A new constitutive relationship for the homogeneous deformation of metals over a wide range of strain

Abstract

The stress–strain relationships of high-purity aluminum and copper were investigated over a wide range of strain by combining data obtained in the conventional tensile and compression testing of annealed samples with data obtained after processing by equal-channel angular pressing (ECAP) to high imposed strains. The true stress–true strain curves were analyzed mathematically taking the absolute strain as zero for the annealed condition and equal to the strain imposed through ECAP for the as-pressed samples. It is shown that, over the entire range of strain inherent in these experiments, the macroscopic stress–strain behavior of Al and Cu may be represented by an exponential power-law constitutive relationship which reduces to the conventional Hollomon power-law relationship at low strains and to the Voce exponential relationship at high strains. It is demonstrated that the results obtained from tensile or compressive testing to low strains at room temperature are sufficient, when used with the new constitutive relationship, to provide detailed information on the nature of the stress–strain behavior to high strains. The validity of the new relationship is supported by theoretical considerations which incorporate the major micro-mechanisms of plastic deformation.