Issue34

Y. Sumi, Frattura ed Integrità Strutturale, 34 (2015) 42-58; DOI: 10.3221/IGF-ESIS.34.04 54 In this case, the conditions corresponding to the crack propagation in the base metal and along butt-weld should be clearly distinguished for the evaluation of the crack arrest capability of welded structures. We shall review some analytical studies in the following subsection. Analytical Model for Crack Path Prediction Investigations are made for a butt-weld joint under a uniaxial tensile stress a  applied normal to the joint [7]. The longitudinal component of welding residual stress r  is assumed to be constant in the region under consideration. As shown in Fig. 10, the initial crack of length 2 a is assumed to be parallel to the welding line. Material deterioration is observed along the heat-affected zone, which is modeled as a line degradation being also parallel to the welding line at a distance S L from the initial crack line. The resistance forces of crack propagation are denoted by c G for base and weld metals, and * c G for the degradation zones, respectively. Brittle crack propagation is assumed to occur from the right-hand side of the crack tip, at which we choose the origin of the Cartesian coordinate system 1 2 O x x  . Since a slightly kinked and curved crack extension may be expected, the crack intersects the degradation line at an angle *  with * 1 x h  . Figure 10 : A mathematical modeling of curved crack propagation along butt-weld. Figure 11 : Crack path destabilizing factors * / α S    and * / α S    [7, 16]. As far as the initial crack tip is embedded in a homogeneous material, a crack path can be determined by the local symmetry criterion by Eqs.(35)-(37), using the stress field parameters such as k I , k II and etc . at the original crack tip. This will simply lead to 0       under the pure Mode-I condition, but this straight crack extension could occur only for the perfect system, which means that the loading condition and the geometry have the perfect symmetry with respect to the crack line. We consider that non-collinear crack propagation is caused by some load-induced or material-induced