The maximum possible stress intensity factor for a crack in an unknown residual stress field

Residual and thermal stress fields in engineering components can act on cracks and structural flaws, promoting or inhibiting fracture. However, these stresses are limited in magnitude by the ability of materials to sustain them elastically. As a consequence, the stress intensity factor which can be applied to a given defect by a self-equilibrating stress field is also limited. We propose a simple weight function method for determining the maximum stress intensity factor which can occur for a given crack or defect in a one-dimensional self-equilibrating stress field, i.e. an upper bound for the residual stress contribution to K_I. This can be used for analysing structures containing defects and subject to residual stress without any information about the actual stress field which exists in the structure being analysed. A number of examples are given, including long radial cracks and fully-circumferential cracks in thick-walled hollow cylinders containing self-equilibrating stresses. - Highlights: • An upper limit to the contribution of residual stress to stress intensity factor. • The maximum K_I for self-equilibrating stresses in several geometries is calculated. • A weight function method can determine this maximum for 1-dimensional stress fields. • Simple MATLAB scripts for calculating maximum K_I provided as supplementary material.