The use of peak stresses for fatigue strength assessments of welded lap joints and cover plates with toe and root failures Giovanni Meneghetti ⇑ Department of Industrial Engineering, University of Padova, Via Venezia, 1, 35131 Padova, Italy article info Article history: Received 24 August 2011 Received in revised form 2 March 2012 Accepted 6 April 2012 Keywords: Local approaches Notch stress intensity factors Strain energy density Finite elements Coarse mesh Welded joints abstract In its original formulation the Peak Stress Method (PSM) was adopted to assess the fatigue strength when only mode I stresses are singular (for example at the toe of fillet-welds) or significant (for example at the root of load-carrying fillet welded cruciforms). Nevertheless in welded lap joints and cover plates both mode I and mode II stresses are singular at the weld root, where fatigue cracks are likely to initiate. In the present paper the PSM is extended to mode II loading conditions and then an equivalent peak stress is derived, which is used to assess either weld toe or weld root fatigue failures. Ó 2012 Elsevier Ltd. All rights reserved. 1. Theoretical background: notch-stress intensity factors and local strain energy density According to the Notch-Stress Intensity Factor (NSIF) approach, the fatigue strength assessment of welded joints failing from the weld toe or the weld root is treated essentially as a notch effect problem. Since the weld toe and root radii q cannot be precisely defined and conventional arc-welding technologies lead to small q values [1–3], they are set to zero and the NSIFs quantify the intensity of the asymptotic stress distributions in the close neighbourhood of the notch tip, as depicted by Fig. 1. In plane problems, the degree of the singularity of the stress fields due to re-entrant corners was established by Williams [4] both for mode I and mode II loading. By using a polar coordinate system (r, h) having the origin located at the sharp notch tip, the NSIFs related to mode I and mode II stress distributions are [5]: K 1 ¼ ffiffiffiffiffiffi 2p p  lim r!0 ½ðr hh Þ h¼0  r 1k 1  ð1Þ K 2 ¼ ffiffiffiffiffiffi 2p p  lim r!0 ½ðs rh Þ h¼0  r 1k 2  ð2Þ where r hh and s rh are the stress components according to the coordinate system shown in Fig. 1 and k 1 and k 2 are Williams’ first eigenvalues for mode I and mode II, respectively. In plane problems Lazzarin and Tovo gave the analytical expressions of the local stress field close to the V-notch tip as a function of the mode I and mode II NSIFs [6]: 0013-7944/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfracmech.2012.04.007 ⇑ Tel.: +39 049 8276751; fax: +39 049 8276785. E-mail address: giovanni.meneghetti@unipd.it Engineering Fracture Mechanics 89 (2012) 40–51 Contents lists available at SciVerse ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech