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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.

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.

The onset of ductile fracture can be described by a simple damage parameter, which accounts for the accumulation of damage under arbitrary deformation. The damage parameter is usually given as integral form of strain over loading history which also has been described as a function of stress state. While the evolution of strain field can be experimentally determined using digital image correlation, experimental measurement of the multiaxial stress state is still a challenging task. Therefore, various uncoupled fracture criteria rely on stress states calculated from phenomenological plasticity model. As a result, the number of mechanical tests required to calibrate the fracture criterion may significantly increase when an anisotropic constitutive model is used. We propose an alternative approach on the basis of a mean field crystal plasticity (VPSC) model, which accounts for the microstructural features such as slip system, crystallographic texture and its evolution. While stress fields can be obtained from the use of full-field crystal plasticity framework, the proposed method utilizes the mean field crystal plasticity framework and repeat the stress estimation on various spatially resolved locations to which DIC technique provides strain history. The repeated VPSC calculations at various locations efficiently provide the map of stress evolution. The resulting map of spatially resolved stress response is further validated by comparing with the bulge stress strain curves.

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.

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 were used to determine the model parameters. The crystal plasticity model was incorporated with the Marciniak-Kuczynski model in order to address the forming limits of the magnesium sheets. Model predictions were matched with the experimental data obtained by Nakajima tests by tuning the respective parameters. The model was further applied to quantify the effect of the initial crystallographic texture on the formability. Virtual textures representing realistic outcome from mechanical working (rolling, extrusion) were generated. The respective effects on the formability were quantified. The resulting forming limit diagrams demonstrate that the variations of crystallographic texture can either lead to an improvement or to a detrimenta...

The flow stress behavior of a bake-hardenable steel during a few simple shear cycles is investigated using a crystal plasticity model. The simple shear test provides a stable way to reverse the loading direction. Stress reversals were accompanied with a lower yield stress, i.e., the Bauschinger effect, followed by a transient hardening stage with a plateau region and, permanent softening. The origins of these three distinct stages are discussed using a crystal plasticity model. To this end, the representative discrete grain set is tuned to capture such behavior by coupling slip system hardening appropriately. The simulated results are compared with experimental forward-reverse simple shear stress-strain curves. It is shown that the characteristic flow stress stages are linked to texture evolution and to the Bauschinger effect acting on the different slip systems.

The current study investigates constitutive models at two different scales: 1) the micromechanical crystal plasticity framework using a dislocation density-based hardening model [1, 2]; 2) macroscale constitutive model based on a yield function that evolves according to the homogeneous anisotropic hardening (HAH) model [3, 4]. The polycrystalline aggregate, tuned for a low-carbon steel, is used to calculate the evolution of the yield surface during monotonic uniaxial tension. The results of the crystal plasticity model are used to train the anisotropic yield function and HAH parameters to demonstrate the flexibility of the macroscale constitutive approach. Through comparison between the two models, an improved rule for the HAH model is suggested.