An elastic foundation modeling approach to bi-material interface crack problems of finite bond length

There have been some significant advances in direct joining of dissimilar materials over recent years for enabling multi-material lightweight structures. As such, both dissimilar material joint design and structural integrity evaluation call for engineering fracture mechanics solutions to bi-material interface crack problems involving finite bond line length. This paper presents a novel elastic foundation modeling approach to address a set of two-dimensional bi-material interface crack problems. The analytical formulation presented enables the extraction of important length-scale parameters for supporting quantitative joint sizing and interrelating the mixed-mode energy release rates to the classical mode-mixity defined by bi-material crack tip singularity fields. The modeling results can be directly used for analyzing some common test configurations, e.g., “lap-shear” (LS) and “coach-peel” (CP) widely used by industry for ensuring optimal bond line sizing for both satisfactory mechanical performance and easy dis-assembly. To demonstrate the practical implications of this research, a group of bi-material (aluminum to steel) lap-shear fracture tests are modeled through a linear superposition of the solutions of the elementary load cases.