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<p>An exact analytical solution to the anti-plane problem of the quasi-static development of plastic strips along the extension of two arbitrarily distant cracks of the same length, located on the same straight line, is obtained. According to this solution, the strips starting from a&#xa0;pair of inner tips meet, while those starting from the outer tips develop in the opposite direction. The plasticity condition is achieved only at the points of the plastic strips. The dependence of the length of plastic strips on the load, the crack length, and the distance between them is established. The critical load at which the plastic strips developing from the inner pair of crack tips merge to form a&#xa0;new crack is determined. The lengths of the strips developing from the inner tips of the cracks are greater than those developing from the outer tips. The difference in their length is more significant at higher loads and is notably smaller for larger, more distant cracks. As the distance between the cracks increases, the lengths of the strips initiating from both crack tips gradually equalize, approaching the length of a&#xa0;strip in an isolated crack. It is shown that at the initial stage, the length of the plastic strips grows proportionally to the square of the load. The corresponding simplified dependencies are presented, and their accuracy is assessed.</p>

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Merging of two collinear shear cracks in a perfectly elastic-plastic body under quasi-static loading

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • V. A. Kryven

摘要

An exact analytical solution to the anti-plane problem of the quasi-static development of plastic strips along the extension of two arbitrarily distant cracks of the same length, located on the same straight line, is obtained. According to this solution, the strips starting from a pair of inner tips meet, while those starting from the outer tips develop in the opposite direction. The plasticity condition is achieved only at the points of the plastic strips. The dependence of the length of plastic strips on the load, the crack length, and the distance between them is established. The critical load at which the plastic strips developing from the inner pair of crack tips merge to form a new crack is determined. The lengths of the strips developing from the inner tips of the cracks are greater than those developing from the outer tips. The difference in their length is more significant at higher loads and is notably smaller for larger, more distant cracks. As the distance between the cracks increases, the lengths of the strips initiating from both crack tips gradually equalize, approaching the length of a strip in an isolated crack. It is shown that at the initial stage, the length of the plastic strips grows proportionally to the square of the load. The corresponding simplified dependencies are presented, and their accuracy is assessed.