On the relation between shape imperfections of a specimen and necking growth rate under dynamic conditions

In this work, the growth rate of necks formed in dynamically loaded tensile steel samples is investigated. For that purpose, a combined experimental-numerical approach, in which the experimental results are systematically compared with finite element calculations, has been developed. The specimens have a machined sinusoidal geometrical imperfection that covers the whole gauge, introducing a characteristic wavelength in the samples. For a given cross-section diameter, specimens with 6 different gauge lengths (i.e. 6 different specimen wavelengths) were tested. Using a high-speed camera, we measured the time evolution of the radial contraction of the central section of the samples (central section of the neck), thus obtaining the growth rate of the necks. The experiments show that the speed of growth of the necks increases non-linearly with the specimen wavelength (concave-downward shape) until saturation is reached for the longest tested specimens. Numerical simulations performed for the strain rates attained in the experiments (from 900 s−1 to 2100 s−1) confirm this trend and demonstrate that the damping of short specimen wavelengths is caused by stress multiaxiality effects. Numerical simulations performed for strain rates greater than those attained in the experiments (above 7500 s−1) show that long specimen wavelengths become damped by inertia effects at sufficiently high strain rates. For strain rates greater than 7500 s−1, the maximum growth rate of the neck corresponds to an intermediate specimen wavelength defined by the joint action of stress multiaxiality and inertia on damping short and long wavelengths, respectively. Altogether, our experimental and numerical results suggest the existence of a specimen wavelength that, when inertia effects become important, determines the maximum growth rate of dynamic necks, in agreement with the predictions of the dynamic stability analyses developed by Molinari and co-workers (Fressengeas and Molinari, 1985, 1994; Mercier and Molinari, 2003, 2004).