604 International Journal of Basic Sciences & Applied Research. Vol., 3 (7), 406-418, 2014 Available online at http://www.isicenter.org ISSN 2147-3749 ©2014 Application of an Extended Strain-Based Forming Limit Curve in Finite Element Simulation of X-Branch Hydroforming R. Hashemi 1* , G. Faraji 2 , A. Shahbazi Mastan Abad 2 , K. Abrinia 2 1 School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran 2 School of Mechanical Engineering , College of Engineering, University of Tehran, Tehran, Iran * Corresponding Author Email: rhashemi@iust.ac.ir Abstract This work presents a numerical framework that implements extended forming limit curves (FLCs) to predict bursting during tube hydroforming process. Here, at first, the extended FLC is calculated for tube material based on the generalized M-K model that takes the through thickness normal stress into account. As a case study, the forming process of X-shaped branch is simulated by ABAQUS/EXPLICIT commercial finite element package. The required incremental plastic equivalent strain and strain ratio, which are required for comparison with the computed extended FLC, are extracted from the results of FE simulation. The robustness of the extended FLC in prediction of necking is tested by comparing with the published experimental data where a satisfactory agreement is found. Keywords: Tube hydroforming, Finite element analysis, Extended strain-based forming limit curve, Generalized M-K model. Introduction Tube hydroforming is a complex metal forming process, which its performance depends on various design parameters including proper geometrical design of the part, its material and the implied boundary conditions. Because of this complexity, various researchers have employed numerical simulation techniques, such as FE analysis, to study the behavior of the hydroforming process (Pourboghrat et al., 2013; Alaswad et al., 2012; Yoon & Stoughton, 2009; Jansson et al., 2008). Bursting is a major design parameter in tube hydroforming which happens as a result of necking of the tube wall. Thus, predicting the necking of the tube is essential step before conducting the detail-design of the processes. Forming limit curves, or FLCs, are a common tool that is used by researcher to predict the onset of the necking in tube hydroforming process (Kim et al., 2004; Hashemi et al., 2009; Hwang et al., 2009). These curves are usually depends on the adopted pre-defined strain paths, which their effect on the FLCs are examined by applying various bilinear strain paths i.e. non-proportional loading histories. Because of high sensitivity of FLCs to the strain path, these curves are not a valid reference for evaluation of the formability in sheet metal forming processes which undergo non-proportional loading paths (Graf & Hosford, 1993; Assempour et al., 2009; Djavanroodi & Derogar, 2010; Shakeri et al., 2000: Marciniak Z., Kuczynski et al., 1967). To reduce the path-dependency of FLCs, instead of strain, stress can be used to as the criterion for the necking. This strategy leads to stress-based forming limit curve or forming limit stress curve or FLSC (Stoughton & Yoon, 2011, 2012; Zimniak, 2000; Nurcheshmeh & Green, 2011; Stoughton & Zhu, 2004). However, because of technical difficulties in finding a proper estimation of the stress level in stamped parts, from application point of view, FLSCs cannot be easily used on the shop floor (Zeng et al., 2009; Nurcheshmeh & Green, 2014). Recently, a new strain-based forming limit criterion has been presented to evaluate necking for sheet metal forming simulations when strain paths are not linear (Stoughton & Yoon, 2012; Zeng et al., 2009). The novelty of this proposed technique is that the FLC is constructed based on the effective strains and material flow direction at the end of forming process (i.e., an extended strain-based forming limit curve). This criterion has the advantages of both FLSCs for their path-independence and the conventional FLCs for their ease of interpretation and implementation in press shops. A through-thickness normal stress has effect on prediction of the FLC, e.g. increasing the absolute value of the through thickness compressive normal stress shifts the FLC up (Smith et al., 2003; Allwood & Shouler, 2009). This stress state happens during tube hydroforming process where the tube contacts the tool surface. Therefore, the effect of the through-thickness compressive normal stress should be considered in prediction of extended FLCs. In this paper, the extended strain-based forming limit curve for necking prediction which is based on the M-K model is presented and used in tube hydroforming. As soon as the tube has contacted the surface of the forming tool, it is not under plane stress condition anymore and thus this assumption is not adopted