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Grain-size dependence of the wear of alumina
WEAR ELSEVIER
Wear 186-187 (1995) 45-49
Grain-size dependence of the wear of alumina R.W. Davidge, F.L. Riley School of Materials, University of Leeds, Leeds LS2 9Sr, UK
Abstract A simple model is presented which, although empirical in nature, is consistent with experimental observations on the wear and abrasion rates of high purity alumina of tailored grain size. It is postulated that the critical wear process, reduced to its simplest terms, involves the nucleation and propagation of grain boundary microcracks. A microcrack is nucleated and travels at a characteristic velocity along a low energy grain face until a multi-boundary junction is encountered, when development of the crack is temporarily inhibited. The crack thus progresses with alternating periods of steady growth and delay, and ultimately causes the local loss of material through grain detachment. It is shown that this model leads to a wear rate grain-size dependence of the form seen for a variety of conditions such as erosion, sawing, grinding and sliding. Keywords: Grain size; Alumina; Abrasion; Cracks; Wear
1. Introduction It is generally recognised that the wear of polycrystalline alumina materials under conditions for which microfracture is an important component varies significantly with the mean grain size G: wear rate W increases with increasing grain size [ 11. In contrast, correlations within a specific class of ceramic material between wear rate and hardness, and macro-toughness (as measured by the diamond indentation or notched beam techniques), are poor though the existence of a relationship with microfracture on the scale of a grain size has been postulated on the basis of a better correlation with crack resistance (the R-curve) for alumina [ 21. We have recently reported [ 31 results of a study of the wet erosion of a set of high purity polycrystalline alumina materials of similar hardness and fracture toughness, where a clear relationship between wear rate and grain size was shown. The trend (Fig. 1) fk grain sizes in the range 1 to _ 15 pm is a smooth concave-downwards curve. For this experimental system the damage inflicting particle size to grain size ratio was +, 100, and scanning electron micrographs of wear surfaces showed for G > 3 pm facetting indicative of whole grain detachment. In materials of grain sizes finer than = 2 pm, plastic deformation or chemical removal of material, also appeared to be significant wear processes. Similar grain size-wear rate relationships are seen for a wide range of materials and wear modes, for example grinding [ 4-71, sliding [ 2,4,5 1 sawing [ 61, and dry erosion [ 81. Data have been fitted, variously, to W as a function of 0043.1648/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDIOO43-1648(95)07171-7
Wet erosive wear
10 0
. ““““““I’,“““(/“‘,, 0 2 4
i 6
8
10
12
14
Grain size / km Fig. 1. Wear rate-grain size dependence in the wet erosive wear of pure polycrystalline alumina. G-
112,
W -’ as a function of G-l”, and W as a function of G plots. A common feature of many attempts to produce semiquantitative models for W-G relationships has been the use of the Hall-Petch expression, but there is no clear case made for why a wear process involving damage on the scale of the sub-grain dimension should be determined by macroscopic strength, or a critical defect size which is assumed to scale as the grain dimension. Indeed it is also clear that the approximately linear W as a function of G- I’* plots (as shown for wet erosion in Fig. 2) are deceptive in that they do not pass through the origin, and that the alternative form of plotting,
R. W. Davidge. F.L. Riley/ Wear 186-187 (1995) 45-49
Wet erosive
I_..
()
wear
Wet erosive
1
I__LI_.--A._I_L
0.2
0.4
0.6
0.8
1.0
i
1.2
0.0
(Grain size /km) -“* Fig. 2. Wear rate as a function polycrystalline alumina.
of G- “’ in the wet erosive wear of pure
Wet
erosive
wear
0.5 1.0 [(G-l) /pm)]-“*
Fig. 4. Wear rate as a function of (Gpure polycrystalline alumina.
1.5
1)-“’ in the wet erosive wear of
It is thus clear that a new unified model is required, to explain these sets of wear data, and to relate the rate of removal of surface material, as the accumulation of localized damage occurring on the micrometre scale, to a material’s composition and microstructure. The primary aim of this paper is to outline the basis for a model for polycrystalline materials in which wear rate is related to grain size, and hence to stimulate thinking and critical experimental investigations.
wear
2. Modelling
0
t_;,,--
0
10
5
15
Grain size I j.tm Fig. 3. W* as a function polycrystalline alumina.
of grain size in the wet erosive wear of pure
using W* as a function of G does not give a straight line (Fig. 3). An attempt to force the line through the origin by using (G-G * ) , where G * is the intercept of the G- I” plot, also results in a curve (Fig. 4), indicating that the apparently simple parabolic relationship must be treated with suspicion. A further feature apparently common to these wear processes is that the wear of single crystal material is considerably slower than that predicted on the basis of an extrapolation of G to infinity. In the case of wet erosion, for example, single crystal sapphire wears at a rate similar to that of a 2.5 p,m grain size polycrystalline material, and at a quarter of the rate for 12 pm grain size material [ 91. This feature has been interpreted [ 21 as due to the deleterious effect in polycrystals of local stresses arising from elastic and thermal expansion anisotropies. In very general terms the presence of high concentrations of grain boundaries (fine grain materials) confers on the material a better wear resistance than that of single crystal material; low concentrations of grain boundaries (coarse grain materials) are associated with wear resistance poorer than that of single crystal material.
A simple model will now be outlined which is partly empirical in nature and, necessarily at this stage of understanding, undefined in precise detail. It is recognised that the erosive wear process is complex, involving a combination of plastic indentation and macroscopic chipping. At opposite extremes contact between grit particles and the material surface may be of the rounded Hertzian type, involving elastic contact over a relatively large area with low stresses, to the pointed or (perhaps more realistically) chisel indentation type, involving higher stresses with plastic indentation and microcrack nucleation and propagation. Under practical conditions the latter is expected to dominate behaviour, as supported by the experimental observation that the wear rate diminishes as abrasive particles become worn from a sharp angular, to a smoother spherical, form. The wear model presented here is thus limited to microfracture; wear by the removal of material through predominantly plastic processes, as found in the erosion of very finegrained materials, or in polishing by fine particles, is excluded. Furthermore, no consideration is given to intrinsic grain boundary stresses, the effects of which should be significant only for grain sizes > 100 pm [lo]. Thus for alumina the appropriate range for our model is considered to be of the order l-100 pm. Cracks may propagate either along grain boundaries or as intracrystalline cleavage through grains. Since the energy of
A. W. Davidge, F.L. Riley/ Wear 186187
Fig. 5. Scanning electron micrograph of the worn surface of a 2.5 urn grain size pure alumina after a wet erosion test (6 h at 1.9 m s- ’in a slurry of 0.5 mm crushed aluminaaggregate) showing predominantly intercrystalline fracture.
,, Surface d /’
F,
I-
---( --i
-r
;-
\ g.,
‘.,
Fracture assumed to be mainly at two-grain boundaries, with the crack held at three-grain junctions.
Fig. 6. Schematic illustration of the intergranular micro-crack development process
ti)d/G
(1)
where tf is the time (proportional grain boundary face of dimension (a constant) taken to realign at a experimentally observed wear rate W=Adlt
f
or
where A is a constant related to the microstructural crack linking process, and the experimental conditions of the test. tf can be eliminated by defining a characteristic grain size (G,) for which tf= tj. Thus
and substitution w=
->=a tt
Fig.
(3)
tf= (G/G&
d
c-3 ti
Time A
7. Schematic illustration of the wear process, as the summation of crack progression and delay steps.
to G) to traverse a two* G/2, and ti is the time three-grain junction. The W is thus (2)
W=AG/2(tf+tj)
Larger grain size
41
grain boundary fracture is about one half of that for crystalline cleavage [ lo] the former process is favoured energetically. Provided therefore that the wear particles, and thus contact areas, are large compared with microstructural features (as considered here) grain boundary fracture is likely to dominate the wear process. This is in accordance with experimental observations and Fig. 5 shows the worn surface of a 2.5 pm grain size pure alumina after a wet erosion test [ 31. In model experiments involving sapphire crystals very small indentation loads have been sufficient to initiate cracks [ 111. A single cycle of loading and unloading can generate both radial and lateral cracks, although these do not generally lead to immediate chipping and wear. Repeated indentation does, however, lead to chipping, particularly when the lateral cracks propagate back to the free surface [ 121. A damagefree surface will thus experience a delay period before wear starts, after which a steady state wear rate should become established, proportional to the rate of propagation and linking of microcracks in the material. The basic features of the model are shown in Figs. 6 and 7. It is assumed that fracture occurs predominantly along twograin boundaries (grain faces), with cracks progressing along individual grain faces at a mean rate characteristic of the material, before experiencing a delay, for readjustment of the direction of propagation, at each three-grain junction, The time t for the crack to progress a specified distance d is given by t=2(tf+
‘1..
(1995) 45-49
(4) into (3) gives
AGG, 2tj(G+G,)
(5)
A proportionality between W and Gl (G + G,) is thus predicted, with the plot passing through the origin. In practice G, can be readily determined on a trial and error basis using the standard linear regression analysis, and the relationship is thus easy to test. G, is expected to vary with the nature of the test conditions which affect particularly the scale of the
R. W. Davidge, F.L. Riley/ Wear 186187
48 Wet erosive
(1995) 4549
wear
Wiederhorn
I
80 I----,
& Hockey:
Dry erosion
I
c 4.0 60 70 i 50 i
:
/
40 1
30
0
0.2
0.4
0.6
I
0.8
0.0
0.2
0.6
0.8
1.o
G/(G+IO)
G / (G+5) Fig. 8. Wet erosive wear rate of pure polycrystalline alumina, treated as a function of G/ (G + G,), where G, = 5 pm.
0.4
Fig. 11. Dry erosion rates for alumina, treated as a function of G/ (G + G,,) , where G,= 10 pm.
Cho et al: Ball-on-Plate
Rice & Speronello:
Sawing
2000
I600
2
2
1200
$
3
X00
LL. 0
0 0.0
0.2
0.4
0.6
0.8
I .o
G / (G + 6.5)
Fig. 9. Sawing rates for alumina, treated as a function of G/ (G= G,), where G,=6.5 pm.
>--.l,
0.1
0.2 0.3 G/(G+ 100)
Fig. 12. Ball-on-plate wear rates for alumina, treated as a function of G/ (G+G,), where G,=lOO pm.
damage and the way that individual chip. Rice & Speronello:
cracks link to create a
Grinding
3. Discussion
0.0
0.2
0.4
0.6 G /
0.8
I .o
(G+l)
Fig. 10. Grinding rates for alumina, treated as a function of G/ (G + G,), where G, = 1 pm.
Several recent papers present data for a range of wear modes, and provide information about wear rate and mean grain size. These data are treated on the basis of Eq. (5)) and wear data are shown in the following figures. The appropriate G, value was the more readily established the more numerous were the datum points. Fig. 8 shows the plot for wet erosive wear [3], for which the best value of G, is 5 pm. Similar plots for sawing (G, = 6.5 pm) [ 31 and grinding (G, = 1 pm) are shown in Figs. 9 and 10. Other work [ 81 using a more narrow range of conditions has also provided data for dry erosion rates, shown in Fig. 11 with G, = 10 p,m, and for ball-on-plate wear rates [2] with G, = 100 pm
R.W. Davidge, F.L. Riley/ Wear 186187
(Fig. 12). While those plots based on the larger numbers of datum points can be treated with more confidence, it is clear that more detailed and precise studies of wear rates, materials fully characterized with respect to using grain size and size distribution, are required for all wear modes, if satisfactory tests of any model are to be made.
4. Conclusions
A wear model is proposed, based on micro-crack propagation along grain boundaries with temporary blocking of progression by three grain junctions. This allows the derivation of a simple expression for the extent of wear by micro-fracture as a function of time, which is shown to fit a wide range of experimental wear rate data. A full test of the model is now required, with concentration on two fronts: the gathering of detailed and reliable wear rate data for materials of known grain size using a full range of wear conditions, and a detailed examination of the mechanisms of micro-crack initiation and propagation at the surfaces of polycrystalline and single crystal materials, and the consequences for material removal.
(1995) 45-49
49
References [I] H. Liu and M.E. Fine, Modelling of grain-size dependent microfracture-controlled sliding wear in polycrystrdline alumina, J. Am. Ceram. Sot.. 76 (9) (1993) 2392-2396. [2] S.-J. Cho, B.J. Hockey, B.R. Lawn and S.J. Bennison, Gram-size and R-curve effects in the abrasive wear of alumina, J. Am. Ceram. Sot., 72 (7) (1989) 1249-1252. [ 31 M. Miranda-Martinez, R.W. Davidge and F.L. Riley, Gram size effects in the wet erosive wear of high-purity polycrystalline alumina, Wear, 172 (1994) 41-48. [4] R.W. Rice, Micromechanics of microstructural aspects of ceramic wear, Ceram. Eng. Sci. Proc., 6 (7-8) (1985) 940-958. [5] C.Cm. Wu, R.W. Rice, D. Johnson and B.A. Platt, Grain size dependence of wear in ceramics, Ceram. Eng. Sci. Proc., 6 (7-8) (1985) 995-1011. [6] R.W. Rice and B.K. Speronello, Effect of microstructure on rate of machining of ceramics, J. Am. Ceram. Sot., 59 (7-8) ( 1976) 330333. [7] D.B. Marshall, B.R. Lawn and F.R. Cook, Microstructural effects on grinding of alumina and glass ceramics, J. Am. Ceram. Sot., 70 (6)
(1987) C-139-C-40. [8] SM. Wiederhom and B.J. Hockey, Effect of material parameters on the erosion resistance of brittle materials, J. Mater. Sci., 18 (1983)
766789. [9] R.W. Davidge and F.L. Riley, unpublished data. [lo] R.W. Davidge, Mechanical Behaviour of Ceramics, Cambridge University Press, 1979, pp. 13 and 83. [ 1l] R.F. Cook and G.M. Pharr, Direct observation and analysis of indentation cracking in glasses and ceramics, J. Am. Ceram. Sot., 73 (4) (1990) 787-817. [ 121 D.A.J. Vaughan and F. Guiu, Cyclic fatigue of advanced ceramics by repeated indentation, Br. Ceram. Proc., 39 (1987) 101-107.
Wear 186-187 (1995) 45-49
Grain-size dependence of the wear of alumina R.W. Davidge, F.L. Riley School of Materials, University of Leeds, Leeds LS2 9Sr, UK
Abstract A simple model is presented which, although empirical in nature, is consistent with experimental observations on the wear and abrasion rates of high purity alumina of tailored grain size. It is postulated that the critical wear process, reduced to its simplest terms, involves the nucleation and propagation of grain boundary microcracks. A microcrack is nucleated and travels at a characteristic velocity along a low energy grain face until a multi-boundary junction is encountered, when development of the crack is temporarily inhibited. The crack thus progresses with alternating periods of steady growth and delay, and ultimately causes the local loss of material through grain detachment. It is shown that this model leads to a wear rate grain-size dependence of the form seen for a variety of conditions such as erosion, sawing, grinding and sliding. Keywords: Grain size; Alumina; Abrasion; Cracks; Wear
1. Introduction It is generally recognised that the wear of polycrystalline alumina materials under conditions for which microfracture is an important component varies significantly with the mean grain size G: wear rate W increases with increasing grain size [ 11. In contrast, correlations within a specific class of ceramic material between wear rate and hardness, and macro-toughness (as measured by the diamond indentation or notched beam techniques), are poor though the existence of a relationship with microfracture on the scale of a grain size has been postulated on the basis of a better correlation with crack resistance (the R-curve) for alumina [ 21. We have recently reported [ 31 results of a study of the wet erosion of a set of high purity polycrystalline alumina materials of similar hardness and fracture toughness, where a clear relationship between wear rate and grain size was shown. The trend (Fig. 1) fk grain sizes in the range 1 to _ 15 pm is a smooth concave-downwards curve. For this experimental system the damage inflicting particle size to grain size ratio was +, 100, and scanning electron micrographs of wear surfaces showed for G > 3 pm facetting indicative of whole grain detachment. In materials of grain sizes finer than = 2 pm, plastic deformation or chemical removal of material, also appeared to be significant wear processes. Similar grain size-wear rate relationships are seen for a wide range of materials and wear modes, for example grinding [ 4-71, sliding [ 2,4,5 1 sawing [ 61, and dry erosion [ 81. Data have been fitted, variously, to W as a function of 0043.1648/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDIOO43-1648(95)07171-7
Wet erosive wear
10 0
. ““““““I’,“““(/“‘,, 0 2 4
i 6
8
10
12
14
Grain size / km Fig. 1. Wear rate-grain size dependence in the wet erosive wear of pure polycrystalline alumina. G-
112,
W -’ as a function of G-l”, and W as a function of G plots. A common feature of many attempts to produce semiquantitative models for W-G relationships has been the use of the Hall-Petch expression, but there is no clear case made for why a wear process involving damage on the scale of the sub-grain dimension should be determined by macroscopic strength, or a critical defect size which is assumed to scale as the grain dimension. Indeed it is also clear that the approximately linear W as a function of G- I’* plots (as shown for wet erosion in Fig. 2) are deceptive in that they do not pass through the origin, and that the alternative form of plotting,
R. W. Davidge. F.L. Riley/ Wear 186-187 (1995) 45-49
Wet erosive
I_..
()
wear
Wet erosive
1
I__LI_.--A._I_L
0.2
0.4
0.6
0.8
1.0
i
1.2
0.0
(Grain size /km) -“* Fig. 2. Wear rate as a function polycrystalline alumina.
of G- “’ in the wet erosive wear of pure
Wet
erosive
wear
0.5 1.0 [(G-l) /pm)]-“*
Fig. 4. Wear rate as a function of (Gpure polycrystalline alumina.
1.5
1)-“’ in the wet erosive wear of
It is thus clear that a new unified model is required, to explain these sets of wear data, and to relate the rate of removal of surface material, as the accumulation of localized damage occurring on the micrometre scale, to a material’s composition and microstructure. The primary aim of this paper is to outline the basis for a model for polycrystalline materials in which wear rate is related to grain size, and hence to stimulate thinking and critical experimental investigations.
wear
2. Modelling
0
t_;,,--
0
10
5
15
Grain size I j.tm Fig. 3. W* as a function polycrystalline alumina.
of grain size in the wet erosive wear of pure
using W* as a function of G does not give a straight line (Fig. 3). An attempt to force the line through the origin by using (G-G * ) , where G * is the intercept of the G- I” plot, also results in a curve (Fig. 4), indicating that the apparently simple parabolic relationship must be treated with suspicion. A further feature apparently common to these wear processes is that the wear of single crystal material is considerably slower than that predicted on the basis of an extrapolation of G to infinity. In the case of wet erosion, for example, single crystal sapphire wears at a rate similar to that of a 2.5 p,m grain size polycrystalline material, and at a quarter of the rate for 12 pm grain size material [ 91. This feature has been interpreted [ 21 as due to the deleterious effect in polycrystals of local stresses arising from elastic and thermal expansion anisotropies. In very general terms the presence of high concentrations of grain boundaries (fine grain materials) confers on the material a better wear resistance than that of single crystal material; low concentrations of grain boundaries (coarse grain materials) are associated with wear resistance poorer than that of single crystal material.
A simple model will now be outlined which is partly empirical in nature and, necessarily at this stage of understanding, undefined in precise detail. It is recognised that the erosive wear process is complex, involving a combination of plastic indentation and macroscopic chipping. At opposite extremes contact between grit particles and the material surface may be of the rounded Hertzian type, involving elastic contact over a relatively large area with low stresses, to the pointed or (perhaps more realistically) chisel indentation type, involving higher stresses with plastic indentation and microcrack nucleation and propagation. Under practical conditions the latter is expected to dominate behaviour, as supported by the experimental observation that the wear rate diminishes as abrasive particles become worn from a sharp angular, to a smoother spherical, form. The wear model presented here is thus limited to microfracture; wear by the removal of material through predominantly plastic processes, as found in the erosion of very finegrained materials, or in polishing by fine particles, is excluded. Furthermore, no consideration is given to intrinsic grain boundary stresses, the effects of which should be significant only for grain sizes > 100 pm [lo]. Thus for alumina the appropriate range for our model is considered to be of the order l-100 pm. Cracks may propagate either along grain boundaries or as intracrystalline cleavage through grains. Since the energy of
A. W. Davidge, F.L. Riley/ Wear 186187
Fig. 5. Scanning electron micrograph of the worn surface of a 2.5 urn grain size pure alumina after a wet erosion test (6 h at 1.9 m s- ’in a slurry of 0.5 mm crushed aluminaaggregate) showing predominantly intercrystalline fracture.
,, Surface d /’
F,
I-
---( --i
-r
;-
\ g.,
‘.,
Fracture assumed to be mainly at two-grain boundaries, with the crack held at three-grain junctions.
Fig. 6. Schematic illustration of the intergranular micro-crack development process
ti)d/G
(1)
where tf is the time (proportional grain boundary face of dimension (a constant) taken to realign at a experimentally observed wear rate W=Adlt
f
or
where A is a constant related to the microstructural crack linking process, and the experimental conditions of the test. tf can be eliminated by defining a characteristic grain size (G,) for which tf= tj. Thus
and substitution w=
->=a tt
Fig.
(3)
tf= (G/G&
d
c-3 ti
Time A
7. Schematic illustration of the wear process, as the summation of crack progression and delay steps.
to G) to traverse a two* G/2, and ti is the time three-grain junction. The W is thus (2)
W=AG/2(tf+tj)
Larger grain size
41
grain boundary fracture is about one half of that for crystalline cleavage [ lo] the former process is favoured energetically. Provided therefore that the wear particles, and thus contact areas, are large compared with microstructural features (as considered here) grain boundary fracture is likely to dominate the wear process. This is in accordance with experimental observations and Fig. 5 shows the worn surface of a 2.5 pm grain size pure alumina after a wet erosion test [ 31. In model experiments involving sapphire crystals very small indentation loads have been sufficient to initiate cracks [ 111. A single cycle of loading and unloading can generate both radial and lateral cracks, although these do not generally lead to immediate chipping and wear. Repeated indentation does, however, lead to chipping, particularly when the lateral cracks propagate back to the free surface [ 121. A damagefree surface will thus experience a delay period before wear starts, after which a steady state wear rate should become established, proportional to the rate of propagation and linking of microcracks in the material. The basic features of the model are shown in Figs. 6 and 7. It is assumed that fracture occurs predominantly along twograin boundaries (grain faces), with cracks progressing along individual grain faces at a mean rate characteristic of the material, before experiencing a delay, for readjustment of the direction of propagation, at each three-grain junction, The time t for the crack to progress a specified distance d is given by t=2(tf+
‘1..
(1995) 45-49
(4) into (3) gives
AGG, 2tj(G+G,)
(5)
A proportionality between W and Gl (G + G,) is thus predicted, with the plot passing through the origin. In practice G, can be readily determined on a trial and error basis using the standard linear regression analysis, and the relationship is thus easy to test. G, is expected to vary with the nature of the test conditions which affect particularly the scale of the
R. W. Davidge, F.L. Riley/ Wear 186187
48 Wet erosive
(1995) 4549
wear
Wiederhorn
I
80 I----,
& Hockey:
Dry erosion
I
c 4.0 60 70 i 50 i
:
/
40 1
30
0
0.2
0.4
0.6
I
0.8
0.0
0.2
0.6
0.8
1.o
G/(G+IO)
G / (G+5) Fig. 8. Wet erosive wear rate of pure polycrystalline alumina, treated as a function of G/ (G + G,), where G, = 5 pm.
0.4
Fig. 11. Dry erosion rates for alumina, treated as a function of G/ (G + G,,) , where G,= 10 pm.
Cho et al: Ball-on-Plate
Rice & Speronello:
Sawing
2000
I600
2
2
1200
$
3
X00
LL. 0
0 0.0
0.2
0.4
0.6
0.8
I .o
G / (G + 6.5)
Fig. 9. Sawing rates for alumina, treated as a function of G/ (G= G,), where G,=6.5 pm.
>--.l,
0.1
0.2 0.3 G/(G+ 100)
Fig. 12. Ball-on-plate wear rates for alumina, treated as a function of G/ (G+G,), where G,=lOO pm.
damage and the way that individual chip. Rice & Speronello:
cracks link to create a
Grinding
3. Discussion
0.0
0.2
0.4
0.6 G /
0.8
I .o
(G+l)
Fig. 10. Grinding rates for alumina, treated as a function of G/ (G + G,), where G, = 1 pm.
Several recent papers present data for a range of wear modes, and provide information about wear rate and mean grain size. These data are treated on the basis of Eq. (5)) and wear data are shown in the following figures. The appropriate G, value was the more readily established the more numerous were the datum points. Fig. 8 shows the plot for wet erosive wear [3], for which the best value of G, is 5 pm. Similar plots for sawing (G, = 6.5 pm) [ 31 and grinding (G, = 1 pm) are shown in Figs. 9 and 10. Other work [ 81 using a more narrow range of conditions has also provided data for dry erosion rates, shown in Fig. 11 with G, = 10 p,m, and for ball-on-plate wear rates [2] with G, = 100 pm
R.W. Davidge, F.L. Riley/ Wear 186187
(Fig. 12). While those plots based on the larger numbers of datum points can be treated with more confidence, it is clear that more detailed and precise studies of wear rates, materials fully characterized with respect to using grain size and size distribution, are required for all wear modes, if satisfactory tests of any model are to be made.
4. Conclusions
A wear model is proposed, based on micro-crack propagation along grain boundaries with temporary blocking of progression by three grain junctions. This allows the derivation of a simple expression for the extent of wear by micro-fracture as a function of time, which is shown to fit a wide range of experimental wear rate data. A full test of the model is now required, with concentration on two fronts: the gathering of detailed and reliable wear rate data for materials of known grain size using a full range of wear conditions, and a detailed examination of the mechanisms of micro-crack initiation and propagation at the surfaces of polycrystalline and single crystal materials, and the consequences for material removal.
(1995) 45-49
49
References [I] H. Liu and M.E. Fine, Modelling of grain-size dependent microfracture-controlled sliding wear in polycrystrdline alumina, J. Am. Ceram. Sot.. 76 (9) (1993) 2392-2396. [2] S.-J. Cho, B.J. Hockey, B.R. Lawn and S.J. Bennison, Gram-size and R-curve effects in the abrasive wear of alumina, J. Am. Ceram. Sot., 72 (7) (1989) 1249-1252. [ 31 M. Miranda-Martinez, R.W. Davidge and F.L. Riley, Gram size effects in the wet erosive wear of high-purity polycrystalline alumina, Wear, 172 (1994) 41-48. [4] R.W. Rice, Micromechanics of microstructural aspects of ceramic wear, Ceram. Eng. Sci. Proc., 6 (7-8) (1985) 940-958. [5] C.Cm. Wu, R.W. Rice, D. Johnson and B.A. Platt, Grain size dependence of wear in ceramics, Ceram. Eng. Sci. Proc., 6 (7-8) (1985) 995-1011. [6] R.W. Rice and B.K. Speronello, Effect of microstructure on rate of machining of ceramics, J. Am. Ceram. Sot., 59 (7-8) ( 1976) 330333. [7] D.B. Marshall, B.R. Lawn and F.R. Cook, Microstructural effects on grinding of alumina and glass ceramics, J. Am. Ceram. Sot., 70 (6)
(1987) C-139-C-40. [8] SM. Wiederhom and B.J. Hockey, Effect of material parameters on the erosion resistance of brittle materials, J. Mater. Sci., 18 (1983)
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