Unstable growth of thermally induced interacting cracks in brittle solids

The growth and stability of thermally induced equally spaced parallel cracks in a half-plane consisting of a homogeneous isotropic linearly elastic brittle material are studied. At the initial time, the uniform temperature of the half-plane is reduced at its surface by a large increment, T₀, and then kept constant (at the surface). Because of heat conduction and possible heat convection due to fluid flow, a temperature gradient forms close to the surface and penetrates into the half-plane. Thermal contraction results in the formation of cracks perpendicular to the free surface. It is shown that if the cracks are initially parallel and equally spaced, and if the possibility of branching is excluded, then they grow in time until a critical state is reached. At this state alternate cracks stop growing, while the others begin to grow at a much faster rate. This process continues until another critical state is attained, where the cracks which had stopped growing (together with some other cracks, depending on the temperature profile), suddenly close, while the cracks which have continued growing, suddenly "snap" into a finitely longer length. At this state the crack spacing is doubled (or quadrupled, depending on the temperature profile). The whole process then repeats itself. Applications to geothermal energy extraction from hot dry rock masses is mentioned.