Wear of polymers

Wear of Polymers

and CompositesDr. Ahmed Abdelbary Textbook & Study Guide

Key Features

PublisherElsevier Science & Technology

Imprint Woodhead Publishing LtdLanguage(s) EnglishFormat HardbackISBN-10 1782421777ISBN-13 9781782421771Date of Publication 2015Place of Publication CambridgeCountry 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

FriedrichInstitute for Composite MaterialsTechnical University of KaiserslauternKaiserslautern - GermanyWear of Polymers and Composites 1st ed. A. Abdelbary 2015

Contents

1. Polymer Tribology

2. Sliding Mechanics of Polymers

3. Fatigue Wear of Unfilled Polymers

4. Wear of Polymers in Wet Conditions

5. Wear of Internally Lubricated Polymers

6. Wear of Polymer Composites

7. Methodology of Testing in Wear

8. Prediction of Wear in Polymers and their Composites


Polymer Tribology

Polymer Tribology


Wear of Polymers

Abrasive Adhesive Fatigue Others

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.

CorrosiveFerreting

Delamination

Delaminated polymer after 50 km of sliding against dry steel, under cyclic load (Fmean= 90N).

Polymer Tribology


Friction of Polymers

𝑭=𝑭 𝒂+𝑭𝒅

𝐹 𝑎=𝜏𝑠 ∙ 𝐴𝑟 1 𝐹 𝑑=𝜎 𝑦 ∙ 𝐴𝑟 2

s shear stress required to produce sliding between the rubbing surfacesy polymer yield pressureAr1 the real contact area of the junctionAr2 the area of the grooved track

Adhesion Deformation

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+𝑨𝝁𝒑𝒗𝒍𝒌𝒔

+𝟒 .𝟐×𝟏𝟎−𝟒𝝁𝑭 𝑵√𝒗𝒃 √𝒍

T* Interfacial TemperatureTenv Environmental temperatureks Thermal conductivityµ Coefficient of frictionp Contact pressure

FN Normal Load v Sliding speed l Semi-length of the sliding body b Semi-width of the sliding bodyA 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=𝝁𝑳𝒏

𝑾𝑭 ∝𝑳𝒏𝟑

Relation between friction force F and applied normal load Lµ 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

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 TemperatureThe 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 𝑵𝝊𝟏𝟐

𝒃√𝒍

𝑻 ∗=𝟎 .𝟐𝟑𝟔𝝁𝑭 𝑵𝝊𝟐 𝒍 (𝒌𝒎+𝒌𝑺 )

Samyn (II)

Zhang (III)

Challen (I) 𝑻 ∗=𝑭 𝑷 ∙𝑭 𝑵+𝑭𝑻𝒃 ∙𝑻 𝒃



Third Body EffectTwo-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 1.2R

0

4

8

12

16

20

Wea

r Fac

tor (

WF)

r-squared = 0.98

0.0 0.2 0.4 0.6 0.8 1.0R

0.5

1.0

1.5

2.0

WFc

yc. /

WFc

onst

.

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 1.6Frequency (f), Hz

0

4

8

12

16

20

Wea

r Fac

tor (

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



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.

𝒅𝒄𝒓𝒊𝒕=𝟐 .𝟕𝟑𝒉𝒐

𝟐𝟑 ( 𝑭𝜼𝒗 )

𝟏𝟑

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 wearX

kmV

mm3WR x10-4 mm3/m

Dry90 1.8

110 180 13.3Wet 60 568 90.4Dry

135 2.790 217 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 LoadN

ho µm

R1 = 0.06Fmin = 10 0.73Fmax = 170 0.17

R2 = 0.64Fmin = 70 0.27Fmax = 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

MaterialHardness

VHN

Density

Kg/m3

Young's ModulusMN/m2

Fracture StrengthMN/m2

Shear StrengthMN/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



Mechanisms of Failure

Fiber fracture Delamination Matrix cracking

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 NLparallel-laminate PLcross-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



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

Fm

ean

Fm

ax

Fm

in

F= Fm

ean sin ωt

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

𝑉𝐿=

𝜇𝐻𝜎 𝜀

Where ,V worn volumeH indentation hardnessL sliding distanceσ fracture strengthµ coefficient of frictionε ultimate strain

𝑉=𝑘𝑊 𝐿𝑡𝑎𝑛𝛿𝜋𝐻

Where, k constant W normal applied loadδ angle of slope of the asperity cone

Ratner (1964)

Lancaster (1969)




Polymers

Where,v sliding speedk wear constantT sliding time

Where, w weight lossa, b, c set of parameters

𝑉=𝑘 .𝑊 .𝑣 .𝑇Lewis (1964)

𝑤=𝑘 .𝑊 𝑎 .𝑣𝑏 .𝑇𝑐

Rhee (1970)




Polymers

Where,C geometrical constant (= 1 for abrasion, =3 for adhesion)

Where, pi penetration depthφ polymer shear anglen number of asperities D width of the slider

Jahanmir (1973)

𝑉𝐿=∑

𝑖=1

𝑛 𝑝𝑖2𝐷2𝐿𝑡𝑎𝑛𝜑

Lee (1985)

𝑉=𝑘𝑊 𝐿𝐶𝐻




Composites

Where,xm, xf volume fraction of matrix and

filler.km, kf, kc specific wear rate of matrix,

filler and composite.

Khruschov (1972)

𝑘𝑐=𝑥𝑚𝑘𝑚+𝑥 𝑓 𝑘𝑓

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

𝑘𝑐𝐸𝑃=(𝑥𝑚𝑏𝑘𝑚+𝑥 𝑓𝑏𝑘 𝑓 )𝑘𝑐𝐸𝑊=(𝑥𝑚𝑏𝑘𝑚

+𝑥 𝑓𝑏𝑘 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=𝑘𝑃𝑥𝑣 𝑦− 𝑧𝑇 𝑦𝛾3−𝑦+𝑧𝐸−3−𝑥+𝑦 (𝐶𝑝

𝐾 )𝑧

Where x, y and z are exponents determined experimentally.

Kar and Bahadur (1974)



Dimensional AnalysisEquation 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 ,𝐶𝑝 ,𝛾 ,𝐸 ,𝑣 ,𝐾 )=0 where Ψ is some arbitrary function.

Using Buckingham Pi theorem, variables was reduced from nine to five dimensionless groups.

(𝑉 𝐸3

𝛾 3 )=Ψ (𝑊𝐸𝛾2 , 𝑣𝐾𝛾𝐶𝑝,𝑇𝐸𝐶𝑝

𝐾 ,𝛼𝐸𝛾 )𝑉=

𝑘𝑤𝑊𝑣𝑇 𝛼𝛾

𝑉=𝑘𝑤𝑊𝑝𝑣𝑞𝑇 𝑟𝛼𝑠𝐸− 3+𝑝+𝑟+ 𝑠 (𝐶𝑝 /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.


http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/glossary.html#node

http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/glossary.html#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. ANNNeurons Type

Training algorithmI/P Hidden O/P

Z. Zang {9[15105]3 1} tan-sigmoid tan-sigmoid pure-linear LM

A. Lada {7[93 ]2 1} tan-sigmoid tan-sigmoid pure-linear CGB

A. Abdelbary {5[201010]3 1} tan-sigmoid tan-sigmoid pure-linear LM

X. Liu {2[8]1 1} - tan-sigmoid pure-linear LM

Z. Jiang {9[1263]3 1} - - - CGB

A. Helmy {35[85]2 1} tan-sigmoid pure-linear pure-linear LM

LM Levenberg-Marquardt algorithm CGB Powell–Beale conjugate Gradient algorithm




Effect of ANN configuration

Comparison of the prediction quality for various ANNs configurations

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.




[201010]3




(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).


Thank You

Wear of polymers

Engineering

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