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Analytical Solution of the Stress Intensity Factors of Multiple Closed Collinear Cracks

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Abstract

Purpose

According to the interaction between multiple cracks, a method for calculating the stress intensity factors of multiple closed collinear cracks in an infinite plate is proposed. In addition, the effects of the crack angle, crack length, crack spacing, lateral pressure coefficient and crack surface friction coefficient on the stress intensity factors are analyzed.

Method

The integral equation of the stress intensity factors is derived by the superposition principle, and the approximate solution of the integral equation is derived by the Chebyshev polynomial. The results obtained are compared with the finite element solutions of the same problem and the solutions of other scholars to verify the correctness of the equation.

Results

The results show that the intensity factor solution obtained by the proposed method is in good agreement with the finite element solution and other scholars’ solutions. A larger crack length, smaller crack spacing, smaller friction coefficient and smaller lateral pressure coefficient can produce larger stress intensity factors, and the stress intensity factors are maximized when the crack angle is 45°.

Conclusions

It is proved that the method based on the initial solution and superposition principle can be effectively applied to the calculation of the stress intensity factors of multiple collinear cracks.

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Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

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Funding

This work was financially supported by the Project of National Natural Science Foundation of China (NO. 51904012), the Key Projects of Natural Science Research in Colleges and Universities in Anhui Province (KJ2019A0099), and the scientific research activities of postdoctoral researchers in Anhui Province (2018B268).

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan, 232001, China

    Shaochi Peng, Laiwang **g, Shuwen Li, Di Wu & Wei **g

Authors
  1. Shaochi Peng
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  2. Laiwang **g
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  3. Shuwen Li
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  4. Di Wu
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  5. Wei **g
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Correspondence to Shaochi Peng.

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Peng, S., **g, L., Li, S. et al. Analytical Solution of the Stress Intensity Factors of Multiple Closed Collinear Cracks. J. Vib. Eng. Technol. 11, 3737–3745 (2023). https://doi.org/10.1007/s42417-022-00779-3

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  • DOI: https://doi.org/10.1007/s42417-022-00779-3

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