Fractal analysis of erosion surfaces
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Recent studies have shown that erodent properties affect the solid-particle erosion response of ceramics and other brittle materials.1"4 In particular, the erosion rates can increase significantly when the erodent particle-to-target hardness ratio Hp/H, increases above Hp/H, = I.1"3 Later results suggested that toughness properties as well as hardness may play a role in these effects.4 Decreasing the ratio Hp/H, for a given target can lead to a reduction in erosion rates, extended transients prior to steady state, and a change in the morphology of single impact events. In particular, using SiC(Hp/Ht > 1) and A12O3(HP/Ht < 1) erodents [SiC (Crystolon 37) and A12O3 (E17) abrasives, Norton Co., Worcester, MA] on selected commercial aluminas and sapphire, the erosion rates could be reduced by almost an order of magnitude.3'4 The size and shape characteristics of these erodents are virtually identical.4 Scanning electron microscopy showed that classical lateral cracking patterns occurred for the SiC erodents, but that plastic punching without lateral cracks occurred for E17 erodents. Most surprisingly, the steady-state erosion surfaces appeared very similar, both showing evidence of lateral-crack controlled fracture processes. Based on such visual inspection of the steady-state surfaces, their similarity suggested that a damage accumulation mechanism is operative such that for less efficient erodents, multiple impacts are needed to produce lateral crack events. The purpose of the present study is to classify quantitatively the nature of steady-state erosion surfaces produced under conditions similar to those used in the earlier work. In particular, SiC and E17 A12O3 erodents will be used to produce steady-state erosion response on sapphire. Measurements of surface texture can be made from scanning electron micrographs of the steady-state surfaces using image analysis techniques.5 This provides a quantitative measure of the surface topography, which is related to the fractal dimension of 2616
http://journals.cambridge.org
J. Mater. Res., Vol. 5, No. 11, Nov 1990
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the surface and hence to fracture characteristics.6 It can be assumed here that the texture value is proportional to the fractal dimension; however, the proportionality constant is not determined. Sapphire was chosen as the target material because it is free of any inherent microstructural size scale. Furthermore, sapphire does not undergo crack-growth resistance effects which might introduce an additional scaling parameter.7 Steady-state erosion surfaces were generated on single crystal sapphire with surface parallel to the A plane (1010) (Saphikon, Inc., Milford, NH). The dose of erodent was 20 and 200 gms, respectively, for SiC and E17 alumina. The mean size of the powder particles was 63 /im and the impact velocity used for the test was 90 m/s at normal incidence conditions. The erosion setup was an air blast type rig which is described in Ref. 4. From Ref. 4, it is clear that these doses will lead to steady-state conditions. Micro
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