Effects Of Elastic Strain Energy Research Articles

Effect of elastic strain energy on precipitation process of Co81Al5V14 alloy based on microscopic phase field method

The L12 phase volume fraction, size, microstructure significantly influences alloy's important physical and mechanical properties in Co-Al-V superalloy. Based on microscopic phase field method and microelasticity theory, precipitation of ordered L12 phase in Co81Al5V14 alloy were studied. The results indicate that precipitation sequence of Co81Al5V14 alloy is minimally influenced by elastic strain energy and precipitation sequence can be divided into four stages. Elastic strain energy does not significantly affect incubation period of alloy, but it does promote the formation of transitional ordered phase L10 with a single orientation and facilitates precipitation of ordered phase L12. Elastic strain energy causes precipitates to grow and coarsen along specific elastic "soft" direction ([100] and [001]). Elastic strain energy promotes process of ordering and atomic occupancy of the alloy. The effects of elastic strain energy on precipitation mechanism, microstructure and atomic occupancy are discussed in this work, which provides theoretical guidance for the design of Co-Al-V alloys with better properties.

Effect of the mechanical properties of the cell membrane on the transition energy barrier of electroporation

The mechanical properties of the cell membrane play an important role in electroporation. This paper studied the influence of the mechanical properties of the cell membrane on the transition energy of electroporation through both modeling and experiments. An electromechanical coupling model of a single pore on the cell membrane was established in COMSOL, and the effect of elastic strain energy on the formation of pores was analyzed. Additionally, to compare the transition energy barrier of pores for different elastic properties of the cell membrane, electroporation experiments were carried out at different temperatures. The simulation showed that the elastic strain energy of the cell membrane increased the transition energy barrier of the pores. The experiments also showed that the transition energy barrier was larger when the elasticity of the cell membrane is intact, which was in good agreement quantitatively with the simulation results. We demonstrated that the mechanical properties of the cell membrane hinder the pore formation, which may be due to the increase of the transition energy barrier. We analyzed the possible mechanism of the effect of cell membrane mechanical properties on electroporation and found the contribution of cell membrane mechanical properties to electroporation during the delivery of exogenous substances, which can provide guidance for improving therapies in electrochemotherapy.

Selection and mechanical evaluation of γ/γ boundary in γ-TiAl alloy

Simulation of lamellar boundary (γ/γ) selection during the transformation of α2’→α2+γ in γ-TiAl alloy has been investigated using an improved 3D Phase Field (PF) model, and the mechanical properties of γ/γ boundaries are evaluated by Molecular Dynamics (MD) simulation. The effects of elastic strain energy and interfacial energy difference among different types of γ/γ interfaces on the occurrence frequencies of the three types of γ/γ boundaries (i.e., true twin (TT), pseudo-twin (PT) and ordered domain (OD)) have been studied. It is found that the boundary fraction of TT increases with increasing elastic strain energy or increasing interfacial energy difference among γ/γ interfaces. Besides TT, the elastic interaction also favors OD while PT is suppressed. The relative fractions of PT and OD could be effectively controlled by elastic strain energy. Furthermore, the frequency of PT or OD can also be adjusted by their interface energy ratio. The simulation results well explain the phenomenon that boundary frequencies via experimental statistics deviate from those under random distribution without interface selection. It can also be found that one-twin-dominant zones (OTDZ) can be induced by higher elastic strain energy and larger interface energy difference among different γ/γ boundaries through the merging of adjacent small clusters with the same γ/γ boundary type under the premise of correlated and sympathetic nucleation. Through MD simulation, it is found that the strengths of the configurations with true twin boundary (TTB) and ordered domain boundary (ODB) are almost the same, while the strength of that with pseudo-twin boundary (PTB) is relatively low. The order of plasticity of the configurations with three types of γ/γ interfaces is ODB > TTB > PTB.

Thermodynamic modeling of YO1.5-TaO2.5 system and the effects of elastic strain energy and diffusion on phase transformation of YTaO4

Thermodynamic parameters of the YO1.5-TaO2.5 system were obtained, and the effects of elastic strain energy and diffusion on phase transformation of YTaO4 were analyzed in this work. The YO1.5-TaO2.5 system was critically modeled using the CALPHAD technique based on our calculated formation energies by DFT and available experimental data. According to DFT calculations, M′-YTaO4 was suggested to be the thermodynamically stable phase at low temperature. For a displacive transformation of T→M between the equilibrium tetragonal and monoclinic YTaO4, our calculations suggested it cannot be hindered by elastic strain energy. For a diffusive transformation of T→M′, it can be divided into T→M and M→M′. Diffusive transition of M→M′ was likely to be impeded due to large diffusion energy barrier, which was calculated to be 3.260 eV. However, the driving force ΔG M→M′ is about -0.121 kJ/mol. The large diffusion energy barrier and small driving force may be the main reason that T cannot transform to M′ after cooling.

Effect of surface tension and geometry on cavitation in soft solids

Unbounded growth of cavity in soft solids subjected to internal pressure is a commonly observed phenomenon. Such phenomenon has been harnessed by developing cavitation rheology technique (CR) to investigate the local mechanical properties of many complex soft materials. The elasticity of the material, surface energy, and geometric factors in combination can dictate the cavitation behavior in a complex manner. We report a finite element based framework capturing the coupled effect of elastic strain energy and surface tension on the cavitation phenomenon. We show results for a spherical cavity in an infinite elastic media and for the CR geometry. The surface tension is shown to increase the critical pressure for cavitation. The energy release rate also depends on the surface tension. In CR geometry, by varying the distance between the needle and the immovable sample boundaries, we have captured the conditions leading to confinement. Our results provide new understanding regarding the effects of geometry and surface tension on the cavitation phenomenon in soft solids.

Effect of elastic strain energy on grain growth and texture in AZ31 magnesium alloy by phase-field simulation**Project supported by the National Key Research Development Program of China (Grant No. 2016YFB0701204) and the National Natural Science Foundation of China (Grant Nos. U1302272 and 51571055).

A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy. The stiffness tensors for different grains are different because of elastic anisotropy of the magnesium lattice. The tensor is defined by transforming the standard stiffness tensor according to the angle between the (0001) plane of a grain and the direction of applied stress. Therefore, different grains contribute to different amounts of work under applied stress. The simulation results are well-explained by using the limited experimental data available, and the texture results are in good agreement with the experimental observations. The simulation results reveal that the applied stress strongly influences AZ31 alloy grain growth and that the grain-growth rate increases with the applied stress increasing, particularly when the stress is less than 400 MPa. A parameter (Δd) is introduced to characterize the degree of grain-size variation due to abnormal grain growth; the Δd increases with applied stress increasing and becomes considerably large only when the stress is greater than 800 MPa. Moreover, the applied stress also results in an intensive texture of the ⟨0001⟩ axis parallel to the direction of compressive stress in AZ31 alloy after growing at elevated temperatures, only when the applied stress is greater than 500 MPa.

The effect of elastic stresses on the thermodynamic barrier for crystal nucleation

For a variety of oxide glass-forming liquids, the thermodynamic barrier for homogeneous crystal nucleation, Wc, exhibits an unusual increase with a decrease in temperature below the maximum nucleation rate. Such behavior differs from the predictions made using the classical nucleation theory. In this article, we seek possible explanations for the increasing Wc by analyzing whether it is caused by internal elastic stresses that arise due to density misfits between the crystal and liquid phases. For this purpose, crystal nucleation rates and induction time data for two glasses that display significantly different density misfits, lithium and barium disilicates, are employed to determine the work of critical cluster formation. To explain the results, quantitative estimates of the effect of the elastic strain energy on the work required to form a critical nucleus are performed for both glasses. The interplay between stress development and relaxation is accounted for. The computations were performed, taking into account not only the possibility of precipitation of the most stable crystal phase but also that different metastable phases may form during the early stages of nucleation. We show that elastic stresses do indeed reduce the thermodynamic driving force for crystallization, and thus increase the barrier to nucleation. However, the sole effect of elastic strain energy cannot explain the aforementioned unusual behavior of the thermodynamic barrier. Hence, a comprehensive explanation to this phenomenon remains an open issue.

Phase field simulation on microstructure evolution in solidification and aging process of squeeze cast magnesium alloy

Phase-field models have been developed to simulate the dendritic growth in pressurized solidification of Mg-Al alloy during squeeze casting and the precipitation of multivariant β-Mg17Al12 phases during the subsequent aging process. For the pressurized solidification, the effects of pressure on the Gibbs free energy and chemical potential of solid and liquid phases, and the solute diffusion coefficient were considered. For the precipitation during aging process, the effects of elastic strain energy, anisotropy of interfacial energy, and anisotropy of interface mobility coefficient were considered. The results showed that the dendritic growth rate tends to increase and the secondary dendrite arms are more developed as the pressure is increased from 0.1 to 100MPa, which showed a good agreement with the experimental results of direct squeeze casting of Mg-Al alloy. The 2D and 3D simulated precipitates had lath shapes with lozenge ends, and the precipitate variants were parallel to the basal plane and oriented in directions with an angular interval of 60 degrees, which is in good agreement with experimental observations.

Phase-field study the effects of elastic strain energy on the occupation probability of Cr atom in Ni–Al–Cr alloy

The occupation probability (OP) of Cr atom at α sublattices and β sublattices of DO22–Ni3Cr and L12–Ni3Al in Ni–Al–Cr alloy was studied by using phase-field microelasticity model. The elastic strain energy (ESE) arised by a coherent misfit has little effect on the precipitation sequence of alloy while it changes the behavior of the temporal evolution OP of Cr atom in DO22 and L12 phases. With the ESE increasing, the OP of Cr atom at both α sublattices and β sublattices in DO22 phase increases, the OP of Cr atom at β sublattices in L12 phase decreases, and the OP of Cr atom at α sublattices in L12 phase increases. Eventually, the ESE leads to directional coarsening of coherent microstructure.

Effects of elastic strain energy and interfacial stress on the equilibrium morphology of misfit particles in heterogeneous solids

This paper presents an efficient sharp interface model to study the morphological transformations of misfit particles in phase separated alloys. Both the elastic anisotropy and interfacial energy are considered. The geometry of the material interface is implicitly described by the level set method so that the complex morphological transformation of microstructures can be accurately captured. A smoothed extended finite element method is adopted to evaluate the elastic field without requiring remeshing. The equilibrium morphologies of particles are shown to depend on the elastic anisotropy, interfacial energy as well as the particle size. Various morphological transformations, such as shape changes from spheres to cuboids, directional aligned platelets and particle splitting, are observed. The simulated results are in good agreement with experimental observations. The proposed model provides a useful tool in understanding the morphological transformation of precipitates, which will facilitate the analysis and design of metallic alloys.

Effect of elastic strain energy on the core-shell structures of the precipitates in Al-Sc-Er alloys

The effect of the elastic strain energy on the core-shell structures was studied in an Al-0.06Sc-0.02Er (at.%) alloy. A theoretical model for the calculation of the elastic strain energy caused by core-shell precipitates, which is applicable to materials with weak elastic anisotropy, was adopted. It was demonstrated that the partitioning of Er to the precipitate core did not reduce the elastic strain energy as expected in the previous study. The resistance due to the elastic strain energy to form an Al3(Sc0.36Er0.64)-Al3(Sc0.8Er0.2) core-shell precipitate was quite small, and could be easily overcome by the decrease of the total interfacial energy, which was consistent with the previous experimental results. On the other hand, the resistance due to the elastic strain energy to form an Al3Er-Al3Sc core-shell precipitate was much larger than that to form an Al3(Sc0.36Er0.64)-Al3(Sc0.8Er0.2) core-shell precipitate, thus the partitioning of all the Er atoms to the core was strongly hindered by the elastic strain energy and was not observed in the experiment of the previous study.

Effects of Elastic Strain Energy on Phase Boundary Morphology in Nanoscale Olivine Particles

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Phase-field study the effect of elastic strain energy on the incubation period of Ni–Cr–Al alloys

With the microscopic phase-field dynamic model, the effect of elastic strain energy on the incubation period of Ni–Cr–Al alloys is studied. The simulation results demonstrate that elastic strain energy does not change the precipitation sequence of alloys. There exits the incubation period of DO 22 phase and L1 2 phase in the alloys with different precipitation sequence. If DO 22 phase precipitates first, the incubation periods of both phases are prolonged with the elastic strain energy increased. If L1 2 phase precipitates first, with the increase of elastic strain energy, the incubation periods of L1 2 phase is shortened while that of DO 22 phase is prolonged.

Microscopic Phase-field Simulation of Effects of Re-ageing Temperature on Precipitation of Ni-Al-Cr Alloys

This article, by means of the ternary microscopic phase-field model, investigates the effects of re-ageing temperature on the precipitation of Ni75Al10Cr15 alloy with the help of atomic pictures, order parameters, particle density, averaged radii, and volume fractions. During pre-ageing at 873 K, DO22 phases first appear through spinodal decomposition mechanism, and then L12 phases begin to form on the DO22 phase-boundaries through non-classical nucleation mechanism. In either of them, ordering process is obviously faster than atom clustering. At the late stage of re-ageing at 923 K, the elastic strain energy seems to exert stronger effects on microstructure, and DO22 and L12 phases exhibit directional alignment along <100> direction to a certain extent. When the temperature increases to 1 023 K, the influence of elastic strain energy begins to weaken, and the precipitated phases become randomly distributed in the matrix. The volume fraction of DO22 phase decreases to zero, whereas that of L12 phase first increases and then decreases with the temperature rising from 923 K to 1 123 K. On the whole, the effects of elastic strain energy make the coarsening behavior of both phases deviate from the time-law predictions by LSW diffusion-controlled growth theory.

Effects of elastic strain energy on the antisite defect of D022–Ni3V phase

A time-dependent phase field microelasticity model of an elastically anisotropic Ni–Al–V solid is employed for a D022–Ni3V antisite defect application. The elastic strain energy (ESE), caused by a coherent misfit, changes the behavior of the temporal evolution occupancy probability (OP), slows down the phase transformation, and eventually leads to directional coarsening of coherent microstructures. In particular, for the antisite defects (NiV, VNi) and ternary alloying elements (AlNi, AlV), ESE is responsible for the decrease in the calculated equilibrium values of NiV, AlNi, and AlV, as well as the increase in the equilibrium value of VNi. The gap between NiV and VNi and AlNi and AlV is narrowed in the system involving ESE, but the calculated equilibrium magnitude of NiV is still greater than that of VNi. The calculated equilibrium magnitude of AlNi was always greater than AlV in this study.

Competition between surface energy and elastic anisotropies in the growth of coherent solid-state dendrites

A new phase-field model of microstructural evolution is presented that includes the effects of elastic strain energy. The model’s thin interface behavior is investigated by mapping it onto a recent model developed by Echebarria et al. [Echebarria B, Folch R, Karma A, Plapp M. Phys Rev E 2004;70:061604]. Exploiting this thin interface analysis, the growth of solid-state dendrites are simulated with diffuse interfaces and the phase-field and mechanical equilibrium equations are solved in real space on an adaptive mesh. A morphological competition between surface energy anisotropy and elastic anisotropy is examined. Two dimensional simulations are reported that show that solid-state dendritic structures undergo a transition from a surface-dominated [Meiron DI. Phys Rev A 1986;33:2704] growth direction to an elastically driven [Steinbach I, Apel M. Phys D – Nonlinear Phenomena 2006;217:153] growth direction due to changes in the elastic anisotropy, the surface anisotropy and the supersaturation. Using the curvature and strain corrections to the equilibrium interfacial composition and linear stability theory for isotropic precipitates as calculated by Mullins and Sekerka, the dominant growth morphology is predicted.

Microscopic phase-field simulation for precipitation behavior of Ni-Al-Cr alloy during two-step aging

Based on the microscopic phase-field model, the pre-aging temperature effects on the precipitation mechanism and microstructure evolution during two-step aging for Ni 75Al 9Cr 16 alloy were simulated. The results show that the early precipitation mechanism of L1 2 phase is the mixed mechanism of spinodal decomposition and non-classical nucleation growth, whereas the early precipitation mechanism of DO 22 phase is spinodal decomposition when the pre-aging temperature is 873 K. The early precipitation mechanism of L1 2 phase is non-classical nucleation growth, whereas the early precipitation mechanism of DO 22 phase is spinodal decomposition when the pre-aging temperature is 973 K. Under the effects of elastic strain energy, the cubic particles exhibit directional alignment along [100] and [010] directions during the late precipitation, which is more obvious at lower pre-temperature. DO 22 phases appear earlier than L1 2 phases under these two kinds of precipitation processes; and the nucleation incubation time becomes long with the increase of pre-temperature.

Microscopic phase-field simulation coupled with elastic strain energy for precipitation process of Ni-Cr-Al alloys with low Al content

The precipitation process of Ni-Cr-Al alloy with low Al content was studied at atomic scale based on the microscopic phase-field kinetic model coupled with elastic strain energy. The aim is to investigate the effect of elastic strain energy on precipitation mechanism and morphological evolution of the alloy. The simulation results show that in the early stage of precipitation, Do 22 phase and L1 2 phase present irregular shape, and they randomly distribute in the matrix. With the progress of aging. L1 2 phase and D0 22 phase change into the quadrate shape and their orientations become more obvious. In the later stage, L1 2 phase and D0 22 phase present quadrate shape with round corner and align along the [100] and [010] directions, and highly preferential selected microstructure is formed. The mechanism of early precipitation of L1 2phase in Ni-17%Cr-7.5%Al (mole fraction) alloy is the mixed style of non-classical nucleation growth and spinodal decomposition and the D0 22 phase is the spinodal decomposition. The mechanisms of early precipitation of L1 2 phase and D0 22 phase in Ni-12.5%Cr-7.5% Al alloy are both the non-classical nucleation and growth. The coarsening process follows the rule of preferential selected coarsening.

Microscopic phase-field simulation including elastic strain energy for early precipitation process of Ni-Al alloys with medium Al content

Abstract The early precipitation process of Ni-Al alloy was studied on the atomic scale based on the microscopic phase-field kinetic model. We investigated the effect of elastic strain energy on precipitation mechanism and morphological evolution of the alloy. Simulation result show that the early stage of precipitation, γ, ordered phase presents non-directional and irregular shape during the process of aging, the γ, ordered phases change into the quadrate shape and their orientations become more obvious; at the later state, the γ, precipitates present quadrate shape with round corner and align along the [100] and [010] directions. The mechanism of early precipitation for Ni-13at. %Al alloy is the mixed mechanism of non-classical nucleation growth, and the mechanism of early precipitation for Ni-15. 8at. %Al alloy is the mixed mechanism of non-classical nucleation growth and spinodal decomposition and near to spinodal decomposition. ∗ Supported by National Natural Science Foundation of China (Grant No. 50...

Effect of elastic strain energy on self-organized pattern formation

This paper studies the growth of self-organized quantum dots in strained semiconductors in the Stranski-Krastanov growth mode using the kinetic Monte Carlo simulation method. The four nearest and four next nearest neighbours of each atom in the square lattice grid with a periodic boundary condition are considered in the calculation of the binding energy among atoms. The elastic strain energy is accurately evaluated by the rigorous point eigenstrain half-space Green's function and is incorporated for the first time into the kinetic Monte Carlo model. The set of relevant growth parameters such as growth temperature, surface coverage, flux rate, and growth interruption time, is investigated and optimal values are identified. It is shown clearly that when the long-range elastic strain energy is included in the simulation, uniform size and ordered spatial distribution can be achieved. Furthermore, the growth of stacked quantum dot layers is also simulated briefly and vertical alignment is observed that could lead to progressively uniform island size and spatial ordering.