Crack-tip stress fields in functionally graded materials with linearly varying properties

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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 Westergaard's 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 discussed. 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. © 2004 Elsevier Ltd. All rights reserved.

Publication Title

Theoretical and Applied Fracture Mechanics