A plastic constitutive equation incorporating strain, strain-rate, and temperature

Abstract

An empirical plasticity constitutive form describing the flow stress as a function of strain, strain-rate, and temperature has been developed, fit to data for three dual-phase (DP) steels, and compared with independent experiments outside of the fit domain. Dubbed the “H/V model” (for “Hollomon/Voce”), the function consists of three multiplicative functions describing (a) strain hardening, (b) strain-rate sensitivity, and (c) temperature sensitivity. Neither the multiplicative structure nor the choice of functions (b) or (c) is novel. The strain hardening function, (a), has two novel features: (1) it incorporates a linear combination coefficient, α, that allows representation of Hollomon (power law) behavior ( α = 1), Voce (saturation) behavior ( α = 0) or any intermediate case (0 < α < 1, and (2) it allows incorporation of the temperature sensitivity of strain hardening rate in a natural way by allowing α to vary with temperature (in the simplest case, linearly). This form therefore allows a natural transition from unbounded strain hardening at low temperatures toward saturation behavior at higher temperatures, consistent with many observations. Hollomon, Voce, H/V models and others selected as representative from the literature were fit for DP590, DP780, and DP980 steels by least-squares using a series of tensile tests up to the uniform strain conducted over a range of temperatures. Jump-rate tests were used to probe strain rate sensitivity. The selected laws were then used with coupled thermo-mechanical finite element (FE) modeling to predict behavior for tests outside the fit range: non-isothermal tensile tests beyond the uniform strain at room temperatures, isothermal tensile tests beyond the uniform strain at several temperatures and hydraulic bulge tests at room temperature. The agreement was best for the H/V model, which captured strain hardening at high strain accurately as well as the variation of strain hardening with temperature. The agreement of FE predictions up to the tensile failure strain illustrates the critical role of deformation-induced heating in high-strength/high ductility alloys, the importance of having a constitutive model that is accurate at large strains, and the implication that damage and void growth are unlikely to be determinant factors in the tensile failure of these alloys. The new constitutive model may have application for a wide range of alloys beyond DP steels, and it may be extended to larger strain rate and temperature ranges using alternate forms of strain rate sensitivity and thermal softening appearing in the literature.