9Wear Maps

9.1 Introduction 9.2 Fundamental Wear Mechanisms of Materials9.3 Wear Prediction

Simulation Model and Materials Selection

9.4 Wear Mapping 9.5 Wear Maps as a Classification System

Parameters and Forms Used in Wear Maps

9.6 Wear Map Construction for Ceramics Experimental Procedures and Materials • Ceramic Wear Maps

9.7 Comparison of MaterialsDry Sliding Conditions • Paraffin Oil-Lubricated Conditions • Water-Lubricated Conditions • Wear Transition Diagrams • Implications and Use of the Maps

9.8 Modeling Wear by Using Wear MapsMetals • Ceramics • Modeling Approaches • Correlation of Data According to Wear Maps • Materials Normalization • Summary

9.9 Advantages and Limitations of Current Wear Map ApproachFuture Wear Maps Research Needs

9.1 Introduction

Wear is not an intrinsic material property. Wear is a complex function of the system which includesmaterial properties, operating conditions (load, speed), contact geometry, surface roughness, and envi-ronment (lubrication, temperature). Therefore, for a given pair of material combination, wear can varyover several orders of magnitude depending on the conditions. This makes evaluation of materials interms of wear resistance difficult. Common practice is to conduct simulation wear tests to rank materialsunder the same operating conditions. If the relationship between wear and the operating conditions (loadand speed) are linear, relative ranking of materials will hold. Under the influence of chemistry orenvironment, unfortunately, wear transitions often occur and the relationship between wear and theoperating conditions is often not linear. The relative ranking of materials, therefore, will change whenthe operating conditions are changed. At the same time, material variations abound. Small changes inthe alloying elements and processing conditions change the wear characteristics. So even though thematerial designation is the same, there is no assurance that the chemical composition and microstructureare identical. Because of these factors, literature reports on material wear characteristics have wide ranges,as shown for ceramics in Table 9.1. For metals, similar ranges are observed for data from all sources. Themetal wear data in Table 9.1 show the effect of lubricants on different metals on a single wear tester ina laboratory (Fein, 1975). This makes selection of materials for wear applications difficult.

Stephen M. HsuNational Institute of Standards and Technology

Ming C. ShenSULZERMEDICA

Current typical industrial practice is to make actual components and put them in actual field trials overa period of time. This way, there can be no dispute with respect to the effectiveness of the materials ormaterial treatment. However, cost and duration make such practice prohibitive, and a very low percentageof new materials are tested. A better way to select and design materials for wear resistance is needed.

This chapter discusses the use of the wear map concept to help resolve some of these issues and providea means to systematically compare and select materials on a common basis. While the discussion willfocus on materials in general, the predominant data available are in the area of ceramics. So ceramicwear maps will be used to illustrate the basic concept and applications of wear maps. The applicabilityof the concept, however, should not be restricted to ceramics.

9.2 Fundamental Wear Mechanisms of Materials

Before we discuss the concept of wear maps as an effective way to understand the various aspects of wear,we need to understand the fundamental wear mechanisms of materials in general.

A large number of wear mechanisms has been identified in the literature. For metals, they includedeformation, adhesion, abrasion, delamination, fatigue, fracture, corrosion, stress corrosion, and oxida-tive wear. For brittle solids such as ceramics, they are fracture, abrasion, tribochemical wear, grain pull-out, intergranular fracture, and corrosion. Broadly speaking, these can be classified into physical andchemical processes and their interplay. In most cases, several wear mechanisms occur simultaneously,and it is difficult to ascertain specific proportional contributions to wear from different mechanisms.

Ying (1996) conducted a series of two-ball collision experiments designed to understand the funda-mental relationship between friction, materials deformation, and wear at the single asperity contact basis.The results are summarized in Figures 9.1 and 9.2. For metals, wear is controlled by the accumulationof the shear strain underneath the contact, lubrication tends to redistribute the stress over a much largerarea, therefore delaying the onset of wear. For ceramics, wear is controlled by the stress intensity whichinduces crack propagation. These observations, while useful, are based on single asperity contact exper-iments. In real contacts, there are multiple asperities and the situation is considerably more complex.Contact asperity temperatures and wear debris interactions to form transfer layers all influence wear.Tribochemical reaction products will exert great influence on friction and wear of materials.

TABLE 9.1 Wear Data from the Literature

Ceramics

Al2O3 Si3N4 SiC PSZ

AVG Range AVG Range AVG Range AVG Range

Fracture toughness, MPa·m0.5

Hardness, GPaElastic modulus, GPaDensity (g/cm3)Wear coefficient (K = HW/FDa)

Dry airHumid/H2OLubricant

416

3703.9

10–5

10–7

10–3

2–611–12

340–4103.8–3.9

10–9–10–3

10–7–10–6

10–7–10–2

4.416.3

3133.2

10–4

10–5

10–6

1.4–613–17

290–3333.1–3.4

10–5–10–4

10–9–10–4

—

2.925

3973.0

10–3

10–5

10–6

1.5–413–34

390–4022.8–3.2

10–6–10–2

——

812

206.05.9

10–4

10–6

10–7

5–1510–14

196–2165.7–6.0

10–7–10–4

—10–8–10–6

Wear Surface Opposing Surface Atmosphere Lubricant Wear Coeff.

52100 steel 52100 steel Dry air None 1.0 × 10–3

52100 steel 52100 steel Air None 1.0 × 10–3

52100 steel 52100 steel Air Paraffinic oil 3.2 × 10–7

52100 steel 52100 steel Air Paraffinic oil/TCP 3.3 × 10–9

52100 steel 52100 steel Air Engine oil <2.0 × 10–10

Mild steel Mild steel Air None 2.3 × 10–3

Carburized steel Carburized steel Air Gear oil 1.6 × 10–9

Aluminum bronze Carburized steel Air Gear lubricant 2.5 × 10–8

a K = wear coefficient, H = hardness, W = wear volume, F = load, D = distance slid.

9.3 Wear Prediction

Modeling of wear in metals has been conducted by many researchers (see Ling and Pan, 1988, and Ludemaand Bayer, 1991, for some approaches). Over the years, many models have been proposed for differentmaterials and applications. Unfortunately, most models are correlational in nature and therefore system

FIGURE 9.1 Wear mechanisms of metals.

FIGURE 9.2 Wear mechanisms of ceramics.

specific: they only work for the particular materials pair, contact geometry, operating condition range,and the particular environment and lubricant. The inability of the models to transcend these restrictionsresults in a divergent collection of parameters and constants. This situation can be illustrated usingerosion as an example, which has been summarized by Ludema (Meng and Ludema, 1995). A total of32 parameters was found to have been used by various authors to describe their erosion data. There isa lack of consensus on the critical parameters that can describe a phenomenon such as erosion. Suchconfusion also exists for most other wear phenomena, e.g., abrasion (Rabinowicz, 1965; Hokkirigawaand Kato, 1989; Larsen-Basse, 1991; Komvopoulos et al., 1986). As a result, given the material propertiesand contact information, there is no model currently available that can predict wear a priori.

9.3.1 Simulation Model and Materials Selection

Bayer (1991) discusses at length the essential elements for design-oriented model building and testing.The key is simulation — for all critical aspects of the application environment. The range of applicabilityof any model must be defined. The ruggedness of the model (does it behave properly when parametersare expanded somewhat out of the usual ranges) needs to be tested. Most important, the overall approachmust be system-oriented, not merely focused on materials, or lubricants, or mechanics.

Other discussions of this approach can be found in the literature. Godet (1988) has identified theessential elements of simulation wear testing. He includes the need to measure the stiffness and dampingcharacteristics of the test system as well as its wear behavior, all under a controlled mechanical environ-ment. The aim is to ensure that the operating environment is adequately represented in the model andits validation. In the summary of a workshop on this subject (Ling and Pan, 1988), it was noted thatdesign-oriented modeling also requires knowledge and identification of failure mechanisms, possibly inthe form of maps that relate failure boundaries to operating parameters.

9.4 Wear Mapping

Measuring and understanding the wear of a material are complex and difficult tasks. There is a generalrecognition that wear of a material depends on load, speed, temperature, time, contact geometry, surfaceroughness, oxygen availability, lubricant chemistry, and material surface compositions. The dependenceon such a large number of variables has been a significant barrier in achieving a comprehensive repre-sentation of wear. Furthermore, for advanced materials such as ceramics, the variations in materialsthemselves make comparisons of wear test results of the “same” material unusually difficult. Therefore,there is a strong need for a methodology to define and measure wear of a material in definitive terms.

Wear mechanism studies and wear modeling efforts also suffer from this lack of definition. To minimizethese effects, wear studies are often done under a single set of conditions as a function of time. However,mechanistic interpretations and models proposed on the basis of such data have limited significance.The dominant wear mechanism in one operating region may not be the dominant mechanism in another.While this difficulty is recognized by many, proposed solutions are few.

Lim and Ashby (1987) have demonstrated the use of a wear map to correlate the massive literaturedata on wear of steels. Their wear map is shown in Figure 9.3. Normalized parameters based on anassumed dominant variable were used to construct the map. The asperity temperature at the contact isassumed to dominate the dry sliding of steels on pin-on-disk wear testers. Wear regions based on theasperity temperatures they calculated are developed. Based on the temperature, various dominant wearmechanisms and models are developed. These wear regions, however, describe fairly severe wear levels.In engineering applications, acceptable wear levels are orders of magnitude lower.

Beerbower proposed a conceptual wear mechanism diagram for steel under lubricated conditions asa function of the specific oil film thickness as shown in Figure 9.4 (Beerbower, 1972). While the variousmechanisms were reported in the literature, the diagram was constructed based on inferences and isolateddata. However, it illustrates the complex nature of lubricated wear of steel.

deGee (1989) proposed a simpler system on steel under well-lubricated conditions based on a largebody of data generated under a set of standardized conditions. He referred to his maps as transitiondiagrams. He pointed out that as the severity of the wear test increases, as reflected by speed and load,

FIGURE 9.3 Wear map for steel under dry sliding conditions. (From Lim, S.C. and Ashby, M.F. (1987), Wear-mechanism maps, Acta Metall., 35(1):1-15. With permission.)

FIGURE 9.4 Wear map for steel under lubricated conditions. (From Beerbower, A. (1972), Boundary Lubrication,U.S. Army, Office of the Chief of Research and Development, Contract No. DAHC19-69-C-0033.)

the wear of steel under well-lubricated conditions progresses from no wear to mild wear, and then toscuffing. Similar to Lim and Ashby’s work, deGee found the concept of flash temperature useful inexplaining the wear behavior.

These studies illustrate the complexity of examining wear in a comprehensive and systematic manner.

9.5 Wear Maps as a Classification System

The concept of wear maps can be used to classify wear based on the recognition that there are manyvariables involved. The dependent variable is wear. The independent variables can be divided into twotypes: continuous variables (speed, load, temperature, and time) and discrete variables (dry, nonreactivelubricant, reactive lubricant, environment, and contaminants). For a given material pair and a fixeddiscrete variable, there are five three-dimensional wear maps that can be used to describe wear system-atically: wear vs. speed and load; wear vs. speed and temperature; wear vs. speed and time; wear vs. loadand temperature; and wear vs. load and time. Therefore, for a given material pair, a set of 20 wear mapswill systematically define the wear behavior. These maps include: five wear maps under dry slidingconditions; five wear maps under nonreactive fluid (to avoid chemical reactions but to remove the heatat the interface so that the true wear behavior can be observed); five wear maps under reactive lubricantconditions (formation of chemical films similar to industrial applications); five wear maps under thesame environment and contaminants conditions (e.g., engine blowby gases, soot particles, and oxygenstarvation conditions as in a typical diesel engine ring wear simulation). In many instances, a completeset of wear maps is not needed in order to define the wear behavior but a selected set of maps will serveto define the critical limits and operational boundaries for the materials pair in terms of acceptable wearbehavior within those ranges.

Within each discrete parameter, the wear characteristics of the material pair will exhibit wear transi-tions, tribochemical reactions, oxide formation, plastic deformation, and fracture. The location of thespeed and load (contact pressure, asperity temperature profile, surface roughness evolution) at whichsuch phenomena occur will differ as the discrete parameter changes from one to the other. Somephenomena will occur in one set of environments but will not occur in another set of environments.

These variations of wear behavior actually take place in many experiments; some are controlled andsome occur accidentally. While these explain the wide variation in wear results and mechanisms reportedin the literature, the resulting confusion about the definitive wear behavior inhibits theoretical develop-ment in effective wear modeling. When the wear behavior for a material pair is fully defined by thesemaps, it will become obvious that a single wear model will not be sufficient to describe or predict wearbehavior for a material pair in general. Separate models will be required to describe the wear behaviorunder different operating conditions and environments.

9.5.1 Parameters and Forms Used in Wear Maps

Lim and Ashby (1987) proposed using normalized parameters such as the following to describe wearresults:

where W′ = wear volume per unit distance slid, An = apparent contact area, ro = radius of the apparent contactarea, F = normal force, H0 = room temperature hardness, V = sliding velocity, and a = thermal diffusivity.

˜

˜

˜

WW

A

FF

A H

VVr

a

n

n

o

= ′

=

=

0

In their work on metals, Lim and Ashby suggested that these parameters were able to correlate datafrom different sources, using specimens of different shapes and sizes. W can be considered as a dimen-sionless wear coefficient; F is the nominal pressure divided by the surface hardness; V is the sliding velocitydivided by the velocity of heat flow.

Rabinowicz (1965) defined an alternative wear coefficient, k, in the following form:

where W = wear volume, F = normal force, D = distance slid, and H0 = room temperature hardness.Thus, k could also be expressed as:

Rabinowicz suggested that “wear coefficient represents the probability that, during the contact of thetwo surfaces at an asperity, a sizeable wear particle is produced.” While these parameters have someintrinsic advantages in representing wear, they also carry with them some hidden assumptions about thewear behavior and also assume other parameters are not critical (such as grain size and microstructurein ceramics).

What parameter to use in plotting the wear maps and the form of representation are importantconsiderations in constructing wear maps. To understand this, one needs to examine the actual wearprocesses in a wear test as a function of time. Figure 9.5 shows typical relationships among wear volume,contact pressure, and the normal force. The pressures include the Hertzian pressure for ideal elasticcontacting surfaces and the mean contact pressure calculated as the applied normal force divided by theactual wear scar area measured at the end of each wear step. Neither of these common measures of contactstress in a wear junction accounts for the microscopic morphology. Both measures assume conformingsurfaces. Thus, the wear transition that occurred at 180 N normal force in Figure 9.5 is not reflected bythe Hertzian pressure at all, and is seen as a sudden decrease in the mean pressure. In contrast, someresults (Hisakado, 1986) seem to suggest that as the machine load is increased, the real contact area forceramic-on-ceramic increases only fractionally, and hence the actual pressures at the tip of the micro-scopic asperities increase rapidly. This situation is quite different from ductile metals. For metals, surfaceconformity can be very high under certain speed and load regions, approaching 70 to 80% of thetheoretical nominal contact area, and hence mean pressure may be a reasonable measure of the stress atthe contact. For ceramics, the conformity typically is about 10 to 15%, and the resulting mean contact

FIGURE 9.5 Relationship among wear volume, measures of pressure and normal force illustrated with data onalumina.

kWH

FDo=

kW

F=

˜

˜

pressure, therefore, is not a good representation of the relevant contact stress. Consequently, it is preferableto use the normal force divided by the initial contact area to represent the load without any assumptionabout the microscopic contact morphology.

Wear volume, W, may be less susceptible to misinterpretation than other measures. Normalizedmeasures of sliding speed have a similar difficulty in practice. The relevant thermal diffusivity is the valueat the elevated contact temperature for which estimates are difficult to make. Again, it may be preferableto use linear velocity to represent the sliding speed.

9.6 Wear Map Construction for Ceramics

9.6.1 Experimental Procedures and Materials

Wear data from a single laboratory are selected to illustrate the wear map concepts. Four ceramic materialsare used to create a self-consistent database to construct the maps. The materials are selected for theirrepresentative behavior within each material class. In ceramics, given a generic name and chemicalcomposition such as silicon nitride, there are numerous variations in mechanical properties, microstruc-tures, sintering aids, and surface properties. Tribologically, they may behave very differently for a givenset of operating conditions and environments. Yet there are some general patterns of characteristicsassociated with each class of material. This chapter focuses on these general patterns, but we caution thereader that each ceramic material should be treated as a unique sample.

The material properties and the mechanical properties of the ceramics studied are listed in Table 9.2.The alumina used is a sintered α-alumina with a density close to the theoretical density. The grains areequiaxed and the average grain size is about 5 µm with the range from 2 to 15 µm.

The zirconia ceramic used is a pressureless-sintered polycrystalline zirconia doped with 4.7 weightpercent yttria. The as-received material is 100% tetragonal. The grain size is about 1 µm in diameter.The density is 99% of theoretical, resulting in porosity of about 1%.

The silicon nitride used is a hot-isostatically-pressed silicon nitride. The material is a mixture of α-Si3N4

and β-Si3N4. The α-phase is primarily in equiaxial grains of size ≈0.5 µm, while the β-phase formselongated grains, up to 1 µm in diameter and 2 to 5 µm in length. Examination of the fractured surfaceby energy dispersive X-ray analysis indicates that trace amounts of magnesium, iron, and tungsten arepresent.

TABLE 9.2 Material Properties of the Ceramics in Wear Map Studies

Description Al2O3 Y-TZP SiC Si3N4

ProcessSintering aid/ImpuritiesDensity, g/cm3

PhaseAverage grain size, mElastic modulus, GPaPoisson’s ratioHardness, GPa (20°C)(500°C)(1000°C)Fracture toughness, MPa.m1/2

Compressive strength, GPaSpecific heat, J/g°CThermal conductivity, W/m°CThermal expansion, 1/°C

Sintered—3.9

2–153720.2216 ± 0.88 ± 0.44 ± 0.24.52.60.8835.67.1 × 10-6

SinteredAl2O3, Y2O3

6.05t-ZrO2

~1.0220 0.2813 ± 0.74 ± 0.23 ± 0.28.5 1.90.41.810 × 10-6

Sintered and post-HIPAl> 3.17

3–84300.1631 ± 1.6 18 ± 0.910 ± 0.53.22.50.95110 4.1 × 10-6

HIPa

Mg, Fe, Al, W3.25

0.3–23100.2824 ± 1.217 ± 0.913 ± 0.75.43.00.6533.03.5 × 10-6

(Hardness values are measured by Vicker’s indentation with 1-kg load and a duration of 15 s).a HIP = hot-isostatically-pressed

The silicon carbide used in this study is a sintered and post-HIPped silicon carbide mixed with equiaxedgrains and elongated (rod-shape) grains. Elongated grains are up to 2 µm in diameter and about 10 to20 µm in length.

Wear experiments are conducted on a Four-Ball Wear Tester using a ball-on-three-flats contact geom-etry. The ball and the flats used are made of the same ceramic material. The diameter of the ball is12.7 mm. The flats are circular discs of 6.35 mm in diameter with a thickness of 1.59 mm. The finalpolish is done by using 1-µm diamond paste. Prior to testing, the ball and the flat specimens are cleanedin an ultrasonic bath by using successive solvents of hexane and acetone followed by a detergent washin water. Afterwards, the specimens are rinsed with deionized water, then blown dry with dry nitrogen.

The test procedure used is a step-loading procedure at several fixed sliding speeds. At each slidingspeed, the applied load increases in a stepwise manner. For loads lower than 20 N, the load steps followa sequence of 2 N, 4 N, 8 N, 12 N, and 20 N. Beyond 20 N, the load increment of each step is 20 N. Themaximum load is 360 N. The duration of each load step is 5 min. Wear tests sometimes are terminatedbefore 360 N is reached due to extreme wear, such as in the dry sliding case. The sliding speeds are 1.9,14.4, 38, 190, 380, and 570 mm/s. Additional speeds have also been used in some cases. In lubricatedtests, an amount of 1.5 ml fresh lubricant is used in each load step. The worn surfaces are not washedbefore examination.

All tests are conducted at room temperature with the room air at a relative humidity of 50 to 55%.For dry air conditions, dry cylinder air is circulated through the wear tester at a rate of 0.76 L/min. Thewear scar diameters on the three flat specimens are measured after each load step. For lubricated cases,purified paraffin oil (PPO, 4 Cst viscosity oil percolated through an activated alumina column prior towear tests) is used as the nonreactive lubricant for ceramics. (Separate studies had been done to dem-onstrate that paraffinic oil did not chemically react with ceramics to form chemically active boundarylubricating films.) Water is used as the reactive fluid. Constant condition tests had also been conductedto cross check the step loading procedure. Similar wear results were obtained. For detailed discussion onthe test procedures, see Shen and Hsu, 1996.

The precision of the wear measurement is generally within ±10%. When the data are plotted in athree-dimensional plot, some data smoothing occurs. The data smoothing tends to reduce the uncertaintyand throw out the outliers.

9.6.2 Ceramic Wear Maps

Three-dimensional wear maps showing wear as a function of speed and load for alumina, zirconia, siliconcarbide, and silicon nitride were constructed.

9.6.2.1 Alumina

Figure 9.6 shows the wear maps of alumina under dry air, purified paraffin oil (PPO, nonreactive fluid),and water (reactive fluid)-lubricated conditions. Figure 9.6a shows the alumina wear as a function ofspeed and load in room temperature and atmosphere conditions (dry air was supplied to the sampleholder throughout the test). The map illustrates the simultaneous functional dependence of wear withrespect to speed and load. If both speed and load influence wear, the interaction of the speed and loadon wear can usually be observed in the surface topographical features such as valleys and plateaus. Inthis case, it can be seen that this alumina under this set of conditions has very strong load dependence.Wear increases rapidly as load increases at low speed. When the speed reaches about 20 mm/s, the loaddependence accelerates and an abrupt sharp increase in wear occurs. This wear transition is probablydue to the introduction of additional thermal shock stresses (Shen and Hsu, 1996). The speed dependenceis mild under low load but a wear transition occurs due to speed when the load reaches 80 to 90 N.Therefore a low wear region in the shape of a rectangle is defined. There is probably some tribochemicalinfluence in the middle of the speed range as reflected in a “valley.” When PPO was used, basically thespeed (thermal shock) effects are minimized (Figure 9.6b); the map shows basically load dependence ofwear with some speed influences. When water is used, the effect of speed is much more pronounced than

in PPO’s case. This is probably due to the tribochemical reactions that occurred between the aluminaand water under certain speeds (Gates et al., 1989).

9.6.2.2 Zirconia

Specific to zirconia material is the possibility of phase transformation from the tetragonal phase to themonoclinic phase with an accompanying increase in volume. Also, water is known to react with zirconia,causing embrittlement and aging-related fracture (Rühle et al., 1984). The phase transformation could bebeneficial to wear if the stresses at the trailing edge of the contact are high enough to cause instantaneous

FIGURE 9.6 Wear maps of Al2O3 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.

(a) Dry air

(b) PPO (c) Water

phase transformation, the resulting volume increase will produce a compressive stress on the surface,thus resisting the tensile cracks produced by the contact. However if the phase transformation occursbeneath the surface under hydrostatic pressure, then the volume increase will create an internal stressthat is detrimental to wear resistance.

The wear maps of zirconia are presented in Figure 9.7. The wear characteristics of Y-TZP under drysliding conditions are shown in Figure 9.7a. Wear data are not available at the high-speed, high-loadcorner because the severity of the test conditions caused rapid seizure. A relatively low wear region isbound by 20 N load and 20 mm/s speed. Beyond this region, wear increases rapidly as a function of loadand speed. The load dependence is rapid and increases in stepwise fashion. The speed dependence withinthe experimental conditions appears to approach a steady-state plateau at low loads. Under high loads(~80 N+), the speed effect is very dramatic, resulting in an exponential rise in wear. Under purified

FIGURE 9.7 Wear maps of Y-TZP under (a) dry air, (b) PPO, and (c) water-lubricated conditions.

paraffinic oil (PPO) lubricated conditions (nonreactive fluid), the speed sensitivity is essentially elimi-nated. This confirms the existence of thermal shock and temperature effects observed in dry slidingconditions. The wear is almost linearly dependent on load.

Under water-lubricated conditions (reactive fluid), complex surface topographic features can be seen,suggesting the influence of chemical reactions between water and zirconia producing reaction productsthat influence friction and wear. At low loads and speeds, the tribochemical reactions protect the surfaces,effectively creating a low wear region that is the lowest among the three conditions. At high loads andhigh speeds, the presence of water exacerbates the wear rate and it exhibits an exponential rise in wear atboth the critical speed and load. At high speeds, rapid wear with increasing sliding speed for this materialhas been attributed to accelerated stress corrosion due to frictional heating (Nakayama and Hashimoto,1991). Formation of Y(OH)3 may also contribute to the overall destabilization of Y-TZP by yttria depletionproducing monoclinic nucleus. The individual contributions of stress corrosion and hydroxide formationto wear are, however, difficult to ascertain. Increased speed also introduces additional stress from thermalshock at localized hot spots. Consequently, the rapid increase in wear rate as speed is increased beyondthe low-wear region may be due to the combination of thermal shocks and cracking from hydrolysis.

9.6.2.3 Silicon Nitride

Figure 9.8 presents the wear maps of silicon nitride under dry air, water, and purified paraffinic oil (PPO)-lubricated conditions. The wear behavior of silicon nitride in dry air exhibits both speed and load dependencewith a low-wear region in the form of a valley. Wear transitions can be observed on both the speed and loadaxes when a critical load and a critical speed are reached. At those critical loads and speeds, wear risesexponentially, thus defining an unusable region for tribological applications. When the same material coupleis under PPO-lubrication conditions (nonreactive fluid), one can see the effects of speed almost disappearwithin the range of the test conditions at most of the loads. At high loads, the frictional heating begins toinfluence the wear. The disappearance of the topographical features by the use of PPO is illustrative of theeffects of surface temperatures on the wear of the silicon nitride couple. For the water-lubricated case, again,tribochemical reactions exert a major influence (Mizuhara and Hsu, 1992; Tomizawa and Fischer, 1987).Silicon nitride reacts with water to form Si(OH)4, which under certain speed and load conditions furtherreacts to form silicic acids and high-molecular-weight products. The hydrides, as demonstrated in Tomizawaand Fischer (1987), could form solid cylinders perpendicular to the direction of sliding. Figure 9.8c showsthat the tribochemical reactions are activated by speed, or interfacial temperatures at the asperity tips. Thereis a load limit beyond which the tribochemical products are not able to protect the surface.

9.6.2.4 Silicon Carbide

The wear maps of silicon carbide are presented in Figure 9.9. The wear characteristics are similar to thoseof silicon nitride. The major difference is that the tribochemical influence is different from those of siliconnitride. This may be reasonable since chemically, the two materials have been observed to exhibit differentresponses to the same chemistry (Hsu, 1991). Some results (Nakayama and Hashimoto, 1991) suggest thatsilicon nitride emitted far more electrons, charged particles from wear, than silicon carbides. Althoughthe link between emission intensity and lubrication has not been clearly established, this lends support tothe observation that silicon nitride and silicon carbide exhibit different chemical responses to water.

9.7 Comparison of Materials

Once the wear maps have been constructed for the materials, the maps can be used as effective tools tocompare materials under the same environmental conditions.

9.7.1 Dry Sliding Conditions

Figure 9.10 presents the wear maps of the four ceramics for the dry sliding case. The scale of the wear rateis the same for all four materials, from 10–10 to 10–2 mm3/s. There are low-wear regions in the low-speed,

low-pressure corners for all four materials. As the severity of the contact increases (an increase in speedand/or pressure), a rapid increase in wear takes place when the conditions approach the transition zones.The locations of the transition zones and the slopes of the increase depend on the individual material. Wearaccelerates as conditions become more severe. All four materials show both speed and load dependence andrapid transitions to severe wear. Alumina has a different speed dependence than the other three, probablybecause of the inadvertent reaction with water in the air. Zirconia shows more dependence on both speedand load than the other three. Therefore for zirconia, overdesign is necessary to protect the component/sys-tem. The silicon-based materials are relatively “tougher” in that the sensitivity to speed and/or load changesis less compared with either zirconia or alumina (Hsu et al., 1994).

Under dry sliding conditions, material properties such as hardness, thermal conductivity, and densityare important in determining wear resistance. Table 9.2 shows that in terms of hardness and thermal

FIGURE 9.8 Wear maps of Si3N4 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.

(a) Dry air

(b) PPO (c) Water

conductivity, silicon carbide has the highest value and zirconia has the lowest value. In terms of fracturetoughness, zirconia has the highest value and silicon carbide has the lowest. This may explain the highsensitivity of zirconia with respect to change in speed and load yet zirconia has some of the lowest wearrates at low-load and low-speed regions.

Microstructural features such as grain size (He et al., 1993), grain size distributions (Hsu et al., 1995),and grain shapes (He, 1995; Zutshi et al., 1994) all have significant effects on the wear of ceramics. Forthe four samples examined in this study, both silicon nitride and silicon carbide have duplex grains(elongated grains mixed with small and medium-size equiaxed grains). This kind of grain design usuallyhas a slightly higher wear rate under low load, but a lower wear rate under high load. Zirconia has thesmallest equiaxed grains among the four materials; therefore it has some of the lowest wear rates at thelow-speed and low-load region. The equiaxed grain structure, however, once it begins to crack, is difficultto stop, and wear accelerates rapidly (Liu and Hsu, 1996; Wang and Hsu, 1996a). The picture that isemerging is that wear is a function of many parameters even for materials properties and microstructures.There are no simple rules to predict wear behavior.

FIGURE 9.9 Wear maps of SiC under (a) dry air, (b) PPO, and (c) water-lubricated conditions.

9.7.2 Paraffin Oil-Lubricated Conditions

Figure 9.11 shows the wear maps of the four materials under purified paraffin oil-lubricated conditions. Forthese four ceramics, the purified paraffin oil itself does not react with the ceramics nor does it containimpurities that will react with the ceramics (Wang and Hsu, 1996b; Deckman et al., 1991; Gates and Hsu,1991; Deckman et al., 1999). Therefore the effect of the presence of the paraffin oil is to remove the highinterfacial temperatures and lower the flash temperatures in the contact. Therefore the most dominant effectshould be the moderation of the speed dependence under low or moderate loads. This is indeed the case.Figure 9.11 shows that the addition of paraffin oil clearly removes most of the speed dependence at low loads.For Si-based ceramics, the wear rates at low loads and speeds are much lower now than those of zirconiaand alumina. In addition, at high loads and speeds, both alumina and zirconia exhibit rapid transitions tohigh wear. For alumina, the wear transition is basically load induced with some speed effects beyond the

FIGURE 9.10 Wear maps under dry sliding conditions.

(a) Al 2O3 (b) Y-TZP

(c) SiC (d) Si3N4.

critical speed. This probably reflects the fracture behavior of large grain sized microstructures (Liu and Hsu,1996; Cho et al., 1992). For zirconia, both speed- and load-induced wear transitions are evident. The duplexmicrostructure of silicon nitride and carbide avoids the wear transitions (Hsu et al., 1995).

9.7.3 Water-Lubricated Conditions

Water is a chemically reactive agent to alumina (Gates et al., 1989), zirconia (Michalske et al., 1986), SiC,and Si3N4 (Mizuhara and Hsu, 1992; Tomizawa and Fischer, 1987) under certain tribological conditions.The wear maps in Figure 9.12 reveal different wear regimes directly contradictory to the wear character-istics observed for the same material under the dry sliding and or the paraffin oil-lubricated cases. Thiscan be illustrated using the silicon nitride case. At low loads, the wear increases with speed up to about15 mm/s, then the wear decreases as speed increases. Tribochemical reactions producing silicon hydroxides

FIGURE 9.11 Wear maps under paraffin oil-lubricated conditions.

(a) Al2O3 (b) Y-TZP

(c) SiC (d) Si3N4

have been observed (Tomizawa and Fischer, 1987). For the four materials, wear increases significantly interms of the baseline data. This agrees with observations made by others (Sasaki, 1989). Water has beenobserved to produce very low friction under certain operating conditions but accelerates the wearprocesses by corrosion and stress corrosion cracking.

In the alumina case, the tribochemical reactions change the primarily load induced transition to moreof a load- and speed-induced transition compared to the paraffin oil-lubricated case. Different aluminumhydrides can be produced, and they have different “lubrication” characteristics (Gates et al., 1989).Therefore, different wear zones are observed as a function of load and speed. In fact, for all four materials,speed dependence comes back in as in the dry case. This suggests that speed activates the tribochemicalreactions, and the reaction products change the wear behavior.

In the Si3N4 case, a low-wear zone occurs in the low-load, high-speed regime. In this regime, the wearis accompanied by an extremely low friction coefficient (< 0.04). Silicon hydroxides have been found inthis region in the form of slender rollers inside the contact zone. The reaction products are thought toprovide some limited hydrodynamic lift to lower friction. However, the reaction in a water environment

FIGURE 9.12 Wear maps under water-lubricated conditions.

(a) Al2O3 (b) Y-TZP

(c) SiC (d) Si3N4

seems to be somewhat corrosive because the wear level is noticeably higher than the one in the sameregime when paraffin oil is present. In the SiC case, an extremely low coefficient of friction is alsomeasured in the high-speed, low-pressure regime. But the resulting wear does not show any noticeablereduction as in the Si3N4 case. Based on the wear maps shown so far, wear maps of different lubricationenvironments are clearly required in order to describe fully the complete spectrum of wear characteristicsfor the same material pair under different environments.

9.7.4 Wear Transition Diagrams

Wear transitions can be defined as the sudden increase in wear over a small increment of the operatingconditions (speed, load, temperature, time). They usually signify a change in wear mode accompaniedby a change in the dominant wear mechanism, e.g., onset of third-body wear induced by the generationof wear particles. Wear transitions have been observed in both metals and ceramics under unlubricatedand lubricated conditions. Because the onset of transitions can often lead to rapid wear and eventualcatastrophic failures, the transition phenomena have been extensively studied. In ceramics, the transition

FIGURE 9.13 Wear transition diagrams of Al2O3 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.

phenomena have been studied by many (He et al., 1993; Liu and Hsu, 1996; Wang and Hsu, 1996a,b;Cho et al., 1992; Wang et al., 1995). The locations of the transition zone with respect to the operatingparameters are important to design engineers to safeguard proper material selection and design.

Given a set of three-dimensional wear maps, the maps can be sliced at a plane to produce a set ofcontour maps of different wear rates as a function of speed, load, or any other parameter such astemperature and time under different environmental conditions. From the contour maps, the weartransition zone can be easily identified on the contour map as the lines of constant wear rates bunchtogether to represent a steep ascend. These boundaries then can be plotted to show where the transitionsoccur. There may be one or more wear transitions in a given map, usually from mild to severe wear ora transition from severe wear to ultra-severe wear. The locations of these wear transition zones changewith different lubricants.

Figures 9.13 through 9.15 show the wear transition diagrams of the four ceramics under differentlubrication conditions. The effects of lubrication on the locations of the wear transition zones can beclearly seen. In addition, the functional dependence of the wear transition lines on speed and load canalso be observed.

FIGURE 9.14 Wear transition diagrams of Y-TZP under (a) dry air, (b) PPO, and (c) water-lubricated conditions.

Figure 9.13 shows such wear transition diagrams for alumina under dry sliding conditions; there is acritical speed and a critical load that will precipitate the transition from mild to ultra-severe wear. Forthe PPO-lubricated case (Figure 9.14), it is basically a series of critical loads under different speeds. Inthe presence of water, (Figure 9.15), the transition loads are much lower, and another transition fromsevere to ultra-severe wear occurs at the high-speed and high-pressure region. The transition behaviorsfor zirconia under the three lubrication conditions are shown in these figures. The transitions dependon both speed and load due to the low thermal conductivity. Note the location of the mild to severetransition moves from the dry case to PPO’s case. This measures the effects of the PPO on the transitionbehavior. For silicon nitride and silicon carbide, the behaviors are similar. The effects of PPO are quitedramatic. Water, in terms of wear, moderates the ultra-severe wear transition but does not change themild to severe wear transition that much for silicon nitride.

These figures also compare the transition diagrams of the four materials under the same lubricationcondition. The locations of the transition zones as well as the functional dependence provide powerful

FIGURE 9.15 Wear transition diagrams of Si3N4 under (a) dry air, (b) PPO, and (c) water-lubricated conditions.

tools to compare different materials for a given application. Transient spikes in an application can beestimated and examined in the transition diagrams to assess the potential of premature failure.

The results shown above demonstrate the need to construct wear maps to better describe the wearcharacteristics of a material under a particular lubrication condition. Without such maps, it will be verydifficult to grasp the complicated interactions of operating parameters, lubrication conditions, andmaterials microstructures and properties. The results also reveal that significant differences are presentin the wear characteristics of a material under different lubrication environments.

9.7.5 Implications and Use of the MapsOnce the wear maps for a given pair of materials are constructed, they can be used as material selectionguides as well as design guides for different engineering applications. The wear maps can be used toconstruct wear mechanism maps by performing additional experiments in various regions to understandthe dominant wear mechanism taking place as defined by the operating conditions, environment, andcontact conditions.

Given the understanding of the detailed wear mechanisms and their processes, wear models fordifferent regions for the same materials pair may be constructed. Models developed based on a singleset of operating conditions and environment clearly have limited applicability. Such models and methodshave failed to address the real needs of the engineering community (Meng and Ludema, 1995). Wearmaps therefore can give rise to the concept of a set of models for a given materials pair based on operatingconditions and environment.

9.7.5.1 Wear Mechanism Maps

The availability of the wear transition diagrams provides the opportunity to study the different wearmechanisms in each region for a material under a lubrication environment. The transition diagramdefines the minimum number of dominant wear mechanisms operating for a given system. By examiningthe contour maps (lines of constant wear rate), lines of equal spacing and lack of curvature usuallyindicate the same dominant wear mechanism. Valleys and plateaus usually suggest some change in thewear mode. In this way, regions with potentially different wear mechanisms can be identified. Criticalexperiments can then be conducted within those regions to identify the dominant wear mechanism. Inthis way, wear mechanism maps were constructed (Hsu et al., 1991).

The experimental verification process is illustrated below. Based on the wear map and wear transitiondiagram of Y-TZP under paraffin oil-lubricated conditions, two sets of operating conditions can be chosento examine the dominant wear mechanism in each region. Figure 9.16 shows two worn surfaces under highpressure but at different speeds, one is in the mild-wear regime and the other one is in the severe-wearregime. The worn surface taken from the mild wear case shows mostly grooves, indicative of micro-abrasion and asperity scale fracture being the dominant wear mechanisms. Meanwhile, the worn surfacetaken from the severe-wear regime exhibits evidence of microfracture and brittle fracture. Brittle fracturehas become the dominant wear mechanism. The onset of the brittle fracture is caused by intergranularcracks giving rise to wear particles in the interface. A series of separate experiments has been conductedto follow the onset of such transitions for alumina (Cho et al., 1992). These results suggest that significantwear increase as well as change in wear mechanism is associated with this wear transition. In this manner,wear mechanism maps for the four ceramics are constructed and are shown in Figures 9.17 through 9.19.

These wear mechanism maps serve as a powerful tool to compare different materials and their wearbehaviors as functions of wear mechanisms under the same operating conditions. Materials propertiesare used to understand the wear behaviors rather than being used to judge the wear behaviors.

Figure 9.17 shows the wear mechanisms maps for the four materials under dry sliding conditions.When Figure 9.17 is compared with Figure 9.13, one can see there are zones within each region in whichthe wear mechanisms are different, but the change in wear mechanisms does not increase wear to the

extent that wear transitions are formed. In a way, it can be pointed out that within a wear zone, there isa severity issue or a progression of severity until some events occur to trigger the wear transition.Figure 9.18 shows more delineation of the mild wear mechanisms of the materials when a nonreactivelubricant such as PPO is used. The functional dependence of some of these mechanisms is also important.For example, for alumina, in the presence of a lubricant, the transition and severity progressions arealmost linearly load dependent. The influence of speed is minimum. For silicon-based ceramics, tribo-chemical zones are both speed and load dependent with speed having a higher influence. When the fluidis changed to water (Figure 9.19), most of the mechanisms are influenced by both speed and load, andthe detailed mechanisms are difficult to determine because of the complexity of reactions taking placebetween water and the ceramics. This suggests that modeling tribochemical wear will be most difficultbecause of the lack of detailed mechanistic understanding of the processes.

Based on these mechanistic results, effective prediction of wear for a single material pair under differentlubrication conditions will require a set of equations classified according to the wear regime and dominantmechanisms. This is similar in concept to Ashby’s map; wear equations are developed based on thedifferent wear mechanisms. So, the first conclusion of wear mapping is that a family of equations isrequired to predict wear accurately.

At the same time, it must be pointed out that it is an issue of precision of prediction. As will be seenlater in the wear modeling section in this chapter, for one or two orders of magnitude prediction, all

FIGURE 9.16 SEM micrographs of representative worn surfaces of Y-TZP under paraffin oil-lubricated condition.

four ceramics can be treated as a single material pair under a particular lubricating condition. This isthe global model based on fracture mechanics. Of course, the global wear model cannot predict someof the wear mechanisms.

9.7.5.2 Material Design and Selection Guide

If we take the wear transition diagrams for different materials, we can superimpose them on a singlediagram to compare the locations of the transition lines under different conditions. Figure 9.20 illustratessuch diagrams for the four ceramics under dry sliding, PPO, and water-lubricated cases. The stress andthe speed of the application can be calculated and examined in light of the transition diagrams. For agiven safety margin, material pairs that can safely operate in a specified region can be estimated.

Conversely, given the three-dimensional representations of the four materials, for a given contactpressure, these three-dimensional maps can be sliced along the constant contact pressure lines and thefour materials’ wear levels superimposed in a single diagram for comparison. Figure 9.21a is such a

FIGURE 9.17 Wear mechanism maps under dry sliding conditions.

diagram for 1 GPa contact pressure under dry sliding conditions. For this contact pressure, alumina hasthe lowest wear of the four materials. Similarly, the maps can be sliced along a single speed; then thewear rate as a function of load or contact pressure can be examined. Figure 9.21b shows the case for thefour ceramics at 10 mm/s linear sliding speed under dry sliding conditions. In this case, alumina willwork fine in the low-pressure region; SiC will be more suitable at higher pressures. Figure 9.21c illustratesthe speed and contact pressure ranges that are available for use with these four materials under dry slidingconditions given a wear rate of 10–7 mm3/s. Similarly, Figure 9.22 illustrates the case for these fourmaterials under PPO-lubricated conditions. At 2 GPa contact pressure, SiC has the lowest wear(Figure 9.22a). Note the intersections of the constant wear lines among the four materials. Figure 9.22bshows the comparison of materials at a constant speed of 100 mm/s. For a constant wear rate of10–7 mm3/s, Figure 9.22c shows the safe operating regions for the four materials. These derivative mapsillustrate how one can select materials for a particular operating condition under a specific lubricatingenvironment.

FIGURE 9.18 Wear mechanism maps under paraffin oil-lubricated conditions. (The boundaries are derived fromwear contour maps and verified experimentally. Not all zones had been verified.).

9.8 Modeling Wear by Using Wear Maps

9.8.1 Metals

Lim and Ashby (1987) used pin-on-disk (steel on steel) wear data under dry sliding conditions from theliterature and constructed a wear mechanism map (Figure 9.14). The map uses normalized load and speedas parameters, and the data are successfully partitioned into different regions. Asperity temperatures arethe key underlying parameter for the wear mechanisms, e.g., delamination wear, oxidation wear, melt wear,and seizure. Even though the asperity temperature calculation is based on the asperity scale, the coefficientsof friction used are the average values for the macrocontact. Wear equations are developed for each mech-anism, and these equations are shown in Table 9.3. As discussed before, this approach is successful for severewear regimes where high asperity temperatures dominate wear mechanisms. For mild wear and lubricated

FIGURE 9.19 Wear mechanism maps under water-lubricated conditions. (The boundaries are derived from wearcontour maps and verified experimentally. Not all zones had been verified.).

cases, asperity temperatures are important parameters but not controlling (boundary lubricating films,tribochemical wear, elastohydrodynamic lubrication, etc.); such an approach is not effective.

The asperity level temperatures are also critical in analyzing chemical reactivity and surface filmformation (Hsu, 1991). The use of measured “average” friction coefficients to estimate asperity temper-atures has been shown to be inadequate (Hsu et al., 1988). When the localized wear event and theaccompanying measured asperity friction (based on a two-ball collision experimental set up) was incor-porated in a mechanical wear model, the resulting temperature became consistent with those estimatedfrom chemical reactivity analysis (Hsu et al., 1994). This suggests that, for an asperity model, the asperitycoefficients of friction are needed.

The linkage between asperity events and system parameters such as load, temperatures, and speed, foreach lubricating environment, lies in the concept of relative surface “conformity.” The actual surfaceroughness during wear is an ever-changing parameter. When lubrication remains effective, a steady-stateconformity of the two contacting surfaces is usually reached (Wang et al., 1991). From the degree of surfaceconformity, one could possibly link asperity contact conditions to the measured macrocontact conditions.

Wear mapping has pointed to the fact that a family of equations is needed to account for wear for agiven materials pair in a given environment. No effective wear models for metals are available for themild-wear and well-lubricated conditions.

FIGURE 9.20 Material comparison based on mild-to-severe wear transitions under (a) dry air, (b) PPO, and (c)water-lubricated conditions.

9.8.2 Ceramics

9.8.2.1 Basic Wear Mechanisms

The dominant wear mechanisms for different regimes are different. These mechanisms are summarizedin Table 9.4. The stress intensity in the contact is a critical parameter that underlies the formation ofdifferent wear regimes. In mild wear, the nominal contact produces stress intensity insufficient to causemacroscopic scale fracture. Wear occurs primarily at the asperity scale in the form of abrasion andmicrofracture. This micro-abrasion will generate subsurface damage/cracking at the micron scale. As thelocalized stress intensity exceeds K1C of the material, microfracture occurs and generates intergranularcracks. This leads to subsequent grain pullouts. In severe wear, the nominal contact produces stressintensity that exceeds K1C and causes macroscopic fracture such as tensile cracks (Hsu et al., 1994). Theedge effect of those tensile cracks represents a source of wear particles (Ying et al., 1997). These particlesform third bodies in the contact zone and cause more localized fracture and grain pullouts. The combined

FIGURE 9.21 Material selection guides by using (a) fixed contact pressure, (b) fixed sliding speed, and (c) wearrate level. (The condition is dry sliding.).

wear particles and pulled-out grains are commonly observed in all four ceramics in the severe wearregime. In the ultra-severe wear regime, intragranular fracture is commonly observed. High loads, highsliding speed, and/or their combination cause the much increased stress intensity beyond K1C. The endresults are the presence of large quantities of large wear debris.

9.8.2.2 Theoretical Analysis of Critical Parameters Based on Wear Mechanisms

Figure 9.23 shows the schematic of the different contact configurations in different wear regimes. In themild wear regime, wear is caused primarily by abrasion at the asperity scale. So the wear at the asperitycontact can be quantified by the product of wear depth, contact width, and length of this contact withineach “sliding cycle,” as illustrated in Figure 9.23a. The sliding cycle can be described by the total distanceslid l divided by the Hertzian contact width 2a, i.e., l/2a. Under this set of assumptions, wear can beexpressed by the following equation:

FIGURE 9.22 Material selection guides by using (a) fixed contact pressure, (b) fixed sliding speed, and (c) wearrate level. (The condition is paraffin oil-lubricated sliding.)

TABLE 9.3 Wear Equations Derived from Wear Mechanism Maps in Lim and Ashby, 1987

Seizure

Melt wear

Mild oxidational wear

Severe oxidational wear

Plasticity-dominated wear

TABLE 9.4 Classification of the Wear Map Data under Dry Sliding Conditions

Wear Regime Wear (mm3) Wear Mechanism

Mild wear(stress intensity < K1C)

10–7–10–4 (Asperity scale failure mode)AbrasionIntergranular cracksSubsurface damage/cracksGrain pulloutTribochemical

Severe wear(stress intensity > K1C)

10–5–10–2 (Nominal scale failure mode)Fracture mechanicsTensile cracks → edge effects3rd-bodies (linked to grain pullout)

Ultra-severe wear(stress intensity � K1C)

10–3–101 (Nominal scale + few pieces large debris)Thermal shock (nominal scale)

˜ ln ˜Fá ì

T T

T âít

b o=+( )

−−( )

1

11

20

10

21 2

6

m

˜˜

˜˜WT T

T *

H

L âíáìFí

T *â

T Tm o 0

m o

=−

( ) −

11

˜ exp˜

˜WC A r

Z a

Q

RT

F

ío o

c

o

f

=

−

2

˜˜ ˜

˜W = fK T T FN

L a áìáì

aH â

K T T

F

Ní -1m

ox mox

b

ox

o

ox mox

b

−( )( )−( )

1 21 2

˜ ˜ ˜W =2a f

fFo v

A*

Definitions of the terms:Ao Arrhenius constant for oxidation Tm melting temperatureC constant used in the model for mild Tm

ox melting temperature of oxideoxidation wear W normalized wear rate

F normalized pressure on sliding surface Zc critical thickness of oxide filmH0 room temperature hardness of metal a thermal diffusivity of metalKox thermal conductivity of oxide fA

* critical area fraction of voidsL latent heat of fusion per unit volume for metal fm volume fraction of molten materialLox latent heat of fusion per unit volume for oxide during slidingN total number of contacting asperities fv volume fraction of inclusionsQ0 activation energy for oxidation r0 radius of pinR molar gas constant ν normalized velocityT* an equivalent temperature for metal α heat distribution coefficientTo 300°K αt constant in Tabor’s junctionTb bulk temperature growth equationTf flash temperature β dimensionless parameter for bulkγ cumulative plastic shear strain heatingµ coefficient of friction

(9.1)

where Pm = mean Hertzian pressure, Hv = hardness, Ci = dimensionless geometric factor, and di = asperitycontact width. The terms in the parentheses represent the wear depth, which is assumed to be proportionalto the ratio of Pm and hardness and a fraction of the contact width di. The 2a term inside the bracketsrepresents the upper bound of length li of such asperity-scale abrasive wear within a single cycle. Sincethe ratio of Pm/Hv is constant throughout all the asperity contacts, the summation term will be propor-tional to the real contact area. In the literature, the real contact area between rough surfaces has beenmodeled by many (Lee and Cheng, 1992; Greenwood and Williamson, 1966). The results appear to varydue to different assumptions, but the functional dependence of real contact area can be expressed asfollows:

where N = load and E′ = composite Young’s modulus. The roughness parameters include asperity radius(Greenwood and Williamson, 1966), r.m.s. roughness (Lee and Cheng, 1992; Greenwood and Williamson,1966), and/or autocorrelation length (Lee and Cheng, 1992). By substituting the real contact area intoEquation 9.1, the mild wear can be represented by the following equation:

(9.2)

For the data set considered here, the surface roughness of all specimens for the four ceramics is controlledto the same roughness; therefore f can be considered as a constant in this analysis. Hence, the mild wearis directly proportional to Pm∗N∗l, which relates to the operating conditions, and inversely proportionalto material properties, Hv and E′.

FIGURE 9.23 Illustrations of the contacts for modeling wear in different wear regimes. (a) asperity scale abrasionin mild wear regime, (b) tensile cracks inside the nominal contact in severe wear regime, and (c) gross fracture inthe nominal contact in ultra-severe wear regime.

WearVol ∝ ∗

∗ ∗

∗∑ P

HC d d a

l

am

v

i i i

i

22

AN

Efreal ∝

′∗ ( )roughness parameters

Wear Vol ∝ ∗′∗ ( )∗P

H

N

Ef lm

v

roughness parameters

In severe wear regime, because of the presence of cracks, edge effects from those cracks, and third-body wear particles, the asperity contacts have very different characteristics, as illustrated in Figure 9.23b.The total wear volume may be expressed as follows:

(9.3)

where σMAX = maximum tensile stress (Adachi et al., 1997), T* = interfacial temperature of the nominalcontact (Archard, 1958-9), To = ambient temperature at 20°C, K1C = fracture toughness, d50 = mean grainsize, bi = geometric factor, di = contact width. Here the wear depth is assumed to be proportional to thecontact width di by using the ratio of a stress intensity from tensile stress divided by K1C and anothergeometric factor bi. The crack length in the measure of the stress intensity is assumed to be equivalentto the mean grain size d50. Because of the potential thermal effects from frictional heating, the tensilestress is further modified by multiplying a temperature ratio of (T*/To). The interfacial temperature T*is calculated by using Archard’s temperature equation (Archard, 1958-9). In so doing, the nominal contactis treated as a single asperity and the interfacial temperature is applicable within a layer thickness of halfof the Hertzian contact width, i.e., this temperature exists within a thickness of a. The multiple of thetwo di inside the bracket appears to represent the real contact area, as in the mild wear case. However,in the severe wear situation, a different interpretation may be needed to account for the edge effects dueto cracking and third-body wear. This area is assumed to be proportional to the ratio of N/Hv (Wangand Hsu, 1996a). As a result, Equation 9.3 can then be rewritten as follows:

(9.4)

In Equation 9.4, the hardness value is the hardness at the asperity temperature. Equation 9.4 is quitesimilar to the tensile crack model proposed by Hsu (Wang and Hsu, 1996a). But the temperature effectshave been added. Also, the use of fracture toughness eliminates the need for a special material propertyσD, which is the critical damage stress (Wang and Hsu, 1996a).

In the ultra-severe wear regime, one assumes that the thermal shock is attributed to a temperaturegradient between the heated interface and cold substrate or a hot spot with its surrounding surface area.Since the interfacial temperature exists in a layer with a thickness of half Hertzian width, the wear equationin Equation 9.4 can be extended by substituting the d50 term with a. Namely, the crack length thatdetermines the stress intensity is equivalent to a, as illustrated in Figure 9.23c. This gives rise to thefollowing:

(9.5)

Apparently, the increased (T*/To) ratio and crack length a and a decrease in Hv(T*) will push wear tomuch elevated levels, as compared to the severe wear described in Equation 9.4.

9.8.3 Modeling Approaches

For brittle materials, wear can be linked to the stress intensity as described previously. One approachwill be to examine and correlate wear data according to a severity scale, i.e., as the conditions of contactbecome more severe, higher wear should result. After the data are lined up according to the contactseverity, then the materials will be normalized using material property data. In principle, this normal-ization process will make different materials appear to be the same. Wear for these materials thatexperienced similar wear mechanisms will be similar, as if they are a single material.

Wear Vol ∝

∗ ∗ ∗

∗∑σMAX

C oi i i

i

d

K

T

Tb d d a

l

a50

1

22

*

Wear Vol ∝

∗ ( ) ∗σMAX

C o V

d

K

T

T

N

H Tl50

1

*

*

Wear Vol ∝

∗ ( ) ∗σMAX

C o V

a

K

T

T

N

H Tl

1

*

*

9.8.3.1 Severity Index

The contact severity can be defined in terms of the operating conditions. Let us examine each of thewear equations derived from simple theoretical analysis. In mild wear, Equation 9.2 contains two sets offactors. The Pm∗N∗l term is directly related to the operating conditions. The Hv∗E′ is just a product ofmaterial properties. Similarly, the σMAX∗(T*/To)∗N∗l term in Equation 9.4 and the σMAX∗ ∗(T*/To)∗N∗lterm in Equation 9.5 are directly linked to the operating conditions. Meanwhile, the /(K1C∗Hv(T*))is the material property term in Equation 9.4 and K1C∗Hv(T*) in Equation 9.5. Up to this point, one canplot the wear data in each wear regime against the corresponding severity parameter and observe datascatter among different materials. If the above equations are valid, the degree of data scatter will measurethe deviations from the “ideal.”

For a global approach, the severity parameters from the three wear regimes are not the same. In orderto employ a unified severity parameter across all three wear regimes, some adjustments are needed. First,the common factor in all three wear regimes is N∗l. The uncommon term in mild wear is Pm, andσMAX∗(T*/To) in severe wear, and σMAX∗ ∗(T*/To) in ultra-severe wear. However, the Pm and σMAX arerelated through the friction coefficient (Ying et al., 1997). Moreover, the (T*/To) is relatively close to unityin the mild wear regime for the four ceramics, except for Y-TZP. Therefore, the severity parameter canbe generalized to σMAX∗(T*/To)∗N∗l.

9.8.3.2 Materials Normalization

Materials are characterized by their material properties such as hardness, elastic modulus, toughness,thermal conductivity, thermal diffusivity, and their temperature dependence. In wear, the issue of materialproperties at the proper scale is very important. While the bulk material properties influence wear, thelocal properties at the asperity scale often control the wear process. For example, under mild wearconditions, the macrocontact pressure is less than the K1C; therefore, fracture of the contact due to themacrocontact pressure induced tensile stresses will not take place. The asperity contact pressure, however,may exceed K1C and may cause local, grain level fracture. This fracture behavior is governed by localhardness, local fracture toughness, grain size, the ratio of grain boundary energy release rate to grainenergy release rate (He and Hutchinson, 1989), residual thermal stress in the grain boundary from thesintering, and the crack length. If the microstructure is a duplex structure, i.e., elongated grains intermixedwith equiaxed grains, crack deflection by the elongated grains has to be taken into account, i.e., the aspectratio of grain defined by grain length divided by grain diameter. If the detailed wear mechanism in eachregime for each material is known, many of these material properties can be considered. Whether thereis a set of universal material normalization parameters for the four ceramics or not is open to question.

Iteration between the severity index and material normalization parameters will help to define whatparameters are important and what parameters can be set aside. The optimized combination of param-eters will best describe the wear data.

9.8.4 Correlation of Data According to Wear Maps

In the following sections, various severity parameters will be tested with the wear map database, followedby the generalized severity parameter determined above.

9.8.4.1 Historical Severity Indexes

There are several versions of the so-called severity index (Adachi et al., 1997; Kim et al., 1986; Kim et al.,1994). They are described below.

.

where Po = maximum Hertzian pressure and RMAX = maximum surface roughness. The Sc is originallyderived from modeling stress intensity factor by using the maximum Hertzian pressure and a crack length

a

d50

a

SP R

Kco MAX

C

=1

equivalent to the maximum surface roughness (Kim et al., 1986). Subsequently, the severity index hasbeen modified by incorporating stresses introduced by friction, and a slightly different form was derived(Kim et al., 1984), as shown below:

where µ = friction coefficient and the rest of the parameters are the same as in SC. More recently, a newseverity index has been derived from using the maximum tensile stress in estimating the threshold stressintensity, Scm (Adachi et al., 1997). The maximum tensile stress is simplified in Scm as shown below:

where (1+10µ)Po is the simplified tensile stress.The maximum surface roughness, RMAX, is the same for all specimens tested in our database. Because

it represents the equivalent crack length in the estimate of stress intensity, one can employ an alternativeinterpretation of this term by using the mean grain size.

Figure 9.24 shows the effects of the various severity indexes to correlation plots of the wear map datafor the four ceramics under dry sliding conditions. The data for the mean grain size, d50, of the fourceramics are listed in Table 9.5. SC and SCF have similar results. Within each material, different wear levelscan be present at the same severity index. Wear is primarily correlated by the maximum Hertzian pressurein SC, and friction coefficient has some contributions in SCF. When all four materials are combined, theyform two groups. Alumina and SiC are in one group at a higher severity. Silicon nitride and zirconia arein a lower severity group. These are due to the combination of larger mean grain size and relatively lowerfracture toughness in the alumina and SiC. On the other hand, Figure 9.24c shows that the wear datamingle more by using Scm. Because all these severity indexes already contain material properties, nomaterial normalization can be applied. Therefore, one may conclude that these parameters do notcorrelate with the entire wear database adequately.

Figure 9.25 shows the application of a single parameter of mean Hertzian pressure to the database.Again, the results show that it is inadequate to represent a unified severity parameter for this database.

9.8.4.2 New Correlation Parameters

Figure 9.26a shows the wear data plotted against σMAX∗(T*/To). This parameter has a range of about threeorders of magnitude. As compared to the total range of wear volume of nine orders of magnitude, thisparameter is extremely sensitive to the wear level. On the other hand, Figure 9.26b shows the results ofusing the severity parameter σMAX∗(T*/To)∗N∗l. This parameter has a range of seven orders of magnitude,much more compatible to the wear levels. Also the data in each wear regime appear to form clusters,suggesting the severity parameter has the ability to order the wear process. Inclusion of and hasalso been tested. Only slight change is obtained.

9.8.5 Materials NormalizationThere are different ways to normalize the wear results for the purpose of direct comparisons. One way isto normalize all materials with respect to a particular material. Another is to determine the average value,and then all materials will be normalized with respect to the average. The latter approach is taken here.

Figure 9.27a shows the mild wear data only plotted against the severity parameter. This will be thebaseline to begin the material normalization process. Figure 9.27b shows the data being normalizedagainst the average HV and average E′. The average HV for the four materials is 21 ± 8 GPa and the averageE′ is 176 ± 44 GPa. Because wear in this regime is inversely proportional to HV and E′ (Equation 9.2),

SP R

KCF

o MAX

C

=+ µ( )1 2

1

SP R

Kcm

o MAX

C

=+ µ( )1 10

1

d50 a

FIGURE 9.24 Correl Scm. These indexes were defined in the text.

ational results from using historical severity indexes: (a) SC, (b) SCF, and (c)

the material normalization is carried out by multiplying the wear volume by the ratios of E′/E′mean andHV/HV,mean. For example, the wear volume data of SiC are multiplied by 1.48 and 1.26, since its hardnessand Young’s modulus are both higher than the mean values. Figure 9.27b displays that, after materialnormalization, the Si-based ceramics are separated from the oxides. Because the functional dependenceon the severity parameter is different between these two groups of data, a different wear mechanism iscontrolling the wear. One possible interpretation is that this may be caused by the presence of tribo-chemical reactions which are not taken into account in the mechanism-based modeling. Figure 9.27cpresents a conventional material normalization scheme using the wear coefficient, defined as wearvolume∗HV/(N∗l). The results appear to suggest that it is not adequate for this large database.

Figure 9.28 shows the material normalization carried out for data in the severe wear regime. Accordingto Equation 9.4, wear volume is inversely proportional to the product of HV(T*)∗K1C/ . The averagefracture toughness for the four materials is 5.4 ± 2.3 MPa.m1/2, and the average d50 is 2.4 ± 2 µm.Figure 9.28b shows that the wear data among the two Si-based ceramics and Y-TZP appear to be morepacked, but the alumina data fall farther away from the line. Again, this may be caused by tribochemicalreactions with the wear debris generated in this regime.

The material normalization used in Evans and Marshall (1980) that correlated the grinding data amongdifferent ceramics is also tested, i.e., (K1C

0.625∗Hv0.5)(8/9), but only slight shifts are found.

Figure 9.29 shows the material normalization carried out for the ultra-severe wear data. The materialnormalization includes the product of hardness and fracture toughness. The improvement from thematerial normalization appeared to be slight.

The material normalization schemes discussed above show that different degrees of data shifts areobtained for data in the different wear regimes. Clearly, the process of selecting a severity parameter and

TABLE 9.5 Microstructural Parameters of the Four Ceramics

Al2O3 Y-TZP SiC Si3N4

Mean grain size, d50 (µm) 5 1 3 0.5Grain size ratio, d90/d50 3 2 2.6 2Aspect ratio, A 1 1 5 4

FIGURE 9.25 Correlational results from using mean Hertzian contact pressure.

d50

the material normalization process for that severity parameter will have to be an iterative one. At thistime, the overall data scatter after the material normalization is about ±1 order of magnitude.

9.8.6 SummaryThe large wear database used to construct ceramic wear maps presents a unique opportunity to testcorrelational wear parameters. The database consists of self-consistent data with wide variations inoperating conditions and material properties. This database was used to test the concept of test severity

FIGURE 9.26 Correlational results from using (a) maximum tensile stress multiplied by a temperature ratio ofT*/T0 to take into account the thermal effects, and (b) a severity parameter derived from the current study.

FIGURE 9.27 Mater b) wear volume normalized by using the product of modified hardness andYoung’s modulus, and

ial normalization in the mild wear regime: (a) baseline (no normalization), ( (c) normalization by using the wear coefficient.

parameters to separate the different wear regimes. The determination of the severity parameters is basedon the understanding of the wear mechanisms derived from the wear maps. After the wear data of allfour ceramics have been separated by using the severity parameter, material normalization is carried outfor the data in the individual wear regimes. Results show that grouping of data among different ceramicscan be achieved through using the first sets of severity parameter and material normalization parameters.This is quite promising, in light of the huge variations present in the experimental conditions andmaterials. Further refinements through iterations will be necessary to improve the result.

9.9 Advantages and Limitations of Current Wear Map Approach

There are two ways to approach a systematic construction of wear maps. One is to capture the key variableand divide the regions based on that parameter. This essentially is the Ashby approach. His wear map isconstructed based on the fact that wear is controlled by the asperity temperatures due to sliding. Equations

FIGURE 9.28 Material normalization in the severe wear regime: (a) baseline (no normalization), and (b) wearvolume normalized by the product of modified HVK1C / .d50

FIGURE 9.29 Mater ion), (b) wear volume normalized by the product of modified hardness andfracture toughness, an

ial normalization in the ultra-severe wear regime: (a) baseline (no normalizatd (c) normalization by using wear coefficient.

can then be developed to describe wear according to the asperity temperature scales such as mildoxidation, severe oxidation, and melt wear. The shortcoming of this approach is that regions not dom-inated by this parameter lose their importance. The choice of parameters to construct the wear mapsreflects the approach taken.

The other approach is the one described in this chapter. As can be seen, the wear maps, once constructed,can be very powerful in mechanistic determination and materials selection. The wear maps can also providea design guideline for contact geometry, lubrication environment, and wear life estimation. There arelimitations to this approach as well. First of all, many wear experiments are needed to construct the wearmaps. In fact, how much data are “sufficient” for a wear map is a real issue. Using the step-loading testprocedures saves a tremendous amount of work, but the test procedure itself has limitations. The step-loading takes advantage of the fact that a steady state of wear rate is often achieved for most systems undermild wear conditions. This assumption is true for most lubricated systems but may or may not be truefor some high-wear regions. One needs to check the validity of this assumption periodically and performexperiments under constant loading conditions to validate the step-loading results.

Long-term time effects such as low-cycle fatigue on wear are difficult to include in the current wearmaps. Tribochemical reactions that require an induction time period to be effective are hard to deal withusing a step-loading procedure. Many of these phenomena require a long-duration constant machinesetting condition to measure properly. The test procedures effective in measuring lubrication (tribochem-ical effects) are not the same as those procedures useful for measuring materials wear.

There are many operating wear mechanisms in a wear test. Sometimes several mechanisms coexist ina region to render relatively mild wear, such as deformation, tribochemical wear, and microabrasion.The individual contributions from these coexisting wear mechanisms are difficult to separate. In orderto collect critical data for wear modeling, more consistent, careful experiments are required. In addition,accumulation of wear damages by microfracture and microabrasion mechanisms is potentially a fatigueprocess. Therefore, time effects on wear will also need to be addressed. Microstructural parameters suchas grain size, grain size distribution, grain boundary phase, etc., have noticeable effects on the wearcharacteristics of polycrystalline ceramics (Hsu et al., 1995). How to account for them is a challenge.Furthermore, there are many possible lubrication chemistries for a single ceramic (Gates and Hsu,1995a,b, 1997). Each chemistry is unique, so it is difficult to map out all the possible permutations oflubrication chemistries for a given material pair.

9.9.1 Future Wear Maps Research NeedsWear map research was originally developed in an attempt to provide a wear classification system forceramics as well as to provide a sufficient database for the development of wear models. So far the firstgoal has been met. The progress in wear model development is ongoing. A single universal parameter tofit all the data has been demonstrated to be unrealistic, but one may ask if such parameter(s) exists ineach wear mechanism zone. This question remains unanswered at this time. The current database islimited to a narrow speed and load range because of the need to simultaneously measure wear andlubricant chemistry effects. To extend the speed and load ranges will necessitate the use of several weartesting machines. How this will affect the internal consistency needs to be investigated.

In summary, wear mapping represents a new approach to examining the age-old issue of wear andhas shown it presents an integrated view of wear that cannot be seen otherwise. Much more work needsto be done to fully develop this approach for practical applications.

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