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.

• Periodical: Key Engineering Materials (Volumes 611-612)
• Pages: 643-649
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.611-612.643
• Online since: May 2014
• Authors: Anne Claire Jeanson*, Gilles Avrillaud, Gilles Mazars, Jean Paul Cuq-Lelandais, François Bay, Elisabeth Massoni, Nicolas Jacques, Michel Arrigoni
• Keywords: Dynamic Behavior, Identification, Magnetic Pulse Forming, Tube Expansion

References

[1] M. Dehra. High velocity formability and factors affecting it, Phd Thesis, Ohio State University, (2006).

[2] P. L'Eplattenier, I. Caldichoury, EM Theory Manual, Electromagnetism and Linear Algebra in LS-DYNA, LS-DYNA v980 Revision Beta, (2011).

[3] P. Follansbee, U. Kocks. A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable, Acta Metallurgica 36 (1988), 81-93.

DOI: 10.1016/0001-6160(88)90030-2

[4] G. Cowper, P. Symonds. Strain hardening and strain rate effect in the impact loading of cantilever beams, Technical report, Brown University, Division of Applied Mathematics, (1957).

DOI: 10.21236/ad0144762

[5] G. Johnson, W. Cook. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, Proceedings of the 7th international symposium on ballistics, Hague, Netherlands, pp.541-547, (1983).

[6] W. Gourdin. Analysis and assessment of electromagnetic ring expansion as a high-strain-rate test, Journal of Applied Physics 65-2(1989), 411-422.

DOI: 10.1063/1.343121

[7] G. S. Daehn, Y. Zhang, S. Golowin, K. Banik, A. Vivek, J. R. Johnson, G. Taber, G. K. Fenton, I. Henchi, P. L'Eplattenier, Coupling experiment and simulation in electromagnetic forming using photon Doppler velocimetry, 3rd International Conference on High Speed Forming, (2008).

[8] I. Henchi, P. L'Eplattenier, G. Daehn, Y. Zhang, A. Vivek, N. Sander. Material constitutive parameter identification using an electromagnetic ring expansion experiment coupled with LS-DYNA and LS-OPT, Proceedings of the 10th International LS-DYNA Users' Conference, (2008).