  The focus of the article is on fracture criteria for dynamic crack
propagation in elastic materials with microstructures. Steady-state propagation
of a Mode III semi-infinite crack subject to loading applied on the crack
surfaces is considered. The micropolar behavior of the material is described by
the theory of couple-stress elasticity developed by Koiter. This constitutive
model includes the characteristic lengths in bending and torsion, and thus it
is able to account for the underlying microstructures of the material. Both
translational and micro-rotational inertial terms are included in the balance
equations, and the behavior of the solution near to the crack tip is
investigated by means of an asymptotic analysis. The asymptotic fields are used
to evaluate the dynamic J-integral for a couple-stress material, and the energy
release rate is derived by the corresponding conservation law. The propagation
stability is studied according to the energy-based Griffith criterion and the
obtained results are compared to those derived by the application of the
maximum total shear stress criterion.
