On the ability of coupled mixed mode cohesive laws to conform to LEFM for cracks in homogeneous orthotropic solids

The ability of coupled cohesive laws to conform to the predictions of linear elastic fracture mechanics (LEFM) in the case of small-scale-yielding (SSY) is explored. The study is concerned with cracks in homogeneous orthotropic solids and the results apply also for the case of isotropy. Both potential based and non-potential based cohesive laws are considered. It is shown that the initial stiffnesses of the cohesive law must be matched to the elastic moduli of the orthotropic solid in order to achieve a constant ratio of the cohesive stress components ahead of the crack tip. A simple condition for this is provided. For non-potential based laws an additional apparently sufficient condition on the non-linear part of the cohesive law is identified: The traction vector must not change direction if the direction of the separation vector is constant. Fulfillment of this condition provides a uniform local mode mix in the cohesive zone with a value equal to the global mode mix. It is demonstrated that potential based cohesive laws display a varying local mode mix at the crack tip for cases with a mode dependent work of separation. This is identified as a complicating feature in terms of calibrating the parameters of a cohesive law to experimental data.