13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Analysis of Metallic Ductile Fracture by extended Gurson models Wei Jiang1,*, Yazhi Li1, Yixiu Shu1, Zhenxing Fan1 1 Department of Aeronautics, Northwestern Polythchnical University, 710000, China * Corresponding author: jiangwei0525@mail.nwpu.edu.cn Abstract Ductile fracture of metallic materials is usually the result of void nucleation, growth and coalescence. The original Gurson-Tvergaard (GT) model deals with the homogenous deformation related to void nucleation and growth. However, it takes no consideration on the localized deformation due to the void coalescence. In this paper extended GT damage models incorporating two different void coalescence criteria are developed, respectively. One of the void coalescence criteria is based on the plastic limit load model by Thomason; the other decides the onset of void coalescence by a critical equivalent plastic strain as a power law of stress triaxiality (defined by the ratio of the hydrostatic stress over the equivalent stress). Hence, void coalescence is controlled by physical mechanisms, rather than by a critical void volume fraction which cannot be taken as a constant. The extended constitutive models are implemented into an implicit finite element code via a user defined material subroutine (UMAT) in ABAQUS. Detail analyses are performed for a series of notched round tensile bars. The predictions of the fracture behavior based on the proposed approach, from void nucleation to final material failure, are compared with experiment data. Both results agree pretty well. In the end, the effects of stress triaxiality are discussed. Keywords ductile failure, mechanism-based approach, Gurson model, void coalescence 1. Introduction Mechanism-based fracture mechanics attempts to link micro-structural variables and continuum properties of material to macroscopic fracture behavior. The macroscopic ductile fracture process due to the presence of voids can be separated into two phases, the homogenous deformation with void nucleation and growth, and the localized deformation due to void coalescence (Zhang et al., 2000) [1].The famous porous material model for analyzing the ductile failure, in which the material yielding is coupled with damage (void volume fraction, f ) and hydrostatic stress, was proposed by Gurson (1977) [2]. Tvergaard (1981, 1982) [3], [4] modified Gurson model by introducing two adjustment factors to account for void interaction effects and material strain hardening. Needleman and Tvergaard (1984) [5] extended Gurson model to simulate the rapid loss of load carrying capacity during void coalescence. Chu and Needleman (1980) [6] supplemented it by various kinds of void nucleation criteria. In the early research, the criterion for the onset of void coalescence states that void coalescence starts at a critical void volume fraction cf which has tend to be regarded as a material constant. However, further studies show that cf depends strongly on parameters such as initial void volume fraction, void shape, void spacing, stress triaxiality, as well as strain hardening, etc.(Zhang et al., 2000; Pardoen and Hutchinson, 2000) [1], [7]. Thomason (1985, 1998) [8], [9] proposed a plastic limit load model for void coalescence. In this model, the start of void coalescence is controlled by the mechanism of the plastic localization in the void ligament, which is able to unify the material and stress states dependencies. Bao (2005) [10] conducted a series of experiments and finite element analyses on an aluminum alloy 2024-T351 and obtained a coalescence criterion in terms of the critical equivalent strain cE as a function of the stress triaxiality ratio T . When the macroscopic equivalent strain reaches the critical value cE , void coalescence occurs and the material quickly loses its load carrying capacity. However, Gao and Kim (2006) [11] argued that the extra parameter lode angle θshould be introduced and the critical equivalent strain should have the
RkJQdWJsaXNoZXIy MjM0NDE=