Interaction Between A Main-crack And A Collinear Micro-crack Or Two Parallel Micro-cracks

Abstract

The analysis of the interaction of a main crack with an array of microcracks, placed near the tip of the main crack, has been performed considering 2-D polycarbonate flat specimens. Analytical results, based on the elastic potential theory for the stress intensity factor K, have been well compared with experimental results obtained through the application of the caustic method. Two different specimen configurations have been analysed involving one and two microcracks. INTRODUCTION The problem of the interaction of a main crack with an array of microcracks placed near its tip, of strong relevance in the prediction of the reliability of structural materials, can be experimentally analyzed by applying the caustic method on 2-D specimens. In fact, the method of caustics can be applied to the determination of the stress intensity factors at crack tips approaching other crack tips or boundaries of the specimen. Several problems of interaction of cracks with other cracks or boundaries have been reported [1,2]. In these problems two special cases can be distinguished: in the first case, the crack tip at which the stress intensity factor is determined does not lie very near another crack or boundary [3]. In the second case the crack tip lies very near another crack tip (or boundary) and the shape of the caustic around this crack tip is influenced by the other crack (or boundary). On the other hand, the elastic interaction between both types of cracks can be analytically studied by applying a method based on the combination of the double layer potential technique and the Willis polynomial conservation theorem stating that the COD of a crack embedded into a polynomial stress field of degree N has the form (ellipse)x(polynomial) [4]. Following this approach and Transactions on Modelling and Simulation vol 10, © 1995 WIT Press, www.witpress.com, ISSN 1743-355X 620 Computational Methods and Experimental Measurements expressing the displacement field as well as the stress field by an integral of the double layer potential type, the problem can be reduced to the one of finding vectorial functions-microcrack CODs b(x) and the stress intensity factor K, at the macrocrack tip from the system obtained by solving the system of integral equations which express the boundary conditions on the crack faces. The microcrack CODs are represented in the form (ellipse)x(polynomial) where the first multiplier corresponds to the crack embedded into a uniform stress field and the second multiplier accounts for crack interactions. Thus, the system of singular integral equations is reduced to a system of linear algebraic equations which must be solved to obtain the polynomial coefficients. POTENTIAL REPRESENTATION THEORY The schematic representation of a main crack (-L, i) which can interact with one microcrack is shown in Fig. La and with two microcracks in Fig.l.b. In order to describe the elastic interaction between both cracks, plane stress conditions and Mode I are assumed. Moreover, the case where the microcrack is embedded into the stress field of the main crack tip is considered. Using the constant approximation the stress field within the microcrack line (c-l, c+l) may be approximated by a constant equal to the value of the field at the microcrack centre (x-c) and, following symmetry, a* = â fcj is the only stress component acting along the microcrack line. Fig.l .a: Main crack collinear with one microcrack. Transactions on Modelling and Simulation vol 10, © 1995 WIT Press, www.witpress.com, ISSN 1743-355X Computational Methods and Experimental Measurements 621 Thus, the overall stress field in the vicinity of the main crack tip is given by the superposition: