Cohesive zone models in history dependent materials

Abstract

Cohesive zone model is a well known concept in nonlinear fracture mechanics of elasto-plastic materials. In contrast to that, we discuss a development of the cohesive zone model to linear, but time and history dependent, materials. The stress distribution over the cohesive zone satisfies a history dependent rupture criterion for the normalised equivalent stress, represented by a nonlinear Abel-type integral operator. The cohesive zone length at each time step is determined from the condition of zero stress intensity factor at the cohesive zone tip. It appeared that the crack starts propagating after some delay time elapses since a constant load is applied to the body. This happens when the crack tip opening displacement reaches a prescribed critical value. A numerical algorithm to compute the cohesive zone and crack length with respect to time is discussed and graphs showing the results are given