Fourier basis for the engineering assessment of cracks in residual stress fields

A theoretical basis is presented for determining the significance of a residual stress distribution of arbitrary shape on the crack tip stress intensity factor for a centre-cracked plate as a function of crack length. The Fourier series based approach enables one to increasingly add more spatial definition to the stress field and thereby determine the level of detailed knowledge of the residual stress required to make a reliable assessment of structural integrity. The approach is applied to examples of measured symmetric distributions of residual stresses in welded plates and used to determine the significance of residual stress length-scales in fracture mechanics analysis.