3.3 Dynamic constitutive relation of the fragment and steel In order to describe the structure response to the explosive impact load, several conditions should be taken into account: the strain strengthening phenomenon of the material, the material behaviors under large strain, high strain rate and high temperature, even the material behaviors under the influence of the strain state change and the load history change. Johnson-cook (JC) strength model [3] is widely used in commercial nonlinear finite-element because of its simple form, distinct concept and precise veracity. JC model is a kind of empirical viscoplasticity constitutive relation, it can describe the hardening effect, strain rate effect and softening temperature effect of metal materials very well. * * ( )(1 ln )(1 ) n m A B C T σ ε ε = + + − & (6) (7) σis equivalent stress(N), εis equivalent strain, * 0 ε ε ε =& && is dimensionless plastic strain rate, 0ε&is static experiment strain,，T is the sample surrounding temperature, rT is room temperature, mT is fusion point. ( )n A B ε + describes strain strengthening effect; * (1 ln )ε + & describes strain rate strengthening effect; * (1 ( ) )m T − describes softening temperature effect. Parameter value shown as follows. Table1 JC constitutive relation parameters of 4340steel A(MPa) B(MPa) n C m ε& Tm(K) 791 510 0.26 0.014 1.03 1 1793 4. Results and analysis 4.1 Damage process of the synergetic effect 0.998ms 1ms 1.245ms * ( ) ( ) r m r T T T T T = − −
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