Wear Mechanisms. 7.1 Introduction. Koji Kato. Koshi Adachi

Transcription

1 7 Wear Mechanisms Koji Kato Tohoku University Koshi Adachi Tohoku University 7.1 Introduction 7.2 Change of Wear Volume and Wear Surface Roughness with Sliding Distance 7.3 Ranges of Wear Rates and Varieties of Wear Surfaces 7.4 Descriptive Key Terms 7.5 Survey of Wear Mechanisms Adhesive Wear Abrasive Wear Fatigue Wear Corrosive Wear Mechanical Wear of Ceramics under Elastic Contact 7.6 Concluding Remarks 7.1 Introduction Wear has been recognized as meaning the phenomenon of material removal from a surface due to interaction with a mating surface. Almost all machines lose their durability and reliability due to wear, and the possibilities of new advanced machines are reduced because of wear problems. Therefore, wear control has become a strong need for the advanced and reliable technology of the future. Wear rate changes drastically in the range of to 10 1 mm 3 /Nm, depending on operating conditions and material selections (Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978; Rabinowicz, 1980). These results mean that design of operating conditions and selection of materials are the keys to controlling wear. As one way to meet these requirements, wear maps have been proposed for prediction of wear modes and wear rates (Lim and Ashby, 1987; Hokkirigawa and Kato, 1988). A wear map is considered one of the best descriptions of tribological conditions and is useful in selecting materials in a wide range of operating conditions. In order to design tribosystems and select materials based on the wear map, an understanding of wear rate, varieties of wear modes, and wear mechanisms is essential. Wear is the result of material removal by physical separation due to microfracture, by chemical dissolution, or by melting at the contact interface. Furthermore, there are several types of wear: adhesive, abrasive, fatigue, and corrosive. The dominant wear mode may change from one to another for reasons that include changes in surface material properties and dynamic surface responses caused by frictional heating, chemical film formation, and wear. Wear mechanisms are described by considering complex changes during friction. In general, wear does not take place through a single wear mechanism, so understanding each wear mechanism in each mode of wear becomes important. Our present understanding of the mechanisms of the four representative wear types is described in the following sections.

2 FIGURE 7.1 Three representative types of wear curves in repeated contacts. FIGURE 7.2 Three representative types of surface roughness changes in repeated contacts. 7.2 Change of Wear Volume and Wear Surface Roughness with Sliding Distance Wear volume, wear surface roughness, and wear particle shape give us important information in characterizing wear. Three representative types of wear volume curves are shown schematically in Figure 7.1. Type I shows a constant wear rate throughout the whole process. Type II shows the transition from an initially high wear rate to steady wear at a low rate. This type of wear is quite often observed in metals (Chiou et al., 1985). Type III shows catastrophic transition from initial wear of low wear rate to wear of a high rate, such as fatigue fracture. This type of wear is often observed in ceramics (Cho et al., 1989). The amount of sliding before catastrophic wear is the period at which crack initiation takes place and depends on the initial surface finish, material properties, and frictional conditions. On the other hand, three representative types of roughness curves on wear surfaces are shown in Figure 7.2. Type I shows the case of steady wear, where the surface roughness does not change from the initial value. Type II shows the case of steady wear, where surface roughness increases to a certain value and stays there. Type III illustrates initial running-in and steady wear, where surface roughness decreases drastically in the running-in process. It is typically observed in lapping and polishing for surface finishing. 7.3 Ranges of Wear Rates and Varieties of Wear Surfaces In general, wear is evaluated by the amount of volume lost and the state of the wear surface. The degree of wear is described by wear rate, specific wear rate, or wear coefficient. Wear rate is defined as wear

3 FIGURE 7.3 Distribution of specific wear rate of metallic materials in sliding contact under different lubrication conditions. (Data from Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978; Rabinowicz, 1980). FIGURE 7.4 themselves. Distribution of specific wear rates and friction coefficients of ceramics in unlubricated sliding against volume per unit distance, which corresponds to the slope of the wear volume curve shown in Figure 7.1. Specific wear rate is defined as wear volume per unit distance and unit load. Wear coefficient is defined as the product of specific wear rate and the hardness of the wearing material. The distributions of specific wear rates of metallic materials in sliding contact under different lubrication conditions are summarized in Figure 7.3 (Archard, 1953; Bhansali, 1980; Hirst, 1957; Hokkirigawa, 1997; Holm, 1946; Lancaster, 1978; Rabinowicz, 1980). Observed specific wear rates show a wide distribution in the range of to 10 1 mm 3 /Nm by the differences in lubrication states. Figure 7.4 shows the distributions of specific wear rates and friction coefficients measured in unlubricated sliding of four kinds of ceramics against themselves under different normal loads, sliding velocities, and temperatures. The specific wear rates range from 10 9 to 10 2 mm 3 /Nm, depending on materials and friction conditions, even in the case of contact between similar materials. Figure 7.5 shows the varieties of wear surfaces of ceramics observed under different contact conditions. Wear surfaces look quite different depending on materials and friction conditions. This means that wear can change drastically when small changes in contact conditions are introduced into the tribosystem. The results shown in Figures 7.3, 7.4, and 7.5 clearly illustrate the following remark about wear (Bayer, 1994): Wear is not a material property. It is a system response. Wear changes drastically even with a relatively small change in a tribosystem, which is composed of dynamic parameters, environmental parameters, and material parameters.

4 FIGURE 7.5 Variety of worn surface morphologies of three kinds of ceramics under different operating conditions. The arrows indicate relative sliding directions of counterfaces. 7.4 Descriptive Key Terms There are many terms used to describe wear, and they are not always well differentiated. This sometimes makes understanding wear mechanisms confusing and difficult. Further effort must be given to achieve greater clarity in our approach to the analysis of wear mechanisms. In this section, descriptive key words of wear and their interrelations are summarized. This summary is shown in Figure 7.6 Wear is sometimes investigated from the viewpoint of the types of contact interaction of solid surfaces. There are many different contact configurations in practice. Normal or inclined compression and detachment, 2001 by CRC Press LLC

5 FIGURE 7.6 Descriptive key words of wear and their interrelations. unidirectional sliding, unidirectional rolling, reciprocal sliding, reciprocal rolling, and rolling with slip are all different contact configurations classified from the viewpoint of motion of contacting bodies. Furthermore, free solid particles sometimes become unique substances, which attack interacting surfaces. This is also a contact configuration. Wear in these contact types is described as sliding wear, rolling wear, impact wear, fretting wear, or slurry wear. These descriptions of wear are all technical and based on the appearance of the contact type. They do not represent wear mechanisms in a scientific way. In order to focus on the wear mechanisms from the viewpoint of contact configurations, apparent and real contact conditions at the contact interface are introduced without particularizing about these contact configurations. Severity of contact, such as elastic contact or plastic contact, is the simplest and most direct way to think about wear mechanisms, and is a tribosystem response determined by dynamic parameters, material parameters, and atmospheric parameters. The following four wear modes are generally recognized as fundamental and major ones (Burwell, 1957/58): 1. Adhesive wear 2. Abrasive wear 3. Fatigue wear 4. Corrosive wear Adhesive wear and abrasive wear are wear modes generated under plastic contact. In the case of plastic contact between similar materials, the contact interface has adhesive bonding strength. When fracture is supposed to be essentially brought about as the result of strong adhesion at the contact interface, the resultant wear is called adhesive wear, without particularizing about the fracture mode. In the case of plastic contact between hard and sharp material and relatively soft material, the harder material penetrates to the softer one. When the fracture is supposed to be brought about in the manner of micro-cutting by the indented material, the resultant wear is called abrasive wear, recognizing the interlocking contact configuration necessary for cutting, again without particularizing about adhesive forces and fracture mode.

6 In the case of contact in the running-in state, fatigue fracture is generated after repeated friction cycles. When surface failure is generated by fatigue, the resultant wear is called fatigue wear. In the case of contact in corrosive media, the tribochemical reaction at the contact interface is accelerated. When the tribochemical reaction in the corrosive media is supposed to be brought about by material removal, the resultant wear is called corrosive wear. In air, the most dominant corrosive medium is oxygen, and tribochemical wear of metals in air is generally called oxidative wear. Fatigue wear and corrosive wear can be generated in both plastic and elastic contacts. The material removal in adhesive, abrasive, or fatigue wear is governed by deformation and fracture in the contact region, where fracture modes are fatigue, brittle, or ductile fracture. Such deformation and fracture are generated by mechanically induced strains and stresses. Therefore, this type of wear is generally described as mechanical wear. The material removal in corrosive wear is governed by the growth of chemical reaction film or its chisolution on wear surface, where chemical reactions are highly activated and accelerated by frictional deformation, frictional heating, microfracture, and successive removal of reaction products. This type of wear is generally described as chemical wear or tribochemical wear. In some cases, material removal is governed by surface melting caused by frictional heating or by surface cracking caused by thermal stress. These types of wear are described as thermal wear, where frictional heating and partial high temperature govern the process. The macroscopic classifications in terms of mechanical, chemical, and thermal wear are useful to a comprehensive understanding of wear because almost all models of wear are included in these three types. The descriptions of wear by different definitions are summarized in Figure 7.6 to show the relative relations. 7.5 Survey of Wear Mechanisms As the traditionally accepted representative wear modes, the four wear modes shown in Figure 7.7 are considered, and the wear mechanisms based on those wear modes are explained in detail. In addition, the wear mechanism based on mechanical wear of ceramics is explained Adhesive Wear If the contact interface between two surfaces under plastic contact has enough adhesive bonding strength to resist relative sliding, large plastic deformation caused by dislocation is introduced in the contact region under compression and shearing. As a result of such large deformation in the contact region, a FIGURE 7.7 Schematic images of four representative wear modes.

7 crack is initiated and is propagated in the combined fracture mode of tensile and shearing. When the crack reaches the contact interface, a wear particle is formed and adhesive transfer is completed. This type of wear, which occurs when there is enough adhesive bonding at the contact interface, is called adhesive wear Estimation of Adhesive Wear Volume If it is assumed that the real contact is composed of n contact points of equal size and if a new contact point is formed after the disappearance of the former one, the total number of contacts n stays constant during sliding. By supposing a circular contact area of radius a, the possible volume of wear particles generated after sliding the distance of 2a is assumed as the half sphere volume described by 2πa 3 /3. Based on these assumptions, the possible wear volume V for n contact points after sliding the distance L is given by: 2 3 L V = n πa 3 2a (7.1) Since the normal contact pressure with plastic deformation is almost equal to the hardness value H of the wearing material, the total real contact area for n contact points nπa 2 is expressed by: 2 W nπ a = H (7.2) By substituting Equation 7.2 into Equation 7.1, possible wear volume V under normal load W after sliding distance L is given by: V 1 = 3 WL H (7.3) Equation 7.3 shows that the adhesive wear volume is proportional to the normal load and the sliding distance, and is inversely proportional to the hardness of the wearing material. Considering the relationship of Equation 7.2, it is proportional to the total real contact area during sliding. In practice, however, adhesive wear can occur through various modes, as shown in Figure 7.8 (Kayaba and Kato, 1981), and the size of the wear particles does not simply correspond to the size of the contact. Furthermore, a wear particle is not always generated only from the relatively soft material but can come from both materials. The probability of wear particle generation at each contact point is also not equal. It depends on the microscopic shape of the contact, microstructure of the material in the contact region, microscopic surface contamination, and other disturbances in the surroundings. In order to accommodate all these variables, a parameter K ad is introduced in Equation 7.3 as a modifier, and the wear volume is described by: V = K WL ad H (7.4) where K ad is called the wear coefficient for adhesive wear. It is a principal value for a friction pair to describe its wear rate. The physical meaning of K ad is the wear volume fraction at the plastic contact zone, and it is strongly affected by the material properties and the geometry of the zone in compression and shearing. In the adhesive wear of metals (Archard, 1953; Hirst, 1957), wear coefficient K ad varies between 10 7 and 10 2 depending on the operating conditions and material properties. It should be recognized that a wear coefficient K ad is not a constant value but is a possible value in the range of adhesive wear rate.

8 FIGURE 7.8 Schematic diagram of representative adhesive transfer process observed in the adhesive wear process; adhesive transfer of a thin flake-like wear particle (a) and a wedge-like wear particle (b). (From Kayaba, T. and Kato, K. (1981), The adhesive transfer of the slip-tongue and the wedge, ASLE Trans., 24, 2, With permission.) Adhesive Wear Mode Tangential shear under compression at the contact interface of strong adhesive bonding generates slips along slip planes in the contact region. As a result of the slips, flake-like shear tongues are formed, as shown in Figure 7.8a, and are followed by a crack initiation and propagation in the combined fracture mode of tensile and shear in the leading region of the contact. The large plastic deformation in the contact region sometimes forms a wedge-like shape, which is followed by crack initiation and propagation in the combined fracture mode of tensile and shear in the trailing region of the contact, as shown in Figure 7.8b. Fractographic analysis of the fracture surfaces of wear particles of Figure 7.8a and b indicates that the larger part of the fracture surface of the flake-like wear particle shows the fracture mode of compression and shear, and that all parts of the fracture surface of the wedge-like wear particle in Figure 7.8b shows a tensile and shear fracture mode. Both wear modes which produce flake-like and wedge-like wear particles are basic ones in adhesive wear. In the adhesive wear process, transfer and retransfer from one surface to the mating surface take place in many cases. As a result, relatively large wear particles composed of two surfaces are formed. This is another basic part of the adhesive wear mechanism (Sasada, 1979). In the successive process of repeated sliding, these wear particles leave the contact interface as free particles or stay on either surface and form prows to scratch the counterface (Vingsbo and Hogmark, 1980; Chen and Rigney, 1985). Even if the contact is made between flat surfaces of similar materials and

9 FIGURE 7.9 Abrasive wear of ductile material, which is dominated by plastic deformation (a) and one of brittle fracture, which is dominated by brittle fracture (b). (From Evans, A.G. and Marshall, D.B. (1981), Wear mechanism in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439. With permission.) the contact interface is at first parallel to the sliding direction, the interface rotates and becomes inclined and wavy as a result of the combined effect of normal and tangential forces in sliding (Cocks, 1962). This is another aspect of deformation at a contact interface which explains why the adhesive wear mode of Figure 7.8a or Figure 7.8b occurs commonly in practice Abrasive Wear If the contact interface between two surfaces has interlocking of an inclined or curved contact, ploughing takes place in sliding. As a result of ploughing, a certain volume of surface material is removed and an abrasive groove is formed on the weaker surface. This type of wear is called abrasive wear. Here, we assume a single contact point model where a hard, sharp abrasive is indented against the flat surface and forms a groove on it by ploughing. When wearing material has a ductile property, a ribbonlike, long wear particle is generated by the mechanism of microcutting. In the case of brittle material, however, a wear particle is generated by a crack propagation (Evans and Marshall, 1981). These differences are summarized schematically in Figures 7.9a and b Abrasive Wear of Ductile Material Even in the case of sliding contact between smooth surfaces of the same ductile material, parallel grooves are generally found on the wear surface after sliding. The peak and the valley coincide well with the mating surfaces, as shown in Figure This result means that the hard abrasive asperities are formed on the mating surface because of, for example, work hardening, phase transitions, and third-body formation at the contact interface during repeated sliding contact. Therefore, abrasive wear is recognized as a more representative wear mode of ductile material in repeated sliding Estimation of Abrasive Wear Volume The first point to understand in the abrasive wear mechanism is the estimation of wear volume from which wear particles can be generated. Here, we assume a simplified contact model in which the abrasive has a conical shape with an angle θ, and the indentation depth of the abrasive is d, as shown in Figure 7.11.

10 FIGURE 7.10 sliding. The cross-sectional profiles of two mating wear surfaces of 0.45% carbon steel after pin-on-ring FIGURE 7.11 Typical model of abrasive wear by a conical indentor. Based on this assumption model, the possible wear volume V, which is ploughed by harder asperities after sliding a distance of L, is given by: V = d 2 tan θ L (7.5) Since the normal contact pressure under plastic contact can be assumed to be equal to the hardness value H of the wearing material, real contact area of π(dtanθ) 2 /2 is expressed by: 2 W ( ) = H v 1 π d tanθ 2 (7.6) By substituting Equation 7.6 into Equation 7.5, possible wear volume V under normal load W and after sliding distance L is given by: V = 2 π tanθ WL H v (7.7) Equation 7.7 gives the wear volume for the case of ideally plastic abrasive grooving in microcutting shown in Figure 7.12a. There are two other modes of wedge forming and ploughing in abrasive grooving, as shown in Figures 7.12b and c (Hokkirigawa and Kato, 1988) where the wedge does not grow from its initial size in Figure 7.12b, and no wear particles are generated in Figure 7.12c. It means that wear volume in abrasive grooving is not always equal to the groove volume. In order to accommodate all these meanings, a parameter K ab is introduced in Equation 7.7 as a modifier, and the wear volume is described by: V = K WL ab H (7.8)

11 FIGURE 7.12 Three different modes of abrasive wear observed by SEM: Cutting mode (a), steel pin on brass plate; wedge-forming mode (b), steel pin on stainless steel plate; ploughing mode (c), steel pin on brass plate. (From Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear, Tribology Int., 21, 1, With permission.) FIGURE 7.13 Effect of hardness on the relative wear resistance of pure metals. (From Khruschov, M.M. (1957), Resistance of metals to wear by abrasion as related to hardness, Proc. Conf. Lubrication and Wear, Inst. Mech. Engr., With permission.) Equation 7.8 shows that the abrasive wear volume is proportional to the normal load and the sliding distance, and it is inversely proportional to the hardness of the wearing material. In fact, abrasive wear resistance is linearly proportional to hardness of wearing metals, as shown in Figure 7.13 (Khruschov, 1957). The proportional constant K ab is called the wear coefficient for abrasive wear. It is a principal value for a friction pair in describing its wear rate. The physical meaning of K ab is the wear volume fraction against the nominal groove volume zone, and it depends on the ductility of wearing material, shear strength at the contact interface, and the shape of the abrasive asperity. In the abrasive wear of metal (Rabinowicz, 1980), wear coefficient K ab varies between 10 4 and 10 1, depending on the contact conditions and material parameters. It should be recognized from these data that wear coefficient K ab is not a constant value in abrasive wear. By comparing K ab with K ad in adhesive

12 FIGURE 7.14 Schematic diagram of effect of hardness ratio on wear rate of abraded material against abrasive. wear, it is clear that abrasive wear gives a relatively large wear coefficient. That is why abrasive wear is recognized as severe wear. Abrasive grooving by the hard and sharp asperity is possible only when the asperity is not flattened or fractured in sliding. Therefore, the abradability of the hard, sharp asperity must be evaluated Hardness Ratio and Shape of Abrasive Asperity The hardness of the abrasive asperity is important in abrasive wear. Generally, when the hardness ratio r (mating material hardness/abrasive hardness) stays below a certain critical value r c1 (0.5 to 0.8; Khruschov, 1974; Rabinowicz, 1983), abrasive wear clearly takes place. However, with the increase in hardness ratio r above the critical value r c1, wear volume of mating material decreases, and finally almost no wear is observed when r is close to a critical value r c2 (1 to 1.4; Rabinowicz, 1983). This relation is shown schematically in Figure The results in Figure 7.14 require consideration as to the yield criterion of asperity in grooving action. Theoretical analysis was made by the slip line field theory, and the critical condition for the yield of an asperity is given in Figure 7.15 (Kayaba et al., 1983) between the hardness ratio r and the critical asperity tip angle θ c. The parameter f in Figure 7.15b is the ratio of the shear strength of the interface to the shear strength of the softer material, and Figure 7.15a shows the relation at f = 0. Plastic grooving by the asperity is possible when its tip angle θ is larger than the critical value θ c, and this value changes depending on the values of hardness ratio r of two surfaces and f, as shown in Figure 7.15b. These figures show that the asperity with large θ can plough the mating surface even when the hardness ratio r is very close to unity theoretically. This is evidence of the high possibility of groove formation at the sliding interface between similar ductile materials Abrasive Wear Mode As mentioned above, abrasive wear takes three different modes: microcutting, wedge forming, and ploughing, as shown in Figure Wear particles are formed differently depending on these three modes. In the cutting mode, long and curled ribbon-like wear particles are formed. Low friction assists in this wear mode. In the wedge-forming mode, a wedge-like wear particle is formed at the tip of the grooving asperity as shown in Figure 7.12b and stays there working as a kind of built-up wedge to continue grooving. Sliding takes place at the bottom of the wedge where adhesive transfer of a thin layer from the underlying counterface continues to grow the wedge slowly. This wear mode appears as a combined effect of adhesion at an inclined or curved contact interface and shear fracture at the bottom of the wedge. High friction or strong adhesion assists in this wear mode. In the ploughing mode, a wear particle is not

13 FIGURE 7.15 Relationship between the critical tip angle θ c and the hardness ratio r where the normalized shear strength f is zero in (a) and changes from zero to 1.0 in (b). (From Kayaba, T., Kato, K., and Hokkirigawa, K. (1983), Theoretical analysis of the plastic yielding of a hard asperity sliding on a soft flat surface, Wear, 87, With permission.) generated by a single pass of sliding and only a shallow groove is formed. Repeated sliding and accumulation of plastic flow at the surface is necessary for the generation of wear particles. These three abrasive wear modes are theoretically predictable with two dimensional models of the slip line field theory (Challen and Oxley, 1979). Theoretical predictions agree well with experimental results of spherical pin-on-disk tests, which are shown in the abrasive wear mode diagram of Figure 7.16 (Hokkirigawa and Kato, 1988) by introducing the following parameter D p for the degree of penetration: D p = R πh πh W W R (7.9) where R is the pin tip radius, H the hardness of the wearing material, and W the load. The parameter f in Figure 7.16 has the same meaning as that in Figure Theoretical solid lines are drawn according to the theory (Challen and Oxley, 1979) by substituting the relationship of D p = 0.8 (1 cosθ)/sinθ where θ is the attack angle. In all these three abrasive wear modes, grooves are formed as the result of wear particle generation and plastic flow of material to form ridges on both sides of a groove. If we introduce the groove volume V g per unit sliding distance observed below the initial surface level and the ridge volume V r per unit sliding distance observed above the initial surface level on both sides of the groove, ( V g V r ) gives the wear volume at one groove in one pass of sliding. With these descriptions, the concept of degree of wear β at one groove is introduced, as shown in Figure 7.17 and is given as follows: Vg Vr β= V g (7.10) where β = 1 corresponds to the state of ideal material removal without forming ridges, and β = 0 means the ideal ploughing of no material removal.

14 FIGURE 7.16 Abrasive wear mode diagram: abrasive wear modes of ductile material as a function of degree of penetration D p and normalized shear strength f at the contact interface. Solid lines are theoretically induced with modified two-dimensional model. (From Hokkirigawa, K. and Kato, K. (1988), An experimental and theoretical investigation of ploughing, cutting and wedge formation during abrasive wear, Tribology Int., 21, 1, With permission.) FIGURE 7.17 Schematic diagram of cross-sectional profile of groove formed after scratching. V g : groove volume and V r : two side ridges volume of two sides. The degree of wear β defined in this way is a function of the hardness H of the wearing material and the degree of penetration D p as shown in Figure 7.18 (Hokkirigawa and Kato, 1989) for heat treated steels. This β is related to the abrasive wear coefficient K ab mentioned above at one groove as follows: K ab VH g =β W (7.11) It is clear in Equation 7.11 that β represents the fracture property of the wearing material and ( V g H/W) represents the deforming property of the wearing material under the effect of f and the shape of the indentor.

15 FIGURE 7.18 Degree of wear β as a function of degree of penetration D p observed with heat-treated steel of different hardness H (kgf/mm 2 ). (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance based on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp With permission.) The parameter β and V g are given from the result of a pyramidal scratch test as (Zum Gahr, 1987): β = H 0 1 exp 2 H 13 ε s ln ε c (7.12) where H 0 is the original hardness of the wearing material, H is the hardness after deformation by grooving, ε s is the strain on the groove surface, and ε c is the strain above which material is removed from the groove. ε s in Equation 7.12 is given by: ε s W = 2ln E ( 1+ 10µ ) HR 23 θ tan 2 (7.13) where E is the Young s modulus of the wearing material, µ is the friction coefficient, θ is the angle of the pyramid, and R is the tip radius of the pyramid: θ W HR π V = 1 g ( H + µ ) tan 2 1 θ 2 W tan 2 (7.14) By introducing Equations 7.12, 7.13, and 7.14 into Equation 7.11, the wear coefficient K ab is expressed theoretically in terms of material parameters, geometrical parameters, and frictional conditions of load and friction coefficient. If the expression for volumetric is introduced by defining the inverse of wear rate (sliding distance/wear volume), it is given by (β V g ) 1. The comparisons of experimental and theoretical values of the volumetric wear resistance show good agreement, as shown in Figure 7.19 (Zum Gahr, 1987). The expressions of Equations 7.9 through 7.14 and Figures 7.15 through 7.19 are all for simple abrasive scratching. But in practical abrasive contact, there are many abrasive contact points at the same time,

16 FIGURE 7.19 Theoretical abrasive wear resistance vs. experimental abrasive wear resistance measured on different materials by using a diamond scratch of attack angle θ = 90 and tip radius r = 8 mm under load W = 2N. (From Zum Gahr, K.H. (1987), Microstructure and wear of materials, Tribology series, Elsevier, With permission.) FIGURE 7.20 Relationship between abrasive wear resistance and hardness of worn material observed experimentally and estimated theoretically. (From Hokkirigawa, K. and Kato, K. (1989), Theoretical estimation of abrasive wear resistance based on microscopic wear mechanism, in Proc. Int. Conf. on Wear of Materials, ASME, pp With permission.) and each of them is at a different state of deformation and wear. Therefore, it becomes necessary to introduce a model for the distribution of contact geometry, contact load, and the resultant abrasive wear mode. If we know the distribution of D p at multiple abrasive contacts of a surface, the total wear rate of the surface can be introduced by summarizing all the values of β at all contact points. Figure 7.20 (Hokkirigawa and Kato, 1989) shows the experimental data and theoretical solid and broken lines obtained in this way. Good agreement of experimental data and theoretical lines is confirmed Abrasive Wear of Brittle Material In the case of brittle material, which is indented and ploughed by the abrasive, a wear particle is generated due to mainly brittle fractures caused by initiation and propagation of cracks, such as the median and

17 FIGURE 7.21 Relationship between abrasive wear resistance and fracture toughness of yttria-doped zirconium oxide. (From Fischer, T.E., Anderson, M.P., and Jahanmir, S. (1989), Influence of fracture toughness on the wear resistance of yttria-doped zirconium oxide, J. Am. Ceram. Soc., 72, 2, With permission.) FIGURE 7.22 Abrasive wear model for brittle material. lateral cracks shown in Figure 7.10b. Therefore, wear rate of the brittle material is strongly dependent on fracture toughness. Figure 7.21 (Fischer et al., 1989) shows the effect of fracture toughness on the wear rate of zirconium oxide under abrasive contact. It is clear that fracture toughness is an important parameter to determine the abrasive wear rate of the brittle material. Wear volume in scratching the brittle material is described by the model shown in Figure 7.22 (Evans and Marshall, 1981). It is assumed that a wear particle is generated by lateral crack propagation which

18 reaches to the surface. If the crack is propagated by the residual stress, crack length c is defined by the function of normal load W, fracture toughness K c, hardness H, and Young s modulus E as follows: c = W K H 58 α c E H 35 (7.15) where α 1 depends on the shape of the abrasive and is determined by calibration on a material with wellcharacterized fracture properties. The depth b of lateral fracture is estimated by the radius of plastic contact zone, and is given by: b = α 2 E H W H (7.16) where α 2 is a material-independent constant. Based on these assumptions, the wear volume V in scratching of the brittle material with a hard asperity is given by the following equation: V = W K H 98 α c E H 45 L (7.17) where L is the sliding distance and α 3 is a material-dependent constant determined by calibration on a material with well-characterized fracture properties. Another analysis (Evans and Wilshaw, 1976) on a similar model with different assumptions gives a slightly different equation of abrasive wear volume of brittle materials as follows: V W K H L =α 4 54 c (7.18) where α 4 is a constant. It is clear from Equations 7.17 and 7.18 that abrasive wear rate depends strongly on both hardness and toughness. Wear rate predicted by both equations agrees well with experimental data, as shown in Figure 7.23 (Evans and Marshall, 1981) and Figure 7.24 (Buljan and Sarin, 1985) Fatigue Wear Repeated cycles of contact are not necessary in adhesive and abrasive wear for the generation of wear particles. There are other cases of wear where a certain number of repeated contacts are essential for the generation of wear particles. Wear generated after such contact cycles is called fatigue wear. When the number of contact cycles is high, the high-cycle fatigue mechanism is expected to be the wear mechanism. When it is low, the low-cycle fatigue mechanism is expected Fatigue Wear in Rolling and Sliding Contact under Elastic Contact In the case of the elastic contact generally observed in rolling elements, the main wear mechanism is high-cycle fatigue fracture in the contact region. The critical number of rolling cycles N f for the generation of wear particles by spalling or flaking is given experimentally as follows (Lundberg and Palmgren, 1952): N f 1 n W (7.19)

19 FIGURE 7.23 Correlation between abrasive wear resistance and (hardness) 5/8 (toughness) 1/2. (From Evans, A.G. and Marshall, D.B. (1981), Wear mechanism in ceramics, in Fundamentals of Friction and Wear of Materials, Rigney, D.A. (Ed.), ASM, 439. With permission.) FIGURE 7.24 Relationship between abrasive wear resistance and (toughness) 3/4 (hardness) 1/2. (From Buljan, S.T. and Sarin, V.K. (1985), The future of silicon nitride cutting tools, Carbide Tool J., May/June, 4-7. With permission.) where W is the normal load and n is a constant which depends on the shape of the rolling element. In the case of rolling bearings, the value of n is about 3. This empirical law has been widely accepted in the design of rolling bearings. Its basic premise is that spalling or flaking can be treated as statistical fracture phenomena following the modified theory (Weibull, 1930). Although the apparent practical contact pressure is not so high as to introduce yield in the contact region, local yield is generated in the contact region because of the existence of microdefects in the material. A single crystal has slip planes for preferential sliding under shear stress. A polycrystal has grain boundaries, inclusions, and vacancies. Because of these inhomogeneities, the local stress in the contact

20 FIGURE 7.25 The change in the hardness distribution beneath the surface during the repeated rolling of steel (0.45C, 0.27 Si, 0.85 Mn). (From Kayaba, T. and Suzuki, S. (1976), An investigation of surface damages by rolling contact, Technology Report, Tohoku Univ., 41, 1, ) region exceeds the yield stress of the material even when the theoretical stress for the homogeneous material does not exceed the yield stress (Dufrane and Glaeser, 1976). There is a state where a plastically deformed region appears beneath the interface without reaching the surface. In this case, work hardening takes place in the yield region as a result of repeated contact. This is shown in Figure 7.25 (Kayaba and Suzuki, 1976), where the hardness peak is located about 130 µm beneath the surface, and the value of maximum hardness increases with an increase in the number of rolling cycles. The maximum hardness value of about 400 kgf/mm 2 is reached after about cycles, when pits start to appear on the surface. Repeated friction under elastic or elastoplastic contact causes the accumulation of local plastic strain around some stress concentration points, and cracks are generated after reaching a certain number of frictional cycles. The mechanism of crack initiation and propagation in such a situation is that of fatigue fracture, which is a kind of rate process controlled by the inhomogeneity of the microstructure of a material Fatigue Wear in Sliding Contact under Plastic Contact In the friction between metallic materials, conformity at the contact interface without catastrophic wear is easily observed as the ploughing mode shown in Figure 7.12c (Hokkirigawa and Kato, 1988). In this mode, a wear particle is not generated by a single pass of sliding and only a shallow, conformable groove is formed. In the case of repeated contact of abrasive sliding at the same grooves, plastic burnishing (ploughing mode in Figure 7.12c) becomes predominant. In this ploughing mode, fatigue fracture is expected to take place after a critical number N f of plastic strain cycles in the wave. Figure 7.26 (Akagaki and Kato, 1987) shows the effect of repeated sliding on the growth of plastic flow wear particles of steel under boundary lubrication. It is seen that a thin surface layer protrudes in the

21 FIGURE 7.26 Flow wear process for steel during repeated sliding in boundary lubrication. (From Akagaki, T. and Kato, K. (1987), Plastic flow process of surface layers in flow wear under boundary lubricated conditions, Wear, 117, With permission.) FIGURE 7.27 Amount of flow wear of the surface layer as a function of sliding cycles under the same sliding conditions. (From Akagaki, T. and Kato, K. (1988), Simulation of flow wear in boundary lubrication using Vickers indentation method, STLE, Trib. Trans., 31, 3, With permission.) direction of sliding, and grows as the number of sliding cycles increases. Figure 7.27 shows the amount of plastic flow of the surface layer as a function of the sliding cycles for the two different contact pressures (Akagaki and Kato, 1988). The flow rate observed is a few micrometers per 10 4 cycles of sliding. Conforming between two sliding surfaces occurs by this gradual surface plastic flow and wear in metallic triboelements. This phenomenon is representative of low fatigue wear under plastic contact.

22 If we suppose that the plastically deformed layer is detached as wear particles by low-cycle fatigue failure, N f would be given by the modified Coffin Manson relationship: N f Cs = γ s D (7.20) where C s is the monotonic effective shear strain, γ s is the effective shear strain increment per wave pass, and D is a constant usually taken as 2. By considering the plastic work needed to produce unit volume of wear and introducing the relationship of Equation 7.20, the specific wear rate w s defined by wear volume/load/distance is described by Challen et al. (1986) as follows: w s = kc r µ p D D s γ 1 s (7.21) where r p is the ratio of plastic to total work of sliding and k is the average shear flow stress of the wearing material. By introducing the relation of k = H(Hardness)/(3 3 1/2 ) into Equation 7.21, the fatigue wear coefficient K f, defined in the same way as K ad and K ab mentioned above, can be expressed as: K f 3 rp = wsh = 3 12 µ D 1 D C γ s (7.22) The three parameters of γ s, r p, and µ are functions of the attack angle α (= π/2 θ), where θ is defined in Figure 7.11, and the normalized shear strength f. The parameter f has the same meaning as in Figures 7.15 and 7.16; it is the ratio of shear strength τ at the contact interface to the shear flow stress k of the wearing material, i.e., f = τ/k. From Figure 7.28 (Challen et al., 1986), which shows the calculated values of K f by changing the values of θ and f, it can be seen that K f is predicted to vary in the range from 10 6 to nearly 1 for α and f values ranging from 0.1 to 10 and from 0 to 0.99, respectively. The contact between a hard asperity and a groove generally becomes milder in repeated sliding as a result of deformation and wear in the groove surface layer. Better conformity between asperity and groove surfaces is attained where the contact pressure is decreased and elastic strains have to be considered. If the maximum Hertzian contact pressure is above the critical value of the elastic shakedown limit in an elastic plastic half-space of the wearing body, repeated plastic deformation takes place in the form of cyclic plasticity or ratcheting (Johnson, 1994). In cyclic plasticity, a cycle of axial plastic strain which comprises a reversing (fatigue) component ε a acts parallel to the surface. If it were acting alone, the number N f of cycles to surface failure would be given by the Coffin Manson relationship as follows: N f C = 2 ε a 2 (7.23) where C is the monotonic fracture strain. In ratcheting, unidirectional plastic shear strain γ r per cycle acts and is accumulated until the total strain reaches a critical value C where surface failure is generated. The number N r of cycles to failure in ratcheting is given by Johnson (1994) and Kapoor and Johnson (1994) as: N r C = γ r (7.24) where γ r is the ratcheting shear strain per cycle. In this ratcheting region, however, it is not quite clear whether ultimate failure would be caused by fatigue or by ductile fracture. It would be reasonable to

23 FIGURE 7.28 Variation of wear coefficient K f in sliding friction assuming a low-cycle fatigue wear mechanism with attack angle α and normalized shear strength f. (From Challen, J.M., Oxley, P.L.B., and Hockenhull, B.S. (1986), Prediction of Archard s wear coefficient for metallic sliding friction assuming a low cycle fatigue wear mechanism, Wear, 111, With permission.) suppose that each fatigue wear mode described by Equation 7.20, 7.23, or 7.24 has the possibility of being the prevailing wear mode depending upon the contact condition, and two or three of them may coexist in some cases. Careful experimental observation (Black et al., 1996) gives the value of D = 1.67, which suggests the possibility of a mixture of these two modes of fatigue wear Corrosive Wear When sliding takes place, especially in corrosive liquids or gases, reaction products are formed on the surface mainly by chemical or electrochemical interactions. If these reaction products adhere strongly to the surface and behave like the bulk material, the wear mechanism should be almost the same as that of the bulk material. In many cases, however, such reaction products behave very differently from the bulk material. Therefore, wear is quite different from that of the bulk material, and is dominated by the reaction products formed by the interaction of solid materials with the corrosive environment. This kind of tribochemical wear accelerated by corrosive media is called corrosive wear. In corrosive wear, tribochemical reaction produces a reaction layer on the surface. At the same time, such layer is removed by friction. Therefore, relative growth rate and removal rate determine the wear rate of the reaction layers and, as a result, of the bulk material. Therefore, models of the reaction layer growth and those of the layer removal become very important Oxidative Wear of Metals Oxidative wear is the most representative mode of corrosive wear of metals. Based on the oxidative reaction between steel and normal atmospheric air and assuming the film removal model where an oxide film of steel is supposed to detach from the surface at a certain critical thickness, corrosive wear coefficient K c defined in the same way as K ad and K ab has been expressed by Quinn (1987) as: K c da Q = exp v RT ξρ 2 2 g (7.25)

24 where A is the Arrhenius constant, Q the activation energy, R g the gas constant, T the absolute temperature, ρ the density of oxide, v the sliding velocity, and L the distance along which a wearing contact is made. It is generally assumed that activation energy does not vary substantially between static and sliding conditions. Making this assumption, the experimental wear results for oxidation of steels give a value of the Arrhenius constant in Equation 7.25 which is times larger than one in static oxidation (Quinn, 1987). This means that oxidation is much more rapid under sliding contact than in the static condition. This seems to be supported by another experimental result where the thickness of oxidative wear layers of steel and titanium are more than 500 times larger than those grown under static conditions (Krause and Scholter, 1978). Therefore, estimation of real activation energy at the sliding surface becomes important. Furthermore, the real temperature at the real contact interface is important in the determination of the wear rate, because the reaction rate required to form a chemical product is strongly affected by the temperature induced by friction. On the other hand, if the reaction rate is not high enough to grow an oxide film to the critical thickness within a cycle of sliding, oxidative wear of the steel may not occur. Even in this case, the reaction rate also determines the wear rate Oxidative Wear of Ceramics Tribochemical Wear of Ceramics The hydroxide of silicon nitride in water is very weakly bonded on the surface, is easily removed from the surface by rubbing, and it dissolves in water (Fischer and Tomizawa, 1985). If the reaction rate is high, a lot of silicon nitride hydroxide can be formed and worn away quickly. The reaction rate determines the wear rate in this case. If it is assumed that friction heating also accelerates chemical reaction at the contact interface, the wear coefficient K c of nonoxidative ceramics sliding against themselves is explained by Kitaoka et al. (1997) as: K c Ac Q = ρv exp RT g (7.26) where Q is the activation energy, R g the gas constant, T the reaction temperature, ρ the density of oxide, and v the sliding velocity. It is clear from both models (Quinn, 1967; Kitaoka et al., 1997), that the corrosive wear mechanism is difficult to understand without first understanding the process of the formation of the reaction layer from the viewpoint of the combined effect of mechanical activation and chemical reaction, namely, from the viewpoint of tribochemistry Mechanical Wear of Ceramics under Elastic Contact In the contact of ceramics, wear particles are generated mechanically without the mechanism of fatigue wear even under elastic contact. It is the wear governed by the microscopic brittle fracture at surface microcracks under nominal elastic contact. This is the representative wear mechanism of ceramics when specific wear rate is larger than 10 6 mm 3 /Nm (Adachi et al., 1997). Figure 7.29 shows a schematic diagram of the model, where a wear particle is generated by the propagation of a predominant surface crack in brittle manner. Such crack propagation can be enhanced by the tensile stress induced by friction under elastic contact. Based on the linear elastic fracture mechanics model, the critical condition for the crack propagation is expressed by the following equation: Bσ max πd K c (7.27)

25 µ p Hertzian Contact (a) Tensile stress (b) (c) (d) FIGURE 7.29 Wear model of brittle material, in which wear particles are generated by propagation of preexistent crack under elastic sliding contact: (a) sliding contact under elastic contact; (b) application of tensile stress to crack tip; (c) propagation of crack; and (d) generation of wear particle. where σ max is the maximum tensile stress at the crack tip, d preexistent crack length, K c fracture toughness of the wearing material, and B constant. Sliding generates the friction force which introduces the shear stress at the contact interface in addition to the compressing stress. As the result, the maximum tensile stress σ max is induced at the trailing edge of the contact, which is expressed by the following equation (Hamilton, 1983) in the case of the Hertzian contact: σ max = P max 1 2ν 4 ν + + πµ 3 8 (7.28) where P max is the maximum Hertzian contact pressure, ν Poisson s ratio, and µ friction coefficient. Assuming that the Poisson s ratio is 0.25, Equation 7.28 is simplified as follows: σ max ( ) Pmax 1+ 10µ = 6 (7.29) Substituting Equation 7.29 into Equation 7.27, the critical condition for surface crack propagation is given by the parameter S c,m defined as follows: S cm, ( 1+ 10µ ) Pmax d = C K C m (7.30) where C m (= 6/(Bπ 1/2 )) is a constant. S c,m gives mechanical severity of contact from the viewpoint of contact stress and its concentration against K c. Wear particles are generated by brittle fracture induced by tensile stress under elastic contact when S c,m exceeds the threshold value C m.