Steady-state mode I crack propagation in a brittle solid

Abstract

A steady-state, finite element analysis of brittle, dynamic crack propagation in PMMA is presented. The steady-state assumption means that all time derivatives are translated into a spatial derivative instead. The bulk PMMA is modelled as a linear elastic, isotropic material. The crack is modelled by use of a non-standard cohesive zone model that ensures that material stability is maintained. The cohesive zone contains two lengths, which allows for a regularisation of the crack problem. The boundary conditions were adjusted so that the results could be compared to experimental studies. The stress and strain fields at the crack tip resulting from the numerical analysis were shown, and the possible implications for damage evolution and crack branching were discussed. The study supports the idea that microcracks are initiated at some distance from the crack plane and then grow and join the main crack. The study suggests that the propagating crack goes from a ’simple crack’ to an unstable crack when the peak in the maximum principal strain – which appears at some distance from the crack plane – exceeds the dynamic fracture strain of the material.