Nonequilibrium brittle fracture propagation: Steady state, oscillations, and intermittency

A minimal model is constructed for two-dimensional fracture propagation. The heterogeneous process zone is presumed to suppress stress relaxation rate, leading to non-quasistatic behavior. Using the Yoffe solution, I construct and solve a dynamical equation for the tip stress. I discuss a generic tip-velocity response to local stress and find that noise-free propagation is either at steady state or oscillatory, depending only on one material parameter. Noise gives rise to intermittency and quasiperiodicity. The theory explains the velocity oscillations and the complicated behavior seen in polymeric and amorphous brittle materials. I suggest experimental verifications and new connections between velocity measurements and material properties.