A simple cohesive zone model that generates a mode-mixity dependent toughness

A simple, mode-mixity dependent toughness cohesive zone model (MDGc CZM) is described. This phenomenological cohesive zone model has two elements. Mode I energy dissipation is defined by a traction-separation relationship that depends only on normal separation. Mode II (III) dissipation is generated by shear yielding and slip in the cohesive surface elements that lie in front of the region where mode I separation (softening) occurs. The nature of predictions made by analyses that use the MDGc CZM is illustrated by considering the classic problem of an elastic layer loaded by rigid grips. This geometry, which models a thin adhesive bond with a long interfacial edge crack, is similar to that which has been used to measure the dependence of interfacial toughness on crack-tip mode-mixity. The calculated effective toughness vs. applied mode-mixity relationships all display a strong dependence on applied mode-mixity with the effective toughness increasing rapidly with the magnitude of the mode-mixity. The calculated relationships also show a pronounced asymmetry with respect to the applied mode-mixity. This dependence is similar to that observed experimentally, and calculated results for a glass/epoxy interface are in good agreement with published data that was generated using a test specimen of the same type as analyzed here.