RESEARCH PAPER The peak stress method for fatigue strength assessment of tube-to-flange welded joints under torsion loading Giovanni Meneghetti Received: 30 September 2012 / Accepted: 15 January 2013 / Published online: 7 February 2013 # International Institute of Welding 2013 Abstract It was shown in previous papers that in plane problems the elastic tangential stress and the elastic shear stress evaluated at the weld toe or at the root of fillet-welded joints by means of a finite element analy- sis, with a well-defined pattern of elements, are propor- tional to the mode I and mode II Notch Stress Intensity Factors (NSIFs), respectively. On the basis of such properties, the so-called Peak Stress Method (PSM) is a simplified, finite element-oriented application of the N-SIF approach to fatigue analysis of fillet-welded joints with un-machined weld seams. In the present paper, the PSM is extended to torsional loading condi- tions, which induce mode III stresses at the weld toe and at the weld root. First, it is shown that the finite value of the elastic anti-plane shear stress evaluated at the weld toe by means of a finite element analysis is directly proportional to the mode III N-SIF. Afterwards, taking advantage of the strain energy density criterion, an equivalent local stress is derived. Finally, a synthesis of experimental results of fatigue tests on tube-to-flange fillet welded joints subject to torsion loading and failing either from the weld toe or from the weld root is presented. Keywords (IIW Thesaurus) Welded joints . Fatigue . Design . Static fracture test . Finite element analysis . Weld Toes 1 Theoretical background: Notch-Stress Intensity Factors and Peak Stress Method for mode III loading 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. With ref- erence to conventional arc-welding technologies and un- machined welds, the weld toe and root radii ρ are set to zero, and the NSIFs quantify the intensity of the as- ymptotic stress distributions in the close neighbourhood of the notch tip [1–4]. Let us consider a typical welded joint geometry subjected to torsion loading, as depicted in Fig. 1. At the weld toe and root, mode III (anti- plane) shear stresses are present, as shown in the figure with reference to the weld toe side. While in plane problems, where mode I and mode II stresses are pres- ent, the degree of singularity of the stress fields was established by Williams [5], Qian and Hasebe [6] deter- mined the local stress distributions for mode III: t θz t rz   ρ¼0 ¼ K 3 ffiffiffiffiffi 2p p  r  11 3 ð Þ  cos 1 3 θ ð Þ sin 1 3 θ ð Þ   ð1Þ By extending the definition proposed by Gross and Mendelson [7] for mode I and II loadings, the mode III Notch-Stress Intensity Factor in Eq. (1) quantifies the intensity of the asymptotic stress distribution and can be defined as follows: K 3 ¼ ffiffiffiffiffi 2p p  lim r!0 t θz ð Þ θ¼0  r 11 3 ð Þ ð2Þ where the stress singularity exponent l 3 is given by: 1 3 ¼ p 2g ð3Þ Doc. IIW-2340, recommended for publication by Commission XIII "Fatigue of Welded Components and Structures". G. Meneghetti (*) Department of Industrial Engineering, University of Padua, Via Venezia, 1-35131 Padua, Italy e-mail: giovanni.meneghetti@unipd.it Weld World (2013) 57:265–275 DOI 10.1007/s40194-013-0022-x