A New Dynamic Constitutive Model For Metallic Materials

Metallic materials have been widely used in both defense industry and civil engineering.An understanding of the response and failure of metal structures subjected to intense dynamic loadings is of great significance for the design and safety assessment of weapons as well as protective structures.In order to study the dynamic behaviour of metallic materials under complex loading conditions(namely,large deformations,high strain rates and high temperatures),it is essential to establish a dynamic constitutive model and failure criterion for metals.The main contents and results of this thesis are as follows:(1)A critical assessment is made herein on the accuracy of the Johnson-Cook(JC)constitutive model by comparing the model predictions with the test data for 2024-T351 Aluminum alloy,6061-T6 Aluminum alloy,OFHC copper,4340 steel,Ti-6Al-4V alloys and Q235 mild steel.It transpires that the JC constitutive model is applicable to Mises materials at quasi-static to intermediate strain rates and low to moderate temperatures.It also transpires that the agreement between the JC constitutive model predictions and the experimentally obtained true stress-true strain relationships for non-Mises materials and those at high strain rates and high temperatures are poor.It also transpires that the JC fracture criterion has failed to predict the failure of various metals under different loading conditions as it takes no account of Lode angle effect.Numerical simulations are carried out of the ballistic perforation of 2024-T351 aluminum alloy plates by flat-ended projectiles using the JC constitutive model.The numerical results are found to be in poor agreement with the experimental data,which lend further support to the conclusion that both the JC constitutive model and the JC fracture criterion have some shortcomings.(2)A new plasticity and failure model is developed for metallic materials subjected to dynamic loadings on the basis of the analysis of some available material test data.The new model consists of two parts:a strength model and a failure criterion.The strength model takes into consideration both tension and shear true stress-true strain relationships as well as the effects of strain rate and temperature.The failure criterion takes into account the effects of stress triaxiality,Lode angle,strain rate and temperature.In particular,a new function of dynamic increase factor is suggested for the effects of strain rate,and the dynamic increase factor at any plastic strains can be obtained from that at a specific plastic strain;Based on the experimental observation that the true stress-true strain curves under different strain rates are approximately parallel,a new coupling form of strain hardening term and strain rate effect is proposed;a new non-linear function is suggested for the effect of temperature in the strength model.The quasi-static part of failure criterion has only two constants which can be determined by two laboratory tests such as smooth bar tension test and pure shear test.(3)The usefulness and accuracy of the newly developed plasticity and failure model is demonstrated by comparing the model predictions with available material test data for many metals in terms of true stress-true strain curves in both tension and shear,strain rate effect,temperature effect and fracture under different loading conditions.It is found that the theoretically predicted true stress-true strain curves both in tension and shear are in good agreement with the experimental results.It is also found that the theoretically predicted fracture strains are in good agreement with the test data for metals under different loading conditions as it takes into consideration both the effects of stress triaxiality and Lode angle.(4)The new model is implemented in the commercial hydrocode LS-DYNA and its usefulness and accuracy of the model are validated by numerical simulations.The usefulness and accuracy of the new model are first verified by using the single element simulation approach.Its usefulness and accuracy then are verified by good agreement between the present model predictions and the cup and cone failure patterns observed experimentally in 2024-T351 aluminum alloy smooth and R12 notched round bar quasi-static tensile tests at room temperature.Finally,its usefulness and accuracy are further validated by good agreement between the numerically predictions and the experimentally observed in terms of residual velocities,ballistic limits and failure models(i.e.plugging and petalling)in the case of the penetration of 2024-T351 aluminum alloy plates struck transversely by flat-ended and spherical projectiles.(5)Numerical simulations are performed on the dynamic response and perforation of Q235 mild steel monolithic plates struck transversely by a flat-ended projectile using the newly developed constitutive model for metals.It transpires the numerical predicted ballistic limits and residual velocities are in good agreement with some available test data,that the numerically predicted critical thickness for the transition in failure modes from simple shear plugging failure with global deformations to localized adiabatic shear plugging is about 6.0-7.0 mm which agreement with the theoretically value of 6.2 mm.Numerical simulations are also performed on the dynamic response and perforation of Q235 mild steel double and three-layered plates impacted normally by rigid projectiles and thickness of each layered plates is the same as that of the monolithic plate examined.The ballistic limit velocities are greater than those of monolithic plate.Based on the analysis of the ballistic limit and specific energy,it is demonstrated the numerical results show that the penetration resistance of a double-layer target is slightly higher than that of monolithic plate with the same thickness when the total thickness of the target is less than He.It is also demonstrated when the total thickness of the target is between He and 2H_c,the penetration resistance of a double-layered plate is much higher than the monolithic plate with the same thickness and the penetration resistance of a double-layer target with a gap of the same layer thickness is the best.