Healing of Cracks in Anisotropic Bodies
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HEALING OF CRACKS IN ANISOTROPIC BODIES V. P. Sylovanyuk1, 2 and N. A. Ivantyshyn1
UDC 539.3
We obtain the solution of a plane problem of the theory of elasticity on the phenomenon of “healing” of a crack in an anisotropic body. By using the model of Winkler’s base, this problem is reduced to a singular integrodifferential equation for the displacements of points of the crack surface. In the case of a defect in the form of flattened ellipse, we obtain the exact analytic solution of the problem. The limit equilibrium state of the plate with a filled crack is estimated by using the energy criterion. We also determine the optimal strength of the injection material after hardening (maximizing the strength of the plate). Keywords: “healing” of a crack, anisotropic body, inclusion, strength.
Introduction Fracture is a quite complicated process even for the idealized macroscopic homogeneous, and isotropic materials. Parallel with homogeneous isotropic materials, contemporary structures also contain anisotropic materials with different elastic properties in different directions. At present, the theory of elasticity of anisotropic bodies is fairly well developed [1, 2], and the solutions of numerous problems of the theory of cracks have been obtained on this basis [3‒12]. At the same time, some important aspects of fracture mechanics are poorly studied. As an example, we can mention, in particular, the effect of hardening of piecewise homogeneous anisotropic bodies with crack-like defects under the action of static and cyclic loads caused by the phenomenon of “healing” of the defects. In the engineering practice, in order to restore the bearing ability of damaged building structures intended for long-term operation, it is customary to use the technology of injection hardening of defective zones [13‒15]. It is based on the introduction of liquid materials under pressure into the damaged regions (with cracks, exfoliations, cavities, etc.) of concrete and reinforced-concrete structures and buildings. After crystallization or polymerization, these liquid materials form strong adhesion bonds with concrete matrices. As a result, the structural elements are hardened and become capable of sustaining the operating loads. In order to estimate the residual serviceability of the restored objects, it is necessary to solve the problems of limit equilibrium of bodies with filled cracks, which can be regarded as a separate class of boundary-value problems for elastic continua. Unlike cracks whose surfaces are free of stresses, we need additional conditions for filled defects reflecting the interaction of the matrix and filler materials. The presence of this interaction, which transfers a part of loading applied to the body with filled cracks, is the main idea of the proposed effect of “healing.” For isotropic bodies, these problems were analyzed in [14‒18]. From the mathematical point of view, these problems are equivalent to the problems of thin inclusions in elastic bodies [19]. 1 2
Karpenko Physicomechanical Institute, Ukrainian Natio
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