A boundary layer framework considering material gradation effects

This paper describes the development and application of a novel modified boundary layer (MBL) model for graded nonhomogeneous materials, e.g. functionally graded materials (FGMs). The proposed model is based on a middle-crack tension, M(T), specimen with traction boundary conditions applied to the top and lateral edges of the model. Finite element analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates elements with graded elastic and plastic properties. Elastic crack-tip fields obtained from the proposed MBL model show excellent agreement with those obtained from full models of the cracked component for homogeneous and graded nonhomogeneous materials. The K-T dominance of FGMs is investigated by comparing the actual stress fields with the asymptotic stress fields (the Williams' solution). The examples investigated in the present study consider a crack parallel to the material gradient. Results of the present study provide insight into the K-T dominance of FGMs and also show the range of applicability of the proposed MBL model. The MBL model is applied to analyze the elastic-plastic crack-tip response of a Ti/TiB FGM SE(T) specimen. The numerical results demonstrate that the proposed MBL model captures the effect of T-stress on plastic zone size and shape, constraint effects, etc. for such configurations.