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1

Nürnberger, Florian, Mirko Schaper, Friedrich-Wilhelm Bach, Iryna Mozgova, Kostjantyn Kuznetsov, Anna Halikova, and Olga Perederieieva. "Prediction of Continuous Cooling Diagrams for the Precision Forged Tempering Steel 50CrMo4 by Means of Artificial Neural Networks." Advances in Materials Science and Engineering 2009 (2009): 1–10. http://dx.doi.org/10.1155/2009/582739.

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Quenching and tempering of precision forged components using their forging heat leads to reduced process energy and shortens the usual process chains. To design such a process, neither the isothermal transformation diagrams (TTT) nor the continuous cooling transformation (CCT) diagrams from literature can be used to predict microstructural transformations during quenching since the latter diagrams are significantly influenced by previous deformations and process-related high austenitising temperatures. For this reason, deformation CCT diagrams for several tempering steels from previous works have been investigated taking into consideration the process conditions of precision forging. Within the scope of the present work, these diagrams are used as input data for predicting microstructural transformations by means of artificial neural networks. Several artificial neural network structures have been examined using the commercial software MATLAB. Predictors have been established with satisfactory capabilities for predicting CCT diagrams for different degrees of deformation within the analyzed range of data.
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2

Polevoi, E. V., Yu N. Simonov, N. A. Kozyrev, R. A. Shevchenko, and L. P. Bashchenko. "Phase and structural transformations when forming a welded joint from rail steel. Report 2. Isothermal diagram of decomposition of supercooled austenite of R350LHT rail steel." Izvestiya. Ferrous Metallurgy 64, no. 4 (June 4, 2021): 266–72. http://dx.doi.org/10.17073/0368-0797-2021-4-266-272.

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An isothermal diagram of decomposition of supercooled austenite of R350LHT steel was constructed based on the results of dilatometric, metallographic and hardness analysis of this decomposition during continuous cooling and under isothermal conditions. When comparing the thermokinetic and isothermal diagrams, it was found that the thermokinetic diagram plotted during continuous cooling shifts downward and to the right in comparison with the isothermal diagram. This result is fully consistent with the known regularities. During the research, the critical points of R350LHT steel were determined: Ас1 = 711 °С; Мn = 196 °С. This isothermal diagram was used to determine the temperature of the minimum stability of overcooled austenite, which was 500 °C. Under isothermal conditions, pearlite-type structures appear in the temperature range from 700 to 600 °C. At 550 °C, a mixture of pearlitic and bainitic structures is formed. In the temperature range from 500 to 250 °C, bainitic structures are formed: at 500 – 400 °C – upper bainite; at 350 ° C – a mixture of upper and lower bainite; at 300 – 250 °С – lower bainite. Almost in the entire studied temperature range of overcooled austenite isothermal decomposition, an increase in the hardness of the transformation products is observed with a decrease in the holding temperature from 246 HV (at 700 °C) to 689 HV (at 250 °C). However, at a temperature of 500 °C, a slight drop in hardness occurs, which is apparently caused by the appearance of retained austenite during the development of bainitic transformation.
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3

Irani, Missam, Sukhwan Chung, Mincheol Kim, Kwangoh Lee, and Mansoo Joun. "Adjustment of Isothermal Transformation Diagrams Using Finite-Element Optimization of the Jominy Test." Metals 10, no. 7 (July 10, 2020): 931. http://dx.doi.org/10.3390/met10070931.

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A practical method for adjusting and optimizing isothermal transformation (IT) diagrams using the Jominy test is presented. The method is based on a finite-element optimization procedure, which iteratively minimizes the error between the target phase fractions and the corresponding finite-element solutions at the sample points using an optimization tool. A standard Jominy test of AISI 52100 bearing steel is used to investigate the feasibility and reliability of the method. Three optimization parameters for each IT diagram curve are mathematically applied to the modified Kirkaldy model. These parameters are the design variables in the optimization. The curves obtained from the modified Kirkaldy model are used as the initial guesses in the optimization and they approach the experimental IT diagram by minimizing the error. Good agreement is observed between the optimized diagram and the experimental diagram reported in the literature. The predicted phase fractions using the experimental IT diagram, the IT diagram obtained from the modified Kirkaldy model, and those obtained from the optimized model are compared and demonstrate that the adjustment or optimization procedure significantly improves the accuracy of the predicted phase fraction of the model. The applicability of the method is investigated in a practical case study.
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4

Mioković, T., J. Schwarzer, V. Schulze, O. Vöhringer, and D. Löhe. "Description of short time phase transformations during the heating of steels based on high-rate experimental data." Journal de Physique IV 120 (December 2004): 591–98. http://dx.doi.org/10.1051/jp4:2004120068.

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During surface hardening of steels like laser hardening, rapid thermal changes are imposed to the material. The modelling of these hardening processes allows the determination of time-dependent temperature fields and phase transformations within the affected zones. While there are many investigations on the transformation behaviour during cooling, there is a lack of data concerning the transformation during heating at very high heating rates. Therefore, experiments simulating the fast temperature changes are necessary to implement the effects of short time phase transformation during hardening into simulation. In this paper the effect of heating rates up to 10000 K/s on the austenitizing behaviour of the steel AISI 4140 (German grade 42CrMo4) are presented and described using an Avrami-function. The results obtained are summarized in time-temperature-transformation diagrams for continuous heating and isothermal time-temperature-transformation diagrams which may be used as input data for the simulation.
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5

Kessler, O., R. von Bargen, Fabian Hoffmann, and H. W. Zoch. "Continuous Cooling Transformation (CCT) Diagram of Aluminium Alloy Al-4.5Zn-1Mg." Materials Science Forum 519-521 (July 2006): 1467–72. http://dx.doi.org/10.4028/www.scientific.net/msf.519-521.1467.

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Age hardening is one of the most important processes to strengthen aluminium alloys. It usually consists of the steps solution annealing, quenching and aging. For heat treatment simulations as well as for the appropriate choice of quenching processes in heat treatment shops, knowledge of the temperature- and time-dependent precipitation behaviour during continuous cooling is required. Quenching should happen as fast as necessary to reach high strengths, but also as slow as possible, to reduce residual stresses and distortion. This optimal quenching rate of an aluminium component depends on its chemical composition, initial microstructure and solution annealing parameters as well as on its dimensions. Unfortunately continuous cooling transformation (CCT) diagrams of aluminium alloys do almost not exist. Instead isothermal transformation (IT) diagrams or given average quenching rates are used to estimate quenching processes, but they are not satisfying neither for heat treatment simulations nor for heat treatment shops. Thermal analysis, especially Differential Scanning Calorimetry (DSC) provides an approach for CCT-diagrams of aluminium alloys, if the relevant quenching rates can be realized in the DSCequipment. The aluminium alloy Al-4.5Zn-1Mg (7020) is known for its relatively low quenching sensitivity as well as for its technical importance. The complete CCT-diagram of 7020 with cooling rates from a few K/min to some 100 K/min has been recorded. Samples have been solution annealed and quenched with different cooling rates in a high speed DSC. The resulting precipitation heat peaks during cooling have been evaluated for temperature and time of precipitation start, as well as their areas as a measure for the precipitate amount. Quenched samples have been further investigated regarding their microstructure by light and electron microscopy, hardness after aging and precipitation behaviour during re-heating in DSC. The CCT-diagram correlated very well with the microstructure, hardness and re-heating results. A critical cooling rate with no detectable precipitation during continuous cooling 155 K/min could be determined for 7020. A model to integrate the CCT-diagram in heat treatment simulation of aluminium alloys is under development.
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6

Umemoto, Minoru, and Imao Tamura. "Computer simulation of isothermal transformation diagrams in steels." Bulletin of the Japan Institute of Metals 25, no. 6 (1986): 497–504. http://dx.doi.org/10.2320/materia1962.25.497.

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7

Bahmani, M., and R. Elliott. "Isothermal transformation diagrams for alloyed ductile cast iron." Materials Science and Technology 10, no. 12 (December 1994): 1050–56. http://dx.doi.org/10.1179/mst.1994.10.12.1050.

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8

Piekarska, W. "Modelling and Analysis of Phase Transformations and Stresses in Laser Welding Process / Modelowanie I Analiza Przemian Fazowych I Naprężeń W Procesie Spawania Laserowego." Archives of Metallurgy and Materials 60, no. 4 (December 1, 2015): 2833–42. http://dx.doi.org/10.1515/amm-2015-0454.

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The work concerns the numerical modelling of structural composition and stress state in steel elements welded by a laser beam. The temperature field in butt welded joint is obtained from the solution of heat transfer equation with convective term. The heat source model is developed. Latent heat of solid-liquid and liquid-gas transformations as well as latent heats of phase transformations in solid state are taken into account in the algorithm of thermal phenomena. The kinetics of phase transformations in the solid state and volume fractions of formed structures are determined using classical formulas as well as Continuous-Heating-Transformation (CHT) diagram and Continuous-Cooling-Transformation (CCT) diagram during welding. Models of phase transformations take into account the influence of thermal cycle parameters on the kinetics of phase transformations during welding. Temporary and residual stress is obtained on the basis of the solution of mechanical equilibrium equations in a rate form. Plastic strain is determined using non-isothermal plastic flow with isotropic reinforcement, obeying Huber-Misses plasticity condition. In addition to thermal and plastic strains, the model takes into account structural strain and transformation plasticity. Changing with temperature and structural composition thermophysical parameters are included into constitutive relations. Results of the prediction of structural composition and stress state in laser butt weld joint are presented.
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9

Uhm, Sang Ho, Joo Noh Moon, Chang Hee Lee, Ji Hyun Yoon, and Bong Sang Lee. "Bainitic Transformation Model in Low Alloy Carbon Steels Considering the Effect of Reaction Constant in JMA Equation." Materials Science Forum 475-479 (January 2005): 3157–60. http://dx.doi.org/10.4028/www.scientific.net/msf.475-479.3157.

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As a part of a study on modeling the microstructural evolution during the welding process, a prediction model of TTT diagram for bainite transformation was studied. This model consisted of a thermodynamic model for the bainite-start(Bs) temperature and a kinetic model for the bainite transformation. A kinetic model was empirically established for low alloy carbon steels, based on Johnson-Mehl-Avrami(JMA) equation. Reaction constants seemed not to have noticeable tendencies for temperatures and were averaged for each alloy. It was, however, found that the mean reaction constant significantly affected the reproducibility for the isothermal kinetics. Therefore, a calibration method to the kinetic parameter was proposed. From calibrations, rate constants were formulated as a function of alloying element and temperature. And TTT diagrams were calculated and compared with experiments.
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10

Domański, T., and A. Bokota. "Numerical Models of Hardening Phenomena of Tools Steel Base on the TTT and CCT Diagrams." Archives of Metallurgy and Materials 56, no. 2 (June 1, 2011): 325–44. http://dx.doi.org/10.2478/v10172-011-0036-6.

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Numerical Models of Hardening Phenomena of Tools Steel Base on the TTT and CCT DiagramsIn work the presented numerical models of tool steel hardening processes take into account thermal phenomena, phase transformations and mechanical phenomena. Numerical algorithm of thermal phenomena was based on the Finite Elements Methods in Galerkin formula of the heat transfer equations. In the model of phase transformations, in simulations heating process, isothermal or continuous heating (CHT) was applied, whereas in cooling process isothermal or continuous cooling (TTT, CCT) of the steel at issue. The phase fraction transformed (austenite) during heating and fractions of ferrite, pearlite or bainite are determined by Johnson-Mehl-Avrami formulas. The nescent fraction of martensite is determined by Koistinen and Marburger formula or modified Koistinen and Marburger formula. In the model of mechanical phenomena, apart from thermal, plastic and structural strain, also transformations plasticity was taken into account. The stress and strain fields are obtained using the solution of the Finite Elements Method of the equilibrium equation in rate form. The thermophysical constants occurring in constitutive relation depend on temperature and phase composite. For determination of plastic strain the Huber-Misses condition with isotropic strengthening was applied whereas for determination of transformation plasticity a modified Leblond model was used. In order to evaluate the quality and usefulness of the presented models a numerical analysis of temperature field, phase fraction, stress and strain associated hardening process of a fang lathe of cone shaped made of tool steel was carried out.
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11

Kurkin, A. S. "Study of isothermal decomposition of austenite using methods of mathematical modeling." Industrial laboratory. Diagnostics of materials 87, no. 6 (June 18, 2021): 25–32. http://dx.doi.org/10.26896/1028-6861-2021-87-6-25-32.

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The capabilities of the numerical simulation of technological processes are limited by the accuracy and efficiency of determining the properties of materials which continuously change with repeated heating and cooling. The parameters of structural transformations are the principal factors affecting the properties of alloyed steels. We present a method for determining the parameters of formulas describing C-shaped curves of experimental diagrams of isothermal decomposition of austenite. The proposed approach makes it possible to reconstruct the entire C-shaped curve using a relatively small fragment near the «nose» (by three points). Joint processing of a series of curves provided determination of the parameters of ferritic, pearlitic and bainitic transformation kinetics. However, it is important to take into account the features of the diffusion decomposition of austenite. For example, ferrite and pearlite are formed in overlapping temperature ranges and have similar mechanical properties, but their combining into a single ferrite-pearlite structure complicates the construction of a mathematical model of transformation. The bainitic transformation has a transient character from diffusion to diffusionless one. As for the transformation temperature range, the limiting degree is a function of temperature (as in the case of martensitic transformation). It was shown that for ferrite-pearlite transformation the best results are obtained by the Kolmogorov – Avrami equation, and for the bainitic one — by the Austin – Rickett equation modified with allowance for an incomplete transformation.
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12

J. Da Costa Teixeira, L. Héricher, B. Appolaire, E. Aeby-Gautier, G. Cailletaud, S. Denis, and N. Spath. "Prediction of the kinetics of the phase transformations and the associated microstructure during continuous coolingin the Ti17." Journal de Physique IV 120 (December 2004): 93–101. http://dx.doi.org/10.1051/jp4:2004120010.

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The aim of this paper is to present recent experimental results and related simulation about the β → αGB + αWGB and → αWI transformations which occur in the Ti17 alloy during the thermal treatments following the heating in the β phase field. These phase transformations were experimentally studied under isothermal conditions in samples with negligible thermal gradients. The IT diagram was obtained, on the basis of electrical resistivity measurements and microstructural SEM observations. The kinetics of the phase transformation was further numerically simulated for continuous cooling on the basis of a formerly developed model giving the amount of each morphology (αWGB, αWI). Experimental and calculated results are compared.
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13

Rezende, A. B., F. M. Fernandes, S. T. Fonseca, P. F. S. Farina, H. Goldenstein, and Paulo Roberto Mei. "Effect of Alloy Elements in Time Temperature Transformation Diagrams of Railway Wheels." Defect and Diffusion Forum 400 (March 2020): 11–20. http://dx.doi.org/10.4028/www.scientific.net/ddf.400.11.

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The Heavy-Haul railroad wheels started to use higher wear resistance steels microalloyed with niobium, vanadium, and molybdenum [1]. During continuous cooling, these elements depress the temperature of the pearlite formation, producing smaller interlamellar spacing that increases the hardness of the steel, besides to favor the precipitation hardening through the formation of carbides [2, 3]. Also, they delay the formation of difusional components like pearlite and bainite during isothermal transformation. The effects of these alloy elements on microstructure during isothermal transformation were studied in this work using a Bähr 805A/D dilatometer. Three different compositions of class C railway wheels steels (two microalloyed and one, non microalloyed) were analyzed in temperatures between 200 and 700 °C. The microstructure and hardness for each isothermal treatment were obtained after the experiments. Comparing with non microalloyed steel (7C), the vanadium addition (7V steel) did not affect the beginning of diffusion-controlled reactions (pearlite and bainite), but delayed the end of these reactions, and showed separated bays for pearlite and bainite. The Nb + Mo addition delayed the beginning and the ending of pearlite and bainite formation and also showed distinct bays for them. The delays in diffusion-controlled reactions were more intense in the 7NbMo steel than in 7V steel. The V or Nb + Mo additions decreased the start temperature for martensite formation and increased the start temperature for austenite formation.
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14

Nam, J. M., Tomoyuki Terai, Masashi Mino, Y. Aikawa, and Tomoyuki Kakeshita. "Relationship between Particle Size and Martensitic Transformation in an Fe-30at%Ni Alloy." Materials Science Forum 654-656 (June 2010): 146–49. http://dx.doi.org/10.4028/www.scientific.net/msf.654-656.146.

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We have investigated the effect of particle size on martensitic transformation by using single crystalline specimens of an Fe-30at%Ni alloy by scanning electron microscope (SEM) observation, X-ray diffraction(XRD), magnetic susceptibility and magnetization measurements. As a result, we have found that an athermal martensitic transformation changes to an isothermal martensitic transformation with decreasing particle size. Considering the result of the TTT diagram, we have estimated the driving force for the martensitic transformation and the cluster size for nucleation of the isothermal martensitic transformation based on the model previously proposed.
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15

Koyama, Toshiyuki, and Hidehiro Onodera. "Phase-Field Modeling of the Microstructure Evolutions in Fe-Cu Base Alloys." Materials Science Forum 539-543 (March 2007): 2383–88. http://dx.doi.org/10.4028/www.scientific.net/msf.539-543.2383.

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The phase transformations and the microstructure developments in Fe-Cu base alloys during isothermal aging are simulated based on the phase-field method. Since the chemical free energy used in this simulation is obtained from the thermodynamic database of phase diagrams, the calculated microstructure changes are directly related to the phase diagram of the real alloy system. Firstly the phase decomposition and the microstructure changes in the Fe-Cu binary alloy system are demonstrated as the simple example of the phase-field modeling, i.e., the phase decomposition in bcc phase where the Cu-rich phase forms, the structural phase transformation from bcc to fcc phase in the Cu-rich nano-particle, and the shape change of fcc-Cu precipitates from sphere to rod. Secondly, the phase decomposition in bcc phase of the multi-component alloys such as the Fe-Cu-X (X=Mn,Ni) ternary system and the Fe-Cu-Mn-Ni quaternary alloy is simulated. At the early stage of aging, the Cu-rich zone with bcc structure begins to nucleate, and the component X (=Mn, Ni) is partitioned to the Cu-rich phase. When the Cu composition in the precipitate reaches equilibrium, the component X inside the precipitates moves toward to the interface region between the precipitate and matrix. Finally, there appears the shell structure that the Cu precipitates surrounded by the thin layer with high concentration of component X.
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16

Toleuova, Ainagul, Bakhyt Balbekova, and Irina Erakhtina. "Optimization of the Composition and Structure of Deformable Heat Resistant Aluminum Alloy." Materials Science Forum 946 (February 2019): 156–61. http://dx.doi.org/10.4028/www.scientific.net/msf.946.156.

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The necessity of finding scientifically grounded methods for the development of new heat-resistant, wear-resistant and corrosion-resistant aluminum alloys is presented in the present work. For this purpose, the analysis of modern methods for computer calculation of phase diagrams in multicomponent metal systems using the Thermo-Calc program was carried out. Therefore, a quantitative analysis of the phase diagram the Al-Cu-Mn-Zr system was carried out, as the basis of deformable high-temperature aluminum alloys. Isothermal and polythermal sections of the phase diagram were calculated in this system. The temperatures of phase transformations were calculated. The mass and volume fractions of the phases in the studied alloys were calculated. The range of concentrations and temperatures at which the maximum amount of dispersoids Al20Cu2Mn3 may be achieved, was defined. The minimum amount of Al2Cu phase is calculated, which should correspond to the best heat resistance of alloys. It is substantiated that in the alloys of a new generation of ALTEK type, the use of homogenization and quenching operations is inexpedient, which implies the possibility of a significant reduction in the cost of heat treatment in comparison with industrial alloys, such as 1201.
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17

Buza, Gabor, Hans Paul Hougardy, and Marton Gergely. "Calculation of the isothermal transformation diagram from measurements with continuous cooling." Steel Research 57, no. 12 (December 1986): 650–53. http://dx.doi.org/10.1002/srin.198600842.

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18

Vinokur, Bertold. "The isothermal diagram of transformation of the residual austenite by tempering." Metallurgical and Materials Transactions A 24, no. 12 (December 1993): 2806–10. http://dx.doi.org/10.1007/bf02659504.

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19

Wang, Qing Feng, Cai Chao Zhu, De Zhong Xin, Ming Jin Zhang, and Xi Wei Wang. "Research on Isothermal Phase Transformation Kinetics of TC21 Alloy." Advanced Materials Research 750-752 (August 2013): 743–47. http://dx.doi.org/10.4028/www.scientific.net/amr.750-752.743.

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The kinetics of the martensite decomposition in TC21 alloy under isothermal conditions has been studied using dilatometry technique. The typical morphologies of decomposition products were also directly observed. At 500°C and 550°C, the mechanism of martensite decomposition occur by, at temperature between 600°C and 750°C, the martensite decompose by . up 800°C, the martensite directly transform to α and β phase. Time–temperature–transformation diagram with iso-lines tracing the amount of the martensite decomposition have been established.
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20

Liu, Mengyun, Zhan Zhang, Francis Breton, and X. Grant Chen. "Quench Sensitivity and Phase Transformation Kinetics of AlSi7MnMg High Pressure Vacuum Die Casting." MATEC Web of Conferences 326 (2020): 02001. http://dx.doi.org/10.1051/matecconf/202032602001.

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The quench sensitivity of an AlSi7MnMg alloy in high-pressure vacuum die (HPVD) casting was investigated by time-temperature-transformation and time-temperature-property diagrams with an interrupted quench technique. The quench sensitive temperature range of the alloy is from 260 to 430 °C and its nose temperature is 350 °C. The mechanical strength versus cooling rates of the HPVD casting was predicted using quench factor analysis method and verified by experimental results. The critical cooling rate is 6 °C/s to remain 95% of the maximal mechanical strength. The coefficients k2 - k5, related to the nucleation and precipitation kinetics of TTP curves, and phase transformation diagrams were determined. The precipitation of Mg2Si phase in the castings was observed during isothermal treatment using transmission electron microscope. Moreover, the quench sensitivity and kinetics of the phase transformation of AlSi7MnMg alloy and AlSi10MnMg alloys were compared. It reveals that the quench sensitivity and phase transformation rate of the former are lower than that of the latter.
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21

Karyakin, Y. E., I. Y. Karyakin, and Svetlana V. Karyakina. "Software Application of Material Structure Prediction." Materials Science Forum 906 (September 2017): 88–94. http://dx.doi.org/10.4028/www.scientific.net/msf.906.88.

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The developed software application allows the user to model phase transformations under isothermal conditions for a specified steel grade at arbitrary tempering temperature. Architecture of the software application using scheme of the chart of distributed computation of simulation model kinematic parameters for reducing time expenditures during computer experiments. The recognition algorithm of raster images on the isothermal and thermokinetic diagrams has been proposed. The imaging algorithm of the material structure after heat treatment have been developed.
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22

Makhneva, Tat’ana, Arkadiy A. Sukhikh, Vyacheslav B. Dementyev, and Sergey S. Makarov. "Diagrams of Isothermal Decomposition of Overcooled Austenite in Maraging Steel at Uniaxial Tensile Loading." Materials Science Forum 1037 (July 6, 2021): 409–14. http://dx.doi.org/10.4028/www.scientific.net/msf.1037.409.

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It has been established that external uniaxial tensile stresses influence the character and kinetics of the g®a-transformation in cold-rolled martensite steel at sub-zero temperatures (down to -60 °C).
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23

Millet, P., C. Decaux, R. Ngameni, and M. Guymont. "Fourier-Domain Analysis of Hydriding Kinetics Using Pneumato-Chemical Impedance Spectroscopy." Research Letters in Physical Chemistry 2007 (October 9, 2007): 1–5. http://dx.doi.org/10.1155/2007/96251.

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Analysis of phase transformation processes observed in hydrogen absorbing materials (pure metals, alloys, or compounds) is still a matter of active research. Using pneumato-chemical impedance spectroscopy (PIS), it is now possible to analyze the mechanism of hydriding reactions induced by the gas phase. Experimental impedance diagrams, measured on activated LaNi5 in single- and two-phase domains, are reported in this paper. It is shown that their shape is mostly affected by the slope of the isotherm at the measurement point. By considering the details of the multistep reaction paths involved in the hydriding reaction, model impedance equations have been derived for single- and two-phase domains, and fitted to experimental impedance diagrams. The possibility of separately measuring surface and phase transformation resistances, hydrogen diffusion coefficient, and hydrogen solubility in each composition domain is discussed.
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24

Bach, F. W., M. Schaper, Z. Yu, F. Nürnberger, T. Gretzki, D. Rodman, and R. Springer. "Computation of isothermal transformation diagrams of 42CrMo4 steel from dilatometer measurements with continuous cooling." International Heat Treatment and Surface Engineering 4, no. 4 (December 2010): 171–75. http://dx.doi.org/10.1179/174951410x12851626813096.

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25

Dudás, Zoltán. "Comparing of the Processes of the Isothermal Phase Transformations of the Material Type 50 CrV 4 Using Different TTT Diagrams and Applying FEM Based Phase Elements." Materials Science Forum 473-474 (January 2005): 321–28. http://dx.doi.org/10.4028/www.scientific.net/msf.473-474.321.

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The application of the FEM based phase elements is very useful for evaluation of the effects of TTT phase transformations diagrams. The comparison of the different TTT diagrams of the same type of the 50 CrV 4 steels shows that fine differences are possible to be evaluated and approximated by this simulation. Examples are presented for the use of the multiple regression calculation applying the data of the suitable TTT diagrams.
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26

Li, Chia-Ying, and Jenq-Gong Duh. "Phase Equilibria in the Sn-Rich Corner of the Sn–Cu–Ni Ternary Alloy System at 240 °C." Journal of Materials Research 20, no. 11 (November 2005): 3118–24. http://dx.doi.org/10.1557/jmr.2005.0391.

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The interfacial reactions between solders and under bump metallization (UBM) have been of great interest recently in flip chip technology. Intermetallic compounds (IMCs), i.e., (Cu,Ni)6Sn5 and (Ni,Cu)3Sn4, usually formed between solders and UBM. To fully understand the interfacial reactions and phase transformation phenomenon, a suitable phase diagram concerning solders, IMCs, and UBM materials is required. In particular, a Sn-rich phase region in the Sn–Cu–Ni ternary diagram is very critical in determining the concentration tendency of x and y values in (Ni1−x,Cux)3Sn4 and (Cu1−y,Niy)6Sn5 compounds. In this study, ternary Sn–Cu–Ni alloys were prepared and annealed at 240 °C. Three equilibrium phases, Sn, Ni3Sn4, and Cu6Sn5, were identified by x-ray diffraction analysis and also showed in backscattered electron imaging. Using electron probe microanalysis quantitative analysis, three acme compositions of the ternary region in the Sn–Cu–Ni isotherm near the Sn-rich corner were determined as 98.5 at.% Sn, (Ni0.80, Cu0.20)3Sn4 and (Cu0.59,Ni0.41)6Sn5. In addition, the solubility of Cu and Ni in (Ni,Cu)3Sn4 and (Cu,Ni)6Sn5 compounds was evaluated. Finally, the isothermal section of the ternary Sn–Cu–Ni system at 240 °C was proposed on the basis of experimental results in this study.
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27

Liu, Sheng, Di Tang, Hui Bin Wu, and Zheng Xu Cai. "Isothermal Transformation of Wustite for Low Carbon Micro-Alloyed Steel." Advanced Materials Research 683 (April 2013): 457–63. http://dx.doi.org/10.4028/www.scientific.net/amr.683.457.

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The isothermal transformation of wustite (FeO) in the range of 650~350°C was studied using Gleeble 3500 thermal simulated test machine, electron back-scatter diffraction (EBSD) and scanning electron microscopy (SEM). A wustite layer was initially formed by oxidizing low carbon micro-alloyed steel in air at 880°C for 20 seconds. The layer was then isothermally annealed at 650-350°C in argon for up to 10000 seconds. The transformation of FeO was comprised by a proeutectoid reaction and a eutectoid reaction. FeO initially transformed to Fe3O4 by proeutecioid reaction and then the retained FeO transformed to lamellar mixture Fe+Fe3O4 by eutectoid reaction. The proeutectoid and eutectoid reactions both followed a C-curve trend and the nose temperatures were 475°C and 425°C, respectively. An isothermal transformation (IT) diagram was summarized based on our results.
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28

Pusterla, Julio M., Emanuel Schneck, and Rafael G. Oliveira. "Phase Diagram of Purified CNS Myelin Reveals Continuous Transformation between Expanded and Compacted Lamellar States." Cells 9, no. 3 (March 10, 2020): 670. http://dx.doi.org/10.3390/cells9030670.

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Purified myelin membranes (PMMs) are the starting material for biochemical studies, from individual components up to the isolation of detergent-resistant membrane (DRM) fractions or detergent-insoluble glycosphingolipid (DIG) fractions, which are commonly believed to resemble physiological lipid rafts. The normal DIG isolation protocol involves the extraction of lipids under moderate cooling. The isolation of PMMs also involves the cooling of myelin as well as exposure to low ionic strength (IS). Here, we addressed the combined influence of cooling and IS on the structure of PMMs. The phase behaviour was investigated by small angle X-ray diffraction. Analysis of the diffraction peaks revealed the lamellar periodicity ( d ), the number of periodically correlated bilayers ( N ), and the relatives fractions of each phase. Departure from physiological conditions induced a phase separation in myelin. The effect of monovalent and divalent ions was also compared at equivalent IS, showing a differential effect, and phase diagrams for both ion types were established—Ca2+ induced the well-known over-compacted phase, but additionally we also found an expanded phase at low IS. Na+ promoted phase separation, and also induced over-compaction at sufficiently high IS. Finally, exploring the whole phase diagram, we found evidence for the direct isothermal transformation from the expanded to the compacted phase, suggesting that both phases could in fact originate from the identical primary lateral phase separation, whereas the apparent difference lies in the inter-bilayer interaction that is modulated by the ionic milieu.
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29

Yu, Liyang, Andrew M. Zeidell, John E. Anthony, Oana D. Jurchescu, and Christian Müller. "Isothermal crystallization and time-temperature-transformation diagram of the organic semiconductor 5,11-bis(triethylsilylethynyl)anthradithiophene." Journal of Materials Chemistry C 9, no. 35 (2021): 11745–52. http://dx.doi.org/10.1039/d1tc01482j.

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The time-temperature-transformation diagram describing crystallization of the semiconducting molecule TES-ADT from its melt was constructed and found to correlate with the thin-film micro/nanostructure and electronic performance.
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30

Opitek, Bartosz, Janusz Lelito, Michał Szucki, Grzegorz Piwowarski, Łukasz Gondek, and Łukasz Rogal. "Analysis of the Crystallization Kinetics and Thermal Stability of the Amorphous Mg72Zn24Ca4 Alloy." Materials 14, no. 13 (June 26, 2021): 3583. http://dx.doi.org/10.3390/ma14133583.

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The aim of this study was to analyze the crystallization of the Mg72Zn24Ca4 metallic glass alloy. The crystallization process of metallic glass Mg72Zn24Ca4 was investigated by means of the differential scanning calorimetry. The glass-forming ability and crystallization are both strongly dependent on the heating rate. The crystallization kinetics, during the isothermal annealing, were modelled by the Johnson–Mehl–Avrami equation. Avrami exponents were from 2.7 to 3.51, which indicates diffusion-controlled grain growth. Local exponents of the Johnson–Mehl–Avrami equation were also calculated. In addition, the Mg phase—being the isothermal crystallization product—was found, and the diagram of the time–temperature phase transformation was developed. This diagram enables the reading of the start and end times of the crystallization process, occurring in amorphous ribbons of the Mg72Zn24Ca4 alloy on the isothermal annealing temperature. The research showed high stability of the amorphous structure of Mg72Zn24Ca4 alloy at human body temperature.
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31

Rosas, G., and R. Perez. "On the relationships between isothermal phase diagrams and quasicrystalline phase transformations in AlCuFe alloys." Materials Science and Engineering: A 298, no. 1-2 (January 2001): 79–83. http://dx.doi.org/10.1016/s0921-5093(00)01342-3.

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32

Wang, Gang, De Chang Zeng, and Zhong Wu Liu. "Evaluation of Glass-Forming Ability for Metallic Melts by Phase Field Approach." Advanced Materials Research 490-495 (March 2012): 3129–33. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.3129.

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Evaluation of glass-forming ability (GFA) is important in the development of amorphous alloys. Based on phase field theory, the kinetic model of liquid-to-solid phase transition is build, and the time-temperature-transformation (TTT) diagram is plotted according to the phase field simulations of isothermal phase transformation kinetics for a model system. Furthermore, the critical cooling rate for glass formation is calculated on the basis of the TTT curve and is taken as the intrinsic criteria of reflecting the GFA for metallic melts.
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33

Khaskov, M. A. "The using of thermal analysis methods for the construction of isothermal transformation diagrams of thermosets." Polymer Science, Series B 59, no. 1 (January 2017): 51–61. http://dx.doi.org/10.1134/s1560090417010080.

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34

Nusskern, Philipp, Jürgen Hoffmeister, and Volker Schulze. "Austenite-Bainite Transformation Kinetic Model for the Powder-Metallurgical Steel Astaloy 85 Mo." Materials Science Forum 706-709 (January 2012): 1485–90. http://dx.doi.org/10.4028/www.scientific.net/msf.706-709.1485.

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A new approach for case hardening of powder metallurgical steels is surface densification prior to heat treatment, hence avoiding hardening to the core caused by open porosity. With regard to this process chain a porosity and carbon dependent model of the transformation kinetics is essential. In powder metallurgical materials the transformation behavior is mainly influenced by the chemical composition, homogeneity and porosity. Using a prealloyed powder, e.g. Astaloy 85 Mo, a homogeneous distribution of alloying elements after sintering can be assumed and the transformation behaviour is mainly determined by pores and the carbon profile caused by case hardening. The effect of carbon is widely known but up to now, only a few details about the effect of porosity on the transformation can be found in literature. It is reported that a decreasing relative density causes a reduction of incubation and overall isothermal transformation time. In the present study, the transformation kinetics of a powder metallurgical steel based on Astaloy 85 Mo were investigated for the carbon levels 0.5 and 0.8 wt% as well as the relative densities 6.8, 7.2 and 7.8 g/cm³. The investigations were carried out using a high-speed quenching dilatometer. The isothermal time temperature transformation diagrams for this powder-metallurgical alloy are presented and Avrami-type equations are fitted to the measured data. A good correlation can be found for the transformation model and the experimental results verifying the used modeling approach showing the potential to be applied within case hardening simulations.
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35

Mirzaev, D. A., K. Yu Okishev, and K. D. Mirzaeva. "Analytical Solution of the Problem of Diffusional Transformation Under Continuous Cooling Condition Based on Isothermal Transformation Diagram Data." Materials Performance and Characterization 2, no. 1 (April 17, 2013): 20120023. http://dx.doi.org/10.1520/mpc20120023.

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36

Ma, Xiao Hua, Sun Bai, Li Wu, and Zhi Liang Jin. "Metastable Phase Equilibrium of a Ternary System of K+,Mg2+/B4O72--—H2O at 25°C." Advanced Materials Research 662 (February 2013): 468–72. http://dx.doi.org/10.4028/www.scientific.net/amr.662.468.

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The isothermal solubility of the ternary system K+,Mg2+/B4O72-—H2O at 25°C has been studied and the phase diagram is determined. The results show that the system is of the simple eutonic type and can be in metastable equilibrium state within 8—16 hours. The phase diagram consists of two solubility branches corresponding to the crystallization areas of K2B4O7•4H2O and MgB4O7•9H2O. The composition of the eutonic point is MgB4O7,0.5279%(Wt%) and K2B4O7,13.9629%(Wt%) respectively. The replicate experiments proved that the phase transformation of hungtsaoite (MgB4O7•9H2O) occurs after a 20 hours epuilibrium.
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37

Peniel, Matthieu, Houda El Bekkachi, Olivier Tougait, Mathieu Pasturel, and Henri Noël. "An Experimental Investigation of the U-Mo-C Ternary Diagram." Solid State Phenomena 194 (November 2012): 26–30. http://dx.doi.org/10.4028/www.scientific.net/ssp.194.26.

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The isothermal sections of the U-Mo-C ternary system have been established at 1000°C and 1400°C, using powder X-ray diffraction, scanning electron microscopy coupled with energy dispersive X-ray analysis for the quantification of U and Mo and differential thermal analysis. The main differences between the two sections are the appearance of liquid phase at about 1230°C, due to the peritectic decomposition of γ-UMo, and the peritectoid decompositions of MoC and β’’ Mo2C. No other transformation was detected in this temperature range, especially one involving the two only ternary phases found, UMoC2 and U2Mo2C3.
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38

Mirzaev, D. A., K. Yu Okishev, A. A. Mirzoev, and A. N. Makovetskii. "Austenite to Ferrite Transformation Kinetics in Fe-9 %Cr Alloys - I. General Kinetic Analysis." Materials Science Forum 946 (February 2019): 210–14. http://dx.doi.org/10.4028/www.scientific.net/msf.946.210.

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The paper considers theoretical aspects of the kinetics of austenite → ferrite transformation in an Fe–9 %Cr alloy, a common model of diffusionless transformation. In previous studies it was shown that this transformation under isothermal conditions shows a behaviour typical for nucleation site saturation, including the change of the Avrami exponentn(determined as the slow of transformation curve on double logarithmic scale) from 4 to 1. Activation energies determined in two ways: by the ‘nose’ temperature of the normal C-curve and by the slope of the C-curve re-drawn on a reverse temperature scale are unexpectedly similar (272–315 kJ/mole) and not temperature-dependent. But the complete TTT diagrams calculated using these values determined directly from experimental data and the precise formula of Cahn’s solution of grain face nucleated transformation problem do not provide good agreement with experiment in the whole temperature range. This may mean that the theory of site saturation needs some correction.
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39

Hackenberg, Robert E., Heather M. Volz, Pallas A. Papin, Ann M. Kelly, Robert T. Forsyth, Tim J. Tucker, and Kester D. Clarke. "Kinetics of Lamellar Decomposition Reactions in U-Nb Alloys." Solid State Phenomena 172-174 (June 2011): 555–60. http://dx.doi.org/10.4028/www.scientific.net/ssp.172-174.555.

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Discontinuous precipitation (DP) and discontinuous coarsening (DC) reactions have been observed in numerous alloy systems [1]. DP has been observed in the U-Nb system [2, 3, 4, 5]. The U-Nb phase diagram (Fig. 1) exhibits a continuous γ-BCC solid solution at high temperatures and a two-phase mixture of a-orthorhombic and γ-BCC below the 647°C monotectoid isotherm. The DP reaction occurs during continuous cooling and isothermal aging over 300-647°C. No metallographic evidence of a DC reaction in U-Nb has been published, although this is suggested from x-ray observations of distinct changes in the Nb content of the γ phase upon prolonged holding after the DP reaction [2, 3, 6]. This study will provide direct evidence for a DC reaction. Discontinuous and other aging reactions [7] are undesirable in U-Nb alloys, since they degrade corrosion resistance [5], ductility [8], and the shape-memory effect [9]. Hence, an improved understanding of the kinetics of these discontinuous phase transformations in U-Nb alloys is of practical interest.
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40

Lutz, Stefan, Johannes Weninger, Bastian Helldörfer, and Marion Merklein. "Numerical Investigation of Temperature and Phase Development of (Deformation-) Dilatometer Specimens." Key Engineering Materials 611-612 (May 2014): 1539–44. http://dx.doi.org/10.4028/www.scientific.net/kem.611-612.1539.

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The Gleeble 3500 thermo-mechanical testing machine with ISO-Q dilatometer set-up allows the creation of time temperature transformation diagrams at high cooling rates, after deformation and under constant load with a simple experimental set-up. An isothermal plane with temperature gradients perpendicular to this plane arises in the sample which is used for dilatometrical evaluation. The homogeneity and size of this isothermal region has a decisive influence on the measurement results, but cannot be measured with sufficient accuracy. To gain an accurate understanding of the processes in the sample, a coupled thermo-electrical, thermo-metallurgical, thermo-mechanical finite element model of the experiments is set up. To map the temperature control circuit of the machine, a PID controller is implemented, which controls the voltage of the conductive sample heating between the simulation steps. By comparing the temperature and hardness distribution with the experiments, it is shown that in this way the temperature distribution and phase transformation can be mapped. By the findings, the experimental setup was adjusted. This led to an improvement of the measurement results.
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41

Suriñach, S., E. Illekova, G. Zhang, M. Poulain, and M. D. Baró. "Optical fiber-drawing temperature of fluorogallate glasses." Journal of Materials Research 11, no. 10 (October 1996): 2633–40. http://dx.doi.org/10.1557/jmr.1996.0331.

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The thermal properties and the crystallization behavior of fluorogallate-based glasses were analyzed. The kinetic nature of the glass transition was used to determine the temperature dependence of the viscosity and from it an estimation of the appropriate drawing temperature for an optical fiber was established. The crystallization kinetics were studied by using both isothermal and continuous heating regimes. The temperature range for nucleation was evaluated and for samples previously nucleated the activation energy of the growth process was found. The results were used to estimate the empirical nucleation and crystal growth rates from which the time-temperature-transformation curves and the temperature-heating rate-transformation diagrams were constructed. The results obtained agree with experimental data and are discussed in the light of minimizing the volume of crystals formed during fiber drawing.
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42

Vestfálová, Magda, and Pavel Šafařík. "About the operational determination of the state and parameters of flowing moist air." EPJ Web of Conferences 213 (2019): 02091. http://dx.doi.org/10.1051/epjconf/201921302091.

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The presented paper deals with the solution of moist air parameters for the needs of aerodynamic research or design. From the thermodynamic theory of moist air, a p-t diagram of moist air is designed to allow the operative expression of the process and state of the moist air. Using this diagram, it is possible to illustratively describe the course of parameters at various state changes in moist air such as isentropic expansion and compression, isothermal expansion and compression, isobaric state change, isochoric state change, or general polytrophic state change. The initial state of moist air is determined by the pressure, temperature and moisture of the air. In the p-t diagram, the process is expressed by the applicable curve; the identification of the parameters in which the phase transformation occurs in moist air is significant. Uncertainty analysis is performed.
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43

Maldonado, Yadira G., Claudia Barraza de la P., Sergio Rodríguez A., A. Humberto Castillejos E., and Brian G. Thomas. "Estimation of Time–Temperature-Transformation Diagrams of Mold Powder Slags from Thermo-analysis of Non-isothermal Crystallization." Metallurgical and Materials Transactions B 46, no. 1 (September 25, 2014): 286–303. http://dx.doi.org/10.1007/s11663-014-0185-x.

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44

Kim, Yoon-Jun, L. Scott Chumbley, and Brian Gleeson. "Determination of isothermal transformation diagrams for sigma-phase formation in cast duplex stainless steels CD3MN and CD3MWCuN." Metallurgical and Materials Transactions A 35, no. 11 (November 2004): 3377–86. http://dx.doi.org/10.1007/s11661-004-0174-9.

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45

Säubert, Steffen, Rainer Jungwirth, Tobias Zweifel, Michael Hofmann, Markus Hoelzel, and Winfried Petry. "Neutron and hard X-ray diffraction studies of the isothermal transformation kinetics in the research reactor fuel candidate U–8 wt%Mo." Journal of Applied Crystallography 49, no. 3 (May 16, 2016): 923–33. http://dx.doi.org/10.1107/s1600576716005744.

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Exposing uranium–molybdenum alloys (UMo) retained in the γ phase to elevated temperatures leads to transformation reactions during which the γ-UMo phase decomposes into the thermal equilibrium phases,i.e.U2Mo and α-U. Since α-U is not suitable for a nuclear fuel exposed to high burn-up, it is necessary to retain the γ-UMo phase during the production process of the fuel elements for modern high-performance research reactors. The present work deals with the isothermal transformation kinetics in U–8 wt%Mo alloys for temperatures between 673 and 798 K and annealing durations of up to 48 h. Annealed samples were examined at room temperature using either X-ray or neutron diffraction to determine the phase composition after thermal treatment, andin situannealing studies disclosed the onset of phase decomposition. While for temperatures of 698 and 673 K the start of decomposition is delayed, for higher temperatures the first signs of transformation are already observable within 3 h of annealing. The typical C-shaped curves in a time–temperature–transformation (TTT) diagram for both the start and the end of phase decomposition could be determined in the observed temperature regime. Therefore, a revised TTT diagram for U–8 wt%Mo between 673 and 798 K and annealing durations of up to 48 h is proposed.
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46

Błyskun, P., J. Latuch, and T. Kulik. "Isothermal Stability and Selected Mechanical Properties of Zr48Cu36Al8Ag8 Bulk Metallic Glass." Archives of Metallurgy and Materials 62, no. 3 (September 26, 2017): 1749–53. http://dx.doi.org/10.1515/amm-2017-0266.

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AbstractThe aim of this work was to investigate the influence of isothermal annealing on the amorphous structure stability of the Zr48Cu36Al8Ag8alloy. A series of continuous heating examinations was performed on the differential scanning calorimeter in order to determine the temperature limits for isothermal annealing series where the time to crystallization was measured. The obtained results were calculated and a time-temperature-transformation diagram was created and discussed. Static compression test as well as microhardness measurements of the as-quenched samples gave a mechanical properties results supplement. The measured properties (σc= 1800 MPa and 614 HV0.05) are comparable to the literature results for this alloy. Fractographic observations with the scanning electron microscope were also performed in order to prove some plasticity observed during the strength tests.
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47

Li, Zhao Dong, Zhi Gang Yang, Tao Pan, Zhi Xin Xia, and Chi Zhang. "Analytical Modeling of Austenite Growth and Phase Evolution during Reverse Transformation from Pearlite in High Carbon Steels." Solid State Phenomena 172-174 (June 2011): 1201–6. http://dx.doi.org/10.4028/www.scientific.net/ssp.172-174.1201.

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Based on an analytical one-dimensional model, austenite growth into pearlite lamella and the corresponding phase evolution during isothermal reverse transformation to austenite at 1000-1183 K in Fe-C fully pearlitic steels containing 0.6-1.0 mass% C (in the austenite single phase field of Fe-C phase diagram) were simulated. It was found that the rate of austenite growth into ferrite increases faster with increasing reversion temperature than into cementite. Three types of phase evolution dependent on reversion temperature and carbon content were classified: 1) cementite rather than ferrite disappears first; 2) ferrite and cementite simultaneously disappear; 3) ferrite rather than cementite disappears first. The type of phase evolution in a hypoeutectoid steel heated above its Ae3temperature possibly changes in the order of 1), 2) and 3) as the reversion temperature increases. For eutectoid and hypereutectoid steels, the phase evolution during isothermal reversion always obeys the type 3).
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48

Choi, Ju Young, Takashi Fukuda, and Tomoyuki Kakeshita. "Isothermal Martensitic Transformation in a Sensitized SUS304 Stainless Steel under Magnetic Field." Materials Science Forum 654-656 (June 2010): 130–33. http://dx.doi.org/10.4028/www.scientific.net/msf.654-656.130.

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We have investigated effect of magnetic field at cryogenic temperature on the stability of austenitic phase in a sensitized SUS304 stainless steel. The sensitization of the steel was made by heat-treatment in vacuum at 973 K for 100h after the solution treatment at 1323 K for 0.5 h. Isothermal holding of the sensitized specimens was made under a static magnetic field of 5 T in the temperature range between 60 and 260 K for various holding times. As a result, the TTT diagram under the magnetic field corresponding to the formation of 0.5 vol. % of -martensite shows a double-C curve with two noses. We found that by the application of magnetic field, the nose temperature and the incubation time of upper part of the C-curve, that is due to the    transformation, become lower and shorter, respectively. On the other hand, the nose temperature of lower part of the C-curve, that is due to the      transformation, does not change under the magnetic field although the incubation time shortens by the application of magnetic field.
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49

Schur, D. V., S. Yu Zaginainchenko, Afer Veziroglu, T. N. Veziroglu, N. A. Gavrylyuk, A. D. Zolotarenko, M. T. Gabdullin, T. S. Ramazanov, Al D. Zolotarenko, and An D. Zolotarenko. "Prospects for producing hydrogen-ammonia fuel using lithium-aluminum amide." Izvestiya vysshikh uchebnykh zavedenii. Fizika 64, no. 1 (2021): 78–89. http://dx.doi.org/10.17223/00213411/64/1/78.

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A statistical theory of the phase transformation of lithium aluminum amide with the release of ammonia is developed. The free energies of the phases are calculated, their dependence on temperature, pressure, hydrogen concentration and energy parameters is established. The phase diagram is built. The equations of the thermodynamic equilibrium state are calculated. Investigated isoprocesses in phases. The coefficients of rectangularity and uniformity of isotherms are obtained. A feature of the temperature dependence of the concentration of hydrogen in phases is established.
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50

Lebrun, E., P. Svec, S. Nowak, B. Denand, Y. Millet, and Frédéric Prima. "Phase Transformations of TIMETAL-18 as a New Titanium Alloy with Bimodal Microstructure." Advanced Materials Research 922 (May 2014): 418–23. http://dx.doi.org/10.4028/www.scientific.net/amr.922.418.

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In this work, we have investigated the microstructural evolutions and the phase transformations of a new near-beta alloy with a nominal composition of Ti-5.5Al-5V-5Mo-2.4Cr-0.75Fe-0.15O (weight percent), the TIMETAL 18 [here after called Ti-18]. The complete microstructural state of the Ti-18 during heat treatments, from as quenched metastable state, has been first investigated. The phase transformations have been studied by combination of X-ray diffraction analysis, metallurgical observations and electrical resistivity measurements. From a series of isothermal treatments, the first complete TTT diagram has been then established displaying three C-curves corresponding to different precipitation domains for alpha phase.
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