The prediction of dynamic fracture evolution in PMMA using a cohesive zone model

Abstract

A cohesive zone model was used in conjunction with the finite volume method to model the dynamic fracture of single edge notched tensile specimens of PMMA under essentially static loading conditions. In this study, the influence of the shape of the cohesive law was investigated, whilst keeping the cohesive strength and separation energy constant. Cohesive cells were adaptively inserted between adjacent continuum cells when the normal traction across that face exceeded the cohesive strength of the material. The cohesive constitutive law was therefore initially rigid, and the effective elasticity of the material was unaltered prior to insertion of the cohesive cells. Notch depths ranging from 2.0 to 0.1 mm were considered. The numerical predictions were compared with experimental observations for each notch depth and excellent qualitative and quantitative agreement was achieved in most cases. Following an initial period of rapid crack tip acceleration up to terminal velocities well below the Rayleigh wave speed, subsequent propagation took place at a constant rate under conditions of increasing energy flux to an expanding process region. In addition, attempted and successful branching was predicted for the shorter notches. It was found that the shape of the cohesive law had a significant influence on the dynamic fracture behaviour. In particular, the value of the initial slope of the softening function was found to be an important parameter. As the slope became steeper, the predicted terminal crack speed increased and the extent of the damage decreased.