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A mode-III fracture analysis of two collinear cracks in a functionally graded material using gradient elasticity theory

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Abstract

In this paper, we have studied the behaviour of two symmetric mode-III collinear cracks in a functionally graded material (FGM). The fundamental goal of this paper is to provide insight on the interaction of two cracks in FGMs with the strain gradient effect. To assess the influence of gradient elasticity, we have considered two key parameters \(\ell \) and \(\ell ^{\prime }\), which describe the size scale effect caused by the underlying microstructure and are related to volumetric and surface strain energy, respectively. The crack boundary value problem have been solved by the approach involving Fourier transforms and the innovative hyper-singular integro-differential equation method, where the integral equation contains the two terms in integrals for the both cracks. A system of equations has been constructed by employing the Chebyshev polynomial expansion and then by choosing the suitable collocation points the system of equation have been solved. Our investigation involves the determination of stress intensity factors at both crack tips. These factors are vital for understanding the material’s fracture behavior and structural integrity. Furthermore, we explore the variations in the displacement profile when the distance between the cracks is reduced to close proximity. This particular scenario is of significant interest as it provides insights into how the interaction between the cracks impacts the overall structural response.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Rajasthan, Kishangarh, Ajmer, 305817, India

    Rakesh Kumar Sharma & Kamlesh Jangid

  2. Department of Mechanical Engineering, State University of New York, Korea, Incheon, 21985, Republic of Korea

    Y. Eugene Pak

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  1. Rakesh Kumar Sharma
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  2. Y. Eugene Pak
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Correspondence to Kamlesh Jangid.

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Sharma, R.K., Pak, Y.E. & Jangid, K. A mode-III fracture analysis of two collinear cracks in a functionally graded material using gradient elasticity theory. Acta Mech (2024). https://doi.org/10.1007/s00707-024-03920-3

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  • DOI: https://doi.org/10.1007/s00707-024-03920-3

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