13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- (b) Flat-ended projectile Figure 1. Finite element model for Weldox460E steel plate struck normally by conical-nosed and flat-ended projectile. As shown in Fig.1, the target was meshed with eight node brick elements, and all the meshes contained three regions: a finely zoned region which had noticeable effect on computational accuracy, a coarsely zoned region which did not have noticeable effect on computational accuracy, and a transitional region between the two regions above. The meshing method adopted here resolved the contradiction between mesh size and computational accuracy and efficiency to some extent. The element size in finely zoned region was taken to be 0.3mm×0.3mm×0.3mm approximately [5][9]. The diameter of the finely zoned region was 18mm (about 1.5 times as great as projectile diameter). The element size in transitional region and coarsely zoned region was increased from the central part to the outer part of the target. The element type used in the model was 8-node reduced integration elements (C3D8R). Contact between the projectile and target was assigned using the general contact algorithm. The value of coefficient of friction was hard to be measured accurately from experiments, and often taken to be 0~0.05 in literatures for penetration and perforation of metal plates by conical-nosed projectiles [5][7][11][13], and a coefficient of friction of 0.03 was considered here. For the perforation of Weldox460E steel plates by flat-end projectiles, a coefficient of friction of 0.0 was considered [10-12]. 2.2. Constitutive relation The modified Johnson-Cook constitutive relation is adopted for Weldox460E steel target [6]. The model includes linear thermoelasticity, the von Mises yield criterion, the associated flow rule, isotropic strain hardening, strain-rate hardening and softening due to adiabatic heating, and is valid for metals subjected to large strains, high strain rates and high temperatures. The equivalent stress is expressed as * * 1 1 c n m eq eq eq A B T (1) where A，B，C，n，m are material constants; εeq is the equivalent plastic strain; * 0 eq eq is the dimensionless strain rate, where 0 is a user-defined reference strain rate; * r m r T T T T T is the homologous temperature, where T is the absolute temperature, Tr is the room temperature, Tm is the melting temperature of the target material, respectively. Johnson and Cook also developed a failure criterion that accounts for temperature, strain rate
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