Modeling the behavior of metals at high strain rates

Modeling the behavior of materials at high strain rates is a scientific field that took off in the second half of the 20th ^e century. It is linked to specific industrial developments. Early work was motivated by military problems concerning the perforation of metal armour. In this case, the range of strain rates is very high, and the loading is close to a state of pure pressure, corresponding to a state of spherical stress. Material characterization is then carried out using plate-on-plate impact tests at very high speeds (several hundred meters per second).

Such loads and their associated models will not be considered here. Instead, we'll be looking at loads in which plasticity phenomena come into play, and for which the deviatoric part of the stress tensor determines most of the response of the materials under load.

The corresponding industrial situations are encountered in particular in automotive crash studies, a field in which the range of deformation speeds is below 1000 s ^–1 . In this field, most metals exhibit dynamic hardening phenomena, which are qualitatively accounted for by certain classes of behavior models. These phenomena must also be taken into account when analyzing metal forming processes, particularly by machining where the range of strain rates can exceed 10 ⁴ s ^–1 .

Numerical calculations in the field of car crashes are most often carried out using so-called explicit industrial codes, since at least the time integration algorithm is explicit (the best-known publishers in France are ESI, Mecalog and Dynalis, whose codes go by the trade names PAM-CRASH, RADIOSS and DYNA respectively). Initial calculations were carried out using plasticity models that did not take velocity effects into account. Taking the latter into account proved to be necessary in view of the need for predictive calculations. For historical reasons, empirical models were developed, known as dynamic plasticity models, in which deformation velocity is an additional parameter.

The development of relevant behavioral models and their adaptation to the explicit codes used in dynamics remain open problems.

This naturally requires an experimental characterization phase, in which significant strain rates must be brought into play. This calls for special testing methods, the most classic of which is the Hopkinson bar system.

The modeling phase is neither strictly consecutive to the characterization phase, nor strictly prior to the calculation phase. The assumptions classically used for static tests, of...