Determination of High Strain-Rate Behavior of Metals: Applications to Magnetic Pulse Forming and Electrohydraulic Forming

Abstract

The design of processes like magnetic pulse forming and electrohydraulic forming involves multiphysical couplings that require numerical simulation, and knowledge on dynamic behaviour of metals. The forming process is completed in about 100 μs, so that the workpiece material deforms at strain-rates between 100 and 10 000 s-1. In this range, the mechanical behaviour can be significantly different than that in quasi-static conditions. It is often noticed that the strength and the formability are higher. The main goal of this study is to use an electromagnetically driven test on tubes or sheets to identify the constitutive behaviour of the workpiece material. In the case of tube, an industrial helix coil is used as inductor. Simulations with the code LS-Dyna® permit to find a configuration where the tube deforms homogeneously enough to allow axisymmetric modelling of the setup. The coil current is measured and used as an input for the simulations. The radial expansion velocity is measured with a Photon Doppler Velocimeter. The parameter identification is lead with the optimization software LS-Opt®. LS-Dyna axisymmetric simulations are launched which different set of parameters for the constitutive behaviour, until the computed expansion velocity fits the experimental velocity. The optimization algorithm couples a gradient method and a global method to avoid local minima. Numerical studies show that for the Johnson-Cook constitutive model, two or three experiments at different energies are required to identify the expected parameters. The method is applied to Al1050 tubes, as received and annealed. The parameters for the Johnson-Cook and Zerilli-Armstrong models are identified. The dynamic constitutive behaviour is compared to that measured on quasi-static tensile tests, and exhibits a strong sensitivity to strain-rate. The final strains are also significantly higher at high velocity, which is one of the major advantages of this kind of processes.

Research on Constitutive Relation of Metals under High Strain Rate

“…In the process of explosion, impact, etc., strain rate of the material can reach 10 2 -10 4 s -1 or even higher. The mechanical behavior of many metals under high strain rates is significantly different from that under quasi-static loads [1]. The constitutive relationship of material relates the relationship between stress and strain, strain rate, temperature, deformation history, etc.…”

Suitability of the electromagnetic ring expansion test to characterize materials under high strain rate deformation

“…This situation also highlights the definite requirement of the material calibration for respective strain rates. More information on the material calibration using ring expansion test could be found elsewhere [32][33][34][35]. The discrepancy could also arise from the numerical conditions such as mesh convergence and the time step used in this study.…”