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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 three-dimensional elastoplastic phase-field model is developed to study the microstructure evolution during strain-induced martensitic transformation in stainless steels under different stress states. The model also incorporates linear isotropic strain hardening. The input simulation data is acquired from different sources, such as CALPHAD, ab initio calculations and experimental measurements. The results indicate that certain stress states, namely uniaxial tensile, biaxial compressive and shear strain loadings, lead to single variant formation in the entire grain, whereas others, such as uniaxial compressive, biaxial tensile and triaxial strain loadings, lead to multivariant microstructure formation. The effects of stress states, strain rate as well as temperature on the mechanical behavior of steels are also studied. The material exhibits different yield stresses and hardening behavior under different stress states. The equivalent stress is higher at low strain rate, whereas a higher elongation is obtained at high strain rate. The deformation temperature mainly affects the hardening behavior of the material as well as the transformation, i.e. martensite volume fraction decreases with increasing temperature. Some of the typical characteristics of strain-induced martensite, such as the formation of thin elongated martensite laths, shear band formation and nucleation of martensite in highly plasticized areas, as well as at shear band intersections, are also observed. [Copyright &y& Elsevier]

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: In the present work a multi-length scale model is developed to study both the athermal and stress-assisted martensitic transformations in a single crystal of 301 type stainless steel. The microstructure evolution is simulated using elastoplastic phase-field simulations in three dimensions. The input data for the simulations is acquired from a combination of computational techniques and experimental works. The driving force for the transformation is calculated by using the CALPHAD technique and the elastic constants of the body-centered cubic phase are calculated by using ab initio method. The other input data is acquired from experimental works. The simulated microstructures resemble a lath-type martensitic microstructure, which is in good agreement with the experimental results obtained for a stainless steel of similar composition. The martensite habit plane predicted by the model is in accordance with experimental results. The Magee effect, i.e. formation of favorable martensite variants depending on the loading conditions, is observed in the simulations. The results also indicate that anisotropic loading conditions give rise to a significant anisotropy in the martensitic microstructure. [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]

Abstract: A 3D elastoplastic phase-field model is employed to study various driving forces associated with martensitic transformations, plastic deformation behavior as well as the habit plane concept. Usage of thermodynamic parameters corresponding to Fe–0.3%C alloy in conjunction with anisotropic physical parameters of steels as the simulation parameters have yielded the results in reasonable agreement with experimental observations. From the simulation results, it is concluded that there exist three critical driving forces that control the transformation and also that the plastic deformation behavior of the material greatly affects the transformation. The model predicts the initial habit plane of the first infinitesimal unit of martensite as (−111). The model also predicts that, as the transformation progresses, the above mentioned martensite domain rotates and finally orients along the new habit plane of (−211). [Copyright &y& Elsevier]

Abstract: In the present work a 3-D elastoplastic phase-field (PF) model is developed, based on the PF microelasticity theory proposed by A.G. Khachaturyan and by including plastic deformation as well as anisotropic elastic properties, for modeling the martensitic transformation (MT) by using the finite-element method. PF simulations in 3D are performed by considering different cases of MT occurring in an elastic material, with and without dilatation, and in an elastic perfectly plastic material with dilatation having isotropic as well as anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to an Fe–0.3%C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The simulation results clearly show autocatalysis and morphological mirror image formation, which are some of the typical characteristics of a martensitic microstructure. The results indicate that elastic strain energy, anisotropic elastic properties, plasticity and the external clamping conditions affect MT as well as the microstructure. [Copyright &y& Elsevier]