13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- and strain path in addition to the triaxiality of the stress state. The damage variable D has the basic form eq f D (2) where Δεeq is the increment of accumulated plastic strain and εf is the fracture strain given as 4 * * * 1 2 3 5 exp 1 1 D f eq D D D DT (3) where D1、D2、D3、D4、D5 are material constants, σ *=σH/σeq is the stress triaxiality ratio and σH is the mean stress. The temperature increment ( T ) during perforation is calculated as 0 eq eq eq t p d T C (4) where t is the material density, Cp is the specific heat, is the coefficient that represents the proportion of plastic work converted into heat. The damage variable D (Eq. 2) takes values between 0 (undamaged) and 1 (fully broken). When the damage variable D equals to 1, the damaged element will be removed from the mesh in the simulations. Meanwhile, the erosion strain (εc) of 2.0 is defined in the simulations in order to ensure that elements which are heavily deformed will not stop the computation process. The erosion strain (εc) of 2.0 is high enough to avoid any problems with mass erosion in the target [7]. When the equivalent plastic strain (εeq) is greater than the erosion strain (εc), the element will be removed. The Gruneisen equation of state is employed, viz. 2 0 0 0 2 1 (1 ) (1 ) 2 t t m P C E s (5) where P is hydrostatic pressure, 0C , 1S and 0 are material constants, mE is specific internal energy of target material, and 0 1 / V V , where V is current volume and 0V is initial volume. The material parameters for Weldox460E steel target given in Table 1 are taken from Dey et al. [6]. E is the elastic moduli and is the Poisson’s ratio of the target. 2.3. Simulation results Fig.2 shows comparisons of the simulation results and the experimental data obtained by Borvik et al. [4] in terms of residual velocity for 12mm thick Weldox460E steel plates struck normally by conical-nosed projectiles with diameter (20mm), mass (197g) and cone angle (θ=33o). Fig.3 shows comparisons of the simulation plot and the experimental image of the target after full perforation when the strike velocity of the projectile is 300.3m/s.
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