

 

 

 

_3§770Ij(sff¢2:I’/Z 5 ds d¢ rSa ..
a,=< 3W“) p¢’s) (3.24)
L_;5[;!i(s2+zz)m s ds dd r>a
where
_ —r cos diJrzcos2¢+(a2—r2) rSa
512— r cos diJaZ—rzsinzd r>a

This reduces the problem to the solution of an integral equation involving
the contact circle generally it has no closed form solution and can be evaluated
by numerical integration. The same procedure could be used to formulate the

. . . . I
solution rnvolvrng any other stress component or drsplacement. 32*!

3.3.4 The Viscoelastic Contact
Viscoelastic materials exhibit time-dependent behavior in their stress-
strain relationships. At the instant of contact, viscoelastic material would

respond in a way similar to elastic material. However, the viscoelastic

35

characteristics, progressively lead to a gradual divergence from the elastic
classical contact due to viscous properties.

The compression of an intact fruit exhibits three consecutive and

indeﬁnite stages of deformation, namely, the elastic stage, the viscoelastic pre-
failure stage, and the viscoelastic post-failure stage (Peleg et al., 1976). In the
elastic stage no permanent physical changes take place and the deformation is
independent of the strain rate. Irreversible physical changes due to failure in the
microstructurc may occur as the deformation passes the bioyield point. This
produces a permanent deformation and triggers the enzymatic actions that induce
bruising.
The behavior in this stage is still viscoelastic, but it is considerably different
from that of the pre-failure stage. Consequently, different rheological models are
necessary to represent the same material in each stage. Hence, in this study we
are concerned with the attributes in the pre-failure stage prior to the bioyield.

Lee and Radok (1960) deduced the viscoelastic counterpart solution of
the Hertz contact problem between a rigid sphere and the viscoelastic half space
using the Maxwell model. The dimensionless pressure distribution is plotted
versus the dimensionless contact radius in Fig. 3.8. Initially, the pressure
distribution corresponds to the Hertz elastic solution. As time progresses, the
contact area grow and a gradual departure from Hertz distribution is observed.
The recently contacted area at the periphery of the circle continues to follow
Hertz solution, while at the central region; the stress relaxes such that the

pressure distribution is ﬂattened, eventually resulting in a dip.

36

 

 

 

 

l

-l.0 -0.5

 

Fig. 3.8 Variation of the pressure distribution against dimensionless
radius at particular times (Lee and Radok, 1960)

3.3.5 Onset of Bioyield

Yielding of a material is initiated at regions of high stress that become
high strain regions. Failure of brittle material occurs abruptly without
considerable distortion, while yielding of ductile materials begins by the
formation of a neck and signiﬁcant change in shape occurs at the yielding zone
before failure.

When brittle material fails in tension or compression, the maximum stress
criterion can be applied, this simply states that the material break down when a
principal stress component reaches the ultimate tensile strength of the material.
In the case of ductile materials the most satisfactory failure criteria are the von
Mises criterion and the Tresca yield criterion. To present these criteria a few

deﬁnitions should be understood.

37

The state of stress at any point can be split into a hydrostatic stress

component and a deviatoric stress component, such that:

e. a. 7.. are... I... a. 0;. 0 0
I... e. I... = r... cry-0;. r.» + 0 0;. 0 (3.25)
r... a. 0; a. 7.. 0-05. 0 0 0..

Where 0;,..=’/3(07 +0}+ 03) is the average of the principal stresses, which

represents the hydrostatic component of stress and only affects the size by
producing material dilatation, but does not affect the shape or produce material
distortion. On the other hand, the average of the deviatoric stresses is zero, thus,
it only affects the angle(s) between surfaces due to shear deformation and causes
material distortion.

The onset of yielding is independent of the orientation of the coordinate
system; thus it can be expressed in terms of the so-called invariants. The type
and orientation of the coordinate axis, as the name suggests, are functions of the
stress that do not affect the invariants. Krishnamachari (1993) deﬁned the ﬁrst,

second, and third invariants of stress in terms the principal stresses as:

J , = (II + 0'2 + 0'3
J.=0.G.+G.G.+G.G. (3.26)
J3 = 610'2(3I3
The von Mises criterion states that the onset of plasticity takes place when a

function of the deviatoric of the invariants f (J ’, J 3, J §)=0; the prime is referred

to the deviatoric stresses. Since J ’1 =0 and J 3 can be dropped off for material

38

that doesn’t exhibit strain-hardening or strain-softening (i.e. Bauschinger Effect),
the von Mises criterion simply states that the onset of plastic yielding is initiated

when the distortion strain energy exceeds a constant value:

I I I I I I I 2

J2 = (5,62 +0263 +636] 2 —K (3.27)
The value of K can be estimated from the uniaxial loading test such that
3K2=Oy2,thus:

2

(a. -0.)2 +(02 -a.)2 +(a. -0.) 2203 (3.28)

In two-dimensional problems (63:0), the von Mises criterion can be

represented, geometrically, by an ellipse whose axis is tilted 45 degrees from the

horizontal direction on the 0102 plane as indicated in Fig. 3.9.

When the point (0'1, 0'2) lies inside the ellipse, the material does not

yield. Yielding begins as the point passes the elliptic contour. Note that in the

shaded regions the material doesn’t yield based on von Mises criterion, even

though the principal stress is higher than the yield strength (Cy).

39

 

No Yield

 

 

 

Fig. 3.9 von Mises failure criterion in two-dimensional body

The Tresca yield criterion is based on considering the maximum shear
stress as the dominant factor for creating distortion instead of the maximum
shear strain energy, therefore yielding occurs whenever any of the shear

components exceed the yield strength:

Max {/01 — 02 A /02 —03l /03 -01 /)2 Jr (329)

3.4 Summary

The classical contact problems in the elastic domain provided an
understanding of the contact between the probe and apple. Hertz contact of
concaved bodies, and the Boussinesq contact with a rigid cylindrical plunger are
two extreme cases that could not be used in apple ﬁrmness estimation. Both of
them are characterized by non-uniform contact stress distributions that if applied
in apple ﬁrmness testing would cause excessive damage and the failure of the

fruit tissue would take place gradually. Thus, an ill-deﬁned bioyield point would

40

result that could not be measured. The variability of the contact area in Hertz
problem further complicates the objective of estimating the bioyield strength of
the fruit tissue. A probe that applies a uniform contact stress distribution with
constant contact area should be used. A uniform stress is necessary to inspire the
bioyield failure of the entire contact area simultaneously that produces a well-
deﬁned bioyield point, and can be measured easily and reliably.

For the contact of elastic material, the component of displacement in the
axial direction (indentation) is given by Eq. 3.12, and the components of contact
stress are given by Eqs 3.15 and 3.16. The contact stress distribution is expected
to decrease with time in a way similar to that shown in Fig. 3.8 due to the
relaxation behavior of the viscoelastic apple material. Finally, failure criteria
that might be able to explain apple tissue failure in the bioyield test were

considered.

41

Chapter4
Finite Element Simulation of the Contact Problem

A numerical solution of the probe contact with apple can be obtained
using the Finite Element Method (FEM). A close form analytical solution is
unattainable due to the complexities of apple geometry and viscoelastic behavior
of its material, which would be evaluated experimentally. The FE scheme would
be used to investigate the effect of several probe design parameters and fruit
parameters on the contact stress distribution. Accordingly, a number of probe
designs would be built and evaluated experimentally in the next chapter (Chapter
6) for nondestructive apple ﬁrmness evaluation.

At the bioyield point the deformation increases without an increase in the
applied load, computer simulation of the contact problem with apple is promising
in gaining a thorough understanding of the mechanism of bioyield phenomenon.
Sherif (1976) applied the ﬁnite element technique to investigate the stress
distribution in cylindrical samples of apples, peaches and potatoes. The material
was assumed homogenous, isotropic and elastic, the apple samples failed by the
maximum shear strength. Rumsey and Fridley (1977) used a two-dimensional,
viscoelastic FE computer program to analyze the internal stress distribution of
the contact-loading situation. De Baerdemaeker (1975) used the ﬁnite element
technique to solve the viscoelastic boundary value problem of contact with a
rigid ﬂat plate. Chowdhury (1995) studied stress distribution due to contact with

a sphere to explore bruise susceptibility of potatoes. Wu et al. (1994) developed

42

a three-dimensional ﬁnite element model to predict apple behavior between two
parallel plates.

An axisymmetric ﬁnite element model of apple—probe contact will be
used to investigate the effects of different parameters on the contact stress
distribution. Apple material is non-homogeneous and anisotropic. Sample’s
orientation and location in the fruit signiﬁcantly affect the mechanical properties
of apples (Abbott and Lu 1996). For simplicity, apple material is assumed to be
an isotropic viscoelastic material, while the rubber is assumed to be elastic
material in the moderately low range of stresses required for apple tissue

bioyielding.

4.1 The Concept of the Finite Element Method

The ﬁnite element method is a general technique for structural analysis; it
is based on the distinctive feature of dividing the complex geometrical domains
into a set of simple subdomains called ﬁnite elements. The procedure involved
in the ﬁnite element technique to analyze a typical problem are summarized by
Roddy (1993) in the following steps:

1. Discretization: the given problem domain is represented by a mesh

of simple ﬁnite elements interconnected at points called nodes.

2. Derivation of the elemental equations: the governing constitutive

equations are approximated in a variational form evaluated at

selective points in the element.

43

3. Assembly: the equations of the elements are assembled using the
continuity of the solution and the balance of the internal ﬂuxes, to
obtain the equations of the whole problem. The force-displacement

relation for a linear static problem takes the form:

Ku = f (4.1)

Where K is the system stiffness matrix, which is symmetric banded
matrix, u is the displacement vector of the nodes, and f is the force
vector.

4. The boundary conditions are imposed at selected nodes.

5. Solution of the assembled algebraic equations.

6. Postprocessing of the solution to present the results of concern in a

tabular or a graphical form.

A commercial ﬁnite element program called MARC was used to simulate
the apple-probe contact problem. The analysis of the apple contact behavior
requires the ability to model the contact phenomena by tracking the
displacements of the elements at the interface of the contacted bodies to avoid
penetration. The non—penetration constraint can be applied by several techniques
using the Lagrange multiplier, penalty functions, or solver constraint. The later

technique is used to analyze the contact problem (MARC, 2000).

4.2 Probe Design Considerations

Probe designs based on either Hertz theory or Boussinesq contact, which
use a spherical or a rigid cylindrical plunger, respectively, are inappropriate for
nondestructive bioyield point evaluation.

The classical Hertz contact is characterized by variable contact area and
the stress distribution is elliptic. Hence the bioyield of apple tissue originates at
the center of the contact area, and gradually, expands outward; a severe
penetration is produced, which degrades the fruit due to bruising. A spherical
probe causes the gradual failure of the ﬂesh over a period of time, which makes
it undesirable and inefﬁcient for the bioyield point measurement. Chowdhury
(1995) was not able to assess the yield point of potato tuber by compression with
a spherical indenter. However, the sudden drop of the load was observed when
excessive failure of the entire contact area occurred which was accompanied with
skin separation, while the onset of ﬂesh bioyielding has taken place at the
center of contact area and continued gradually in the linear range of force-
deforrnation curve but could not been detected.

On the other hand, the contact area with a rigid cylindrical die
“Boussinesq contact” is constant. But the stress concentration at the sharp edge
has excessive destructive effects. A uniform stress distribution induces
simultaneous bioyielding of the tissue (gross failure) beneath the contact area,
such that the bioyield failure stress is integrated into a measurable force

associated with a hook in the force-deformation curve.

45

Since rubber material exhibits a high degree of elastic deforrnability
under the action of comparatively small stresses, the use of rubber at the end of
the cylindrical steel probe (Fig. 4.1) will assist in the following improvements of
the contact situation:

1. The full contact with skin is achieved at lower load, after that the
contact area remains constant.

2. The stress concentration is eliminated, which enhances the
uniformity of the contact stress distribution.

3. Eliminate gradual failure that accompanies the variable contact
area.

4. Enhance bioyield point measurement through simultaneous
bioyielding of the entire ﬂesh tissue within the contact area.

5. Reduce tissue bruising.

6. Provide an average value of the bioyield stress.

 

 

I
(1 Steel
1
I
I I
t r Rubber
1 \ J 34

 

 

 

Fig. 4.1 Probe geometry

46

Comparison of the force-deformation curve of apple contact with
cylindrical probe indicates that the use of a rubber tip tends to produce a smooth
curve and the bioyield tissue failure is observed obviously at a single point.
While in the case of rigid steel probe a series of micro failures occur over a wide
range of deformation (Fig. 4.2). Note that the force value at the bioyield point

doesn’t change and the change in the slope is due to the elasticity of the rubber.

  
 

 

 

60 . . .
BIOYIeId Range
A40 ~
.2,
8 —with rubber
53 —without rubber
20 -
O I l r 1
0 4

2
Deformation (mm)

Fig. 4.2 Comparison of apple bioyield test by a cylindrical steel
probe with and without rubber tip

4.3 Objectives
The primary objective of the ﬁnite element simulation was to design a
probe that would produce the most uniform stress distribution over the entire
contact area. This probe was considered to be optimal in accomplishing
nondestructive or minimally destructive detection of the bioyield point. In

addition, the displacement of the contact area (indentation) would be evaluated

47

by the ﬁnite element method since it is associated with apple bruise
susceptibility.
The speciﬁc objectives were to:

1. Investigate the distributions of stresses and deformation in the vicinity of
the contact area.

2. Study the effects of probe parameters, such as the rubber modulus of
elasticity (ER), thickness (t), probe diameter (d), and ﬁllet radius (r) at the
outer edge of the rubber tip.

3. Study the effects of apple fruit parameters including fruit size (D), skin
modulus of elasticity (Es), and skin thickness (ts).

4. Study the effect of the contact friction between the fruit’s skin and the

probe.

4.4 The Finite Element Model

The basic ﬁnite element model is described in this section. Investigation
of the effect of a parameter was carried out by altering that parameter, while the
rest of the parameters were held constant. The ﬁndings were considered in the
construction of a few of probes that would be evaluated experimentally in
Chapter 5.

The apple-probe contact problem was assumed to be axisymmetric in the
neighborhood of the contact point where the variation with the transverse angular
coordinate about the probe axis was neglected. Therefore, the contact problem

was reduced to a two-dimensional problem, resulting in a signiﬁcant saving in

48

the required computational memory. This saving is primarily due to two factors:
1) the ﬁnite elements of revolution are simple and require a lesser number of
nodes per element; and 2) the total number of the elements which constitute the
axisymmetric mesh is much less than that used to construct the complex three-
dimensional mesh. Furthermore, since the other half of the fruit on the opposite
side of the contacted region doesn’t contribute signiﬁcantly to the contact
solution, only one quarter of the fruit cross-section needs to be considered (De
Baerdemaeker 1975, Rumsey and Fridley, 1977, and Chowdhury 1995). A zero
displacement boundary condition was imposed at the nodes of symmetry (see
Fig. 4.3).

The proﬁle of the longitudinal cross-section of an average “Beauty
Rome” apple sample was traced and used as the basis of the model. The apple
sample was 92 mm in diameter and 73 mm in height. The fruit ﬂesh is divided
into 793 triangular elements, taking into consideration that the mesh is reﬁned in
the locality of the contact region. The Poisson’s ratio was taken as 0.3
(Clevenger and Humann, 1968). The material is isotropic and viscoelastic. The
material properties of the ﬂesh were obtained as the average of 15 cylindrical
samples of three apple varieties tested experimentally. The ﬂesh modulus of
elasticity was about 5.0 MPa, and the relaxation function, corresponding to a

two-element generalized Maxwell model, is given by:

e(t)=eo(r=.,e“/Tl +1326“2 +15) (4.2)

49

where

0: Compression stress.

eo= 0.1 2 initial strain.

t = time (second).

E1 = 0.488, E2 = 0.590, and E3 = 1.13 MPa 5 stiffness of the springs.
1:1: 2.27sec, t2 =45.6 sec 2 the ﬁrst and the second time constants.

The material properties of the core carpel are different from the apple
ﬂesh, but it is located far away from the contact region and their effect can be
neglected.

A thin layer enclosing the apple ﬂesh was used to model apple skin. Skin
thickness of 0.5 mm and a modulus of elasticity of 10 MPa were used in the
model (Clevenger and Humann, 1968). The layer is divided into 46 quadratic
elements.

A rigid ﬂat plate models the steel end of the probe, and the diameter of
the probe was d=7/l6 inch, similar to the Magness—Taylor pressure tester. The
tip was divided into 284 triangular elements. The rubber modulus of elasticity
(ER=3.27 MPa) was taken from the stress-strain relationship of rubber samples
(Fig. 4.4). The linear relationship in the range of compression stress, which is
below the bioyield strength of apple fruit, suggested that an elastic model of
rubber would be satisfactory. A Poisson’s ratio of 0.48 of nearly incompressible
material was used for rubber.

The contact process originated when the ﬂat plate was moved against the

rubber part at a constant speed (i.e. constant strain rate) of 0.5 mm/sec (1.18

50

inch/min) downward in the negative x-direction. The apple and the rubber tip are
deformable bodies that respond to the applied load and the nodes at the axis of
symmetry were not allowed to separate. The skin was assumed to be glued to the
apple ﬂesh and the plate glued to the upper surface of the rubber tip. The glue
option implied that there was no relative tangential motion. The plate moved a
total of 4 mm displacement. This displacement was divided into 100 equal steps.
At each step the distances between each node and the surfaces of other bodies
were checked and compared with a preset small contact tolerance. If the distance
was below the tolerance, the no-penetration constraint was applied; an iterative
procedure was continued until both the equilibrium of the element was achieved,
such that the node was held in contact with the surface.

The degree of uniformity of the contact stress distribution was
considered the measure of the suitability of the probe design for bioyield point
detection. The uniformity was estimated by computing the standard deviation of
the normal stress at the nodes located within the contact area; the lower the

standard deviation the more uniform the stress.

51

 

 

 

 

 

zero displ. BC.

Fig. 4.3 The ﬁnite element model showing the model components, the boundary
condition, and the path AB in the zoomed view of the contact area

52

4.5 Results and Discussion

4.5.1 Validation of the Finite Element Solution

The validity of the ﬁnite element solution was established in comparison
with experimental data. The measured force—deformation relationship of the
bioyield point evaluation test of a particular apple was used for this purpose.
The ﬁnite element model represents only the upper half of the apple, as shown in
Fig. 4.3. Although the compression strain was small away from the contact
point, strain at the plastic seat was expected to be signiﬁcant, and deformation of
the lower half of the apple should be considered.

A Fuji apple, 81 mm in equatorial diameter, and 70 mm in height, with a
231 gram mass, and Magness-Taylor ﬁrmness measured to be 49.4 N was tested
with the small-thick probe (1/4 inch in diameter with 1/8 inch rubber thickness).
This probe was found to be the most suitable for ﬁrmness assessment.

The whole apple was compressed by the probe and the force-deformation
(F w-Dw) curve was obtained experimentally, where the subscript W stands for
“Whole apple”. The bioyield point occurred at 27.2 N load, which
corresponded, to a total deformation of 2.02 mm (Fig. 4.5).

The material properties of the same apple were obtained by testing two
cylindrical samples (20 mm in diameter and 12.4 mm height). The samples are
taken from the locality of the tested point. One sample is tested in compression.
The average slope of the stress-strain diagram in the linear range between 0.037
and 0.27 MPa stress (Fig. 4.4) was used to determine the modulus of elasticity

(EA=4.01 MPa). The other sample was tested in relaxation from the initial

53

compression strain of 80:01: the stress-time relationship was ﬁtted to the two-
element generalized Maxwell model given in Eq. 4.2. The constants are: E;
=l.51 MPa, E3 = 0.50 MPa, E3 = 0.53 MPa, 1') = 1.14sec, and T2 =13.87 sec. The

above tests of the whole apple, including the MT firmness test, were all
conducted on the upper half of the apple. After testing the whole apple, the
upper half was cut and removed, and the lower half was compressed with a rigid
ﬂat plate against the seat. The force-deformation curve (FL-D1,) of the lower half

apple was obtained, where L stands for “Lower half".

0.8 " p
Linear ranges ’3’
O’_Apple=4.01€-0.05 ' ’ a '

O' Rubber=3.278-0.16 a'

0.6 "' _ ’v

Stress (MPa)
:3
h

 

—Apple
- - - Rubber
X Bioyield Point

.°
N
a

 

 

 

 

0.0 -
0.0

 

0.2 0.3

Strain

Fig. 4.4 Uniaxial compression of cylindrical samples of apple and rubber,
the horizontal and vertical lines identify the linear ranges

54

The superposition principle was applied to compute the force
deformation curve of the upper half of the apple that was used in the FE mode].
The net deformation of the modeled half is the difference between the
deformation of the whole apple and the deformation of the lower half of the
apple DN=Dw-DL, where the deformations were evaluated at common force
measurements, such that F w=FL= F N.

The simulated force and deformation of the probe from the FE model
correspond to the Force and Position of the plate, where the rigid plate resembled
the steel part of the probe. The time variations of any variable can be tracked
using the history option in MARC and the data was collected at a speciﬁed
increment.

A comparison of the force-deformation curve from the FE model using
the elastic modulus for the same apple that computed from Fig. 4.4 with that of
the net curve FN-DN computed from the experiments is shown in Fig. 4.5. The
curves are in good agreement; the high correlation between the measured and
simulated force (r =0.99) indicates that the ﬁnite element model is adequate in
simulating the actual apple-probe interaction. The deviation beyond 0.8-mm
deformation might be explained by the strain hardening (slope increase at higher
strains) of the rubber material and the nonlinear behavior of apple tissue at larger
deformations (Fig. 4.4).

The ﬁnite element model computed that, at the bioyield point, the
average rubber deformation was 0.6 mm, whereas the apple deformation was 0.8

mm. This deformation can be divided into elastic deformation, and a permanent

55

plastic deformation in the form of a bruise. However, the bruise volume was too

small to be observed.

B.Y Point

30 - (1.25, 27.2)
Bioyield Experiment

 

  
   

—-I—Finite Element
20 -

Force (N)

10~

 

   

 

U I

0.0 0.5 1.0 1.5
Net defamation of the upper half of the apple, 0,. (mm)

Fig. 4.5 Comparison of the FD-curve of experimental and FE
simulation results of a particular apple

4.5.2 Development of Bioyield Failure Criterion
It is conventionally believed that either shear or normal stress causes the
fruit tissue failure, depending on the loading condition. Segerlind and Fabbro
(1978) proposed the normal strain as a criterion for apple failure, such that apple
ﬂesh fails when the strain exceeds a critical value. Because of discrepancies in
the data, which were attributed to the effect of loading rate, the strain failure

criterion was questioned by Chen and Sun (1984).

56

Several failure criteria were examined to recognize which one could
accurately explain the failure of tissue at the bioyield point. It was done by
comparing the value of the proposed criterion for the uniaxial loading with that
of the tri-axial loading condition. The former was obtained from the
compression of a cylindrical sample between parallel plates, while the later were
estimated by the ﬁnite element model for the probe-apple contact at the bioyield
point.

The bioyield of the whole apple occurred at a force of 27.2 N,
corresponding to 1.25-mm net displacement. The bioyield force rather than
displacement was used as the basis of comparison between the model and the
experiment. This was due to two reasons: 1) The stress was thought to be more
important than strain in causing the bioyield failure. 2) The inaccuracy involved
in estimating the net displacement at the bioyield point. The plus sign in Fig. 4.5
indicates the point at which the apple material bioyielded. This point was
associated with the increment number 35 of the FE model, where the probe

displacement was 1.4 mm.

The images of the FE solution in this chapter were presented in colors,
each color corresponds to a range of results as indicated in the associated scale
bar (F ig.s 4.6—4.11). Examination of Fig. 4.6 indicated that the gradient of the
axial displacement was greatest near the contact area. Only about 10% of the
probe displacement (0.14mm) was recorded at about 2 cm away from the contact
area. Most of the effects due to contact with the probe were mainly conﬁned to a

small region in the neighborhood of the contact area as shown in Figs. 4.7-11.

57

Therefore, the contact with probe is expected to be insensitive to the variation of
apples geometry of different apple varieties. In this study, the actual surface of a
particular apple proﬁle was used in the FE model, the model was assumed to be
axisymmetric about the stem—calyx axis. A sphere was used to model the apple
and potato geometry by some researchers (Rumsey and Fridley, 1977, De

Baerdemaeker 1975, and Chowdhury, 1995).
The component of compression stress in the x-direction (O'x: component

11 of stress) is shown in Fig. 4.7 at the bioyield load, which occurs at increment
35. The maximum compression stress of about 0.51 MPa took place directly
under the contacted skin; the stress was uniformly distributed at the skin in
accordance with our goal. The value of compression stress at failure in tri-axial

FE model was signiﬁcantly higher than that measured in the uni-axial loading
condition (O’By=0.36 MPa, Fig. 4.4). Therefore, the maximum stress failure

criterion was unable to predict the onset of tissue failure in the bioyield test.
This might be explained by the inﬂuence of the hydrostatic pressure inside the
apple fruit as compressed by the probe on the maximum axial stress that apple
material could withstand without failure. Such that the compressive and the total
axial stresses were excluded as parameters that predict tissue failure (Miles and
Rehkugler, 1973)

The shear stress (component 12 of stress) was concentrated under the
outer edge of the probe (Fig. 4.8). The maximum value of shear was about 0.15
MPa, which was very small compared with the compression stress. The failure

surface was observed to be, approximately, of a paraboloid shape pointing

58

downward with a circular base at the contact area, while the shear stress was
maximum along a circular ring located directly under the probe sharp edge.
Thus the maximum shear failure criterion was not a suitable criterion to explain
the bioyield failure. This appears to be out of perspective of Fridley et al.,
(1968), that tissue failure under a rigid ﬂat plate was due to the maximum shear
stress.

The strain failure criterion states that apple tissue fails when the normal
strain exceeds a critical value. For the uniaxial loading of the cylindrical sample,
the bioyield point occurred at about 11.9% normal strain, whereas in the tri-axial
loading of a whole apple, the maximum compression strain at failure was
predicted by the FE model to be 10% strain. Both the experimental and the FE
prediction of the critical strain were within the range of 0.10—0.15 that was
speciﬁed by Segerlind and Fabbro (1978). The locus of the nodes of maximum
strain was also very close to the actual failure location. Therefore, the critical
strain failure is a possible criterion for the bioyield failure prediction.

The strain energy density of the uniaxially compressed cylindrical sample
can be obtained by integrating the shaded area under the stress-strain curve of
Fig. 4.4 and divide it by the sample volume. It was estimated as 0.0224 MJ/m3
[J/cm3], in comparison with the maximum value of the strain energy density that
was predicted by the FE solution (Fig. 4.10). The maximum energy density
occurred at a circular disc adjacent to the internal skin surface of 0.0255 MJ/m3
value, with 0.00159 J/cm3 standard deviation, which was slightly greater than

that of a uniaxial sample. The location of the actual failure was far away from

59

the zone of maximum strain energy density. Therefore, the strain energy density
was not able to predict the failure of apple tissue when tested by the probe.

The von Mises stress is the distortion component of strain energy, which
is function of the three components of principal stress. The von Mises failure
expects tissue failure to occur wherever Eq. 3.28 is satisﬁed. A numerical output
(not shown) indicated that the locus of the nodes of local maximum von Mises
stress was along the green line indicated in Fig. 4.11. The value of the von
Mises stress directly under the probe edge (at the arc beginning) was 0.41 MPa,
and at 1.3 mm below the center of contact (at the arc end), it was 0.36 MPa in
comparison with the bioyield stress for the uniaxially loaded cylindrical sample,
which was taken from the same apple of 0.357 MPa (Fig. 4.4). The high value of
the von Mises stress under the probe edge was due to the high shear stress
concentration, which is a major parameter of distortion effect. Therefore, the
onset of tissue fracture is believed to originate at the point below the probe edge
and propagates along the locus of maximum Von Mises stress towards the
central end of the locus. The actual failure surface in three dimensions was
observed as a circular paraboloid. The failure of cylindrical samples took place
along a conical surface (Miles and Rehkugler 1973). The locus of maximum
von Mises stress as obtained by the ﬁnite element model was approximately
coincident with the cross section of the actual failure zone, and the numerical
values were comparable with the bioyield strength. Therefore, the von Mises
stress was a possible failure criterion that enabled to predict apple tissue failure.

The von Mises stress was also considered satisfactory criterion to explain tissue

60

failure of potato tuber as contacted with a spherical probe (Chowdhury, 1995),
its value was exceeded the bioyield strength in the actual failure zone below the
surface of contact.

In summary, the FE model of apple-probe contact at the onset of
bioyielding was compared with the uniaxial compression of cylindrical sample
taken from the same apple. The critical normal strain and the von Mises
equivalent stress were able to predict the failure of apple tissue whereas the
normal stress, shear stress and the strain energy density were not able to predict
the failure of apple tissue. They were rejected as possible failure criteria because
either their values were different from the corresponding uniaxial compression,
and/or the loci of their maximum values were located far away from the actual

failure zone.

61

Inc: 35
Time: 2.800e+OO

1.177e-13

-1.4008-01

2.8009-01

A

.2009—01

 

U'I

.6009-01

\1

.0009-01

0)

.4009—01

{D

.8009-01

p

.1209+00

p

.2609+00

p

.4009+00

 

Fig. 4.6 Displacement in the axial direction (mm)

62

Inc:

Time:

N

p

.6999-01

.2269-01

.467e—02

.7209—01

.1929-01

.6659-01

.1382-01

.611e—01

.084e—01

.056e+00

.203e+00

35
2.8009+00

 

 

Fig. 4.7 Component of stress in the axial direction, ox (MPa)

63

Inc: 35
Time: 2.800

7

a 2.1089-01
A 1.5499—01
9.8899—02
4.291e—02
—1.307e-O2
—6.904e-02

-1.2509-Ol

 

-1.810€-Ol

-2.370e—01

—2.9309-01

-3.4899—01

e+00

 

Fig. 4.8 Shear stress concentration under the outer edge (MPa)

64

Inc: 35
Time: 2.800e+00

3.4929-02

1.044e-03

-3.283e—02

-6.671e-02

-1.006e-01

-1.345e—01

-1.6839-01

-2.022e-01

-2.361e-01

2.7009-01

—3.039e-01

 

Fig. 4.9 Axial component of total strain (6”)

65

 

Inc: 35
Time: 2.8009+00

1.6212-01

1.442e-01

1.263e-01

1.083e-01

9.043e-02

7.2529-02

5.4619-02

3.6709-02

1.879e—02

8.764e-04

—1.703e-02

 

 

Fig. 4.10 Total strain energy density (J/cm3)

66

II : 5h
Tt'a: 2.3631100

 

1.03ce-30

ID
M
w
£-
III
I
1.:
p

?.P3ﬂ‘-J1

b.ZUJ--)1

’.Ihﬁ -Jt

2.097: 31

 

1.0765-31

s.30L:-33

 

Fig. 4.11 Equivalent von Mises Stress, the green line indicates the
locus of local maximum stress

67

4.5.3 Effects of Probe and Fruit Parameters

The objective of this study was to develop a mechanical probe that would
apply a quasi-uniform stress over the contact area. The uniform compression
stress distribution over the contact area would enable accurate estimation of the
bioyield point. In order to achieve this objective, it is crucial to examine
different probe design parameters and fruit parameters that might alter the
uniformity of the contact stress distribution.

The displacement and the normal stress values at the nodes along the path
AB (Fig. 4.3) were estimated as the stress approaches a threshold value of
bioyield strength. Note that the path AB is located at the apple ﬂesh-skin
interface right underneath the contact area. A threshold value of 0.64 MPa was
assigned to the bioyield point strength, which corresponds to an average apple
with Magness-Taylor ﬁrmness of 14 lb. (Ababneh et al., 2000). When a stress
concentration occurred at the probe outer edge, the threshold value was only
applied to a few central nodes for comparison purposes. However, stress
concentration is a serious problem, which tends to occur at the outer edge of the

contact area that causes apple bruise; hence it should be eliminated.

4.5.3.1 Rubber Elastic Modulus
The solution of the contact problem is compared for different values of
rubber elastic modulus (ER); a low value corresponds to soﬁ rubber, while a large

value to rigid rubber. The normal stress distribution is shown in Fig. 4.12, for

ER= 2.5, 4, 5, 7.5, 10,15, 25, 100, and 1000 MPa. A rubber with elastic modulus

68

of less than 10MPa or two times that of the apple (ER<2EA), generated a
satisfactory degree of uniformity, such that the standard deviation was less than
12% of the bioyield strength. A very soft rubber was not practical because it
bulges at a pressure corresponding to the bioyield strength of apple.

The stress concentration factor at the outer edge was 1.14 for ER: EA=5
MPa, and increases to 1.28 for ER= 2EA=10 MPa. As the rubber modulus
increases ﬁirther, the stress converges to the Boussinesq solution of the rigid
cylindrical die in contact with a semi-inﬁnite elastic body as given by equation
3.17 as shown in Fig. 4.12. However, due to the apple curvature, a slight
deviation was discerned as the radial distance was increased. The stress
concentration at the outer edge increased the applied load required to reach the
bioyield strength, enhanced skin deformation and consequently would produce

larger bruise volume.

  
 
 
 
     
 
 
 
 

2.0 -
+ E=2.5 MPa + 4

1.6 ' + 5 + 7.5
—)I(— 10 —e— 15
—e— 25 —a— 100

1'2 ' -B— 1000 — Boussinesq

.°
O
a

.....
/. .——— .d- 7.:— ..—" _‘.

_—--.——H

.°
‘1
a

 

Normal contact stress (MPa)

 

P
O
.1
q

1 2 3 4 5 6 7
Radial distance from the first contact point (mm)

C

Fig. 4.12 Effect of rubber modulus of elasticity on the normal stress distribution

69

4.5.3.2 Probe Diameter

The diameter of the probe ((1) is a crucial factor in bruise volume
consideration. The ﬁnite element solution indicated that the maximum
deformation at the center or the bruise depth has a linear relationship with the
diameter of the probe. The volume of the bruise would be proportional to the
cubic power of the diameter (d3). The uniformity of the stress distribution, on
the other hand, was not inﬂuenced by probe diameter for ds 7/16 inch (Fig.
4.13). Hence, a small probe diameter is recommended for a nondestructive

measurement of apple ﬁrmness.

 

 

 

’ccT +d=3/16" —a—1/ "
C1. 1.2 -
g +5/16" +3/8"
g +7/16" —e—1/2"
o
t: +9/16"
(I)
.5 0.84
.9
C hr " "t: T. ‘
o
o
E
E 0.4 -
o
2

0.0 v .

0 1 2 3 4 5 6 7

Radial distance from the first contact point (mm)

Fig. 4.13 Effect of probe diameter on the normal contact stress distribution

70

4.5.3.3 Rubber Tip Thickness

The use of a rubber piece at the end of the steel tends to lower the
effective stiffness of the probe, the effect of increasing the tip thickness (t) would
be equivalent to that of using softer rubber material. Fig. 4.14 indicates the
normal contact stress distribution for t=0,1,2 ...5 mm. A thickness of 2 mm or
greater should be used to produce a quasi-uniform contact stress. For t=2 mm,
the maximum deformation was less than 1.25 mm, and the standard deviation
was below 4.2% of the normal stress. The standard deviation was a decaying
function of the thickness (t), such that the uniformity of stress distribution was
increased for increasing thickness. However, when large thickness was used in a
preliminary study, which was equal to the probe diameter or greater, testing
instability was observed in the laboratory. A thin rubber produces stress
concentration and would prevent the simultaneous failure of the tissue under the
contact so as to detect the bioyield point. Again, the state of t=0 approaches the
Boussinesq rigid die stress distribution, but the apple curvature would mitigate

the stress concentration.

4.5.3.4 Probe Edge Fillet Radius
Stress concentration occurs at sharp corners. In this study, for a rigid
probe with sharp edge, stress concentration was a serious problem in as
discussed earlier in Section 3.3.2.2. A gradual variation of the cross section, by

introducing a round ﬁllet at the sharp edges, is a common practice to alleviate the

71

Normal contact stress (MPa)

Normal contact stress (MPa)

 
 
 
 
 
 
 

-l
0|
0

i
O
1

.°
01
l

 

P
O
.1

 

O

1 2 3 4 5 6 7
Radial distance from the first contact point (mm)

Fig. 4.14 Effect of rubber tip thickness on the normal contact stress
distribution

1.5-
+r=0mm -I- 1
+ 2 —e— 3
+ 4 -)l(-Sphere

A
O
r

 
  

.°
0|
1

 

 

0.0 u
0 1 2 3 4 5 6 7

Radial distance from the ﬁrst contact point (mm)

Fig. 4.15 Effect of ﬁllet radius on the normal contact stress distribution

72

stress concentration. In the ﬁnite element model, values of radius of the ﬁllet of
r=0,1...4 and 5.6 mm (Fig. 4.1) were examined. The last value represents a
hemispherical tip. The normal stress distribution for these values is plotted in
Fig. 4.15. The ﬁllet has altered the contact stress distribution when the contact
area changed with load, the stress distribution got a sort of Hertz proﬁle, and a
peak stress outgrew in the outer part of the contact area. The outgrowth of the
stress distribution can be explained as increased load that should be supported by
the outer portion of the contact area after the contact with the ﬂat portion is
established. On the other hand, the newly contacted part at the outmost of the
contact area would provide lower support.

The probe with the sharp edge (r=0) had the most uniform normal contact stress;
the ﬂexibility of rubber eliminates the stress concentration associated with a rigid
probe. Therefore, the ﬁllet technique was not recommended, and sharp edge

probes were used in the experimental study of the bioyield point determination.

4.5.3.5 Apple Size
A suitable design of the ﬁrmness sensor that would be practical for
online apple sorting should be independent of fruit size. The proposed bioyield
test is based on contacting a small area of the fruit by the probe. Although apple
size is related to the magnitude of the radius of curvature at the contacted region,
the geometric irregularity of the real fruit may offset the effect of fruit size. The
ﬂexibility of the rubber would make up for slight variation of the radius of

curvature and take care of the small clearance that exists between the probe end

73

and fruit skin at zero load. Small apple size affects only in delaying the
achievement of full contact with the probe.

The use of a small probe compared with the apple diameter, would
ensure a quick developing of full contact with the apple at a relatively low
normal stress. After full contact, the primary duty of compression is carried out;
the effect of stress distribution required for full contact is comparatively
insigniﬁcant on the stress distribution at the onset of tissue bioyield.

The effect of fruit size was investigated by the FE method through three
apple sizes; small, medium and large. The size of the original model was
considered as the medium one with an equatorial diameter DM=3 11/16 inch
(93.7 mm). The small size was obtained by sealing down the original apple by a
factor of 20%, the small diameter was Ds=2 15/ 16 inch (74.9 mm), whereas the
large size by scaling up by a factor of 20%, the large diameter was DL=4 7/ 16
inch (112.4 mm).

Even for the largest probe that was used (d=7/l6 inch) the normal stress
distribution was not affected signiﬁcantly by apple size (Fig. 4.16). Note the
small range of probe to apple diameter ratio, which was between 0.10 and 0.15
for large sized and small sized apples respectively.

The delayed contact of the outer edge of the probe with the small apple
reduced the stress at that area and increased the stress at an intermediate area
(about 4 mm from the contact center). Therefore the total load was not affected
and the measured bioyield strength would be independent of apple size,

especially when a smaller probe is used.

74

1.6 -

-A-Sma|l
1'2 ' -e-Medium
-8- Large

 

Normal contact stress (MPa)

 

 

0 1 2 3 4 5 6 7
Radial distance from the first contact point (mm)

Fig. 4.16 Effect of fruit size on the normal contact stress distribution

1.6 -
—A— E_skin = 5MPa
1.2 ‘ —e— 10MPa
—E+— 20MPa
0.8 -

 
 
 

Normal contact stress (MPa)
.°
.5

 

P
c

 

I U I I l I I

1 2 3 4 5 6 7
Radial distance from the ﬁrst contact point (mm)

0

Fig. 4.17 Effect of skin modulus of elasticity on the normal contact stress
distribution

75

5.3.6 Apple Skin

Skin thickness and modulus of elasticity varies with and within apple
variety. The possible effects of their variations were investigated in this section.
Apple skin does not only protect the fruit from environmental conditions, but
also protects from mechanical damage. A stiffer, thicker skin layer would
withstand mechanical load and reduce the fruit susceptibility to injury.
However, apple skin is comparatively thin and ﬂexible, which is expected to
provide an extremely low bending resistance; therefore, ﬂesh integrity or
ﬁrmness would be the dominant factor, which speciﬁes the bioyield point
measurement. Yet, skin can withstand shear and tensile loading so it can resist
cut and injury.

The tensile secant modulus of elasticity for Golden and Red Delicious
apple skins ranged from 1450 psi to 1930 psi (IO-13.3 MPa) and thickness
ranged from 0015-0022 inch (0.38-0.56 m) (Clevenger et al., 1968). Note
that the measurement of the compression modulus of elasticity of the skin is not
feasible.

Values of skin modulus E3 = 5, 10 and 20 MPa that cover an extended
range were used in the FE model, but no signiﬁcant effect on the stress
distribution was indicated (Fig. 4.17). Skin thickness of ts = 0.3, 0.5 and 0.8 mm
was considered in the ﬁnite element model; again the effect on stress distribution
was negligibly small (Fig. 4.18). Hence the skin modulus of elasticity is an

unimportant factor in bioyield point measurement.

76

A stiffer skin (high elastic modulus and/or large thickness retards the
response of the internal ﬂesh in the same way that the small radius of curvature

of small apple reduced the stress at the outer edge.

 

 

1.6 -
A +t_s=0.3 mm
I!
E 1.2 - —e- 0.5 mm
§ -e— 0.8 mm
3 0.8 -
0
8
5
3 0.4 -
N
E
O
z 0.0 . . . . . . .
0 1 2 3 5 6 7

Radial distance from the first contact point (mm)

Fig. 4.18 Effect of skin thickness on the normal contact stress distribution

4.5.3.7 Friction

The effect of friction between the probe and the fruit skin was
investigated using the FE model. Two limiting cases were considered: the case
of no friction and the case of maximum friction in which the apple skin was
glued to the probe, such that there was no relative tangential motion. Friction
increased the shearing stress signiﬁcantly (Fig. 4.19), especially at the outer zone
of the contact area, whereas, the friction effect on the contact stress was
insigniﬁcant. Thus, friction would be ignored in analyzing failure at the bioyield

point.

77

1.6-

-9- Compression-No Friction
1,2 . +Compression- With Friction
+Shear -No Friction

-I— Shear-Wlth Friction

Normal contact stress (MPa)

 

 

 

0 1 2 3 4 5 6

Radial distance from the first contact point (mm)

Fig.4.19 Effect of friction on the compression and shear stress distributions

4.6 Summary and Conclusions

The ﬁnite element model has described the quasi-static compression of
the viscoelastic apple fruit effectively. The prediction of the FE model for the
force-deformation curve of testing a particular apple for bioyield point was in
good agreement with the experimental curve. The numerical results of the FE
model indicated that the critical strain and the von Mises stress were two
possible failure criteria for predicting the onset of tissue bioyielding. This was
in part due to the magnitudes of their maximum values that were approximately
matching those found experimentally from the compression of the cylindrical
sample taken from the same apple. Also, the locations of these maximum values
were approximately coincident with the actual failure location. The shape of the

tissue failure could be approximated by a three-dimensional circular paraboloid

78

pointing downward with a height of 1.3 mm, and a base coinciding at the contact
area.

The application of a quasi-uniform contact stress to detect the bioyield
point could be facilitated by using a mechanical probe with the following
features:

1. The rubber modulus of elasticity should be less than two times that
of apple ﬂesh.

2. A smaller size should be used to reduce the bruise volume and
eliminate the curvature effect.

3. The rubber thickness should be at least 2 mm, but not greater than,
roughly, the probe diameter, because it would cause test instability.

4. Sharp rubber edge (r = 0) should be used to maintain a constant
contact area and a quasi-uniform stress distribution.

Apple size, skin elasticity, skin thickness and friction have negligible

effects on the normal contact stress distribution.

79

Chapter 5

Experimental Evaluation

5.1 Introduction

This chapter is primarily devoted to the experimental evaluation of a few
mechanical probes. The force, deformation at bioyield point, slope of the force-
deformation curve and the energy of compression will be investigated for each
probe to determine the most appropriate measurement parameters that are related
to the ﬁrmness of the fruit. An optimal probe would be selected based on the
ability to predict the MT ﬁrmness while causing minimal damage.

Apple material properties were measured and used for the FE study in the
previous chapter. The properties included the modulus of elasticity and the
relaxation parameters. The FE study has provided general guidelines for probe
design that would be able to measure the bioyield point with minimal damage.
The performance of six probes (3 diameters x 2 thickness to diameter ratios) will
be investigated experimentally. Five of six probes were designed according to
the FE guidelines, whereas the other design differed with the guidelines, in that
its rubber thickness was below 2 mm in order to examine the validity of the FE

ﬁndings.

5.2 Objectives

The primary objective of the experimental study was to estimate the

material properties of the average apple and evaluate the performance of a few

80

probe designs in apple ﬁrmness prediction based on the assessment of bioyield

point detection.

The speciﬁc objectives were to:

l.

2.

Estimate the average modulus of elasticity of apple ﬂesh.

Determine the viscoelastic characteristics of apples and develop a
suitable rheologic model to describe the relaxation behavior of apple
ﬂesh.

Explore the relationships of the measured bioyield deformation, force,
slope of the F-D curve, and the compression energy required to
achieve the bioyield point with the standard Magness-Taylor
ﬁrmness.

Investigate the performance of the probes to assess their suitability as
nondestructive ﬁrmness sensors.

Compare the bioyield point measurement with the standard MT

ﬁrmness measurement.

5.3 Materials and Methodology

The Universal Testing Machine, model 4202 (Instron Corporation,

Canton, MA.) was used throughout the entire experimental study. The probe

was attached to the load cell, which was mounted to the crosshead of the Instron

machine (Fig. 5.1). The loading rate is “apparently a less important factor than

might be supposed” Magness and Taylor (1925). A large increase in the loading

81

rate would cause a small increase in the MT ﬁrmness and the yield point.

(Boume, 1965).

 

Fig. 5.1 The bioyield point test setup using the Instron Universal
Testing Machine.

The force measurement of the load cell and the extension (deﬂection) of
the crosshead assembly, can be sampled at any desired rate. The software series
XII was used to control the Instron machine, record the data and perform

preliminary analysis, subsequent analyses were performed using MS Excel.

82

5.3.1 Measuring Apple Material Properties

Compression and relaxation tests were conducted to measure the
modulus of elasticity and the relaxation behavior of apple material for use in the
FE simulation. Typical values reported in the literature were used for the
Poisson’s ratio, and apple skin properties.

Apple cylindrical specimens of 20 mm (25/32-inch) in diameter were
taken from the equatorial zone by driving a sample borer radially into the apple.
Then each specimen was cut to 12.4-mm (1/2 inch) thickness with a parallel
blade tool Fig. 5.2. The sample was tested using two parallel ﬂat plates F ig.5.3.

Four apple varieties were used in the experiment: Golden Delicious, Red
Delicious, Fuji and Gala. A total of 20 apples (4 varieties X 5 apples / variety)

were tested to evaluate the average material properties of apple ﬂesh.

5.3.1.1 The Compression Test
Compression test was conducted by loading the cylindrical sample
between two parallel ﬂat plates (Fig. 5.3) at a rate of 0.5 mm/sec (1.18
inch/min). This rate was the same that was used in the MT ﬁrmness
measurement. The specimen was compressed until failure occurred. Complete

force-deformation curve was recorded; a typical curve is indicated in Fig. 4.4.

83

 

Fig. 5.3 Compression test or relaxation test of the sample
between two parallel plates

84

A stress relaxation test was executed by compressing the specimen between two
parallel ﬂat plates and letting it relax for a certain period. Theoretically,
compression should occur suddenly in order to depict the relaxation behavior
(Mohsenin, 1986). However, inﬁnite loading rate is unfeasible, hence a loading
rate as high as 500 mm/sec was used. The crosshead of the testing machine was
stopped at 10% strain, which is just below the bioyield strain. The specimen was
then allowed to relax for 120 seconds. The relaxation test code is included in
Appendix (A.1). Load variation with time was recorded and analyzed later in

the section of results and discussions.

5.3.2 The MT Firmness Test and The Bioyield Test
The bioyield test was developed to measure the bioyield point of apple
tissue with minimum destruction. This test was designed to assess fruit ﬂesh
strength underneath the skin. Based on a preliminary study the Magness-Taylor

ﬁrmness was presumed to correlate to the bioyield point.

5.3.2.1 The Magness-Taylor Firmness Test
Fruit ﬁrmness is an assessment of quality, which is inﬂuenced by cell
turgor pressure, cell wall strength, and intercellular cohesion.
Magness-Taylor ﬁrmness was measured by an 11.1 mm (7/16 inch)
puncture probe (Ballauff Manufacturing Co., Laurel, MD.) as shown in Fig. 5.4.
The probe was penetrated into a peeled apple to a 7.9 mm (5/ 16 inch) depth at a

rate of 30 mm/min. The peak force during penetration was considered as the MT

85

ﬁrmness measurement of the fruit. This force was recorded in the computer

connected to the Instron machine.

1

 

Fig. 5.4 The Magness-Taylor ﬁrmness test

5.3.2.2 The Bioyield Point Test

The bioyield point was detected by applying a specially designed probe
against the intact fruit until a sudden drop of the load took place due to tissue
failure under the contact area. The interaction of the probe with the fruit was
comparable with that of the ﬁrst stage of the Magness-Taylor test prior to ﬂesh
penetration, but it produced signiﬁcantly less damage. The test must not result
in fruit degrading, and bruise size must be within the allowance for Extra Fancy
that stated in page 2.

The test was conducted at the apple equator. A doughnut shaped hard
plastic seat was used to support the intact apple. The stem-calyx axis was
positioned horizontally as shown in Fig. 5.1. The contact area with the seat was
comparatively large such that the contact stresses were insigniﬁcant compared to
that at the test point, which would eliminate any susceptible injury or bruise at
the contact with the seat. The probe was programmed to move at constant rate of
30 mm/sec against the intact fruit until a sudden drop in load was detected (Fig.
5.7). As can be seen in the programming code for the test (Appendix A.2) the
test was terminated as the instantaneous load dropped by 0.01%, at this instant
the probe was stopped and no further penetration is allowed as shown in the case
of Fig. 4.2. The load drop was due to tissue failure at the bioyield point, which
is the peak point on the F-D curve. An audible crunchy signal was detected due
to tissue micro-failure. The program recorded the peak load, the displacement at

the peak load, the compression energy to peak load and the least square modulus

87

in a preset loading range. The test of every fruit was repeated for each of the six

probes.

5.3.2.3 The Mechanical Probes

The FE modeling of the probe-apple contact has designated certain
features that should be considered so as to produce a quasi-uniform contact stress
distribution. The probe consisted of cylindrical steel rod with elastic rubber tip
glued at the ﬂat end. The ﬁnite element study indicated that the rubber elastic
modulus should be less than two times that of apple material. The rubber tip
should be greater than 2 mm (0.08 inch) in thickness, and the outer edge of the
rubber should be sharp. Concerning the uniformity of the contact stress, the
diameter of the probe was not a parameter, but it has crucial inﬂuence on the
volume of the generated bruise. A larger probe diameter and small size fruit
enhance the ﬂat plate effect prior to the developing of full contact with the skin.
Smaller probe reduces the effect of apple curvature. It has a higher perimeter to
area ratio, which tends to increase the effect of skin strength. The volume of the
bruise can express the degree of destructiveness.

Six probes were constructed using rubber pieces of two thickness to
diameter ratios (t/d) on the tip of three probe sizes (d=1/4, 3/8 and 7/16 inch).
These sizes were referred to as small, medium and large respectively. Rubber
pieces were cut into cylindrical shapes and bonded ﬁrmly with a glue to the steel
probe-end. Based on the t/d ratio the probes were classiﬁed into two groups, the

group with t/d=1/2 was termed as thick, whereas the thin group had t/d=1/4. The

88

names of the probes were abbreviated by using the initial letter of the size name
and the last letter of the group (since the two groups start with the same initials).
For example, the SK-probe stands for the small-thick probe. The dimensions and

abbreviations of the probes are shown in table 5.1 and Fig. 5.5.

Table 5.1 Dimensions and abbreviations of the probes. The 3'“ and 4“l
columns contain the thick and thin groups, respectively. The
probe abbreviation is indicated under the thickness

 

 

 

 

 

 

 

 

 

 

   

 

. . t/d=‘/2 Ud=%
Size Probe Diameter Thickness Thickness
d (Inch) 1 (mm) t (mm)
3.18 1.59
Small 1/4 SK SN
. 4.76 2.38
Medium 3/8 MK MN
Large 7/16 5&6 2&8
_ , I:
__ “I, r...
. Lr.’ .9 a
Large Medium Small
(LK) (MK) (SK)
E. L V (51.4; at
Li 5 1.
Large Medium Small
(LN) (MN) (SN)

Fig. 5.5 The mechanical probes used in the bioyield test; the thick group
is shown in the top row and the thin group in the bottom row

89

5.3.3 Testing Procedure

Each of the six probes was used to detect the bioyield point of every
individual fruit successively. Two opposite sites on the equator of the fruit were
selected for the MT puncture test. Adjacent to each MT site, three spots marked
by (x) signs - about '/2 inch apart - were assigned for the bioyield tests of a set of
three probes as shown in Fig. 5.6. The MT ﬁrmness was measured twice for two
reasons. Firstly, to estimate the variation of ﬁrmness measurements within the
individual fruits. And secondly, to eliminate the effect of this variation by
comparing the bioyield measurement and the ﬁrmness measurement that were
conducted at the same side. All the bioyield tests were made prior to ﬁrmness
measurement so as to eliminate the peeling and puncture effects on the bioyield
point measurement.

A total of 640 apple samples of four varieties (160 Golden Delicious,
160 Red Delicious, 160 Gala, and 160 Fuji) were tested. A set of 40 apples was
examined per day in February and March 2001. These apples were harvested in
late September or early October from Michigan State University Clarksville
Horticultural Experiment Station in Clarksville, MI, and were stored in
controlled atmosphere conditions. Prior to testing, the fruits were left about 24
hours to equilibrate to room temperature, except one set of each Red Delicious
and Fuji varieties that had been kept at room conditions for four days to allow

for fruit softening.

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91

5.4 Results and Discussion

5.4.1 Typical Bioyield Test

Fig. 5.7 shows a typical force-deformation curve of a Golden Delicious
apple tested with the small-thick (SK) probe. At the beginning of contact, the
curve is concave upward due to the increasing contact area prior to full contact
with the skin. Once the full contact was achieved, in this case, at about 0.2 mm
probe deformation, a linear relationship proceeded up to a well-deﬁned bioyield
point (B.Y.). The coordinates of the bioyield point are (Xy, Fy), where Xy and
Fy are the probe displacement and load, respectively. As the applied load
reaches the bioyield point, a sharp drop in the applied force can be observed,
accompanied by an audible crunchy sound due to bulk failure of the tissue
beneath the contact area.

Since the force-deformation curve is highly linear with a correlation
coefﬁcient of r>0.99, the slope and the energy of compression can be
approximated by the quotient and half the product of the force and deformation
at the bioyield, respectively. The slope of the curve (Sy =Fy/Xy) is related to the
combined elastic modulus of the fruit and the probe materials. The nominal
bioyield strength was estimated by dividing the force at the bioyield point (Fy)
by the cross-sectional area of the probe. The bioyield energy (toughness) on the
other hand, is the work required to cause tissue failure. The bioyield energy can
be integrated using the bioyield test code or approximated by the area under the
force-deformation curve (Ey=Fy><Xy/2). Note that only a small fraction of this

energy was stored in the rubber tip. In view of rubber as linear elastic material,

92

for the test shown in Fig. 5.7, the fraction of energy stored in the rubber tip
constitutes about 23% of the total loading energy. The remaining energy was

irreversibly consumed in apple tissue failure depicted as a permanent plastic

distortion of the bruise.

12 -
B.Y. (Xy, Fy)

Force (N)
O)

 

O ' I I I I I I I I

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Deformation (mm)

Fig. 5.7 Typical force-deformation relationship of the bioyield test generated by
the small-thick probe

93

5.4.2 The Modulus of Elasticity

The slope of the stress-strain relationship in the linear elastic range
estimates the apparent modulus of elasticity. A typical curve is plotted in Fig.
4.4 for the validation of the FE model against the experiment. The average value
of the modulus of elasticity of apple ﬂesh was 5.05 MPa (729.8 psi) with a
standard deviation of 0.94 MPa (136 psi). This is comparable to 5.94 MPa (859
psi), the average of 16 values of the apparent elastic modulus as tabulated by
Mohsenin (1986) from several studies for six apple varieties including:
Delicious, Golden Delicious, McIntosh, Melba, Rome Beauty and Stayman,
whose MT ﬁrmness ranges from 8-21 lb. In this study, a modulus of elasticity of

5.0 MPa was used for apple ﬂesh material in the FE model.

5.4.3 The Stress Relaxation Function

The stress relaxation function describes the viscoelastic behavior of apple
material. Due to the distinctive nature of the biological material, it couldn’t be
simulated by a speciﬁc model with ﬁxed number of elements throughout the
entire compression procedure (Peleg and Calzada, 1976). Therefore, the
material characteristics in the neighborhood of the bioyield point were of major
concern for simulating the bioyield process. The sample was strained to an
extent just prior to the bioyield point where the viscoelastic pattern, which the
material underwent would be as close as possible to that exhibited during the

bioyield test.

94

Nevertheless, previous studies had shown that the generalized Maxwell
model, which consists of a few simple Maxwell elements connected in parallel,
could satisfactorily simulate the viscoelastic behavior of apple material.

The basic Maxwell element consists of a spring in series with a dashpot.
Since the dashpot is unlimited in ﬂow, the simple Maxwell element is
characterized by a decaying stress that eventually converges to zero. However,
in the real case, the stress in apple sample does not vanish completely.
Therefore, a linear spring was introduced in parallel with the Maxwell model.
This spring is manifested by a constant term in the relaxation function, which
represents the stress at equilibrium. Fig. 5.8 shows the generalized Maxwell
model composed of two simple Maxwell elements and the parallel spring that
was used to represent the rheological behavior of apple ﬂesh.

When a constant stress is applied, the model exhibits an instantaneous
elastic response due to the three springs. The material shows limited creep when
the stresses carried by the Maxwell elements vanish due to the ﬂow of the
viscous dashpots, but the parallel spring (E3) limits the ultimate strain.

When the model is subjected to constant strain 80, the stress relaxes with
time. The spring E3 maintains the equilibrium stress at value greater than zero.

The stress relaxation function can be written as:
— t/ r, — t/ r,
0(t) = 60 Ele + Eze + E2 (5.1)

Where:

80 E the initial strain (mm/mm).

95

t 5 time (sec).
E1, E2 and E3 5 the stiffness of springs.
m, 112 a the viscosity coefﬁcients of the dashpots.
and 1:1: m/El, 12 = Tiz/Ez a the ﬁrst and the second time constants.
The average stress for experimental data of the relaxation test of 20 apple

specimens was computed at each time step. The data were best ﬁtted to a two-

term exponential function according to Eq. 5.1.

 

 

 

 

 

Fig. 5.8 The generalized Maxwell model of two simple elements

96

The constants of relaxation function for average apple material was approximated
by:

80:0.10

E1: 0.488, E2: 0.590, and E3 = 1.13 MPa.

11: m/E1= 2.27 sec, 12 = nz/E2= 45.6 sec.

m=l.lO8, and n2=26.9 MPa.sec.

The uniaxial stress relaxation curve is shown in Fig. 5.9 for a time
interval of 70 seconds. However, the bioyield test is accomplished within less
than a 4 second interval. The high correlation coefﬁcient between the model and
experimental data (r=0.992) shows the accuracy of the generalized Maxwell

model in representing the relaxation characteristics of apple material.

0.3 -

c(t)=o.113+o.0448 exp(‘t/2.27)+0.059 apt-Vase)
93:0.99

 

 

 

 

’n?
o.
E
U)
m
93
85
0.1 -
<> Experirrent
—Nbdel
O T I T T
0 15 30 45 60

time (see)

Fig. 5.9 The stress relaxation curve of apple material

97

5.4.4 The Bioyield Point Test and Firmness Prediction

The bioyield test resulted in a well-deﬁned bioyield point for most of the
test fruits. For probes with rubber tip thickness greater than 2 mm (all probes
except the SN—probe), the percentage of samples that demonstrated a well-
deﬁned bioyield point from the ﬁrst trial was 98%. Whereas, in the case of the
SN-probe with rubber thickness of t=l.59mm (i.e. < 2 mm), the percentage
decreased to 87%, the bioyield point was not measurable in 13% of the samples.
In this case, the bioyielding of tissue had taken place, but the absence of a load
drop was due to the gradual failure of the tissue cells within the contact area as a
result of the non-uniform contact stress distribution. It can be deduced that the
increase in force due to the progressive compression exceeded the decline in
force due to cell failure.

The ﬁnite element investigation of the SN-probe indicated stress
concentration at the probe outer edge; the thin rubber was inadequate to diminish
the effect of the rigid die and generation of the quasi-uniform stress distribution.
Therefore, the injury of fruit skin was observed in some samples when tested by
the SN-probe. Concerning the completeness of data, when the bioyield point
was not obtained from the ﬁrst trial, the experiment was repeated at a spot of
small radius of curvature so as to enhance the stress uniformity, which increase
the tendency of bulk failure associated with a measurable bioyield point.

The load drop at the bioyield point was sharper for ﬁrm fruits, especially

when a large cross-sectional probe was used.

98

Apple fruit is sensitive to the environmental conditions during storage.
Some apple varieties may become mealy after a period of cool storage. Fruit
mealiness is physiologically associated with low bonding between neighboring
cells and a high resistance to cell rupture (Harker and Hallett, 1992). In the
bioyield experiment of the Red Delicious group that was exposed to room
temperature for about 4 days, 12 samples out of 40 did not exhibit a well-deﬁned
bioyield point regardless of the testing probe. The apples had mealy texture,
with a brownish color and off ﬂavor. The force in the F-D curve of the mealy
apples was increasing continuously without a noticeable drop because the cells
under the contact area did not break, as no crunchy sound was detected. This can
be explained by the increased air space and the loose intercellular pectin bonds
that permit the glide of the individual cells alongside each other without cell wall
rupture (Mohsenin, 1986).

Tu and De Baerdemaeker (1995) analyzed the mealiness in fruit texture
using the texture proﬁle analysis (TPA) in which a food piece is compressed
twice to resemble the mouth mastication process. The raw apples showed no
adhesion (peak negative force during the upper stroke of the ﬁrst cycle). For ripe
apples, stored for 7 days at room conditions, the adhesion and the internal air
space increased, while the cohesion (ratio of compressive energy of the second
cycle to that of the ﬁrst cycle) was decreased.

On the contrary, the apples group from Fuji variety —well known for its
high ﬁrmness range — that were exposed for four days to room conditions did not

become mealy in texture nor underwent signiﬁcant ﬁrmness decline.

99

Nevertheless, the cell turgor pressure was brought down due to water loss,
causing the bioyield point to occur at a larger deformation. In fact, the increase
in the interstitial air space enlarged the required strain necessary to raise the cell
turgor pressure to the value that causes cell wall breakage. A similar turgor
effect was observed also in potato tubers, such that “increasing turgor resulted in
significantly decreasing failure strain and tissue toughness, increasing secant
modulus, and a slight decrease in failure stress” according to Bajema et al.
(1998). The decrease in turgidity also explains why fruit are more susceptible to

bruising at harvest than after storage (Garcia et al., 1995).

5.4.4.1 Regression Analysis

Linear regression analysis was carried out between the measured
Magness-Taylor ﬁrmness and four different variables evaluated at the bioyield
point. Each variable was investigated as a potential parameter to predict the MT
ﬁrmness. The variables were the force at the bioyield point (Fy), the
deformation (Xy), the slope of the force-deformation curve (Sy), and the bioyield
energy (By).

The experimental data corresponding to samples from the four apple
varieties and the linear regression line are plotted on scatter diagrams against the
MT ﬁrmness measurement. Regression analysis was repeated for each of the
four variables as measured by each of the six probes. Each variable
measurement was plotted against the MT ﬁrmness, which was measured on the

same side (see Fig. 5.6).

100

In the regression model, the MT ﬁrmness was the effect or the response
variable and the measurement at the bioyield point (Fy, Xy, Ey, or Sy) was the
independent variable or predictor, with the bioyield force (F y) as the independent

variable, a simple linear regression model can be written as:

MT =a+ b Fy (5.2)

The constant a indicates the intercept with the MT—axis and b is the slope of the
straight line, which represents the predicted change of the MT ﬁrmness
associated with a unit change of the force measurement (Fy). The least square
method was used to ﬁnd the estimates of the regression parameters of the best-ﬁt
regression line.

The coefﬁcient of correlation between the MT ﬁrmness and the variable
in concern is a measure of the closeness of the relationship to a straight-line
model. It can be used as an index to express the accuracy of predicting the fruit
ﬁrmness by measuring the bioyield point. The values of the correlation

coefﬁcient are tabulated in Table 5.2 for the six probes.

The force at the bioyield point (Fy) was well correlated with the MT

ﬁrmness. The correlation coefﬁcient was equal to or greater than 0.792 for any

probe, which is relatively high compared to the other variables. The deformation at

bioyield point (Xy) did not correlate well with the MT ﬁrmness measurement

050.571). The lack of ﬁt to a linear model was due to the deﬁciency of an obvious

pattern, in such a way the data were highly scattered. Indeed, ﬁrmness is not the

only parameter that speciﬁes the deformation at bioyield point. Other unknown

101

causal parameters such as apple variety, irrigation schedule, date of harvest, and
storage conditions may affect this value.

The slope of the F-D curve (Sy) and the compression energy (Ey) have
somewhat lower correlation coefﬁcients with the MT ﬁrmness. These correlation
coefﬁcients were less than that of the bioyield force (Fy) itself because of the
inclusion of the modestly correlated variable “the deformation” in their expressions.
The scatter diagrams and the best-ﬁt trendlines for MT ﬁrmness measurement
versus Fy are shown for the six probes in F ig.’s 5.10- 5.15, the ﬁgures includes the
Mean Square of the Residual (MSR) from the regression line.

From Tables 5.1 and 5.2, it can be concluded that decreasing the diameter of
the mechanical probe generally enhances the correlation between the MT ﬁrmness
and the force (F y). In addition, probes with large rubber thickness to diameter ratio
(t/d=0.5) produced higher correlation than those with small ratio (t/d=0.25), which

have identical diameters.

Table 5.2: The correlation coefﬁcient (r) between the Magness-Taylor firmness
and force, deformation, slope or energy at the bioyield point.

 

 

 

 

 

 

 

 

 

 

 

 

Force Deformation Slope Energy

Probe (Fy) (Xy) (Sy) (Ey)
LK 0.803 0.526 0.753 0.708
MK 0.819 0.560 0.744 0.726
SK 0.828 0.571 0.733 0.740
LN 0.792 0.333 0.749 0.604
MN 0.801 0.309 0.746 0.610
SN 0.806 0.249 0.712 0.615

 

 

102

Experimental results indicated that the average value of deformation
necessary to reach the bioyield point (Xy) increases by increasing the diameter of
the probe or the thickness of the rubber (Fig. 5.19). This ﬁnding was also
observed in the ﬁnite element study (Chapter 4). Furthermore, since failure
originates at the entire area of contact, then regardless of the geometrical shape
of the bruise, its volume (V) is proportional to the probe area as well.
Consequently, bruise volume is related to the cubic power of the probe diameter
(Vocd3). The proportionality of rubber deformation at a given stress with its
thickness explains the increase of the gross deformation of the probe for the thick
set of probes. In addition, applying a small probe for bioyield point detection
reduces the curvature effect; therefore, a small diameter probe was highly
suggested and seemed more promising for subsequent studies. Accordingly, the
small-thick (SK)-probe was the optimal probe among the six probes evaluated.
Detailed regression statistics of this probe are presented in the next section.

The slope of the MT-Fy relationship (Figs. 5.10-5.15) is proportional to
the cross-sectional area of the probe. Hence, the bioyield stress rather than the
bioyield force itself is the dominant factor in tissue bioyielding. Data points
from the probes with three different diameters are clustered around a straight line
on the scatter diagrams (Figs. 5.17 and 5.18) for the probes with thick and thin
rubber, respectively. The slopes of the best-ﬁt trendlines are 65.9 and 71.4 mmz,
and are signiﬁcantly below the cross-sectional area of the standard MT puncture
probe (96.9 mmz). This inconsistency between the values is a consequence of

the deviations between the physics of MT ﬁrmness test from that of the bioyield

103

test in terms of the fruit-probe interaction. The following are some aspects of
comparison between the bioyield test and the MT test that might explain the

inconsistency of the two measurements:

1. In the bioyield test the failure of the tissue under the skin is mostly
caused by the normal compression stress, while in the ﬁrmness
puncture test, failure is due to a combined effect of shear and

compression stresses.

2. The MT ﬁrmness is deﬁned as the maximum resistive force during
the entire penetration course, whereas the bioyield measurement
corresponds to the rupture of the ﬁrst layer when the test is
terminated.

3. The blunt end of the MT probe tends to lower the penetration
resistance, while the lateral expansion of the rubber tip of the

developed probe increases the effective contact area with fruit skin.

4. The anisotropy of apple material properties might contribute to this
deviation. The cells immediately under the skin are of smaller size
(<5011m), rounded shape, and randomly oriented. The cellular size
gradually increases towards the fruit center, becoming radially
elongated, and stacked in radial columns with radial air space
channels in between the cells (Khan and Vincent, 1991). The local
ﬂesh ﬁrmness has a maximum value immediately under the skin,

where the bioyield point test is conducted. This part is disregarded

104

 

in the MT puncture test since “peeled ﬂesh” is considered, such that

the MT test measures the ﬁrmness of the interior softer part.

5.4.4.2 The Small-Thick Probe

The small-thick probe (SK) has the highest potential for nondestructive
ﬁrmness sensor because of its correlation with the MT ﬁrmness. Additionally, it
was the least destructive and the most reliable probe for detecting the bioyield
point.

The correlation coefﬁcient of the measured bioyield force with the MT
ﬁrmness was 0.828 (Fig. 5.9). When 2% outlier data points were neglected, the
correlation coefﬁcient was improved to 0.853 (Fig. 5.20). The neglected outlier
data points with maximum standardized residuals have the highest attenuation on
the correlation coefﬁcient. The standardized residuals of the neglected outlier
data were greater than 2.56. This correlation was considerably satisfactory in
comparison with the ultimate limit that can be anticipated. The ultimate limit
corresponds to the correlation of the MT ﬁrmness with itself as measured on
opposite sides of the fruit. Experimental estimation of this limit was r=0.9l9
(Fig. 5.16).

The upper limit for the 99% conﬁdence interval for probe displacement at
the bioyield point was 1.8 mm, hence using the loading rate of 0.5 mm/s, the
bioyield testing can be completed within 3.6 seconds. this is relatively slow

compared with the required grading speed in the fruit industry.

The regression analysis resulted in a very small p-value (sz). The 95%

conﬁdence intervals for the slope and the intercept were 2.007<b<2.209 and

105

 

4.621<a<9.289, respectively. Fig. 5.20 indicates the 95% conﬁdence and
prediction intervals. The conﬁdence interval (CI) is the narrow band about the
ﬁtted regression line which speciﬁes the range of the population mean of all
ﬁrmness values corresponding to a given value of the bioyield force
measurement. The prediction interval (PI), on the other hand, is the wide band
about the ﬁtted regression line, which determines the range of ﬁrmness
corresponding to an individual measurement of the bioyield force (MINITAB,

1994).

The repeatability of the bioyield test is tested by relating the
measurements of the two probes that have the highest correlation with the MT
ﬁrmness, because two measurements of the same probe are not available. Fig.
5.21 shows the correlation of the bioyield point measurements by the small-thick
and the medium-thick probes, the correlation coefﬁcient (r=0.889) is very close
to that of the MT ﬁrmness correlation with itself shown in Fig. 5.16 (r=0.919).
However, the value of the mean square of residual (MSR=8.0 N) which measures
the scattering of the data points around the straight line was signiﬁcantly less

than that of the MT ﬁrmness measurements (MSR=38.1 N).

106

 

SK

   

 

1:1 Golden
A Red MSR=78.6
11o - 0 Fuji

f x Gala o

I 90 - o

In

0

C

.E r

IL 70 a :

§ 1

s L

h l”:

3, 50 - E

W I

0

C .

O

I!

z 30 4 y = 2.10951: + 7.4579
R2 = 0.6855 "

10 U T I I
5 15 25 35 45

Bioyield force (N)

Fig. 5.10 Correlation of the Magness-Taylor firmness of four apple varieties

with the force at the bioyield point measured by the small-thick
probe (SK): diameter = 1/4”, with rubber thickness to diameter
ratio of ‘/2

107

MK

 

 

 

0 01:1 0 MSR=82.4
0 d
9 :1 Golden no 8 000 o
A Red - ( O .65)

g 0 FUji '
3 7o . x Gala
O
C
.E
u.
L-
2
>. 50 .
1?
a
a
O
C
D
g

30 -

V
”('1 y = 0.9405x + 8.0285
R2 = 0.6702
10 I I I I
10 30 so 70 90
Bloyield force (N)

Fig. 5.11 Correlation of the Magness-Taylor firmness of four apple varieties with

the force at the bioyield point measured by the medium-thick probe
(MK): diameter = 3/8”, with rubber thickness to diameter ratio of ‘/2

108

120 - LK

El Golden
A Red MSR-88.7
100 - 0 Fuji 0 O
)K Gala D
0 €53
.

Magness-Taylor Firmness (N)

 

20‘

y = 0.7064x + 11.514

 

 

R2 . 0.6448
0 I I I I W
20 4o 60 80 100 120

Bioyield force (N)

Fig. 5.12 Correlation of the Magness-Taylor ﬁrmness of four apple varieties
with the force at the bioyield point measured by the large-thick
probe (LK): diameter = 7/16”, with rubber thickness to diameter
ratio of 1/z

109

 

SN

 

  

 

 

El Golden
MSR=92.9
120 - A Red

0 Fuji .
’z‘ x Gala O 00 f
V o
8 9o - “”00
g I.
E ° 1'
E
:5 6o , ;
>~ :
ﬂ 1.
'8
a 3° ‘ y = 2.3888x + 5.9091
g R2 = 0.6499

0 . . .
5 15 25 35

Bioyield force (N)

Fig. 5.13 Correlation of the Magness-Taylor ﬁrmness of four apple varieties
with the force at the bioyield point measured by the small thin probe
(SN): diameter = 1/4”, with rubber thickness to diameter ratio of '/4

110

1:1 Golden MSR=95.2
1201 A Red
0 Fuji o
X Gala o 0
9o - <59 0 °

30-

Magness-Taylor Firmness (N)
8

 

y =1.148x + 10.101
R2 . 0.6413

 

o I I I I
10 20 30

40 5? 60 70 80
Bioyield force N)

Fig. 5.14 Correlation of the Magness-Taylor ﬁrmness of four apple varieties with
the force at the bioyield point measured by the medium-thin probe (MN):
diameter = 3/8”, with rubber thickness to diameter ratio of ‘/4

111

 

 

LN
Cl Golden
A Red MSR=99.0
120 - ,
0 Full
x Gala o
00
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y 3 0.813)! + 12.958
R2 - 0.6271
0 I I I I I I I I I
10 20 30 40 50 60 70 80 90 100

Bioyield Force (N)

Fig. 5.15 Correlation of the Magness-Taylor ﬁrmness of four apple varieties
with the force at the bioyield point measured by large-thin probe
(LN): diameter = 7/ 16”, with rubber thickness to diameter ratio of ‘/4

112

ll'llld'l.

L-‘L‘K .1 II

 

MT

   
  
 

 

 

E1 Golden MSR=38.1
A Red 0
2 10° ' 0 Fuji
: o
4- x Gala O
0
:9
.3 80 -
m o
m
0
E
i: 60 '1
‘6
_>.
(I
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10 40 -
8 y = 1.0018x
: 2
m x R = 0.8446
1‘
E
20 . u u u
20 40 60 80 100

Magness-Taylor Firmness [side 2] (N)

Fig. 5.16 Comparison of the Magness-Taylor ﬁrmness measurements at
opposite sides of the fruit of four apple varieties

113

  
 
  

 

 

120 - c-Thick
2 1001 Dd=7l16" :1 m
v A 3/8" ”A ‘ ‘5.
In D ' ‘ I A O F
‘0 II 1
0: 0 1]
E 80 - l
i:
55 60 -
«1
17 5
m .
8 4° 1
c:
g ‘3 '- "
E 20 - . a n o y = 65.949x + 9.806
R2 = 0.652
o I I I l I
0 0.3 0.6 0.9 1.2 1.5
Bioyield Stress (MPa)
Fig. 5.17 Correlation of the Magness-Taylor ﬁrmness of four apple varieties with the F1
stress at the bioyield point measured by three probe diameters (1/4, 3/8, ; if
and 7/16 inch), with the constant rubber thickness to diameter ratio of 1/z i l
.4

114

120 -

   
  

 

 

O—thin
u d=7l16"
D O A
g 100 ' A 3I8" A A 00
3 o 114" ”2,
“a 80 . 00
E o
L-
1:
_'5 60 -
>4
II
'T
g 40 .
C
E y = 71.401x + 13.743
2° ' R2 = 0.5805
0 I I I I I
0 0.3 0.6 0.9 1.2 1.5

Bioyield Stress (MPa)
Fig. 5.18: Correlation of the Magness-Taylor ﬁrmness of four apple varieties with

the stress at the bioyield point measured by three probe diameters (1/4,
3/8, and 7/ 16 inch), with constant rubber thickness to diameter ratio of V.

115

h
I

 

 

13'
E 0 thick
53‘ 0 thin
.n 3 -
E Xy _K = 5.841d + 0.3606
.2 ’5‘ R2 = 0.9674
'6 £2 .
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.2 X
G!
U
3, 1 - Xy_N = 3.43:1 + 0.3019
g R2 = 0.9778
>
<
o I I 1
1/8 1/4 3/8 1I2

Probe diameter, d (inch)

Fig. 5.19 Variation of the deformation required for tissue bioyield with the
diameter of the probe for thin and thick rubber tips, t/d= ‘/4 and '/2,
respectively

116

120 _ 95% Pl
Y = 6.95488 + 2.10789X ’

R-Squared = 0.728 ix" .gzzi-

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MT -ﬁ1mness (N)
O

20 — “30"3/

 

 

10 20 30 4o
Force at the bioyield point , Fy (N)

Fig. 5.20 Scatter plot of MT ﬁrmness versus the bioyield force measured by the
small-thick SK-probe, showing the prediction interval (PI) and
conﬁdence interval (CI), based on 95% conﬁdence level, after
eliminating 2% outlier data with the highest standardized residuals

117

  

 

 

MSR=8.0
o
g 1:1 Golden o
E 40 1 o
0) A Red
E
9 0 Fuji
D
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8 20 4
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‘65
E A
:43 y = 0.4012x + 2.4639
E R2 = 0.79
a)
o I I I
0 30 60 90

Medium-thick probe measurement (N)

Fig. 5.21 Scatter plot of bioyield force measurements of the small-thick SK—probe
and the medium-thick MK-probe

118

5.5 Summary and Conclusions

The fundamental material properties including both elastic and
viscoelastic properties were measured. A generalized Maxwell rheological
model composed of two simple Maxwell elements was constructed to explain
the viscoelastic relaxation characteristics of average apple material. These
priorities were used in the ﬁnite element simulation to assist in designing

mechanical probes.

Based on the ﬁnite element study, six probes were built with three
sizes and two rubber tip thickness to diameter ratios. The probes were
investigated for nondestructive bioyield point detection. As the testing probe
pressed against the fruit skin at a constant rate of 30 mm/min the contact load
increased linearly with probe extension since the contact area was constant.
The probe was stopped at the bioyield point, where a sharp drop of the load

was demonstrated.

The bioyield point was well-deﬁned in a majority of the tested
samples. The rubber tip creates a uniform contact stress distribution, causing
simultaneous failure of apple tissue under the contact area. When a probe
with small rubber thickness of less than 2 mm was used, the resultant non-
uniform stress distribution caused skin injury at the outer edge with gradual
tissue failure that might complicate the bioyield point detection. On the other

hand, mealy fruit didn’t exhibit well-deﬁned bioyield regardless of the probe,

119

which may be attributed to the changes of cellular structure and its greater

capability of resisting cell rupture.

The stress at the bioyield point (or the force for a speciﬁc probe size)
provided the best estimator of the Magness-Taylor ﬁrmness. In general,
decreasing the probe diameter increased the correlation with ﬁrmness, which
also reduced the effect of apple size on bioyield point measurement. Besides,
probes with higher thickness to diameter ratio (t/d= l/2) tended to have better
ﬁrmness prediction, were more practical, and somewhat more accurate than
those with lower thickness to diameter ratio (t/d= Vs). However, as the quasi-
uniform stress distribution is achieved, the correlation could not be improved
further by increasing the thickness; the probe instability became a serious
problem when too thick rubber is used. Moreover, the bruise volume was
related to the cubic power of the probe diameter. For example, the bruise
volume due to testing by a 1/4 inch diameter probe was less than one third
that of 3/8 inch probe. These results and observations led to the conclusion
that the small-thick (SK) probe with a diameter of ‘A inch and a rubber
thickness to diameter ratio of t/d= ‘/2 was the optimal design among the six
probes evaluated. It produced a correlation coefﬁcient with the MT ﬁrmness
of r=0.853 after excluding only 2% outlier data, in comparison with the
ultimate correlation coefﬁcient (r=0.919) of the MT ﬁrmness measurements
on opposite sides of the fruit. The force at bioyield point occurs at an
average probe displacement of 1.78 mm, including the deformation of the

elastic rubber piece. Therefore, the proposed probe leaves only a tiny bruise,

120

which is hardly noticeable and would not degrade the fruit. For sorting
purposes, bruises may be completely avoided for the ﬁrm (good) apples by
compressing up to a predetermined threshold value. Soﬁ apples will bioyield
below that value but the ﬁrm ones will not. Thus, ﬁrm fruits whose bioyield
force are greater than the threshold value could be recognized without

creating any bruise.

Since the standard deviation of the bioyield point measurement
around the regression line was lower than that of the MT ﬁrmness, the of the

bioyield point measurement was more repeatable than the MT ﬁrmness.

121

Chapter 6

Overall Summary, Conclusions and

Recommendations
6.1 Summary

Fruit ﬁrmness is an important quality attribute of apples. It is the key
to ensure consumer satisfaction, proper fruit storage, and shelf life.
Therefore, it is considered a crucial parameter in the postharvest operations
from the orchard to the consumer. F irrnness is affected by many factors in
the preharvest and postharvest stages and these effects are still uncertain.
Determining and retaining apple fruit ﬁrmness are two major issues in the
apple industry. The widely used Magness-Taylor ﬁrmness test requires
penetration of a steel probe into the fruit ﬂesh, which is destructive and
cannot be used to inspect every individual fruit in a given lot that may have

great variation in ﬁrmness.

The overall objective of the research was to develop a nondestructive
sensor that is capable of estimating apple ﬁrmness. The estimate should
correlate to the destructive Magness-Taylor measurement. Since ﬁrmness is
a measure of apple tissue strength or integrity for resisting probe penetration,
the bioyield strength of the fruit tissue appears to be a reasonable estimator

for apple ﬁrmness.

122

Previous quasi-static studies were primarily based on evaluating the
apparent modulus of elasticity and considered the elastic modulus to be a
measure of ﬁrmness. Most studies had used a spherical rigid indenter that
was characterized by non-uniform stress distribution and an unknown contact

area. However, the elastic modulus does not correlate well with ﬁrmness.

A quasi-static method was used to detect the bioyield point by direct
contact with apple skin. A rubber piece was bonded to the end of a circular
steel probe, the deforrnability of rubber material produced a uniform contact

stress distribution on the fruit.

The ﬁnite element simulation of the contact problem with the fruit
suggested the use of rubber material with a modulus of elasticity of less than
twice that of the apple material. A smaller size probe reduced the resulting
bruise volume and the fruit curvature effect. A sharp edged probe eliminated
the variability in the contact area. A rubber thickness greater than 2 mm was
necessary for quasi-uniform contact stress distribution. The maximum
critical strain and von Mises failure criteria were found to be useful in

explaining the tissue failure.

The Instron Universal Testing Machine with a constant loading rate
of 30 min/min was used in all tests. The bioyield point test was conducted
using six mechanical probes (3 diameters x 2 ratios of thickness to diameter).
The probes were pressed against the fruit skin at a constant rate of

deformation. The Instron was programmed to stop at the instant a small drop

123

in the contact force was detected. The force—deformation curve was linear
due to the unchanging contact area after the full contact with skin was
developed. The radial expansion of the rubber tip was neglected. The force
at the bioyield point had a higher correlation coefﬁcient with MT ﬁrmness
measurement compared with the deformation, apparent modulus of elasticity,
or compression energy necessary for tissue bioyielding. A rubber thickness
below 2 mm was inadequate to detect the bioyield point due to the lack of
uniform stress distribution. The study also found that mealy fruit did not
exhibit tissue failure, so the bioyield phenomenon could not be measured

regardless of the testing probe.

The small-thick probe of %” in diameter and 1/8” tip thickness was
concluded as the optimal probe for measuring the bioyield strength of the
fruit tissue. The force at the bioyield point that was measured with this probe
had the maximum correlation coefﬁcient with the MT ﬁrmness measurement
(r=0.853). The correlation coefﬁcient of MT ﬁrmness measurements on
opposite sides of the fruit was (r=0.919), which was considered the limit of

the potential sensor.

6.2 Conclusions

The following conclusions can be drawn from this study:

1. The force at bioyield point was a satisfactory estimator of the ﬁrmness of

apple fruit.

124

The bioyield point measurement was independent of the size of the fruit.

The skin of the fruit was an insigniﬁcant factor in the bioyield measurement.
The developed probe minimally destructive and did not degrade the fruit.
Bruise volume was proportional to the probe diameter raised to the power 3.
The effect of friction between the probe and the skin of the apple was
negligible.

The critical strain and the von Mises stress were able to explain the failure of
apple tissue underneath the contact area.

Increasing the rubber tip thickness enhanced the uniformity of the contact
stress distribution. However, measuring instability due to misalignment
became a serious problem when rubber thickness was equal to the probe

diameter.

6.3 Recommendations

The following recommendations are suggested for ﬁirther research:

1.

2.

3.

For less bruise volume, a smaller probe size (diameter <% inch) with thickness
to diameter ratio of ‘/2 should be examined.
To meet the sorting rate requirement in the fruit industry, a higher loading
rate should be investigated experimentally.
Development of a portable electronic hand held version of the probe would

be a useful tool for detecting fruit ﬁrmness in the postharvest system.

125

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131

Appendices

132

Appendix A

The Testing Codes

133

A.1 The Relaxation Testing Code

 

: Batch Information :
Batch descriptor 1 Relaxation test of cylindrical apple sample
Batch descriptor 2 for 120 second after compression to 0.25MPa
stress
Batch descriptor 3 24th April 2001
Gauge length 12.400 mm
Parameter File c:\hs\RELATN.CTP
Date Read 20 August 2001
Time Read 17:05:16

 

 

 

 

: Specimen Information :
Specimen information required prior to test No
Specimen cross-sectional shape Circular
Diameter 20.0 mm

 

 

 

: Sequence Setup :

Number of sequence repetitions 1
Number of blocks deﬁned 1
Number of markers in sequence 1
Sequence order

Marker 1 Block 1 : Relax

 

 

 

: Test Control Data :

Block Number 1

Select block type Relaxation

Control mode Displacement

Limit type Strain

First level 0.00

Second level -0.10

Crosshead speed 500 mm/sec

End test/Break detect No action

Dwell time 0.0 sec

Relaxation terminator Time
Relaxation time 120.0 sec

Transition to start level Yes

Crosshead action at end of block Crosshead return

 

134

 

 

: Data Logging Selection :

 

Block number 1
Is logging required for this block? Yes
Should data be logged on basis of time? Yes

Time increment 0.1 sec

Should data be logged on basis of displacement? No
Should data be logged on basis of load? No
Block number 1
Is a plot required for this block? Yes
Realtime Plot Size Half Page
Plot Grid Yes
Axes through Origin Yes
X axis

Type Time

Minimum 0.000 sec

Maximum 120.000 sec
Y axis

Type Stress

Minimum 0.000 MPa

Maximum -0.250 MPa

 

 

 

: Results Selection :
Results Page 1

Column 1 Peak Load

Column 2 Peak Stress

Column 3 Strain at Peak Load
Column 4 Specimen Area

135

A2 The Bioyield Point Testing Code

 

: Batch Information :

 

Batch descriptor 1 New test programming for bioyield point detection
Batch descriptor 2 A rubber tipped probe compresses apple until
bioyield point

Batch descriptor 3 @ 30 mm/min bioyielding claimed when load falls
by 0.01% and auto stop

Parameter File c:\hs\HUSSAIN.CTP

Date Read 10 July 2001

Time Read 15:20:11

 

 

' S ecimen Information '
l I

 

Specimen information required prior to test No
Specimen cross-sectional shape Circular
Diameter 11.11 mm [ probe diameter]

 

 

 

: Sequence Setup :

Number of sequence repetitions 1
Number of blocks deﬁned 1
Number of markers in sequence 1

Sequence order

Marker 1 Block 1 : Preconditioning

 

 

 

: Test Control Data :

Block Number 1

Select block type Pre-conditioning
Control mode Displacement
Crosshead speed 30.000 mm/min

End test/Break detect Load falls by given % below peak load
Amount below peak load 0.1 %

136

Dwell time 0.0 sec

 

 

Preload -9.000 N
Anvil Height 8.00 mm
Upper limit given by: Absolute Displacement
Displacement 6.00 mm
Number of Cycles 1
Action on Specimen Failure Stop test
Below % of ﬁrst cycle max load 1 %
Crosshead action at end of block No action / Next block
: Data Logging Selection :
Block number 1
Is logging required for this block? Yes
Should data be logged on basis of time? Yes
Time increment 0.05 sec

Should data be logged on basis of displacement? No

 

 

 

Should data be logged on basis of load? No
: Plot Setup :

Block number 1

Is a plot required for this block? Yes

Realtime Plot Size Half Page

Plot Grid Yes

137

Appendix B

The Bioyield Test Results

138

 

B.l Golden Delicious

 

 

 

Test date: Feb. 12, 2001 . Group: A
Probe: MT_K MT_N LK LK MK MK SK SK LN LN MN MN s~ SN
Fy Xy Fy Xy Fy Xy Fy Xy Fy Xy F Xy

NO- ("1 (N) ("1 (mm) (N) (mm) ("1 (mm) W) 4mm) (N) (mm) 1’(N) (mm)
1 25.0 25.1 26.6 2.03 23.7 1.97 9.8 1.32 28.5 1.68 15.5 1.29 12.4 1.17
2 33.9 35. 7 41.4 2.22 34.1 1.87 14.9 1.27 24.1 1.39 24.1 1.13 12.5 0.84
3 35.5 33. 7 39.6 2.22 29.4 2.17 14.0 1.42 32.5 1 .47 25.8 1.19 12.3 0.86
4 34.9 34.4 37.6 2.14 34.6 2.17 15.0 1.42 27.0 1.39 33.5 1.54 14. 6 0.97
5 34.0 32. 7 36.8 1.94 33.7 2.32 11.7 1.19 32.9 1.37 21.4 1.22 11.0 0.96
6 27.5 30.3 21.8 1.54 29.1 1.86 9.9 0.99 25. 7 1.14 28.6 1.64 15.2 1.06
7 34.6 32.0 47.9 2.39 40.8 2.27 17.8 1.54 30.4 1.34 27. 7 1.19 13.8 0.82
8 29.0 30.3 34.4 2.12 31.9 1.97 16.0 1.55 32.8 1.44 24.4 1.24 10. 7 0.91
9 40.4 42.5 42.9 2.39 44.7 2.67 19.0 1.59 42. 7 1.71 42.0 1.46 19. 7 1.29
10 36.3 34.1 40.2 2.04 33.2 2.12 13.9 1.24 28.4 1.32 33.0 1.27 18.1 1.08
1 1 32.7 34. 7 37.9 2.29 34.4 2.39 13.9 1.31 36. 7 1.74 27.0 1.59 12.3 1.09
12 34.3 36.2 36.0 2.05 36.2 2.22 14.9 1.44 31.9 1.54 23.3 1.09 16. 7 1.04
13 41.3 32.0 47.0 2.59 40.2 2.34 19.0 1.64 30.8 1.79 22.0 1.22 12. 6 0.97
14 29.0 32.1 35.3 1.91 33.0 2.05 13.1 1.27 34. 6 1.46 25.5 1.14 13.2 0.97
15 37.9 38.2 48.1 2.47 40.6 2.31 17.7 1.54 35. 7 1.72 29.1 1.39 16.7 1.02
16 42.6 30.3 62.9 3.14 36.2 2.24 21.6 1.59 33.5 1.56 22.6 1.17 14.3 0.94
17 26.6 25.4 26.9 1.72 27.5 1.99 10.9 1.21 26.6 1.37 18.4 1.05 12.2 0.89
18 37.0 30.5 45.4 2.44 42.6 2.52 19.1 1.49 29.1 1.34 23.4 1.22 15.4 1.06
19 29.4 36.0 33.8 2.02 32.4 1.95 13.4 1.24 42.8 1.52 23.0 1.29 15.3 1.17
20 30.2 34.3 34.0 1.77 25.2 1.64 13.1 1.21 36.4 1.60 18. 7 1.14 15.0 0.99
21 39.7 40. 7 58.0 2.67 41.9 2.54 20.9 1.72 44.4 1.68 26.5 1.30 17. 7 1.16
22 34.9 32.0 45.3 2.57 31.8 2.06 16.8 1 .49 33.6 1 .59 22.8 1.47 12.3 0.96
23 32.2 34.1 37.3 2.29 33.2 2.24 13.0 1.32 26.5 1.53 26.2 1.76 14.2 0.99
24 32.2 32.1 41.2 2.32 31.4 2.49 12.9 1.29 34.2 1.63 31.4 1.59 13.8 1.19
25 32.1 29.5 26.4 1.54 37.4 2.31 15.7 1.47 27.2 1.42 22.1 1.12 12. 6 1.04
26 33.6 30. 7 51.6 2.60 30.7 1.74 19.6 1.54 36.9 1.49 29.2 1.24 14. 9 1.02
27 27.6 28.9 36.3 1.89 28.8 1.77 14.4 1.32 24.3 1 .27 23.3 1 .34 14.5 0.89
28 39.7 36.2 45.1 2.29 36.4 2.17 15.4 1.36 31.2 1.44 29. 7 1.34 16.0 0.97
29 36.5 35.8 48.7 2.39 34.9 2.04 17.4 1 .54 34.9 1 .49 25.8 1.27 15. 1 1.09
30 30.5 33.4 26.2 1.79 28.1 2.02 11.1 1.17 33.9 1.44 20.7 1.12 11.7 1.09
31 35.0 34.4 44.1 2.26 32.0 2.19 14.5 1.37 36.7 1.44 17.3 1.01 13.0 0.92
32 33.8 33. 6 40.8 2.22 31.6 2.04 14.5 1.34 38.6 1.78 26.3 1.22 16.4 1.03
33 34.8 33.0 42.1 2.24 37.7 2.09 17.0 1 .62 24. 1 1 .22 28. 6 1.59 15.0 0.99
34 32.0 30.0 38.2 2.02 32.0 1.87 16.2 1.44 29.8 1.31 17.4 1.04 11.5 0.87
35 32.7 33.0 40.2 2.24 35.7 2.29 14.9 1 .47 26.0 1 .62 25.1 1 .37 14. 0 1.12
36 33.4 29.5 40.0 2.29 32.7 2.17 13.9 1.45 26.5 1.27 21.3 1.14 12.1 0.92
37 32.5 35.1 40.1 2.09 28.4 1.82 15.5 1.46 31.3 1.44 30.5 1.26 11.3 0.84
38 33.9 35.9 39.4 2.02 37.8 2.02 15.1 1.42 41.8 1.69 31.1 1.39 14.5 1.22
39 33.5 33.4 45.6 2.42 33.8 2.02 14.4 1.39 38.9 1.57 26.3 1.39 15.5 1.13
40 32.8 32.8 39.6 2.02 30.1 1.89 12.6 1.19 27.2 1.39 23.5 1.17 14.2 0.96

 

139

 

 

Test date: Feb. 17, 2001. Group: B

 

Probe: MT_K MT_N LK LK MK MK SK SK LN LN MN MN SN SN

 

Fy Xy Fy Xy Fy Xy Fy Xy Fy Xy F Xy
N0. (N) (N) (N) (mm) (N) (mm) (N) ("in“) (N) (mm) (N) (mm) YlN) (mm)

 

41 67.2 58. 9 60.8 2.97 60.8 2.97 27.2 1.74 49.4 1 .69 39.2 1 .59 25.0 1.29
42 62.9 54.5 59.8 2.82 59.8 2.82 28.6 1 .89 56. 1 1 .89 42.1 1 .60 22.0 0.94
43 33.3 35.6 32.9 2.02 32.9 2.02 15.6 1.37 33.2 1.39 22. 0 1.19 14.1 0.99
44 67.0 64.4 67.7 2.79 67.7 2.79 24.0 1.69 58.1 1.67 47.5 1.54 21.5 1.09
45 68.4 71.0 52.2 2.79 52.2 2.79 27.2 1.97 62.3 1.92 48.5 1.81 23.5 1.14
46 67.8 70.8 66.4 3.06 66.4 3.06 26.1 1.74 57.5 1.92 47.4 1.61 22.2 1.14
47 61.1 61. 5 45.5 2.44 45.5 2.44 23.6 1.72 54.3 1.72 31. 7 1.49 25.5 1.44
48 73.5 64.8 45.7 2.14 45.7 2.14 28.6 1.92 60.3 1.92 48.0 1.52 21.5 1.07
49 64.3 63.5 61.1 2.87 61.1 2.87 24.6 1.82 57. 7 1.67 49.5 1.59 27.2 1.19
50 82.9 80. 2 55.5 2.59 55.5 2.59 19.5 1.67 46. 7 1.39 44. 6 1.42 20.6 1.02
51 63.3 74. 7 58.3 2.69 58.3 2.69 25.1 1.77 69.2 2.02 50.2 1.54 25. 9 1.27
52 65.0 69.0 51.7 2.89 51.7 2.89 25.3 1.79 52.9 1.99 46.2 1.46 22.9 1.19
53 87.5 91.0 54.7 3.09 54.7 3.09 27.9 2.19 63.0 2.42 47.4 1.89 22.0 1.36
54 66.1 63.2 59.3 2.87 59.3 2.87 25.7 1 .87 55. 7 1 .59 42. 6 1 .49 27.5 1.22
55 65.2 68.0 58.0 2.66 58.0 2.66 27.3 1.79 45.4 1.67 47. 7 1.64 25.5 1.14
56 69.7 73.8 65.4 2.92 65.4 2.92 26.1 1 .84 60.2 1 .77 51.5 1 .77 22.0 1 .12
57 90.7 92.3 63.9 3.19 63.9 3.19 24.7 2.27 67.4 2.54 56.4 2.09 27.4 1.69
58 68.6 60.9 48.2 2.54 48.2 2.54 22.3 1.57 56.4 1.84 45.9 1.49 24.3 1.19
59 54.2 59.4 50.3 2.49 50.3 2.49 24.5 1.77 56.0 1 .92 49.4 1.57 20.1 1.09
60 82.2 84. 9 53.0 2.59 53.0 2.59 23.0 1.64 61.5 1.78 44.6 1.92 22.2 1.07
61 61.7 63.9 48.8 2.56 48.8 2.56 23.5 1.79 62.2 1.69 42.9 1.39 21.9 0.99
62 35.9 32.5 35.3 2.17 35.3 2.17 18.0 1.57 28.7 1.37 25.0 1.34 13.0 1.02
63 59.2 66.0 55.1 2.47 55.1 2.47 25.8 1.87 42.1 1.44 35.9 1.64 19.8 1.19
64 30.4 31.0 34.5 2.04 34.5 2.04 13.3 1.39 29.9 1.21 19.2 1.13 12.9 0.94
65 38.8 41.2 37.2 2.09 37.2 2.09 15.3 1.26 33. 7 1.54 35.3 1.27 17.8 0.94
66 37.9 37.1 34.5 2.22 34.5 2.22 13.3 1.32 37.8 1.52 25.9 1.39 15. 6 0.94
67 29.4 28.2 34.3 2.04 34.3 2.04 9.9 1.04 23.8 1.12 21.4 1.19 11.8 0.84
68 35.1 36.0 33.7 2.17 33.7 2.17 16.5 1.44 46.8 1.79 27.4 1.39 14.0 0.92
69 38.5 38.2 36.9 2.04 36.9 2.04 16.6 1.54 36.2 1.49 28.2 1.29 14.3 0.89
70 32.0 33.3 33.5 2.02 33.5 2.02 15.7 1 .36 34. 1 1 .47 24. 6 1 .23 12.1 1.04
71 34.7 34.1 31.4 1.99 31.4 1.99 14.1 1.29 28.2 1.39 22.6 1.14 13.5 1.09
72 36.6 33.0 33.8 2.17 33.8 2.17 16.4 1.47 28.3 1.44 22.9 1.24 13.0 0.79
73 42.9 3 7.0 49.7 2.49 49.7 2.49 20.2 1.37 49. 8 1.57 29.5 1.24 14.6 0.94
74 34.0 33.8 43.8 2.34 43.8 2.34 16.9 1.56 47.6 1.74 28.6 1.24 19.1 1.07
75 . 35.6 37. 7 37.7 2.32 37.7 2.32 15.3 1.44 40.8 1.46 26.2 1.39 15.3 0.89
76 31.1 37. 7 29.7 1.84 29.7 1.84 14.4 1.44 44.5 1.64 24.9 1.21 14.3 1.07
77 38.5 28.9 39.3 2.52 39.3 2.52 18.9 1.64 26. 7 1.39 22. 6 1.14 12.5 0.87
78 28.5 33.9 30.6 1.87 30.6 1.87 12.1 1.18 31.1 1.27 19.5 1.16 11.8 0.82
79 32.2 33. 7 33.8 1.97 33.8 1.97 13.6 1.18 40.8 1.71 29.8 1.17 16.8 1.09
80 35.4 35. 7 38.6 2.29 38.6 2.29 16.9 1 .43 39.5 1 .54 29.3 1 .29 15.0 0.94

 

 

140

 

Test date: March 14, 2001.

Group: C

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

No.

Fv
(N) (N) (N)

Xy
(mm)

Fy
(N)

Xy
(mm)

Fy
(N)

Xy
(mm)

Fy
(N)

Xy

Fy

(mmL (N)

Xy
(mm)

F
Y(N)

Xy
(mm)

 

81
82
83
84
85
86
87
88
89
90
91
92

101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120

47.9
39.2
35.2
29.6
29.4
36.4
36.0
31 .2
42.7
33.8
42.4
32.6
38.2
37.4
36.8
36.4
36.6
45.7
41 .9
43.5
37.8
37.0
52.6
54.4
43.9
55.8
44.9
51.1
54.1
56.8
54.2
50.6

42.6 '

39.4
46.2
41.3
37.6
43.4
34.2
50.5

44.6
41.2
32.6
34.5
31.7
37.9
35.9
34.9
40.6
31.2
40.9
38.3
35.2
33.2
36.7
31.0
32.5
41. 7
51. 7
39.8
40.8
35.5
57.0
49. 7
52.5
51.7
52.0
62.0
49.1
50.2
57.9
43.6
46.2
42.6
49. 7
42.3
49.9
45.3
33.1
49.4

59.7
47.1
39.1
49.0
37.2
48.0
49.9
34.8
54.1
36.6
47.6
33.9
45.1
42.4
47.1
42.2
45.1
58.9
48.2
63.7
41.9
38.1
82.3
74.1
51.0
54.0
48.7
68.7
78.7
58.3
62.0
73.6
49.4
40.7
49.5
47.5
51 .4
65.4
46.1
62.4

2.79
2.39
2.21
2.32
2.07
2.59
2.44
2.22
2.69
2.21
2.30
2.07
2.29
2.54
2.19
2.24
2.27
2.69
2.59
2.99
2.02
2.07
3.34
3.24
2.49
2.61
2.52
2.84
3.39
2.82
2.99
3.24
3.02
2.17
2.59
2.51
2.42
3.12
2.39
2.74

49.7
40.1
26.3
27.6
25.0
38.8
37.1
32.9
38.6
34.6
43.5
26.2
33.0
33.5
35.0
35.9
40.4
43.5
36.6
46.1
27.2
35.6
58.4
62.2
36.9
42.9
39.2
53.0
59.6
51.9
52.6
54.8
53.6
32.1
37.0
39.3
38.0
49.2
42.4
49.9

2.87
2.49
1.72
1.87
2.07
2.22
2.29
1.94
2.41
2.07
2.54
1.92
2.09
2.32
2.04
2.29
2.26
2.36
2.27
2.54
1.77
2.13
2.92
3.54
2.39
2.41
2.44
2.67
2.97
2.89
2.82
3.17
2.87
2.04
2.57
2.24
2.27
2.79
2.32
2.54

20.0
20.2
12.9
15.4
14.4
20.7
18.2
14.1
17.7
16.5
19.3
1 1.3
17.2
13.9
16.0
17.5
18.9
23.5
16.9
23.3
20.0
16.3
30.3
27.6
16.9
20.8
19.3
24.9
26.0
22.8
22.6
23.2
20.9
16.5
18.4
15.1
18.5
23.0
17.7
21.3

1.72
1.84
1.17
1.42
1.44
1.82
1.49
1 .41
1.67
1.49
1.84
1 .24
1.54
1 .44
1 .47
1.62
1.52
1 .74
1 .52
1.82
1.72
1.49
2.05
2.04
1.52
1.72
1 .64
1 .92
1 .78
1 .76
1.69
1.82
1.74
1.54
1 .74
1.49
1 .64
1 .89
1 .59
1 .67

46.0
43.0
36.2
37. 1
31.9
32.0
45.6
38.5
38.4
19. 1
47.2
32.5
37.2
27.0
38.2
27. 7
33.3
46.3
52. 7
43.6
42.2
37.5
69.8
61.8
44.9
47.6
42.9
75.2
45.4
57.0
64.8
42.2
53.4
52.5
48. 7
47.2
55.5
50. 7
40.2
57.4

1.74
1.79
1.37
1.39
1.59
1.37
1.96
1.59
1.61
1.27
2.12
1.52
1.56
1.34
1.47
1.32
1.35
1.69
1.62
1.66
1.54
1.77
2.36
1.97
2.24
1.69
1.64
2.12
1.76
1.74
2.07
1.79
1.89
2.29
1.88
1.72
1.86
1.84
1.61
1.82

38.3
32.9
21.2
32. 7
23.4
25.9
27.4
25. 7
31.5
21.2
29.4
23.4
26. 1
27.2
25.0
25. 7
29.4
36.6
34.6
36.9
35.8
28.8
48.2
45.9
36.5
28. 1
35.3
43.5
40.3
39. 7
48.3
28.5
34. 1
30.2
31.5
28.3
36.9
31.9
24.4
38.4

1.62
1.51
1 .17
1 .32
1.42
1.47
1.34
1.37
1.39
1.19
1.29
1 .24
1 .27
1 .29
1.37
1.27
1.29
1 .44
1.57
1.27
1 .34
1 .27
1.69
1.77
1.37
1.42
1 .43
1 .71
1 .54
1 .59
1.67
1.34
1 .64
1.67
1 .52
1 .44
1 .40
1 .42
1 .34
1.62

15.3
13.6
14.4
15.1
13.4
14.4
17.7
13.2
16.9
12.8
16.4
13.7
11.0
13.4
15.0
12.0
13.6
18.6
19.9
18.5
19.9
12.2
24.2
22.0
19.0
16.5
19.1
24.2
18.1
22.5
23.4
15.9
21.5
15.1
18.6
17.6
21.7
18.2
15.6
22.6

1.07
0.97
0.92
1.01
1.03
0.92
0.99
0.99
1 .22
0.89
1 .09
0.99
0.87
0.92
0.94
0.99
0.94
1.02
1.17
0.99
1.04
0.99
1.34
1.17
1.07
1.19
1.07
1.19
1 .29
1.47
1.24
1.14
1.32
0.91
1.13
1.12
1.20
1.09
1.07
1.12

 

141

 

 

Test date: March 26, 2001.

Group: D

 

Probe:

MT _K

M T_N

LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

No.

 

(N)

 

(N)

 

F)!
(N)

 

Xy
(mm)

 

(N)

 

Xv
(mm)

 

(N)

 

Xy
(mm)

 

(Ni

 

Xy
(mm)

 

Fy
(N)

 

Xy
(mm)

 

y(N)

 

Xy
(mm)

 

121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160

36.6
41 .0
45.1
38.8
43.8
36.8
35.3
39.7
35.2
33.0
50.2
54.7
45.7
37.0
52.1
40.2
42.1
47.9
44.3
41.8
41.1
46.2
46.2
43.8
55.3
49.7
45.3
43.1
55.1
61 .4
38.2
44.4
46.5
39.9
43.0
37.3
59.7
42.1
46.2
44.4

36.5
38.4
52.0
45. 7
42.3
41.1
35.2
37.2
37. 7
36.3
43. 7
51.9
49.1
42.4
42.5
38.6
55.0
43.7
49. 7
46.4
37.4
43.9
48.1
44.6
49.5
48.1
47.1
36.7
48.2
55.6
37.0
44.9
49.2
35.9
39.3
36.6
46.4
40.9
44.6
39.2

43.4
50.6
55.3
35.8
40.5
51.0
32.7
44.2
58.5
44.1
54.8
56.3
53.6
45.5
66.3
44.6
56.6
62.3
63.9
53.4
49.7
58.3
60.3
57.6
54.6
75.8
54.6
45.1
45.0
53.2
45.6
55.5
58.6
42.7
49.6
53.1
74.5
48.4
64.4
56.1

3.27
2.66
2.50
2.24
2.47
3.81
2.32
2.24
2.54
3.84
2.69
3.09
2.64
2.49
2.96
2.56
2.77
2.85
3.02
2.84
2.64
3.04
2.92
2.76
3.14
3.39
2.74
2.34
2.33
3.01
2.57
2.99
2.87
2.59
3.17
2.39
3.27
2.44
2.94
2.67

33.8
40.8
37.2
32.4
30.0
37.5
34.4
35.1
36.2
31.6
48.0
41 .8
39.9
36.6
64.2
43.4
43.5
44.9
46.8
41.5
47.2
38.2
46.4
46.4
47.2
55.0
34.0
36.5
39.6
46.7
28.3
42.6
48.6
29.2
49.2
41.7
67.5
40.0
51.8
46.6

2.64
2.57
2.17
2.20
2.04
3.29
2.29
2.14
2.09
2.97
2.63
2.44
2.37
2.54
3.09
2.59
2.32
2.72
2.57
2.42
2.66
2.32
2.86
2.54
2.84
2.82
2.09
2.34
2.72
2.94
2.09
2.72
2.87
2.02
2.54
2.44
3.42
2.54
2.87
2.58

13.1
18.6
12.9
16.7
17.2
17.5
12.7
17.3
16.9
12.8
15.8
24.7
18.0
15.9
25.1
17.8
21 .3
19.6
21.3
17.0
18.9
16.5
15.3
19.0
18.0
25.9
18.4
17.7
16.3
23.2
14.1
19.0
20.9
13.8
19.1
18.8
24.2
13.3
19.5
20.3

1.76
1.62
1.42
1.59
1.59
2.29
1.62
1.44
1.67
1.81
1.59
2.12
1.77
1.49
1.97
1.72
1.77
1.64
1.74
1.54
1.72
1.69
1.77
1.69
1.77
1.97
1.67
1.72
1.44
2.01
1.49
1.81
1.77
1.47
1.63
1 .64
2.03
1.44
1.64
1.77

45.4
49. 7
48.9
48.8
41. 1
47.4
41.9
37.6
40.4
42.5
32.3
48.5
49.0
34. 7
50.9
43.2
58.6
45. 7
56. 1
44.4
41.0
38.2
56.9
42. 1
48.8
49. 7
48. 7
35. 6
39.0
56. 1
40.3
46.4
43. 1
26. 1
43. 1
38.2
47.3
45. 1
55.9
44.4

2.44
2.04
1.77
1.87
1.71
2.99
1.64
1.39
1.52
2.94
1.34
2.04
1.62
1.77
1.81
1.79
1.92
1.57
1.98
1.49
1.57
1.77
1.92
1.64
2.17
1.79
1.87
1.69
1.67
1.69
1.74
1.74
1.86
1.32
1.69
1.39
1.74
1.59
1.84
1.44

30.6
30.2
34.4
33.0
35. 7
42.4
28.1
23.0
31.4
35.1
31.4
36.7
33.0
29.9
43.3
32. 7
47.4
37.5
35.5
30.1
21.0
31.4
37.0
41.4
37.8
40. 7
30.2
27.7
28.2
35.2
27.8
37.8
35.8
26.6
24.8
21.4
39.5
22.9
45.2
34.4

1.97
1.37
1 .37
1.39
1 .47
2.62
1.57
1 .14
1.37
2.64
1.64
1.74
1.47
1.29
1.59
1.49
1.72
1.49
1.52
1.47
1.04
1.54
1.39
1.67
1.64
1.49
1.34
1.39
1.24
1.59
1.42
1.64
1.49
1.37
1 .17
1.09
1 .42
1 .09
1.54
1.42

11.4
18.1
27.5
15.4
16.9
17.4
14.1
17.1
18.2
16.1
16.1
25.1
16.0
13.2
19.7
14.4
26.5
13.1
23.0
16.5
15.4
13.4
17.9
16.3
19.3
18.9
17.8
14.8
13.7
17.3
14.4
16.0
14.8
12.9
17.8
16.0
19.1
15.8
22.0
18.6

1.59
1.29
1.99
1.04
1.21
1.77
1.17
1.04
1.19
1.77
1.02
2.27
1.01
0.97
1.17
1.24
1.29
0.99
1.34
1.04
1.02
1.11
1.14
1.04
1.36
1.12
1.13
1.09
1.16
1.24
1.34
1.17
1.14
1.04
1.04
1.02
1.12
1.02
1.14
1.22

 

142

 

 

8.2 Red Delicious
Test date: Feb. 8, 2001. Group: A

 

Probe: MT_K MT_N LK LK MK MK SK SK LN LN MN MN SN SN

 

Fy Xy Fy Xy Fy Xy Fy Xy Fy Xy F Xy

 

M (N) (N) (N) ("N") (N) (min) (N) (mm) (M (mm W) (mm) Y(N) (mm)
1 49.6 57.7 51.6 2.62 42.1 2.48 20.2 1.59 67.9 1.97 41.5 1.49 20.9 1.17
2 51.6 54. 0 62.6 2.79 48.2 2.49 18.9 1.56 48. 7 1.64 33. 6 1.35 18.4 0.92
3 61.3 55.8 84.4 3.41 63.4 3.06 24.6 1.87 69.0 1.84 45. 7 1.48 19.5 1.12
4 60.3 59.3 82.2 3.27 53.6 2.87 26.1 1.89 46. 6 1.62 40.0 1.60 18.3 0.89
5 57.1 62. 8 73.5 3.00 57.9 2.71 23.1 1.67 70.2 2.34 49. 6 1.69 24.1 1.16
6 61.3 53. 7 75.7 3.13 45.5 2.66 26.4 2.09 45. 7 1.64 41. 7 1.44 20.0 1.22
7 63.0 50.1 81.3 3.50 58.8 3.07 23.8 1.69 48.4 1.84 41.0 1.52 19.6 1.04
8 53.0 58.3 69.3 3.18 49.2 2.99 21.1 1.84 61.3 2.47 36.7 1.59 20.5 1.09
9 50.3 52.4 70.0 3.09 54.8 2.97 25.3 1.78 56. 1 1.79 46.0 1.59 19.6 0.94
10 56.1 60.2 51.5 2.54 48.0 2.64 23.5 1.79 51.5 1.89 42.1 1.53 21.0 1.24
11 64.0 57.1 65.6 2.79 50.9 2.69 23.5 1.79 57.9 1.79 56.9 2.14 20.2 1.31
12 71.0 60.1 70.9 3.14 62.0 3.22 26.1 1.87 59.4 1.74 48.3 1.84 23.5 1.18
13 51.6 55.6 61.1 2.69 47.4 2.74 22.8 1.72 61.7 2.19 45.8 1.69 23.7 1.19
14 61.7 57.9 66.4 3.14 58.5 3.04 23.8 1.94 59.9 2.14 51.5 2.07 20.8 1.09
15 61.5 60.4 58.1 2.77 54.0 3.22 23.0 1.84 69.0 2.07 42.2 1.54 24.2 1.12
16 58.5 60.0 79.5 3.26 55.9 2.89 22.4 1.87 55.3 1.67 45.8 1.59 25.9 1.14
17 59.0 57.0 53.2 2.34 40.3 2.34 18.1 1.57 45.2 1.57 41.1 1.59 20.9 1.05
18 62.8 55. 7 82.9 3.42 67.6 3.17 25.9 1 .77 57. 1 1 .82 48.5 1 .48 25.2 1 .09
19 51.3 53. 1 49.5 2.51 43.8 2.52 20.5 1.69 48.1 1.96 39.9 1.49 22.7 1.04

20 57.1 57.1 50.8 2.89 45.8 2.52 21.7 1.61 63.2 1.97 45.3 1.64 21.0 1.07

21 56.6 55.9 63.0 2.79 60.4 3.02 24.7 1.84 58.1 1.94 43.2 1.47 23. 7 1.27

22 60.6 63.1 74.7 3.12 57.9 2.84 26.4 1.87 64.1 1.97 43.3 1.79 24.0 1.21

23 58.1 62.5 75.1 3.07 48.1 2.92 23.0 1.69 66.9 1.87 45.1 1.69 22.7 1.29

24 58.6 54.2 55.4 2.54 56.9 2.76 24.2 1.84 56.7 1 .69 45.5 1.42 25.2 1.82

25 59.6 52.4 78.8 3.39 50.5 2.99 25.7 1 .89 59. 6 2.14 48.9 1.66 22.9 1.27

26 55.2 54.2 63.4 2.54 53.2 2.77 31.2 2.39 54. 6 1.67 45.8 1.49 18.1 1.06

27 61.9 56.8 70.1 3.02 51.9 2.97 23.5 1.74 54.6 1.77 41.5 1.57 20.3 1.04

28 47.9 56.1 54.6 2.49 38.8 2.62 20.8 1.82 51.9 1.81 47.3 1.91 21.1 1.12

29 56.4 52.4 59.2 2.69 41.7 2.34 18.2 1.57 61. 7 2.19 41.1 1.74 18.7 1.17

30 68.3 54.2 71.3 2.97 55.4 2.93 20.9 1.84 61.6 1.91 39.3 1.39 16.5 1.04

31 56.3 63. 7 73.9 3.12 50.5 2.82 23.2 1.89 65.1 1.92 51.4 1.54 23.0 1.22

32 61.6 57.9 66.3 2.88 53.8 2.84 21.0 1.74 59.4 1.82 45.2 1.60 20.2 1.04

33 53.9 59.9 65.4 2.96 37.4 2.34 22.6 1.76 62.4 2.12 43.1 1.72 21.6 1.17

34 53.9 54.5 65.6 2.86 39.2 2.47 20.8 1.67 59.4 2.19 44.8 1.57 20.0 1.27

35 59.5 70. 9 71.9 3.25 63.9 2.84 24.3 1.72 66.8 1.94 46.1 1.59 23.3 1.24

36 54.3 62. 5 77.8 3.59 55.6 2.97 20.8 1 .67 66.8 1 .94 42.2 1 .59 22.4 1 .07

37 54.7 51.0 61.0 2.89 53.2 2.89 24.3 1.72 53.2 1.89 40.1 1.58 16.4 1.04

38 64.4 62.9 67.6 3.26 44.5 2.54 25.7 1 .82 54. 6 1 .99 52.4 1.56 20.9 1.09

39 36.5 29.2 47.0 2.38 34.2 2.24 20.6 1.74 31.9 1.32 20.0 0.99 16.1 0.97

40 26.7 29.0 33.6 1.79 28.0 2.02 17.2 1.79 36.0 1.47 27. 6 1.17 13. 6 0.86

 

 

143

 

 

 

 

Test date: Feb. 20 & 21, 2001. Group: B
Probe: MT_K MT_N LK LK MK MK SK SK LN LN MN MN SN SN
Fy Xy Fy Xy Fy Xy Fy Xy Fy Xy F Xy
N0. (N) (N) (N) (mm) (N) (mm) (N) (mm) W) (mm) (N) (mm) YlN) (mm)
41 40.1 39.4 50.3 2.84 35.1 2.49 21.2 1.69 43.9 1.81 31.8 1.39 14.7 1.19
42 34.8 43.2 36.0 2.59 31.1 1.92 16.9 1.49 33.4 1.36 26.8 1.34 14.1 0.92
43 44.6 43.3 56.2 2.64 23.8 1.84 20.7 1.67 31.0 1.77 33.8 1.39 18.3 1.09
44 43.2 44.2 35.2 2.17 34.4 2.32 17.1 1.67 27.7 1.59 30.3 1.42 18.2 1.17
45 38.5 38.2 32.9 2.16 21.6 1.74 13.9 1.49 31.3 2.17 27.7 1.44 13.6 0.97
46 44.3 49.6 48.4 2.42 40.3 2.39 20.2 1.74 32.6 1.36 32.4 1.48 17.6 1.09
47 38.2 41.9 39.1 2.14 32.5 1.89 12.9 1.19 36.2 1.54 29.0 1.22 15.6 0.92
48 45.5 40.8 40.2 2.32 37.2 2.24 16.2 1.52 35.1 1.44 28.8 1.42 15.9 0.89
49 37.5 38.7 36.4 2.04 40.4 2.54 17.4 1.54 39.6 1.79 25.8 1.61 20.1 1.42
50 37.3 38.9 41.0 2.64 33.4 2.19 16.2 1.41 29.2 1.44 32.6 1.39 17.7 1.12
51 24.3 27.0 34.0 2.52 28.2 1.87 11.2 1.16 42.5 2.67 25.0 1.17 13.7 0.77
52 42.0 41.0 35.1 2.07 42.4 2.57 14.0 1.32 35.5 1.47 31.4 1.29 15.5 1.14
53 43.9 48.3 53.4 2.49 53.0 2.67 24.2 1.79 45.0 1.64 37.0 1.52 19.9 1.09
54 40.3 43.1 38.5 2.32 31.8 2.09 15.9 1.39 27.6 1.32 26.3 1.17 10.7 0.84
55 49.1 46.7 35.0 1.89 29.8 2.07 13.9 1.19 26.4 1.39 19.7 1.13 12.9 0.92
56 42.3 40.9 55.9 2.64 42.1 2.44 20.0 1 .69 45.5 1.44 28.6 1.21 21.3 1.04
57 47.4 46.0 38.4 2.36 29.3 1.92 14.4 1.24 28.9 1.37 25.4 1.19 14.7 1.14
58 36.8 39.2 52.5 2.47 34.9 2.47 18.5 1.47 41.3 1.61 33.7 1.29 19.0 1.07
59 29.0 26.3 35.4 2.24 30.3 2.29 12.5 1.27 42.9 2.49 25.4 1.17 14.0 1.14
60 38.9 31.9 33.9 1.97 28.5 2.31 18.3 1.59 34.0 1.57 29.4 1.24 15.0 1.14
61 42.8 39.3 46.1 2.54 34.4 2.44 19.3 1.59 41.1 1.69 36.2 1.54 17.6 1.22
62 32.9 33.1 39.4 2.12 29.6 1.72 17.7 1.44 42.9 1.87 29.9 1.17 17.9 0.87
63 41.1 43.4 38.6 2.29 30.4 1.94 18.3 1.57 33.6 1.62 31.6 1.42 17.3 1.09
64 45.6 41.3 48.1 2.39 44.0 2.37 20.2 1.56 44.2 1.64 34.1 1.29 16.2 0.99
65 44.9 40.6 58.8 2.64 39.5 2.57 22.0 1.67 33.3 1.59 33.4 1.36 19.0 1.04
66 42.6 44.7 41.9 2.06 34.2 2.29 19.4 1.72 36.1 1.49 27.2 1.22 19.3 1.17
67 43.0 40.2 50.9 2.72 42.3 2.52 22.7 1.67 46.5 1.82 38.1 1.34 18.0 1.07
68 37.2 31.1 46.6 2.13 41.0 2.04 17.8 1.41 37.7 1.29 23.3 1.07 16.6 0.99
69 42.1 42.0 46.1 2.27 30.6 2.24 17.6 1 .54 37.6 1.72 30.0 1.39 18.3 0.98
70 42.4 42.2 43.1 2.49 29.8 1.89 16.2 1.56 30.0 1.27 25.5 1.32 15.7 0.89
71 50.4 45. 9 50.1 2.57 46.2 2.64 22.4 1.64 44.4 1.54 28. 6 1.24 17.3 0.89
72 42.3 44.2 43.6 2.39 41.3 2.11 19.8 1.49 46.3 1.86 27.2 1.56 19.1 1.02
73 40.2 40.8 46.3 2.57 38.4 2.36 13.5 1.29 34.3 1.44 36.3 1.64 16.2 1.14
74 51.4 46.0 36.6 1.99 38.1 2.02 15.8 1.29 40.4 1.47 32.9 1.29 19.2 1.09
75 46.4 39.0 43.7 2.49 41.1 2.24 19.0 1.67 33.1 1.59 27.9 1.21 17.5 1.04
76 47.7 39.6 44.4 2.19 36.2 2.19 19.7 1.64 40.9 1.64 31.3 1.29 17.1 0.88
77 65.8 57.1 76.7 4.04 62.4 3.42 28.5 2.17 62.8 2.92 51.0 2.49 27.0 1.79
78 50.3 56.7 69.8 3.47 46.5 2.54 23.4 1.91 70.8 2.59 49.0 1.77 22.2 1.39
79 61.1 54.8 63.2 3.42 56.9 3.09 27.9 1.99 74.3 2.44 50.2 2.02 25.6 1.42
80 57.1 51.0 68.3 3.61 50.1 3.14 22.6 2.20 66.2 2.57 48.9 1.83 22.7 1.29

 

 

 

Test date: Feb. 24, 2001.

Group: C

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

No.

Fy
(N) (N) (N)

Xy
(mm)

H!
(N)

Xv
(mm)

P)!
(N)

Xy
(mm)

Fy
(N)

Xy
(mm)

Fy
(N)

(mm)

W)

Xv
(mm)

 

81
82
83
34
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120

66.9
47.2
59.7
66.6
74.6
75.0
82.2
63.7
41 .2
79.3
73.6
75.4
63.4
72.2
70.0
67.5
59.4
69.6
69.4
60.8
72.8
65.9
71 .9
62.3
65.0
77.5
67.5
65.8
71 .4
48.0
68.8
61.2
66.7
76.1
63.5
66.9
75.2
72.3
77.2
73.6

64.5
53.3
63. 7
75.6
75.2
74.2
73.4
59. 7
53. 1
67. 1
70.8
58.3
79.8
79.4
67.3
64.8
62.8
75.5
79. 7
58.9
72. 1
65. 1
68.8
62.8
68.5
72.6
71.2
67.6
74.2
70.3
77.5
57.3
58.3
66.0
68.5
59.4
74.3
71.9
80.4
78.5

75.7
58.4
77.7
88.5
65.1
67.2
63.1
65.1
68.4
64.7
80.2
70.4
55.7
66.9
72.8
82.2
60.8
73.3
74.3
66.9
74.0
75.3
63.4
60.7
92.7
68.1
73.6
72.4
63.7
56.8
46.2
79.8
75.4
54.8
80.5
66.2
52.2
53.2
80.0
87.9

2.64
2.57
2.79
3.12
2.87
2.62
2.52
2.59
2.89
2.72
2.87
2.49
2.19
2.54
2.79
2.80
2.54
2.76
2.67
2.59
2.71
2.69
2.67
2.62
3.07
2.39
2.99
2.69
2.64
2.32
2.09
3.21
2.98
2.39
2.87
2.52
2.06
2.43
2.94
3.19

69.6
51 .7
52.9
78.6
51 .2
59.7
43.2
53.3
44.7
54.0
54.5
60.8
48.9
63.3
46.1
52.9
49.0
57.5
56.3
48.4
58.3
54.1
48.4
48.5
70.9
58.4
54.0
48.8
49.4
44.9
46.7
73.6
54.5
45.5
63.5
58.5
45.0
55.5
57.7
62.9

3.34
2.76
2.32
2.96
2.34
2.59
1.99
2.12
2.25
2.54
2.27
2.29
2.29
2.84
2.42
2.44
2.26
2.94
2.49
2.24
2.57
2.49
2.27
2.29
2.89
2.56
2.49
2.24
2.44
2.09
1.97
3.09
2.27
2.07
2.84
2.61
2.14
2.50
2.90
2.64

24.1
22.7
27.4
35.2
22.4
24.7
22.6
21 .2
16.7
23.3
25.3
29.7
24.6
30.1
28.2
26.8
17.7
25.0
28.4
24.1
21 .4
23.4
21.0
22.7
28.0
29.0
20.2
22.3
21.6
18.6
18.5
31.2
22.5
22.4
31.7
22.8
17.1
22.7
23.1
29.8

1.57
1.82
1.74
1.94
1.59
1.82
1.54
1.54
1.29
1.57
1.69
1.72
1.64
1.89
1.69
1.67
1.26
1.69
1.84
1.64
1.46
1.54
1.52
1.59
1.65
1.74
1.67
1.52
1.49
1.39
1.27
1.87
1.54
1.54
2.17
1.49
1.26
1.64
1.59
1.87

56.1
47.9
57.2
49.0
52.0
35.6
63. 7
59.6
40.2
46. 7
66.8
60.5
62. 1
81.4
49.9
63.3
56.9
41.9
62.9
47.0
66.4
57.3
38.9
49.9
84.0
65.6
60. 7
61.3
67. 7
40.3
46.9
61. 1
61. 7
60.2
63.2
50.2
44.0
50.9
58.0
62. 7

1.94
1.64
1.51
1.42
1.77
1.19
1.77
1.80
1.22
1.56
1.92
1.39
1.92
2.12
1.59
1.36
1.74
1.44
1.62
1.27
1.69
1.51
1.11
1.21
1.96
1.91
1.57
1.87
1.69
1.24
1.47
1.56
1.44
1.57
1.79
1.36
1.24
1.37
1.49
1.66

42. 1
40.2
45.8
39.2
31.4
36.2
41.8
40.9
42.2
42.0
60.0
47.5
43. 7
45.2
37.0
47.0
36.2
42.0
47.1
39.1
38.0
37. 7
37. 7
39. 7
46.5
49.2
37.2
46.2
39. 7
50. 1
36.3
41.9
46.0
40.9
52.1
36.8
32.4
42.4
41.0
60.0

1.39
1.39
1.29
1.14
1.22
1.32
1.19
1.34
1.26
1.24
1.72
1.24
1.42
1.41
1.15
1.39
1.34
1.49
1.42
1.36
1.33
1.24
1.09
1.14
1.62
1.52
1.24
1.77
1.33
1.56
1.14
1.24
1.39
1.47
1.42
1.04
1.06
1.39
1.24
1.82

22.1
20.8
21.0
16.8
19.6
20.1
24.4
19.0
21.5
21.5
23.3
24.6
24.0
25.0
18.5
20.7
20.6
27.7
23.9
17.2
19.6
19.5
15.7
18.0
26.4
23.5
19.0
16.3
23.1
21.5
23.5
20.3
23.3
19.0
22.9
18.6
16.0
18.9
18.8
29.0

0.92
0.94
0.94
0.94
1.04
1.07
0.99
0.96
0.87
0.94
1.24
0.99
1.07
0.99
0.92
0.97
0.79
1.66
0.89
0.87
0.84
1.12
0.74
0.89
1.22
1.07
1.02
0.82
0.89
0.92
0.87
0.91
0.94
1.14
1.02
0.89
0.77
0.89
0.89
1.09

 

145

 

 

Test date: March 20, 2001.

Group: D

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

No.

(N)

(N)

F)!
(N)

Xy
(mm)

P)!
(N)

Xy
(mm)

H!
(N)

Xy
(mm)

Fy

Xy

(NL (mm)

Fy
(N)

Xy
(mm)

F
y( N)

X)
(mm)

 

121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160

59.2
55.8
48.9
59.8
61 .3
69.1
57.2
63.3
58.4
63.6
74.7
57 .3
55.2
61 .8
51 .5
53.1
55.6
57.5
57.5
62.1
59.9
54.4
66.8
60.0
46.6
49.3
71.4
56.6
58.1
62.3
58.5
60.9
60.9
58.9
65.1
58.7
61 .8
59.6
65.2
61.0

58.0
54.0
50. 7
61.9
58. 9
71.0
60. 7
70. 6
5 7. 1
64.2
58.4
58.4
53. 6
60.4
63. 0
57.4
54. 6
44. 6
66.2
58. 8
62.5
53.0
67.3
63. 7
53.0
52.2
77. 1
56. 7
58.9
48. 6
64.2
57. 6
68.9
6 7. 6
69.5
59.4
60. 6
57.8
5 7.8
55.5

73.7
57.9
57.9
61 .1
65.6
77.1
57.1
58.8
59.5
73.7
66.8
62.9
73.7
73.1
63.9
44.1
53.9
60.1
53.3
67.8
73.2
51 .5
60.4
52.7
54.1
74.7
51.5
60.9
63.7
86.8
70.6
57 .4
62.1
71 .9
72.4
71.9
46.8
69.8
56.0
57 .8

3.19
2.67
2.99
2.69
3.04
3.07
2.59
2.39
2.64
3.14
2.92
3.32
3.39
3.27
2.84
2.29
2.32
2.52
2.57
2.91
3.79
2.66
2.62
2.54
2.42
3.59
2.64
2.72
3.49
3.84
3.17
2.49
2.84
2.89
2.87
2.97
2.37
3.67
2.52
2.87

66.1
54.2
56.5
40.3
52.7
60.0
43.7
40.7
45.9
49.3
46.5
55.7
61 .7
58.6
52.7
53.5
44.4
42.2
54.9
58.1
55.3
59.3
54.1
45.2
47.6
56.9
49.4
43.9
57.3
58.8
56.5
47.1
48.4
51.9
47.7
52.7
35.9
55.7
44.2
47.0

3.09
2.56
2.74
2.29
2.84
3.22
2.39
2.27
2.51
2.52
2.44
2.74
3.49
2.64
2.69
2.74
2.27
2.14
2.72
2.84
3.24
3.07
2.74
2.69
2.52
3.19
2.52
2.27
3.09
3.37
3.09
2.42
2.54
2.64
2.56
2.57
2.29
3.64
2.26
2.59

27.2
23.8
24.7
19.6
24.1
24.8
18.9
22.3
20.9
23.0
26.2
21.7
25.9
27.4
21 .2
22.3
20.2
23.6
17.2
27.8
24.4
23.8
26.0
22.2
22.7
22.0
24.5
20.2
23.9
31 .1
24.9
25.5
24.2
27.0
23.0
24.0
21 .0
23.7
23.2
21.2

1.94
1.59
1.84
1.56
1.79
1.77
1.54
1.59
1.57
1.77
1.99
1.56
2.19
1.97
1.59
1.72
1.59
1.72
1.49
1.94
2.04
1.89
1.82
1.61
1.71
2.04
1.77
1.62
1.92
2.29
1.79
1.76
1.77
1.97
1.72
1.82
1.69
2.19
1.77
1.81

61.9
51.4
64.6
43.6
50.0
51.3
58.6
56.5
49.5
73.5
58.5
54.4
68.7
53.6
47.7
53.7
61.0
43.8
53.4
61.7
70.7
57.9
49.0
47.6
51.3
60.5
56.1
47.3
67.2
46.8
64.3
58.3
70.5
72.2
59.4
47.9
49.0
63.0
60.5
31.0

2.32
1.64
1.94
1.34
1.69
1.79
1.84
1.84
1.69
2.22
1.87
1.69
2.69
1.69
1.59
1.69
1.89
1.64
1.77
1.77
2.61
2.32
1.57
1 .54
1.67
2.44
1.87
1.56
2.27
1.97
2.17
2.12
2.27
1.92
1.97
1.54
1.77
2.37
1.84
1.49

38.5
35.2
39.4
41. 9
38.3
42.9
42.3
34.4
45. 7
48.9
40. 1
38.5
50.9
36. 9
38. 1
40.3
44. 1
3 7. 1
45. 7
43. 7
49.5
49.5
40.4
36. 7
42.9
52.2
39.2
50.9
52. 7
36.8
43.3
39.4
51. 1
51.2
40.0
35.2
32. 1
50.4
39. 7
35. 1

1.27
1.24
1.29
1.37
1.44
1.29
1.29
1.16
1 .42
1.37
1.37
1.38
2.09
1.27
1.62
1.49
1.47
1.24
1.39
1.62
2.19
1.82
1.44
1 .14
1.26
2.29
1.39
1.66
2.27
1.47
1.52
1.42
1.32
1.47
1.29
1.27
1.34
1.99
1.39
1.24

20.4
26.2
23.4
18.3
20.5
22.7
24.3
20.0
19.3
26.2
20.6
18.4
25.0
20.2
17.3
21.0
19.2
21.0
23.7
25.3
21.0
25.7
19.6
15.7
21.3
20.2
21.4
22.1
21.7
21.4
22.9
17.8
23.1
24.5
21.4
17.3
22.2
21.7
23.3
18.5

0.99
1.59
1.07
1.04
0.94
0.94
1.14
1.12
0.94
1.19
1.07
0.92
1.29
1.09
0.92
1.12
1.09
1.02
1.09
1.22
1.67
1.47
1.04
0.99
0.99
1.41
0.99
1.06
1.39
1.22
1.22
1.07
1.22
0.99
0.89
1.17
1.14
1.19
1.49
1.12

 

146

 

 

Test date: Feb. 15, 2001.

B.3 Fuji

Group: A

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

Fy
(N) (N) (N)

Xy
(mm)

F)!
(N)

Xv
(mm)

Fy
(N)

Xy
(mm)

Fy
(N)

Xv
(mm)

Fy
(N)

Xv
(mm)

F

Xy

lelgmm)

 

omﬂmmth—sg

64.7
61.5
57.5
63.2
69.1
51.1
60.2
62.2
61.8
56.0
68.3
56.8
73.7
61 .9
50.4
62.6
65.2
52.0
52.3
52.1
54.8
69.8
51 .0
62.7
58.2
70.2
55.4
59.8
67.7
63.5
58.4
63.3
67.4
57.7
67.3
68.1
66.7
61 .8
61.3
57.7

66.3
61.4
47.6
60.3
69. 7
54.0
65. 1
72.2
57.8
51.4
55. 1
56.8
62. 7
61.5
70.0
67.2
58. 7
52.0
62.3
59.3
65.2
57.3
55. 1
66.9
55.0
53.5
57.4
57.6
76.8
57. 1
56.3
63.2
68. 7
57.5
53. 1
55. 7
75.2
51.6
72.8
58.3

64.3
87.3
74.0
88.1
74.5
84.7
63.2
67.0
89.0
73.2
94.0
61.8
103.1
70.5
60.3
75.3
77.3
71 .6
80.7
70.7
84.7
93.9
69.1
75.3
80.5
85.3
60.3
78.8
98.7
81 .3
80.6
69.1
69.0
78.7
83.9
86.8
94.1
82.7
76.7
77.4

2.93
3.14
3.09
3.57
2.87
2.94
2.46
2.82
3.34
2.99
3.34
2.64
3.31
2.89
2.69
3.07
2.76
2.94
3.19
3.06
3.27
3.19
2.72
2.99
3.27
3.29
2.72
2.96
3.29
3.09
3.19
2.77
2.77
3.17
3.07
3.07
3.27
3.34
2.77
3.09

56.6
58.8
84.7
71 .1
63.2
74.5
62.1
59.9
52.1
55.4
76.5
41 .4
81.0
59.5
54.0
66.2
54.2
62.5
69.7
64.5
62.1
73.0
55.0
65.2
72.9
63.0
62.0
67.1
75.7
74.2
60.5
59.7
63.3
74.0
69.8
59.7
71.1
66.9
64.8
64.1

2.94
2.72
3.32
3.04
2.64
3.24
2.82
2.74
2.62
2.79
2.99
2.19
3.17
2.89
2.57
2.82
2.69
2.82
2.89
2.96
2.79
3.17
2.91
3.09
3.29
2.99
2.67
3.14
2.94
3.34
2.77
2.77
2.82
3.27
2.87
2.87
2.97
2.83
2.86
2.83

20.9
26.1
30.2
31.3
28.2
29.0
23.2
31.2
29.3
21.5
33.7
22.7
36.9
28.7
28.1
26.8
26.4
28.3
29.2
29.8
31.2
31.9
29.5
27.1
32.0
30.1
28.1
26.2
35.1
31.1
26.6
25.3
24.6
31.0
28.5
29.1
28.8
28.2
28.1
30.2

1.72
1.69
1.97
1.94
1.77
2.12
1.72
1.89
1.79
1.59
2.14
1.74
2.07
1.92
1.87
1.92
1.72
1.87
1.89
1.97
2.09
2.02
1.86
1.84
2.09
2.14
1.82
1.89
1.97
1.94
1.87
1.79
1.74
2.09
2.07
2.01
2.04
1.87
1.84
1.87

60. 1
68.6
54.5
58.2
80.9
80.0
55. 7
49.9
51.5
58.3
64.5
54. 1
75.6
60.3
68. 7
53.9
53. 7
73. 7
53.2
67.3
69.4
67.0
56.0
64.2
64.4
48.3
62. 1
52.4
70.3
66.3
58. 1
63.9
69.0
66.9
50.4
52.3
79.2
64.2
51.4
51 . 7

1.82
2.07
1.72
1.69
2.09
2.04
1.91
1.52
1.87
1.74
1.68
1.79
1.89
1.99
2.09
1.54
1.59
2.54
1.82
2.02
2.09
1.87
1.92
2.07
1.87
1.62
1.87
1.69
1.89
1.99
1.86
1.79
2.01
2.19
1.72
1.54
2.34
2.67
1.80
1.67

44.9
59. 7
46.0
41.6
45.6
45.9
43.2
47.9
63.6
41.3
61 . 7
56.2
56.9
40.8
65.8
52.9
47.5
40.9
57.1
40.6
55.8
49.3
42.4
43.8
52. 7
43.0
37.5
54.8
58.3
55.9
47.6
49.4
49.1
56.3
39.2
37.3
55.8
37. 7
51.0
41 . 1

1.48
1.79
1.44
1.41
1.49
1.41
1.49
1.37
1.94
1.44
1.58
2.42
1.69
1.44
1.82
1.62
1.57
1.32
1.72
1.52
1.59
1.49
1.62
1.67
1.77
1.67
1.33
1.52
1.70
1.47
1.52
1.46
1.54
1.74
1.24
1.22
1.82
1.27
1.47
1.44

28. 7
29. 1
27. 1
25.3
28.2
24. 1
22.9
24. 7
23.5
23.5
26.5
22.2
29.6
23.0
29.4
23.8
25. 1
27.8
28. 7
26.8
24.5
26.5
22. 1
27. 7
29. 1
23.0
22.8
26.4
24.5
25.0
27. 7
29.2
33.6
30.8
19.3
24.2
36. 1
23.6
24.9
24. 6

1.22
1.17
1.17
1.34
1.22
1.14
1.16
1.07
1.01
1.14
1.19
1.29
1.22
0.99
1.37
0.99
1.09
1.82
1.26
1.17
1.17
1.17
1.14
1.14
1.24
1.19
1.07
1.09
1.09
1.12
1.37
1.37
1.22
1.27
0.97
0.97
1.34
1.04
1.22
1.14

 

147

 

 

Test date: Feb. 22, 2001.

Group: B

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

N0.

(N)

(N)

F)!
(N)

Xv
(mm)

Fv
(N)

Xy
(mm)

F)!
(N)

Xv
(mm)

(Ni

Xy
(mm)

Fr
(N)

Xy
(mm)

F
W)

Xy
(mm

 

41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

70.6
85.8
78.3
75.6
72.7
64.5
77.2
78.6
68.0
76.6
78.6
74.1
84.1
81 .3
76.0
78.7
78.0
83.6
69.5
71.6
78.5
85.1
82.5
74.5
77.2
66.6
86.5
76.3
78.7
77.0
73.4
83.9
67.0
86.0
73.1
101.2
76.8
74.6
76.2
78.9

68. 1
74.3
87.6
82. 7
78.6
6 7.3
81. 1
87.9
78.3
77.6
80.2
78.0
91. 7
86.8
74.5
86.3
68.3
82.0
73.1
70.4
71.2
74. 1
77.6
77.2
81. 7
80.9
78.5
73.9
98.6
72. 7
82.5
72.9
80.0
81.2
87.9
92.3
83.3
94.5
87.4
78.2

91.3
81 .9
87.1
98.4
75.1
80.8
83.0
83.2
79.5
69.2
73.8
95.7
93.0
77.3
82.7
60.8
65.6
1 14.4
80.1
82.9
84.3
92.0
67.8
69.9
96.0
79.4
90.3
78.8
87.4
72.7
71 .3
83.0
76.5
67.7
99.2
88.6
76.0
70.0
57.8
73.7

3.62
2.92
2.92
3.27
2.62
2.82
2.89
2.66
2.76
2.67
2.64
3.19
3.09
2.89
2.97
2.37
2.52
3.61
2.96
3.07
2.84
2.94
2.49
2.57
3.52
2.74
3.02
3.26
3.87
2.82
2.77
3.04
2.72
2.64
3.32
3.14
2.84
2.89
2.21
3.19

67.4
57.4
73.7
65.9
68.4
61.8
73.7
64.5
64.9
56.2
58.6
70.8
62.2
68.3
69.3
57 .7
59.7
75.2
57.5
78.2
76.2
72.8
58.6
60.1
63.4
70.7
74.7
68.7
72.6
50.9
55.5
81 .5
65.9
67.1
71.3
74.7
58.9
68.5
61.2
63.2

2.84
2.62
2.91
2.74
3.42
2.74
2.77
2.74
2.74
2.44
2.62
2.79
2.79
2.79
2.92
2.49
2.62
3.04
2.47
3.17
2.87
3.02
2.62
2.54
2.69
2.97
3.14
2.79
3.37
2.32
2.37
3.34
2.79
2.87
2.89
3.22
2.77
2.84
2.64
2.97

31.2
28.0
32.8
33.3
27.4
28.6
35.2
30.4
28.0
25.2
25.7
36.5
30.9
31.8
31.5
27.9
26.3
36.0
30.0
34.7
30.8
35.9
25.4
29.3
30.8
28.9
32.4
29.1
37.5
21.7
27.3
28.5
29.7
27.9
34.1
33.8
29.7
31.1
27.8
28.9

2.07
1.84
1.97
1.87
1.82
1.87
1.94
1.77
1.69
1.72
1.67
1.99
1.79
1.92
1.82
1.74
1.64
2.42
1.94
2.02
1.87
2.04
1.67
1.87
1.89
1.74
1.97
1.84
2.49
1.77
1.79
1.96
1.87
1.84
1.89
1.96
1.84
1.84
1.79
1.89

64.6
68. 1
73.2
68.9
70. 1
56.2
83.3
76.9
64. 7
68.2
49.5
86.0
69.6
66.4
81.4
68.3
56.6
66.8
81.4
75.6
60. 7
78.2
79.4
59.6
61 . 7
67.3
56.5
54. 1
80.9
60.4
61 . 1
72.8
82.3
58.9
73.8
65.3
62.0
76.4
84. 7
70.8

1.66
1.87
1.99
1.72
1.82
1.44
1.92
1.66
1.52
1.79
1.32
2.04
1.61
1.62
1.89
1.62
1.67
1.84
2.02
1.82
1.47
1.99
1.92
1.54
1.67
1.74
1.59
1.54
1.96
1.52
1.52
1.79
1.92
1.66
1.77
1.77
1.56
1.77
1.79
3.74

56.6
56.3
61. 7
55. 7
49.9
59.3
59.5
54.2
36.3
48.5
43.9
54. 1
55. 7
49.5
57.5
57.3
50.9
57. 1
44.0
55. 1
48. 7
49.6
50. 7
46.2
42.9
56.5
45.3
42.2
54.4
40.2
46.9
51 . 7
57.0
49. 1
59.2
62.3
43.5
57. 1
60.9
53.2

1.67
1.54
1.54
1.44
1.34
1.54
1.39
1.37
1.26
1.37
1.32
1.32
1.64
1.27
1.42
1.49
1.44
1.57
1.27
1.49
1.22
1.39
1.47
1.19
1.44
1.34
1.19
1.19
1.42
1.19
1.44
1.52
1.52
1.24
1.47
1.59
1.32
1.54
1.44
2.14

28.8
27. 7
33.9
25. 7
22. 7
21.9
32.4
25.5
25.3
25. 7
26. 7
29.0
28. 7
24.6
32. 1
25.5
25.8
30.3
27.0
24. 7
30.5
29.5
27. 7
23.4
28.3
26.8
23.2
21. 1
33.6
29.6
24. 7
27. 7
35.8
23.3
33.3
27. 7
25. 1
29. 7
30.6
32.3

1.22
1.12
1.22
0.99
1.02
1.09
1.09
1.17
0.99
1.09
1.09
1.16
1.19
1.01
1.12
1.12
1.07
1.29
1.14
0.94
1.14
1.04
1.19
0.97
1.22
1.06
1.19
1.04
1.19
1.27
0.96
1.07
1.27
0.99
1.14
1.09
0.94
1.27
1.29
2.32

 

148

 

 

Test date: Feb. 27, 2001.

Group: C

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

FY
N0- (N1 1N) (N)

Xy
(mm)

(N)

Xy
(mm)

(N)

Xv
(mm)

Fy
(N)

Xy
(mm)

Fy

Xy

(N; (mm)

F
W)

Xy
(mm)

 

81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120

69.5
57.8
67.6
64.7
77.2
58.5
59.9
63.9
66.3
63.0
83.1
70.6
62.8
59.5
78.2
63.4
72.8
62.2
64.4
59.6
66.2
67.0
67.0
78.1
75.3
64.3
71.1
76.8
63.1
74.6
62.2
75.8
67.4
76.3
59.1
83.4
67.6
80.3
74.3
65.1

58. 7
58.9
73.2
75.5
75.2
66. 1
72.4
69.5
71.8
59. 1
86.9
63.3
62.9
57.8
78.9
66.2
69. 7
59. 7
72.4
63. 1
69.4
79.9
61 . 7
77.6
76.9
61.4
65.4
74. 7
62. 7
64. 1
72.2
72.6
91.8
67.2
66.2
70.9
64. 1
80.4
64.5
61.5

89.1
63.2
93.6
80.5
89.2
70.0
77.6
77.7
89.4
77.8
105.0
82.4
77.4
99.0
98.2
75.3
79.7
77.3
80.3
76.9
94.3
96.7
91.9
100.0
100.1
76.3
98.0
98.6
76.5
95.7
70.1
102.0
93.5
1 12.4
67.6
100.0
83.8
104.0
93.9
79.2

3.94
3.59
4.94
3.69
4.84
3.47
3.92
4.29
4.57
3.59
5.04
4.57
3.62
4.44
4.89
4.52
4.39
3.72
3.69
3.54
4.74
4.61
4.39
3.77
5.12
3.54
4.17
3.82
3.72
4.84
3.54
4.22
4.47
4.12
3.29
5.52
3.49
4.64
4.29
4.47

66.5
56.0
82.1
65.0
68.1
65.7
73.1
70.2
63.5
66.6
74.2
64.1
63.2
73.0
74.6
62.8
77.3
56.6
63.3
63.7
80.0
74.2
66.1
63.0
63.8
55.6
76.5
70.9
63.9
86.3
60.3
78.9
73.6
68.7
61.1
69.2
65.4
72.5
73.7
64.8

3.17
3.44
5.11
3.87
4.54
3.41
3.79
4.09
4.09
3.57
4.74
4.32
3.49
3.97
4.09
3.97
3.64
3.29
3.34
3.12
4.44
4.02
3.96
2.74
4.14
3.44
3.66
3.26
3.24
4.54
3.17
3.89
4.04
3.21
3.44
4.99
3.19
4.04
3.69
4.04

35.0
28.0
31 .7
29.6
35.2
29.2
32.7
29.5
30.0
27.2
39.6
28.2
28.7
28.5
35.4
27.6
32.4
27.7
26.1
27.1
30.3
31 .0
32.6
35.0
30.6
25.0
32.5
30.4
28.7
37.0
22.1
32.2
32.1
32.5
25.9
36.3
30.7
30.5
31.4
27.3

2.27
2.42
3.24
2.34
3.17
2.32
2.72
2.67
2.77
2.14
3.19
2.79
2.27
2.59
2.94
2.59
2.42
2.36
2.09
2.24
2.52
2.59
2.74
2.27
2.77
2.14
2.49
2.24
2.24
2.92
2.09
2.72
2.62
2.21
2.11
3.59
2.22
2.56
2.49
2.62

64.2
61.0
93.8
78.3
84.2
71.2
84.5
70.4
78.2
75.6
95.9
76. 1
67.9
64. 7
73.8
59.4
67. 1
72.6
87.3
72.8
93.2
84.9
71.6
74.9
84.3
87.0
78.6
81.8
71.9
73. 1
80.0
72. 1
1 10. 7
78.4
65.3
95.3
74.0
78.8
83. 7
71.6

2.07
2.69
3.57
2.42
3.24
2.59
2.84
2.94
3.34
2.59
3.89
3.12
2.29
2.59
3.07
2.94
2.44
2.64
3.02
2.29
3.34
3.04
2.71
2.02
3.47
2.77
2.32
2.42
2.34
3.52
2.74
2.62
3.78
2.22
2.17
4.10
2.06
3.19
2.81
3.22

36.9
42.4
56.5
61.8
62.9
64.0
59.9
54.8
53.2
5 7. 1
66.2
50.6
62. 1
54.4
64.5
49.2
54. 7
48.8
56.9
53.4
60.2
61.3
57.3
52. 7
71.2
43.0
53.3
52. 7
50. 1
61.9
46.3
70.0
62.3
58.5
54.2
62.4
47.8
54.6
65.4
44. 1

1.76
2.47
2.77
2.14
2.67
2.49
2.31
2.69
2.72
2.07
3.09
2.77
2.19
2.32
2.59
2.69
2.07
2.07
2.06
1.82
2.57
2.44
2.34
1.57
3.04
1.97
1.82
1.89
1.79
2.71
1.82
2.49
2.42
1.84
1.89
3.39
1.84
2.47
2.46
2.39

23.9
22.8
30.4
33.0
30.8
30.2
31.0
25.8
26.6
28.5
32. 1
28.0
28.5
24.5
29.3
26.6
27. 7
25.4
30.5
26.3
31.6
29.2
25. 7
31.9
28.9
25.0
27.8
26.8
29.2
23.8
25.3
31.5
36.6
30.0
26.0
31.9
26. 7
26. 1
33.0
24. 1

1.41
1.57
1.94
1.47
1.89
1.64
1.89
1.79
1.84
1.49
2.14
2.04
1.44
1.54
1.69
2.12
1.39
1.64
1.85
1.41
1.87
1.82
1.79
1.39
2.09
1.44
1.34
1.29
1.54
1.71
1.52
1.52
1.89
1.57
1.34
2.21
1.57
1.82
1.66
1.89

 

149

 

 

Test date: March 19, 2001.

Group: D

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

No.

(N)

(N)

Fy
(N)

X)!
(mm)

Fy
(N)

Xv
(mm)

FY
(N)

Xy
(mm)

Fy
(N)

Xv
(mm)

FY
( N)

Xy
(mm)

F

Xy

y(NL (mm)

 

121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160

81.0
89.2
80.6
81.7
74.5
80.2
84.1
79.4
85.2
86.8
82.7
84.7
79.1
73.5
77.0
78.6
80.3
84.0
82.4
75.7
95.4
72.1
76.6
78.5
90.1
72.5
81.2
82.0
81.6
78.9
76.5
78.0
76.1
80.9
93.5
76.1
79.6
73.8
74.8
64.3

76.0
94.6
83.4
71.5
78.6
78.2
86. 1
73.0
85. 1
81.3
81.5
86. 1
78. 7
65.6
78.6
77. 7
73.9
70.4
79.6
68. 1
98. 1
81.3
77.0
83.0
84. 1
77. 1
86.5
103. 7
78. 7
77.5
80. 1
77. 7
75.4
83. 7
76.5
81 . 7
80.9
89.4
86.6
72.2

73.3
91.4
61 .5
96.9
76.7
81.1
81.3
67.6
64.1
83.7
78.0
90.7
92.2
77.6
74.6
72.3
79.9
81 .0
71.5
71 .8
111 .0
81.6
77.4
83.9
83.9
78.5
87.6
71.4
76.4
92.2
66.5
85.8
76.7
79.5
84.3
85.6
82.0
87.4
110.9
68.1

2.92
3.19
2.59
3.66
2.76
3.06
3.12
2.49
2.86
3.12
2.96
3.42
3.52
2.86
3.12
2.76
3.02
3.01
2.67
2.64
3.72
2.94
2.94
2.89
3.34
3.19
3.17
2.89
2.99
3.37
2.61
3.12
3.07
3.21
3.17
3.24
2.92
3.22
4.02
2.70

60.3
70.8
54.5
69.7
64.3
69.1
70.2
54.9
76.6
80.0
62.2
69.9
86.2
55.6
61.3
57.0
69.1
66.7
64.7
57 .8
83.2
59.0
67.7
66.6
55.3
56.9
77.2
58.2
61.2
63.3
60.5
47.1
59.9
59.8
62.3
65.2
57.3
84.9
74.9
58.0

3.17
3.02
2.66
3.17
2.89
2.99
2.92
2.69
2.99
3.44
3.07
2.84
3.29
2.47
2.71
2.54
2.99
2.82
2.96
2.77
3.22
2.64
2.92
2.97
2.69
3.21
3.22
2.77
2.87
2.79
2.89
2.59
2.79
3.02
2.72
2.84
2.54
3.24
3.24
2.79

29.1
45.4
29.4
35.6
20.3
32.0
28.4
24.2
25.0
31.2
30.6
31.6
33.9
26.4
25.7
24.4
32.9
30.8
31.0
29.9
41 .4
28.5
31 .2
34.4
27.8
33.4
28.8
29.6
27.1
31.6
26.4
30.8
19.8
28.4
29.2
25.8
32.0
24.3
34.7
27.0

1.96
2.94
1.92
2.79
1.67
2.02
2.00
1.64
1.74
2.14
1.99
2.12
2.04
1.87
2.07
1.87
2.12
2.04
2.04
1.97
2.34
1.96
2.12
2.14
2.09
2.24
1.92
1.94
1.99
2.02
1.84
2.42
1.64
1.97
1.92
1.84
2.07
1.79
2.34
1.87

60.6
85. 1
6 7. 1
66.0
59.9
55.8
67.3
55.6
53. 7
75.0
6 7. 1
55.9
64.0
66.4
43.8
59.6
46.0
69.6
70.3
65.0
83.3
60.0
54.0
77. 7
56.9
96.6
77.4
55.9
72.4
5 7. 1
54.3
60.3
80. 7
71.2
62.5
88.8
55.3
88.5
83. 1
63.8

1.72
2.14
1.94
1.79
1.54
1.57
1.64
1.54
1.54
1.84
2.01
1.59
1.92
1.61
1.84
1.75
1.42
1.94
1.64
1.74
2.09
1.42
1.84
1.91
1.67
2.29
1.82
1.67
2.19
1.44
1.64
1.82
1.99
1.82
2.09
1.80
1.37
1.99
1.74
1.64

49.9
59.1
43.2
46. 7
44.4
35.8
47.1
43.3
44.0
62.9
46.0
49.9
41.8
50.5
38.6
66. 7
54.6
43.2
50.6
41.4
42.4
73.1
59.3
44.5
41.9
44.6
51.4
54.5
49.1
46.9
49.9
46.0
43.6
50.4
45.9
41.0
57. 7
49.6
57.9
54.4

1.46
1.59
1.34
1.34
1.32
1.19
1.49
1.42
1.31
1.74
1.47
1.39
1.24
1.64
1.39
2.34
1.47
1.52
1.54
1.34
1.44
1.76
1.52
1.46
1.37
1.37
1.66
1.57
1.64
1.41
1.52
1.47
1.42
1.44
1.67
1.47
1.52
1.34
1.42
1.64

25.3
30.6
27.6
27.4
25. 7
25.9
23.0
22.0
24.8
29. 7
27.8
27.4
23.3
28.3
27.6
29.4
23.8
30.2
23.0
21. 7
32.9
27.8
26.2
28.8
23. 1
28.3
36. 7
21. 7
36.8
26. 7
21.5
23. 7
30.8
27.5
25.3
29.4
23. 1
22. 1
29.2
19. 7

1.18
1.24
1.09
1.02
1.04
1.09
1.06
0.99
1.15
1.22
1.37
1.09
1.12
1.19
1.27
1.09
1.09
1.32
1.01
1.30
1.34
1.19
1.07
1.24
1.07
1.14
1.61
0.91
1.84
1.19
1.12
0.94
1.21
1.14
1.06
1.23
0.92
1.14
1.09
1.06

 

150

 

 

B.4 Gala
Test date: March 1, 2001. Group: A

 

Probe: MT_K MT_N LK LK MK MK SK SK LN LN MN MN SN SN

 

Fy Xy Fy Xy Fy Xy Fy Xy Fy Xy F Xy
N0. (N) (N) (N) (mm) (N1 (mm) (N) (mm) (N) (mm) (N) (mm) W) (mm)

 

1 36.6 38.2 38.3 2.22 35.3 2.24 17.3 1.44 33. 6 1.37 22. 6 1.10 17.2 0.99
2 51.4 49.5 67.5 3.62 53.0 3.32 23.0 2.06 35.5 1.68 43.2 1.84 18. 7 1.19
3 41.1 40. 6 49.2 2.84 39.3 2.69 19.7 1.79 39. 9 1.72 34.2 1.37 18.8 1.04
4 52.5 55.2 56.5 2.84 48.6 2.79 20.9 1.82 51 . 6 2.11 40.5 1.56 20.1 1.42
5 46.6 53.0 51.4 3.24 51.9 3.09 18.5 1 .74 44. 6 2.12 36.5 1.77 20.9 1.47
6 46.8 52.8 47.3 2.54 41.2 2.69 19.4 1.64 43.4 1.87 37.0 1.61 21 . 7 1.22
7 39.1 39.8 36.6 2.14 35.9 2.17 12.4 1.32 20.1 1.14 26.6 1.22 13.0 0.91
8 50.7 55. 6 56.0 2.94 47.7 2.86 18.3 1.62 48.4 1.94 39.5 1.67 20.3 1.09
9 38.7 39.1 38.8 2.50 37.1 2.44 15.5 1.55 38. 3 1.59 21.2 1.42 13.5 1.04
10 41.8 38.8 41.8 2.22 34.9 2.32 12.3 1.34 30.8 1.19 23.8 1.04 15.4 1.02
1 1 51.6 52. 6 56.7 3.03 32.0 2.54 19.9 2.09 40.4 1.79 32.2 1.44 17. 6 1.19
12 43.6 45.2 58.0 2.94 37.6 2.44 17.2 1.82 55.9 2.19 31. 7 1.64 18.6 1.29
13 67.6 70.1 74.8 3.84 57.8 3.52 25.3 2.33 62.0 2.64 48.2 2.34 26.5 1.89
14 54.0 46.2 59.8 2.67 49.5 2.59 21.4 1.77 38. 7 1.54 36.1 1.29 18.4 0.92
15 32.5 34. 7 42.0 3.19 27.9 1.87 13.7 1.37 32.4 1.59 25.9 1.29 15.4 1.16
16 39.8 41.3 43.6 2.56 34.7 2.24 14.8 1.62 35. 7 1.72 24.5 1.34 13.3 1.07
17 34.1 40. 7 45.6 2.32 34.8 2.04 14.1 1.36 36.4 1.44 31.9 1.19 13.9 0.91
18 39.3 32.2 45.6 2.67 36.7 2.74 17.1 1.67 37.8 1.69 31.8 1.51 13.3 1.22
19 32.8 30.8 30.3 2.14 29.7 1.94 13.0 1.31 26. 9 1.29 20.0 1.12 12.5 0.87
20 59.5 53.2 59.8 3.37 52.7 3.12 20.9 1.82 48.2 2.06 36.4 1.62 21.0 1.28
21 61.4 48.3 59.8 2.96 52.3 3.07 22.5 1.84 52.8 2.01 41 . 7 1.67 19.9 1.24
22 47.5 54.2 52.2 2.77 45.1 2.89 19.0 1.82 52.8 2.07 34.8 1.99 18.2 1.04
23 47.2 3 7.9 43.7 2.62 35.9 2.17 15.6 1.47 29.1 1.32 26.8 1.34 19.3 2.17
24 49.5 50.0 59.9 2.87 48.5 2.59 22.2 1.74 39.3 1.64 29.1 1.36 19.0 1.27
25 48.8 53. 7 52.1 2.84 41.6 2.67 18.0 1.72 45. 6 1.94 27.1 1.41 17.2 1.22
26 48.2 59.9 53.0 2.54 39.8 2.34 19.6 1.66 48. 6 1.84 3 7.0 1.51 22.0 1.37
27 42.4 3 7. 7 57.0 3.46 45.3 3.37 18.5 1.96 45.8 1.91 32.5 1.94 16.8 1.27
28 25.7 27.1 26.2 1.62 21.7 1.56 11.6 1.29 19.1 1.34 25. 7 1.36 9. 7 0.94
29 36.0 37. 6 43.6 2.46 32.3 2.32 14.4 1.44 29. 6 1.36 23. 7 1.06 15.6 0.99
30 62.7 44.8 45.3 2.56 47.6 2.94 21.4 1.95 29. 9 1.48 24.9 1.27 13.4 0.84
31 69.5 66.9 74.3 3.44 52.0 2.99 23.5 1.99 52.5 1.91 42.8 1.69 22.5 1.34
32 41.2 46.1 55.8 3.07 35.8 2.29 20.9 1.99 31.0 1.37 28.8 1.29 15.1 1.02
33 43.7 59.1 48.6 3.09 44.1 2.77 20.0 2.09 51.0 2.41 39.9 2.03 21.0 1.41
34 67.6 71. 9 62.6 3.36 47.1 2.57 24.5 2.06 74.2 2.72 50. 7 1.96 25.6 1.67
35 46.8 37.2 48.1 2.37 42.4 2.44 19.3 1.82 45.6 1.84 29.0 1.36 18.5 1.06
36 45.2 39.3 40.8 2.14 40.5 2.27 15.3 1 .44 28. 7 1.27 25.4 1.27 13.9 0.87
37 42.3 43.9 50.1 2.59 30.0 2.14 17.1 1.69 34.1 1.73 27.2 1.37 16.3 1.34
38 64.7 41.2 69.4 3.72 46.5 2.89 28.0 2.34 49.3 1.81 30.2 1.42 20.0 1.14
39 55.3 5 7.2 65.4 3.04 50.1 2.84 22.3 1 .77 62. 6 2.24 44.3 1 .74 22.3 1.44
40 53.7 55.4 70.9 3.19 52.7 2.94 21.7 2.04 47.0 1.93 33. 0 1.46 20.0 1.29

 

 

151

 

 

 

 

Test date: March 11, 2001. Group: B
Probe: MT_K MT_N LK LK MK MK SK SK LN LN MN MN SN SN
Fy Xy Fy Xy Fy Xy Fy Xy Fy Xy F Xy
NO- ("1 (N) (N) (mm) (N) (mm) (N) (mm) W) (mm) W) (mm) Y(N) (mm)
41 51.8 45. 9 48.0 2.94 49.5 3.17 20.7 1.94 32.2 1.79 32.2 1.49 16.3 1.12
42 60.5 50. 6 53.8 3.12 44.5 2.97 24.9 2.32 46.5 2.32 34. 7 1.63 18.3 1.36
43 50.1 51 . 1 41.3 2.37 41.7 2.44 17.1 1.59 40. 6 1.77 30.0 1.46 17.3 1.03
44 64.5 58. 9 76.4 3.94 54.9 3.32 26.7 2.36 65. 7 2.62 35.4 1 .79 20.8 1 .60
45 36.5 35.9 31.3 2.19 28.0 2.22 14.7 1.64 30.5 1.84 30. 7 1.75 14.3 1.19
46 40.6 45. 5 54.6 2.89 38.6 2.62 17.7 1.77 33.9 1.59 31.0 1.60 18.5 1.22
47 56.5 58.2 59.8 3.59 43.2 2.89 25.1 2.07 57.0 2.09 40. 1 1.87 18.9 1 .27
48 54.2 51.4 56.5 3.12 47.3 2.77 19.9 1.72 36.5 1.97 34.1 1.49 15.4 1.19
49 30.7 38.5 40.1 2.72 32.1 2.41 13.0 1.69 32.6 2.02 24.5 1.54 15.6 1.27
50 34.9 44.4 40.8 2.54 40.8 3.02 17.3 1.84 36.9 1.79 32. 7 1.56 15. 7 1.17
51 46.2 54.2 63.4 3.64 52.9 3.59 20.0 2.02 52. 1 2.69 39.0 2.37 22. 6 1 .84
52 40.9 39.0 43.9 2.42 35.9 2.22 20.2 1.87 30. 7 1.62 31.6 1.39 16.3 1.24
53 43.1 48.4 60.1 3.39 51.3 3.12 23.1 2.02 48.1 2.07 36.8 1.67 17.2 1.37
54 48.8 38. 5 65.2 3.92 48.9 3.47 21.6 2.29 45. 7 2.39 30.0 1 .97 16.4 1.54
55 57.9 61 . 0 66.2 3.59 57.9 3.37 22.7 2.04 46. 6 2.04 40.8 1 .99 17.4 1.29
56 49.4 40.6 52.2 2.84 50.5 2.84 19.8 1.92 38.9 1.72 28.8 1.44 17.9 1.05
57 43.3 44.2 67.6 3.19 49.5 2.86 22.9 2.04 44.8 1.97 33.9 1.61 17.3 1.22
58 41.8 40. 1 44.9 2.42 42.5 2.64 17.3 1.53 44. 7 1.86 29. 6 1 .44 1 7. 5 1.12
59 29.6 24.0 28.0 1.84 28.5 2.01 10.6 1.34 20. 7 1.49 16.5 1.29 11.2 0.92
60 35.4 45. 6 46.5 2.62 35.7 2.42 17.3 1 .69 35.2 1 .79 30. 7 1 .57 16.2 1 .24
61 38.4 38.4 54.4 3.19 41.4 3.24 21.0 2.34 37.4 2.04 30.2 1.74 13.0 1.42
62 40.3 47.1 48.7 3.02 40.3 2.79 20.0 1.97 49.6 2.12 38.9 1.92 18.5 1.27
63 35.2 36. 0 44.2 2.49 34.5 2.17 16.2 1 .62 43.6 1.74 29. 1 1 .42 14.6 1 .16
64 42.1 37.5 55.1 3.14 44.2 2.96 22.7 2.12 44.0 2.29 26.6 1.74 16.2 1.39
65 55.9 65.3 61.2 3.14 47.1 2.79 21.8 2.09 60.5 2.32 36.6 1.82 19.0 1.39
66 52.8 59.8 58.6 3.34 47.0 2.89 19.7 2.08 46.3 2.29 43.2 2.12 20.1 1.84
67 37.7 39.5 36.7 2.29 34.7 2.67 16.5 1 .71 35.2 1 .64 20.8 1 .29 10.2 1.14
68 30.8 27.5 47.7 2.87 31.0 2.44 14.0 1.62 36.8 2.11 31.9 1.89 12.9 1.19
69 41.3 45.3 38.6 2.17 37.9 2.59 18.4 1.62 47.1 1.96 31.4 1.57 17.4 1.19
70 55.7 60.2 59.3 3.19 41.2 3.02 20.5 1.97 41.3 2.22 39.4 1.72 19.5 1.54
71 54.9 46.4 57.3 2.84 49.1 2.74 20.3 1.72 53. 7 2.07 37.3 1.74 18.3 1.46
72 36.5 40.0 41.9 2.59 32.3 2.24 13.0 1.66 26.9 1.49 20. 7 1.32 13. 7 1.04
73 46.4 50.0 45.3 2.59 48.1 3.02 19.0 1.88 41.5 2.14 29.4 1.74 17.0 1.42
74 43.7 37.0 38.5 2.62 36.1 2.51 13.9 1.62 34.8 1.87 26.8 1.59 11.9 1.19
75 39.3 41 . 7 33.2 2.19 38.0 2.29 15.6 1.65 27.1 1.42 23.0 1.22 12.6 0.96
76 38.3 49.3 55.5 3.54 37.5 2.79 18.5 1.97 44.4 2.39 35.3 1.96 16.9 1.52
77 40.4 38.2 41.7 2.47 42.3 3.07 18.7 1.79 39.1 2.14 29.2 1.67 15.2 1.14
78 35.6 33.5 44.9 2.64 37.6 2.64 15.4 1 .86 30.1 1.52 26.2 1 .54 12.9 1 .12
79 30.1 32. 7 37.7 2.67 34.0 2.64 13.7 1.64 28.1 1.67 19.8 1.32 14.4 1.11
80 49.6 56.5 66.7 3.39 57 .4 3.27 23.3 1.87 51.6 2.63 44.2 1.92 20.9 1.54

 

152

 

 

Test date: March 12, 2001.

Group: C

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN

SN

 

No.

(N)

(N)

Fy
(N)

Xy
(mm)

H!
(N)

X)
(mm)

(N)

Xv
(mm)

Fy
(N)

Xy
(mm)

Fy
(N)

Xy
(mm)

F
)1 N)

Xy
(mm)

 

81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120

38.1
42.6
45.2
56.0
44.0
56.2
36.8
36.1
38.7
46.5
46.2
49.9
38.8
33.0
40.9
44.1
53.7
59.2
37.7
47.8
61.3
41.2
43.5
41.8
64.5
22.1
38.5
37.7
41.9
43.0
38.8
42.8
46.8
58.2
46.2
34.2
52.3
51.5
36.8
45.0

44.9
50. 7
51.9
50.0
36. 7
58.3
42.5
35.5
38. 7
40.2
46. 1
49.2
36.0
35.8
41.9
51.2
59.1
66.5
36. 7
55.4
59.4
41.3
45.4
46.2
50.5
27.6
38. 7
46.4
49.1
40.8
43.4
41.6
42.9
58.4
45.5
35.2
52. 1
66.2
38.3
37. 7

46.4
54.2
49.3
59.8
36.0
79.6
60.1
33.0
38.4
41.3
53.4
51 .1
51.4
53.2
55.3
55.1
63.7
55.9
34.0
55.7
71.5
51 .1
50.1
44.4
67.5
30.3
29.3
41.9
71.7
53.5
34.7
42.3
44.3
61.9
42.1
35.6
60.4
46.9
35.9
44.0

2.82
2.69
2.62
3.04
2.02
3.37
3.09
1.99
2.22
2.39
2.87
2.74
2.77
2.62
2.82
2.97
2.94
2.69
2.09
2.84
3.17
2.56
2.51
2.34
3.02
1.79
1.89
2.47
3.69
2.64
1.89
2.19
2.57
3.17
2.22
2.07
2.82
2.34
2.12
2.47

34.1
34.1
27.7
46.0
39.1
57.3
35.7
29.2
31.0
39.4
46.0
40.1
47.9
40.1
42.0
40.4
42.5
41 .8
26.5
44.5
55.8
31.8
41 .4
39.2
49.6
24.5
38.4
36.6
41.9
50.5
34.1
31 .2
40.1
54.6
40.2
27.1
42.7
42.2
31 .8
35.9

2.47
2.19
2.09
2.96
2.60
2.97
2.42
1.90
2.07
2.34
2.72
2.41
2.87
2.31
2.49
2.76
2.69
2.72
2.01
2.53
3.14
2.14
2.74
2.59
2.67
1.87
2.49
2.39
2.82
2.74
2.14
2.14
2.74
3.04
2.32
1.99
2.47
2.54
1.94
2.37

17.8
19.2
16.0
25.6
16.7
26.8
18.8
14.4
15.1
20.7
20.5
17.1
19.0
17.5
14.9
17.2
21.8
17.8
13.8
18.8
19.6
19.0
19.6
17.1
18.1
12.1
14.1
13.4
20.9
16.8
13.7
14.7
16.0
23.9
17.8
13.8
20.0
17.1
12.4
18.6

1.77
1.69
1.57
2.17
1.62
2.04
1.92
1.34
1.54
1.71
1.77
1.54
1.79
1.57
1.44
1.79
1.77
1.64
1.26
1.69
1.62
1.67
1.67
1.66
1.82
1.24
1.61
1.67
2.09
1.62
1.39
1.30
1.82
2.19
2.14
1.41
1.79
1.64
1.42
1.69

35.3
39.4
46. 1
41.5
27.4
49.3
39.9
28.4
32. 7
45.3
47. 1
42.9
36.5
35.2
42. 7
41 . 7
38. 1
52.5
21.3
61.3
48.6
36. 6
33.8
36.9
41.0
24.6
25. 7
56. 7
46.2
3 7. 1
22.5
23. 1
36.9
57.0
33.3
33.9
42. 6
54. 7
22.3
35.0

1.79
1.74
1.74
1.64
1.22
1.70
1.84
1.44
1.49
1.84
1.79
1.74
1.69
1.47
1.81
1.99
1.82
1.84
1.12
2.87
1.93
1.77
1.32
1.41
1.72
1.42
1.39
2.14
2.06
1.59
1.17
1.27
1.92
2.04
1.39
1.44
1.77
1.79
1.24
1.54

39.2
30.5
36.4
23.2
22.2
52. 1
34. 1
18. 1
26.9
26.5
32.8
35.4
30.8
20.3
39.3
29.0
33.9
35.2
18.6
35. 7
32.8
28.2
27.4
27.2
35.8
22.2
23.5
36.6
32.6
39.0
19.4
23.0
26.4
40.5
26.5
23.5
31. 1
33.4
23.5
33.0

1.69
1.32
1.69
1.47
1.29
1.79
1.67
1.14
1.15
1.29
1.69
1.61
1.39
1.32
1.82
1.69
1.62
1.49
1.04
1.47
1.44
1.34
1.27
1.17
1.79
1.39
1.19
1.72
1.72
1.54
1.12
1.22
1.56
1.72
1.39
1.27
1.41
1.49
1.24
1.39

21.0
15.7
15.2
18.2
13.6
21.5
19.0
13.9
14.9
15.9
19.4
17.3
18.4
15.8
20.4
15.1
20.7
23.3
12.8
18.7
19.0
13.3
13.3
11.9
18.2
11.7
12.3
19.2
14.9
12.6
13.1
12.7
16.8
20.2
16.7
13.0
14.0
19.0
11.0
14.6

1.37
1.21
1.22
1.34
1.14
1.22
1.49
1.07
1.29
1.17
1.42
1.46
1.22
0.97
1.47
1.12
1.37
1.24
0.99
1.17
1.04
1.07
0.94
1.07
1.34
0.94
1.19
1.38
1.49
1.12
0.87
0.87
1.24
1.52
1.12
1.04
1.19
1.14
0.89
1.33

 

153

 

Test date: March 13, 2001.

Group: D

 

Probe: MT_K MT_N LK

LK

MK

MK

SK

SK

LN

LN

MN

MN

SN SN

 

Fy
No. (N) (N) (N)

Xy
(mm)

F)!
(N)

X)
(mm)

Fv
(N)

Xy

Fy

(mm) (Ni

Xv
(mm)

Fy
(N)

Xy
(mm)

F Xy
NM (mm)

 

 

121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160

32.0
43.9
36.6
51 .6
41 .5
35.1
52.4
52.3
42.2
38.0
51 .9
34.5
49.1
38.0
43.1
54.2
29.4
41 .0
44.9
43.9
42.7
41 .3
46.1
46.1
38.0
46.4
36.7
32.7
32.7
45.0
43.7
66.6
47.0
47.4
44.4
49.0
72.4
53.8
60.5
78.0

35. 1
38.4
40. 1
50.4
40.4
36. 7
51.5
58.2
45.0
36.5
59.5
28.5
58.3
41.3
35.2
43.3
55.0
29. 7
39.8
59. 7
45.8
46.8
50. 6
44.9
47.4
43.3
38.5
41. 6
45.0
52.0
41.8
44.8
46.9
46.5
35.3
56.9
68.5
62. 6
61. 1
84.0

40.0
56.1
45.8
48.9
51 .8
39.9
75.8
64.1
57.2
44.5
69.4
36.7
49.5
44.2
45.5
49.1
60.0
38.2
39.3
52.5
56.4
37.2
48.1
48.5
47.7
58.5
66.3
47.8
40.6
55.0
59.9
61 .2
67.5
54.1
50.8
52.0
77.0
72.8
55.5
72.8

2.31
3.1 1
2.69
2.63
2.82
2.09
3.79
3.46
3.27
2.44
4.19
2.44
2.52
2.49
2.84
2.84
3.02
2.57
2.32
2.77
2.84
2.14
2.57
2.92
2.39
3.04
3.64
2.77
2.57
2.54
3.44
3.39
3.67
3.06
2.67
2.74
4.17
3.34
2.89
3.02

32.5
46.9
33.6
39.8
33.3
34.2
53.2
50.0
39.7
32.4
49.2
33.1
41 .6
34.7
39.0
37.3
44.1
27.3
32.4
49.3
48.6
45.7
35.9
44.5
36.7
38.8
40.7
39.8
33.3
48.5
48.9
47.6
52.1
39.7
42.8
37.1
58.3
49.1
42.6
52.3

2.32
3.29
2.44
2.29
2.12
2.14
3.24
2.89
2.39
2.32
3.17
2.24
2.51
2.16
2.64
2.31
2.79
2.17
2.06
2.87
2.78
2.64
2.31
2.79
2.31
2.42
2.57
2.74
2.27
2.72
3.26
2.87
2.89
2.49
2.42
2.34
3.64
3.04
2.62
3.04

13.2
21.4
18.5
19.5
17.1
14.2
21.8
23.5
18.4
12.5
25.6
14.3
18.2
12.5
20.1
13.7
18.4
12.2
17.1
19.2
19.5
15.6
11.8
13.9
14.6
15.0
20.4
16.6
15.7
19.8
24.8
25.4
22.9
21.4
16.7
16.9
24.6
21.5
19.1
21.5

1.44
1.99
1.84
1.64
1.55
1.36
2.29
1.99
1.87
1.27
2.39
1.57
1.66
1.37
1.84
1.38
1.82
1.46
1.39
1.73
1.89
1.59
1.31
1.57
1.54
1.79
1.91
1.69
1.57
1.62
2.24
2.17
2.04
1.87
1.49
1.62
2.19
1.94
1.84
1.99

31.4
40. 7
29.9
45.4
44.2
28.9
54. 7
49. 7
48.6
40.4
53.5
25.9
46.0
27.4
41.0
43.2
52.4
31 . 7
39.2
69.8
50.8
38.2
39.2
44.4
45.0
50.5
34.8
47.9
43.9
51.5
42.5
44.4
60.0
56.8
28. 7
57.8
54. 1
42.8
54.2
63.3

1.44
2.20
1.84
1.69
1.94
1.39
2.27
2.14
2.19
1.54
2.79
1.84
1.72
1.56
1.74
1.74
2.19
1.64
1.39
2.66
2.1 1
1.59
1.67
1.97
1.74
1.81
1.79
2.22
1.94
1.79
2.19
1.77
2.29
2.37
1.52
2.19
3.02
1.82
2.16
2.65

21.6
24.4
22.2
33.9
30. 7
24.2
52.9
41.9
27.3
26.4
50.3
20.2
28. 1
29.2
35.0
24. 7
37.4
20.2
28.2
42.8
36.4
32. 7
29. 7
28.2
31.3
30.2
28.8
32.9
35.9
36.6
31.6
33.4
44. 7
32.0
32.3
46. 7
44.8
42.5
35.6
43.9

1.44
1.39
1.42
1.37
1.64
1.39
2.12
1.64
1.51
1.29
2.24
1.59
1.29
1.36
1.47
1.44
1.93
1.44
1.22
1.99
1.84
1.42
1.62
1.62
1.57
1.62
1.69
1.62
1.76
1.56
1.87
1.44
1.87
1.60
1.37
1.96
2.22
1.91
1.69
1.81

15.0 1.12
15.6 1.27
13.2 1.24
20.4 1.34
15.1 1.17
12.7 0.92
27.5 1.62
23.2 1.34
16.1 0.99
15.2 1.07
25.8 1.67
13.4 1.16
18.1 1.39
14.4 1.19
15.9 1.04
16.3 1.22
19.8 1.39
11.6 1.39
15.0 1.01
21.4 1.40
19.3 1.37
15.7 0.97
15.2 1.17
17.7 1.32
22.4 1.47
20.8 1.29
17.6 1.29
20.7 1.48
20.7 1.48
17.2 1.02
18.5 1.09
18.2 1.24
17.6 0.99
19.5 1.32
20.2 1.40
21.0 1.30
21.4 1.72
21.5 1.57
19.8 1.27
21.5 1.39

 

154

 

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