Non-linear mechanical response of various metals. VII. Stress-strain relations for simple compression, tension and torsion

Abstract

For pt.VI, see ibid., vol.14, no.6, p.1071-86 (1981). The correlation of stress-strain curves characteristic of the mechanical response of a material tested in simple tension, compression and torsion is considered with the object of obtaining a universal stress-strain curve. Using a proposed form of piece-wise continuous yield condition, it is shown that stress-strain relations can be obtained for simple tension, compression and torsion in a form which, in principle, combine to give a single universal stress-strain curve. However, in order to obtain a single universal stress-strain curve it is necessary to reinterpret the physical significance of the scalar multiplier appearing in the general constitutive equation. The stress-strain relations, combined in the form of a single universal stress-strain curve, which are finally compared with experiment, make use of the proposed piece-wise continuous yield condition, the correlation being based on an incremental type constitutive equation for an isotropic, incompressible, strain-hardening, elastic-plastic solid with large deformation. For aluminium, direct use of the Swift effect gives stress-strain curves for simple compression and simple torsion which are indistinguishable over the whole available range of shear strain. The satisfactory correlation now extends over a much wider range of effective strain.