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Elastic Fields of Double Branched and Kalthoff-Winkler Cracks in a Half-Plane

Yangjian Si^1,2, Yujie Wei^1,2,*

1 LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China
2 School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

* Corresponding Author: Yujie Wei. Email:

The International Conference on Computational & Experimental Engineering and Sciences 2024, 29(1), 1-1. https://doi.org/10.32604/icces.2024.011974

Abstract

Edge cracking represents one of the most prominent damage modes in engineering practice and hence receives immense attention from academic societies. When branched cracks or multiple cracks are present at the edge, their propagation may be affected by the interaction between the cracks. In this talk, we may cover the elasticity of a cracked half-plane with two typical scenarios: a double branched crack with two rays emanating from one point on the edge and two edge cracks spaced by a certain distance (Kalthoff–Winkler cracks). By adopting the combination of the Schwartz-Christoffel conformal mapping and the Muskhelishvili theory with fractional function series, we supplied a general way to solve the elasticity problem of cracks with complicated geometries, for both branched cracks and Kalthoff–Winkler cracks under typical loading conditions including far-field uniform tensile stress and concentrated loads along either the tangential or the normal direction of the free surface. The theory is validated by comparing the finite-element results in terms of stress intensity factors (SIFs), stress fields, and crack opening displacement (COD). The shielding effect for Kalthoff–Winkler cracks of length is revealed: the SIF decays with their space d, K₁ = K⁰₁ + K¹₁ exp(−a/d) , where K⁰₁ and K¹₁ are two coefficients. When d approaches infinity, K₁ converges to the SIF of a single edge crack [1].

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Keywords

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