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Novel boundary crack front elements with Williams' eigenexpansion properties for 3D crack analysis

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Abstract

The new crack front elements with Williams' eigenexpansion properties for 3D crack problems are proposed in this paper. In the presented method, the dual boundary integral equations are collocated on the uncracked boundary and one of the crack surfaces. The unknowns of the integral equations may be displacements, tractions and crack open displacements on the crack faces. To characterize the Williams' eigenexpansion properties of displacements around the crack front, the crack front elements with Williams' eigenexpansion properties are developed. The construction method of these elements is based on the first order of the Williams' series eigenexpansion, and the two-point formula is used to construct the elements by using the crack surface opening displacement and the relationship between crack opening displacement and stress intensity factor. Several numerical examples are given to validate our method. The numerical results of the proposed method agree very well with those of other methods and exact solutions.

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Acknowledgements

Thanks to all authors for their help in writing and revising the paper. In addition, this work was partly supported by the National Natural Science Foundation of China (11602229 and 52075500), partly supported by key scientific and technological project of Henan Province (222102240077), and partly supported by the Natural Science Foundation of Henan Province (202300410505).

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  1. Henan Provincial Key Laboratory of Intelligent Manufacturing of Mechanical Equipment, Mechanical and Electrical Engineering Institute, Zhengzhou University of Light Industry, Zhengzhou, 450002, Henan, China

    Yudong Zhong, Guizhong Xie, Liangwen Wang, Xinsheng Wang & Wenbin He

  2. Hangzhou Vocational and Technical College, Hangzhou, 310023, Zhejiang, China

    Ke Li

  3. Henan Huanghe Whirlwind Co., Ltd, Changge, 461500, Henan, China

    Shuguang Wang

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  1. Yudong Zhong
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Zhong, Y., Xie, G., Wang, L. et al. Novel boundary crack front elements with Williams' eigenexpansion properties for 3D crack analysis. Arch Appl Mech 93, 745–760 (2023). https://doi.org/10.1007/s00419-022-02296-x

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