M-integral analysis for two-dimensional solids with strongly interacting microcracks. Part I: in an infinite brittle solid

摘要

This paper addresses an alternative description for brittle solids with strongly interacting microcracks. The basic idea starts from the M-integral analysis customarily used in single crack problems. As an initial attempt, the discussion is limited to the infinite two-dimensional cases and the microcracks are assumed to be stationary. It is proved from the global-local coordinate translations that the M integral is divided into two distinct parts. First of them is induced from the well-known relation between the integral and the stress intensity factors (SIFs) at all the crack tips (Freund, 1978). The second is contributed from the two components of the J(k) vector (Knowles and Sternberg, 1972, Budiansky and Rice, 1973) and the coordinates of each microcrack center. The later is concerned not only with the crack tip SIFs, but also with the contribution arising from the traction-free surfaces of each crack (Herrmann and Herrmann, 1981). A detailed proof for the vanishing nature of the J(k) vector along a closed contour surrounding all the microcracks is presented, from which the confusion about the dependence of the M integral on the origin selection of global coordinates is clarified. Two numerical examples are shown in tables and figures to confirm the derived conclusions. It is shown that the M integral is equivalent to the decrease of the total potential energy of the microcracking solids although the strongly interacting situations are taken into account. Therefore, a simple relation between the M integral and the L integral is established under the assumption mentioned above. It is concluded that the M-integral analysis, from the physical point of view, does play important role and provide an effective measure in evaluating the damage level of brittle solids with strongly interacting and randomly distributed microcracks. Although only the stationary microcracks are considered in the present investigation, the derived conclusions could actually be extended to treat much more useful problems, in which the multi-cracks may become critical and may grow during loading histories. (C) 2001 Elsevier Science Ltd. All rights reserved. [References: 34]