A rate dependent interface model for stick-slip fracture in adhesives and polymer glasses

Abstract

In stick-slip fracture, a crack stays still or only propagates a small amount until it reaches a critical energy release rate. Then, it suddenly grows rapidly, causing the energy release rate to drop and the crack to stop again. This behavior is common in many polymers, including glassy polymers and soft materials like adhesives. However, the theoretical understanding of this phenomenon is fragmented and incomplete. Here we propose a unified theory based on a rate-dependent cohesive model to explain these phenomena. Using this model, we demonstrate that an elastic backing layer in a zero-degree peel test can experience different types of stick-slip instability depending on the peeling rate. At slow peeling rates, the crack grows slowly until it reaches a maximum velocity, corresponding to a fixed maximum force, after which the growth becomes unstable. However, above a certain critical peeling rate, there is no slow crack growth: the crack enters the stick-slip regime once the critical energy release rate is reached for a reduced value of the applied force. Although our mathematical modeling is developed in a specific geometry that makes the computations easier, this behavior can be argued to be a more general feature of most materials and geometries presenting stick-slip fracture.