Viscoplasticity theory based on overstress: the modeling of ratchetting and cyclic hardening of AISI type 304 stainless steel

Abstract

At room temperature, annealed AISI type 304 stainless steel exhibits rate dependence that manifests itself in rate sensitivity, creep and relaxation. It is also the driving force behind incremental elongation under zero-to-tension load-controlled loading, called ratchetting. It is shown to increase with decreasing stress rate and is independent of stress rate sequence. Accumulated ratchet strain has the same hardening effect as the strain in a monotonic test. For cyclic loading with load or strain reversal, significant cyclic hardening is observed. It is well known that this hardening depends on the path and seems to be most pronounced under 90° out-of-phase cycling. Other paths show various degrees of cyclic hardening. At the same effective strain range, the hardening under nonproportional loading is much more pronounced than under proportional loading. Experiments show that the rate sensitivity is, as a first approximation, unchanged by the significant hardening, which is therefore rate independent. The small-strain, isotropic viscoplasticity theory based on overstress (VBO) is used to model these phenomena. The theory is of the unified type and does not employ yield or loading/unloading criteria. The inelastic strain rate is a function of the overstress, the difference between the stress and the equilibrium stress, which is a state variable of the theory. Its growth law is the repository for modeling nearly elastic regions and hysteresis. Under constant strain rate loading, the theory admits asymptotic solutions, which show that the stress is composed of viscous, rate-independent (plastic) and kinematic contributions. For the modeling of cyclic hardening, a growth law for the rate-independent contribution to the stress is formulated. It models a different type of growth for proportional and nonproportional as well as cyclic and monotonic loadings. Numerical experiments for homogeneous states of stress are performed by integrating the stiff, nonlinear ordinary differential equations using the IMSL routine DGEAR. They demonstrate the modeling capabilities for step-down and step-up two-amplitude loadings, for proportional and nonproportional cyclic loadings including elliptical and square paths as well as for ratchetting.