Comparison between cohesive zone models

Cohesive zone models (CZMs) are widely used for numerical simulation of the fracture process. Cohesive zones are surfaces of discontinuities where displacements jump. A specific constitutive law relating the displacement jumps and proper tractions defines the cohesive zone model. Within the cohesive zone approach crack nucleation, propagation, and arrest are a natural outcome of the theory. The latter is in contrast to the traditional approach of fracture mechanics where stress analysis is separated from a description of the actual process of material failure. The common wisdom says that only cohesive strength - the maximum stress on the traction-separation curve - and dthe separation work - the area under the traction-separation curve - are important in setting a CZM while the shape of the traction-separation curve is subsidiary. It is shown in our note that this rule may not be correct and a specific shape of the cohesive zone model can significantly affect results of the fracture analysis. For this purpose four different cohesive zone models - bilinear, parabolic, sinusoidal, and exponential - are compared by using a block-peel test, which allows for simple analytical solutions. Numerical performance of the cohesive zone models is considered. It appears that the convergence properties of nonlinear finite element analyses are similar for all four CZMs in the case of the block-peel test.