Analysis of forming limits based on a new ductile damage criterion in St14 steel sheets Xinkai Ma, Fuguo Li ⇑ , Jinghui Li, Qianru Wang, Zhangwei Yuan, Yong Fang State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China article info Article history: Received 28 September 2014 Accepted 18 December 2014 Available online 27 December 2014 Keywords: Ductile damage criterion Forming limit diagram Numerical simulation Nakazima’s test abstract Analytical and numerical analyses of forming limit in sheet metal hydraulic bulging test under combined internal pressure and independent axial feeding are researched in this paper. To predict the initiation of fracture, a new normalized ductile damage criterion based on strain hardening exponent, stress triaxiality and strain lode parameters are adopted. Eventually, elastic modulus is chosen as a characterization parameter to measure the ductile damage during the process of plastic deformation of the material. In addition, the explicit expressions of elastoplastic constitutive equations related to this damage criterion are compiled and implemented in ABAQUS/CAE software as the user subroutines. After compared against the analytical and the experimental forming limit diagrams (FLDs), the simulative FLDs demonstrate to be reasonable so that this model can be extended to predict a wide range of sheet metals’ forming processes. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Sheet metal forming is widely used for producing various struc- tural components, especially in automotive and aeronautic indus- tries [1]. Forming limit diagrams (FLDs) are commonly used in evaluating the workability of sheet metals and diagnosing produc- tion problems in the forming processes. The formability analysis was required to determine whether the amount of deformation exceeds the forming limit at any point of the formed part. The formability limit of sheet metal and tube are usually determined by the initiation of localized necking that precedes fracture [2,3]. Marciniak and Kuczynski [4] presented the most well-known method (e.g., the M–K theory) to calculate sheet metal forming limits. They assumed that an initial inhomogeneity in the thickness of the material was existent, and they assessed plastic instability phenomenon using two-zone model. In literature, there are many researches (e.g. [5–8]), using the M–K method to obtain the FLDs. Yoshida et al. [9] simulated the hemispherical punch stretching using the elasto-plastic three-dimensional finite element program ‘‘ROBUST’’. They predicted the limited cup height and rupture loca- tion for mild steels, high-strength steels, austenitic stainless steels, and aluminum alloy using FE calculation results and FLD curve pro- posed by Storen and Rice [10]. They found that the calculated results are in well accordance with the experimental results. Therefore, numerical analysis is proposed for the forming limits. Some researchers have presented a methodology to predict the forming limit stress diagram (FLSD) and to reexamine the effect of strain path or through-thickness normal stress on it [6,11]. The methodology is based on the M–K model. To calculate sheet metal limiting strains and stresses, a numerical approach applying the modified Newton–Raphson with globally convergence method has been used. The evaluation of the theoretical results has been performed by using the published experimental data for ST12 low carbon steel alloy. Hashemi et al. [12] investigated the influence of sheet thickness on sheet metal forming limits. Some investigations indicate that it is worthwhile to consider the effect of thickness on the forming limit diagrams, while others suggest that it is of less importance. His results strongly support the conclusion that the absolute value of the thickness has no influence on forming limits of St14 steel sheet. Besides he [13]also established an extended strain-based FLD based on equivalent plastic strains and materials flow direc- tion at the end of forming, which showed much less strain path dependent than the conventional FLD and more easier to use and interpretation than FLSD. The extended strain-based FLD was verified by some available published experimental [14–17]. Drucker [18] and later Hill [19] introduced a general condition for non-bifurcation which was based on the positiveness of the second-order work. This primarily diffuse necking criterion pro- vides a lower bound and appears to be too conservative for the accurate prediction of FLDs in practical applications [20]. Ozturk and Lee [21] pointed out that all the common criteria could not be used to determine the FLD of sheet metal alone. A http://dx.doi.org/10.1016/j.matdes.2014.12.029 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +86 29 88474117; fax: +86 29 88492642. E-mail address: [email protected] (F. Li). Materials and Design 68 (2015) 134–145 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes
Analysis of forming limits based on a new ductile damage criterion in St14 steel sheets
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