ABRASIVE WEAR OF BRITTLE SOLIDS M. A. MOORE** and F. S. KING

Prévia do material em texto

Wear, 60 (1980) 123 - 140 
0 Eisevier Sequoia S.A., Lausanne -Printed in the Netherlands 
123 
ABRASIVE WEAR OF BRITTLE SOLIDS* 
M. A. MOORE** and F. S. KING 
National Institute of Agricultuml Engineering, Silsoe, Bedford (Gt. Britain) 
(Received October 15,1979) 
Summary 
The wear on flint and Sic abrasives, and the indentation properties of a 
wide range of engineering ceramics and brittle solids have been studied. An 
attempt has been made to assess the roles of plastic deformation and fracture 
in the wear process and to determine the effect of mechanical properties on 
wear. The investigation showed that the mechanism controlling the rate of 
material removal differed for different materials and wear environments. 
Fracture mechanisms may cause the rate of material removal to be about ten 
times that for plastic deformation mechanisms. Fracture mechanisms pre- 
dominate when the depth of indentation of the abrasive is high, the abrasive 
is sharp and the ratio of fracture toughness to hardness of the material is 
low. No simple relation between wear and mechanical properties exists, but 
wear is generally low for material of high hardness and high fracture tough- 
ness and for high values of the ratio of fracture toughness to hardness. 
1. Introduction 
Because they possess a useful combination of properties, such as hard- 
ness, stiffness, low density, high strength and refractoriness, ceramics are 
being used increasingly in engineering applications [ 1 - 41. One important 
application is for components subject to abrasive wear. In spite of this few 
data on the abrasive wear of ceramics exist and the mechanisms of wear of 
brittle materials have not been thoroughly studied. 
Although ceramics are very brittle, with values of fracture toughness 
Kc lower than 10 MN m-3’2, there is evidence [ 5 - 1 l] that plastic deforma- 
tion occurs during indentation and abrasive wear. This plasticity has been 
attributed to the inhibition of fracture by the hydrostatic pressure associated 
with indentation [ 12,131 and to the considerable reduction of yield stress 
*Paper presented at the International Conference on Wear of Materials 1979, 
Dearborn, Michigan, April 1979. 
**Present address: Fulmer Research Institute Limited, Stoke Poges, Slough, 
Gt. Britain. 
124 
resulting from a large increase in temperature of the plastic zone [ 8, 91. 
There is support from data on ductile materials [ 141 that the former mech- 
anism allows very high plastic strains to develop during abrasive wear. How- 
ever, the tensile stresses associated with indentation can cause cracks to 
propagate from the plastic zone [ 121, and with very lightly loaded or blunt 
indenters contact may be purely elastic and result in Hertzian fracture [ 151. 
Thus fracture processes are expected to play an important role in material 
removal during abrasion of brittle solids [ 10 - 12,15,16]. Since both plastic 
deformation and fracture are likely to occur during the abrasive wear of 
brittle materials it is fundamental to the development of improved materials 
to know under what conditions either plastic deformation mechanisms or 
fracture mechanisms might predominate and control the rate of material 
removal. 
The abrasive wear and indentation properties, hardness and fracture, of 
a wide range of engineering ceramics and brittle solids have been studied. 
The objectives were to provide comparative data for potential users of such 
materials, to assess the roles of plastic deformation and fracture in the abra- 
sion of brittle materials, to relate wear to mechanical properties and to assess 
the importance of microstructure in the wear process. 
2. Measurement and observation of abrasive wear and mechanical properties 
2.1. Volume wear 
Abrasive wear tests were carried out on commercial bonded flint and 
Sic abrasive paper and cloth discs. For each of the two abrasives two grit 
sizes were used, 180 and 40 grit (nominal mean sizes of 84 and 384 pm) for 
the flint and 180 and 60 grit (nominal mean sizes of 84 and 250 pm) for the 
Sic. The test materials (Table 1) had ground 5 mm diameter cylindrical tips 
and were worn under an applied load per unit area of 1 MN rnd2 and a speed 
of 0.5 m s-l (Fig. 1). 
The specimens traversed a spiral track of length 8 m on the abrasive 
discs such that each segment was only passed over once. Before any measure- 
ments were made the specimens were run-in for one complete run and were 
thoroughly cleaned after each run to remove adhering wear debris. Wear was 
measured by weight loss taking an average of three runs, and volume wear 
was calculated from these data and the measured density. In the majority of 
tests the scatter on the results was better than +lO%. Table 2 shows the 
mean volume wear results, volume wear per unit contact area (mm2) of the 
specimen and per unit distance run (m), and the ranking order of the test 
materials for each of the wear environments. 
Some further tests were carried out with a 97.5% sintered alumina 
(specimen 27) to investigate the dependence of volume wear on load. Wear 
was measured for applied loads per unit area of 0.125 - 1.5 MN rnT2 on the 
180 and 60 grit Sic abrasives. The calculated volume wear results (Fig. 2) 
indicated a power relation of the form 
Va 13” 
125 
(1) 
where V is the volume wear (mm3) and u is the applied load per unit area 
(MN m-‘). Least squares linear regression fits of log,,V and log,,o gave 
values for the exponent n of 0.61 and 1.04 for wear on the 180 grit and 
60 grit abrasives respectively. 
2.2. Surface damage 
Scanning electron microscope observation of the worn surface of a 
selection of materials chosen to span the range of hardness and fracture 
toughness values yielded qu~i~tive information on the nature of the surface 
damage. Materials in this group, specimens 5,7,8,10,17,24 and 27, dis- 
played a range of surface damage. 
The damage on the low hardness low fracture toughness fused silica 
(Figs. 3(a) and 3(b)) consisted of continuous plastically deformed grooves 
(A in Fig. 3) with adjacent fracture damage. Lateral cracks following 
cleavage planes have resulted in material removal (B in Fig. 3) and median 
cracks (C in Fig. 3) are visible in the same area. In contrast, damage on the 
much higher hardness and fracture toughness hot-pressed Si3N, (Figs. 3(c) 
and 3(d)) was mainly in the form of grooves formed by plastic deformation 
(D in Fig. 3) with some fracture damage of the specimen worn on the 60 grit 
Sic associated with material below the grooves (E in Fig. 3). In both cases 
fracture damage was greater on the coarse abrasive. Figure 3(e) shows 
damage on 95% sintered alumina after wear on 40 grit flint which consists of 
extensive areas of both plastic deformation F and fracture G. Figure 3(f) 
shows at a higher magnification delamination damage H at the base of a 
plastically impressed groove in a 97.5% sintered alumina. These observations 
are similar to those made in previous investigations [ 10,111. 
There were also significant differences in the surface damage of the 
same materials worn on the flint and Sic abrasives, particularly for the 
harder materials. Figures 3(g) and 3(h) illustrate this for a reaction-bonded 
SIC. Continuous plastically impressed grooves I with adjacent fracture 
damage J were visible on the specimen worn on 60 grit Sic compared with 
the more diffuse texture of discon~nous grooves and fracture damage on the 
surface of the specimen after wear on 40 grit flint (Fig. 3(h)). 
2.3. Mechanical properties 
The mechanical properties of brittle materials are very sensitive to both 
specimen size and test environment [ 4,. 161. Thus hardness H and fracture 
toughness K, data were estimated from micro-Vickers diamond pyramid 
indentations, for which the stress system is similar to that for sliding 
abrasion,made at an indentation load of about 1.5 N which is close to the 
estimated highest load of 1.2 N on an abrasive particle in the wear tests, A 
limited number of indentations were also made at loads from 1 to 50 N, and 
within this range the estimated hardness and fracture toughness were inde- 
pendent of indention load. 
126 
TABLE 1 
Chemical, physical and measured mechanical properties of the test materials 
Material Specimen Chemical 
no. composition 
Grain Density Vickers Fracture 
size (g ml-l) micro- toughness K, 
(Pm) hardness (MN rnV312) 
(GN mh2) 
Soda-lime glass 
Glass ceramic 
Cast basalt 
Fused SiO2 
Reaction-bonded 
SiaN4 
Hot-pressed 
Si3 N4 
Reaction-bonded 
Sic 
Sintered B4C 
Hot-pressed 
B4C 
Sintered TiOz 
Mineral flint 
Sintered 
SiAlON 
WC-CO 
composites 
Hot-pressed 
A1203 
Cold-pressed and 
sintered Al203 
Flint abrasive 
Sic abrasive 
7 3.22 15.9 9.1 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
2.57 
2.45 
Low substitution 3.09 
SiAlON + metal oxide 
93% WC, 5% co 1 - 1.3 14.6 
94% WC, 6% Co 2.7 15.0 
93% WC, 6% Co 2.0 14.5 
92% WC, 8% Co 2 - 2.7 14.7 
21 
22 
23 88% Al203 
24 95% Al203 
25 95% Al203 
26 96% Al203 
27 97.5% Al,O, 
28 99.5% Al203 
29 99.5% Al203 
30 99.7% Al203 
31 99.7% Al,O, 
32 99.7% A1,03 
8 - 12% free Si 
2.71 4.5 3.8 
2.60 4.5 2.6 
2.54 2.2 1.3 
2.89 4.9 2.2 
2.09 5.3 3.3 
2.27 7.0 4.6 
3.14 20.3 
3.08 16.2 
90% dense 2.34 
2.57 
2.43 
2.06 
24.0 
29.4 
30.9 
7.4 
6.5 
6.1 
11.5 
14.3 7.2 
12.5 6.3 
12.9 6.5 
12.1 6.1 
=8 
-4.5 
=8 
28 
3-5 
14 
3 
3 
20 
3.9 13.7 
3.9 17.2 
3.57 8.4 
3.67 12.8 
3.72 12.1 
3.74 11.8 
3.77 15.2 
3.94 14.6 
3.81 14.5 
3.9 11.9 
3.87 12.4 
3.76 12.0 
7.1 
21.3 
9.0 
7.6 
9.7 
7.8 
9.4 
2.5 
4.8 
4.0 
7.1 
5.4 
7.2 
3.1 
5.7 
3.9 
4.6 
8.1 
3.7 
5.6 
4.2 
4.0 
3.9 
4.6 
6.3 
After careful metallographic polishing the materials were tested on a 
Reichert Vickers microhardness machine. At least three indentations, and in 
most cases five, were made on each material. As is common with brittle 
127 
Fig. 1. Abrasive wear testing equipment. 
solids the impressions were clearly defined with cracks visible at the surface 
running from the comers of the impression into the material. Figure 4 shows 
such an impression in soda-lime glass; the cracks with planes perpendicular to 
the surface are median cracks [ 121 and the light areas around the impression 
are reflections from lateral cracks with planes approximately parallel to the 
surface. In some cases the lateral cracks propagated to the surface causing 
material around the impression to be removed and the impression to be ill 
defined. These impressions were not used for hardness and fracture tough- 
ness estimates. 
The diagonals of the impressions and the lengths C, of the median 
cracks from the comers of the impressions were measured. From these data 
the Vickers hardness was calculated and the fracture toughness was 
estimated using the empirical relation established by Evans and coworkers 
[17,18] : 
KC = 0.45(H/@)a 1/Z log,,(4.5a/C,) (2) 
where @ is the indentation constraint factor defined as H/o,, u,. is the yield 
stress, a is the half-diagonal of the impression and a and C, are in micro- 
metres. Evans and Charles [ 181 estimate that an expression such as eqn. (2) 
gives values of K, with an accuracy to about 30%. To solve eqn. (2) @ was 
estimated for each material from an equation derived by Studman et al. 
[13] : 
Q, = H/ay 
= 1.16 + 0.66 ln(k,E@/H) (3) 
128 
TABLE 2 
Volume wear data and ranking order of the test materials 
Material Specimen Volume wear (mm3 mme2(m MN me2)) and ranking order 
no. 
Flint abrasive Sic abrasive 
84 pm 384 &m 84 pm 250 flrn 
Soda-lime glass 1 0.023 31 0.27 30 0.053 31 0.66 31 
2 0.019 30 0.30 31 0.045 30 0.63 30 
Glass ceramic 3 0.093 32 0.32 32 0.17 32 0.58 28 
Cast basalt 4 0.0064 28 0.044 28 0.033 28 0.22 26 
Fused SiOa 5 0.0064 28 0.062 29 0.036 27 0.58 28 
Reaction-bonded 6 0.00094 25 0.015 26 0.025 26 0.20 25 
SiaN4 
Hot-pressed SiaN, 7 0.000081 11 0.00018 9 0.0062 12 0.015 10 
Reaction-bonded 8 0.000036 4 0.00019 10 0.0036 9 0.015 10 
Sic 9 0.000041 7 0.00030 12 0.0055 11 
Sintered B,C 10 0.000036 4 0.000082 2 0.00082 3 0.011 8 
Hot-pressed B4C 11 0.000093 12 0.000096 5 0.00033 1 0.00090 1 
12 0.000013 1 0.00011 6 0.00047 2 0.0026 2 
Sintered Ti02 13 0.0039 27 0.020 27 0.050 29 0.28 27 
Mineral flint 14 0.00069 22 0.0047 25 0.022 25 0.15 23 
15 0.0011 26 0.0046 24 0.021 24 0.16 24 
Sintered SiAlON 16 0.000047 8 0.000066 1 0.0039 10 0.014 9 
17 0.000020 2 0.000085 3 0.0022 4 0.0058 3 
WC -co 18 0.000032 3 0.00012 7 0.0031 7 0.0090 6 
composites 19 0.000040 6 0.000090 4 0.0033 8 0.0087 5 
20 0.000052 9 0.00016 8 0.0029 5 0.010 7 
Hot-pressed Al203 21 0.00037 20 0.0012 16 0.0087 15 0.015 10 
22 0.000075 10 0.00026 11 0.0030 6 0.0062 4 
Cold-pressed and 23 0.00035 19 0.0022 19 0.013 19 0.043 22 
sintered A1203 24 0.00025 15 0.0017 18 0.011 17 0.028 16 
25 0.00032 18 0.00099 14 0.011 17 0.035 18 
26 0.00026 17 0.0013 17 0.0071 14 0.022 14 
27 0.00024 14 0.00051 13 0.0064 13 0.025 15 
28 0.00020 13 0.0026 22 0.014 21 0.042 21 
29 0.00073 23 0.0023 20 0.016 22 0.031 17 
30 0.00025 16 0.0011 15 0.0093 16 0.015 10 
31 0.00038 21 0.0025 21 0.016 22 0.040 19 
32 0.00075 24 0.0036 23 0.013 19 0.041 20 
where iz, is a constant depending on indenter geometry, here equal to 0.12, 
and E is Young’s modulus. 
Table 1 shows the mean microhardness and estimated fracture tough- 
ness data together with some other information about the test materials. The 
scatter in results for microhardness was mostly within +lO%, but for the 
129 
005 
i 
. . 
0.1 
Applied load -MNm-’ ’ 1 
Fig. 2. Volume wear us. applied load for 97.5% sintered alumina worn on 180 grit (m) and 
60 grit (*) Sic. 
fracture toughness data it was somewhat larger, being between +15% and 
+ 20%. 
3. Material removal mechanisms 
The data in Table 2 show that the volume wear of brittle solids can vary 
over a very wide range for different materials and wear environments; there 
is nearly five orders of magnitude difference between the lowest and highest 
values. Wear increases rapidly with increase in grit size and is as much as an 
order of magnitude higher on the Sic than on flint abrasive of a correspond- 
(a) 
Fig. 3. 
(b) 
(d) 
w (h) 
Fig. 3. (a) Fused silica worn on 180 grit Sic. (b) Fused silica worn on 60 grit Sic. (c) 
Hot-pressed silicon nitride worn on 180 grit SIC. (d) Hot-pressed Si3N4 worn on 60 grit 
SIC; (e) 95% sintered alumina worn on 40 grit flint; (f) 97.5% sintered alumina worn on 
60 grit Sic; (g) reaction-bonded Sic worn on 60 grit Sic; (g) reaction-bonded Sic worn 
on 40 grit flint. 
131 
Fig. 4. Typical hardness impression and indentation fracture for a brittle solid. 
ing size. The effects on wear of both grit size and abrasive type are very 
much greater for the brittle solids than for metallic materials [ 19, 201. 
For metallic materials Richardson [19] has attributed the effect of 
abrasive type to different rates of deterioration of the abrasive. Such a mech- 
anism is supported by the common dependence of volume wear measured on 
a range of abrasives on the ratio H/H, of hardness of the wearing surface to 
hardness of the abrasive. Richardson [ 191 suggested that the rate of de- 
terioration of the abrasive increases up to an H/H, value of about 0.8, and so 
volume wear decreases rapidly over this range. Figure 5 shows volume wear 
data from Table 2 plotted against H/H,. Although there is considerable 
scatter of the data, data for corresponding grit sizes of flint andSic abrasive 
lie approximately on common curves and there is a rapid decrease in volume 
wear up to an H/H, value of 0.6 - 0.8. This behaviour and the difference in 
surface damage after wear on Sic and flint abrasives (Figs. 3(g) and 3(h)) 
suggest that deterioration of the abrasive is an important factor determining 
wear rates of brittle materials. In comparison with metallic materials [ 19, 
201 brittle materials have higher volume wear at corresponding values of 
H/H, and the change in wear due to change in grit size at constant H/H, is 
also much greater. 
That both plastic deformation mechanisms and fracture mechanisms 
contribute to material removal during wear of brittle solids is evident on the 
scanning electron micrographs (Fig. 3). It is also clear that fracture damage is 
always associated with plastically formed grooves under the contact condi- 
tions used for the wear tests. For brittle materials blunt indenters cause 
conical cracks to extend into the material under elastic contact [ 151, i.e. 
132 
Fig. 5. Volume wear us. H/H, for 160 grit flint and Sic (0) and 40 grit flint and 60 grit 
Sic (m). 
Hertzian fracture. Since these conical cracks are unlikely to join up to 
enclose a volume of material bounded by the free surface, material removal 
by Hertzian fracture is virtually impossible during abrasive wear. However, at 
small radii of curvature of the indenter contact becomes elastic-plastic [ 12 - 
171 because the radius has a larger effect on the plastic indentation load 
than on the Hertzian fracture load. The largest indenter radius for elastic- 
plastic contact increases as the hardness of the material decreases and as the 
fracture toughness increases. Under these conditions contacting abrasive 
particles can form a groove by plastic deformation but, as for metallic 
materials, only a proportion of these contacts will result in material removal 
and only a proportion of the volume of these grooves will be removed. 
Published data for metallic materials [ 21 - 25) would suggest that about 60% 
of contacting particles result in removal of about 60% of their groove 
volumes. If the abrasive deteriorates by plastic flow or by fracture [ 193, the 
proportion of grooves resulting in material removal and the groove volume 
decrease and thus volume wear decreases. Severe blunting of abrasive 
particles in contact with brittle materials may also result in el~tic-pl~tic 
contacts becoming purely elastic and again volume wear will decrease. 
Elastic-plastic indentation in brittle materials results in initiation and 
propagation of median and lateral vent cracks [ 12,171 when the indentation 
reaches a critical size [ 261. The minimum size for fracture increases as the 
hardness of the material decreases and as the fracture toughness increases, 
and is higher for blunt than for sharp indenters. These static indentation 
phenomena also apply qualitatively to sliding indenters but reduced loads are 
required to produce fracture [ 271. The crack lengths scale with the size of 
the indentation and are larger for materials of low fracture toughness [ 171. 
Under these contact conditions abrasive particles form plastically deformed 
grooves with adjacent cracks. Material is removed by a fracture mechanism if 
lateral cracks adjacent to the grooves intersect those from other grooves or 
133 
propagate to the surface. The volume of material removed can be much 
greater than the groove volume since the lateral cracks extend well beyond 
the boundaries of the groove. If the abrasive deteriorates by plastic flow and 
blunts, the indentation size may become smaller than the critical size so the 
mechanism of material removal changes from a fracture to a plastic deforma- 
tion mechanism and volume wear will rapidly decrease. If the abrasive 
deteriorates by fracture, sharp cutting facets may be regenerated with little 
effect on the material removal mechanism or on volume wear. 
Quite clearly the predominant material removal mechanism during the 
abrasion of brittle materials will depend on the scale of indentation, as Lawn 
et al. [ 261 have observed, and on the shape of the abrasive particles. The 
scanning electron micrographs (Fig. 3) show that fracture damage is more 
prominant after wear on the coarse abrasives. This scale effect can be 
illustrated graphically for static Vickers indentation under the mean normal 
loads W per abrasive particle for the 60 grit and 180 grit abrasive which are 
0.5 and 0.055 N respectively. Figure 6 shows plots of the indentation depth 
of a Vickers indenter versus Hw112 and estimates of the critical indentation 
depth for fracture, C, = 0, from the equation derived by Lawn et al. [ 261 
and data from the indentation fracture experiments: 
p&t = 0.29a(a/a + cry (4) 
For the 60 grit load the depths of indentation are greater than the critical 
depths but for the 180 grit load the depths of indentation are mostly close 
to or less than the critical depths (Fig. 6). For indenters sharper than a 
Fig. 6. Indentation depth vs. H W2 for a Vickers diamond pyramid indenter under two 
loads (solid lines) and the estimated critical indentation depths for fracture of the 
materials used in the wear tests. 
134 
Vickers diamond pyramid the indentation depths will be somewhat greater 
than those shown on Fig. 6 and pcrit will be somewhat less. Under these 
conditions the 180 grit load indentation depths may tend to be greater than 
the critical depths. In contrast, blunt indenters will have reduced indentation 
depths and petit will increase. Under these conditions both the 60 grit and 
180 grit load indentation depths may tend to be less than the critical depths. 
The preceding observations are generally consistent with the exper- 
imental evidence. For wear on the coarse abrasives fracture mechanisms 
predominate (Fig. 3) and volume wear is high, particularly for low fracture 
toughness materials. The predominant surface damage after wear on the 
coarse abrasive changes from fracture to plastic deformation as H/H, 
increases (Fig. 3) and thus volume wear decreases rapidly as H/H, increases 
(Fig. 5). For wear on the fine abrasives plastic deformation mechanisms pre- 
dominate, except for very low fracture toughness materials, and volume wear 
is about an order of magnitude less than on the coarse abrasive. The reduc- 
tion in volume wear with increase in H/H, is also much less than for the 
coarse abrasive because deterioration of the abrasive has less effect on 
material removal by plastic deformation than by fracture mechanisms. The 
volume wear of brittle solids is still somewhat higher than that of metallic 
materials at the same value of H/H,, presumably because fracture mech- 
anisms do account for some material removal. Certainly indentation fracture 
occurs on materials of low fracture toughness, but the proportion of the 
groove volume removed may also be higher because of delamination failure 
(Fig. 3). Swain [lo] has proposed that delamination of material beneath 
plastically deformed grooves will occur when the stress caused by pile-ups of 
dislocations at grain boundaries close to the surface which is unlikely to be 
relieved by slip in adjacent grains nucleates grain boundary failure. 
For the experiment on load dependence of wear in which 97.5% 
sintered alumina was worn on Sic the H/H, ratio was about 0.7. Consider- 
able deterioration of the abrasive is expected at this value and material 
removal was by a combination of plastic deformation with delamination and 
fracture mechanisms (Figs. 3(e) and 3(f)). A simple mechanistic understand- 
ing is not possible for such a complex wear situation. However, it is probable 
that load dependence of wear will vary for different materials and wear 
environments [ 151 and thus requires further study. 
4. Relation between wear and mechanical properties 
Simplemodels for material removal during wear of brittle materials 
(see Appendix A) give the volume wear (mm3) per unit contact area (mm2) 
and unit distance run (m) for material removal by plastic deformation 
mechanisms 
V= 0.10/H 
and for material removal by fracture mechanisms 
(5) 
(6) V z 2-, 5/4d 1/2K c 
-3/4H- 112 
where u is the applied load per unit area (MN me2), H is the hardness 
(GN me2 ), d is the abrasive grit diameter (mm) and K, is the fracture tough- 
ness (MNm -3’2) . Clearly neither of these models on their own can account for 
the wear of brittle solids because in practice, for a wide range of materials, 
material removal is by a combination of plastic deformation and fracture 
mechanisms. In addition there is considerable uncertainty as to the values of 
the constants in eqns. (5) and (6) because of the effect of abrasive deteriora- 
tion on abrasive particle geometry and contact. Neither model accounts for 
the observed load dependence nor on their own for the effect of grit size on 
wear. 
Thus Fig. 7 shows a plot of eqn. (5) and data for brittle materials worn 
on 180 grit SIC for which plastic deformation is expected to be predom- 
inant. For comparative purposes data for metallic materials [19, 201 are also 
plotted with H as the hardness of the worn surface [ 281, and this plot 
shows the general validity of the plastic deformation model for wear of 
ductile materials. Data for the,brittle solids show considerable scatter at high 
values of hardness and non-linear dependence on l/H. Wear is considerably 
higher than predicted by eqn. (5) at low values of hardness presumably be- 
cause of the increasing contribution of fracture mechanisms to material 
removal. Figure 8 shows a plot of eqn. (6) and data for brittle materials worn 
on 60 grit Sic and 40 grit flint for which fracture is expected to be predom- 
inant. There is considerable scatter of the data which suggests that there is 
no functional relation between volume wear under these conditions and 
135 
Kc- 3/4H- 112. 
. 
. 
. 
Fig. 7. Some data for volume wear on 180 grit Sic us. H-l of brittle materials (0) and 
metallic materials [ 201 (m). 
Fig. 8. Some data for volume wear on 60 grit SIC (0) and 40 grit flint (A) us. 
&-3/4H-1/2. 
136 
Division of eqn. (6) by eqn. (5) shows #at fracture mechanisms can 
cause about ten times as much wear as plastic deformation mechanisms. 
Thus volume wear will depend markedly on the proportion of material re- 
moved by fracture and the proportion removed by plastic deformation. This 
balance of mechanisms for material removal will depend on the relative 
values of the mean abrasive particle indentation depth and the critical 
indentation depth for fracture as discussed in Section 3. When the critical 
indentation depth is a constant, i.e. for one material, the volume wear may 
be significantly different for different abrasive particle indentations brought 
about by changing grit size or load. The data in Table 2 show that the ratio 
of volume wear on 60 grit Sic to volume wear on 180 grit SiC varies from 
about 2 to 16 compared with a value of about 1.5 for metallic materials. 
When grit size and load are constant the volume wear may vary considerably 
for quite small variations of hardness and critical indentation depth. The 
effect of hardness is clearly shown in Fig. 7. Lawn et at. /26] have shown 
that the critical indentation size is dependent on the ratio of fracture tough- 
ness to hardness: 
(7) 
The effect of (Kc/H)2 is shown by the data in Table 2 for reaction-bonded 
Sic, hot-pressed B*C, sintered B4C and SiAlON (specimen nos. 8,10,12 and 
16) which have (K,/Hj2 values of about 0.2,0.1, 0.15 and 0.4 respectively. 
There are changes of ranking order of these materials in the four wear 
environments: on the 180 grit flint the high hardness, high fracture 
toughness hot-pressed B.+C has the lowest wear, whereas on the 40 grit flint 
the SiAlON with the lowest hardness and fracture toughness has the lowest 
wear; on 180 grit Sic the sintered B4C has twice the volume wear of the hot- 
pressed B,C and the SiAlON has about the same as that of the reaction- 
bonded Sic, whereas on the 60 grit Sic the corresponding materials have 
volume wear ratios of about 4 and 1 respectively. These changes are almost 
certainly due to the effect of the relative values of abrasive particle indenta- 
tion depth and critical indentation depth for fracture on the proportion of 
material removed by fracture mechanisms. Thus the ratio ?QH is likely to be 
as important in determining wear as the absolute values of R, and H, and 
materials with high &/H ratios will tend to have low wear. 
5. Conclusions 
(1) Both plastic deformation mechanisms and fracture mechanisms 
cause material removal during the abrasive wear of brittle solids. The 
predominant and rate-controlling mechanism differs for both different wear 
environments and different materials. 
(2) Since the rate of material removal by fracture mechanisms may be 
about an order of magnitude greater than that by plastic deformation mech- 
anisms, the volume wear of brittle solids varies over a wide range. 
(3) Plastic deformation is favoured when the load on the abrasive 
particles is small, i.e. for small abrasive particle sizes or low applied loads, 
when the abrasive is blunt or blunts during contact and when the ratio of 
fracture toughness to hardness of the material is high. 
(4) Indentation fracture is favoured when the load on the abrasive 
particles is high, i.e. for large abrasive particle sizes or high applied loads, 
when the abrasive is sharp or remains sharp because it fractures on contact 
with the wearing material and when the ratio of fracture toughness to hard- 
ness of the material is low. 
(5) Because material removal is by a combination of plastic deforma- 
tion and fracture mech~isms there is no simple relation between wear and 
the mechanical properties of brittle solids. 
(6) Hardness is certainly one major factor determining wear because of 
the effect it has on the rate of deterioration of the abrasive and thus on 
abrasive particle geometry and contact. 
(‘7) Hardness also determines the depth of indentation of the abrasive 
particles. If this depth is greater than the critical indentation depth for frac- 
ture, fracture mechanisms of material removal predominate and volume wear 
is high. The critical indentation depth for fracture is proportional to (K$Q2 
and is thought to be as important as the absolute values of K, and H in 
determining wear. High fracture toughness will increase the critical indenta- 
tion depth for fracture and decrease the volume of material removed when 
fracture mechanisms occur. 
(8) Delamination of material beneath plastically deformed grooves also 
causes material removal during abrasive wear of brittle solids although it is 
not clear for what proportion of the total wear this accounts. Such a mech- 
anism is likely to be sensitive to microstructural properties of the material 
such as grain size, grain boundary strength and grain strength. This and other 
features of the wear of brittle solids suggest that an area of further investiga- 
tion should be the relation between wear and microstructure. 
Acknowledgments 
This work was financed by the Agricultural Research Council and is 
part of a continu~g study in the Machine Division of the Nations Institute 
of Agricultural Engineering of the application of ceramics to agricultural soil 
working equipment. The authors are indebted to Dr. R. L. Bell, Director, 
and T. C. D. Manby, Head of Machine Division, National Institute of Agricul- 
tural Engineering, for their critical comments and for permission to publish. 
V. A. McLees carried out the electron microscopy and A. W. Barker 
assisted greatly with preparation of the specimens. The following providedfree samples of material: Advanced Materials Engineering Ltd., AERE 
Harwell, Anderman and Ryder Ltd., British Nuclear Fuels Ltd., Edgar Allen 
Tools Ltd., Firth Brown Tools Ltd., Creenbank-Cast Basalt Engineering 
Company Ltd., Joseph Lucas Ltd., New Metals and Chemicals Ltd., Royal 
Worcester Industrial Ceramics Ltd., Smiths Industries Ltd. and UKAEA 
Sp~n~ields Laboratories. 
138 
Nomenclature 
i 
cr 
d 
E 
H 
kl, kz 
K, 
L 
; 
P 
Pcrit 
G”v 
w 
cl 
GY 
cp 
half-diagonal of a Vickers hardness impression 
cross-sectional area of a wear groove 
crack length from the corner of a hardness impression 
diameter of abrasive particle 
Young’s modulus 
hardness 
constants 
critical stress intensity factor, fracture toughness 
sliding distance 
power dependence of volume wear on applied load 
number of abrasive particles contacting a surface per unit area 
depth of indentation of indenter or abrasive particle 
critical indentation depth for fracture, C, = 0 
volume wear 
volume wear per abrasive particle contact 
mean normal load on an abrasive particle 
applied load per unit area 
yield stress 
H/ay , indentation constraint factor 
References 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
T. I. Barry, A summary appraisal of engineering ceramics, NPL Rep. Chem. 58, 
National Physical Laboratory, Teddington, Nov. 1976. 
P. Kennedy and J. V. Shennan, Engineering applications of Refel silicon carbide, 
Atom, 206 (Dec. 1973) 1 - 8. 
R. J. Lumby, B. North and A. J. Taylor, Properties of sintered sialons and some 
applications in metal handling and cutting. In J. J. Burke, E. N. Lenoe and R. N. Katz 
(eds.), Ceramics for High Performance Applications, Brookhill, Chestnut Hill, Mass., 
1978, pp. 893 - 906. 
R. W. Davidge, The mechanical properties and design data for engineering ceramics, 
Cemmurgia Znt., I (2) (1975) 75 - 80. 
D. M. Marsh, Plastic flow in glass, Proc. R. Sot. London, Ser. A, 279 (1378) (1964) 
420 - 435. 
B. J. Hockey, Plastic deformation of alumina by indentation and abrasion, J. Am. 
Ceram. Sot., 54 (5) (1971) 223 - 231. 
C. A. Brookes, Hardness of diamond and other crystals, Znd. Diamond Rev., 33 (394) 
(1973) 338 - 341. 
R. L. Aghan and R. McPherson, Mechanism of material removal during abrasion of 
rutile, J. Am. Ceram. Sot., 56 (1) (1973) 46 - 47. 
I. A. Cutter and R. McPherson, Plastic deformation of A1203 during abrasion, J. Am. 
Cemm. Sot., 56 (5) (1973) 266 - 269. 
M. V. Swain, Microscopic observation of abrasive wear of polycrystalline alumina, 
Wear, 35 (1975) 185 - 189. 
T. F. Page, G. R. Sawyer, 0.0. Adewoye and J. J. Wert, Hardness and wear behaviour 
of Sic and SiaN4 ceramics, Proc. Br. Ceram. Sot., 26 (1978) 193 - 208. 
B. Lawn and R. Wilshaw, Indentation fracture: principles and applications, J. Mater. 
Sci., 10 (1975) 1049 - 1081. 
C. J. Studman, M. A. Moore and S. E. Jones, On the correlation of indentation exper- 
iments, J. Phys. D, 10 (1977) 949 - 956. 
139 
14 M. A. Moore and R. M. Douthwaite, Plastic deformation below worn surfaces, Metall. 
Trans., 7A (1976) 1833 - 1839. 
15 T. R. Wilshaw and N. E. W. Hartley, Hertzian fracture and the abrasion of quartz, 
silica and soda-lime glass, Proc. 3rd European Symp. on Comminution, Verlag 
Chemie, 1972, pp. 33 - 50. 
16 B. R. Lawn, A model for the wear of brittle solids under fixed abrasive conditions, 
Wear, 33 (1975) 369 - 372. 
17 A. G. Evans and T. R. Wilshaw, Quasi-static particle damage in brittle solids - I. 
Observations, analysis and implications, Acta Metall., 24 (1976) 939 - 956. 
18 A. G. Evans and E. A. Charles, Fracture toughness determination by indentation, 
J. Am. Ceram. Sot., 59 (7 - 8) (1976) 371 - 372. 
19 R. C. D. Richardson, The wear of metals by relatively soft abrasives, Wear, 11 (1968) 
245 - 275. 
20 R. C. D. Richardson, The wear of metals by hard abrasives, Wear, 10 (1967) 291 - 
309. 
21 M. F. Stroud and H. Wilman, The proportion of groove volume removed as wear in 
abrasion of metals, Br. J. Appl. Phys., 13 (1962) 173 - 178. 
22 T. 0. Mulhearn and L. E. Samuels, The abrasion of metals: a model of the process, 
Wear, 5 (1962) 478 - 498. 
23 J. Larsen-Badse, Influence of grit size on groove formation during sliding abrasion, 
Wear, 11 (1968) 213 - 222. 
24 T. C. Buttery and J. F. Archard, Grinding and abrasive wear, Proc. Inst. Mech. Eng., 
London, 185 (1970 - 71) 537 - 551. 
25 M. Y. Friedman, S. M. Wu and P. T. Suratkar, Determination of geometric properties 
of coated abrasive cutting edges, J. Eng. Znd., 96 (1974) 1239 - 1244. 
26 B. R. Lawn, T. Jensen and A. Arora, Brittleness as an indentation size effect, J. Mater. 
Sci., II (1976) 573 - 575. 
27 B. Bethune, The surface cracking of glassy polymers under a sliding spherical 
indenter, J. Mater. Sci., 11 (1976) 199 - 205. 
28 R. C. D. Richardson, The maximum hardness of strained surfaces and the abrasive 
wear of metals and alloys, Wear, 10 (1967) 353 - 382. 
Appendix A 
Simple models of material removal 
Material removal by plastic deformation 
We assume that a contacting abrasive particle forms a groove by plastic 
deformation and that a proportion of this groove volume is removed from 
the surface. Published data [21, 241 for metallic materials suggest that a 
mean value for this proportion is about 60%. Thus the volume worn away is 
6 v = 0.6AL (Al) 
where A is the cross-sectional area of the groove and L is the sliding distance. 
We make the following further assumptions. 
(a) The abrasive particles approximate to 120” right cones [ 251 so the 
cross-sectional area of the groove is 
A = d3p2 (A2) 
where p is the depth of indentation of the abrasive particle. 
(b) The abrasive particle acts like a scratch indenter with the normal 
load W being carried on the leading half-cone surface. Then the hardness of 
the surface [Al] is 
H = WJd3np2 (A3) 
140 
(c) The number of particles that contact the surface per unit area is 
N = k,d+ (A41 
where k, is a constant and d is the mean particle diameter. 
(d) Only a proportion of the abrasive particles that contact the surface 
result in material removal. Published data [ 231 for metallic materials suggest 
that this proportion is about 60%. 
From eqn. (A4) the mean normal load per particle that contacts the 
surface is 
W = ad2/k2 (A51 
where u is the applied load per unit area, and from eqns. (AZ), (A3) and 
(A5) the cross-sectional area of the groove is 
A = v/3ad2/d3nk2H (A61 
Thus the sum of AV for N contacts per unit area, i.e. the volume wear per 
unit area, is from eqns. (Al), (A4) and (A6) 
V = OSLO/H (A71 
where V is in units of mm3 mm-‘, u is in units of MN rnv2 and H is in units 
of GN rn-‘, 
Mate~l removal by ~~de~tatio~ fracture 
Lawn [ 161 and Evans and Wilshaw (171 proposed models of abrasive 
wear of brittle materials in which material is removed by indentation frac- 
ture when lateral cracks intersect each other or propagate to the surface. 
Evans and Wilshaw [ 171 predict that there is an upper limit for volume 
wear per unit area per unit sliding distance: 
V C NW 5/4/~ 
0 
3/4~1/2 
WV 
On substituting for N from eqn. (A4) and for W from eqn. (A5) this becomes 
Published data 122,231 for metallic materials suggest that the value of k, 
may be approximately 0.1 mm-‘, and thus eqn. (A8) becomes 
where V is in units of mm3 per unit area’(mm2) and unit sliding distance 
(m), u is in units of MN rnA2, d is in units of mm, K, is in units of MN rnw3j2 
and H is in units of GN rnF2. 
Reference to appendix 
Al C. A. Brookes, P. Green, P. H. Harrison and B. Hoxiey, Some observations cm scratch 
and indentation hardness rne~~rernen~, J. Phys. I), 5 (1972) 1284 - 1293