Methods and models for fracture mode partitioning: A review

Abstract

In the problem of a crack lying in the interface between two dissimilar materials, the mathematical expressions for the stress and displacement fields, derived from linear elastic fracture mechanics, feature oscillatory singularities near the crack tip. This makes it impossible to define the mode mixity mathematically. To overcome this issue, several alternative methods for mode partitioning and analytical, semi-analytical, empirical, or combined models performing mode partitioning in linear elastic, mixed-mode fracture problems have been proposed over the last 35 years. This paper attempts the first review of the topic. It begins by recalling the fundamental scientific problem through reference on the fracture mechanics of bimaterial interfaces. Next, it collects over 36 models performing mode partitioning, proposes classifying them into five broad categories (models based on the global method, models based on the local method, models employing crack-tip force measures, models employing a cohesive interface, and special models), and describes and critically reviews them. A comprehensive discussion is then provided, and the paper closes with justification of concluding remarks and prospective directions for future research.