The effect of residual stress on a centre-cracked plate under uniaxial loading

Abstract

The behaviour of a crack in the centre of a plate subject to a far-field applied stress perpendicular to the crack surface has been studied. The plate contains an initial, self-equilibrated residual stress, symmetric to the central position of the crack. The component of the residual stress perpendicular to the crack at the centre of the plate can be tensile or compressive. Elastic and elastic–plastic material behaviours have been considered and crack closure effects have been included in the analyses. For elastic behaviour a series of analyses based on stress intensity factor solutions have been developed to calculate the crack opening and the stress intensity factor for cracks of different lengths relative to the size of the residual stress field. Different magnitudes of applied stress relative to the magnitude of the residual stress were applied. Crack behaviour maps have been developed that show the behaviour of the crack for different crack lengths and magnitudes of applied stress. For elastic–plastic behaviour a strip yield model has been used to develop a similar set of analyses to those for the elastic case. The results compare favourably with those produced by finite element analysis. The work provides the basis for a first estimate of the likelihood of fracture for a component containing residual stress and subject to applied load.