A Semi-Analytical Study of the Interaction Between Surface Cracks and Arbitrary Inhomogeneities: Systematic Analysis of Crack Angles, Material Contrasts, and Positional Effects

Yang Bozheng; Song Hengxu; Li Pu; Jin Xiaoqing

doi:10.21656/1000-0887.460204

Volume 47 Issue 8

Aug. 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(8): 978-989

Yang Bozheng, Song Hengxu, Li Pu, Jin Xiaoqing. A Semi-Analytical Study of the Interaction Between Surface Cracks and Arbitrary Inhomogeneities: Systematic Analysis of Crack Angles, Material Contrasts, and Positional Effects[J]. Applied Mathematics and Mechanics, 2026, 47(8): 978-989. doi: 10.21656/1000-0887.460204

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A Semi-Analytical Study of the Interaction Between Surface Cracks and Arbitrary Inhomogeneities: Systematic Analysis of Crack Angles, Material Contrasts, and Positional Effects

doi: 10.21656/1000-0887.460204

Yang Bozheng^1,2,
Song Hengxu^{1,3
,
,},
Li Pu⁴,
Jin Xiaoqing²

1. State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Science, Beijing 100190, P.R. China;
2. College of Aerospace Engineering, Chongqing University, Chongqing 400030, P.R. China;
3. School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, P.R. China;
4. Key Laboratory of Advanced Spatial Mechanism and Intelligent Spacecraft (Ministry of Education), Robotic Satellite Key Laboratory of Sichuan Province, School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, P.R. China

Funds:

52575201

The National Science Foundation of China(52205192

12502114)

Received Date: 2025-11-17
Rev Recd Date: 2025-12-08

Available Online: 2026-07-30

Publish Date: 2026-08-01

Abstract

Abstract

A unified semi-analytical framework combining the numerical equivalent inclusion method (NEIM) and the distributed dislocation technique (DDT) was employed to investigate the interaction between surface cracks and arbitrarily shaped inhomogeneities in a half-plane. Several representative examples were simulated to systematically examine the effects of crack angles, inhomogeneity stiffnesses, and the inhomogeneity distances from the free surface on the stress intensity factors and local stress fields. The results show that, the crack angle leads to notable changes in the crack-tip field and induces pronounced mode coupling. Stiff inhomogeneities decrease Mode Ⅰ stress intensity factor but increase Mode Ⅱ, whereas soft inhomogeneities exhibit the opposite trend. As the inhomogeneity moves farther from the free surface, its perturbation to the crack-tip field becomes significantly weaker. The semi-analytical results agree well with the finite element solutions, with discrepancies below 4.5%, demonstrating the accuracy and efficiency of the present framework. The numerical examples provide clear insight into the dominant mechanisms governing crack-inhomogeneity interaction under multiple influencing parameters.
- surface crack,
- inhomogeneity,
- semi-analytical method,
- stress intensity factor

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References(28)

References

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