Fatigue growth prediction of elliptical cracks in welded joint structure: Hybrid and energy density approach B.K. Hachi a , Y. Belkacemi b , S. Rechak b, * , M. Haboussi c , M. Taghite c a Department of Mechanical Engineering, Djelfa University, BP 3117 Ain-Cheih, 17000 DJELFA, Algeria b LGMD, Department of Mechanical Engineering, E.N.P., BP 182 Harrach, 16200 ALGIERS, Algeria c LEMTA, Nancy-University, CNRS, 2 avenue de la Forêt de Haye, BP 160, 54504 VANDOEUVRE CEDEX, France article info Article history: Available online 19 June 2010 Keywords: Fatigue crack growth Strain energy density factor Stress intensity factor Weight function Elliptical crack Welded joints abstract A hybrid weight function approach (HWFM) is presented for the fatigue life prediction of infinite body and welded joint structure containing elliptical cracks. A self-containing computer code has been devel- oped for this purpose. Numerical computations were first conducted on cracked infinite body showing a physical fact, that the elliptical shape of the crack becomes circular during its evolution. The prediction of the fatigue crack growth shows that the present results are in perfect concordance with those reported in the literature. Then, numerical tests were carried out on two types of specimens of welded joint structure. The present results were compared to the experimental and predicted ones of other authors, demonstrat- ing that the hybridization method is a powerful numerical technique, and that the SEDF approach (using the Sih’s law) is more valid for the critical cases of welded joints than the SIF approach (using the Paris law). A parametric study has been conducted on the stress ratio ‘‘R” showing that the fatigue life to failure decreases with the increase of ‘‘R”. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Fatigue life prediction of elliptically cracked infinite body and welded joint structure were reported in the literature by many researchers [1–4], in which the well-known Paris law [5] based on the stress intensity factor (SIF) approach has been used. Other studies [6–10], using strain energy density factor (SEDF) approach known as Sih’s law [11], have also been attempted in the analysis of fatigue crack growth of such structures. In those last investiga- tions, the using of the SEDF approach has permitted the taking into account of the influence of the mixed mode and the stress ratio R. Those two physical factors, when included, certainly give better estimation of the fatigue crack growth. The present study has two main folds. The first one, is to present an alternative numerical technique based on the hybridization of weight functions and to show its efficiency in the treatment of fatigue crack growth through applications of cracked infinite bodies and of welded industrial structures. The novelty of the method is to hybrid among two existing weight functions, and to divide the crack into two regions [12–14]. The second one, is a comparative study between the usage of the SEDF approach and the other laws based on the SIF approach in the fatigue life prediction of welded joints struc- ture by varying two of the loading parameters: the stress range Dr = r max  r min , and the stress ratio R = r min /r max , for two cases of the curvature radius of welded joints (q = 0 mm, q = 30 mm). Hence, the numerical computations are carried out via HWFM (the self-containing computer software based on the present hybrid weight function approach). In the first application, a ductile infinite body containing penny-shaped and elliptical crack were considered. As long as the shape is concerned, an elliptical crack becomes circular during its fatigue growth evolution which is in perfect agreement with the results reported in the literature [3,4]. In a sense, this application serves to validate the proposed approach. The second type of application deals with a mechanical component named ‘‘out-of-plane gusset welded joint” which is a part of airplane structure [8]. It is observed that the radius of cur- vature of the welded joints had some effects not only on the fatigue life of the considered structure, but also on the efficiency of fatigue crack growth models, i.e. the SEDF and the SIF based models. A parametric study conducted on the stress ratio R demon- strates that the fatigue crack growth model based on the SEDF ap- proach estimates better the fatigue life of such components. It is also observed that, as the stress ratio parameter ‘‘R” increases, the fatigue life to failure decreases. In the next section, the hybridization technique is briefly pre- sented along with its implementation in fatigue. In Section 3, we present the results obtained via the HWFM using both SIF and SEDF approaches. At the end of the same section, the results were discussed in which a comparison between the two fatigue crack 0167-8442/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tafmec.2010.06.010 * Corresponding author. E-mail address: srechak@hotmail.com (S. Rechak). Theoretical and Applied Fracture Mechanics 54 (2010) 11–18 Contents lists available at ScienceDirect Theoretical and Applied Fracture Mechanics journal homepage: www.elsevier.com/locate/tafmec