Engineering Tribology Episode 2 Part 11 doc

FUNDAMENTALS OF CONTACT BETWEEN SOLIDS 475 Radius r Angular velocity ω Elastic deformation of contact ∆r Tangential velocity, v 1 = ωr Tangential velocity, v 1 = ωr Tangential velocity v 2 = ω(r − ∆r) Micro-slip compensates for lower surface speed, v 1 - v 2 = ω∆r FIGURE 10.23 Schematic illustration of micro-slip and creeping movement in a rolling contact. When the roller or sphere sustains traction, the micro-slip increases in level and extent over the rolling contact area [94,95]. When micro-slip prevails over the entire rolling contact area, gross sliding or skidding of the roller (or sphere) will commence. A fundamental difference between rolling and sliding friction is that other energy dissipation mechanisms, which are negligible for sliding friction, become significant for rolling because of the very low friction level. Major sources of energy dissipation, which are not discussed further here, are aerodynamic drag of the rapidly rotating roller and repetitive compression of air inside a pneumatic tyre. Another important source of energy dissipation is hysteresis in the mechanical response of the rolling material. Hysteresis means that the compressive stresses ahead of the centre of the rolling contact are greater than the compressive stresses behind the rolling contact. Ahead is defined as not yet reached by the centre of the rolling contact while behind is defined as already rolled on by the centre of the rolling contact. The resulting asymmetry in compressive stresses generates reaction forces that oppose the rolling motion. For example, hysteresis is found to be the principal component of rolling friction in polymers [87]. An effect similar to mechanical hysteresis may also be generated by adhesion between the roller and rolled surface [96]. Adhesion behind the rolling contact causes the compressive forces behind the rolling contact to be less than the compressive forces ahead of the rolling contact. Adhesive effects are significant for rubbers [96] where the adhesion is generated by van der Waals bonding between atoms of the opposing surfaces [97]. Rolling is nearly always associated with high levels of contact stress, which can be sufficient at high contact loads to cause plastic deformation in the rolling contact. Plastic deformation not only causes the surface layers of the roller and rolled surface to accumulate plastic strain, but may also cause corrugation to occur. Corrugation is the transformation of a smooth, flat surface into a surface covered by a wave-form like profile aligned so that the troughs and valleys of the wave-form profile lie perpendicular to the direction of rolling. The wavelength of corrugations varies from 0.3 [mm] on the discs of Amsler test machines to 40 ~ 80 [mm] on railway tracks [98]. Another term used to describe corrugations, especially longer wavelength corrugations, is facets. Although the causes of corrugation are unclear, there is evidence that vibration of the rolling wheel and metallurgical factors exhibit a strong influence [99,100]. It was found that the peaks of the corrugations on steel surfaces were significantly harder than the troughs between the corrugations [101]. It is believed that corrugation occurs when a lump of plastically deformed material is formed at the leading edge of the rolling contact. TEAM LRN 476 ENGINEERING TRIBOLOGY This lump periodically grows to a maximum size before being released behind the rolling contact to form a corrugation [88,89]. According to theoretical models of the deformation and slip involved in rolling friction, it appears that there is a linear relationship between contact force and the drag force opposing rolling [84]. The geometry of the rolling contact has a strong influence on rolling friction, and the coefficient of rolling friction is inversely related to the rolling radius. At low loads where elastic deformation dominates, the coefficient of rolling friction is inversely proportional to the square root of the rolling radius, at higher contact loads where plastic deformation is significant, the coefficient of rolling friction is inversely proportional to the rolling radius [90]. Basic materials parameters also exert an effect, the coefficient of rolling friction is inversely related to the Young's modulus of the rolling material [90]. Temperature exerts a strong effect on the coefficient of rolling friction of polymers since the mechanical hysteresis of the polymer is controlled by temperature [92]. The coefficient of adhesion in a rolling steel contact was found to decline with speed in the range of 20 [km/hr] to 500 [km/hr] [91]. Concentration of Frictional Heat at the Asperity Contacts The inevitable result of friction is the release of heat and, especially at high sliding speeds, a considerable amount of energy is dissipated in this manner. The released heat can have a controlling influence on friction and wear levels due to its effect on the lubrication and wear processes. Almost all of the frictional heat generated during dry contact between bodies is conducted away through the asperities in contact [24]. Since the true contact area between opposing asperities is always considerably smaller than the apparent contact area, the frictional energy and resulting heat at these contacts becomes highly concentrated with a correspondingly large temperature rise as illustrated schematically in Figure 10.24. Load Frictional temperature rise if energy is dissipated uniformly Actual temperature rise Sliding speed Frictional power Frictional power to sustain sliding is dissipated as heat over small asperity contact areas FIGURE 10.24 Concentration of frictional energy at the asperity contacts. This concentration of frictional energy over small localized areas has a significant influence on friction and wear. Local temperatures can rise to very high values even with a relatively small input of frictional energy. For example, a frictional temperature rise was exploited by paleolithic man to ignite fires by rotating a stick against a piece of wood. TEAM LRN FUNDAMENTALS OF CONTACT BETWEEN SOLIDS 477 Surface heating from frictional energy dissipation also causes the surface layers of a material to expand. Where such heating is localized, a small area of surface becomes elevated from the rest of the surface which has not sustained thermal expansion. This effect is known as a ‘thermal mound’ since the shape of this temperature-induced structure resembles a gently sloping hill or mound. When the wearing surface is flat, the distribution of thermal mounds tend to be random along with the distribution of frictional energy dissipation. When the contact of the wearing surface is controlled by asperities, the asperities which sustain the greatest amount of frictional energy dissipation will expand the most and lift apart the remaining asperities. The effect of thermal mound formation results in the concentration of frictional energy dissipation and mechanical load on a few asperities only. This effect is transient and once the source of frictional energy is removed, i.e. by stopping the moving surfaces, the thermal mounds disappear. Shear rates between contacting solids can also be extremely high as often only a thin layer of material accommodates the sliding velocity difference. The determination of surface temperature as well as the observation of wear is difficult as the processes are hindered by the contacting surfaces. In the majority of sliding contacts, the extremes of temperature, stress and strain can only be assessed indirectly by their effect on wear particles and worn surfaces. The frictional temperatures can, for example, be measured by employing the ‘dynamic thermocouple method’ [24]. The method involves letting two dissimilar metals slide against each other. Frictional temperature rises at the sliding interface cause a thermo-electric potential to develop which can be measured. For example, significant temperature rises were detected by this method when constantan alloy was slid under unlubricated conditions against steel at a velocity of 3 [m/s] [24]. Momentary temperature rises reaching 800°C but only lasting for approximately 0.1 [ms] occurring on a random basis were observed. It is speculated that these temperature rises are the result of intense localized metal deformation between asperities in contact. Wear Between Surfaces of Solids As already discussed the contact between surfaces of solids at moderate pressures is limited to contacts between asperities of opposing surfaces. Most forms of wear are the result of events occurring at asperity contacts. There could, however, be some exceptions to this rule, e.g. erosive wear which involves hard particles colliding with a surface. It has been postulated by Archard that the total wear volume is proportional to the real contact area times the sliding distance [37]. A coefficient ‘K’ which is the proportionality constant between real contact area, sliding distance and the wear volume has been introduced, i.e.: V = K A r l = K l H W (10.9) where: V is the wear volume [m 3 ]; K is the proportionality constant; A r is the real area of the contact [m 2 ]; W is the load [N]; H is the hardness of the softer surface [Pa]; l is the sliding distance [m]. TEAM LRN 478 ENGINEERING TRIBOLOGY The ‘K’ coefficient, also known as the ‘Archard coefficient’ is widely used as an index of wear severity. The coefficient can also be imagined as the proportion of asperity contacts resulting in wear. The value of ‘K’ is never supposed to exceed unity and in practice ‘K’ has a value of 0.001 or less for all but the most severe forms of wear. The low value of ‘K’ indicates that wear is caused by only a very small proportion of asperity contacts. In almost all cases, asperities slide over each other with little difficulty and only a minute proportion of asperity contacts result in the formation of wear particles. It has also been suggested that wear particles are the result of a cumulative process of many interactions between randomly selected opposing asperities [38]. The combination of opposing asperities during sliding at any one moment can easily be imagined as continuously changing. A gradual or incremental mode of wear particle formation allows for extensive freedom for variation or instability in the process. Statistical analysis of wear data reveals that there is a short term ‘memory’ inherent in wear processes, i.e. any sample of a wear rate is related to the immediately preceding wear rates, although there seems to be no correlation with much earlier wear rates [39]. Therefore wear prediction is extremely difficult. 10.5 SUMMARY Real surfaces are composed of surface features ranging in size from individual atoms to visible grooves and ridges. Most surface features affect wear and friction. Since almost all surfaces are rough, in terms of solid contact they cannot be approximated by a flat plane. The basic laws of friction are a result of the control of solid contact by rough surfaces. The topography of the contacting surfaces therefore has a decisive effect on wear and friction. Rough surfaces have very small areas of real contact with the opposing surface and this causes wear and friction to be determined by high contact stresses and extreme concentrations of frictional energy even though the nominal contact stress and total frictional energy can be small. Friction has traditionally been divided into static and kinetic friction. Exact measurements of microscopic sliding movements reveal that as the friction force acting on a contact is progressively increased, microscopic sliding movement occurs for all levels of friction force and the maximum friction force occurs at some specific sliding speed. The basic difference between gross sliding and sliding movements at small levels of friction force is that these latter movements are reversible. A major consequence of the difference between static and kinetic coefficients of friction is ‘stick-slip’ or discontinuous sliding. Stick-slip is often present when the supporting structure of the sliding contact has insufficient stiffness to follow the rapid changes in frictional force that can occur. Wear results from direct contact between the individual asperities at sliding interfaces and, in almost all situations, many asperity interactions are required before wear occurs. REFERENCES 1 J. Benard (editor), Adsorption on Metal Surfaces, Elsevier, Amsterdam, 1983. 2 D. 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Soc., London, Series A, Vol. 327, 1972, pp. 159-173. 29 P.R. Nayak, Random Process Model of Rough Surfaces, Transactions ASME, Journal of Lubrication Technology, Vol. 93, 1971, pp. 398-407. 30 A.W. Bush, R.D. Gibson and T. R Thomas, The Elastic Contact of a Rough Surface, Wear, Vol. 35, 1975, pp. 87- 111. 31 P.K. Gupta and N.H. Cook, Junction Deformation Models for Asperities in Sliding Interactions, Wear, Vol. 20, 1972, pp. 73-87. 32 B. Bhushan, Tribology of Mechanics of Magnetic Storage Devices, Sprigler-Verlag, 1990. 33 B. Bhushan, Analysis of the Real Area of Contact Between a Polymeric Magnetic Medium and a Rigid Surface, Transactions ASME, Journal of Tribology, Vol. 106, 1984, pp. 26-34. 34 J.M. Challen, L.J. MacLean and P.L.B. Oxley, Plastic Deformation of a Metal Surface in Sliding Contact With a Hard Wedge: Its Relation to Friction and Wear, Proc. Roy. Soc., London, Series A, Vol. 394, 1984, pp. 161- 181. TEAM LRN 480 ENGINEERING TRIBOLOGY 35 J.T. Burwell and E. Rabinowicz, The Nature of the Coefficient of Friction, Journal of Applied Physics, Vol. 24, 1953, pp. 136-139. 36 M. Eguchi and T. Yamamoto, Dynamic Behaviour of a Slider Under Various Tangential Loading Conditions, Proc. JSLE. Int. Tribology Conference, 8-10 July 1985, Tokyo, Japan, Elsevier, 1986, pp. 1047-1052. 37 J.F. Archard, Single Contacts and Multiple Encounters, Journal of Applied Physics, Vol. 32, 1961, pp. 1420- 1425. 38 Y. Kimura and H. Okabe, Review of Tribology, Youkandou Press, Tokyo, (in Japanese), 1982. 39 S.C. Lim, C.J. Goh and L.C. Tang, The Interdependence of Wear Events During Slow Sliding - a Statistical Viewpoint, Wear, Vol. 137, 1990, pp. 99-105. 40 K. Naoi, K. Sasjima and T. Tsukuda, A Quantitative Evaluation of Truncation Wear Based on Three- Dimensional Surface Asperity Changes, Proc. JAST, Vol. 4, 1999, pp. 452-459. 41 D.J. Whitehouse, Handbook of Surface Metrology, Bristol; Philadelphia: Institute of Physics Pub., 1994. 42 C.Y. Poon, B. Bhushan, Comparison of Surface Roughness Measurements by Stylus Profiler, AFM and Non- Contact Optical Profiler, Wear, Vol. 190, 1995, pp. 76-88. 43 H. Zahouani, R. Vargiolu, Ph. Kapsa, J.L. Loubat, T.G. Mathia, Effect of Lateral Resolution on Topographical Images and Three-Dimensional Functional Parameters, Wear, Vol. 219, 1998, pp. 114-123. 44 P. Podsiadlo and G.W. Stachowiak, Scale-Invariant Analysis Tribological Surfaces, Proceedings of the International Leeds-Lyon Tribology Symposium, ‘Lubrication at the Frontier’, September 1999, Elsevier, 2000. 45 G.W. Stachowiak and P. Podsiadlo, Surface Characterization of Wear Particles, Wear, Vol. 225-229, 1999, pp. 1171-1185. 46 P. Podsiadlo and G.W. Stachowiak, 3-D Imaging of Wear Particles Found in Synovial Joints, Wear, Vol. 230, 1999, pp. 184-193. 47 W.P. Dong, P.J. Sullivan and K.J. Stout, Comprehensive Study of Parameters for Characterising Three- Dimensional Topography. IV: Parameters for Characterising Spatial and Hybrid Properties, Wear, Vol. 178, 1994, pp. 45-60. 48 Z. Peng and T.B. Kirk, Two-Dimensional Fast Fourier Transform and Power Spectrum for Wear Particle Analysis, Tribology International, Vol. 30, 1997, pp. 583-590. 49 D.M. Tsai and C.F. Tseng, Surface Roughness Classification for Castings, Pattern Recognition, Vol. 32, 1999, pp. 389-405. 50 Y. Wang, K. S. Moon, A methodology for the multi-resolution simulation of grinding wheel surface, Wear, Vol. 211, 1997, pp. 218-225. 51 X.Q. Jiang, L. Blunt, K.J. Stout, Three-Dimensional Surface Characterization for Orthopaedic Joint Prostheses, Proceedings of Institute of Mechanical Engineers, Part H, Vol. 213, 1999, pp. 49-68. 52 J L. Starck, F. Murtagh, A. Bijaoui, Image Processing and Data Analysis: The Multiscale Approach, New York, Cambridge University Press, 1998. 53 G. Borgerfors, Distance Transforms in Arbitrary Dimensions, Comp. Vision, Graphics Image Proc., Vol. 27, 1984, pp. 321-345. 54 P. Grassberger and I. Procaccia, Characterisation of Strange Attractors, Phys. Rev. Letters, Vol. 50, 1983, pp. 346-349. 55 K. Judd, An Improved Estimator of Dimension and Comments on Providing Confidence Intervals, Phys. D., Vol. 56, 1992, pp. 216-228. 56 J.C. Russ, Fractal Surfaces, Plenum Press, New York, 1994. 57 M.G. Hamblin and G.W. Stachowiak, Application of the Richardson Technique to the Analysis of Surface Profiles and Particle Boundaries, Tribology Letters, Vol. 1, 1995, pp. 95-108. 58 W. P. Dong, P. J. Sullivan and K. J. Stout, Comprehensive Study of Parameters for Characterising Three- Dimensional Surface Topography, II: Statistical Properties of Parameter Variation, Wear, Vol. 167, 1993, pp. 9-21. 59 M.G. Hamblin and G.W. Stachowiak, Measurement of Fractal Surface Profiles Obtained from Scanning Electron and Laser Scanning Microscope Images and Contact Profile Meter, Journal of Computer Assisted Microscopy, Vol. 6, No. 4, 1994, pp. 181-194. 60 C. Tricot, P. Ferland and G. Baran, Fractal Analysis of Worn Surfaces, Wear, Vol. 172, 1994, pp. 127-133. TEAM LRN FUNDAMENTALS OF CONTACT BETWEEN SOLIDS 481 61 M. Hasegawa, J. Liu, K. Okuda, M. Nunobiki, Calculation of the Fractal Dimensions of Machined Surface Profiles, Wear, Vol. 192, 1996, pp. 40-45. 62 J. Lopez, G. Hansali, H. Zahouani, J.C. Le Bosse, T. Mathia, 3D Fractal-Based Characterisation for Engineered Surface Topography, International Journal of Machine Tools and Manufacture, Vol. 35, 1995, pp. 211-217. 63 S. Ganti, B. Bhushan, Generalized Fractal Analysis and Its Applications to Engineering Surfaces, Wear, Vol. 180, 1995, pp. 17-34. 64 S. Peleg, J. Naor, R. Harley and D. Avnir, Multiresolution texture analysis and classification, IEEE Transactions on Pattern Analysis Machine Intelligence, Vol. 4 , 1984, pp. 518-523. 65 J.J. Gangepain and C. Roques-Carmes, Fractal Approach to Two Dimensional and Three Dimensional Surface Roughness, Wear, Vol. 109, 1986, pp. 119-126. 66 K.C. Clarke, Computation of the Fractal Dimension of Topographic Surfaces Using the Triangular Prism Surface Area Method, Computers and Geosciences, Vol. 12, 1986, pp. 713-722. 67 B. Dubuc, S.W. Zucker, C. Tricot, J-F. Quiniou and D. Wehbi, Evaluating the Fractal Dimension of Surfaces, Proc. Roy. Soc. London, Series A425, 1989, pp. 113-127. 68 C.A. Brown, P.D. Charles, W.A. Johnsen and S. Chesters, Fractal Analysis of Topographic Data by The Patchwork Method, Wear, Vol. 161, 1993, pp. 61-67. 69 P. Podsiadlo and G.W. Stachowiak, The Development of Modified Hurst Orientation Transform for the Characterization of Surface Topography of Wear Particles, Tribology Letters, Vol. 4, 1998, pp. 215-229. 70 P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, New York, 1990. 71 M.F. Barsney and L.P. Hurd, Fractals Everywhere, Academic Press, San Diego, 1988. 72 Y. Fisher (editor) Fractal Image Compression. Theory and Application, Springer-Verlag, New York, 1995. 73 K.L. Johnson, Contact Mechanics and the Wear of Metals, Wear, Vol. 190, 1995, pp. 162-170. 74 A. Kapoor, K.L. Johnson and J.A. Williams, A Model for the Mild Ratchetting Wear of Metals, Wear, Vol. 200, 1996, pp. 38-44. 75 A. Kapoor, J.A. Williams and K.L. Johnson, The Steady State Sliding of Rough Surfaces, Wear, Vol. 175, 1995, pp. 81-92. 76 A.F. Bower and K.L. Johnson, The Influence of Strain Hardening on Cumulative Plastic Deformation in Rolling and Sliding Line Contact, Journal of Mech. Phys. Solids, Vol. 37, 1989, pp. 471-493. 77 B. Bhushan, Contact Mechanics of Rough Surfaces in Tribology: Single Asperity Contact, Appl. Mech. Rev., Vol. 49, 1996, pp. 275-298. 78 G. Liu, Q. Wang and C. Lin, A Survey of Current Models for Simulating the Contact Between Rough Surfaces, Tribology Transactions, Vol. 42, 1999, pp. 581-591. 79 M. Chandrasekaran, A.W. Batchelor and N.L. Loh, Direct Observation of Frictional Seizure of Mild Steel Sliding on Aluminium by X-ray Imaging, Part 1, Methods, Journal of Materials Science, Vol. 35, 2000, pp. 1589-1596. 80 M. Chandrasekaran, A.W. Batchelor and N.L. Loh, Direct Observation of Frictional Seizure of Mild Steel Sliding on Aluminium by X-ray Imaging, Part 2, Mechanisms, Journal of Materials Science, Vol. 35, 2000, pp. 1597-1602. 81 A.A. Seireg, Friction and Lubrication in Mechanical Design, Marcel Dekker Inc., New York, 1998. 82 Y. Fu, A.W. Batchelor and N.L. Loh, Study on Fretting Wear Behavior of Laser Treated Coatings by X-ray Imaging, Wear, Vol. 218, 1998, pp. 250-260. 83 D. Dowson, History of Tribology, Longmans Group, 1979, page 25. 84 J.J. Kalker, Three-Dimensional Elastic Bodies in Rolling Contact, Kluwer Academic Publishers, Dordrecht, 1990. 85 J.J. Kalker, A Fast Algorithm for the Simplified Theory of Rolling Contact, Vehicle System Dynamics, Vol. 11, 1982, pp. 1-13. 86 J.J. Kalker, The Computation of Three-Dimensional Rolling Contact With Dry Friction, Int. Journal for Numerical Methods in Engineering, Vol. 14, 1979, pp. 1293-1307. 87 D. Tabor, The Mechanism of Rolling Friction; II The Elastic Range, Proc. Roy. Soc., London, Series A, Vol. 229, 1955, pp. 198-220. TEAM LRN 482 ENGINEERING TRIBOLOGY 88 W.R. Tyfour, J.H. Breynon and A. Kapoor, The Steady State Behaviour of Pearlitic Rail Steel Under Dry Rolling Sliding Contact Conditions, Wear, Vol. 180, 1995, pp. 79-89. 89 A. Kapoor, Wear by Plastic Ratchetting, Wear, Vol. 212, 1997, pp. 119-130. 90 Y. Uchiyama, Control of Rolling Friction, The Tribologist, Journal of Japanese Society of Tribologists, Vol. 44, 1999, pp. 487-492. 91 K. Ohno, Rolling Friction And Control Between Wheel and Rail, The Tribologist, Journal of Japanese Society of Tribologists, Vol. 44, 1999, pp. 506-511. 92 I. Sekiguchi, Rolling Friction and Control of Polymeric Materials, The Tribologist, Journal of Japanese Society of Tribologists, Vol. 44, 1999, pp. 493-499. 93 F.W. Carter, On the Action of a Locomotive Driving Wheel, Proc. Roy. Soc., London, Series A, Vol. 112, 1926, pp. 151-157. 94 J.J. Kalker, Wheel Rail Rolling Contact Theory, Wear, Vol. 144, 1991, pp. 243-261. 95 K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, 1985. 96 M. Barquins, Adherence, Friction and Wear of Rubber-Like Materials, Wear, Vol. 158, 1992, pp. 87-117. 97 K.L. Johnson, K. Kendall and A.D. Roberts, Surface Energy and Contact of Elastic Solids, Proc. Roy. Soc., London, Series A, Vol. 324, 1971, pp. 301-313. 98 D. Pupaza and J.H. Beynon, The Use of Vibration Monitoring in Detecting the Initiation and Prediction of Corrugations in Rolling-Sliding Contact Wear, Wear, Vol. 177, 1994, pp. 175-183. 99 Y. Suda, Effects of Vibration System and Rolling Conditions on the Development of Corrugations, Wear, Vol. 144, 1991, pp. 227-242. 100 E. Tassilly and N. Vincent, Rail Corrugations, Analytical Model and Field Tests, Wear, Vol. 144, 1991, pp. 163-178. 101 H.G. Feller and K. Walf, Surface Analysis of Corrugated Rail Treads, Wear, Vol. 144, 1991, pp. 153-161. TEAM LRN ABRASIVE, EROSIVE 11 AND CAVITATION WEAR 11.1 INTRODUCTION Wear by abrasion and erosion are forms of wear caused by contact between a particle and solid material. Abrasive wear is the loss of material by the passage of hard particles over a surface [1]. Erosive wear is caused by the impact of particles against a solid surface. Cavitation is caused by the localized impact of fluid against a surface during the collapse of bubbles. Abrasion and erosion in particular are rapid and severe forms of wear and can result in significant costs if not adequately controlled [2]. Although all three forms of wear share some common features, there are also some fundamental differences, e.g. a particle of liquid can cause erosion but cannot abrade. These differences extend to the practical consideration of materials selection for wear resistance due to the different microscopic mechanisms of wear occurring in either abrasion, erosion or cavitation. The questions are: where are abrasive, erosive or cavitation wear likely to occur? When do these forms of wear occur and how can they be recognized? What are the differences and similarities between them? Will the same protective measures, e.g. material reinforcement, be suitable for all these forms of wear? What is the effect of temperature on these wear mechanisms? Will the use of hard materials suppress all or only some of these forms of wear? The practising engineer needs answers to all these questions and more. The fundamental mechanisms involved in these three forms of wear and the protective measures that can be taken against them are discussed in this chapter. 11.2 ABRASIVE WEAR Abrasive wear occurs whenever a solid object is loaded against particles of a material that have equal or greater hardness. A common example of this problem is the wear of shovels on earth-moving machinery. The extent of abrasive wear is far greater than may be realized. Any material, even if the bulk of it is very soft, may cause abrasive wear if hard particles are present. For example, an organic material, such as sugar cane, is associated with abrasive wear of cane cutters and shredders because of the small fraction of silica present in the plant fibres [3]. A major difficulty in the prevention and control of abrasive wear is that the term ‘abrasive wear’ does not precisely describe the wear mechanisms involved. There are, in fact, almost always several different mechanisms of wear acting in concert, all of which have different characteristics. The mechanisms of abrasive wear are described next, followed by a review of the various methods of their control. TEAM LRN 484 ENGINEERING TRIBOLOGY Mechanisms of Abrasive Wear It was originally thought that abrasive wear by grits or hard asperities closely resembled cutting by a series of machine tools or a file. However, microscopic examination has revealed that the cutting process is only approximated by the sharpest of grits and many other more indirect mechanisms are involved. The particles or grits may remove material by microcutting, microfracture, pull-out of individual grains [4] or accelerated fatigue by repeated deformations as illustrated in Figure 11.1. Direction of abrasion a) Cutting Direction of abrasion b) Fracture c) Fatigue by repeated ploughing Direction of abrasion d) Grain pull-out Direction of abrasion Repeated deformations by subsequent grits Grain about to detach FIGURE 11.1 Mechanisms of abrasive wear: microcutting, fracture, fatigue and grain pull-out. The first mechanism illustrated in Figure 11.1a, cutting, represents the classic model where a sharp grit or hard asperity cuts the softer surface. The material which is cut is removed as wear debris. When the abraded material is brittle, e.g. ceramic, fracture of the worn surface may occur (Figure 11.1b). In this instance wear debris is the result of crack convergence. When a ductile material is abraded by a blunt grit then cutting is unlikely and the worn surface is repeatedly deformed (Figure 11.1c). In this case wear debris is the result of metal fatigue. The last mechanism illustrated (Figure 11.1d) represents grain detachment or grain pull-out. This mechanism applies mainly to ceramics where the boundary between grains is relatively weak. In this mechanism the entire grain is lost as wear debris. Cutting Much of this more complex view of abrasive wear is relatively new since, like all forms of wear, the mechanisms of abrasive wear are hidden from view by the materials themselves. Until recently, direct demonstrations of abrasive wear mechanisms were virtually non- existent. The development of the Scanning Electron Microscope (SEM) has provided a means of looking at some aspects of abrasive wear in closer detail. In one study [5] a rounded stylus was made to traverse a surface while under observation by SEM. In another study [6] a pin on disc wear rig was constructed to operate inside the SEM, to allow direct observations of wear. Two basic mechanisms were revealed: a cutting mechanism and a wedge build up mechanism with flake like debris [5]. This latter mechanism, called ‘ploughing’, was found to be a less efficient mode of metal removal than ‘micro-cutting’. In a separate study with a similar apparatus it was found that random plate-like debris were formed by a stylus scratching cast iron [7]. It is probable that in an actual wear situation the effect of cutting alone is relatively small since much more material is lost by a process that has characteristics of both cutting and fatigue. TEAM LRN [...]... − 1 72 − 25 0 29 4 566 − 850 714 − 795 1038 110 3 − 126 0 1500 1600 120 0 − 1648 20 60 − 27 20 8000 − 10 000 2 36 109 190 A more complex constraint is the brittleness of the abrasive If the grits are too brittle then they may break up into fine particles, thus minimizing wear [2] If the abrasive is too tough then the grits may not fracture to provide the new cutting faces necessary to cause rapid wear [2, 7,8]... abrasive agents than angular particles [27 ] as illustrated in Figure 11. 12 TEAM LRN 496 ENGINEERING TRIBOLOGY 1 2 3 Very brittle grit 1 2 3 4 Self-sharpening grit of moderate brittleness 4 3 1 2 Initial angular shape Final rounded shape Very tough grit FIGURE 11. 12 Effect of grit brittleness and toughness on its efficiency to abrade Another factor controlling the abrasivity of a particle is the size and... surface pressure is given in the form: p crit = φ 2 λK IIC 2 / (Dab 2 Hµ 2 ) (11. 13) where: 2 is a geometrical factor relating to the effectiveness of the shape of the abrasive particle on abrasive wear A typical value for a pyramidal shape particle is 2 ≈ 1; λ is the mean free path between brittle defects [m], e.g for martensitic steels λ = 40 - 120 [µm] is typical; K IIC is the fracture toughness... (Figure 11. 6) [m] Substituting for ‘d’ from equation (11. 1) into equation (11 .2) results in an expression for the worn volume of material in terms of the load on the grit, the shape of the grit, and the sliding distance, i.e.: V g = 2ltanα × W g πH (11. 3) The total wear is the sum of the individual grit worn volumes of the material: Vtot = ΣV g = 2ltanα × ΣW g πH or: Vtot = 2ltanα × Wtot πH (11. 4) where:... shown in Figure 11. 10 µ 2. 5 f = 0.0 f = 1.0 0.9 0.8 2. 0 0.1 0 .2 0.3 0.4 0.5 0.6 Cutting model 0.7 0.7 0.6 0.5 Wear model 0.4 1.5 0.8 0.3 0.9 0 .2 1.0 0.1 1.0 0.0 Rubbing model 0.5 0 0 10 20 30 40 50 Hard asperity angle [°] 60 70 80 90 α FIGURE 11. 10 Variation of coefficient of friction in three models of soft surface deformation by hard wedge-shaped asperities [10] TEAM LRN 494 ENGINEERING TRIBOLOGY It... erosive wear [109 ,110 ,113 ] This is illustrated in Figure 11. 15 where TEAM LRN 498 ENGINEERING TRIBOLOGY the abrasive wear rates obtained with chalk counter-samples are plotted against the angularity parameters Particle boundary θ Particle Start point Apex Area h Ba se (ste pl eng th) a) End point s rmean Spike 2 θ Spike 1 m (apex) rlocal max O e b) a) Average wear rate [mm/min] Figure 11. 14 Schematic... the abrasive particle [22 ] Very slow abrasive wear persists until the hardness of abrasive and worn material are equal Some materials with soft phases or not fully strain hardened may sustain some wear until the material hardness is 1 .2 to 1.4 times the hardness of the abrasive [22 ] A conceptual graph of wear resistance versus the ratio of material to abrasive hardness is shown in Figure 11. 11 Wear resistance... and ‘A 2 are negative because the brittle material does not pile up at the sides as with ductile material but instead fractures to further widen the groove and the expression for ‘fab’ becomes: f ab = 1 + |A1 + A2 | / Av (11. 10) The expression for linear wear rate in the brittle mode is given by the expression [21 ]: ∆V d,brittle = φ 1p / Hdef + φ 3A fD abp 1.5H 0.5µ 2 / KIC2 TEAM LRN (11. 11) A BRASIVE,... by Tabor [23 ] and Mott [24 ] The hardness of typical minerals given in Mohs and Vickers is listed in Table 11. 1 [23 -25 ] Silicon carbide which is an artificial mineral has a hardness of 3000 [VHN] (Vickers Hardness Number) or 30 [GPa] Quartz (110 0 [VHN]) and harder minerals are the main cause of abrasive wear problems of tough alloy steels which have a maximum hardness of 800 [VHN] Quartz is particularly... 0.5π(dcotα) 2 H (11. 1) where: Wg is the individual load on the grit [N]; d is the depth of indentation [m]; α is the slope angle of the cone (Figure 11. 6); H is the material's yield stress under indentation (hardness) [Pa] The approximate volume of the material removed by the cone is the product of the crosssectional area of the indentation ‘d2cotα’ and the traversed distance ‘l’, i.e.: V g = ld2 cotα (11 .2) . Elsevier, 20 00. 45 G.W. Stachowiak and P. Podsiadlo, Surface Characterization of Wear Particles, Wear, Vol. 22 5 -22 9, 1999, pp. 117 1 -118 5. 46 P. Podsiadlo and G.W. Stachowiak, 3-D Imaging of Wear Particles. ASME, Journal of Tribology, Vol. 1 12, 1990, pp. 20 5 -21 6. 20 A. Majumdar and C.L. Tien, Fractal Characterization and Simulation of Rough Surfaces, Wear, Vol. 136, 1990, pp. 313- 327 . 21 M.V. Berry. Transactions ASME, Journal of Tribology, Vol. 113 , 1991, pp. 1 -11. 11 E.J. Abbott and F.A. Firestone, Specifying Surface Quality, Mechanical Engineering, Vol. 55, 1933, pp. 569- 5 72. 12 E.F. Finklin, The