An Improved Method of Evaluating the Stress Intensity Factor for a Penetrating Circumferential Defect in a Self-Balancing Residual Stress Field in a Weld

Abstract

It is required to determine the stress intensity factor (SIF) contributed from a through-wall residual stress distribution when assessing the structural integrity of a welded joint containing flaws. By decomposing the through-wall residual stress distribution into a membrane stress component (σm), bending stress component (σb) and self-balancing stress component (σsb), the total SIF from the through-wall residual stress distribution (Ktotal) comprises Km (due to σm), Kb (due to σb) and Ksb (due to σsb). Km and Kb can be relatively easy to determine as there are standard solutions available for common geometries and flaw types. However, it is not straightforward to calculate Ksb owing to the arbitrary distribution of the self-balancing stress component. In particular, no SIF solutions are available for a through-wall penetrating defect in a plate or a cylinder subjected to an arbitrary through-wall self-balancing stress distribution other than for three special distributions (cosine, triangular and square distributions). Neglecting the contribution of σsb to the Ktotal could significantly underestimate the crack driving force, thus leading to a non-conservative assessment of limiting defect size. Therefore, the calculation of Ksb for a though-wall penetrating defect in a plate or a cylinder under an arbitrary stress distribution is of the primary concern in this work. Understandably, finite element analysis (FEA) can be used to calculate the Ksb in these situations, but it is costly to perform such analysis. In this work, a simple method is proposed for estimating Ksb due to the self-balancing component which has a different distribution from the cosine, triangular and square distributions. This method is an extension of the approach adopted by Annex Q, BS 7910:2013 in dealing with the calculations of Ksb resulted from the σsb profiles which are decomposed from the proposed upper bound through-wall welding residual stress profiles. Some typical through-wall welding residual stress distributions are investigated with the proposed method in estimation of the Ksb for a through-wall penetrating defect in a plate or a cylinder. Discussion and highlights are given in the aspects of the effects of welding residual stress profiles on SIFs, the implications for limiting defect sizes, and the likelihood of underestimating the Ksb when using the equation established in R6 Revision 4 with a cosine distribution for any other distributions.