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VISCOELASTIC BEHAVIOR AND WEAR OF
POLYMERIC LINERS FOR JOINT
REPLACEMENT

presented by

XIAOYAN LU

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VISCOELASTIC BEHAVIOR AND WEAR OF POLYMERIC LINERS
FOR JOINT REPLACEMENT

By

XIAOYAN LU

A THESIS

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
for the degree of

Master of Science
Chemical Engineering

2010

ABSTRACT

VISCOELASTIC BEHAVIOR AND WEAR OF POLYMERIC LINERS FOR JOINT
REPLACEMENT

By
XIAOYAN LU

Ultra high molecular weight polyethylene has been widely used as the liner
material in joint replacements. Further improvement requires a model for wear
that takes into account the viscoelastic behavior of UHMWPE.

The ﬁrst step to achieve this task is to chararcterize the linear viscoelastic
behavior of UHMWPE with dynamic mechanical experiments. The compression
molded and ram extruded UHMWPE rectangular bars were tested ﬁrst in strain
sweep test in order to ﬁnd the linear viscoelastic region at body temperature.
They are then tested in frequency sweep test for the storage and loss modulus
data and the resulting data were used to estimate the relaxation spectrum of the
material through GENEREG ﬁtting program.

The wear test is also conducted on Taber Abrasor wear machine. The H-18
Calibrade wheels are selected for the tests. The compression molded and ram
extruded UHMWPE discs are tested separately and the results are compared.

Archard’s law is applied to the wear test results to ﬁnd the wear factor.

ACKNOWLEDGMENTS

I would like to express my gratitude to my supervisor, Dr. K. Jayaraman,
whose expertise, understanding, and patience, added considerably to my
graduate experience. I appreciate his vast knowledge and skill in many areas,
and his assistance in writing thesis.

I would also like to thank my group members: John Mills, Tanmay Pathak,
Katie Shipley, Amit Chaudhary and Rahul Rane. They have helped me a lot in my
research.

Very special thanks go out to Michael Rich, Ed Drown and composite center
which has provided me with equipments and helped, me in my tests. I must also
acknowledge MediTECH Medical Polymers in Indiana and Lou Matrisciano to

provide me with the samples needed for tests.

Table of Contents

LIST OF TABLES

 

LIST OF FIGURES

"II
v"

 

LIST OF SYMBOLS
CHAPTER 1 Introduction

.A

 

 

Joint Replacement

 

1.1
1.2 Ultra High Molecule Weight Polyethylene
1.3 Wear problem of UHMWPE

 

 

1.4 Research purpose and work
CHAPTER 2 Wear and \fisooelasticity

N U'IOON—‘t

 

 

2.1 Wear of UHMWPE
2.2 Wscoelasticity

 

 

CHAPTER 3 Experiment Procedures

20
20

 

3.1 \flscoelastic Experiments
3.2 Wear experiments of UHMWPE

23

 

CHAPTER 4 Viscoelastic Experiments Results

27

 

27

 

4.1 Strain Sweep Tests

 

4.2 Frequency Sweep Test
4.3 GENEREG Data Fitting

29
31

 

 

CHAPTER 5 Wear tests results

42
42

 

5.1 Selection of wheels

43

 

5.2 Results of wear experiments

 

5.3 Calculation of parameters
CHAPTER 6 Conclusion and Future Work

BIBLIOGRAPHY

AO

‘YU

52

 

iv

List of Tables

 

Table 3.1 Summary of mean values 21
physical and tensile mechanical properties of UHMWPE sample

 

 

Table 3.2 Technical data of ARES 21
Table 3.3 Standards components of Abraser Model 5130 24
Table 4.1Eight pairs of relaxation time and relaxation spectrum ---------32

for compression molded UHMWPE GUR 1050

Table 4.2 Eight pairs of relaxation time and relaxation spectrum 33
for ram extruded UHAMWPE GUR 1050

 

Table 4.3 Eight pairs of G5 and ill-for compression molded UHMWPE-W35
GUR 1050

Table 4.4 Eight pairs of G,- and 1.,- for ram extruded UHMWPE GUR 1050—~36

 

 

 

 

Table 5.1 Wear results for three kinds of wheels 43
Table 5.2 Wear test compression molded GUR 1050 44
Table 5.3 Wear test ram extruded GUR1050 44
Table 5.4 Estimated contact area and pressure for different loads 46

Table 5.5 Estimate the wear factor for compression molded GUR 1050-----—47

 

Table 5.6 Estimate the wear factor for ram extruded GUR 1050 48

List of Figures

Figure 2.1 Four kinds of modes of wear in THR 9

 

Figure 4.1 The effects of strain on the dynamic storage modulus (G‘ ) and—«~28
loss modulus (G") for compression molded UHMWPE GUR 1050

 

 

 

Figure 4.2 The effects of strain on the dynamic storage modulus (G' ) and 28
loss modulus (G") for ram extruded UHMWPE GUR 1050

Figure 4.3 Storage modulus and loss modulus at different frequency for-----30
compression molded UHMWPE GUR 1050

Figure 4.4 Storage modulus and loss modulus at different frequency 30
for ram extruded UHMWPE GUR 1050

Figure 4.5 Experiment results and predicted results of loss modulus -- 37

at different frequency for compression molded UHMWPE GUR 1050

Figure 4.6 Experiment results and predicted results of storage modulus 38

at different frequency for compression molded UHMWPE GUR 1050

 

Figure 4.7 Experiment results and predicted results of loss modulus—----—---38
at different frequency for ram extruded GUR 1050

Figure 4.8 Experiment results and predicted results of storage modulus at ---39
different frequency for ram extruded GUR 1050

Figure 4.9 Relaxation time distribution of compression molded- GUR 1050-——40
Figure 4.10 Relaxation time distribution of ram extruded UHMWPE GUR 1050-40

Figure 4.11 Comparison of relaxation spectrum of compression molded and-41
ram extruded GUR 1050 at 37°C

vi

THR

TKR

PTFE
UHMWPE
FIE

AP

G

G’

G”
GENEREG

ARES

Key to Symbols or Abbreviations

total hip replacements

total knee replacements
polytetrafluoroethylene known as Teﬂon
ultra-high molecule weight polyethylene
ﬂexion/extension

anterior-posterior

stress-relaxation modulus

shear storage modulus

dynamic shear loss modulus

generalized nonlinear regularization method

advanced rheometric expansion system

vii

Chapter 1 Introductions
1.1 Joint replacement

Joint replacement is conducted to replace damaged parts of joints with
artiﬁcial ones to allow joint movement. Total joint replacement can be performed
on any joint in the body. Among all the joint replacements, the total hip
replacements (T HR) and the total knee replacements (T KR) is the most common
ones which have helped millions of patients lead to more active life after
osteoarthritis or joint injury.

The joint replacements are considered as one of the most successful surgical
procedures in surgery history. According to the statistics, in 2004, 234,000 total
hip replacements and 478,000 total knee replacements performed in United
States [1]. However, the cases are increasing very fast, especially in the US. The
scientists estimated that the number would reach 3.5 million per year in US for hip
replacement alone by the year of 2030 [2].

The general mode for joint replacement, taking hip replacement as an
example, is an acetabular component, a femoral component and a femoral ball
(head). For the acetabular cup, it is often designed as a cementless component
with a bearing liner installed on the metal backing. The implant for a total knee
replacement is composed of 4 parts: the tibial and femoral components, an inner
liner and the patella. The inner liner acts as the bearing surface which may be

made from different materials such as ceramic, metal or plastic.

The ﬁrst joint replacement reported is a hip replacement in German and ivory
is used to replace the femoral head in the surgery. The modern design of an
artiﬁcial joint went back to Sir Chamely in 19605 [3]. His design of artiﬁcial joint is
a plastic on metal articulation and he chose polymer material as liner based on his
assumption that an extremely low coefﬁcient of friction is needed in articulation.
When Sir John Chamley ﬁrst carried out his design of joint replacement, he used
polytetraﬂuoroethylene (PTFE), commonly known as Teﬂon as the bearing
material. His ﬁrst hip replacement device is an artiﬁcial socket surrounding a
metal ball of 41.5mm in diameter. The diameter of the metal ball gradually
decreased to 22.25mm due to the wear of PTFE. Teﬂon was found to be
inappropriate due to its poor performance of resisting creep deformation and wear
[4]. Hence, the use of PTFE is replaced by a kind of polymer exhibits greater wear
resistance. Ultra-high molecule weight polyethylene(UHMWPE) came into use in
1962 by Sir John Chamley and became the most widely used liner material for
total hip and knee replacements in the 19705 [5].

Although several kinds of materials, including metallic alloy and ceramics are
used as the liner, the most successful total hip and knee replacements are based
on UHMWPE-metal-joints [5].

1.2 Ultra High Molecule Weight Polyethylene
UHMWPE is an organic polymer that is widely used as the bearing material in

hip, knee and elbow joint replacements. It is also used in automotive and bottling

industries due to its resistance to wear and impact [6].

UHMWPE is polymerized by ethylene, and its average molecular weight can
reach more than 106. UHMWPE is a semicrystalline polymer which has both
crystalline and amorphous phases. From micro-structure, the crystalline domain is
I actually embedded in an amorphous matrix. The crystals of UHMWPE are in the
shape of ribbon lamellae, which sandwich amorphous layers. The polyethylene
chains are in ﬁxed position in lamellae to form a lattice structure [7].

Conventional UHMWPE is produced to resin from ethylene gas. Since 19505,
the UHMWPE powders have been produced by Trcona through Ziegler process.
Ethylene gas and hydrogen are the reactants and titanium tetra chloride acts as
the catalyst. Then the resin is consolidated through compression molding or ram
extrusion. Orthopedic components can be machined from the consolidated
material or can be molded directly from the resin.

UHMWPE has been chosen as liner in joint replacement because of its
biocompatibility, toughness, and good sliding abrasion resistance. Although
UHMWPE has gained widely acceptance as the liner in joints, the wear problem
of UHMWPE is now the main barrier that limits the longevity of knee or hip joint
replacement [8].

1.3 Wear problem of UHMWPE
The wear problem has not been recognized until 19903. The concern is not

that the UHMWPE liner can be worn out since the wear rate is only 0.1 to 0.2 mm

per year. Local osteolytic reaction to submicron-sized polyethylene wear debris
can lead to aseptic loosening, which is the main failure of total joints replacements
[9]. Aseptic loosening means that the bond between the skeleton and the artiﬁcial
joints weakened and left the joints loosen.

In order to solve the wear problem, scientists have made efforts to change
the chemical structure, crystalline organization or other properties to improve its
mechanical performance. One of the successful methods is cross-linking of
UHMWPE. The wear resistance can be increased by cross-linking of UHMWPE.

In recent years, cross-linking of linear UHMWPE has been studied by
different research groups. Wear tests have shown that the wear rate decreases
with the increase of cross-linking density of UHMWPE [10]. Cross-linking of
UHMWPE can be achieved through ionizing, radiation or chemical methods with
the use of peroxides and silanes. These methods can generate free radicals,
which further react to form covalent bonds to crosslink polymers. Although
cross-linking improves the wear resistance, it also reduces the mechanical
properties of UHMWPE, especially the decrease of elongation at break and
impact toughness. There is a reported decrease in the static and cyclic fracture
behavior of UHMWPE on cross-linking [11].

Some other researchers are also trying to develop proper polymer composite
to solve wear problem. Tanniru and Misra [12] found that the inclusion of inorganic

calcium carbonate particles increased the impact toughness of UHMWPE by up to

50% of the decrements caused by cross-linking. Gong Guofang [13]
incorporated the mineral kaolin during UHMWPE polymerization and reduced the
wear rate by over 40% comparing to the pure UHMWPE with the same molecule
weight. Similar results were found using quartz [14], alumina [15], quasicrystals
[16] carbon ﬁber and a variety of nano—ﬁllers. The use of more compliant materials,
either as a stand-alone bearing material or as a composite constituent in polymer
composites [17] may reduce contact pressures and friction coefﬁcients at wear
interfaces, thereby reducing the total wear rate. However, the biocompatibility of
many of these materials is not well established, and thus, other avenues must
continue to be investigated.
1.4 Research purpose and work

In order to evaluate the new design and material for bearing surfaces in joint
replacement, wear evaluation methods will need to be developed. The commonly
used wear testing methods are pin-on-disc wear testing and wear simulator.
There are shortcomings of both ways of wear testing. Wear simulator is time and
money-consuming, while pin-on-disc test cannot simulate the actual situation
which makes it not accurate enough. Computational wear prediction delivers
high-speed, low-cost simulations designed to either replicate in—vitro conditions or
else directly simulate in-vivo conditions [18]. The computational wear prediction
can provide a more convenient way to evaluate the new materials and design of

joint replacements and it can also serve as a theory guide for further study of wear

problem.

Although different computational models have been developed before, there
is no model involving the nonlinear behavior of UHMWPE. Further improvement
requires a model for wear that takes into account the viscoelastic behavior of
UHMWPE. ln wear prediction model, a wear equation and a material stress-strain
relation equation are needed. In my work, two parts of work have been done.

The viscoelastic behavior of UHMWPE is described by strain sweep test and
frequency sweep test. The relaxation spectrum can be calculated through
GENEREG data ﬁtting. The relaxation spectrum is the parameter that can be
used for modeling linear viscoelastic or non-linear viscoelastic behavior of
UHMWPE. The viscoelastic model of material can then help predict the pressure
on the liner more precisely. The wear test is conducted on Taber Abrasor wear
machine. The compression molded and ram extruded UHMWPE discs are tested
and the results are compared. Archard’s law is applied to the wear results in order

to calculate the wear factor.

Chapter 2 wear and viscoelasticity
2.1 Wear of UHMWPE
UHMWPE is extensively used as a bearing material in joint replacements for
over forty years [19]. During the last 10 years, it has become recognized that
UHMWPE particles is a major cause to failure of joint replacement [20].
2.1.1 Wear mechanism and wear mode of UHMWPE

Wear can occur through ﬁve major mechanisms, abrasion, adhesion, third
body, fatigue and corrosion [9]. Abrasive, adhesive and fatigue wears are the
dominant wear mechanism in acetabular hip and tibial knee components.

The abrasive wear occurs between surfaces of different relative hardness.
The micro roughened regions and very small asperities on the harder surfaces will
plow through the softer surfaces and remove the softer material away.

The adhesive wear occurs when the atomic forces occurring between the
materials in two surfaces under relative load are stronger than the inherent
material properties of weaker surfaces. in joint replacements, adhesive wear
usually occurs when polyethylene surface adhere to the metal bearing surface.

Third-body wear occurs when hard particles become embedded in a soft
surface. It is actually a kind of abrasive wear. ln joint replacement, the third-body
wear usually happens when metallic or bone particles embedded in a
polyethylene bearing surface. Hard third-body particles such as bone cement can

cause wear to both polymer liner and metallic alloy parts as well [21].

Fatigue wear occurs when surface shear stresses or strains on the softer
surface exceed the fatigue limit of the material. Under the repeated and cyclic
loading conditions, subsurface delamination and cracking may happen and
eventually lead to release of polyethylene particles. The fatigue wear of
polypropylene has been attributed to the surface damage of material [22].

Corrosive wear is one kind of third body wear. In corrosive wear, the liberated
corrosive debris acts as a third body in wear mechanism.

Except for wear mechanism, wear mode is another concept related to the
wear of joint replacement. Most of the wear occurs at the articulating (bearing)
surfaces, but some of it also occurs at nonarticulating surfaces. This led McKellop
group to introduce four kinds of modes (Mode l to Mode lV) [23][9] to describe it.

Mode l involves motion occurring only between the two primary bearing
surfaces, such as the UHMWPE liner of the acetabular cup and the head of the
femoral component in. Mode ll involves articulation between a primary bearing
surface and a secondary one and occurs when one primary bearing surface has
penetrated the other following excessive mode I wear. An example is the rubbing
of the femoral head against the acetabular cup metal shell following the
penetration of the liner by the head. Mode lll involves articulation between the
primary bearing surfaces but with interposition of third-body particles, such as
acrylic bone cement fragments. Mode lV involves micro motion between

secondary surfaces as happens, for example, between the liner and shell of the

acetabular cup or at the Morse-taper junction in a modular THR.

A

     

Mode-1 Mode-2 Mode-3
Normal wear Micro-separation wear 3—body abrasive wear

D E

..-,-;-,:::'-'-,';=':‘.‘;'; tr.

    

Mode-4A
impingeme
nt wear
Modes of Debris
Generation in
'Mode-4B THR

'Backside' wear

Figure2.1: Four kinds of modes of wear in THR (From Implant Wear in Total Joint
Replacement: Clinical and Biologic Issues, Material and Design Considerations)

It is important to realize that one or more wear mechanisms may operate
during the duration of its clinical life. The most important mechanism is the
adhesive and abrasive wear. The four different kinds of mode may all happen in
joint replacements. Mode l is the prime mode in the joint replacements, which
is also the reason to improve the wear resistance of UHMWPE liners. On the
other hand, Mode II, III and IV often trace back to the design of joint replacement

and they are not in consideration here in the research.

2.1.2 Wear Testing Methods

Wear testing is an important part in the research of joint replacement and in
the work of improving the wear resistance of UHMWPE. There are mainly two
kinds of wear test for UHMWPE in joint replacement—the joints simulator and the
pin-on-disc experiment. The complicated machine known as hip simulator or knee
simulator can imitate the clinical gait. Take knee simulator for example, it can not
only produce the cyclic loading, but also the ﬂexion/extension (FIE), tibial rotation,
anterior-posterior (AP) sliding, and other freedom of human knee [24]. However,
the price of this kind of simulator is usually more than two hundred thousand
dollars, which is expensive for all the research to take. In addition, a joint
simulator test will usually take relatively long time.

A less expensive and more convenient way is to do the pin-on-disc wear
testing. Although it is not as precise as the simulator, it is a good way to generally
evaluate the performance of UHMWPE in joint replacement. Pin-on-disc testing
method is the standard method to test the friction coefﬁcient and wear resistance.
The pin-on-disc tester usually contains a stationary pin and a rotating disc. The
pin-on-disc wear testing machine for joint replacements tests is often consisted of
a ﬂat pin of UHMWPE and a metallic alloy disc—the component of load bearing in
arthroplasty. When pin-on-disc wear test is conducted, the lubricant type, load
magnitude, magnitude of the relative surface velocity, and several other

parameters will all need to be investigated and adjusted [25].

10

2.1.3 Wear prediction by modeling methods

In order to understand the wear mechanism and improve wear resistance of
UHMWPE, researchers have paid special attention to the numerical modeling of
the wear and material property.

There are mainly two concerns on wear prediction of UHMWPE in joint
replacements. First of all, it can help test the existing methods used for
decreasing wear in joint replacement. There are shortcomings of both ways of
wear testing. Wear simulator is time and money-consuming, while pin-on-disc test
cannot simulate the actual situation which makes it not accurate enough.
Computational wear prediction is an attractive concept for evaluating new total
knee replacement designs prior to physical testing and implementation [26]. It
provides a more convenient way to evaluate the new materials and design of joint
replacement. More importantly, with wear prediction relates the wear and material
properties, a theory guide can be provided for further study of wear problem.
Although progress has been made in reducing wear, there is not enough theory to
guide the attempts. If a model that relates the material property and wear can be
developed, it can direct the research on improving wear resistance of materials.

Different models have been proposed for predicting wear. The models
require the input of the in vivo surface kinematics and contact pressure. In the
study of computational models, explicit ﬁnite element models and the material

properties models are applied to predict contact pressure and joint kinematics

11

during a gait cycle. A parametric material model needs to be developed to
describe the stress-strain behavior of UHMWPE in the model.

In the wear prediction of total knee replacements, early models only
incorporated monotonic loading and were based on bilinear elastic or
elastic—plastic approximations of the stress-strain behavior of UHMWPE [27]. For
example, Estupinan et al. simulated the effect of a moving cyclic load on the
stress distributions near the surface of an idealized, two-dimensional UHMWPE
block. The UHMWPE was modeled using a quadrilinear approximation of the
yielding behavior up to a true strain of 0.12, and then was simulated by classical
isotropic J2-plasticity theory [28]. Godest et al. [29] and Sathasivam S [30]. has
used a three-dimensional ﬁnite element method with an elastic-plastic model to
predict the wear of UHMWPE. However, the mechanical behavior of polymeric
materials is time— and temperature-dependent, and the stress—strain behavior
even prior to yield is often nonlinear. Thus, constitutive relationships for polymeric
materials should incorporate a continuous description of material response as it
transitions from linear elastic to viscoelastic and viscoplastic behavior. Fregly et al.
[31] has used an elastic model to predict the contact pressure of UHMWPE in
total joint replacement. The stress strain behavior in his prediction is a nonlinear
material model.

In the wear prediction of total hip replacement, the situation is the same as

the knee replacement models. The early models also use a simple elastic or

12

elastic-plastic material model. Maxian [32] ﬁrst proposed the ﬁnite element
computational wear models based on simple wear theory—Archard's equation
and a linear elastic equation for UHMWPE material model. Scifert [33] provided a
more complex 3-D nonlinear ﬁnite element to analyze the hip stress distribution.
S.H. Tech [34] involved the elastic-plastic model in the ﬁnite element modeling.
2.1.4 Archard’s law

In order to predict the wear rate of UHMWPE in joint replacements, a wear
theory is needed to combine the relevant components such as load, geometry or
material properties together. The precise mechanisms of TKR and THR wear are
different, but the wear rate for both of them can be attributed to contact stress,
contact area and motion of contact area [35].

A simple wear theory—Archard’s law can be used to calculate surface wear of
UHMWPE in joints. Although Archard’s law was ﬁrst designed for dry sliding of

metals, it can also be used for polymeric materials [36].

n n
§wear = kZpidi = kZPiIViIAt (1)
i=1 i=1
kis material wear factor which can be determined by experiment. nis the
number of instants that we measure other variables in the equation and i is the
i th instant. pi is the contact pressure on liner on certain instant. di is the

sliding distance that can be represented by velocity multiple by time [37]. Wear

13

factor can be determined from actual simulator or wear test. For example, T M

McGloughlin has proposed a wear factor 2.64X 10 '7mm3/Nm in 2004[38].
However, one thing we need to consider is that whether this simple linear

Archard's law is suitable for UHMWPE wear. There is more complex equation for

Archard’s law for polymer,

VZKWthn (2)

Where, v is the velocity, t is the time and n is the functional
time-dependence (often less than 1). This exponential form of law has also been
suggested [39].

2.2 Viscoelasticity

Ever since the nineteenth century, Maxwell, Boltzmann and some other
scientists found that materials like silk, rubber, or glass showed time-dependent
phenomena in elastic response. At different strain rate, which is the rate at which
deformation occurs or the time rate of loading a test specimen, the polymer
actually behaves differently. When the strain rate is low, the elastic-plastic
behavior can roughly represent the behavior of polymer. When the strain rate is
high, the viscoelastic behavior cannot be neglected.

Polymer is a kind of viscoelastic body, which means that polymer is elastic
when it recovers and viscous when it creeps. Unlike purely elastic or viscous

substances, a viscoelastic substance has an elastic component and a viscous

14

component. in linear viscoelasticity, the stress strain relationship is the
combination of simple elastic behavior which obeys Hook’s Law and simple
viscous behavior which obeys Newton’s viscous law [40]. For the non-linear
viscoealsticity, it is often occurs when the deformation is large. Because of the
viscosity of the polymer, it has a time-dependent strain and stress respond. Creep
and stress relaxation are two phenomena related to viscoelasticity of polymer.
2.2.1 Creep and Stress Relaxation

Creep is the strain response at a ﬁxed stress [41]. For a creep experiment, a
constant stress is applied to polymer specimens at the time t o and removed at
timet, and the strain of the specimens displays to betime-dependent. It is often
increases with time under a certain stress.

Creep compliance J (t) is deﬁned as the ratio of strain and stress. 0' is the

ﬁxed stress and 7(t) is the measured strain at different time t .

J“): 7;!) <3)

 

Stress relaxation experiment describes the respond stress to constant stain
of polymers. A polymer specimen is held to a constant strain 71' from time to to
t , and the stress is found to be decreasing as the time increases.

The stress-relaxation modulus at timet is deﬁned as

G ___ art)
(t) 7, <4)

15

7 is the ﬁxed strain and 0(t) is the measured stress at different time t.

From the plot of stress relaxation curve, we can see the stress jumps to a
certain value and then decays exponentially. The G(t)— t is also often plotted
on log-log plot. G(t) and J (t) can represent each other by mathematical
equations[42].
2.2.2 Dynamic Experiment

In addition of creep and stress relaxation experiments, another type of
measurement is also quite common for the viscoelastic behavior of polymers. The
stress and strain in the experiments is an oscillatory function with an angular
frequency to, which has the unit of rad/s. The dynamic experiments can give the
dynamic shear storage modulus (G‘) and dynamic shear loss modulus (G") [41].

During the test, the force amplitude with the proper geometric quantities of
the samples will give the stress amplitude 0'0. The motion detector with the
thickness of the sample between the plates will give the amplitude of the shear

strain 70. The ratio of these two would be the modulus. The two kinds of modulus

are deﬁned:
G'= (0'O /70)cos5 (5)
G'=(0'0/70)sin6 (6)

G‘ is the shear storage modulus and G" is the shear loss modulus. G‘ is

actually the stress measured at the maximum strain divided by the strain

16

amplitude 70 , which is the strain of wt=n/2. G" is the stress divided by 70 at

zero strain, which is wt=0. i5 is the phase angle.

tan 6 is the loss tangent. It is the ratio of lost energy to stored energy.

tan 5 = — (7)

0
2.2.3 Linear Viscoelasticity

All viscoelastic material has the linear viscoelastic region when applied
relative small strains. The linear viscoelasticity is a simple model combines the
elastic and viscous behavior. The elastic part obeys Hook’s Law and viscous part
obeys Newton’s viscous law [43]. Also, the stresses act independently and strains
can add linearly for viscoelastic response. This property can be described by
Boltzmann Superposition.

Boltzmann Superposition Principle can be used to predict the linear
viscoelastic behavior of polymer.

The main theme of Boltzmann superposition is that the stress resulted from
one step is independent of the other steps. For the same reason, we can also say
that the strain resulted from one step of stress is independent of the others.
Boltzmann Superposition principle is one of the most important theories in
polymer physics. With this theory, the two stresses on the polymer act
independently and the strains can add linearly [44]. The principle can also be

expanded to several stresses and expressed by:

17

7(t)=ZUiJ(t—Si) (8)

i=1
In the equation, 0',- is i th the stress increment, J is the creep

compliance. If a continuous stress is applied, an integration result can be used:

 

y(t) = [00 62:8).1 (t — s)ds (9)

According to analogous method, we can also ﬁnd the equation for stress

0(t) given by the continuous strain 7(t):

0(t) = [w-alagﬂat — s)ds (10)

2.2.4 Relaxation time and relaxation spectrum
The relaxation function, by its physical meaning, is a decreasing function time
having zero limit at t and at 0°. The functions of such type can be presented by

the integral:
G(t) = [H (ZR—”d1 (11)
0

Where I1 is the relaxation time and H (’1) is a function of distribution of

relaxation times, or relaxation time spectrum as measured in shear.
From a mathematics point, relaxation spectrum is called Laplace transform.
The theory in mathematics says that any decreasing function, such as relaxation

function, can be represented by the Laplace integral.

18

However, relaxation spectrum cannot be directly determined on an
experimental grounds. There are two reasons for it. First, no experiment can be
performed from zero to inﬁnity, neither in time scale nor in frequency scale. The
inﬂuence of the experimental error on the results of calculations, especially
considering that the integral transform are non-linear, is uncertain and can be
large [45]. A relaxation spectrum can be found from ﬁtting the experimental data
based on the integral equations. This is the inverse problem.

On a molecular scale, the relaxation time of a polymer indicates the order of
magnitude of time required for a certain proportion of the polymer chains to
relax—that is, to respond to the external stress by thermal motion. The chains are

in constant thermal motion whether there is an external stress or not.

19

Chapter 3 Experiment Procedure
3.1 \frscoelastic experiments

The linear viscoelastic behavior may be described through linear relaxation
spectrum [46]. Strain test is conducted to ﬁnd the linear viscoelastic region and
frequency test is carried out in order to test storage modulus G' and loss
modulus G". Relaxation spectrum can be found through GENEREG data ﬁtting.
Compression molded and Ram extruded UHMWPE GUR 1050 samples are
tested in the research.
3.1.1 Samples and ARES

The samples are provided by MediTECH Medical Polymer located in Indiana.
There are two kinds of UHMWPE tested—the compression molded and ram

extruded GUR 1050 UHMWPE bar. The rectangular bar is white and

semi-transparent. The compression molded ones have the density of 931 kglm3

and the ram extruded ones have the density of 932 kg/m3(see table3.1). The
rectangular samples used in the test are 46mm in length, 12mm in width and 3mm

in thickness.

20

Table 3.1Summary of mean values physical and tensile mechanical
properties1 of UHMWPE sample

 

 

 

, 2 3 Yield Tensile Elongation
samp'e Dens'ty (“9"") (MPa) (MPa) (%)
Molded GUR1050 931 22.3 53.1 421
extruded GUR1050 932 21.2 45 384

 

 

 

 

 

 

 

The instrument is the ARES (Advanced Rheometric Expansion System, see
table 3.2) manufactured by TA Instrument. The TA ARES can measure steady and
dynamic shear properties such as steady shear viscosity, complex viscosity,
storage modulus (0'), loss modulus (G"). The instrument uses various shaped
and sized samples including: parallel plates, cone and plate, couette.

Table 3.2: Technical data of ARES (Handbook of ARES)

 

Angular displacement range 005-500 mrad (Dynamic mode)

 

1X10"5 -500 rad/sec (Dynamic mode)
0.001 - 100 rad/sec (Steady mode)
Torque range 2 - 2000 g-cm or 0.2 - 200 g-cm

Frequency range

 

 

Maximum operating frequency 100 rad/sec (15.92 Hz)

 

 

 

 

 

 

 

 

 

Thermal drift 0.002 % per °C maximum
Normal force range 2 - 2000 gmf
Temperature range -150 - 600 °C
Strain resolution and7 rad

1 ASTM D-638

2 ASTM D-1505

21

3.1.2 Strain sweep test of UHMWPE

Strain sweep is conducted to determine the linear viscoelastic region of
UHMWPE. The samples are subjected to a shear stress at a given frequency. As
the stress increases, the strain will also increase in response to it. The storage
modulus and loss modulus are measured and recorded during the process. In the
linear viscoelastic region, the storage modulus is independent of deformation and
remains to be the same value.

In the test, the frequency and temperature are ﬁxed while the strain is varied
from 0.01% to 0.5%. The frequency is set to be 1.0 rad/s and the temperature is
37 Celcius degree. The temperature is set to correspond to the human body.
temperature. The viscoelastic region is within the range that the storage modulus
G‘ keeps constant.

3.1.3 Frequency sweep test of UHMWPE

In the frequency sweep test, the sample is subjected to an oscillatory strain in
linear viscoelastic region. The response storage modulus and loss modulus is
recorded with different frequency.

In the test, the strain is 0.02% and the temperature is 37 Celcius degree. The
initial frequency is 0.01 and the ﬁnal frequency is 100. According to the strain
sweep test, the strain 0.02% is within the range of linear viscoelastic for both
compression molded and ram extruded UHMWPE GUR 1050. The linear

relaxation spectrum can be obtained from the test results of frequency sweep test

22

through GENEREG ﬁtting.
3.2 Wear experiments of UHMWPE

The wear rate of UHMWPE has been tested by Taber Abraser Model 5130
manufactured by Taber Industry. It is used for evaluating resistance to abrasion of
a wide variety of materials through the measure of volumetric or weight loss of a
specimen exposed to the action of a normalized abrasive medium secured to a
rotating disc. In this test, the weight loss method is used for calculating wear.
3.2.1 Samples and Taber abrasion machine

The samples used in wear test are the compression molded and ram
extruded UHMWPE GUR 1050 provided by MediTECH Medical Polymer in
Indiana. The disc is white and semitransparent. The square disc is 4 inches in
diameter and 0.25 inch in thickness.

The wear test equipment used in the test is the Taber Abraser Model 5130 by
Taber Industry (see table 3.3). The Taber Abraser is used to several standard test
methods in American Standards for Tests and Material (ASTM), for example, the
ASTM D1044-91 test for resistance of transparent plastics to surface abrasion,
ASTM 04060-90 abrasion resistance of organic coatings by Taber Abraser. The
Abraser is used to measure the resistance of surfaces to rubbing abrasion. The
equipment can test the solid materials, painted, lacquered, electroplated surfaces,

plastic coated materials, textile fabrics and so on.

23

Table 3.3: Standards components of Abraser Model 5130

 

 

 

 

 

 

 

 

 

 

 

 

 

Description Quantity
Auxiliary Weights 2509 2
Auxiliary Weights 5009 2
Auxiliary Weights 10009 2
Specimen Holder (E100—125) 1
Hold Down Ring (E-100-101) 1
Hex wrench for retaining ring 1
Refacing Discs (8-11) 100
8-12 long handled hand brush 1
Specimen Plates (8-16) 10
Calibrase® Abrading Wheel Set (CS-10) 2
Calibrade® Abrading Wheel Set (H-18) 2
Vacuum Unit with Suction Hose & Round Brush 1

 

 

 

 

The machine of Taber Abraser can produce the abrasion wear according to
the ﬁve wear mechanisms mentioned in chapter 2.1. The wear of Abraser is
produced by the contact of a test sample turning on a vertical axis, against the
sliding rotation of two abrading wheels. The wheels are driven by the samples in
opposite directions about a horizontal axis displaced tangentially from the axis of
the sample. One abrading wheel rubs the specimen ”outward toward the periphery
and the other inward toward the center. The resulting abrasion marks form a

pattern of crossed arcs over an area of approximately materials.

24

A vacuum pump is connected to the wear machine when it is working to
remove the debris away. Three levels of vacuum 50%, 80% and 100%can be set
in the test. The loads in the test are provided by adding standard weights on the
shoulder of the wheel supporter. Three different loadings are provided, which are
250, 500 and 1000 grams. Hence the total load on the discs are 500, 1000 and
2000 grams.

3.2.2 Experiment procedure

The samples provided are 4-inches-diameter discs. In order to carry out the
test, a 0.25 inch diameter hole needed to be drilled on the disc ﬁrst.

Different wheels need to be applied to the different materials. The wheels can
be generally divided to two categories, Calibrase Wheels and Calibrade Wheels.
The Calibrase Wheel is the resilient wheel composed of rubber and aluminum
oxide abrasive particles and the Calibrade Wheel is the non-resilient wheel
composed of vitriﬁed and silicon carbide abrasive particles. In the test, one
Calibrase Wheel (CS-10) and two kinds of Calibrade Wheel (H-18, H-22) are used.
The 08-10 Calibrase wheel is a resilient, medium abrasive wheel which has a
mild abrading action like that of normal handling, cleaning, and polishing. The
H-18 and H-22 Calibrade wheel are non-resilient, vitriﬁed wheels. They are
recommended for abrading rubber, certain woven textile fabrics, ﬂexible plastic
sheet and other soft, resilient materials.

Before conducting the test, the new wheels need to be refaced. A new set of

25

Calibrase wheels must be given two refacing of 50 refacings of 50 cycles each to
insure perfect contact of the abrading faces with the specimen surface. The test
can begin after the refacing process.

In the wheel-selecting test, the ram extruded GUR1050 UHMWPE discs are
tested. CS-10 wheels, H-22 wheels and H-18 wheels are used. The cycles for
each test are 1000 cycles. The vacuum is set as 100%. The loadings are
2509rams, 500 grams and 1000 grams for different tests.

After the wheel H-18 is selected, the compression molded and ram extruded
samples are tested under H-18 wheel for three different loads and two different
cycles. The loads used are 250, 500 and 1000 grams on each wheel. The cycles
are 500 and 1000.

The contacting area between the wheel and the disc are actually a rectangle.
The contact length and contact width on the disc are measured by the calibrator.
The contact area and pressure can be calculated from the loads and contact area.

The sliding distance is also calculated from the tracking on the discs.

26

Chapter 4 Wscoelastic Experiments Results
4.1 Strain sweep tests

Strain test is conducted to ﬁnd the linear viscoelastic region and frequency
test is carried out in order to test storage modulus G' and loss modulus G".
Relaxation spectrum can be found through GENEREG data ﬁtting. Compression
molded and ram extruded UHMWPE GUR 1050 samples are tested in the
research.

The ﬁgure4.1 and 4.2 show the effects of strain on the dynamic storage
modulus (G‘) and loss modulus (G") for compression molded and ram extruded
UHMWPE GUR 1050. The results are shown on a log-log scale plot. The x axis
scale is the percent strain (from 0.001 to 1) and the y axis scale is the storage and
loss modulus of the material. For compression molded GUR 1050, the storage
modulus is independent of strain when strain is less than 0.05%, and when strain
exceeds 0.05%, G' will decrease as the strain increases. The region in which
the storage modulus keeps constant is the linear viscoelastic region. For ram
extruded samples, the results are almost the same as the compression molded
ones. From the strain sweep test, 0.02% strain is within the linear viscoelastic

region of both compression molded and ram extruded UHMWPE GUR 1050.

27

 

 

 

 

 

 

 

 

1.00E+09
m“...
‘5
E
m
2
g 1.00E+08 -
0 W
E
+storage modulus
-o—loss modulus
1.00E+07 . r
0.001 0.01 0.1 1

strain(%)
Figure 4.1 the effects of strain on the dynamic storage modulus (G') and loss
modulus (G") for compression molded GUR 1050 at 37°C

 

 

 

 

 

 

 

 

1.00E+09
Wane—.1...“-
1?
E:
g 1.00E+08 ~
3 M
-o
o
E
1.00E+07 -
+storage modulus
-e-loss modulus
1.00E+06 I 4
0.001 0.01 0.1 1

strain(%)

Figure 4.2 the effects of strain on the dynamic storage modulus (G‘ ) and loss
modulus (G") for ram extruded GUR 1050 at 37°C

28

4.2 Frequency sweep test

From the strain sweep test, 0.02% strain is within the linear viscoelastic
region of both compression molded and ram extruded UHMWPE GUR 1050.

Figure 4.3 shows the experiment results of frequency sweep test for
compression molded UHMWPE GUR 1050. Figure 4.4 shows the results of
frequency sweep test for ram extruded UHMWPE GUR 1050. The storage
modulus G'—frequency w curve and the loss modulus G"-frequency to curve
are plotted on a log-log scale diagram.

Both the compression molded and ram extruded UHMWPE GUR 1050
samples have the same trend in storage modulus and loss modulus. The storage
modulus is increasing with frequency increasing and the loss modulus ls
decreasing with increment of frequency. The shear storage modulus (G‘ ) for ram
extruded UHMWPE GUR 1050 is larger than that of the compression molded
UHMWPE GUR 1050. For shear loss modulus (G"), the ram extruded UHMWPE

GUR 1050 has higher loss modulus comparing to the compression molded ones.

29

1 .00E+09

 

 

 

 

 

 

 

 

‘3 W
a ,
0 +experiment storage modulus
g1.00E+08 ~ -o—experiment loss modulus
E
1:
o
E
1.00E+07 . . r .
0.01 0.1 100

1 10
frequency w (radls)

Figure 4.3 Experiment storage modulus and loss modulus at different frequency
for compression molded GUR 1050 at 37°C

 

 

 

 

 

 

 

 

1.00E+09
9.: +experiment storage modulus
31.00E+08 - -e—experiment loss modulus
3
'5
'0
o
E
1.00E+07 . . r .
0.01 0.1 100

frequenc1y w (radls) 10

Figure 4.4 Experiment storage modulus and loss modulus at different frequency
for ram extruded GUR 1050 at 37°C

30

4.3 GENEREG data ﬁtting
Relaxation spectrum, which can be used in linear and nonlinear viscoelastic
models, is found with the help of available program based on a regularization
algorithm. In curve ﬁtting in storage and loss modulus, we use generalized
nonlinear regularization method (GENEREG). GENEREG is designed to solve the
ill-posed problems, which refers to the problem that the function needed to be
achieved by ﬁtting experiment data instead of directly by experiment.

The parameters that need to be set are as following:

MS is the number of points at which the function f is calculated.

SMiN is the lower bound of the interval in which the function f is calculated.

SMAx is the upper bound of the interval in which the function f is calculated.

N is total number of data points.

In the ﬁtting process, for both compression molded and ram extruded
frequency sweep test, we set the parameters as following:

Ns=8

The ﬁnal results will have 8 pairs of data.

SMIN =0.03

The lowest frequency used in the program is 0.03 rad/s

S~u0(=40

The highest frequency tested is 40 rad/s

N=41

31

There are 41 points of G‘ and frequency data. The storage
modulus-frequency data is applied in the data ﬁle for ﬁtting.

After GENEREG data ﬁtting, a series of s,- and fi is given by the computer
program. The Si represents ’11-, which is the relaxation time. The fi represents
In H, which is the natural log of relaxation spectrum.

For compression molded UHMWPE GUR 1050 samples, the eight pairs of
liand In H parameters are shown in the following table 4.1. For ram extruded
UHMWPE GUR 1050 samples, the eight pairs of x1,- and In H parameters are
shown in the following table 4.2. The relaxation spectrums are decreasing with
increasing relaxation time.

Table 4.1 Eight pairs of relaxation time and relaxation spectrum directly from
GENEREG for com ression molded GUR 1050

 

 

 

 

 

 

 

 

 

1.,- In H
1 0.050 8.91
2 0.143 8.43
3 0.412 7.98
4 1.181 7.59
5 3.388 7.27
6 9.719 6.95
7 27.884 6.76
8 80.000 6.53

 

 

 

 

 

32

Table 4.2 Eight pairs of relaxation time and relaxation spectrum directly from
GENEREG for ram extruded GUR 1050

 

 

 

 

 

 

 

 

 

 

 

 

 

1i In H
1 0.050 9.08
2 0.143 8.75
3 0.412 8.24
4 1.181 7.97
5 3.388 7.53
6 9.719 7.12
7 27.884 6.87
8 80.000 6.64

 

However, the direct results from the program should be iterated to ﬁt the
results of the tests. The ﬁrst step of the ﬁtting is to transfer the relaxation spectrum
data to modulus data. From the natural log of relaxation spectrum (In H), the
modulus corresponding to a certain relaxation time can be calculated.

When i=2, 3, 4, 5, 6, 7,

Gi = Hid In 111' (12)
When i=1,8,
Gi = 2Hid1n I1." (13)

Then the series of 4i and In H can be transformed to the series of ’1,-
and Gi- Then the estimated G‘and G"is compared with the experiment data.

From A; and Gi data, the shear storage modulus G‘ and shear loss

33

modulus G"can be estimated.

 

 

s: 0.160402 (14)
’ ”(any

.._ 0.104.- (15)
" 1+ (co). ,)2

In equation (14) and (15) , i=1, 2, 3, 4, 5, 6, 7, 8. Gi and Gi are

estimated at relaxation time 4i. w is a particular frequency, rad/s. The ﬁnal

storage modulus and loss modulus at a certain frequency are the sum of the eight
1 N

G - and G- . .
l 1 . We can then compare the expenment storage and loss modulus With

the predicted ones.

The direct results of predicted storage modulus G‘ and loss modulus G"
calculated from GENEREG are smaller than that of the test results. After iteration,
a better ﬁtting can be achieved by the following set of 2.1-and Hi In the iteration
process, a factor which is the results of experiment modulus over predicted
modulus is used to multiply the original results. The 111° and Hi series for
compression molded samples are in table 4.3. The liandHi series for ram

extruded samples are in table 4.4.For storage modulus data( G" )

G' exp eriment (16)
G'estimated

Then the new 0' can be calculated,

 

factor =

G'new = G'original x factor (17)

For different G'form number 1 to 8, there are different factors. The newly

predicted loss modulus can be calculated through adding them together. The new
0' is then again compared with the experiment ones. The whole adjusting
process is called iteration. Several iterations may be needed to ﬁnd the ﬁnal
results. When the predicted storage modulus and loss modulus can match with
the experiment ones, the corresponding stress relaxation time and modulus are
the ﬁnal results.

Table 4.3 Eight pairs of H i and lifor compression molded GUR 1050

 

 

 

 

 

 

 

 

 

31' Hi
1 0.050 9.73x10 7
2 0.143 3.77x10 7
3 0.412 7.86X10 7
4 1.181 6.94X10 7
5 3.388 6.02X10 7
6 9.719 5.07x10 7
7 27.884 4.37x10 7
8 80.000 3.14x10 7

 

 

 

 

 

 

 

35

Table 4.4 Eight pairs of Hi and lifor ram extruded GUR 1050

 

 

 

 

 

 

 

 

 

1,“ Hi
1 0.050 1.08><10 8
2 0.143 9.12x10 7
3 0.412 8.16X10 7
4 1.181 7.24><1o7
5 3.388 6.21 x10 7
6 9.719 5.30x10 7
7 27.884 4.69X10 7
8 80.000 3.47x10 7

 

 

 

 

 

Figure 4.5 and 4.6 are the ﬁtting results of loss modulus and storage modulus
of compression molded UHMWPE GUR 1050. Figure 4.7 and 4.8 are the results
loss modulus and storage modulus of ram extruded UHMWPE GUR 1050.

The predicted storage modulus in the ﬁgures is calculated by the equation (14),
in which ’7’! is the value in table 4.3 and 4.4. Gi is calculated from Hi from
table 4.3 and 4.4. The frequency w is selected as the same value as the

experiment ones. The predicted loss modulus in the ﬁgures is calculated through

36

equation (15). In the ﬁgures, the predicted lines can almost overlap with the
experiment lines. Hence, the predicted can almost ﬁt that of the experiment data.
From the ﬁgures, we can see that the above relaxation time and relaxation
spectrum in table 4.3 and 4.4 can be used to estimate the storage modulus and
loss modulus of compression molded and ram extruded UHMWPE GUR 1050.
Comparing the compression molded and ram extruded samples, the ram
extruded UHMWPE GUR 1050 has higher relaxation spectrum than that of the

compression molded ones at the same relaxation time.

 

 

 

 

 

 

 

 

 

1.00E+08
is?
9:
to
O
3
3
'u
o
E
3
2 +predicted loss modulus
+eyeriment loss modulus
1.00E+07 r . . .
1.000E-02 1.000E-01 1.000E+00 1.000E+01 1.000E+02
frequency w (radls)

Figure 4.5 Experiment results and predicted results of loss modulus at different
frequency for compression molded GUR 1050 at 37°C

37

1 .00E+09

 

 

 

 

 

 

1?

E:

E9

G

2

:3

'u

o

E

e

a

g +predicted stor modulus
v5 +exgeriment stor modulus

1.00E+08 1 ﬂ .

 

 

1.000E-02 1.000E-01 1.000E+00 1.000E-I-01

frequency w (radls)

1.000E+02

Figure4.6 Experiment results and predicted results of storage modulus at different
frequency for compression molded GUR 1050 at 37°C

 

 

 

 

 

 

    
 

 

 

1.00E+08

7:?

9;

to

w

:3

3

u

o

E

a

O)

2
+predicted loss modu
+experiment loss modu

1.00E+07 . .

0.01 0.1

frequency w (radls) 1

100

Figure 4.7 Experiment results and predicted results of loss modulus at different

frequency for ram extruded GUR 1050 at 37°C

38

 

1.00E+09

 

 

 

 

 

 

 

Ti

9;

E9

0)

3

.5

.5

o

E

g» +predicted stro modulus

3 +experiment stor modulus

’6

1.00E+08 . r r
0.01 0.1 1 10 100
frequency w (radls)

Figure 4.8 Experiment results and predicted results of storage modulus at
different frequency for ram extruded GUR 1050 at 37°C

The relaxation spectrum to relaxation time relationship is shown in the
following two ﬁgures (see ﬁgure 4.9 and ﬁgure 4.10). It is shown more clearly that
the relaxation spectrum of both kinds of samples decrease with relaxation time
increases and the ram extruded samples have higher spectrum than the

compression molded ones at the same relaxation time in ﬁgure 4.11.

39

 

1.00E+08 -

Hi(Pa)

 

 

 

 

 

 

 

+relaxation spectrum
1 .00E+07 . . .
1.00E-02 1.00E-01 1A .ogr)3+oo 1.00E+01 1.00E+02

Figure 4.9 Relaxation spectrum of compression molded GUR 1050 at 37°C

 

 

 

 

 

 

 

 

1.00E+08 ~
76
9;
E +relaxation spectrum
1.00E+07 . I .
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02
Ai (s)

Figure 4.10 Relaxation spectrum of ram extruded GUR 1050 at 37°C

40

 

1.00E+08 -

 

 

 

 

 

 

 

i?
2:
E
+relaxation spectrum com
+relaxation spectmm ram
1.00E+07 . . .
1.00E-02 1.00E-01 1.00E+00 1.00E+01 1.00E+02
A i (s)

Figure 4.11 Comparison of relaxation spectrum of compression molded and ram
extruded GUR 1050 at 37°C

41

Chapter 5 Wear tests results

5.1 Selection of wheels

In the test, the ram extruded UHMWPE GUR1050 discs are tested. CS-10
wheels, H-22 wheels and H-18 wheels are used. The cycles for each test are
1000 cycles. The vacuum is set as 100%. The loadings are set to be 2000 grams
total for each of the wheel Selecting tests.

The wheels used for Taber Abraser can be divided into two categories:
Calibrase Wheels and Calibrade Wheels. The Calibrase wheel is a kind of
resilient wheel composed of rubber and aluminum oxide abrasive particles. CS-10,
CS-10F, CS-17, CS-O and 06-5 are the Calibrase wheels. The Calibrade Wheel is
the kind of non-resilient wheel composed of vitriﬁed and silicon carbide abrasive
particles. H-10, H-18, H-22 and H-38 wheels are Calibrade wheels.

In order to determine the wheels suitable for UHMWPE, three different pairs
of wheels are ﬁrst tested. The ﬁrst wheel is the CS-10 wheel. it is a resilient
medium abrasive wheel that has a mild abrading action. The H-18 and H-22
Calibrade wheels can provide relatively course abrasion. The condition for the test
is 10009/wheel for loading, 1000 cycles, and 100% vacuum level. The results are

shown in the table5.1 below.

42

Table 5.1 Wear results for three kinds of wheels

 

 

 

 

Wheel . AW(9)
CS-10 0.0021
H-22 0.0050
H-18 0.0150

 

 

 

 

The weight losses for discs under 03-10 and H-22 are 0.0021 and 0.0050
gram respectively. The amount of loss is too small for further calculation since the
number can be easily inﬂuenced by system errors. The H-18 wheels are selected
for tests.

5.2 Results of wear experiments

The wear results for both compression molded and ram extruded UHMWPE
GUR 1050 are shown in the following table5.2 and 5.3.

There are three different kinds of load is 5009, 10009 and 20009 (each wheel

is 2509, 5009 and 10009).

43

Table 5.2 wear test results of compression molded GUR 1050

 

 

 

 

 

 

 

 

Ioad(9) time(s) AW(g)
445 0.002049
250
887 0.003447
443 0.003876
500
878 0.006463
439 0.009877
1 000
882 0.012045

 

 

 

 

Table 5.3 wear test results of ram extmded GUR1050

 

 

 

 

 

 

 

load(g) time(s) AW(9)
440 0.002493
250 ’
884 0.004367
438 0.004968
500
875 0.008567
447 0.010498
1000
880 0.016933

 

 

 

 

 

The times in the table is time recorded by stopwatch for ﬁve hundred and a
thousand cycles of discs rotating on cycling abrasor. The discs are measured
before and after the wear testing method in order to get the weight difference.

A W = W ﬁnal _ W initial (18)

According to experiment results, the wear rate of compression molded

UHMWPE GUR 1050 is less than ram extruded UHMWPE GUR 1050. The

compression molded UHMWPE GUR 1050 shows an approximate 1/3 reduction
wear than ram extruded UHMWPE GUR 1050. The ﬁrst 500 cycles has shown
higher wear rate than the following 500 cycles.

5.3 Calculation of parameters

The Archard’s law is the model used to calculate the wear parameters from
wear test. In equation (I), kis material wear factor which can be determined by
experiment. It is the number of instants that we measure other variables in the
equation and i is the ith instant. pi is the contact pressure on liner on certain
instant. (I; is the sliding distance that can be represented by velocity multiple
by time . Wear factor can be determined from actual simulator or wear test.

In the test, the loading is changed in different tests and the cycling time
remains to be the same. The pressure on the disc can be calculated according to
the loading on the wheel and the contact area of the wheel on the disc. The
loading of one wheel is 2509, 5009 and 10009, the total loading is 5009, 10009
and 20009. The contact area between the wheel and the disc is a rectangular
area. It can be estimated by the dimension of the wheel and track left after the
sliding on the disc.

The track left after the sliding is a ring with the inner radius and outer radius
as 28.94mm and 40.74mm. The width of the contact area is the width of the track

ring.

45

Ad 2 dour — din (19)

Ad =11 .8mm (20)

The contact length is measured by calibrator. At different pressures, the
contact area is different. It is increasing with the load on the disc. Table of contact
pressure is shown below (see table 5.4). The pressure is calculated from the force
over the contact area.

__ m x g (21)
Contact area

 

Table 5.4 Estimated contact area and pressure for different loads

 

load (9) length(mm) width (mm) area (mmz) pressure (Pa)

 

 

 

1000 7.41 11.8 87.438 1120794
500 6.81 11.8 80.358 60977.15
250 6.12 11.8 72.216 33926

 

 

 

 

 

 

 

The sliding distance can also be calculated from the track of sliding. The
sliding distance for one circle is the perimeter of the track. After 500 cycles, the

sliding distance is a thousand times the perimeter of the track.

lsdl =500X2721’ (22)

After 1000 cycles, the sliding distance is a thousand times the perimeter of

the track.

46

7382 =1000x 2717'

(23)

The radius in this equation is the mean radius of inner and outer radius of the

track rings.

The wear rate is tested directly from the test. Then the parameter k can be

calculated.

Table 5.5 Estimate the wear factor for compression molded GUR 1050

 

 

 

 

 

 

 

 

 

 

 

 

 

load cycles AW(9) P(Pa) distance(m) k

500 500 0.002049 33926 109.3976 1.38E-10
1000 500 0.003876 60977.15 109.3976 1.46E-10
2000 500 0.008877 112079.4 109.3976 1.81 E10
500 1000 0.003447 33926 218.7952 1.16E-10
1000 1000 0.006463 60977.15 218.7952 1.21 E10
2000 1000 0.012045 112079.4 218.7952 1.23E-10

 

 

47

Table 5.6 Estimate the wear factor for ram extruded GUR 1050

 

 

 

 

 

 

 

 

 

 

 

 

 

load cycles - AW(9) P(Pa) distance(m) k

500 500 0.002493 33926 109.3976 1.68E-10
1000 500 0.004968 60977.15 109.3976 1.86E-10
2000 500 0.010498 1120794 109.3976 2.14E-10
500 1000 0.004367 33926 218.7952 1.97E-10
1000 1000 0.008567 60977.15 218.7952 1.61 E10
2000 1000 0.016933 112079.4 218.7952 1.73E-10

 

From the above tables, the wear factor k in the Archard’s law is estimated.
The ram extruded UHMWPE GUR 1050 has higher wear weight loss and wear
factor than the compression molded ones. This difference results from the
processing methods of UHMWPE. The ram extrusion is a kind of solid state
processing in which the process temperature will not exceeds the melting
temperature of UHMWPE resin. The compression molding is a kind of liquid-solid
processing methods in which the temperature can surpass the melting

temperature of UHMWPE resin and melt it. The liquid-solid processed UHMWPE

has better wear resistance according to the test results.

48

 

Chapter 6 Conclusion and future work

From the strain sweep test, the results show that the linear viscoelastic
regions for both compression molded and ram extruded UHMWPE GUR 1050 are
almost the same. It is from 0.01% to 0.05% when frequency is 0.1 rad/s and
temperature is 37 Celsuis degree.

According to the strain sweep test, a 0.02% strain is selected for frequency
sweep test. The storage modulus (G‘) and loss modulus (G") with respect to
frequency is tested in frequency sweep test. Both the compression molded and
ram extruded UHMWPE GUR 1050 samples have the same trend in storage
modulus and loss modulus. The storage modulus is increasing with frequency
increasing and the loss modulus is decreasing with increment of frequency. The
shear storage modulus (G') for ram extruded UHMWPE GUR 1050 is larger than
that of the compression molded UHMWPE GUR 1050. For shear loss modulus
(G"), the ram extruded UHMWPE GUR 1050 has higher loss modulus comparing
to the compression molded ones.

After GENEREG ﬁtting, eight pairs of relaxation times and relaxation
spectrums are obtained. The two parameters can predict the loss modulus and
storage modulus of the samples. The relaxation spectrum of ram extruded
UHMWPE GUR 1050 is larger than that of the compression molded UHMWPE
GUR 1050 at the same relaxation time. The viscoelastic data can be used for

prediction of pressure in the wear equation.

49

The wear test results show that the compression molded UHMWPE GUR
1050 has an almost 1/3 reduction of wear rate than ram extruded UHMWPE GUR
1050. The ﬁrst 500 cycles of the experiment has shown higher wear than the
following cycles. The estimated wear factor k in Archard's law is estimated by the
pressure, sliding distance and wear loss. The ram extruded UHMWPE GUR 1050
has higher wear rate and wear factor than compression molded UHMWPE GUR
1050.

The research shows the compression molded UHMWPE has higher wear
resistance according to the wear test. The previous study [47][48] shows that the
UHMWPE with higher tensile strength and higher elongation will have higher wear
resistance. Comparing the tensile strength and elongation of compression molded
and ram extruded UHMWPE GUR 1050, the compression molded UHMWPE
GUR 1050 has higher values[49,50]. Hence, the compression molded UHMWPE
GUR 1050 should has higher wear resistance. This result corresponds to the
previous work.

The difference of wear test between ram extruded and compression molded
UHMWPE GUR 1050 may result from processing. The compression molding
process is a liquid-solid processing and the ram extrusion is a solid process. The
experiment results show that the compression molded UHMWPE, which is
processed through a liquid-solid phase process will have better wear resistance.

Several improvements can be made in order to get better results in the tests.

50

First of all, the wear test is conducted on the Taber Abrasor wear machine, which
is not usually used in testing the wear of UHMWPE in joint replacement. The
wheel used in the test is composed of vitriﬁed and silicon carbide abrasive
particles. However, in the normal wear test for joint replacement, UHMWPE
samples and metal are used to rub or slide. Although the Taber Abrasor machine
can roughly show the wear of UHMWPE, the wear rate results need to be
compared with the wear rate data from pin-on-disc and other wear testing
methods.

Secondly, the contact area is estimated by measuring the contact length and
the contact width with calibrator. The contact area calculated with the measured
length and width is not accurate enough. A more exact contact area can be
achieved by JKR theory which will take in to account the stiffness of the tested
samples and the wheel.

In the future, a more precise viscoelastic model can be applied to the
pressure prediction process in wear model. The accurate Archard’s law will also

be applied in the wear prediction.

51

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