The GTN damage model based on Hill’48 anisotropic yield criterion and its application in sheet metal forming Chen Zhiying * , Dong Xianghuai National Die and Mold CAD Engineering Research Center, Shanghai Jiao Tong University, Shanghai 200030, China article info Article history: Received 28 January 2008 Received in revised form 11 July 2008 Accepted 15 July 2008 Available online 26 August 2008 PACS: 62.20.x 81.20.Hy 02.70.Dh Keywords: Porous material Ductile damage Anisotropy Sheet forming Finite element method abstract To predict the damage evolution of anisotropic plastic voided ductile materials, Gurson–Tvergaard– Needleman (GTN) yield criterion is developed based on Hill’s quadratic anisotropic yield criterion (1948) and isotropic hardening rule for matrix material. A user-defined subroutine is developed using the above model. An implicit stress integration procedure is modified to adapt the explicit dynamic sol- ver. After performing a series of single element tests, cylindrical tension and thick plate tension are ana- lyzed. Then a benchmark of NUMISHEET’2002, i.e. deep drawing of cylindrical cup, is taken as an example of sheet metal forming. Comparisons are made among the von Mises constitutive model, isotropic and anisotropic plastic GTN damage models. It is found that plastic anisotropy of the matrix in ductile sheet metal has influence on both deformation behavior and damage evolution of the material. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction In recent years, because of its lighter weight, good formability, corrosion resistance and recycling ability, excellent strength to weight ratio and lower emissions, aluminum alloy has been increasingly utilized in the automotive industry as an alternative to steel [1]. The formability of aluminum is limited, so understand- ing of damage development within its microstructure is of great importance [2,3]. Ductile failure process in metallic materials usually consists of three stages, i.e. micro-void nucleation, growth and coalescence. In order to model the plastic flow and fracture of ductile metals, Gurson [4] proposed an approximate mesoscopic yield function for porous materials considering the effects of hydrostatic stress [5]. The metal matrix is firstly assumed to be isotropic elastic-per- fectly plastic and incompressible obeying the von Mises yield func- tion. Tvergaard [6,7] modified the original model through introducing three additional fitting parameters. Now the GTN mod- el is one of well known mesomechanical models for ductile fracture. It has been used for different materials and processes [8–12]. Recently with the rapid development of aluminum alloy and high strength steel, suitable material models are required for accurately describing the plastic behavior in sheet metal forming. Owing to roll- ing processes, the sheet metal usually displays plastic anisotropy. The original Gurson porous plasticity theory can describe damage- induced material softening, but it is not precise for the sheet metals because the matrix material is assumed to be isotropic. There are limited studies on the Gurson-type porous anisotropic plasticity theory. Gologanu et al. [13] extended the Gurson model incorporating void shape effects. Based on Hill’48 quadratic yield criterion, Liao et al. [14] developed an approximate yield criterion for anisotropic porous sheet metals under plane stress condition. Then Chien et al. [15] validated this model by using a three-dimen- sional finite element analysis of a cube containing a spherical void. Three fitting parameters were adopted as proposed by Tvergaard [6,7]. Doege et al. [16] proposed an anisotropic GTN model to sim- ulate a 2D cup deep drawing process. Brunet et al. [17,18] used the anisotropic GTN model to compute the forming limit diagram for sheet metal forming. Prat and Grange et al. [10,19,20] applied the modified anisotropic GTN model to analyze the structural behav- iors and rupture modes of hydrided Zircaloy-4 tubes and sheets. Like Liao’s work, Chen et al. [21] developed a GTN type model through characterizing the matrix material of aluminum with Bar- lat’91 [22] six-component anisotropic constitutive model. 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.07.020 * Corresponding author. Tel.: +86 021 6281 3430; fax: +86 021 6281 3435. E-mail address: chenzhying@gmail.com (C. Zhiying). Computational Materials Science 44 (2009) 1013–1021 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci