Coupled Phase Transformation Research Articles

Morphological and Dimensional Evolution of Nanosized Amorphous Silicon Nitride in α-Fe: Diffusional and Elastic Effects

We present a detailed analysis based on both experimental and 3D modelling approaches of the unique silicon nitride precipitation sequence observed in ferritic Fe-Si alloys upon nitriding. At 570 °C, Si3N4 silicon nitride was shown to form as an amorphous phase into α-Fe ferrite matrix, which is morphologically unstable over time. Precipitates nucleated with a spheroidal shape, then developed a cuboidal shape for intermediate sizes and octapod-like morphology for a longer time. Using transmission electron microscopy, we show that the transition between spheroid and cuboid morphology depended on particle size and resulted from competition between interfacial energy and elastic strain energy. The resulting morphology was then shown to be a cuboid shape whose faces were always parallel to the {100} planes of the α-Fe; the <100> directions of the matrix corresponded to the elastically soft directions. There was a critical size of around 45 nm for which the transition between the cuboid shape and the octapod-like morphology took place. This was characterised by a transformation of quasi-flat facets into concave ones and the development of lobes in the <111> directions of the bcc crystal. To better assess the kinetic effects of diffusion fields and internal stresses on the morphological instability observed, an original 3D model that explicitly coupled phase transformations and mechanical fields was developed and applied. The latter, validated on the basis of model cases, was shown to be able to describe the time-evolution of both chemical and mechanical fields and their interactions in diffusive mass transport. Using a model system, it was shown that the concentration field around the precipitates and the internal stresses played opposing roles in the cuboid to octapod-like morphological instability. This work gives some clarification regarding the morphological evolution of amorphous Si3N4 precipitates, an important point for controlling the mechanical properties of nitrogen steels.

Numerical Simulation of Jominy End Quench Test Using Coupled Heat Transfer and Phase Transformation Model

Jominy end quench test is a standardized metallurgical experiment for obtaining data on steel hardenability. Construction of numerical simulation of the test provides a way for parameterizing and validation of numerical models using the experimental data. In the current work we present the coupled heat transfer, conduction and phase transformation model, which allows for calculation of phase fractions at different positions at the Jominy test piece, and includes the latent heat released by the phase transformations. Also, the temperature and phase fraction dependence of the thermal conductivity is included in the calculation.

Simulation of SMA-based engineering applications considering large displacement and rotation, thermomechanical coupling and partial phase transformation

Shape memory alloys (SMAs) undergo large recoverable deformation due to their inherent diffusionless martensitic phase transformation. Two factors need to be taken into account to incisively emulate the behaviour of SMA based structures: (i) consideration of large displacement and rotation (LDR) effect, and (ii) capturing the consequence of transformation induced material level coupling. In this study, both these effects are apprehended by extending the infinitesimal strain-based constitutive model of SMA as proposed by Lagoudas et al. (2012), assuming small elastic strain but with finite inelastic strain. To preclude any spurious stress generation out of large rotation, the Jaumann stress rate is used, and incremental objectivity for finite rotation between two successive time instants is conserved by rotating the strain increment and spin tensor to the rotation-independent mid-point configuration following Hughes–Winget (Hughes and Winget, 1980) algorithm. In addition, the contribution of thermoelastic and latent heat evolved during transformation is taken into consideration in the thermal equilibrium equation. Moreover, the effect of partial phase transformation yielding minor hysteresis loop has also been captured. The equilibrium equation is expressed in the current configuration following the Updated Lagrangian formulation. The mechanical and thermal equilibrium equations are solved concurrently in block matrix form using the Newton–Raphson (NR) iterative technique, considering the coupling terms resulting from the phase transformation. The efficacy and robustness of the developed finite element model are corroborated through various practical applications of SMA-based members, e.g., SMA ring, SMA-actuated beam, morphing of corrugated airfoil, orthodontic palatal expander, compliant gripper, undergoing LDR while subjected to different thermomechanical loading conditions. The combined effects of LDR along with thermomechanical coupling yield a stiffening behaviour during loading and sluggish response at the time of thermal recovery.

Influence of phase transformation on stress wave propagation in thin-walled tubes

Phase transformation can change the properties of a material and significantly affect the stress wave propagation features. This study presents an analytical model of coupled stress wave propagation in pseudo-elastic shape memory alloy thin-walled tubes subjected to combined longitudinal and torsional impact loading. An incremental constitutive model considering the effect of the hydrostatic pressure and deviatoric stress was employed to describe the mechanical behavior of SMA. The phase transformation ellipses shift along the σ-axis in the σ – τ plane due to the asymmetry of tension and compression induced by the hydrostatic pressure. The generalized characteristic theory was used to obtain the characteristic wave speed,simple wave solution, and the differential equation determining the stress path. The numerical results showed that the wave structure in the thin-walled tube is affected by the initial stress state and the final loading state. For the initially static and unstressed thin-walled tube, there is a special region on the σ–τ plane. When the combined longitudinal and torsion impact load lies in this region, an elastic compression wave, elastic shear wave and coupled phase transformation fast waves appear in the thin-walled tube in turn. The abnormal phenomenon is not observed in the conventional elastoplastic tubes.

Phase-field simulation of misfit dislocations in two-phase electrode particles: Driving force calculation and stability analysis

Dislocations in lithium-ion battery materials significantly influence the performance of the battery. A chemo-mechanical phase-field model combined with a non-singular continuum theory of dislocations is developed to simulate misfit dislocations at the phase boundary of two-phase LiFePO4 particles. The configurational mechanics of dislocations in the mechanically coupled phase transformation problem is proposed and then used to formulate a dislocation formation criterion. The model is numerically implemented using the finite element method to compute driving forces on misfit dislocations. The driving force is further used to study the stability of the misfit dislocation to predict the critical size of dislocation-free two-phase electrode particles. The orthotropic and non-homogeneous elastic constants in two phases, anisotropic misfit strain, different aspect ratios of the particle, and different positions of the phase boundary in equiaxed particles are considered. The large misfit strain at the phase boundary is found to cause a redistribution of the concentration and thus a relaxation of the stress field at the interface. Stress relaxation is crucial to the driving force on the dislocation and ignoring the stress relaxation leads to an underestimation of the critical particle size. The critical particle size decreases with increasing aspect ratios and shows a saturation after aspect ratios above 2. An optimum aspect ratio of the dislocation-free electrode particle is around 1.5 which features the highest specific surface area.

Coupled heat transfer and phase transformations of dual-phase steel in coil cooling

Dual-phase steels are generally used in the car industry due to high tensile strength and good formability, which are obtained by a mixture of bainite and ferrite phases. This microstructure is achieved through slow rate coil cooling. However, the manufacturing of dual-phase steels introduces various challenges such as the instability of the cold rolling process. An important factor affecting this is the non-uniform coil cooling of a hot rolled strip. In coil cooling the cooling rates are not controlled and there are different thermal contacts during coil conveyance causing unequal cooling of the steel coil. Unequal cooling rates lead to non-uniform coil cooling, producing irregular phase transformations on different sides of the coil, which causes periodical variations of the phase fractions in the steel strip. Varying phase fractions cause thickness deviations in the strip during the cold rolling process. A three-dimensional transient heat transfer finite element model was developed and used for modeling the complete coil conveyance chain and coil field cooling of the coil on an industrial scale. A coupled phase transformation model is implemented as a subroutine into the finite element model for calculating the resulting phase fractions. It was found that the different thermal contacts during the coil conveyance produce uneven cooling rates causing length- and widthwise variations in the phase fractions. The heat transfer model is validated by comparing temperature profiles between the simulated and measured coil edges. The phase transformation model is fitted into experimental data and verification is carried out in industrial conditions by comparing the modeled phase fractions and test samples from a cooled and unwound steel coil.

Study of the Fracture Behavior of Tetragonal Zirconia Polycrystal with a Modified Phase Field Model.

The superior fracture toughness of zirconia is closely correlated with stress-induced martensitic phase transformation around a crack tip. In this study, a modified phase field (PF) model coupling phase transformation and fracture is proposed to study the fracture behavior and toughening effect of tetragonal zirconia polycrystal (TZP). The stress-induced tetragonal to monoclinic (t–m) phase transformation around a static or propagating crack is characterized with PF simulations. It is shown that the finite size and shape of the transformation zone under different loads and ambient temperatures can be well predicted with the proposed PF model. The phase transformation may decrease the stress level around the crack tip, which implies the toughening effect. After that, crack propagation in TZP is studied. As the stress field is perturbed by the phase transformation patterns, the crack may experience deflection and branching in the propagation process. It is found that the toughness of the grain boundaries (GBs) has important influences on the crack propagation mode. For TZP with strong GBs, the crack is more likely to propagate transgranularly while, for TZP with weak GBs, intergranular crack propagation is prevalent. Besides that, the crystal orientation and the external load can also influence the topology of crack propagation.

A numerical model coupling phase transformation to predict microstructure evolution and residual stress during quenching of 1045 steel

This article deals with the numerical simulation of quenching in low alloy steels based on finite element method adapting the effect of stress on the martensitic transformation to predict temperature history, microstructure evolution, and internal stresses. By superimposing the cooling curves of selected points on the CCT diagram of 1045 steel, verification of the simulated microstructures in the cylindrical specimen is carried out by comparing it with the micrographs of microstructures. Afterward, steel gears are treated in two cooling mediums to predict volume changes of gear samples quenched in oil and water. A comparison of the experimental results with those of numerical simulation generates an overall good agreement and indicates the well-demonstrated predictive capability of the model associated with kinetics of phase transformation, thermo-physical properties, and latent heat release for real-time quenching applications.

Modeling and simulation of coupled phase transformation and stress evolution in thermal barrier coatings

The thermally grown oxide layer is known to be responsible for the failure of coating systems due to the generation of severely high stresses. In this work, oxidation induced stresses generated in thermal barrier coating (TBC) systems are investigated for high temperature isothermal oxidation. In that sense, a comprehensive model, where phase transformation is coupled with mechanics is developed for the life-time estimation of TBC systems and a modified version of the Allen-Cahn type phase field approach is adopted in order to model the generation of thermally grown oxide (TGO) in finite strain constitutive framework. The top-coat material behavior is modeled using a rate-dependent Gurson type plasticity for porous materials which also accounts for creep. The results for the isothermal phase transformation analysis and the model validation using experimental results are demonstrated. The capability of the model in predicting the local stresses which is the main variable in the analysis of possible delaminations and accurate lifetime estimation of TBC systems is shown.

Coupled nonlinear elasticity, plastic slip, twinning, and phase transformation in single crystal titanium for plate impact loading

High purity single crystal titanium (Ti) under shockwave loading in plate impact experiment is modeled and simulated, with help of the finite element. A thermodynamically consistent system of equations is formulated in the frame of large deformation to consider material anisotropy, rate dependence, and multi-physics including nonlinear elasticity, dislocation based plastic slip, deformation twinning, and phase transformation. A novel kinematics is proposed to consider phase transformation in the α twin variants and also to consider the dislocation based slip in all of components of parent material, primary twins and the ω phase. The thermodynamically consistent driving forces for plastic slip, twinning, and phase transformation are developed based upon the second law of thermodynamics. For nonlinear elasticity, the stiffness matrix is dependent on the volume fractions of all components, and the volumetric part of Cauchy stress is obtained from the nonlinear equation of state. Dislocation based plastic slip in multi-variant and multiphase heterogeneous materials is developed and interactions of dislocations among all slip modes are taken into account. A mechanism for dislocation density evolution during twinning and phase transformation is proposed. The shock loading along the [0001] and [101¯1] directions of single crystal high purity Ti is investigated computationally. Very good correspondence between simulation and experiment is obtained, which includes pole figures, volume fractions of components, free surface velocity, peak pressure, and phase transformation pressure. Multiple experimental phenomena are interpreted based upon the progression of dislocation slip, deformation twinning, and phase transformation. In compression with the [101¯1] crystal, a higher volume fraction in the primary twins but a lower secondary twin volume fraction in the [0001] crystal in experiment was observed. The higher propensity for phase transformation occurs in the [0001] crystal is reproduced. In addition to material texture, distributions of temperature, stresses, and plastic strains dependent on the impact loading directions are revealed.

A coupled phase transformation and solute diffusion model for bainitic transformation

AbstractIn materials science one distinguishes between upper and lower bainite, where both microstructures develop due to different diffusion processes. In this work we describe these different mechanisms with a new diffusion model coupled to a multiphase‐field equation. Numerical examples demonstrate the expected behavior. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mechanisms for phase transformation induced slip in shape memory alloy micro-crystals

Compression of a single crystal, superelastic NiTi shape memory alloy (SMA) micro-pillar and the stress-field around an ellipsoidal twinned martensite (M) plate embedded in an austenite (A) matrix were simulated using a coupled phase transformation and crystal plasticity model. Post-mortem transmission electron microscopy (TEM) analysis of the dislocation structures in a foil extracted from a compressed NiTi micro-pillar was also performed. Based on these modeling and experimental data, we propose mechanisms for phase-transformation-induced defect generation in superelastically stressed NiTi SMA. The geometry of the simulated slip bands shows that dislocations nucleate and grow in the austenite phase adjacent to a growing or receding martensite plate to accommodate local strain gradients. The simulated resolved shear stress on individual slip systems, and Burgers vector analysis of dislocations in the TEM data show that the slip system and amount of slip activity depend on the magnitude of the strain gradients, which are controlled by the martensite crystallography, the dynamics of martensite plate growth, and scale of the twinned structure and A-M interface. In addition to a[0 1 0] (1 0 1¯) and a [0 0 1] (1¯1 0) slip systems observed in prior experiments, we report the activation of a third slip system: a[0 0 1](1 1 0). We show that the three slip systems are likely to be active at different locations around a martensite plate. The modeling component in this work complements ex-situ TEM characterization by furnishing the resolved shear stress and slip activity on austenite slip systems throughout the cyclic loading.

A Simulation Coupling Phase Transformation and Mechanical Behavior of Solid Oxide Fuel Cell Material Based on Phase-field Method

A Simulation Coupling Phase Transformation and Mechanical Behavior of Solid Oxide Fuel Cell Material Based on Phase-field Method

Coupled domain wall motion, lattice strain and phase transformation in morphotropic phase boundary composition of PbTiO3-BiScO3 piezoelectric ceramic

High energy synchrotron X-ray diffraction, in situ with electric field, was carried out on the morphotropic phase boundary composition of the piezoelectric alloy PbTiO3-BiScO3. We demonstrate a strong correlation between ferroelectric-ferroelastic domain reorientation, lattice strain and phase transformation. We also show the occurrence of the three phenomena and persistence of their correlation in the weak field regime.

Modeling of coupled phase transformation and reorientation in shape memory alloys under non-proportional thermomechanical loading

In the present study, a new 3D thermodynamic coupled model is proposed for SMAs. The behavior of SMA structures is described through several strain mechanisms, each associated with its proper internal variables. This model is built to capture the particular behavior of SMAs when subjected to complex loading, namely non-proportional thermomechanical loading. To achieve this task, a new approach to describe the martensitic reorientation mechanism has been introduced in conjuction with a new method to account for forward and reverse transformation. Thermomechanical coupling, related to dissipation and latent heat is fully implemented. The validity of the model is demonstrated by comparing experimental results of complex thermomechanical loading paths of SMA structures with numerical simulations.

固体酸化物燃料電池材料の相変態-変形連成解析

固体酸化物燃料電池材料の相変態-変形連成解析

A model coupling plasticity and phase transformation with application to dynamic shear deformation of iron

A simple model that brings together well-established thermo-mechanical models of plasticity with those of martensitic phase transformation into a single thermodynamic framework is proposed. The presentation is in one space dimension, but the framework is general so that the model may be extended to higher dimensions. The model is used to study recent experiments on the α⇔∊ martensitic phase transformation of pure iron under dynamic, shear-dominant loading conditions. It is shown that the model fitted to established thermodynamic data and selected experiments is able to reproduce the experimental observations in a wide range of loading rates ranging from quasistatic to 104s−1 as well as a wide range of phenomena ranging including overall rate hardening and thermal softening. In doing so, the model also provides new insight into the α⇔∊ phase transformation in iron.

Simulation and experiment research of phase transformation on the hot stamping of 22MnB5 high strength steel

Take the special high strength boron steel 22MnB5 as research object, a thermomechanical coupling and metallographic phase transformation model is established by ANSYS/LS-DYNA. After the simulation of the transient temperature field and phase transformation in the process of hot stamping, dwelling and quenching of the high strength steel sheet, the weight percent (martensite, bainite, pearlite and ferrite), Vickers hardness and yield strength of the sub-phases following austenite decomposition are achieved. The experiments are taken and some relevant conclusions are obtained. The results show that high strength steel sheets from hot stamping are almost composed of lath martensite. The maximum error between simulation hardness and measurement one is 22·5%, which is consistent with the simulation results. It proves that the simulation results are feasible and reliable compared with the experimental results.

Coupled phase transformations and plastic flows under torsion at high pressure in rotational diamond anvil cell: Effect of contact sliding

A three-dimensional large-sliding contact model coupled with strain-induced phase transformations (PTs) and plastic flow in a disk-like sample under torsion at high pressure in rotational diamond anvil cell (RDAC) is formulated and studied. Coulomb and plastic friction are combined and take into account variable parameters due to PT. Results are obtained for weaker, equal-strength, and stronger high pressure phases, and for three values of the kinetic coefficient in a strain-controlled kinetic equation and friction coefficient. All drawbacks typical of problem with cohesion are overcome, including eliminating mesh-dependent shear band and artificial plastic zones. Contact sliding intensifies radial plastic flow, which leads to larger reduction in sample thickness. Larger plastic strain and increased pressure in the central region lead to intensification of PT. However, the effect of the reduction in the friction coefficient on PT kinetics is nonmonotonous. Sliding increases away from the center and with growing rotation and is weakly dependent on the kinetic coefficient. Also, cyclic back and forth torsion is studied and compared to unidirectional torsion. Multiple experimental phenomena, e.g., pressure self-multiplication effect, steps (plateaus) at pressure distribution, flow to the center of a sample, and oscillatory pressure distribution for weaker high-pressure phase, are reproduced and interpreted. Reverse PT in high pressure phase that flowed to the low pressure region is revealed. Possible misinterpretation of experimental PT pressure is found. Obtained results represent essential progress toward understanding of strain-induced PTs under compression and shear in RDAC and may be used for designing experiments for synthesis of new high pressure phases and reduction in PT pressure for known phases, as well as for determination of PT kinetics from experiments.

A condensed variational model for thermo-mechanically coupled phase transformations in polycrystalline shape memory alloys

AbstractWe derive an energy-based material model for thermomechanically coupled phase transformations in polycrystalline shape memory alloys. For the variational formulation of the model, we use the principle of the minimum of the dissipation potential for nonisothermal processes for which only a minimal number of constitutive assumptions has to be made. By introducing a condensed formulation for the representative orientation distribution function, the resulting material model is numerically highly efficient. For a first analysis, we present the results of material point calculations, where the evolution of temperature as well as its influence on the mechanical material response is investigated.