Constitutive Equations for Large Plastic Deformation of Metals

Calculations of deformation behavior in metal forming operations require constitutive equations valid at large plastic strain. This work examines the quality of fit provided by two types of equations, an exponential form which generalizes power laws and a saturation-type relation, to data produced by isothermal, uniaxial testing of annealed 304 stainless steel and Zircaloy-4 at a constant total true strain rate and various temperatures. The use of annealed material reduces the number of independent parameters to three in the exponential equation and to four in the saturation-type equation. Physical reasoning places limits on the values of some parameters and identifies two with the true stress, σm, and true strain, εm, at the maximum load sustained by the specimen. Least-square fits of the data reveal that the Voce form of the saturation-type equation exhibits the lowest standard deviation of all equations studied. Material parameters representing σm, εm, and σs, the saturation stress, generally followed expected trends for the temperature dependence of measures of strength and ductility, except that εm, of 304 stainless steel tended to decrease with increasing temperature.