Bilby–Cottrell–Swinden model for a growing crack with residual stresses

Abstract

For a growing crack the residual stresses caused by plastic flow at previous positions of the crack-tip affect the current plastic zone. This effect is calculated by an extension of the BCS model which replaces the plastic zone by two planar arrays of dislocations emanating from the crack-tips. For a growing crack a succession of such arrays is formed. We consider a crack growing in anti-plane strain with the slip-planes making an almost zero angle with the plane of the crack. The plastic zone size in front of the crack turns out to be the same as for a stationary crack, while the relative displacement of the crack faces is less concentrated in the vicinity of the crack-tip. The rate of plastic dissipation of energy is calculated, and turns out to be identical with the elastic energy release rate.