Full-field solution for Mode III crack in couple stress elastic materials with two characteristic lengths

The problem of a stationary semi infinite crack in an elastic solid with microstructures subject to remote classical KIII field is investigated in the present work. The material behaviour is described by the indeterminate theory of couple stress elasticity. The adopted constitutive model incorporates the characteristic lengths in bending and torsion of the material and thus it is able to account for the underlying microstructure as well as for the strong size effects arising at small scales. The stress and displacement fields turn out to be strongly influenced by the ratio between the characteristic lengths. In particular, due to the relative rotation of the microstructural particles currently at the crack tip the total shear stress and reduced tractions ahead of the crack tip display the opposite sign with respect to the classical LEFM solution within a zone smaller than the characteristic length in torsion. However, this zone has limited physical relevance and becomes vanishing small for a characteristic length in torsion of zero. Outside this zone, the full field solution exhibits a bounded maximum for the shear stress ahead of the crack tip, whose magnitude can be 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. Moreover, the occurrence of a sharp crack profile indicates that the crack becomes stiffer with respect to the classical elastic response, thus revealing that the presence of microstructures may shield the crack tip from fracture.