Authors: Yao Dai, Xiu Fa Yan, Chang Qing Sun, Wei Tan

Abstract: Crack-tip higher order stress and displacement fields for a mode III crack along the
direction of property variation in a functionally gradient material (FGM), which has a power
variation of shear modulus along the gradient direction, are obtained through the asymptotic
analysis. The asymptotic expansions of crack tip stress fields are derived to explicitly bring out the
influence of non-homogeneity on the structure of the stress field. The analysis reveals that only the
higher order terms in the expansion are influenced by the material non-homogeneity. Moreover, it
can be seen from expressions of higher order stress fields that at least three terms must be
considered in the case of FGMs in order to explicitly and theoretically account for non-homogeneity
effects on crack tip stress fields.

713

Authors: Yao Dai, Peng Zhang, Zhao Quan Zheng, Wei Tan

Abstract: The exponential and power material functions are often applied to functionally gradient materials (FGM). Obviously, it is of fundamental significance to study FGM with arbitrary material function. Because an arbitrary function can be treated as finite linear segments approximately, it is essential to research FGM with a linear material function. Crack-tip higher order stress and displacement fields for an anti-plane crack perpendicular to the direction of property variation in a FGM with a linear shear modulus along the gradient direction are obtained through the asymptotic analysis. The asymptotic expansions of crack tip stress fields bring out explicitly the influence of non-homogeneity on the structure of the stress field. The analysis reveals that only the higher order terms in the expansion are influenced by the material non-homogeneity. Moreover, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGM in order to explicitly and theoretically account for non-homogeneity effects on crack tip stress fields.

1782

Authors: Yao Dai, Shi Min Li, Peng Zhang, Xiao Chong

Abstract: An arbitrarily oriented anti-plane crack with its tip at the physical weak-discontinuous line of the structure which is made up of homogeneous material and functionally graded materials (FGMs) is studied. The analytic solution of the higher order crack tip fields (similar to the Williams’ solution of homogenous material) is obtained by applying the asymptotic series expansion. When non-homogeneous material parameters are degenerated, the solutions become the same as the asymptotic crack tip fields of the homogeneous material. Therefore, the solutions are the basic results of non-homogeneous fracture mechanics, and provide a theoretical basis for solving the fracture problems of one common structure with physical weak-discontinuity.

1309

Authors: Yao Dai, Jun Feng Liu, Lei Zhang, Xiao Chong

Abstract: The Reissner’s plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials(FGMs) plates for a crack parallel to material gradient. By means of the asymptotic expansion method, the crack-tip higher order asymptotic fields which are similar to the famous Williams’ solutions to homogeneous materials are obtained.

1421

Authors: Yao Dai, Lei Zhang, Jun Feng Liu, Xiao Chong, Hong Qian Chen

Abstract: The eigen-problem of a crack in functionally graded Reissner’s spherical shell is analyzed. By adopting the asymptotic expansion method, the higher order crack tip asymptotic fields which are similar to the Williams’ solutions of plane crack problems in homogenous materials are obtained. The grade direction is assumed to be parallel to the crack. The results can be widely adopted in numerical analysis, experimental investigation and the engineering application of FGM shell structure.

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