Unstable growth of tension cracks in brittle solids: Stable and unstable bifurcations, snap-through, and imperfection sensitivity

The growth pattern of a system of tension cracks in a linearly elastic brittle solid, may undergo abrupt changes, e.g. some cracks may stop or actually close, as others snap to finitely longer lengths. For the growth regime of a system of straight edge cracks in plane strain, the concepts of fundamental equilibrium path, stable and unstable bifurcation points and snap-through critical point are introduced and the corresponding behaviors are studied. In particular, it is shown that instabilities of this kind are highly imperfection-sensitive in the sense that, for example, a small material inhomogeneity can decrease by a large amount the critical value of the load parameter at which a growth regime abruptly changes to a new one. For thermally induced tension edge cracks in an infinite strip of finite width, numerical results are presented and various aspects of the theory are illustrated. For the calculation the new combined analytic and finite-element solution method recently given by the authors is employed.