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

Abstract

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

Interaction of cracks with dislocations in couple-stress elasticity. Part II: Shear modes

“…Note that the problem of an antiplane crack under remote mode III loading in couple-stress elasticity was investigated by Gourgiotis and Georgiadis (2007) and Radi (2008), while the steady state dynamic case was examined by Mishuris et al (2012).…”

Dispersion and localisation in structured Rayleigh beams

“…We note that this physical problem has a formal mathematical analogy with the problem of shear wave propagation in couple-stress elastic materials. In fact, the dynamic equation governing the anti-plane motion in a couple-stress elastic material is given by [15]…”

Influence of fracture criteria on dynamic fracture propagation in a discrete chain

“…must be determined accordingly to the new fracture parameters and does not simply equal u s as for the ideal brittle criterion Eq. (11). In this way, also the energy released locally at the crack tip G 0 (v) = ku 2 0 (v)/2 is a function of the crack speed.…”

“…Finally, discrete models can be also treated as the discretization of the corresponding continuum problems where also a choice of the fracture criterion may play an important role when dynamic fracture propagation is in question, for example it may lead to different predictions on the stability of possible steady-state regimes (e.g. [10,11]).…”