Crack instabilities of a heated glass strip

Abstract

Recently, Yuse and Sano [Nature (London) 362, 329 (1993)] have observed that a crack traveling in a glass strip submitted to a nonuniform thermal diffusion field undergoes numerous instabilities. We study two cases of quasistatic crack propagation. The crack extension condition in straight propagation is determined. An asymptotic analysis of the elastic free energy is introduced and scaling laws are derived. A linear stability analysis of the straight propagation is performed, based on the assumption that the crack tip propagation deviates from the centered straight one as soon as it is submitted to a ``physical'' singular shear stress. It is shown that a straight propagation can become unstable after which a wavy instability appears. The condition for instability as well as the selected wavelength is calculated quantitatively. The results are compared with experiments and the agreement is favorable.