Arbitrary system of combined cracks and slots propagating along interface between anisotropic half-planes

摘要

New general closed-form solutions in terms of Cauchy integrals are derived for the in-plane stress/displacement fields in the two interacting dissimilar anisotropic elastic half-planes. The generalized Stroh formalism and new complex potentials are adapted to the mixed boundary value problem with three types of interfacial conditions in several equivalent versions. The basic problem is in analysis of arbitrary sets of the steadily propagating or stationary, closed and open cracks and narrow notches. Therewith, the case of single frictionless contact zone and arbitrary number of open and full-contact regions is reduced to the Riemann-Gilbert boundary value problem by using conform mapping and factorization. Otherwise, a new problem for the complex function vector with combination of Riemann and Dirichlet conditions on the various sections is arisen. The interface narrow slot contained an unknown length slip-region apart its edges and subjected to a remote stress field is studied in details as illustration. The results help us to examine the interaction of various kind and number of interface defects: a macrocrack with the interface microdefects as a damage, etc.