Features of failure waves in highly-homogeneous brittle materials

To describe the deformation and evolution of damage of glassy brittle materials, a kinetic model, which takes into account the transformation of elastic energy into surface energy, is proposed. The failure kinetics are characterized by a power dependence on the dynamic overload, which is equal to the difference between the rates of change of elastic and surface energies relative to the increase in damage of the medium. The model is applied to the problem of a plane failure wave in a half-space arising from the application of a normal load to the boundary. An approximate asymptotic solution is constructed by combining the two power series for the regions of slow and rapid change of the solution. As found in previous experiments, at moderate loads the values of the velocity and longitudinal stress in the regions of elasticity and the failed state of the material are the same. As the load increases, the distribution of these quantities become two-wave, the amplitude of the forerunner being greater than the elastic limit under uniaxial compression. In that case the structure of the failure wave largely depends on the power index of the kinetic function in the neighbourhood of the static state. If the index is less than one, the kinetics exerts an influence only in a finite neighbourhood of the failure front.