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• Elastic properties of Marval X12 and FeCrNiC steels calculated from DFT. • The main effect of C on elastic constants is due to symmetry change. • 3D phase field model predicts a change from lath to mixed martensite morphology. The effect of the carbon concentration on the elastic properties and martensitic microstructure of Marval X12 steel is studied using first principles calculations and phase-field simulations. The density functional theory (DFT) results predict almost no changes of the elastic moduli with an increase of C content. However, there is a sizeable change of the elastic constants due to cubic to tetragonal martensitic transformation. The elastic constants are used as input data for the 3D elastoplastic phase-field model to study the martensitic microstructure evolution in Marval X12 steel. The results, showing that lath martensite is formed in this steel, are in agreement with experiments. With increasing carbon concentration, we observe formation of mixed morphology predominantly composed of martensite laths and some martensite plates. Our results also suggest that different combinations of martensite variants are formed with increasing carbon content. [ABSTRACT FROM AUTHOR]

Graphical abstract Simulated microstructures showing different martensite packets in grains of size (a) 1 (b) 3 (c) 5 and (d) 10 μm. Highlights • Phase-field modeling of the effect of austenite grain size on martensite formation in steels. • Multi- and uni-directional martensite growth in coarse and fine grains, respectively. • Number of packets and martensite block width increase with increasing grain size. • Martensite nucleation is difficult in fine grains compared to coarse grains. • Once martensite is nucleated, fine grains facilitate growth of martensite. Abstract A 2D elastoplastic phase-field model is developed to study the effect of prior austenite grain size on martensitic microstructure evolution in stainless steel. The effects of strain hardening and strengthening by grain size reduction (Hall-Petch effect) have been included in the model. The results show that martensite units form in different packets oriented in different crystallographic directions in simulated coarse grains, whereas uni-directional martensitic growth is observed in simulated fine grains. The number of packets and martensite block width increase with increasing grain size. With a decreasing grain size the martensitic transformation start temperature decreases, indicating strengthening of austenite. Once the transformation is initiated, at a given time, simulated fine grains give rise to higher volume fraction of martensite compared to simulated coarse grains. The von Mises equivalent stress and plastic strain are large in simulated fine grains compared to those in simulated coarse grains. The simulation results are in good agreement with experimental results. [ABSTRACT FROM AUTHOR]

A 3D elastoplastic phase-field model is used to study the effect of thermal cycling on martensitic transformation as well as on mechanical strengthening of both austenite and martensite in stainless steel. The results show that with an increasing number of thermal cycles, martensite becomes more stable. Increase in strain, plastic strain and strain hardening lead to strengthening of austenite. [ABSTRACT FROM AUTHOR]

A three dimensional (3D) elastoplastic phase-field model is developed for modeling the hydrostatic pressure-induced alpha – omega phase transformation and the reverse phase transformation, i.e. omega – alpha, in zirconium (Zr). Plastic deformation and strain hardening of the material are also considered in the model. The microstructure evolution during both phase transformations is studied. The transformation start pressures at different temperatures are predicted and are plotted as a phase diagram. The effect of phase transformations on the mechanical properties of the material is also studied. The input data corresponding to pure Zr are acquired from experimental studies as well as by using the CALPHAD method. Our simulations show that three different omega variants form as laths. On release of pressure, reverse phase transformation initiates at lath boundaries. We observe that both phase transformations are martensitic in nature and also occur at the same pressure, i.e. little hysteresis. The transformation start pressures and the kinetics of the transformation predicted by our model are in good agreement with experimental results. [ABSTRACT FROM AUTHOR]

Abstract: A 3-D elastoplastic phase-field model is developed for modeling, using the finite-element method, the stress-assisted martensitic transformation by considering plastic deformation as well as the anisotropic elastic properties of steels. Phase-field simulations in 3-D are performed by considering different loading conditions on a single crystal of austenite in order to observe the microstructure evolution. The thermodynamic parameters corresponding to an Fe–0.3% C steel as well as the physical parameters corresponding to commercial steels, acquired from experimental results, are used as input data for the simulations. The simulation results clearly show the well-known Magee effect and the Greenwood–Johnson effect. The results also show that even though the applied stresses are below the yield limit of the material, plastic deformation initiates due to the martensitic transformation, i.e. the well-known transformation-induced plasticity (TRIP) phenomenon. It is concluded that the loading conditions, TRIP as well as autocatalysis play a major role in the stress-assisted martensitic microstructure evolution. [Copyright &y& Elsevier]

Abstract: The Phase Field Microelasticity model proposed by Khachaturyan is used to perform 3D simulation of Martensitic Transformation in polycrystalline materials using finite element method. The effect of plastic accommodation is investigated by using a time dependent equation for evolution of plastic deformation. In this study, elasto-plastic phase field simulations are performed in 2D and 3D for different boundary conditions to simulate martensitic transformation in polycrystalline Fe-0.3%C alloy. The simulation results depict that the introduction of plastic accommodation reduces the stress intensity in the parent phase and hence causes an increase in volume fraction of the martensite. Simulation results also show that autocatalistic transformation initiates at the grain boundaries and grow into the parent phase. It has been concluded that stress distribution and the evolution of microstructure can be predicted with the current model in a polycrystal. [Copyright &y& Elsevier]

[Display omitted] A 3D elastoplastic phase-field model is used to study the effect of isochronal heating on martensitic transformation in stainless steel quenched to cryogenic temperature. The results show that the slower the heating, the larger is the martensite volume fraction developed on heating. The simulated microstructures show that the transformation is driven by autocatalysis during the early stages and by coarsening of existing martensite units during later stages of the transformation. The internal stresses are mainly relaxed by autocatalysis during the initial stages of the transformation, whereas they are relaxed by plastic deformation during the later stages of the transformation. The temperature for attaining a certain martensite fraction increases with increasing heating rate, which is consistent with a thermally activated transformation. Kissinger-like analysis of the simulated transformation curves provides an activation energy of 11.9 kJ/mol. [ABSTRACT FROM AUTHOR]