  We consider a linearly elastic body consisting of two equal symmetrically
arranged layers (or half-planes) connected by a structured interface as a
prospective crack path. The interface is comprised by periodic discrete system
of bonds. In the initial state with no external forces, the bonds are assumed
to be stressed in such a way that tensile and compressive forces of the same
value alternate. In the general considerations, the layers are assumed to be of
a general, unspecified {\em periodic} structure, where such self-equilibrated
residual stresses can also exist. A two-line chain and an anisotropic lattice
are examined as illustrative examples. We consider the states of the
body-with-a-crack under the residual stresses and under a combined action of
the remote forces and residual stresses. Analytical solutions to the considered
problems are presented. The solutions are based on a selective discrete
transform introduced. In particular, it is found that a formula for
local-to-global energy release ratio, written in terms of the Wiener-Hopf
equation kernel, is very general. We show that the residual stresses can
manifest themselves in a number of phenomena such as the crack bridging,
`porous' in front of the crack and crack growth irregularities. We also
demonstrate analytically and graphically that the residual stresses can result
in increase as well as in decrease of the crack resistance depending on the
internal energy level. The quasi-static considerations suggest different
scenarios of the crack growth depending on the internal energy level.
