Phase Transformation Theory Research Articles

Analysis of shear bands in bulk metallic glasses based on elastoplastic phase transformation theory

Abstract Shear bands in amorphous alloys have been widely observed in uniaxial tension and compression experiments, reflecting strain localization, with plastic deformation occurring within the shear bands. In many instances, failures of bulk metallic glasses (BMGs) occur along the dominant shear bands. In this study, phase transformation theory is applied to investigate the mechanical properties of shear bands, focusing on the analysis of the two-phase deformations. The shear bands and the regions outside them are treated as two distinct phases in equilibrium. The deformation gradient tensor across the interface between these phases is discontinuous. By applying the jump conditions, governing equations are derived. As a case study, the shear bands and surrounding regions of plastic BMGs under uniaxial compression are analyzed, enabling the calculation of the stress associated with phase transformation and the inclination angle of the shear bands. The results obtained from this theoretical model align well with existing experimental and simulation data.

In situ study of microstructure evolution and α → ω phase transition in annealed and pre-deformed Zr under hydrostatic loading

The detailed study of the effect of the initial microstructure on its evolution under hydrostatic compression before, during, and after the irreversible α→ω phase transformation and during pressure release in Zr using in situ x-ray diffraction is presented. Two samples were studied: one is plastically pre-deformed Zr with saturated hardness and the other is annealed. Phase transformation α→ω initiates at lower pressure for a pre-deformed sample but for a volume fraction of ω Zr, c>0.7, a larger volume fraction is observed for the annealed sample. This implies that the proportionality between the athermal resistance to the transformation and the yield strength in the continuum phase transformation theory is invalid; an advanced version of the theory is outlined. Phenomenological plasticity theory under hydrostatic loading is outlined in terms of microstructural parameters, and plastic strain is estimated. During transformation, the first rule is suggested, i.e., the average domain size, microstrain, and dislocation density in ω Zr for c<0.8 are functions of the volume fraction, c of ω Zr only, which are independent of the plastic strain tensor prior to transformation and pressure. The microstructure is not inherited during phase transformation. Surprisingly, for the annealed sample, the final dislocation density and the average microstrain after pressure release in the ω phase are larger than for the severely pre-deformed sample. The results suggest that an extended experimental basis is required for the predictive models for the combined pressure-induced phase transformations and microstructure evolutions.

Examining the Electron Phase Transformation Theory in the Context of Atomic Structure

The shortcomings of the Rutherford atomic model can be eliminated by the suggested phase transformation of the electrons from point to non-revolving surface charge in the vicinity of the nucleus. The energy balance investigations of this atom model indicated that the stability of the surface charge valence electron shell is ensured by the one-dimensional Casimir effect. If this theoretical prediction is correct then the first ionization energies of the elements should correlate linearly to the inverse of atomic diameter. Classical physics approach, the electrostatic attraction of the nucleus and the repulsion of the surface charge electron shell result in an identical relationship. The problem with the classical physics approach is that it does not offer an adequate explanation for the photoelectric effect and the free electrons inside the metal. Therefore, classical electrostatics cannot be considered the right physical process responsible for the stability of the valence electron/s in neutral atoms. The derived theoretical relationship, between atomic diameter and ionization energy, was tested up to 86 elements of the periodic table. The correlation coefficient is 0.9187. The correlation is stronger for individual periods. The empirical relationship between the ionization energy and atomic radii is well known, resulting in the same correlation coefficients. However, the correlation to the atomic radii does not reproduce the theoretically derived constant multiplier, contrarily to the atomic diameter relationship. Thus, the first ionization energy is the function of the atomic diameter. The uncertainties in the reported atomic sizes are relatively high. Therefore, the correlation between theory and experiments should be considered as excellent. The theoretically derived relationship between the first ionization energy and atomic diameter is the consequence of the proposed phase transformation of the electron. Thus the detected strong correlation between theory and experiments adds further support to the proposed atomic structure.

A process-structure-property model via physics-based/data-driven hybrid methods for freeze-cast porous ceramics in Si3N4-Si2N2O case system

For the engineering applications of freeze-cast porous ceramics, the demand targets are often multiple and competing, which is a challenging problem to seek a Nash equilibrium in the high-dimensional design space. An accurate and robust quantification of process-structure-property correlations would provide an effective path to find the set of Pareto optimal materials for one specific need. In this work, using porous Si3N4-Si2N2O ceramics as the model materials, a hybrid model for the quantitative design of the microstructure and mechanical properties is developed from four physics-based process-microstructure models with sintering, solidification, phase transformation and grain growth kinetic theories, and the subsequent data-driven structure-property model utilizing a machine learning method, artificial neural network (ANN). The SHapely Additive exPlanations (SHAP) analysis is further introduced to interpret the ANN model and mathematically identify the contribution of each microstructure feature descriptor toward target mechanical property outputs. These results present a systematic understanding of the process-structure-property relationships through the hybrid model, guiding the optimal design of the freeze-cast porous ceramics with required microstructures and mechanical properties.

Computational Fluid Mechanics with Phase Transitions by Particle Methods

A computational method of simulations for processes of heterogeneous hydrodynamics with take of phase transitions will be discussed. The method is based on relevant approximation of conservation laws for mass, momentum, and energy in integral and differential forms. The time and spatial approximation is natural and numerical simulations are realized as direct computer experiments. It is supposed that the fluids are compressible and non-viscous. Heterogeneities of the fluids are considered as small drops or particles of one fluid within other fluid. Total number of the drops may be large enough and the drops may have phase transitions. Therefore, simulations of the main fluid with small transited drops dynamics are considered. The particle dynamics will be modelled as in the particle-in-cell method, and in the main fluid as in the large particle method. This approach makes it possible to simulate phase transitions under certain assumptions about heterogeneous fluids. The calculation algorithm of this method is implemented as a computer simulation of the dynamics of a multiphase carrier fluid containing particles that can undergo, for example, graphite-diamond phase transitions. Such transitions are modelled on the basis of the theory of phase transformations and the laws of thermodynamics. In fact, the method is a combination of the Harlow's particle-in-cell method, Belotserkovskii's large particles method and Bakhvalov's homogenization method. A modification of this method has also been developed to take into account the effects of viscosity when simulating the dynamics of a multiphase fluid in porous media. A model of the motion of such a liquid in a porous medium is obtained by freezing the motion of particles of the corresponding size in the presented method. The method will certainly be promising for numerical simulations of absorption and diffusion processes in complex fluids with phase transitions.

Direct van der Waals simulation (DVS) of phase-transforming fluids.

We present the method of direct van der Waals simulation (DVS) to study computationally flows with liquid-vapor phase transformations. Our approach is based on a discretization of the Navier-Stokes-Korteweg equations, which couple flow dynamics with van der Waals' nonequilibrium thermodynamic theory of phase transformations, and opens an opportunity for first-principles simulation of a wide range of boiling and cavitating flows. The proposed algorithm enables unprecedented simulations of the Navier-Stokes-Korteweg equations involving cavitating flows at strongly under-critical conditions and 𝒪(105) Reynolds number. The proposed technique provides a pathway for a fundamental understanding of phase-transforming flows with multiple applications in science, engineering, and medicine.

Vibration fatigue behavior and life prediction of directionally solidified superalloy based on the phase transformation theory

Directionally solidified nickel base superalloy DZ125L is the main material that has been widely used to manufacture aviation gas turbine blades and hot-end structural parts. Aeroengine is under vibration load for a long time in the service process, which makes vibration fatigue become one of the main failure modes of aero-engine structures. In this study, vibration fatigue behavior and excitation frequency response curves of DZ125L alloy under different stress levels were investigated through vibration fatigue tests. The fatigue crack initiation and growth mechanism of DZ125L alloy under vibration load is studied based on the results of the vibration fatigue test and finite element simulation. A vibration fatigue life prediction model based on the phase transformation theory is developed. Each parameter has clear physical significance in the model. The comparison between the model prediction results and the test results shows that the theoretical prediction results have reasonable accuracy.

До питання структуроутворення високоміцного чавуну при використанні діаграм стану систем «Fe-Si», «Mg-Si» та «Fe-Si-Mg»

The purpose of the work is to establish the patterns of structural formation of high-strength cast iron using the thermodynamic theory of phase transformations and to analyze state diagrams of the components of Fe-Si-Mg ligatures. The article presents the results of the analysis of patterns of structural formation of high-strength cast iron when using state diagrams of the "Fe-Si", "Mg-Si" and "Fe-Si-Mg" systems. The concept of graphite formation in high-strength cast iron is considered. The structure formation scheme of high-strength cast iron is presented. Disclosure of the mechanism of processes of formation of spherical and vermicular graphite opens wide opportunities for controlling the structure and properties of high-strength cast iron and contributes to the development of effective technological processes for obtaining cast products for various purposes. It has been established that during the modification of cast iron melt, as a result of a significant redistribution of all elements dissolved in it, purification of impurities (sulfur, phosphorus, etc.) takes place, which allows obtaining the structure of cast iron with nodular graphite with the use of modifiers. Diagrams of the "Fe-Si", "Mg-Si" and "Fe-Si-Mg" systems for the development of the composition of high-strength cast iron are given. After analyzing the data of the given state diagrams, it was concluded that in the composition of spheroidizing ligatures, all compounds of elements are low-melting (tpl < 1300 °С) in relation to the melting temperature of cast iron. During the crystallization of cast iron with the release of austenite, a direct microliquation of silicon with a distribution coefficient less than unity is characteristic, manganese is more evenly distributed in the metal, and carbide stabilizing elements are treated in the liquid phase. The regularities of structure formation of modified cast iron under different crystallization conditions have been established. The analysis of the study of the regularities of the process of the formation of spherical and vermicular graphite and the analysis of state diagrams of the "Fe-Si-Mg" liga-tur components were performed.

Heterogeneous phase transformation pathways in additively manufactured Al-Ce-Mn alloys

Heat treatment of additively manufactured Al-Ce based multicomponent alloys leads to complex microstructure evolution. In this research, the ability to extend the phase transformation theories involving nucleation of a product phase from a heterogeneous multi-phase microstructure typical to that of additively manufactured samples is explored. The Al-10Ce-8Mn (wt%) was used as a model alloy system. Under additive manufacturing conditions different solidification microstructures were obtained due to spatial and temporal variations of thermal gradients (G) and liquid-solid interface velocities (R) within a given melt pool. Near the melt pool boundary (high G and low R, referred as MPB region), initially, Al20Mn2Ce forms from the liquid followed by a eutectic of FCC Al and Al11Ce3. In the melt pool interiors (low G and high R referred as ES region) a eutectic structure between FCC Al and Al20Mn2Ce is observed. During subsequent heat treatments, the MPB and ES regions transform into different sets of microstructures. In the MPB region, a fine globular microstructure containing FCC Al, Al11Ce3, Al6Mn, and Al12Mn results from the decomposition of Al20Mn2Ce. In the ES region a faceted Al51Mn7Ce4 plate phase results from the decomposition of Al20Mn2Ce. The formation of the Al51Mn7Ce4 phase within the eutectic microstructure at the boundaries of FCC Al and Al20Mn2Ce has not been reported in the literature. These two distinct phase transformation pathways are rationalized based on the role of driving force on the nucleation of (Al6Mn) and/or metastable intermetallic (Al51Mn7Ce4) phases at the interface of aluminum (FCC) and the non-equilibrium intermetallic (Al20Mn2Ce) phases.

Hydrogen in magnesium alanate Mg(AlH4)2, aluminum and magnesium hydrides

The developed statistical theory of thermal phase transformations in magnesium alanate, which are realized with increasing temperature, made it possible to explain and justify the phenomenon of dehydrogenation of the thermal decomposition products for magnesium alanate. The free energies of the phases have been calculated, and their dependence on temperature, pressure, hydrogen concentration, and energy parameters has been established. Thermodynamic equilibrium equations are obtained, from which the hydrogen concentrations in the phases are determined.

КИНЕТИКА ПРЕВРАЩЕНИЙ АУСТЕНИТА В ВЫСОКОХРОМИСТЫХ СПЛАВАХ ЖЕЛЕЗА ПРИ НЕПРЕРЫВНОМ ОХЛАЖДЕНИИ

The work develops the models of two principal diffusional transformations in high-chromium iron alloys on continuous cooling, viz. precipitation of secondary carbides (Cr, Fe)7C3 from aus-tenite and pearlitic decomposition of the latter. Literature experimental data for alloys of various composi-tion were used for analysis. Chemical composition of austenite by the end of austenitizing holding was de-termined using previously developed models, and then the exact expression describing isothermal precipita-tion of carbides from supercooled austenite was found based on the general equation following from the ki-netic theory of phase transformations. It was found out that the time exponent n in that expression equals to 3/2, which corresponds to the case of preferred precipitation of very fine carbide particles. For transition to the continuous cooling condition the C-curve of isothermal carbide precipitation was approximated by a square parabola. This permitted to find the relation between cooling rate and the amount of precipitated car-bide phase by means of the Scheil–Steinberg integral. Further comparison with the experimentally observed increase of martensitic point allowed to determine the numerical parameters of the model and their depend-ence on carbide composition of a given alloy. For the pearlitic transformation, a previously developed mod-el describing the parameters of temperature dependence of the Avrami equation coefficients on austenite composition was employed. That model was generalized for the continuous cooling case in the same was as above. As a result, CCT diagrams of diffusional austenite transformations in high-chromium alloys were calculated, that in general corresponded well the experimental ones.

Effect of Graphene on Modified Asphalt Microstructures Based on Atomic Force Microscopy

Atomic force microscopy (AFM) was used to explore the effects of graphene modifier on the microstructure of asphalt. The morphologies of the before- and after-aged base asphalt and modified asphalt were performed and compared with analysis. The formation mechanism of asphaltic “bee structures” and the influence mechanism of graphene on asphalt were discussed from the classical theory of material science (phase transformation theory and diffusion theory). The results show that graphene facilitates the nucleation of “bee structures”, resulting in an increasing number and decreasing volume of “bee structures” in modified asphalt. Additionally, the anti-aging performance of the modified asphalt improved significantly because of graphene incorporation.

Research on microstructure evolution and mechanical properties of steering shaft teeth after pre-heat treatment and carburizing-quenching processes

The influence of pre-heat treatment and carburizing quenching on microstructure and properties in steering gear is studied. The CCT curve and TTT curve of 20CrMnTiH are calculated by JMatPro software. According to the phase transformation theory of undercooled austenite, the pre-heat treatment process is designed and the carburizing and quenching experiments are carried out in a gas carburizing furnace. Results show that the undercooled austenite begins to transform at 814.1 °C and shows unstable at 650 °C, at which the phase transformation speed is the fastest; By controlling the cooling rate of our designed air cooling system, transformation temperature and transformation time during the undercooled austenite transformation, the metallographic structure of axle teeth after pre-heat treatment can reach grade 1, with the brinell hardness distribution is 159HB-166HB and the hardness difference less than 7HB. After carburizing and quenching the carbide grade in the gear surface can reach to grade 1. The acicular martensite and retained austenite can also reach to grade 3. In the surface of the gear the hardness is 704HV. With the request of the engineering technical standard of 0.7mm-0.9mm, the effective hardened layer depth is about 0.85 mm. This research provides a technical basis for the fatherly research on distortion characteristics.

Surface modification with oxygen vacancy in LiNi0.5Co0.2Mn0.3O2 for lithium-ion batteries

The well-distributed smaller sized Graphene-Oxide-treated LiNi0.5Co0.2Mn0.3O2 (GO-treated NCM) layered cathodes are successfully synthesized by hydrothermal method, which has truncated octahedral shape with evenly oxygen vacancy layer on the surface. With temperature ascends progressively, the cathode molding and the modification mechanism of Graphene-Oxide (GO) in the calcination process are keenly studied by Raman spectra. In addition, the synergistic effect of oxygen vacancy and cathode electrolyte interphase (CEI) layer at outer surface accelerates lithium diffusion coefficient during cycling. Especially, GO-treated NCM exhibits the optimal capacity retention as high as 78.8% after 150 cycles at 15 C, compared with NCM whose is only 38.4%. Even at full cell state, GO-treated NCM has better rate performance and displays excellent energy density as high as 310.5 Wh kg−1 after 200 cycles at 1 C (1 C = 160 mAh g−1). Ultimately, the theory of phase transformation of cycled cathodes is expounded in detail in combination with high resolution transmission electron microscopy (HRTEM) and the variation of X-ray diffraction (XRD) peaks positions.

Multi-material circulation optimization of the calcification-carbonation process based on material balance and phase transformation for cleaner production of alumina

The calcification-carbonation process is a novel cleaner production method to recover alkali and alumina from bauxite residue and obtain harmless residue with low aluminum content and no alkali. At present, this method is only limited to laboratory research and has not been put into industrial application. The reason is that the existing research only focuses on the mineral transformation of the solid phase, but lacks consideration of the concentration and availability of the extract in the liquid phase. The calcification-carbonation process is a complex hydrometallurgical series process. Without a complete continuous production line, it is difficult to evaluate the reliable concentration distribution in the system. In order to obtain the concentration distribution of Na2O and Al2O3 in the whole calcification-carbonation process, this paper adopts a combined research method of metallurgical process simulation and experimental research based on the existing solid phase transformation theory. This method turns out to be effective and inexpensive to develop new technology at present. On the basis of the previous experimental results of solid structure transformation and parameter optimization, this study employs the material balance analysis module of METSIM software to analyze the distribution and concentration of Na2O and Al2O3 in the calcification-carbonation process. Combined with the concentration characteristics of input and output and the experimental verification of the key steps, a multi-material circulation optimization scheme of the calcification-carbonation process through the integration of liquid material flow resources is proposed to realize the effective recovery of low-concentration Al2O3 and the circulation of alkali liquor in the system. It promotes the recycling of resources and cleaner production of alumina.

Chernov’s role in creating and developing the doctrine of modern metallurgy and metal science. Part 1. D.K. Chernov’s main theoretical and industrial discoveries

The paper contains informational material about the essence of the discoveries made by D.K. Chernov in the field of metal science, theory and practice of heat treatment, new types of tests and investigations. D.K. Chernov was a real pioneer of extremely important phenomena in the field of phase and structural transformations, casting structure, and study of strength of steel products. Significance of his discoveries, undoubtedly, puts D.K. Chernov’s name on the first place in a row of world scientists – metallurgists and metal scientists. Later his discoveries allowed one to develop the science of metals and its subdisciplines – metallurgy, steel deformability, theory of phase and structural transformations, tests and research of metals, theory and technology of heat treatment.

Molecular dynamics modeling of lithium ion intercalation induced change in the mechanical properties of LixMn2O4.

The objective of this study is to understand the fracture mechanisms in the lithium manganese oxide (LiMn2O4) electrode at the molecular level by studying mechanical properties of the material at different values of the State of Charge (SOC) using the principles of molecular dynamics (MD). A 2 × 2 × 2 cubic structure of the LiMn2O4 unit cell containing eight lithium ions, eight trivalent manganese ions, eight tetravalent manganese ions, and 32 oxygen ions is studied using a large-scale atomic/molecular massively parallel simulator. As part of the model validation, the lattice parameter and volume changes of LixMn2O4 as a function of SOC (0 < x < 1) have been studied and validated with respect to the experimental data. This validated model has been used for a parametric study involving the SOC value, strain rate (charge and discharge rate), and temperature. The MD simulations suggest that the lattice constant varies from 8.042 Å to 8.235 Å during a full discharging cycle, in agreement with the experimental data. The material at higher SOC shows more ductile behavior compared to low SOC values. Furthermore, yield and ultimate stresses are less at lower SOC values except when SOC values are within 0.125 and 0.375, verifying the phase transformation theory in this range. The strain rate does not affect the fully intercalated material significantly but seems to influence the material properties of the partially charged electrode. Finally, a study of the effect of temperature suggests that diffusion coefficient values for both high and low-temperature zones follow an Arrhenius profile, and the results are successfully explained using the vacancy diffusion mechanism.

Dynamic phase transformations in additively manufactured Ti-6Al-4V during thermo-mechanical gyrations

A complex interaction of process parameters, geometry and scan strategies in Additive Manufacturing (AM), can bring about spatial and temporal transients, i.e., Σ T (x, y, z, time), within a part. Published literature focusses on fluctuating thermal cycles on the microstructure evolution. However, the microstructural variations have not been correlated to dynamic flow behavior due to the macro- and micro-scale phenomena, i.e., accumulated plastic strains brought about by large thermal gradients, transformational strains and crystallographic misfit strains. Therefore, we studied the mechanical response of Ti6Al4V alloys produced by AM under externally imposed controlled thermo-mechanical reversals in a Gleeble® thermo-mechanical simulator. The stress-strain behaviors were correlated to phase fractions, lattice strains, and also limited information on crystallographic texture using neutron diffraction techniques at the VULCAN Beamline at SNS, ORNL and also metallographic studies. The results are discussed and rationalized based on theories of static and dynamic phase transformations.

Scale bridging materials physics: Active learning workflows and integrable deep neural networks for free energy function representations in alloys

The free energy plays a fundamental role in theories of phase transformations and microstructure evolution. It encodes the thermodynamic coupling between different fields, such as mechanics and chemistry, within continuum descriptions of non-equilibrium materials phenomena. In mechano-chemically interacting materials systems, even consideration of only compositions, order parameters and strains results in a free energy description that occupies a high-dimensional space. Scale bridging between the electronic structure of a solid and continuum descriptions of its non-equilibrium behavior can be realized with integrable deep neural networks (IDNN) that are trained to free energy derivative data generated by first-principles statistical mechanics simulations and then analytically integrating to recover a free energy density function. Here we combine the IDNN with an active learning workflow to ensure well-distributed sampling of the free energy derivative data in high-dimensional input spaces, thereby enabling true scale bridging between first-principles statistical mechanics and continuum phase field models. As a prototypical material system we focus on Ni–Al. Cahn–Hilliard and Allen–Cahn phase field simulations using the resulting IDNN representation for the free energy density of Ni–Al demonstrate that the appropriate physics of the material have been learned. This work advances the treatment of scale bridging, starting with electronic structure calculations and proceeding through statistical mechanics to continuum physics. Its coupling of Cahn–Hilliard and Allen–Cahn phase field descriptions with nonlinear elasticity through the free energy density ensures a rigorous treatment of phase transformation phenomena.

Kinetic study of grain growth in highly (111)-preferred nanotwinned copper films

We investigated the microstructure changes in abnormal grain growth of nanotwinned Cu (nt-Cu) upon annealing by electron backscattered diffraction (EBSD) and focused ion beam (FIB). The nt-Cu films were produced by electrodeposition on a Si wafer with a barrier/seed layer of TiW/Cu. When a 3 μm thick nt-Cu film was annealed at 350 °C for 45 min, its microstructure was found to have changed from the (111) oriented twins to the (200) oriented grains with an average grain size larger than 100 μm. When the nt-Cu film is thicker than 5 μm, the change can occur at a lower temperature of 300 °C. We observed that there is a critical abnormal grain growth temperature, below which no microstructure change can occur. We propose that it is due to nucleation limitation. After nucleation, the growth is highly anisotropic, where the lateral growth is at the least one order of magnitude faster than the normal growth. We have attempted to use JMAK theory of phase transformation to analyze the abnormal grain growth kinetics, yet we obtained very little success.