A multiscale cohesive zone model for rate-dependent fracture of interfaces

Abstract

Rate-dependent fracture has been observed for a silicon/epoxy interface as well as other polymer interfaces, where both the interfacial strength and toughness increase with the separation rate. Motivated by this observation, we propose a multiscale approach to modeling a polymer interface, from atomic bonds to the macroscopic specimen, considering the energetics of bond stretching, the entropic effect of long molecular chains, the kinetics of thermally activated chain scission, and statistical distributions of the chain lengths. These multiscale features are seamlessly assembled to formulate a rate-dependent cohesive zone model, which is then implemented within a standard finite element package for numerical simulations. This model relates the macroscopically measurable interfacial properties (toughness, strength, and traction-separation relations) to molecular structures of the interface, and the rate dependence results naturally from the kinetics of damage evolution as a thermally activated process. The finite element simulations with the cohesive zone model are directly compared to double cantilever beam experiments for the rate-dependent fracture of a silicon/epoxy interface, yielding reasonable agreement with just a few parameters for the molecular structures of the interface. Such a multiscale, mechanism-based cohesive zone model offers a promising approach for modeling and understanding the rate-dependent fracture of polymer interfaces.