  This paper is concerned with the problem of a semi-infinite crack steadily
propagating in an elastic solid with microstructures subject to antiplane
loading applied on the crack surfaces. The loading is moving with the same
constant velocity as that of the crack tip. We assume subsonic regime, that is
the crack velocity is smaller than the shear wave velocity. The material
behaviour 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 with the length scale of the
microstructure, such as the grain size in a polycrystalline or granular
aggregate.
  The present analysis confirms and extends earlier results on the static case
by including the effects of crack velocity and rotational inertia. By adopting
the criterion of maximum total shear stress, we discuss the effects of
microstructural parameters on the stability of crack propagation.
