Shear crack growth in brittle materials modeled by constrained Cosserat elasticity

The propagation of in-plane shear cracks is investigated in brittle microstructured materials modeled by the constrained Cosserat elasticity. This theory introduces characteristic material lengths in order to describe the scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. An exact solution is obtained based on integral transforms and the Wiener-Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the loading profile, the propagation velocity, and the characteristic material lengths of Cosserat elasticity. It is shown that depending on the Cosserat microstructural lengths the limiting crack propagation velocity can be significantly lower than the classical Rayleigh limit. Moreover, strengthening effects are observed when the characteristic material lengths become comparable to the geometrical lengths of the problem, a behavior that has been experimentally verified in fracture of ceramics.