Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes Tae-Kwang Song a , Yun-Jae Kim a, * , Chang-Kyun Oh b , Tae-Eun Jin b , Jong-Sung Kim c a Department of Mechanical Engineering, Korea University, 5 Ka, Anam-dong, Sungbuk-Ku, Seoul 136-713, Republic of Korea b Korea Power Engineering Company, Yongin-si, Gyeonggi-do 449-713, Republic of Korea c Department of Mechanical Engineering, Sunchon National University, Sunchon, Jeonnam 540-742, Republic of Korea article info Article history: Received 14 June 2007 Received in revised form 19 February 2009 Accepted 5 March 2009 Keywords: Circumferential crack Elbow Elastic–plastic J Finite element limit analysis In-plane bending Net-section limit load Reference stress approach abstract This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load- carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Developing assessment methods of crack-like defects in piping components is important in structural integrity assessment and plant life extension. Significant efforts in developing crack-like defect assessment methods have been made for the last three decades, resulting in a number of methods (see for instance Refs. [1–8]). Among them, one popular method is the net-section stress approach based on limit load analysis [3,4]. Plastic limit load results can be used directly to estimate maximum load-carrying capacities of cracked components, when the material of interest is sufficiently ductile. Furthermore, in the reference stress approach [9,10], adopted in various defect assessment codes [5–8], a limit load can be an important input to calculate the reference stress and thus to estimate elastic–plastic J. For cracked straight pipes, plastic limit load solutions have been well documented (see e.g., Refs. [11–14]). For cracked elbows, several researchers performed both experimental and numerical works to investigate the effect of cracks on plastic limit loads [15–19]. The authors also proposed closed-form approximations of plastic limit loads for circumferential cracked elbows under in-plane bending, via small strain three-dimen- sional (3-D) finite element (FE) limit analyses using elastic– perfectly plastic materials [20,21]. It should be noted that, in the above works, cracks are assumed to be in the centre of the elbows. On the other hand, in piping systems, elbows are often welded to straight pipes. As welded regions are vulnerable to cracking, cracks could occur in welds between elbows and straight pipes, which need to be assessed. One might argue that the crack could be assumed to be located in the straight pipe and thus the solutions for cracked straight pipes could be used to assess cracks in welds between elbows and straight pipes. It will be shown in this work, however, that such an assumption could significantly overestimate the limit load, implying that such a procedure could lead to non-conservative results. Thus a proper crack-like defect assessment method needs to be developed for cracks in welds between elbows and straight pipes. This paper firstly presents limit moments for circumferential cracks in welds between elbows and straight pipes subject to in- plane bending, via small strain FE limit analyses using elastic– perfectly plastic materials. Both circumferential part-through surface cracks and circumferential through-wall cracks (as a limiting case) are considered. Then, based on the proposed * Corresponding author. Tel.: þ82 2 3290 3372; fax: þ82 31 290 5276. E-mail address: kimy0308@korea.ac.kr (Y.-J. Kim). Contents lists available at ScienceDirect International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp 0308-0161/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2009.03.008 International Journal of Pressure Vessels and Piping 86 (2009) 495–507