Crack-tip stress fields in functionally graded materials with linearly varying properties N. Jain, C.E. Rousseau, A. Shukla * Department of Mechanical Engineering and Applied Mechanics, University of Rhode Island, Kingston, RI 02881, USA Abstract Crack-tip stress fields for a stationary crack along or inclined to the direction of property gradation in functionally graded materials (FGMs) are obtained through an asymptotic analysis coupled with WestergaardÕs stress function approach. The elastic modulus of the FGM is assumed to vary linearly along the gradation direction. The first six terms for a crack along the direction of property variation and first four terms for a crack inclined to the direction of property variation in the expansion of the stress field are derived to explicitly bring out the influence of nonhomogeneity on the structure of the stress field. Using these stress fields, contours of constant maximum shear stress and constant out of plane displacement are generated and the effect of inclination of property gradation direction on these contours is dis- cussed. The strain energy density criterion is applied to obtain critical conditions for crack initiation and the effect of property gradation is discussed. It is shown that the materials with varying properties can offer more resistance to crack propagation and will suppress crack growth in some situations. Ó 2004 Elsevier Ltd. All rights reserved. 1. Introduction In todayÕs highly demanding technological environment, one of the main challenges in new material de- sign appears to be combining irreconcilable thermo-mechanical and strength properties in the same com- ponent. A functionally graded material (FGM) is a composite consisting of two or more phases, which is fabricated such that its composition varies in some spatial direction. The design is intended to take advantage of certain desirable features of each of the constituent phases. 0167-8442/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2004.08.005 * Corresponding author. Tel.: +1 401 874 2283; fax: +1 401 874 2355. E-mail address: shuklaa@egr.uri.edu (A. Shukla). Theoretical and Applied Fracture Mechanics 42 (2004) 155–170 www.elsevier.com/locate/tafmec