Thermal gradients, strain rate, and ductility in sheet steel tensile specimens
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I.
INTRODUCTION
M O D E L I N G the plastic flow in sheet metal stretched over a rigid punch requires an accurate constitutive law of the material properties and an appropriate value for friction. Typically, the constitutive law, 1'2'3 Eq. [1], -~ = f(-~,-~,7,M)
[1]
describes the effective .stress ~ as a function of effective strain ~, strain rate ~, normal plastic anisotropy 7, and yield surface shape M. Friction is usually taken to be Coulombic. 4'5 Since the constitutive laws and friction are usually assumed to be independent of temperature, the modeling accuracy can be evaluated only at very slow rates where isothermal conditions prevail. At higher strain rates, thermal gradients from deformation heating can become a significant influence in controlling plastic flow. To include the effects of thermal gradients on plastic flow, both the local temperature and the flow stress as a function of temperature must be known. For very high rates the heating is adiabatic, and the temperature rise AT is given 6 by Eq. [21. AT = ~ / -~d~ pc Jo
[21
In this expression 7/is the fraction of work converted to heat, p is density, and c is the specific heat of the material. For more moderate strain rates, approximately 10 -4 t o 10 -1 S -1 in sheet tensile specimens 63 substantial heat transfer occurs from the gage section and Eq. [2] considerably overestimates AT. For the strain rate regime between isothermal and adiabatic conditions, where most forming operations occur, there is no simple method to predict AT, and a complex heat transfer analysis is required. In an earlier study of thermal effects by Kleemola and Ranta-Eskola, 7 sheet tensile samples were pulled either in still air to allow temperature gradients to grow or in air jets ROBERT A. AYRES is Senior Staff Research Scientist with General Motors Research Laboratories, Warren, MI 48090-9055. Manuscript submitted December 23, 1983. METALLURGICAL TRANSACTIONS A
to develop isothermal conditions. While these investigators reported changes in the strain hardening n and the strain-rate hardening m between isothermal and nonisothermal tests at room temperature, they did not report the total elongation in the specimens. In another similar study on 304 stainless steel, 9 total elongation was reported, but the terminal m value for this material was nearly zero. Neither of these studies reported the temperature gradient in the tensile specimens. This investigation determines the effect of temperature gradients on total elongation in sheet tensile samples pulled at various rates in isothermal and nonisothermal conditions at room temperature. The thermal gradients are measured until failure to relate the instantaneous gradient to the stressstrain curve. The total elongation is taken as the measure of ductility since it includes the effects of both n and m .8 Since these material properties may change with temperature, isothermal tensile tests were performed at elevated temperatures. In this manner, the effect of temperature gradients on ductility can be separated from changes
