Asymptotic stress fields for thermomechanically loaded cracks in FGMs

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The problem of a stationary crack in functionally graded materials (FGM), subjected to a combination of thermal and mechanical loading is considered. An asymptotic analysis coupled with Westergaard's stress function approach is used to characterize the stress field around the crack tip. Thermal and mechanical properties (e.g., elastic modulus, coefficient of thermal expansion, and thermal conductivity) are assumed to vary exponentially. The crack is assumed to be inclined to the direction of the property gradation. The thermal loading is taken to be a uniform heat flow in a direction inclined to the crack. The principal of superposition from linear elasticity is used to solve the problem, whereby the problem is divided into a number of subproblems. The first four terms in the expansion of the stress field are derived to explicitly bring out the influence of nonhomogeneity on the structure of the stress field. It is observed that the presence of heat flow produced no additional singularity and hence the classical inverse square root singularity still prevails around the crack tip. Using these stress field contours of constant maximum shear stress are generated and the effect of thermal loading on the crack-tip stress field is discussed. Copyright © 2006 by ASTM International.

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Journal of ASTM International