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Periodically spaced collinear cracks in a soft ferromagnetic material under a uniform magnetic field

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Abstract

This paper aims at a fundamental perspective of multiple cracks’ interaction on the fracture behavior of magnetoelastic materials. A theoretical study is performed on a soft ferromagnetic solid weakened by an array of periodic cracks under an in-plane magnetic loading. By using the conformal mapping technique and the analytic function boundary value theory, a rigorous analytical solution of the magnetic and stress fields is obtained, and the closed-form expressions for the field intensity factors are presented. Numerical examples of magnetically impermeable and permeable cracks are studied to reveal the relationship of the mode-I stress intensity factor with the period ratio of the cracks, the surrounding medium, and the applied magnetic loading. The analytical solution in this study can serve as a theoretical benchmark for the fracture problem of a magnetoelastic solid containing multiple defects.

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Acknowledgements

Yu appreciates the support of the China Scholarship Council. Yu, and Gao acknowledge the support from the National Natural Science Foundation of China (Grant Number 11872203) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). Chen thanks the Natural Sciences and Engineering Research Council of Canada (NSERC) for the financial support.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, Jiangsu, China

    Chuanbin Yu & Cun-Fa Gao

  2. Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Chuanbin Yu & Zengtao Chen

Authors
  1. Chuanbin Yu
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  2. Cun-Fa Gao
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  3. Zengtao Chen
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Correspondence to Zengtao Chen.

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Yu, C., Gao, CF. & Chen, Z. Periodically spaced collinear cracks in a soft ferromagnetic material under a uniform magnetic field. Acta Mech 231, 1919–1931 (2020). https://doi.org/10.1007/s00707-020-02629-3

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  • DOI: https://doi.org/10.1007/s00707-020-02629-3

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