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A viscoplastic self-consistent crystal plasticity model was used to describe the mechanical behavior of two dual phase steel samples DP780 and DP1000. Mechanical anisotropy of these alloys was observed in uniaxial tests conducted along various directions. Additionally, X-ray diffraction was conducted to obtain the averaged crystallographic texture of ferrite and martensite. The hardening parameters were identified by fitting with the flow stress-strain curve obtained from bulge tests. The model-predicted and experimental flow-stress curves and R-values were compared in order to estimate the adequacy of the crystal plasticity model to describe the anisotropic behavior of the dual-phase steel samples. Furthermore, the crystal plasticity model, in conjunction with the Marciniak-Kuczynski approach, was used to predict forming limit diagram. The predictive accuracy was estimated by comparing with the experimental forming limit strains obtained through Nakazima tests. It turned out that several assumptions made in the current study led to somewhat poorer predictive accuracy in comparison with the previous reports, which implies that certain improvements in the model application are required for successful and valid model applications.

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.

An uncoupled fracture criterion based on a simple damage indicator computed using a mean-field crystal plasticity framework is proposed and applied to predict failure of an AZ31 sheet originating from the edges. The damage indicator quantifies the contribution of strain components along the axes of orthotropy leading to material failure. The model is calibrated by uniaxial tension tests. The damage indicator is validated for various mixed-mode deformation histories realized by modified Arcan tests in various loading configurations. The loading history of respective fracture sites obtained from DIC analyses is directly employed to a visco-plastic self-consistent crystal plasticity model to obtain the stress responses. The results indicate that the damage indicator requires – beside the strain history – an input of stress triaxiality, by which an improved predictive accuracy can be achieved. This effect is quantified for various loading scenarios, in which cracks are initiated near or at the edge of the sample.

A succinct description of advanced constitutive models for applications to forming process simulations is provided. These models are continuum-based because they are more efficient in terms of computation time than microstructure–based models. However, they are so–called advanced because they are considered in many scientific studies but rather scarcely used in industrial applications. In addition, the relationship between these continuum constitutive models and multi-scale approaches based on crystal plasticity, dislocation dynamics and mechanics of multi-phase materials, such as advanced high strength steels, is substantiated.

X-ray diffraction techniques have been developed to measure flow stresses of polycrystalline sheet metal specimens subjected to large plastic deformation. The uncertainty in the measured stress based on this technique has not been quantified previously owing to the lack of an appropriate method. In this article, the propagation of four selected elements of experimental error is studied on the basis of the elasto-viscoplastic self-consistent modeling framework: (1) the counting statistics error; (2) the range of tilting angles in use; (3) the use of a finite number of tilting angles; and (4) the incomplete measurement of diffraction elastic constants. Uncertainties propagated to the diffraction stress are estimated by conducting virtual experiments based on the Monte Carlo method demonstrated for a rolled interstitial-free steel sheet. A systematic report on the quantitative uncertainty is provided. It is also demonstrated that the results of the Monte Carlo virtual experiments can be used to find an optimal number of tilting angles and diffraction elastic constant measurements to use without loss of quality.

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.

In the present study, a viscoplastic self-consistent crystal plasticity model (VPSC-RGBV), which accounts for various microstructural features, including the accumulation and annihilation of dislocations due to slip activity and latent hardening originated from interactions between gliding dislocations on different slip planes, is described. The simulation results of the VPSC-RGBV model are compared with those of a macro-mechanical distortional plasticity model, the so-called homogeneous anisotropic hardening (HAH), and experimental data pertaining to metals undergoing complex loading histories. The differences between the simulated and experimental results under non-proportional loading, including 1) the stress-strain curve, 2) instantaneous r-value after strain-path change, and 3) yield surface evolution, are discussed. Finally, potential improvements are suggested for VPSC-RGBV model.

The present work integrates in-situ neutron diffraction, electron backscatter diffraction and crystal plasticity modeling to investigate the effect of martensitic phase transformation on the behavior of 304 stainless steel under uniaxial tension. The macroscopic stress strain response, evolution of the martensitic phase fraction, texture evolution of each individual phase, and internal elastic strains were measured at room temperature and at 75 °C. Because no martensitic transformation was observed at 75 °C, the experimental results at 75 °C were used as a reference to quantify the effect of formed martensitic phase on the behavior of 304 stainless steel at room temperature. A crystallographic phase transformation model was implemented into an elastic–viscoplastic self-consistent framework. The phase transformation model captured the macroscopic stress strain response, plus the texture and volume fraction evolution of austenite and martensite. The model also predicts the internal elastic strain evolution with loading in the austenite, but not in the martensite. The results of this work highlight the mechanisms that control phase transformation and the sensitivity of modeling results to them, and point out to critical elements that still need to be incorporated into crystallographic phase transformation models to accurately describe the internal strain evolution during phase transformation.

A metallic composite having TiC particle content as high as ~47 vol% in a cold work tool steel matrix was successfully fabricated by a novel infiltration process. The penetration of the liquid steel reached geometrically complex regions, such that no interfacial flaw was observed. The interface between the ferrite matrix and TiC was semicoherent with a faceted morphology consisting of low-index planes of each phase. Owing to these characteristics of the interface, neither interfacial decohesion nor cracking was observed after the tensile fracture. The initial failure occurred in the TiC particle by a {100} cleavage fracture. The cracks formed from each fractured TiC particle interlinked forming a major crack. The hot-isostatically pressed composite exhibited 16% higher strength (919 MPa) than the as-infiltrated composite (791 MPa). The fracture strength of the composite largely depended on the degrees of suppression of the TiC cracking and its propagation. The residual stresses pertaining to the TiC and steel matrix were measured by X-ray diffraction. They were not significant factors responsible for the increased fracture strength of the hot-isostatically pressed composite. The increased strength of the hot-isostatically pressed composite could be explained in terms of the mutually interactive influences of the load transfer mechanism, matrix toughening, reduced TiC contiguity, and M7C3 carbide bridging TiC particles.

Constitutive behaviors of an interstitial-free steel sample were measured using an augmented Marciniak experiment. In these tests, multiaxial strain field data of the flat specimens were measured by the digital image correlation technique. In addition, the flow stress was measured using an X-ray diffractometer. The flat specimens in three different geometries were tested in order to achieve 1) balanced biaxial strain, and plane strain tests with zero strain in either 2) rolling direction or 3) transverse direction. The multiaxial stress and strain data were processed to obtain plastic work contours with reference to a uniaxial tension test along the rolling direction. The experimental results show that the mechanical behavior of the subjected specimen deviates significantly from isotropic behavior predicted by the von Mises yield criterion. The initial yield loci measured by a Marciniak tester is in good agreement with what is predicted by Hill's yield criterion. However, as deformation increases beyond the von Mises strain of 0.05, the shape of the work contour significantly deviates from that of Hill's yield locus. A prediction made by a viscoplastic self-consistent model is in better agreement with the experimental observation than the Hill yield locus with the isotropic work-hardening rule. However, none of the studied models matched the initial or evolving anisotropic behaviors of the interstitial-free steel measured by the augmented Marciniak experiment.

A viscoplastic self-consistent crystal plasticity model was employed to study the formability of two magnesium sheet alloys, i.e., AZ31 and ZE10 at 200 ° C . The flow stress-strain curves obtained by uniaxial tension tests at various strain rates and the crystallographic texture obtained from X-ray diffraction were used to calibrate the model. The crystal plasticity model was incorporated with the Marciniak–Kuczynski model in order to address the forming limits of the magnesium sheets. A good agreement of the model predictions with the experimental data obtained by Nakajima tests was achieved. The model was further studied to quantify the effects of the sample orientation with respect to laboratory axes, the amount of pre-strain applied to the sheet prior to forming, and the initial crystallographic texture. The resulting forming limit diagrams demonstrate the optimal choice of sample orientation and crystallographic texture that can lead to a significant improvement in forming limit strains.

A rate-dependent self-consistent crystal plasticity model was incorporated with the Marciniak–Kuczyński model in order to study the effects of anisotropy on the forming limits of BCC materials. The computational speed of the model was improved by a factor of 24 when running the simulations for several strain paths in parallel. This speed-up enabled a comprehensive investigation of the forming limits of various BCC textures, such as γ, σ, α, η and ϵ fibers and a uniform (random) texture. These simulations demonstrate that the crystallographic texture has significant (both positive and negative) effects on the resulting forming limit diagrams. For example, the γ fiber texture, which is often sought through thermo-mechanical processing due to a high r-value, had the highest forming limit in the balanced biaxial strain path but the lowest forming limit under the plane strain path among the textures under consideration. A systematic investigation based on the results produced by the current model, referred to as ‘VPSC-FLD’, suggests that the r-value does not serve as a good measure of forming limit strain. However, model predictions show a degree of correlation between the r-value and the forming limit stress.