PSI - Issue 68

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I. Shatskyi et al. / Structural Integrity Procedia 00 (2025) 000–000

Ivan Shatskyi et al. / Procedia Structural Integrity 68 (2025) 9–15

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discussed, for example, by Panasyuk et al. (2005, 2014), Shatskyi and Kurtash (2018), Suprun et al. (2022). These publications focus on limit state evaluations of structures with defects filled with low-modulus materials. The purpose of this paper is to develop an engineering methodology for evaluating the effectiveness of restoration of elastic bodies with surface defects. In the course of the study, the previously proposed approach to estimating the limit equilibrium of bodies with cracks partially filled with non-contrast material (Shats’kyi, 2015; Dalyak and Shatsky, 2023) is developed. Problems of a non-contrast interface were also considered by Gao et al. (2022). 2. Materials and methods 2.1. Model of partially healed crack The express methodology for assessing the strength of a body with a partially healed crack (Shats’kyi, 2015) is used for modeling the renovation of bodies with surface defects. A crack in a deformed body is understood as a displacement discontinuity surface . As a result of the restoration of the integrity of the body in some area , we get a new object – a partially healed crack with a discontinuity of movements on the surface (generally multi-connected). For simplification, we adopted the hypothesis that the elastic properties of the body with a healed crack are preserved (the details of the rheology of the connecting layer are neglected). However, the specific surface energy of separation of surfaces or fracture toughness of the material in the healed area is generally different from the corresponding values or in a solid body. Thus, we came to the problem of mechanics of crack in a semi-infinite body homogeneous in terms of elastic properties and heterogeneous in terms of crack resistance. The degree of crack healing was described by two parameters: the ratio of the crack resistance of the body and aggregate materials , which characterizes the quality of the process, as well as the ratio of the areas of the healed area and the initial crack , which describes the quantitative degree of recovery. The efficiency of healing was sought as the ratio of the limit values of the load for the healed and primary crack: . 2.2. Single surface crack Within the assumptions of the plane problem of the theory of elasticity, consider a half-plane with an edge crack of normal separation of length . We will alternately analyze two options for crack healing: near the top of the defect (Fig. 1) and near the edge of the half-plane (Fig. 2). ! ! ! ! ! " ! ! ! ! ! ! " = ! ! " ! " # ! ! ! " ! " ! " ! ! ! " " # # ! ! = = " " # ! " ! " # # %$#"! &'() '() $ ! = # " " ! ! " ! ! " = ! ! !

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Fig. 1. Scheme of healing a crack near the tip.