The dynamics of a single crack moving through a heterogeneous medium is studied in the quasistatic approximation, which may be directly applicable to cracks grown under fatigue. In a model scalar system and for mode III (tearing) loading, the crack surface is found to be self-affine with a roughness exponent of ζ0ex0ex=0ex0ex1/2. Mode I (tensile) loading, however, leads to a crack surface that is only logarithmically rough, quite unlike those seen in most experiments. Residual stresses are found, potentially, to lead to increased crack surface roughness. But elastic wave propagation effects may be needed to explain the very rough crack surfaces observed experimentally.
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Ramanathan et al. (1997) studied this question.
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