Rate-dependent traction-separation relations for a silicon/epoxy interface informed by experiments and bond rupture kinetics

Abstract

In this work, double cantilever beam specimens were used to investigate the rate-dependent fracture of a silicon/epoxy interface. Fracture experiments were conducted at 5 different separation rates, ranging from 0.042 to 8.5 mm/s. For each separation rate, the interfacial properties were extracted by a beam on elastic foundation model and an iterative method, assuming a bilinear traction-separation relation. Rate dependence is observed for the silicon/epoxy interface as both the interfacial toughness and strength increased with the separation rates, which is opposite to the rate dependent fracture behavior of the bulk epoxy in its glassy state. Motivated by this observation, a rate-dependent cohesive zone model is proposed based on a thermally activated bond rupture mechanism. This model relates the interfacial fracture to the breakage of molecular bonds at the interface, and the rate effect develops naturally from the kinetics of damage evolution via the statistical concept of bond survival probability. The double cantilever beam problem with the interfacial bond rupture kinetics was then solved numerically, and the model parameters were extracted by fitting the numerical results to the experimental data. Ideally, this model should be able to explain and predict the rate-dependent fracture of a specific interface (e.g., silicon/epoxy interface) with four parameters, including the bond energy, the critical stress, the initial stiffness and a time scale. However, in order to fit the experimental data, the critical stress had to be adjusted in the present study. Nevertheless, this mechanism-based cohesive zone model offers a promising approach for modeling the rate-dependent fracture, which may also incorporate other mechanisms in future studies.