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Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique

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Abstract

The weight function method provides a powerful approach for calculating the stress intensity factors for a homogeneous cracked body subjected to mechanical loadings. In this paper, the basic equations of weight function method for mode I and mixed mode crack problems in a two-dimensional functionally graded crack system are derived based on the Betti’s reciprocal theorem. The weight functions derived by the virtual crack extension technique are further used to calculate the stress intensity factors of functionally graded materials (FGMs). The practicability and accuracy of this proposed method has been confirmed by the comparison with theoretical or numerical solutions available in the literatures. On account that the repeated extractions of the distributions of normal stress and shear stress in the uncracked component along the prospective crack line under different loadings can be avoided using the method presented in this paper, this method can be potentially used for optimal design for FGMs under multiple-load cases.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11372280, 51275471 and 11002126 and by Zhejiang Provincial Natural Science Foundation of China under Grant Nos. Y6100425 and Y1100108.

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Authors and Affiliations

  1. Key Laboratory of E&M (Zhejiang University of Technology), Ministry of Education & Zhejiang Province, 8, Chaowang Road, Hangzhou, 310014, China

    Huaping Wu, Long Li & Guozhong Chai

  2. College of Education and Technology, Zhejiang University of Technology, 8, Chaowang Road, Hangzhou, 310014, China

    Man Shi

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  1. Man Shi
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Correspondence to Huaping Wu.

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Shi, M., Wu, H., Li, L. et al. Calculation of stress intensity factors for functionally graded materials by using the weight functions derived by the virtual crack extension technique. Int J Mech Mater Des 10, 65–77 (2014). https://doi.org/10.1007/s10999-013-9231-0

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