Initial kinking of an interface crack between two elastic media

Abstract

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 ...

On stability of the equilibrium of a cottrell crack

“…To find its exact solution, we will use the Wiener-Hopf method and Mellin transform [2,4,5,11]. Taking the Mellin transform with a complex parameter p m p m r r dr p * ( ) ( ) = ¥ ò 0 of the equilibrium equations, strain compatibility conditions, and Hooke's law, we obtain…”

Analysis of the plastic zone at the corner point of interface

“…The stress at the corner point is analyzed Keywords: plastic zone, corner point, interface, displacement discontinuity line, Wiener-Hopf method Introduction. There are a great variety of recent publications on plastic and other fracture process zones at cracks tips in anisotropic and piecewise-homogeneous bodies [1,[10][11][12][14][15][16][17][18]. Of current importance are problems related to fracture process zones at corner points of such bodies.…”

A mesomechanical fracture model for an orthotropic material with different tensile and compressive strengths

“…Methods of fracture mesomechanics make it possible to study fracture processes in various natural and man-made materials such as rocks, timber, concrete, ceramics, polymers, composites, and others. Of particular interest is the fracture of anisotropic materials [8][9][10][11].Experiments show that fracture process zones in thin plates are in many cases narrow and wedge-shaped areas located on the continuation of cracks and made of a partially damaged, discontinuous material [5,13]. These experimental data were used in [6] to model a fracture process.…”