Effects of microstructure on antiplane crack growth in couple-stress elastic materials

The problem of a propagating rectilinear crack in an elastic solid with microstructures subject to remote classical KIII field is investigated in the present work. The material behavior is described by the indeterminate 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 microstructure of the material as well as for the strong size effects arising at small scales and observed when the representative scale of the deformation field becomes comparable to the length scale of the microstructure, such as the grain size in a polycrystalline or granular aggregate. The stress and displacement fields near the tip of a Mode III propagting crack are thus expected to be strongly influenced by the microstructural characteristic lengths. The stationary full-field solution, already obtained [1] by using Fourier transforms and Wiener-Hopf technique, showed that ahead of the crack tip within a zone smaller than the characteristic length in torsion, the total shear stress and reduced tractions occur with the opposite sign with respect to the classical LEFM solution, due to the relative rotation of the microstructural particles currently at the crack tip. However, this zone was found to have limited physical relevance and to become vanishing small for a characteristic length in torsion of zero. In this limit case, the solution recovers the classical KIII field with square root stress singularity. Outside the zone where the total shear stress is negative, the full field solution exhibits a bounded maximum for the total shear stress ahead of the crack tip, whose magnitude was adopted as a measure of the critical stress level for crack advancing. The corresponding fracture criterion defines a critical stress intensity factor, which increases with the characteristic length in torsion. In the proposed research the previous analysis will be extended in order to consider the effects of crack speed and inertia terms on the stress and deformation fields, as well as on the stability of the crack propagation in the presence of microstructures.