The plastic zone at a crack tip in a finite anisotropic body is studied. A boundary-value problem is formulated in terms of the components of the covariant displacement vector for small strains. Particular attention is given to the case of plain strain. In this case, a numerical solution is found for a long rectangular body with a central crack under tension. As a result, conditions for the occurrence and development of a plastic zone at the crack tip are established. A plastic zone on the lateral surface of the body is discovered. How both zones extend and coalesce is elucidated. The effect of anisotropy on the occurrence of a plastic zone is evaluated

The Wiener-Hopf method is used to study, under the conditions of plane strain, the direction of development of a thin fracture process zone at the tip of an interfacial crack in a piecewise homogeneous isotropic elastoplastic body. The zone is modeled by a straight line of tangential displacement discontinuity that emerges from the crack tip at an angle to the interface. The dependences of the zone length and the angle on the load and other parameters of the problem are investigated Keywords: piecewise homogeneous isotropic elastoplastic body, interfacial crack, process zone Introduction. In recent years, there has been intensive development of studues in the field of the fracture mechanics of various deformable bodies, including composite materials, welded and adhesive joints, fractured rocks, and concrete and polymers. That was owing to new models of fracture mesomechanics that account, more fully than in the classical models, for the features of fracture process zones at crack tips [2][3][4][10][11][12][13][14][15].Most theoretical studies in the field of the mechanics of interfacial cracks supposed that the fracture process zone is a surface on which the normal or tangential displacements discontinue. This surface is located on the continuation of the crack and does not go beyond the crack plane [2,4,11,12,15].The present paper addresses a piecewise-homogeneous body consisting of elastic and elastoplastic half-spaces. There is a rectilinear crack in the interface between the half-spaces. The body is under the conditions of plane strain. We examine the asymmetric case where a thin fracture process zone modeled by a line of discontinuity of tangential displacements develops in the body. The condition at infinity is formulated so as to account for the influence of the external field on the stress-strain state of the body. The integral Mellin transform is used to derive the functional Wiener-Hopf equation. Its exact solution is expressed in terms of Cauchy integrals and gamma functions. This solution is used to derive an equation for the determination of the length of the zone and to analyze the dependences of its length and angle on the external load and other parameters of the problem.1. Problem Statement. Consider the following plane-strain problem for a piecewise-homogeneous isotropic body: Determine the direction of development of a thin fracture process zone at the tip of a crack located in the interface between two dissimilar homogeneous half-planes with Young's moduli E 1 and E 2 and Poisson's ratios ν 1 and ν 2 . The material of the upper half plane is assumed elastoplastic; therefore, the preferential strains in the process zone, which is a thin layer, follow the shear mechanism. Because of this, we will simulate the thin process zone by a straight line that emanates from the crack tip at an angle α to the interface and on which the tangential displacement discontinues and the tangential stress is equal to a predefined material constant τ. The constant τ is the tangential stress averaged over the length...

The initial kinking of a thin fracture process zone near the crack tip under plane strain is studied using the Wiener-Hopf method. The crack is located at the interface between dissimilar elastic media. The fracture process zone is modeled by a straight line of normal displacement discontinuity emerging from the crack tip at an angle to the interface. The angle between the process zone and the interface is determined from the condition of strain energy maximum in the process zone. The dependences of the length and angle of the process zone on the external load and other parameters îf the problem are studied. The results are compared with theoretical and experimental data obtained by other researchers Keywords: initial crack kinking, interface crack, thin process zone, Wiener-Hopf method Introduction. Studies of the failure mechanism for solids of different physical nature such as composites [2, 5], nanocomposites [18] reinforced ceramics and concrete [11,29], welded and adhesive joints [5] motivate theoretical developments on fracture mechanics based on new nonclassical models that take more complete (than in the classical models) account of the features of fracture process zones at crack tips. This issue is especially important in studying interface cracks between dissimilar media.It follows from [5,10,32,33] that if based on the classical approach (where a crack is regarded as an interface cut with no fracture process zone), a theoretical study of the stress and displacement fields at the edge of a cut-like crack leads to physically incorrect conclusions because the stresses and displacements at the edges of such a crack exhibit oscillatory behavior, which may result in overlapping of the crack faces. To avoid it, new approaches were developed in [3,4,12,13,15]. One approach is based on the studies [12,13,15], where the oscillations of the stresses and displacements are eliminated by introducing contact zones at crack tips. However, it was shown in [15,30] that the contact zone appears extremely small (subatomic) under pure tension, making the methods of continuum mechanics fail. Thus, eliminating one physical incorrectness with the help of the contact model, researchers in some cases arrive at another paradoxical result which raises doubts about this model. In [30], it is recommended to apply this model to pure shear only.The second approach is based on the Barenblatt and Leonov-Panasyuk-Dugdale models and their modifications and various models describing cohesive zones in polymers [2,17,19,21], ceramics [11], concrete [29], composites [2, 11, 19-22, 27, 28].When this approach is applied to cracks at the interface between dissimilar media in [3,4,11,14,17,31], the crack faces do not overlap and the fracture process zone under tensile forces is not extremely small, unlike the contact model.In studying the behavior of cracks at the interface between dissimilar materials (polymer-metal, polymer-composite) in [36], it was experimentally established that if the crack growth rate is low, the crack propagates in the ...