10 60 Fig. 3 Schematic of a cylindrical projectile Fig.4 Finite element model of the projectile-target impacting a rigid wall system 3.2 The strength model Due to simplicity and availability of material coefficients, the Johnson–Cook (JC) material model implemented in AUTODYN was used in the present calculation. The material model should not be confused with the fracture model which will be discussed later. In the JC model the equivalent stress σ is an explicit function of the equivalent plastic strain eff ε , the temperatureT, and the plastic strain rate ε&. * * ( )(1 ln )(1 ) n m A B C T σ ε ε = + + − & (1) Where the reference plastic strain rate * 0 ε ε ε =& &&, * ( ) ( ) r m r T T T T T = − − , rT and mT are the room temperature and the material melting temperature respectively, and A, B, n, C, and m are five material constants. The JC model accounts for isotropic strain hardening, strain rate sensitivity, and thermal softening in the uncoupled form. The first term of the right hand side of Eq. (1) represents the quasi-static stress–strain relation at room temperature; the second term signifies the strain-rate hardening; the third term means the temperature dependence of the stress–strain relation. It should be pointed out that in the computation, the material behaves elastically up to the point of initial yield and then follows Eq.(1). The material parameters in the JC model for Q235 were listed in Table 1. Table 1 Material parameters for Q235 Material A（MPa） B（MPa） n C m Q235 249.2 45.6 0.875 0.32 0.76
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