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

TL;DR

This study investigates the steady-state propagation of a Mode III crack in couple stress elastic materials, incorporating microstructural effects, crack velocity, and rotational inertia, to understand stability and size effects at small scales.

Contribution

It extends static crack analysis to dynamic conditions in couple stress materials, including microstructure and inertia effects, providing new insights into crack stability.

Findings

Microstructure influences crack stability and propagation

Crack velocity affects stress distribution and stability

Rotational inertia impacts dynamic crack behavior

Abstract

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.