Rv. Goldstein et Mb. Konovalov, ASYMPTOTIC ANALYSIS OF A DELAMINATION IN A BI-LAYERED PLATE, Comptes rendus de l'Academie des sciences. Serie II. Mecanique, physique, chimie, astronomie, 324(7), 1997, pp. 419-426
The problem of the static deformation of a bi-layered plate with a cra
ck is considered. The crack is placed at the interface and has arbitra
ry shape in the plan view. A system of integro-differential equations
for the crack opening is obtained. With the assumption that the plate
thickness is much smaller than the crack scale, the asymptotic inner a
nd outer problems are introduced. The inner problem is the 2-D one of
the semi-infinite crack in the bi-material strip. The outer problem is
that of the deformation of two plates clamped along the crack contour
with the boundary conditions determined by the solution of the inner
problem. Matching solutions of the inner and outer problems leads to t
he formulae for the stress intensity factors.