Plane strain transversely anisotropic analysis in sheet metal forming simulation using 6-component Barlat yield function
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Plane strain transversely anisotropic analysis in sheet metal forming simulation using 6-component Barlat yield function Jinyan Wang • Jixian Sun
Received: 1 September 2011 / Accepted: 13 August 2012 / Published online: 19 September 2012 Ó The Author(s) 2012. This article is published with open access at Springerlink.com
Abstract In most FEM codes, the isotropic-elastic and transversely anisotropic-elastoplastic model using Hill’s yield function has been widely adopted in 3D shell elements (modified to meet the plane stress condition) and 3D solid elements. However, when the 4-node quadrilateral plane strain or axisymmetric element is used for 2D sheet metal forming simulation, the above transversely anisotropic Hill model is not available in some FEM code like Ls-Dyna. A novel approach for explicit analysis of transversely anisotropic 2D sheet metal forming using 6-component Barlat yield function is elaborated in detail in this paper, the related formula between the material anisotropic coefficients in Barlat yield function and the Lankford parameters are derived directly. Numerical 2D results obtained from the novel approach fit well with the 3D solution. Keywords 4-Node quadrilateral element Transversely anisotropic Sheet metal forming
J. Wang (&) School of Material Engineering, Shanghai University of Engineering Science, Shanghai 201620, China e-mail: [email protected] J. Sun Livermore Software Technology Corporation, 1740 W. Big Beaver Rd., Troy, MI 48084, USA e-mail: [email protected]
1 Introduction In order to accurately simulate sheet metal forming processes, it is essential to describe correctly the material constitutive behaviors. Since most sheet metals exhibit anisotropic material behaviors, the use of appropriate anisotropic yield criterion is important to predict material behaviors accurately. Moreover, anisotropy has an important effect on the strain distribution in sheet metal forming process, and it is closely related to thinning and formability of sheet metal, so the anisotropy of the material should be properly considered to capture the realistic material behaviors. The influence of plastic anisotropy on sheet metal forming has been studied with the help of FEM codes combined with appropriate anisotropic yield functions. Many such functions have been proposed. The quadratic yield function by Hill (1948) has long been one of the popular choices to represent planar anisotropy and has been widely used in FEM forming simulation. Several non-quadratic criteria were developed by Hill (1979, 1990), Hershey (1954), Hosford (1972), Bassani (1977), Gotoh (1977), Logan and Hosford (1980), Barlat and Lian (1989), Karafillis and Boyce (1993), Bron and Besson (2004), Banabic et al. (2005) and Barlat et al. (1991, 1997, 2003, 2005). In general, Hill (1948) has been useful for explaining phenomena associated to anisotropic plasticity particularly for steels, the others can be used to improve the yielding description of aluminum alloys. But in
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many circumstances Yld89 (Barlat and Lian 1989),
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