Steady-State Propagation of a Mode II Crack in Couple Stress Elasticity

TL;DR

This paper investigates the steady-state propagation of a Mode II crack in couple-stress elastic materials, incorporating microstructural effects and inertial effects, providing exact solutions and analyzing the influence of material length scales on stress and energy release.

Contribution

It extends previous static crack analyses by including inertial and micro-inertial effects, offering an exact solution for propagating cracks in couple-stress elasticity.

Findings

Stress intensity factor depends on propagation velocity and material length scales.

Energy release rate varies with crack speed and microstructural parameters.

Micro-inertial effects influence the stress and energy distribution around the crack tip.

Abstract

The present work deals with the problem of a semi-infinite crack steadily propagating in an elastic body subject to plane-strain shear loading. It is assumed that the mechanical response of the body is governed by the theory of couple-stress elasticity including also micro-rotational inertial effects. This theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. It is assumed that the crack propagates at a constant sub-Rayleigh speed. An exact full field solution is then obtained based on integral transforms and the Wiener-Hopf technique. Numerical results are presented illustrating the dependence of the stress intensity factor and the energy release rate upon the propagation velocity and the characteristic material lengths in couple-stress elasticity. The present analysis confirms and extends previous results within the context of couple-stress elasticity concerning stationary cracks by including inertial and micro-inertial effects.