Initial kinking of an interface crack between two elastic media under tension and shear

Abstract

The initial kinking of a thin fracture process zone near the tip of an interface crack between two elastic media under plane strain is studied using the Wiener-Hopf method. The zone is modeled by the discontinuity plane of the normal displacement. This plane is assumed to emerge from the crack tip at an angle to the interface. The angle between the fracture process zone and the interface is determined from the condition that the potential energy is maximum in the zone. The dependence of the length of the zone and its angle on the external load and other parameters is analyzed in the cases of biaxial tension and pure shear. The results obtained are compared with theoretical and experimental data reported by other researchers Keywords: interface crack, crack kinking, thin process zone, Wiener-Hopf method Introduction. The fracture mechanism for piecewise-homogeneous bodies with an interface crack is addressed, according to [25], in more than 500 publications most of which used mainly the classical approach, some allowed for the contact zones at the crack tips [2, 8-12, 24, 25, 27, 28], and some studied the fracture process zones at the edges of interphase cracks [1,4,5,[18][19][20]26].However, the issue of kinking of interphase cracks has poorly been studied in the literature, though relevant studies have intensified in the last two decades. Noteworthy are experiments on the kinking of an interface crack in polymer-metal and polymer-polymer composites [30], theoretical and experimental studies of the fracture of a metal-ceramic composite [11], and theoretical studies of crack kinking out of the interface between elastic media [24,25].Some of these studies [23,31] are based on the classic approach [28]: the crack is modeled by a cut at the interface between two linear elastic media without a fracture process zone. However, since the stresses and displacements near the edge of such a crack oscillate, it is difficult to determine the kink angle [11]. This is why a different approach was proposed in [24,25]. It is based on the contact crack model [9, 10, 12] that eliminates the oscillation by introducing zones where the crack edges come into contact near the tips.However, as follows from [12,24], the contact zone is extremely small (subatomic) under simple tension (mode I), which makes the methods of continuum mechanics inapplicable in such an important case. In this connection, it is advised in [24,25] to use this approach to study crack kinking under shear.The most promising way of studying the kinking of interface cracks under tension is to develop various Leonov-Panasyuk-Dugdale-type models of fracture process zones at the tips of interface cracks in materials of different physical nature [1,3,4,26]. As shown in [18,20], in this case the crack faces do not overlap and the fracture process zone is not so extremely small as in the contact model.The present paper, based on the earlier theoretical developments [20], calculates the kink angle for the fracture process zone at the edge of an interface crack using the exac...

Discretization of the plane problem for a cracked body with nonlinear stress–strain diagram under tension

“…Figures 1 and 2 show, by solid lines, the plastic zones (aka fracture process zones) for plane strain and plane stress, respectively, for tensile loads p p k The aspect ratio of the plastic zone is of the order of 0.7-0.8 for plane strain and 0.8-1.0 for plane stress, the stress state within the plastic zones being compound and inhomogeneous. This suggests that it is beyond reason to model plastic zones by strips with zero width or by cuts [12,13,17] with indefinite length and direction to which a simple load equal to the yield strength is applied. It is obvious that such a model has nothing to do with the real stress state.…”