13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 3.2 Finite element model for perforation 3.2.1 Material behavior law of 2024 T3 AA A classical Johnson Cook behavior law [6] is used in the finite element code Abaqus [14] to model the viscoplastic behavior where A, B, n, m, C and ̇0 are material parameters, Tmelt is the melt temperature and Troom is the room temperature. The stress σ can also be written as a function of the plastic strain , the plastic strain rate ̇ , and the temperature T : ( )( ( ̇ ̇ ))( −( ) ) (8) The elastic behavior is isotropic (E=74 GPa, ν=0.3). Above a plastic strain threshold, voids appear, grow and coalesce in the material, to produce the rupture [15]. To define this damage, a damage variable D is used in the model. The evolution of D can be written using the Johnson Cook dynamic damage model [16]. The damage D is dependent on the plastic strain rate, materials parameters m, D1, D2, D3¸D4 and D5, the hydrostatic pressure p, the equivalent stress , the melt temperature Tmelt and the room temperature Troom : ̇ ̇ ̇ ( 1+ 3 )(1+ 4 ( ̇ ̇ ))(1 5( − − ) ) (9) Lesuer [12] used an isotropic Johnson Cook hardening and a Johnson Cook rupture model for a 2024 AA with the parameters presented in Table 3. The strain rate parameter ̇0 is taken equal to 1s-1 , Troom equals 298 K and Tmelt equals 775 K. Parameters D1 and D2 are determined to predict the residual velocity after impact, according to the presented experiment. Because of the temperature dependence, the specific heat cp is taken equal to 897 J/kg/K, the inelastic heat fraction equal to 0.9 and the conductivity equal to 237 W/m/K. Table 3. Johnson Cook hardening and fracture law parameters [12] (modified in bolt fonts) A (MPa) B (MPa) n C m D1 D2 D3 D4 D5 369 684 0.73 0.0083 1.7 0.035 0.035 -1.5 0.011 0.0 3.2.2 3D finite element model. A 3D finite element simulation is carried out using ABAQUS/Explicit. Shell elements are known to be well adapted for solving thin sheets’ perforation issues [17]. Thus the 2024 AA sheet is modeled with 3200 S4RT elements and 1869 S3RT elements with the JC law presented above (Table 3.) For stability reason, five integration points are taken in the sheet’s thickness. An analytical rigid surface is used to model the conical striker. The trolley mass is applied on the striker reference point. Interaction between the striker and the sheet is modeled by a perfect contact (hard contact and frictionless). Elements are deleted when the damage D is equal to 1. The sheet is clamped at the edges. The initial velocity is applied on the striker reference point. The striker moves only along the vertical direction. Temperature effects are taken into account but will not be discussed here. Initial
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