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The Δ EVPSC model is a general elasto-visco-plastic self-consistent constitutive formalism based on a Homogeneous Effective Medium (HEM) approach that accounts explicitly for microstructural features such as slip, twinning, and crystallographic texture. Δ EVPSC is improved with respect to the original model reported in (Jeong and Tome, 2020) by introducing an intermediate linearization scheme, which leads to better predictive accuracy of intergranular stress and strain distributions in the polycrystal. The Δ EVPSC model is interfaced with a commercial finite element solver Abaqus/standard as a user-defined material subroutine ( Δ EVPSC-FE). Δ EVPSC-FE shows superior numerical stability and, when using parallel computation and 40 CPU core units, it reduces the computation time by a factor 20 compared to using a single CPU core unit for a structure consisting of 512 solid elements. The Δ EVPSC-FE model is applied to FE analyses of Zr and low-carbon steel bars subjected to a sequence of bending, stress-relaxation, and unloading. It is shown that the hereditary effect is responsible for the spring-forward motion during the early stage of unloading, while the elastic recovery mainly drives the subsequent spring-back.

Constitutive models developed for simulating plastic response upon strain path changes are combined: 1) a macro-mechanical model based on anisotropic yield function, associated flow rule and distortional hardening using Homogeneous Anisotropic Hardening (HAH) approach; 2) a micro-mechanical model using self-consistent crystal plasticity in conjunction with crystallographic dislocation-density based hardening. The micro-mechanical model is employed to probe the yield surface in order to gain the insight required to construct empirical rules appropriate for the macro-mechanical model. Simulation results of the micro-mechanical model under various loading conditions involving strain path changes and different crystallographic textures are presented. The trends captured in the yield surface evolution predicted by the micro-mechanical model were used to validate and improve the empirical rules used in the HAH model.

A novel elasto-visco-plastic self-consistent (EVPSC) formulation based on the scheme of the homogeneous effective medium is presented. The constitutive behavior of a polycrystal is described as that of an elasto-visco-plastic effective medium interacting with grains treated as elasto-visco-plastic ellipsoidal inclusions. The formulation is based on the definition of a unique elasto-visco-plastic compliance, so avoiding the inconsistency arising from assuming superimposed elastic and visco-plastic interaction laws, as made in similar elasto-visco-plastic models. In addition, the elasto-visco-plastic constitutive equation of crystal and aggregate is formulated in terms of stress increments, which leads naturally to a semi implicit solution scheme. The superior numerical stability and computational efficiency of the new incremental EVPSC model (denoted as Δ EVPSC) are demonstrated by applying the model to a 316L austenitic stainless steel and comparing against other elasto-plastic models. The modeling capability for predicting texture, stress-strain response, and Bauschinger effect are demonstrated using a dislocation-density based hardening law applied to low carbon (LC) steel subjected to deformation histories that involve strain-path changes.

Biaxial flow behavior of an interstitial free steel sample was investigated with two experimental methods: (1) Marciniak punch test with in situ X-ray diffraction for stress analysis; (2) hydraulic bulge test. The stress analysis based on X-ray diffraction using {2 1 1} lattice planes was accompanied by the use of stress factors and intergranular (IG) strains. Stress factors and IG strains were experimentally obtained ex situ on samples after prescribed equi-biaxial deformations. An elasto-viscoplastic self-consistent (EVPSC) crystal plasticity model was used to predict the stress factors and the IG strains. The model predictions of the stress factors were in good agreement with the experiments. However, the predictions of IG strains were in poor agreement with their experimental counterparts. As a result, the flow stress solely based on the computationally predicted stress factors and IG strains was unrealistic. The input of the experimental stress factors and IG strains for stress analysis improved the agreement with a reference flow curve obtained by a hydraulic bulge tester. The resulting flow curves based on X-ray diffraction were in good agreement with that of the bulge test up to an effective strain of 0.3. However, an unrealistic softening was observed in larger deformations regardless of whether the stress factor used were experimentally measured or determined from EVPSC calculations.