13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- algorithm provided by Zhang (1995) [17] is adopted in this paper. The coalescence criterion 1, the plastic limit load criterion, and the coalescence criterion 2, the equivalent plastic strain criterion, are totally incorporated into the extended damage model, respectively. As the specimens are axisymmetric, eight-node axisymmetric element with reduce integration (CAX8R) are used in the finite analyses. The finite element meshes of specimens are presented in Fig. 2. The element length of the minimum section where failure will first initiate in the specimen is 0.15mm. API X65 steel is high strength and low alloy and the tensile properties of the present material are Yong’s modulus, 210.7 E= GPa; Poisson ratio, 0.3 ν= ; initial yield strength, 0 464.5 σ = MPa. The uniaxial true stress-strain relationship of the present API X65 steel is approximated using the Ramberg-Osgood form fitted to the test data by Oh et.al (2007) [15]. Figure 1. Geometries of notched tensile specimens Figure 2. Axisymmetric finite element meshes for notched tensile bars 3.1. Determination of damage model parameters In order to apply the present extended damage models to simulate ductile fracture, eight parameters should be first determined, including two adjustment factors for Gurson yield function ( 1q , 2q ); six parameters related to void volume fraction ( 0f , cf , Ff , Nε , Ns and Nf ). The classic values ( 1 1.5 q = and 2 1.0 q = ) given by Tvergaard (1982) [4] have been applied by many researchers as the constants for the GT model. Koplik and Needleman (1988) [18] carried out micromechanics studies about void growth and coalescence and found that the values of 1 1.25 q = and 2 1.0 q = provide best agreement between the GT model and the finite element results of voided cells calculations. Faleskog et al. (1998) [19] found that the q-values exhibit dependence
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