International Journal of Fatigue 21 (1999) 1063–1078 www.elsevier.com/locate/ijfatigue Relationships between local and structural stress in the evaluation of the weld toe stress distribution Roberto Tovo * , Paolo Lazzarin Department of Engineering, University of Ferrara, v. Saragat 1, I-44100 Ferrara, Italy Received 16 December 1998; received in revised form 23 June 1999; accepted 25 June 1999 Abstract This paper deals with the problem of determining, by proper stress analyses, the stress fields near arc-welded joint toes and the use of such distributions in fatigue strength predictions. In particular, the relationships between the local stress field and the structural (geometrical) stress field are investigated under the hypothesis that highly stressed zones remain under linear elastic conditions. The local stress distribution is given for different joints in terms of the relevant notch stress intensity factors (NSIFs), having modelled their weld beads like re-entrant sharp corners. The structural stress distribution is, in contrast, the stress field linearly distributed through the thickness of the welded plates (and sometimes on the plate surfaces), beyond the zone affected by local effects due to the beads. The aim of the proposed methodology is to provide an explicit link between NSIF values and structural stress at a well-defined distance from the weld toe. Such a distance is chosen equal to the main plate thickness. The expressions obtained allow a direct comparison with the well-known “hot-spot stress” approach; it is demonstrated that there are circumstances of practical interest in which the usual hot-spot stress (which is the simple linear extrapolation at the weld root of the structural field) is not able to predict accurately the fatigue behaviour of the joints, whereas the combination of structural field and NSIF-based field is more advantageous. The complete methodology can be simplified for rapid calculations involving weldments of different types. Some examples are also reported and discussed.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Stress analysis; Notches; Welded joints; Fatigue 1. Introduction The problem of evaluating the stress field close to the toe of welded joints and its relationship to weld strength are discussed at large in the literature, particularly as far as fatigue behaviour is concerned. The current approaches can be divided into different categories depending on the type of stress analysis performed on the structural details [1]: one can distinguish criteria based on nominal stress, structural stress and local stress, as well as other methodologies based on residual life predictions carried out, according to linear elastic frac- ture mechanics, on the basis on detected real defects or undetected, assumed crack-like defects. The most recent standards and proposals for standards * Corresponding author. Tel.: + 39-0532-293-820; fax: + 39-0532- 768-602. E-mail address: tovo@ing.unife.it (R. Tovo) 0142-1123/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII:S0142-1123(99)00089-4 [2–6] present such approaches separately, by dis- tinguishing different application fields. However, regard- less of the stress analysis performed by the designer, the fatigue failures are local phenomena. For this reason, in the fatigue design of non-welded details, the prediction of crack initiation is based on maximum values of stress and strain at the notch root. Also, the fatigue crack propagation takes into account the local stress distri- bution usually influenced by local geometrical stress rai- sers. The main problem in extending these criteria to the fatigue of welded joints is the degree of arbitrariness caused by the scatter of the actual geometrical weld shape and the difficulty in defining an exact value for the geometrical parameters [7]. However, several authors have shown the possibility of efficiently model- ling the real arc-weld geometry, which is randomly vari- able, as an ideal triangular-shaped geometry [8–10]; that is, an open notch with an opening angle in most cases equal to 135°.