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Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions

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Abstract

This paper presents an exact solution of the crack tip field in functionally gradient material with exponential variation of elastic constants. The dimensionless Poisson's ratios ν 0 of the engineering materials (iron, glass . . .) are far less than one; therefore, neglecting them, one can simplify the basic equation and the exact solution is easy to obtain. Although the exact solution for the case ν 0≠0 is also obtained, it is very complicated and the main result is the same with the case ν 0=0 (it will be dealt with in Appendix VII). It has been found that the exponential term exp (ax+by) in the constitutive equations becomes exp (ax/2+by/2−kr/2) in the exact solution.

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  1. College of Science, Donghua University, P.O. Box 220, Shanghai, 200051, China

    Tianhu Hao

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  1. Tianhu Hao
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Correspondence to Tianhu Hao.

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The English text was polished by Keren Wang.

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Hao, T. Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions. ACTA MECH SINICA 21, 601–607 (2005). https://doi.org/10.1007/s10409-005-0077-z

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  • DOI: https://doi.org/10.1007/s10409-005-0077-z

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