The strain path dependence of multiaxial cyclic hardening behaviour

Abstract

The small-strain, isotropic deformation theory is used in incremental form to model an additional cyclic hardening for any arbitrary loading path. The theory is of the unified type and does not employ yield or loading/ unloading criteria. The scalar-valued functions involved in the tensorial constitutive equations as well a growth law for these functions are identified based on idea of the equivalent state. Definitions of equivalent stress and equivalent strain have been developed to correlate step by step loading programmes taking the history of deformation into account. Use is made of the total work increment together with an interpolation method for tensor functions to generalize the simple state to a multiaxial behaviour in the strain space for a given strain increment. For the demonstration of model capability, the numerical simulation is undertaken on cyclic nonproportional paths in two-dimensional axial-shear strain space. The results are verified for stainless steel and brass by comparison with the material response experimentally obtained in the stress space.