Stable path of interacting crack systems and micromechanics of damage

Abstract

Micromechanics of damage in brittle heterogeneous materials and composites requires analysis of a system of interacting cracks. The response path of a crack system typically exhibits bifurcations such that the states on each post-bifurcation branch can be stable yet only one branch can be reached in a stable manner. Recent results on thermodynamic criteria for stable states and stable response paths of inelastic structures are reviewed and formulated in terms of the incremental internal entropy of the system. The incremental entropy, which can be expressed in terms of second order work, is then calculated for various points on the response paths of some typical symmetric crack systems. It is shown that while the symmetric states may be stable, the path which leads to them is unstable and cannot occur in reality. Generally, nonsymmetry develops at the beginning of softening. The results show that it is insufficient to model distributed cracking only by means of crack systems and linear elastic fracture mechanics. Further aspects, such as material heterogeneity, residual stresses, and cohesive fracture zones for the microcracks, might have to be taken into account.