Engineering Fracture Mechanics, Vol. 73, No. 5, pp. 593-615, 2006
D.J. Shim, G.H. Paulino and R.H. Dodds Jr.
Department of Civil & Environmental Engineering, University of Illinois at Urbana-Champaign,
Newmark Laboratory, 205 North Mathews Avenue, Urbana, IL 61801, U.S.A.
Abstract
This paper describes the development and application of a novel modified boundary layer (MBL) model for graded nonhomogeneousmaterials, 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 the lateral edges of themodel. Finite element analyses are performed using WARP3D, a fracturemechanics 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 forhomogeneous 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.
KEY WORDS: functionally graded material (FGM); modified boundary layer model; K-T dominance; 3-D finite element analysis; graded element.