Widely discussed in the literature, the crack-microcrack interaction problem is reconsidered in the present communication. Interest in this problem stems from various physical models of crack initiation, a damage zone formation in front of the crack, etc. One of the most popular approaches to the crack-microcrack interaction problem is an iterative procedure which employs the superposition method and reduces the interaction to a single crack problem [1-3]. It can be described as follows. Every step of interation consists of 2 frames (see Fig. 1). Every frame represents a single crack problem. On the (n+l)-th step of iteration in the first frame, the main crack is loaded by the traction o ~o~ calculated at the n-th step (in the case of n=l it is a remote loading). It produces traction p~oรท'~(x) along the line of the microcrack corresponding to the asymptotic stress field with AK(n~increment in the stress intensity factor (SIF) associated with the n-th step (for n=l: K(0~ = K~[o~-q). In the second frame a microcrack loaded by traction p~o~(x) _generates traction o-re(x) along the line of the main crack. Increment in the SIF K{n+a~ corresponding to the (n+l)-th step is proportional to that in the previous step: AK{ n"~ = ~. AK{-~, with ~, < 1 independent on n. The total SIF K~ t~ of the main crack is obtained by summing up all iterative steps, which constitutes a geometrical progression resulting in gl(ยฐ)
K t ' -l _ ~.
Unfortunately, as the crack tips become closer (i.e. for strong crack interaction), this approach gives erroneous results, as can be seen in Table 1.
To understand the source of the error we compare the traction distributions along the microcrack line on the n-th step of iteration (n >_ 2) representing exact and asymptotic stress fields (Fig. 2). Apparently the asymptotic solution gives a gross overestimation of the actual tractions. Thus the conventional 13/~ asymptotic stress field is inadequate within the domain of the microcrack starting from the second step of iteration.