Modelling of nucleation and void growth in dynamic pressure loading, application to spall test on tantalum

Dynamic ductile fracture is a three stages process controlled by nucleation, growth and finally coalescence of voids. In the present work, a theoretical model, dedicated to nucleation and growth of voids during dynamic pressure loading, is developed. Initially, the material is free of voids but has potential sites for nucleation. A void nucleates from an existing site when the cavitation pressure pc is reached. A Weibull probability law is used to describe the distribution of the cavitation pressure among potential nucleation sites. During the initial growth, the effect of material properties is essentially appearing through the magnitude of pc. In the later stages, the matrix softening due to the increase of porosity has to be taken into account. In a first step, the response of a sphere made of dense matrix but containing a unique potential site, is investigated. When the applied loading is a pressure ramp, a closed form solution is derived for the evolution of the void that has nucleated from the existing site. The solution appears to bevalid up to a porosity of 0.5. In a second part, the dynamic ductile fracture of a high-purity grade tantalum is simulated using the proposed model. Spall stresses for this tantalum are calculated and are in close agreement with experimental levels measured by Roy (2003, Ph.D. Thesis, Ecole Nationale Supérieure deMécanique et d’Aéronautique, Université de Poitiers, France). Finally, a parametric study is performed to capture the influence of different parameters (mass density of the material, mean spacing between neighboring sites, distribution of nucleation sites. . .) on the evolution of damage.