A new approach for the modeling of the dynamic expansion of a tantalum sphere. Analysis of the coupled influences of manufacturing operations and anisotropic behavior

Abstract
In recent papers, the expanding spherical shell test has been proposed as a new validation experiment for constitutive relations in the domain of high strain and high strain rate. However, the use of this experiment has to deal with the influence of microstructural modifications associated to the manufacturing operations performed to obtain the shell. In this study, we examine the problem for pure tantalum. The initial material is supplied as an ingot and the shell is formed by closed die forging. The comparison between the results obtained from classical mechanical testing (quasi static and split Hopkinson pressure bars experiments) for the initial and the final materials shows an increase in the major plastic constants (yield and saturation stresses). Moreover, we have performed complementary experiments on the sphere material : comparing the results between the radial, meridian and parallel loading directions, the behavior is found orthotropic, and plane isotropic. So, in order to optimize the original constitutive relation proposed for the ingot material, we suggest to take into account in a first approach, the effects of manufacturing operations (increase of mechanical behavior parameters) and the anisotropic behavior of tantalum. This approach is discussed and conclusions are given for further works.