Cosserat Models Versus Crack Propagation

Abstract

In this paper, we analyze the consequences of Sih’s fracture criterion in a material which behaves according to the Cosserat-type model with free or constrained rotations. Both models are considered and for each of them the first and the second fracture mode is analyzed. To apply Sih’s criterion, the singular part of the stress field and of the couple stress field in the neighborhood of the crack tip are determined. The direction of the crack propagation predicted by the model with constrained rotations contradicts the experimental results for both modes of fracture. The qualitative predictions of the model allowing free rotations are in good agreement with experimental data only if the material constant newly introduced satisfies certain restrictions, which are more severe in the case of the second fracture mode. The conclusion is that the two Cosserat models do not improve significantly the predictions of the classical model of crack propagation in elastic solids.