Fatigue tests on tubular joints have shown that as a crack propagates through the chord wall, it curves under the weld toe. This produces, at the brace-chord intersection, a doubly curved semi-elliptical crack emanating from the weld toe. A doubly curved crack in a tubular joint is a very complex geometry which has proved to be difficult to model. In consequence, previous work on the evaluation of stress intensity factors in tubular joints adopted a simplified approach, ignoring the crack curvature under the weld toe. However, in the absence of benchmark solutions, the effects of any modelling approximation on accuracy are impossible to quantify. To address this problem and as part of the research on fatigue assessment methodologies, a technique which is able to accurately model doubly curved cracks in tubular T-joints has been developed at University of Wales, Swansea. This paper describes a detailed account of the generation of the finite element model and the procedure for evaluating the stress intensity factor solutions. The validation results are also presented to demonstrate the reliability of the model developed. Notation a b e h 11,2,3 ml,2,3 nl,2,3 T t Ur Vn Wt D G K /r(I, II, III M~ Mk Mk3-D Q SCF SIF T Cf 3' A KNhs ~ nora ¢ = crack depth = plate width = crack half width = plate length = local radial direction cosines = local normal direction cosines = local tangential direction cosines = radial distance or weld toe radius = attachment thickness = local radial displacement = local normal displacement = local tangential displacement = chord diameter = elastic shear modulus = stress intensity factor = mode I, II, III stress intensity factors = correction factor for 3-D effects = 2-D attachment correction factor = 3-D attachment correction factor = elliptic crack correction factor = stress concentration factor = stress intensity factor = main plate thickness = length/half diameter (chord) = brace diameter/chord diameter = half diameter/thickness (chord) = stress intensity factor range = hot spot strain = nominal strain = parametric crack front angle 130 D. Bowness and M.M.K. Lee O'hs = hot spot s t r e s s O'nom -~-nominal s t r e s s z, = Poisson's ratio r = brace thickness/chord thickness 0 = radial angle ¢ = weld angle

Weld toe magnification factors are widely used in the evaluation of stress intensity factors for cracks in welded structures. Traditionally, the weld magnification factor has been determined from 2-D plane strain models containing edge cracks. However, it has long been recognised that a semi-elliptical weld toe crack cannot be accurately represented by a 2-D approximation due to the 3-D nature of the geometry. As a consequence, some recent research has been carried out using 3-D numerical modelling, which highlights the limitations of the 2-D approach. Nevertheless, 3-D solutions are still scarce and are of limited validity due to the difficulties associated with creating the numerical models. This paper reports the most extensive 3-D numerical investigation of semi-elliptical cracks in T-butt geometries to date. Based on the numerical results, new and accurate equations for weld magnification factors were derived, which quantify the 3-D effects present and emphasise the importance of the attachment. The results obtained from these equations are then used in an assessment of existing solutions.

Torsional rigidity is an important performance related property of an automotive body-in-white (BIW) structure, which consists of many box hat structures or box sections. An experimental study has been carried out to determine mainly the torsional stiffness but also the elastic limit and the strength of spot-welded and adhesively bonded (and weld-bonded) box sections. The relative contribution of a variety of factors, including joining system used, steel strength, sheet thickness, section area and section design, to the properties of box sections was analysed using factorial design experimentation techniques. It was found that a significant increase in torsional stiffness could be achieved by changing the joining technique, increasing the sheet thickness, increasing the section area and, to a lesser extent, changing the section design. The results are examined and discussed in the context of weight reduction in automotive structures.