Application of fractal geometry measurements to the evaluation of fracture toughness of brittle intermetallics
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Determination of the boundary fractal dimension of planar sections through particles produced by fracturing a series of brittle intermetallic V3AU materials with increasing oxygen content provides a single parameter that describes the surface roughness. This is observed to correlate with the measured fracture toughness, Kic, as determined with an indentation cracking test. The correlation agrees quantitatively with results obtained on several brittle ceramics by other workers.
I. BACKGROUND V3Au is a high temperature intermetallic material that is brittle, with very low toughness. The V 3 Au lattice has the A15 structure. It has been reported by von Philipsborn and Laves 1 that within the relatively complex A15 structure of V3Au, the much simpler ordered structure, L'l 2 , can be produced and stabilized by the interstitial addition of oxygen. Inspection of the x-ray powder patterns made for our alloys described below confirmed that at 0% oxygen the structure was entirely A15, and upon reaching 17.5% oxygen addition, the structure had transformed entirely to L'l 2 . Analysis of relative x-ray line intensities showed that this structure was the L'l 2 metal perovskite structure and not Ll 2 , the Q^Au-type structure. A quantitative measure of volume fraction of L'l 2 was obtained using the point count method on micrographs of polished samples of a different set of similar alloys. Because the L'l 2 structure is significantly less complex than the A15 structure, the transformation from A15 to L'l 2 has been shown to be accompanied by an increasing fracture toughness.2 We therefore investigated the toughness of samples as a function of oxygen content and volume fraction L'l 2 . Since our alloys consisted of small ( 1 - 2 g) arc melted buttons, fracture toughness determination has been conducted by other than standard procedures— namely via the Vickers microhardness indentation technique. We also observed the variation in surface roughness of the fracture surfaces of the series of samples of V 3 Au of different microstructures, i.e., different proportions of the L'l 2 to A15 phases. This was done by delivering a light blow to each specimen with a ball peen hammer in order to split the "button" into two or three pieces, thus creating some relatively large fracture surfaces. These surfaces were then examined with a scanning electron microscope. We observed a qualitative corre1856
J. Mater. Res., Vol. 6, No. 9, Sep 1991
lation between the visual roughness and the results of the indentation toughness tests.
Fractal dimensions For complex surfaces such as these fracture surfaces the amount of roughness and irregularity that we can see is limited by our image resolution. If we could increase the magnification, the amount of surface roughness we would see in the image would increase. The particular type of roughness that is of interest here has a form called self-similarity. This means that the perimeter or surface looks the same, in a statistical sense, under any magnification. Measurements made to describe the roughness an
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