Approximating the upper bound in elastic stress intensity factor for a crack in an unknown residual stress field

A method for approximating an upper bound to the Mode I stress intensity factor for a crack in a two-dimensional object containing unknown thermal or residual stresses is described. It uses eigenstrain analysis and constrained maximisation to find the self-equilibrating stress distribution which imparts the maximum stress intensity after introduction of a crack. As an example we calculate limits on the stress intensity at an edge crack in a plane strain bar for thermal and residual stress loading. It is shown that uniform yield-magnitude stress perpendicular to the crack plane does not necessarily give a bounding estimate of stress intensity.