The dynamics of multiple neck formation and fragmentation in high rate extension of ductile materials

Dynamic necking bifurcation in rapidly extending cylindrical rods is investigated. It has been found that both short wavelength and long wavelength perturbations are suppressed by inertia and an intermediate wavelength is favored. The analysis predicts an increase in the number of necks and an increase in the bifurcation strain with increasing extension rate, in agreement with experimental observations. In terms of the number of necks formed as a function of extension rate, good agreement has been found between the experiments and the analysis. At any given aspect ratio, the model also predicts that beyond a critical extension rate, the mode number of the dominant perturbation increases rapidly and the perturbation begins to look more like a surface instability. This could lead to a fragmentation mechanism at high extension speeds which is different from multiple necking. Currently no experimental results are available to test this prediction. Numerical simulations have been conducted to simulate the fragmentation results, using Gurson s constitutive law along with a porous failure criterion. Good agreement between the experimental observations and the numerical results has been obtained for the fragmentation statistics. However, the numerical results consistently overestimate the number of necks and the fracture strain, possibly due to uncertainty in the constitutive data used, especially at large strains