Unstable growth of thermally induced interacting cracks in brittle solids: Further results

Abstract

This paper is complementary to a previous work[1] in which the growth and stability of a system of thermally induced equally spaced parallel edge cracks in a half-plane consisting of a homogeneous isotropic linearly elastic brittle solid has been studied. Initially the half-plane has a uniform temperature, and the edge cracks are introduced by continuous cooling of its free surface. The cracks grow into the solid at an equal rate with the increasing thickness of the thermal boundary layer which forms close to its free surface. However, because of the interaction between adjacent cracks, a critical state may be reached after which some of the cracks stop growing while the remaining ones grow at a faster rate. This new growth regime may again be interrupted at a new critical state where either the cracks which had stopped growing would then suddenly snap closed while the remaining cracks jump to a finitely longer length, or a different growth regime takes place, depending on the nature of the temperature profile. The present work is concerned with a careful examination of the growth regime at and after the above-mentioned second critical state. This examination requires consideration of three interacting unequal cracks which involves crack extension in both Modes I and II. As in [1] two different temperature profiles, relevant to the problem of heat extraction from hot dry rock masses, are considered. It is shown that when the temperature profile in the solid is in the form of an error function, the inclusion of the third interacting crack changes the previously obtained results qualitatively (i.e. no crack closure is attained in this case), whereas for the second temperature profile our new (more complicated) calculations only confirm the previously obtained results.