On interacting bridged-crack systems

The analysis of a material containing multiple interacting bridged cracks is the principal objective of this paper. The traction-consistency equations in terms of bridging tractions and pseudotractions are developed to enable the decomposition of a problem involving multiple bridged cracks into a number of sub-problems, each involving only a single crack. Bridging law equations are formulated so that the bridging tractions and pseudo-tractions appear as primary unknowns. The current approach is capable of handling multiple interacting crack systems with a general form of bridging laws, linear or nonlinear, isotropic or anisotropic. Both isotropic and anisotropic bridging laws are investigated. It has been observed that the bridging law for a crack can significantly modify the tip behavior of the crack itself, while its influence on neighboring cracks is relatively weak. The influence of bridging anisotropy on crack-tip stress fields is found to be significantly modulated by the loading condition. Bridging effects and interaction effects on stress amplification and retardation are also examined. For nonlinear bridging, a case of fiber pull-out in metal/ceramic laminates is studied to establish the critical ratio of fiber-to-matrix thickness that would avoid single-crack extensions and transfer the deformation, instead, to multiple cracking. For multiple cracking situations, the crack nucleation sites are also predicted.