The Impulse Response Of A Ductile Material: A New Model Of Dynamic Damage And Fracture, Structural Phase Transitions

The responses of solids to shock wave loadings keep absorbing the attentions of scientists in worldwide range since early in last century, because they are important for many civil and military applications. This thesis focus on three aspects of these responses: dynamic damage and fracture of ductile materials, shock compress induced structure phase transition and ab-initio molecular dynamics simulation of (D,u) relation of metal under shock loading condition. A practical model for prediction of dynamic damage and fracture has been proposed, in which the plastic flow of matrix and the evolution of damage are formulated separately after we show that two separated loading sub-surfaces and corresponding normality rules for matrix and damage exist. The equation of the loading sub-surface for the matrix plastic flow is derived by the means of introducing a mapping damage-free solid of matrix material, whose constitutive relation is supposed to have been determined via Hopkinson bar experiments. Based on the results of recovered experiments the law of damage evolution is phenomenally established. The model has been applied to predict some spall experiments carried out on several metals, and results show it predicts the experiments very well. Another novel model for description of shock compress induced structure phase transition has also been put forward. The main differences of this model from previous models are that the effects of shear on phase transition are quantitatively taken into consideration. A differential equation for describing the phase balance surface is derived, which is in terms of pressure, temperature and the second invariant of deviatoric stress tensor. Meanwhile a basic relation between the plastic flows of original and new phase materials during transition process is also deduced out. Combining the two new models, we simulated the phase transition and spall behaves of iron. The unloading shock wave and hysteresis are reproduced in simulations. At last, the (D,u) relation of copper under shock wave loadings are calculated with ab-initio molecular dynamics. Results show theoretical and experimental C₀ and λ are consistent with each other well. It seems to us that no paper openly reported this kind of work before.