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Influence of density variation on the arbitrarily propagating crack tip fields in functionally graded materials

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Abstract

The stress and displacement fields for an arbitrarily propagating crack tip in functionally graded materials (FGMs) with exponential variation of density and shear modulus are obtained. Nonhomogeneous parameters of density and shear modulus are different from each other. The solutions for higher order terms in the dynamic equilibriums are obtained by transforming the general differential equations to the scaled Laplace’s equations. Using the stress fields, the effects of the nonhomogeneous density on stress components is investigated. In addition, the contours of the constant maximum shear stress at a propagating crack tip are generated and the effects of the nonhomogeneous density on the isochromatics are discussed.

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Authors and Affiliations

  1. Department of Automotive Engineering, Kyungpook National University, Sangju City, Kyeongbuk, 742-711, Korea

    Kwang Ho Lee

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  1. Kwang Ho Lee
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Correspondence to Kwang Ho Lee.

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Recommended by Editor Jai Hak Park

Kwang-Ho Lee received a Ph.D. degree in Yeungnam University in 1993. Dr. Lee is currently a professor at the School of Mechanical and Automotive Engineering at Kyungpook National University in Korea. He also had worked in KOMSCO as an engineer and researcher (1982.3–1996.2). He is interested in the fields of fracture and stress analysis on the composite, interface, nano and functionally graded materials by theoretical and experimental mechanics. Specially, his major interest is analysis of dynamic crack tip fields.

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Lee, K.H. Influence of density variation on the arbitrarily propagating crack tip fields in functionally graded materials. J Mech Sci Technol 28, 2129–2140 (2014). https://doi.org/10.1007/s12206-014-0502-y

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  • DOI: https://doi.org/10.1007/s12206-014-0502-y

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