Contact behaviors of multilayered structures with interfacial cracks

Abstract

In this study, a numerical model is developed to address the interactions among multilayered materials with interfacial cracks at line-contact loading. The layers are assumed as inclusions of finite size and the governing equations in the specific zones are formulated with unknown eigenstrains based on Eshelby's equivalent inclusion method. The cracks of mixed modes I/II are approximated as climb and glide dislocations with unknown dislocation densities according to the discrete dislocation technique, and an interfacial one between the neighboring layers is assumed located in the bottom elements of the upper layer or the top elements of the lower layer. The unknowns are iteratively determined based on the stress analysis, and the surface deflection caused by the eigenstrains and edge dislocations are introduced to form a closed-loop algorithm involving the pressure and surface gap. A modified fast Fourier transform algorithm is employed to approach the plane-strain conditions while improving computational efficiency. The calculation is performed until the convergence of the surface displacements, and the effects of the layer moduli as well as the crack length and depth on the pressure distribution and stress fields are revealed. Surface roughness can also be involved in the consideration and should always be taken into account to accurately predict the crack propagation and layer delamination. The solutions may provide insightful views to evaluate the fracture behaviors of multilayered materials and enhance the surface delamination resistance.