Abstract
The paper examines the implications of material heterogeneity on the crack pattern formed during progressive failure of materials. The displacement gradients of the micro-medium are considered to be random stationary fields or fractal fields. Both formulations yield interesting and, surprisingly, analogous results. Two variables are found to affect the crack pattern that will form under loading. The first one is the fluctuations, i.e. coefficient of variation of the displacement gradient fields. The second one is correlations, i.e. correlation length of the random fields as compared to the size of the structure/specimen, or lower, upper cutoffs and fractal dimension of the fractal fields. The (macro) crack pattern that will develop is governed by the interplay of fluctuations and correlations, independent of the elastic constants (for deterministic local Poisson ratio) and fairly independent of the crack formation criterion. Universal constants are found for the coefficients of variation. For values above the universal ones the material will develop a highly irregular crack pattern with multiple crack intersections and/or self-intersecting cracks. This is typically observed in testing of high strength concretes, high strength rocks, metals of ultra high hardness and certain ceramics, composites. Under dynamic load and/or under load control the highly irregular crack pattern is accompanied by an “explosive” burst of chunks of material and high energy release. For values below the universal ones, a single crack (may be accompanied by branches) will develop. This is typical of low strength concretes, soft rocks, low hardness metals, certain ceramics, composites. Energy release is relatively low — characteristic of low strength materials.
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Frantziskonis, G. (1994). Crack Pattern Related Universal Constants. In: Breysse, D. (eds) Probabilities and Materials. NATO ASI Series, vol 269. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1142-3_31
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DOI: https://doi.org/10.1007/978-94-011-1142-3_31
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