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

Keywords

shear crack merging, plastic strips, analytical solution, critical load.

Cite as

Kryven’ V. A. Merging of two collinear shear cracks in a perfectly elastic-plastic body under quasi-static loading. Physicochemical Mechanics of Materials. 2025. 61(6), 113-118.

https://doi.org/10.15407/pcmm2025.06.113

Abstract

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

References

1. A. Chudnovsky, A. Dolgopolsky, and M. Kachanov, “Elastic interaction of a crack with a microcrack array. I – Formulation of the problem and general form of the solution,” Int. J. Solids Struct., 23, Is. 1, 1-10 (1987). https://doi.org/10.1016/0020-7683(87)90028-X
2. M. P. Savruk, and A. M. Ostrechko, “Interaction of arbitrarily placed cracks with an angular notch under antiplane deformation,” Matematychni Metody ta Fiziko-Mekhanichni Polya [in Ukrainian], 48, Is. 4, 165-171 (2005).
3. P. Maruschak, I. Konovalenko, and A. Sorochak, “Methods for evaluating fracture patterns of polycrystalline materials based on the parameter analysis of ductile separation dimples: A review,” Eng. Failure Analysis, 153 (2023). Art. no. 107587. https://doi.org/10.1016/j.engfailanal.2023.107587
4. V. S. Kravets, and M. P. Savruk, “Deformation of an isotropic plate with periodic system of curvilinear holes and plasticity bands,” Mater. Sci., 56, Is. 3, 301-309 (2020). https://doi.org/10.1007/s11003-020-00430-0
5. A. O. Kamuinskiy, and M. F. Selivanov, “Coupling of two collinear cracks of different lengths in a viscoelastic composite plate,” Dopovidi Academii Nauk Ukrainy [in Ukrainian], Is. 6, 58-64 (2014).
6. K. V. Vasiliev, and H. T. Sulym, “Longitudinal shear of anisotropic bimaterial bodies with banded inclusions and interfacial cracks,” Matematychni Metody ta Fiziko-Mekhanichni Polya [in Ukrainian], 65, Is. 3-4, 146-159 (2022). https://doi.org/10.15407/mmpmf2022.65.3-4.146-159
7. K. V. Vasiliev, and H. T. Sulym, “Elastic equilibrium of anisotropic bimaterial bodies with thin elastic anisotropic inclusions under longitudinal shear,” Matematychni Metody ta Fiziko-Mekhanichni Polya [in Ukrainian], 64, Is. 3, 90-103 (2021). https://doi.org/10.15407/mmpmf2021.64.3.90-103
8. V. A. Kriven’, “Continuous and discontinuous solutions of the elastoplastic problem of antiplanar deformation of a crack-containing body,” Soviet Mater. Sci., 21, Is. 6, 514-520 (1986). https://doi.org/10.1007/BF00722232
9. A. V. Kriven, V. A. Valyashek, L. I. Tsybbalyuk, and N. I. Blashchak, “Elastic-plastic problem for a unilaterally delaminated thin inclusion under shear loading,” Matematychni Metody ta Fiziko-Mekhanichni Polya [in Ukrainian], 63, Is. 4, 122-127 (2020). https://doi.org/10.15407/mmpmf2020.63.4.122-127