Development of a prefracture zone from an interface crack at a corner point of an interface of two elastic media

Abstract

UDC 539.375 We perform computation of a prefracture zone in the vicinity of a corner point of an interface from which an interface crack emanates by the Wiener–Hopf method under plane strain. The zone is modeled by a segment of discontinuity of normal displacement. We investigate the dependence of the length of the prefracture zone and its opening displacement at the corner point on load, the angle of interface fracture, and elastic parameters of the media. On the basis of the strain criterion, the conditions of start of the crack are investigated. According to the modern notions of fracture of brittle bodies, a prefracture zone, which is a region of weakened interparticle bonds, forms ahead of the front of a crack. Upon the attainment of a certain limit distance between individual layers of the material in the prefracture zone, adhesion forces between them cannot resist the tensile stress, and bonds rupture, which leads to the propagation of the crack. The determination of the conditions of start of interface cracks in piecewise homogeneous bodies is of great interest for the fracture mechanics of composites, welded and glued joints, building materials, and structures. However, most works on this theme are devoted to cracks located on a plane interface of media [10, 14, 21]. At the same time, the more general problem of an interface crack that emanates from a corner point of a broken interface of media is insufficiently investigated. A corner point of an interface of two different media is a stress concentrator with a power singularity [6], the order of which is determined by the root of the corresponding characteristic equation that is the smallest in the interval (−1, 0) . The propagation of an interface crack from the corner point changes substantially the character of the stress-strain state (SSS) in the vicinity of the vertex of the corner; in particular, in certain intervals of interfacial angles, the characteristic equation may have complex conjugate roots, which cause physically incorrect space oscillations of stresses and displacements [2, 17]. To each root from the interval (−1, 0) there corresponds a singular term in the expansion of stresses into asymptotic series in the vicinity of the corner point. In the investigation of the fine structure of the tip of a crack, one most often restricts oneself to the largest term of the asymptotic expansion. Stress concentration at the corner point leads to the formation of a prefracture zone near it. At the beginning of the stage, when its size is much smaller than the length of the crack, the configuration of the prefracture zone depends substantially on the character of the SSS near the tip of the crack, which is determined by the asymptotic solution of an analogous problem without a prefracture zone. In [4, 5, 11, 13], a calculation of model prefracture zones at the end of a mode I crack reaching a nonsmooth interface of two different media was performed. In [3], a calculation of the initial prefracture zone in the vicinity of the tip of an interface crack at a corner point of an interface of two elastic materials was performed with regard for only one summand with a power singularity. At the same time, ranges of interfacial angles, to which the oscillating singular summands in the expansion of stresses correspond, remained unstudied.