Evolution Of Martensitic Microstructure Research Articles

Effect of pore on the deformation behaviors of NiTi shape memory alloys: A crystal-plasticity-based phase field modeling

Porous NiTi shape memory alloys (SMA) have been developed into important biomedical and damping materials. However, the effect of pore on the martensitic microstructure evolution, functional properties, and plastic deformation has not been fully clear yet. In this work, to reveal the functional properties including superelasticity (SE), elastocaloric effect (eCE), one-way shape memory effect (OWSME), and stress-assisted two-way shape memory effect (SATWSME), as well as plastic deformation of porous NiTi SMAs, the polycrystalline SMA system is considered as a composite containing the grain-interior (GI) and grain-boundary (GB) phases, a thermo-mechanically coupled, grain-size-dependent and crystal-plasticity-based phase field model is proposed for the GI phase, and an elasto-viscoplastic constitutive model is established for the GB phase. The effects of porosity, pore diameter, pore aspect ratio, pore orientation, and pore distribution, as well as the interaction between pore and grain size, are comprehensively revealed and discussed. The simulations demonstrate that the pores cause a heterogeneous stress field, and the interaction among pores and that between pores and grain boundaries can enhance such heterogeneity, which can promote the initiation of martensitic transformation and reorientation. Moreover, the geometrical constraints caused by the pores can significantly affect the morphology and evolution of martensite microstructures. However, due to the diverse microstructure evolutions during SE, OWSME, and SATWSME, their interactions with the pores are quite different, resulting in various dependencies of each functional property and plastic deformation on the pore, and such dependencies are strongly influenced by porosity, pore diameter, pore aspect ratio, pore orientation, and pore distribution. The simulated results in this work are helpful to comprehensively and deeply understand the pore effect and its microscopic mechanism.

Correction to: Martensitic microstructure evolution in austenitic steel: A thermomechanical polycrystalline phase field study

Correction to: Martensitic microstructure evolution in austenitic steel: A thermomechanical polycrystalline phase field study

Phase-field modeling of multivariant martensitic transformation at finite-strain: Computational aspects and large-scale finite-element simulations

Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic anisotropy of the phases, and incorporates Hencky-type elasticity, a penalty-regularized double-obstacle potential, and viscous dissipation. The finite-element discretization of the model is performed in Firedrake and relies on the PETSc solver library. The large systems of linear equations arising are efficiently solved using GMRES and a geometric multigrid preconditioner with a carefully chosen relaxation. The modeling capabilities are illustrated through a 3D simulation of the microstructure evolution in a pseudoelastic CuAlNi single crystal during nano-indentation, with all six orthorhombic martensite variants taken into account. Robustness and a good parallel scaling performance have been demonstrated, with the problem size reaching 150 million degrees of freedom.

A phase field approach to study of transformation induced micro–cracking in a martensitic phase transformation

AbstractIn this study, a coupled phase field (PF) method for the simulation of crack propagation and martensitic phase transformations is developed. In order to investigate the crack field and martensitic microstructure evolution the concept of the thermodynamic driving force, interfacial energy, the elastic energy, and the kinetic of phase field equations are introduced (time dependent Ginzburg Landau equation) [1]. The weak form and an algorithm for the solution of corresponding equations are implemented in the finite element program (FEAP). Since the phase transformation can form during the application of high amount of stresses, the influence of microcrack propagation on the formation of the martensitic phase has been studied. The crack tip produces high amount of concentrated stresses, which lead to a change in the distribution of the martensitic phases and it can also deviate the crack direction [2].

Multi-length scale modeling of carburization, martensitic microstructure evolution and fatigue properties of steel gears

Multi-length scale modeling is performed to (i) predict the carburized case depth of SAE8620 steel gears by solving the Fick’s second law of diffusion, (ii) model the martensitic microstructure evolution in a grain inside the carburized case as well as to study the effect of stress cycling on retained austenite (RA) and martensite using a 3D phase-field model, (iii) simulate the effect of carburization and different RA contents on macroscale fatigue behavior of SAE8620 steel spur gear using the finite element method. The diffusion model predicts that the case depth increases with increasing heat treatment time and temperature. The phase-field simulations show that RA can transform to martensite during fatigue loading, where the extent of the transformation will depend on the type of stresses applied, i.e. stresses in a high stress regime or low stress regime of fatigue loading. Reverse transformation of martensite to austenite is also observed in low RA sample under high stress regime. The macroscale simulations show that the carburized case with high RA gives rise to better fatigue life compared to that with low RA.

Effect of carbon on elastic properties and microstructure of maraging steel: First-principles and phase-field study

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.

Phase-field modeling of austenite grain size effect on martensitic transformation in stainless steels

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.

Microstructural evolution, coarsening behavior of precipitates and mechanical properties of boron bearing steel 25CrMoNbB during tempering

In order to optimize the tempering process of boron bearing steel 25CrMoNbB, the effect of tempering temperature and holding time on martensitic microstructure, precipitation and mechanical properties has been studied. Thermo-Calc software was used to carry out thermodynamic calculation of the equilibrium precipitation. The precipitates growth behaviors were simulated using the program package diffusion-controlled transformations (DICTRA). Field emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), selected area electron diffraction (SAD) and energy dispersive spectrometer (EDS) were used to analyze microstructure and precipitates. B distribution was observed by secondary ion mass spectroscopy (SIMS). Electron back-scattered diffraction (EBSD) and TEM were used to analyze the martensitic microstructure evolution during tempering. The results showed that the B-bearing precipitates had a significant effect on the impact toughness and little effect on the tensile strength. The B atoms segregating at prior austenite grain boundaries (PAG) during austenitizing process promoted precipitation of M2B during tempering. The M2B precipitates mainly contained Fe, Mo, Cr and B elements and significantly reduced the toughness. Therefore, B content in 25CrMoNbB steel should be controlled below 20ppm. In addition, the tempering temperature and holding time should also be optimized to reduce the detrimental effect of M2B on the impact toughness. In as-tempered condition, besides M2B precipitates, M23C6, M7C3, and MC carbides were identified. M7C3 and MC carbides tended to precipitate in the matrix, whereas M23C6 tended to precipitate at PAG and sub-grain boundaries. Although carbides were coarsening with increasing tempering temperature or holding time, the coarsening of martensitic blocks and laths has reduced their detrimental effect on the toughness.

Finite element simulations of microstructure evolution in stress-induced martensitic transformations

Microstructure evolution in single crystal and polycrystal shape memory alloys under uniaxial tension and compression is investigated using the finite element method. To determine stress-strain diagrams and evolution of martensitic microstructure during external loading, a micromechanics based thermo-mechanical material model is used. The results reveal the significant difference between the local and global material behavior when defects are present. It is shown that defects act as nucleation sites and result in transformation localization, which in turn causes a sudden drop in the stress-strain diagram followed by a stress plateau. Moreover, it is found that some regions undergo reverse transformation although the elastic moduli of the phases are equal and the loading is monotonic. Increase in athermal friction, which is the resistance to interface propagation, is found to delay the phase transformation and different magnitudes of hysteresis are obtained at different friction values. The model predicts the tension-compression asymmetry observed in shape memory alloys. The simulation results are in qualitative agreement with several experimental studies.

Stress-assisted martensitic transformations in steels: A 3-D phase-field study

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.

Effects of External Stresses on the Martensitic Transformation in a 3D Polycrystalline Material Using the Phase Field Method

ABSTRACTIn the current study an elasto-plastic phase field (PF) model, based on the PF microelasticity theory proposed by A.G. Khachaturyan, is used to investigate the effects of external stresses on the evolution of martensitic microstructure in a Fe-0.3%C polycrystalline alloy. The current model is improved to include the effects of grain boundaries in a polycrystalline material. The evolution of plastic deformation is governed by using a time dependent Ginzburg-Landau equation, solving for the minimization of the shear strain energy. PF simulations are performed in 2D and 3D to study the effects of tension, compression and shear on the martensitic transformation. It has been found that external stresses cause an increase in the volume fraction of the martensitic phase if they add to the net effect of the transformation strains, and cause a decrease otherwise. It has been concluded that the stress distribution and the evolution of martensitic microstructure can be predicted with the current model in a polycrystalline material under applied stresses.

Three-dimensional phase-field modeling of martensitic microstructure evolution in steels

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.

Evolution of Martensitic Microstructure of Carbon Steel Tempered at Low Temperatures

This work presents the microstructural changes of a carbon steel during tempering at low temperatures (first stage of tempering), and its effects in the second and third stages. These changes are determined by internal friction. Internal friction is measured in a forced vibration mode at 5Hz, in a temperature range from 300 to 600K. Four internal friction peaks appear: S1 at 350K, P1 at 380K, P2 at 440K, P3 at 480K. S1 only appears in the sample tempered at 380K for 20hours, and this can be related to the reduction of the martensite tetragonality. The height of P1 is lowest when the intensity of tempering is increased. This height can be related to the quantity of epsilon carbide than precipitate. The heights of P2 and P3 are not changed significantly, but the difference of temperature between both is lowest when the tempering intensity is increased. This suggests than the dissolution of epsilon carbide and formation of cementite takes places in a lowest range of temperature

Investigation of martensitic microstructures in a monocrystalline Cu–Al–Be shape memory alloy with the grid method and infrared thermography

The objective of the study is to analyze the martensitic microstructure evolution in a shape-memory alloy during a stress-induced transformation. Two full-field measurement techniques are used for this purpose: the grid method to obtain strain maps and infrared thermography to measure temperature variation maps at the same time. The specimen is a monocrystalline Cu–Al–Be alloy which is austenitic at ambient temperature. Austenite progressively transforms into martensite during the mechanical loading and the impact of this transformation in terms of strain and temperature is analyzed in this paper. The spatial resolution of the strain maps obtained enables us to distinguish some typical martensitic microstructures such as martensite needles, habit planes and X-shaped microstructures, so the evolution of these microstructures during the test is presented and discussed with strain maps obtained at some points regularly spaced on the stress–strain curve. Infrared thermography provides some additional information to analyze the transformation phenomena. Maps of latent heat are calculated from temperature maps thanks to a specific post-processing procedure. Interestingly, the microstructure evolution during the loading phase is found to be different of the evolution during the unloading phase although the specimen precisely returns to zero strains at the end of the cycle. In the last part of the paper, the values of the measured in-plane strain components are used to identify the martensite variants that likely appear in the specimen during the loading phase of the test. This identification is based on some crystallographic compatibility calculations.

3D Phase Field Modeling of Martensitic Microstructure Evolution in Steels

Complex martensitic microstructure evolution in steels generates enormous curiosity among the materials scientists and especially among the Phase Field (PF) modeling enthusiasts. In the present work PF Microelasticity theory proposed by A.G. Khachaturyan coupled with plasticity is applied for modeling the Martensitic Transformation (MT) by using Finite Element Method (FEM). PF simulations in 3D are performed by considering different cases of MT occurring in a clamped system, i.e. simulation domain with fixed boundaries, of (a) pure elastic material with dilatation (b) pure elastic material without dilatation (c) elastic perfectly plastic material with dilatation having (i) isotropic as well as (ii) anisotropic elastic properties. As input data for the simulations the thermodynamic parameters corresponding to Fe - 0.3% C alloy as well as the physical parameters corresponding to steels acquired from experimental results are considered. The results indicate that elastic strain energy, dilatation and plasticity affect MT whereas anisotropy affects the microstructure.

Composition, structure and magnetic properties of sputter deposited Ni–Mn–Ga ferromagnetic shape memory thin films

Polycrystalline Ni–Mn–Ga thin films were deposited by the d.c. magnetron sputtering on well-cleaned substrates of Si(1 0 0) and glass at a constant sputtering power of 36 W. We report the influence of sputtering pressure on the composition, structure and magnetic properties of the sputtered thin films. These films display ferromagnetic behaviour only after annealing at an elevated temperature and a maximum saturation magnetization of 335 emu/cc was obtained for the films investigated. Evolution of martensitic microstructure was observed in the annealed thin films with the increase of sputtering pressure. The thermo-magnetic curves exhibited only magnetic transition in the temperature range of 339–374 K. The thin film deposited at high sputtering pressure of 0.025 mbar was found to be ordered L2 1 austenitic phase.

Micromechanical modeling of stress-induced phase transformations. Part 1. Thermodynamics and kinetics of coupled interface propagation and reorientation

The universal (i.e. independent of the constitutive equations) thermodynamic driving force for coherent interface reorientation during first-order phase transformations in solids is derived for small and finite strains. The derivation is performed for a representative volume with plane interfaces, homogeneous stresses and strains in phases and macroscopically homogeneous boundary conditions. Dissipation function for coupled interface (or multiple parallel interfaces) reorientation and propagation is derived for combined athermal and drag interface friction. The relation between the rates of single and multiple interface reorientation and propagation and the corresponding driving forces are derived using extremum principles of irreversible thermodynamics. They are used to derive complete system of equations for evolution of martensitic microstructure (consisting of austenite and a fine mixture of two martensitic variants) in a representative volume under complex thermomechanical loading. Viscous dissipation at the interface level introduces size dependence in the kinetic equation for the rate of volume fraction. General relationships for a representative volume with moving interfaces under piece-wise homogeneous boundary conditions are derived. It was found that the driving force for interface reorientation appears when macroscopically homogeneous stress or strain are prescribed, which corresponds to experiments. Boundary conditions are satisfied in an averaged way. In Part 2 of the paper [Levitas, V.I., Ozsoy, I.B., 2008. Micromechanical modeling of stress-induced phase transformations. Part 2. Computational algorithms and examples. Int. J. Plasticity (2008)], the developed theory is applied to the numerical modeling of the evolution of martensitic microstructure under three-dimensional thermomechanical loading during cubic-tetragonal and tetragonal-orthorhombic phase transformations.

Stress Induced and Magnetic Field Enhanced Twin Variants Reorientation in NiMnGa Single Crystal

The behavior of twin variants reorientation in Ni50Mn27.5Ga22.5 single crystal under the applied mechanical stress and magnetic field was investigated. Through three times of compression, the twinning stress was reduced from 4.4MPa to 0.4MPa, and 2.5% stress induced strain was obtained. During the succedent MFIS measurement, with the increase of measurement number of times, the critical field (μ0H)c at which the MFIS jumps became lower, and the corresponding jumping magnetostrain ε j, and the maximal magnetostrain εmax ascended. At last, a quasi single-variant state was realized, and the sample showed repeatable 6.21% MFIS, which is close to the theoretical value (1-c/a)*100%. The results are discussed from the point of martensitic microstructure evolution.

Martensitic transformations in constrained films

The evolution of martensitic microstructure and stress in a constrained film coupled with a substrate under cooling and heating is considered. Thermodynamic analysis has done using the special phase diagrams constructed in coordinates temperature-film/ substrate misfit.