Steady-state propagation of a Mode III crack in couple stress elastic materials

This paper is concerned with the problem of a semi-infinite crack steadily propagating in an elastic solidwith microstructures subject to antiplane loading applied on the crack surfaces. The loading is movingwith the same constant velocity as that of the crack tip. We assume subsonic regime, that is the crackvelocity is smaller than the shear wave velocity. The material behaviour is described by the indeterminatetheory of couple stress elasticity developed by Koiter. This constitutive model includes the characteristiclengths in bending and torsion and thus it is able to account for the underlying microstructure of thematerial as well as for the strong size effects arising at small scales and observed when the representativescale of the deformation field becomes comparable with the length scale of the microstructure, such asthe grain size in a polycrystalline or granular aggregate.The present analysis confirms and extends earlier results on the static case by including the effectsof crack velocity and rotational inertia. By adopting the criterion of maximum total shear stress, wediscuss the effects of microstructural parameters on the stability of crack propagation.