Wear of polymers

Wear of Polymers
and Composites
Dr. Ahmed Abdelbary
Textbook & Study Guide

Key Features
Publisher Elsevier Science & Technology
Imprint Woodhead Publishing Ltd
Language(s) English
Format Hardback
ISBN-10 1782421777
ISBN-13 9781782421771
Date of Publication 2015
Place of Publication Cambridge
Country of Publication United Kingdom
1st ed.
Wear of Polymers and Composites 1st ed. A. Abdelbary 2015

Foreword
“… there are not too many books dedicated to the education of senior
and graduate students interested in this important issue. The new text
book by Prof. Ahmed Abdelbary on Wear of Polymers and Composites is
therefore a good idea to fill this gap. After a comprehensive introduction
into the field of polymer tribology, in which the possible types of wear
and the factors affecting friction and wear of polymers are described, the
author focuses the attention of the reader on the mechanisms occurring
especially during sliding of polymers against metallic counterparts.”
Prof. Dr.-Ing. Dr. h.c. Klaus Friedrich
Institute for Composite Materials
Technical University of Kaiserslautern
Kaiserslautern - Germany

Contents

Polymer Tribology
Polyamide sliding against
dry steel. Grooves run
across the surface of the
wear pin parallel to the
sliding direction.
Steel counterface showing
transfer film of polyamide
formed after 20 km of
sliding, under 90N.
Corrosive
Ferreting
Delamination
Delaminated polymer after
50 km of sliding against dry
steel, under cyclic load
(Fmean= 90N).

Polymer Tribology
𝑭 = 𝑭 𝒂 + 𝑭 𝒅
𝐹𝑎 = 𝜏 𝑠 ∙ 𝐴 𝑟1 𝐹𝑑 = 𝜎 𝑦 ∙ 𝐴 𝑟2
s shear stress required to produce sliding between the rubbing surfaces
y polymer yield pressure
Ar1 the real contact area of the junction
Ar2 the area of the grooved track

Polymer Tribology
Factors Affecting Friction and Wear of Polymers
Sliding Speed
Specific wear rate of dry
sliding of Derlin on steel.
Friction coefficient vs. sliding speed for some
industrial polymers.
H. Unal, U. Sen, A. Mimaroglu, Dry sliding wear characteristics of some industrial polymers against steel
counterface, Tribology International, 37 (2004) 727–732.

Polymer Tribology
Sliding Temperature
• Low thermal conductivity of thermoplastic polymers is an
important limitation for sliding applications.
• Mechanical properties of a polymer show a transition from
the glassy state into the rubbery state upon heating.
𝑻∗ = 𝑻 𝒆𝒏𝒗 + 𝑨
𝝁𝒑𝒗𝒍
𝒌 𝒔
+ 𝟒. 𝟐 × 𝟏𝟎−𝟒
𝝁𝑭 𝑵 𝒗
𝒃 𝒍
T* Interfacial Temperature
Tenv Environmental temperature
ks Thermal conductivity
µ Coefficient of friction
p Contact pressure
FN Normal Load
v Sliding speed
l Semi-length of the sliding body
b Semi-width of the sliding body
A Contact area

Polymer Tribology
Counterface Roughness
Schematic representation to the wear
factor for Polyethylene sliding on dry
stainless steel.
In polymer-metal sliding, as the
counterface roughness decrease
the friction coefficients of
polymers decrease. But after
reaching a minimum value of RZ
(the mean peak-to-valley) a further
decrease in the roughness causes a
high friction. Adhesion forces
becomes the dominant factor
whereas for higher surface
roughness abrasive wear prevails.

Polymer Tribology
Applied Load and Contact Pressure
At high loads, thermal softening of the polymer and plastic
deformation at the asperity interactions has a dominant role in
determining the real area of contact.
𝑭 = 𝝁𝑳 𝒏
𝑾𝑭 ∝ 𝑳
𝒏
𝟑
Relation between friction force F and applied normal load L
µ is the coefficient of friction and n is an exponential constant
The relationship between wear factor WF and load may
depends on exponent parameter n and that the linear
dependence occurs when n  3

Polymer Tribology
Humidity and Surface Wettability
Effect of water lubrication on
the wear of Polyamide sliding
against steel counterface.
 Water molecules diffuse readily
into the free volume of the
amorphous phase of the polymer
leading to plasticization, swelling
and softening.
 Water has the effect of washing
action for the counterface surface.
 Water might induce an increase in
the chemical corrosion wear of the
metallic counterface.

Polymer Tribology
Humidity and Surface Wettability
The contact angle (ϑ) characterizes the surfaces of different
materials
The increase in the polymer WR in water lubricated condition
can be related to good wettability of the metallic surface.

Polymer Tribology
Fluid Lubrication
External Lubrication Internal Lubrication
Boundary : formation of absorption
and chemical reacted layers.
Hydrodynamic : The higher the speed
and the flatter the geometry, the
thicker the film formed.
ElastoHydrodynamic: occurs at higher
pressure when the surface deformed
within the elastic range.
There could be different effect
of the internal lubrication of the
polymers on the friction and
wear due to the modified
mechanical properties and
surface energy.

Sliding Mechanics of Polymers
Formation of Transfer Film
When a polymer slides over a dry metallic counterface, some parts of the
polymer are transferred onto the counterface forming a transfer film.
During running-in wear, the thickness of the
transfer film increases until a constant value is
reached.
Counterface
Polymer
Running-in Wear
Counterface
Polymer
Steady State Wear
During steady state wear, polymer-metal sliding
becomes that of polymer on transferred polymer.

Wear Regimes
A typical volume loss versus
sliding distance curve
Typical wear curve in polymers
contains three wear regimes.
Currently, it is widely accepted that there are
three different wear regimes for describing a
typical wear process in polymers:
Running-in Wear: is related to the removal
of the artificial surface of the polymer
Steady State Wear: has a lower and linear
wear rate and characterized by formation of a
stable transfer film.
Section B Wear: is a surface fatigue wear,
which takes place after a number of cycles to
failure proportional to the sliding distance.

pv-limit
 is the max. allowable value of pv, where p is the average contact pressure
and v is the sliding speed.
 is the value above which the wear rate increases rapidly and the
maximum pv as the maximum value for continuous operation at a
specified wear rate.
pv-limit measurement
equipment, washer test.
Typical pv curve of polyimide
sliding against a steel counterface.

Asperity Flash Temperature
The temperature produced during rubbing of polymers is a combination of
three separate heat sources:
 Ambient Temperature (Ta ): is the temperature of the medium.
 Bulk Temperature (TS ): is the temperature of the entire polymer body.
 Flash Temperature (T*): occurs in a very short period close to the area of
true contact at which the energy is dissipated.
𝑻∗ = 𝑻 𝒃 + 𝟒. 𝟐 ∗ 𝟏𝟎−𝟒
𝝁𝑭 𝑵 𝝊
𝟏
𝟐
𝒃 𝒍
𝑻∗
=
𝟎. 𝟐𝟑𝟔 𝝁𝑭 𝑵 𝝊
𝟐𝒍 𝒌 𝒎 + 𝒌 𝑺
Samyn (II)
Zhang (III)
Challen (I) 𝑻∗ = 𝑭 𝑷 ∙ 𝑭 𝑵 + 𝑭 𝑻𝒃 ∙ 𝑻 𝒃

Third Body Effect
Two-body abrasion occurs when the wear is
caused by hard particles fixed to a surface. This
mechanism very often changes to three-body
abrasion, where the wear particles act as
abrasives between the two surfaces Schematic of three-body wear
 The rate of material removal in three-body abrasion is one
order of magnitude lower than that for two-body abrasion.
 Third-body can reduce friction and wear by rolling or forming
transfer film, but they can also increase it by cluttering wear
track with debris.
 In contrast to biomedical applications of polymers, third body
debris, can migrate between the articulating surfaces and
result in accelerated wear.

Surface and Subsurface Cracking
 In rolling and sliding of polymers, stress cycling and plastic strain
accumulate and multiple surface, and subsurface, cracks are ultimately
initiated.
 The nature and number of crack initiation sites in the surface depends
on the type of loading and the sliding conditions.
UHMWPE rubbing surface
shows surface cracks
running perpendicular to
sliding direction
 Under cyclic loading, the macroscopic polymer
asperity is cyclically deformed at the frequency
of the loading cycle, and this can produce crack
propagation and surface fatigue within 10 µm
from the surface under the polymer asperity.
 In artificial joints, due to cyclic loading,
subsurface cracking was found in highly
strained regions.
Abouelwafa, M. N. (1979). A study of the wear and related mechanical properties of silicone impregnated
polyethylenes. University of Leeds, Leeds, UK.

Effect of Counterface Defects
 The topography of the metal counterface is a predominant factor
in determining the magnitude of the wear rate of polymers.
 A single small scratch, which is not detected by the average surface
roughness measurement Ra can cause a dramatic increase in the
wear of polyethylene.
 Transverse scratches have a higher effect on the wear rate
compared to longitudinal scratches.
 Transfer film generated on the counterface is irregular in form with
heights ranging up to a few micrometers.

Fatigue Wear of Unfilled
Polymers

Fatigue Wear of Unfilled Polymers
Wear under Fluctuating Load
Effect of Mean Load and Load Ratio
0.0 0.4 0.8 1.2
R
0
4
8
12
16
20
WearFactor(WF)
r-squared = 0.98
0.0 0.2 0.4 0.6 0.8 1.0
R
0.5
1.0
1.5
2.0
WFcyc./WFconst.
r-squared = 0.87
Variation of wear factor (WF) with
load ratio (R).
Change in wear factor (WFcyc/WFconst)
versus applied load ratio (R).

Wear under Fluctuating Load
Effect of Cyclic Frequency
0.0 0.4 0.8 1.2 1.6
Frequency (f), Hz
0
4
8
12
16
20
WearFactor(WF)
r-squared = 0.86
Relation between cyclic frequency (f) and
the corresponding wear factor (WF).

Influence of Surface Defects on Wear of Polymers
Effect of Crack Orientation on Wear
Closed side view of the
polyamide 66 specimen
with imposed vertical crack.
Crack orientation (θ) with
respect to sliding direction.
Effect of surface crack angle (θ) on steady
state wear rate (WR) for different cyclic
loading ratios (R), Fmean= 90N and f = 1.5 Hz.

Effect of Crack Orientation on Wear
Polyamide 66 wear pin surface
after 80 km of sliding, F=90 N.
Polyamide worn surface showing crack face fracture,
pitting, trapped wear debris and wear grooves,
Fmean= 90 N.
Polyamide 66 wear
pin side view after
40 km of sliding,
θ= 00, Fmean= 90 N.

Number of Surface Cracks Effect
RCW due to transverse surface cracks,
cyclic load (Fmean=90N, f=0.25 Hz, R=0.06).
Optical micrographs of wear pin
surface with multiple cracks showing
high density of wear grooves, F= 90 N
after 20 km of sliding.

Effect of Surface Defects on Transfer Film Formation
Optical micrograph of: (a) wear pin
surface showing wear grooves
parallel to the sliding direction and
(b) steel counterface showing
transfer film formed.
Optical micrographs of surface
cracked polymer showing: (a) wear
pin surface with trapped wear
debris inside the crack mouth and
(b) steel counterface with transfer
film formed.

Effect of Surface Defects on Wear Regimes
Plot for sample wear test,
surface crack was imposed
after 80 km of siding, F= 90 N.

Wear of Polymers in
Wet Conditions

Wear of Polymers in Wet Conditions
Factors Contributing in the Lubricated Wear of Polymers
Lubrication Regimes
 Hydrodynamic lubrication: the load carrying surfaces are
separated by a relatively thick film of lubricant.
 Elastohydrodynamic lubrication: the load is sufficiently high
enough for the surfaces to elastically deform during the
hydrodynamic action.
 Boundary lubrication: the load is mainly transferred through the
asperity-asperity contacts of the mating surfaces. This regime is
generally associated with relatively high friction and wear due to
severity of contact between the asperities.
𝒅 𝒄𝒓𝒊𝒕 = 𝟐. 𝟕𝟑 𝒉 𝒐
𝟐
𝟑
𝑭
𝜼𝒗
𝟏
𝟑
dcrit Critical wear scar diameter (m).
ho Fluid film thickness at the edge of the pin (m).
𝜂 Viscosity of the lubricant fluid (Ns/m2).
v Sliding speed (m/s).
F Applied force (N).

Water Absorption
 Swelling of polymer due to water intake could potentially act as a brake,
resulting in increased frictional heating and wear.
 Plasticization of the polymer rubbing surface takes place with two
opposite tribological effects; a decrease in the interface shear strength
and an increase in the area over which contact takes place
 Reduction in the hardness of PAs was also observed when treated
with water.

Wettability
A surface is called hydrophobic when the water contact angle is more than or
equal to 90o , (900 ≤ θC ≤ 1800 ) whereas it is called hydrophilic when water
contact angle is less than 45o, (00 ≤ θC ≤ 450 ). The surface having a water
contact angle between 45o to 90o is defined as the amphoteric
hydrophobic/hydrophilic surface.
At low loads, the lubricating efficiency of the fluid depends on surface
tension and wettability of the fluid.
At high loads, the elevated contact stresses tend to extrude the interposed
fluid out of the interface zone, leading to direct solid–solid contact and, as
a result, a high friction situation.

Wear Behaviour of Polyamide 66 against Steel
Wear at Constant Applied Load
Variation of polyamide 66 wear rates WR
with applied constant load in wet sliding.
F
N
p
MPa
Steady state wear
X
km
V
mm3
WR x10-4
mm3/m
Dry
90 1.8
110 180 13.3
Wet 60 568 90.4
Dry
135 2.7
90 217 18.1
Wet 60 583 95.7
PA 66 worn surface
after 40 km sliding
distance, at 90 N
applied load.

Wear at Fluctuating Load
Effect of fluctuating load parameters (f and R) on
wear rate of PA 66, wet sliding on steel
counterface.
R
(Fmin / Fmax)
Fluctuating Load
N
ho
µm
R1 = 0.06
Fmin = 10 0.73
Fmax = 170 0.17
R2 = 0.64
Fmin = 70 0.27
Fmax = 110 0.22
PA 66 worn surface
after 40 km sliding
distance, f= 1.5 Hz,
R= 0.06).

Wear at Fluctuating Load
(a, b) worn/burnished areas and some
slight scratching and gouging of
UHMWPE tested in orthopedic wear
simulator.
(c, d) scratching and burnished area of
wear surfaces of PA66 (Fmean= 90N, f=
1.5 Hz).

Wear of internally Lubricated Polymers
The use of Silicones in Lubrication
Material
Hardness
VHN
Density
Kg/m3
Young's
Modulus
MN/m2
Fracture
Strength
MN/m2
Shear
Strength
MN/m2
LDPE 2.40 926 38.80 8.34 10.20
LDPE + 1% Silicone 2.20 926 35.09 7.84 9.50
LDPE + 2% Silicone 2.20 925 28.62 6.31 9.10
LDPE + 5% Silicone 2.10 924 36.59 7.87 8.90
LDPE + 10% Silicone 922 29.07 7.18 6.80
UHMWPE 4.87 933 51.90 16.70 21.17
UHMWPE + 10% Silicone 3.47 929 66.70 16.24 15.89
Results of mechanical properties measurements.
Abouelwafa, M. N. (1979). A study of the wear and related mechanical properties of silicone impregnated
polyethylenes. University of Leeds, Leeds, UK.

Wear of internally
Lubricated Polymers

The use of Silicones in Lubrication
Optical microscopy of LDPE + 10% silicone
wear pin surface after 100 km of sliding.
The figure shows no sign of severe pulls or
smears, which is attributed to the relatively low
wear rate of the LDPE + 10% silicone test.
Wear pin surface (a) after 498 km and (b) after
648 km of sliding.
(a) UHMWPE + 10% silicone wear pin
surface shows wear marks running across
the graph in the sliding direction. (b) At
the end of the test, a new feature arose
in the form of large number of blisters
scattered all over the surface.

Tribology of LDPE Impregnated with Silicone Fluid
Most of the wear graphs of LDPE wear tests could be split into two distinct
stages: initial wear and steady state wear. The first part of these wear graphs
has been called "wearing-in" period, since the machining marks were
removed well before the onset of the steady state region. Some wear curves
do show a continuous change in the slope up to the end of the test.

Effect of Silicone Fluid Content
Effect of silicone concentration on
the steady state wear rates for LDPE.
Effect of silicone concentration on the coefficient
of friction of LDPE with different silicone content.
 At least 2 % of silicone fluid should be used and this yields an average
reduction in wear rate of about thirty four percent.
 Silicone migrated to the surface that reduces the coefficient of friction
and in turn reduces temperature rise.
 The silicone fluid reduces the adhesion between the counterfaces.

Wear of Polymer Composites
Classification of Composites

Debonding
Fibre pull-out
Fibre bridging

Wear of Continuous Unidirectional Fiber Composites
 N orientation: fiber-matrix debonding, fiber cracking, and fiber bending.
 P orientation: internal crack propagation, fiber cracking, fiber-matrix
debonding, and fiber fracturing.
Overt, T. C. (1997). Wear of unidirectional polymer matrix composites with fiber orientation in the plane of
contact. Tribology Transaction, 40(2): 227-234.

Wear of Short Fiber Reinforced Composites
Effect of GF relative to CF on the
wear factor of thermoplastics
Effect of fibre length on the specific
wear rate of epoxy composites.
 The application of different fillers gives an opportunity to improve the
tribological behavior of polymers.
 The selection of suitable fibers is often a compromise between the properties of
the polymer and its friction and wear behaviour.
Friedrich, K., Lu, Z., & Hager, A. M. (1995). Recent advances in polymer composites tribology. Wear, 190(2):
139-144.

Wear of Particulate-filled Composites
 The shape, size, volume fraction, and specific surface area of added
particles have been found to affect mechanical properties of composites.
 Micro and Nano tribology are new areas of tribology that arise when one
tries to improve the tribological properties by using fillers with sizes in
the micro- or nano-scale range.
 many kinds of inorganic materials such as metal powders, minerals,
oxides, graphite, and solid lubricants have been used in micro and
nanometer sizes as fillers.
 Generally, fillers have shown effectiveness in reducing the coefficient of
friction, and also increasing the wear resistance in many cases. But in
some cases, the addition of particulate fillers has resulted in the
degradation in wear resistance. Therefore, it is useful for the materials
designer to investigate which fillers are useful for increasing wear
resistance in a particular polymer.

Wear of Laminated Fiber Reinforced Composites
normal-laminate NL
parallel-laminate PL
cross-laminate CL
 Laminate orientation w.r.t the sliding direction
should be considered when assessing the
tribological properties of laminated composites.
 Location of the individual laminate w.r.t the
counterface surface controls friction and wear.
 Fabric geometry (wave of fabric) has a
significant role on tribo-performance of
laminated composites.
Different weave patterns: (a) plain, (b) twill and (c) stain.

Methodology of
Testing in Wear

Methodology of Testing in Wear
Sliding Wear Test
Unidirectional Sliding Reciprocating Sliding
block-on-ring pin-on-drum
pin-on-plate test
The resulting data from this type of
movement may differ from that
experienced by the same materials
in unidirectional sliding.
pin-on-disc

Rolling Wear Test
Four ball apparatus
Twin disc apparatus
The importance of polymers in
rolling applications and particularly
in the gear industry determines
the apparatus used to investigate
its tribological behaviour.
Pure rolling means that there is no
relative slip; both matting surfaces are at
the same velocity. It only occurs in a
fraction of the total footprint of a revolute
shape (ball, roller, wheel, etc.) that rolls
on another surface.

Scratch Wear Test
ASTM G 171 has been used to give a guide to
the abrasive wear resistance of metals,
ceramics, polymers, and coated surfaces.
Circular indenter
(Rockwell diamond tip)
Speed, load, loading rates, number of scratches and scratch length can be
changed to give enough flexibility to define a desired test.
 There are two stylus indenters; circular cross-
sections (cone or sphere) and square-base pyramid
shapes.
 The scratching process produces a measurable
scratch in the tested surface without causing
fracture, spalling, or delamination.

Abrasion Wear Test
sand/rubber wear test apparatus
The main testing methods are two-body
and three-body abrasion test.
Two-body abrasion can be simulated by pins, of
the specimen material, that are loaded and
rotated against a spinning rough counterface
Three-body abrasion test was developed to simulate wear situations in
which low-stress scratching abrasion is the primary mode of wear.
In polymers, dry and wet sand/rubber
wheel test has been suggested to
investigate the influence of various
parameters on this mode of wear, such as
abrasive particle size and shape and
material parameters.

Erosion Wear Test
The determined amount of material volume loss is
normalized by the abrasive flow rate, to provide
the erosion value, which is defined as wear volume
per gram of abrasive
Erosion is a mechanical degradation of a
surface, resulting from solid particle
impingement causing local damage combined
with material removal.
Polymers and their composite materials are
finding increased applications, under
conditions in which they may be subjected to
solid particle erosion

Reciprocating Sliding, Fluctuating Loaded Tribometer
Tribometer
(1) Motor
(2) machine frame
(3) chain drive mechanism
(4) U-beam guide
(5) reciprocating carriage
(6) Spring
(7) eccentric cam
(8) pin holder
(9) dead weights.

3-D View of the reciprocating M/C

A
A
Sce. A-A
1
2
4
3
Chain Drive Mechanism:
(1) double roller chain (3) U-beam guide
(2) Sprocket (4) ball bearing

Friction force Fr= µ.F Sliding direction
Fmean
Fmax
Fmin
F=Fmeansinωt
1
3
5
4
2
Cyclic load system
(1) eccentric cam
(2) compression spring
(3) pin holder
(4) polymer specimen
(5) steel counterface

Procedures of Polymer Wear Test
Dry Sliding Tests
 Control pins should be introduced alongside the wearing pins.
 Specimen located in a specific orientation to insure proper sliding direction.
 After acclimatizing for 3-hours, specimen weighed and measured.
 Required microscopy investigations are to be made.
 Examination of the polymer wear surfaces by optical microscope.
 On restarting tests, the pins located in the same holder and same
orientation.
 During the first period of the test, short time runs conducted in order to
detect the running-in phase. These are to be followed by longer time runs
to give a considerable amount of wear.
 Surface roughness measurements for counterface and the polymer pin
surface performed at the beginning of each test as well as at its end.

Procedures of Polymer Wear Test
Water Lubricated Sliding Tests
 Clean and fresh distilled water was used for every test.
 Water was poured into the wear path until complete submerge of the
counterpart.
 The water level in the reciprocator bath was maintained during test run.
 Control pin is to be applied to monitor the up-taken of.
 A standard acclimatizing period was also considered before
measurements.
 Careful cleaning and drying with hot jet air were performed at the end of
each run.

Prediction of Wear in
Polymers and their
Composites

Prediction of Wear in Polymers and their Composites
Empirical Wear Models
Polymers
𝑉
𝐿
=
𝜇
𝐻 𝜎 𝜀
Where,
V worn volume
H indentation hardness
L sliding distance
σ fracture strength
µ coefficient of friction
ε ultimate strain
𝑉 = 𝑘
𝑊 𝐿 𝑡𝑎𝑛𝛿
𝜋 𝐻
Where,
k constant
W normal applied load
δ angle of slope of the asperity cone
Ratner (1964)
Lancaster (1969)

Polymers
Where,
v sliding speed
k wear constant
T sliding time
Where,
w weight loss
a, b, c set of parameters
𝑉 = 𝑘. 𝑊. 𝑣. 𝑇
Lewis (1964)
𝑤 = 𝑘. 𝑊 𝑎
. 𝑣 𝑏
. 𝑇 𝑐
Rhee (1970)

Polymers
Where,
C geometrical constant
(= 1 for abrasion, =3 for adhesion)
Where,
pi penetration depth
φ polymer shear angle
n number of asperities
D width of the slider
Jahanmir (1973)
𝑉
𝐿
=
𝑖=1
𝑛
𝑝𝑖
2
𝐷
2 𝐿 𝑡𝑎𝑛𝜑
Lee (1985)
𝑉 =
𝑘 𝑊 𝐿
𝐶 𝐻

Composites
Where,
xm, xf volume fraction of matrix and
filler.
km, kf, kc specific wear rate of matrix,
filler and composite.
Khruschov (1972)
𝑘 𝑐 = 𝑥 𝑚 𝑘 𝑚 + 𝑥𝑓 𝑘 𝑓
Wear models are expressed in terms of wear rate or wear
resistance and volume fraction of each constituent by using the
rule of mixtures.

Composites
𝑘 𝑐
𝐸𝑃 = 𝑥 𝑚𝑏 𝑘 𝑚 + 𝑥𝑓𝑏 𝑘 𝑓𝑘 𝑐
𝐸𝑊 =
𝑥 𝑚𝑏
𝑘 𝑚
+
𝑥𝑓𝑏
𝑘 𝑓
−1
Models were explained more mathematically by introducing either equal
wear (EW) or equal pressure (EP) conditions (Axen & Jacobson, 1994).
 Under EW conditions, the matrix and reinforcing phase are assumed to
wear individually, but at an equal linear rate.
 Under EP conditions, the matrix and reinforcing phase carry the same
normal pressure.

Dimensional Analysis
Fundamental variables considered in developing the wear equation are
wear volume V, sliding variables such as load P, speed v, time T, counterface
roughness α, modulus of elasticity E, surface energy γ, thermal conductivity
K and specific heat Cp.
𝑉 = 𝑘𝑃 𝑥 𝑣 𝑦−𝑧 𝑇 𝑦 𝛾3−𝑦+𝑧 𝐸−3−𝑥+𝑦
𝐶 𝑝
𝐾
𝑧
Where
x, y and z are exponents determined experimentally.
Kar and Bahadur (1974)

Dimensional Analysis
Equation was modified by Viswanath and Bellow (1995) include the
counterface roughness, and to be applicable for a wide variety of polymers.
Ψ 𝑉, 𝑊, 𝑇, 𝛼, 𝐶 𝑝, 𝛾, 𝐸, 𝑣, 𝐾 = 0 where Ψ is some arbitrary function.
Using Buckingham Pi
theorem, variables was
reduced from nine to five
dimensionless groups.
𝑉𝐸3
𝛾3
= Ψ
𝑊𝐸
𝛾2
,
𝑣𝐾
𝛾𝐶 𝑝
,
𝑇𝐸𝐶 𝑝
𝐾
,
𝛼𝐸
𝛾
𝑉 =
𝑘 𝑤 𝑊𝑣𝑇𝛼
𝛾
𝑉 = 𝑘 𝑤 𝑊 𝑝 𝑣 𝑞 𝑇 𝑟 𝛼 𝑠 𝐸−3+𝑝+𝑟+𝑠 𝐶 𝑝/𝐾
𝑟−𝑞
For linear relationship
For non- linear relationship

Finite Element Analysis (FEA)
The basic approach used to simulate wear is:
(1) Identify the important parameters affecting the material removal rates.
(2) Determine appropriate wear rates from specimen-level tests.
(3) Perform FEA to progressively remove materials during simulation.
The strength of FEA analysis in wear predictions is its ability to accurately
treat the variation of experimental conditions as well as the progressive
change of the surface geometry caused by material removal.
FEA uses a complex system of points called nodes which make a grid called a mesh.

Finite Element Analysis (FEA)
FE simulation of wear in pin-on-disk configuration
The simulation composes of : (1) FE code used to determine
the contact pressure at each node and (2) wear algorithm that
interprets the nodal position changes.
(a) Schematic of the pin-on-disk configuration, and (b) FE model of the pin.

Artificial Neural Networks (ANNs)
Hidden layers Output layer
Wear Rate
WR
Input layer
Load (F or Fmean)
Maximum load (Fmax)
Frequency (f)
Cracks (n)
Schematic description of an ANN configuration.

Effect of ANN configuration
Ref. ANN
Neurons Type Training
algorithmI/P Hidden O/P
Z. Zang {9[15105]3 1} tan-sigmoid tan-sigmoid pure-linear LM
A. Lada {7[93 ]2 1} tan-sigmoid tan-sigmoid pure-linear CGB
A. Abdelbary {5[201010]3 1} tan-sigmoid tan-sigmoid pure-linear LM
X. Liu {2[8]1 1} - tan-sigmoid pure-linear LM
Z. Jiang {9[1263]3 1} - - - CGB
A. Helmy {35[85]2 1} tan-sigmoid pure-linear pure-linear LM
LM Levenberg-Marquardt algorithm
CGB Powell–Beale conjugate Gradient algorithm

Effect of ANN configuration
Abdelbary A., Abouelwafa, M. N., El Fahham I. M., & Hamdy, A. H. (2012). Modeling the wear of polyamide 66 using
artificial neural network. Materials & Design, 41: 460-469.

Comparison between the measured and predicted running-in wear rate of the (a)
training and (b) test dataset, Dry sliding. Input: Load (F), Stress ratio (R), Load
frequency (f), Number of cracks (nc ) and Output: WR.

(a) Relation between frequency of the cyclic load and the measured wear rates
(b) Relation between frequency of the cyclic load and the corresponding wear rates
(measured and predicted data using the proposed NN).
Application of ANN in predicting the relation between wear rate (WR) and frequency
of the applied cyclic load (f).

Wear of polymers

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