An Analytical Approach to Modeling Thin, Pre-Cracked Specimens Using Traction-Separation

Abstract

Cohesive zone and eXtended Finite Element Modeling (xFEM) are promising methods for modeling the propagation of a crack using coarse meshes and hence saving considerable computational time. The Traction Separation Law (TSL) that is needed for such techniques is, however, mostly derived a posteriori using experiments. This prevents its widespread utilization in structures without high costs. For example, in the modeling of a compact tension test, the TSL is known to evolve as the crack grows. Qualitative physical explanations have been offered for this phenomenon. Necking ahead of the crack tip is thought to have a large effect on crack propagation, while the necking behavior in any given element is influenced by both the state of stress acting on it and the structural boundaries around it. However, a method to account for those explanations a priori in the TSL doesn’t exist. Here, TSLs are developed for the elements along the known crack path in a middle crack tension test and implemented as a damage model in Abaqus. They are derived solely from the material properties and the element dimensions, thus excluding the need for inverse engineering based on experiments. This paves the way for more general applications of traction separation laws within the maritime and offshore industry.