TECHNICAL PAPER K and J-Integral Variations Due to Residual Stresses in Welded Plates Rahman Seifi Received: 7 December 2010 / Accepted: 22 February 2012 / Published online: 21 April 2012 Ó Indian Institute of Metals 2012 Abstract Due to residual stress in a material, stress intensity factors (SIF) and also J-integral values are not constant and become path dependent parameters. Modified relations are used for calculations to take into account the effects of residual stresses. These relations give path independence values for the J-integrals in spite of existing the residual stresses. Effects of residual stresses due to welding on variations of SIF and J-integral are studied. Results have a good agreement with theoretical values obtained by weight function method. Through and surface cracks are considered on welded plate and distributions of J-integral on the crack front are obtained. Effects of lengths, depths and orientation angles of cracks are investigated due to applying only residual stress and also combination of residual and applied stresses. Redistribu- tions of residual stress are determined for welded plates with through cracks and compared with experimental results in literature. Keywords Surface crack  Residual stress  Stress intensity factor  J-integral  Weld 1 Introduction Welding plays a major role in industries. The final strength of welded structures is dependent on the welding quality. It was shown that the welding has four important effects on the parts: the physical properties of the base metal on the near zones of welded areas (heat affected zone HAZ) are changed. The weld metal properties are different and even weaker from the base metal. The welding process induces tension residual stresses in the affected zones. And finally, the different types of defects such as cracks may be formed. Residual tension stresses and weld flaws have critical effects on the integrity of the structures. With repeated loads of the static residual stress alters the fatigue life of components. The changes were introduced in both initia- tion and growth of fatigue cracks [1–3]. Also crack growth affects the redistribution of the residual stresses [4–9]. For study of the crack behavior in residual stress fields, it was necessary to determine these effects on the major param- eters of crack as stress intensity factors (SIF) and/or J-integral. With elastic behavior of materials under external loading and internal residual stress, researchers use the linear elastic fracture mechanics (LEFM) approach to determine the variations of SIF (K) [4, 5, 8–13]. If there is considerable plastic deformations on crack front areas, it is necessary to use the elastic–plastic fracture mechanics (EPFM) approach where crack behavior can be studied by using the J-integral [14–18]. For elastic deformations, we can use the principle of superposition to determine the effects of applied and residual stresses. In this method, the effects of various loads and stresses were determined individually [4, 5, 7–11]. For elasto-plastic behavior of materials, superposition method cannot be used and so determinations of the SIF values aren’t suitable for fracture study. In this case, the J-integral values are used which determined due to applied loadings and residual stresses [14–21]. In this paper, we determined the effects of residual stresses due to welding on the SIF and J-integral values for through and surface cracks. Also redistribution of the residual stresses due to existing of the crack were studied and compared with literature. R. Seifi (&) Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran e-mail: rseifi@basu.ac.ir 123 Trans Indian Inst Met (June 2012) 65(3):239–249 DOI 10.1007/s12666-012-0125-x