Shear testing of a sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress

Abstract

In this paper, a new experimental technique is reported to study behavior of sheet metals in the range of low and high strain rates. The main purpose of this work was to analyse visco-plastic behavior of sheet metals for an industrial application. It may be mentioned that a variety of industrial processes, such as drawing or even crashworthiness, involve a wide range of strain rates. The test method which is based on previous work, (Klepaczko, J.R., 1994. An experimental technique for shear testing at high and very high strain rates. The case of mild steel. Int. J. Impact Engng. 15, 25–39), is a combination of two experimental techniques, that enables one to obtain the range of strain rates from 10−4 to 103 s−1, (Rusinek, A., Klepaczko, J.R., 1998. Etude experimentale du double cisaillement des tôles, modélisation de l'écoulement viscoplastique. Rapport interne, LPMM). The double-shear specimen is loaded by a fast hydraulic machine, and in the second case a specimen of the same geometry can be loaded by the direct impact of a projectile. The combination of direct impact with the double shear specimen, which is based on the Hopkinson tube technique of force measurement, permits to reduce the rise time of loading in comparison to the bar-tube configuration (Campbell, J.D., Ferguson, W.G., 1970. The temperature and strain rate dependence of shear strength of mild steel. Phil. Mag. 21, 63–82). The combination of two schemes of loading assures a complete determination of the shear stress τ(t), the shear strain Γ(t) and shear strain rate Γ̇(t) as a function of time at wide range of strain rates. The test method has been applied to determine the visco-plastic behavior of cold rolled, Al-calmed sheet steel used in the automotive industry. The experimental results obtained with those two experimental techniques are in agreement with other reported data. An original visco-plastic constitutive relation has been proposed. It permits to model the viscoplastic behavior of the sheet metal tested in the whole range of strain rates considered. A general procedure for the identification of the material constants is proposed (Rusinek, A., Klepaczko, J.R., 1998. Etude experimentale du double cisaillement des tôles, modélisation de l'ecoulement viscoplatique. Rapport interne, LPMM.). It offers the advantage of subdividing the total number of constants into groups, this procedure simplifies the problem of identification. The constitutive relation proposed takes into account the strain hardening, the strain rate sensitivity and temperature effects. A comparison with experimental results is presented in the form of stress–strain curves at different strain rates, up to 103 s−1.