Relevant bibliographies by topics / Avrami equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Avrami equations'

Author: Grafiati
Published: 4 June 2025
Last updated: 15 July 2025

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Journal articles on the topic "Avrami equations"

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Villar Goris, N. A., A. R. Selva Castañeda, E. E. Ramirez-Torres, et al. "Correspondence between formulations of Avrami and Gompertz equations for untreated tumor growth kinetics." Revista Mexicana de Física 66, no. 5 Sept-Oct (2020): 632. http://dx.doi.org/10.31349/revmexfis.66.632.

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The classical and modified equations of Kolmogorov-Johnson-Mehl-Avrami are compared with the equations of conventional Gompertz andMontijano-Bergues-Bory-Gompertz, in the frame of growth kinetics of tumors. For this, different analytical and numerical criteria are usedto demonstrate the similarity between them, in particular the distance of Hausdorff. The results show that these equations are similar fromthe mathematical point of view and the parameters of the Gompertz equation are explicitly related to those of the Avrami equation. It isconcluded that Modified Kolmogorov-Johnson-Mehl-Avrami and Montijano-Bergues-Bory-Gompertz equations can be used to describe thegrowth kinetics of unperturbed tumors.
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Kurkin, A. S. "Mathematical research of the phase transformation kinetics of alloyed steel." Industrial laboratory. Diagnostics of materials 85, no. 12 (2019): 25–32. http://dx.doi.org/10.26896/1028-6861-2019-85-12-25-32.

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Regulation of the process parameters allows obtaining the desired properties of the metal. Computer simulation of technological processes with allowance for structural and phase transformations of the metal forms the basis for the proper choice of those parameters. Methods of mathematical modeling are used to study the main diffusion and diffusion-free processes of transformations in alloyed steels during heating and cooling. A comparative analysis of the kinetic equations of phase transformations including the Kolmogorov – Avrami and Austin – Rickett equations which describe in different ways the time dependence of the diffusion transformation rate and attained degree of transformation has been carried out. It is shown that the Austin – Rickett equation is equivalent to the Kolmogorov – Avrami equation with a smooth decrease of the Avrami exponent during the transformation process. The advantages of the Kolmogorov – Avrami equation in modeling the kinetics of ferrite-pearlite and bainite transformations and validity of this equation for modeling the kinetics of martensite transformations during tempering are shown. The parameters for describing the tempering process of steel 35 at different temperatures are determined. The proposed model is compared with equations based on the Hollomon – Jaffe parameter. The diagrams of martensitic transformation of alloyed steels and disadvantages of the Koistinen – Marburger equation used to describe them are analyzed. The equations of the temperature dependence of the transformation degree, similar to the Kolmogorov – Avrami and Austin – Rickett equations, are derived. The equations contain the minimum set of the parameters that can be found from published data. An iterative algorithm for determining parameters of the equations is developed, providing the minimum standard deviation of the constructed dependence from the initial experimental data. The dependence of the accuracy of approximation on the temperature of the onset of transformation is presented. The complex character of the martensitic transformation development for some steels is revealed. The advantage of using equations of the Austin – Rickett type when constructing models from a limited amount of experimental data is shown. The results obtained make it possible to extend the approaches used in modeling diffusion processes of austenite decomposition to description of the processes of formation and decomposition of martensite in alloyed steels.
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Eltahir, Yassir A., Haroon A. M. Saeed, Chen Yuejun, Yumin Xia, and Wang Yimin. "Parameters characterizing the kinetics of the non-isothermal crystallization of polyamide 5,6 determined by differential scanning calorimetry." Journal of Polymer Engineering 34, no. 4 (2014): 353–58. http://dx.doi.org/10.1515/polyeng-2013-0250.

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Abstract The non-isothermal crystallization behavior of polyamide 5,6 (PA56) was investigated by differential scanning calorimeter (DSC), and the non-isothermal crystallization kinetics were analyzed using the modified Avrami equation, the Ozawa model, and the method combining the Avrami and Ozawa equations. It was found that the Avrami method modified by Jeziorny could only describe the primary stage of non-isothermal crystallization kinetics of PA56, the Ozawa model failed to describe the non-isothermal crystallization of PA56, while the combined approach could successfully describe the non-isothermal crystallization process much more effectively. Kinetic parameters, such as the Avrami exponent, kinetic crystallization rate constant, relative degree of crystallinity, the crystallization enthalpy, and activation energy, were also determined for PA56.
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Barbadillo, Fernando, A. Fuentes, Salvador Naya, Ricardo Cao, José Luís Mier, and Ramón Artiaga. "Study of the Degradation of a Polyesther-Polyurethane by TGA and the Logistic Mixture Model." Materials Science Forum 587-588 (June 2008): 525–28. http://dx.doi.org/10.4028/www.scientific.net/msf.587-588.525.

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The logistic mixture model was successfully studied previously in the separation of overlapping steps in some polymeric systems by the authors. In the present work, this method is applied to a polyesther-polyurethane degradation under air and inert atmospheres at several heat rates (5, 10, 15, 20 and 25 °C/min) in dynamic TGA. Every logistic component is fitted by reaction order, Johnson-Mehl-Avrami and Sestak-Berggren kinetics equations in order to calculate its kinetic parameters (activation energy, frequency factor and exponents). The reaction order model gives a good fitting and reproduces accurtelly the experimental curves. Johnson-Mehl-Avrami and Sestak- Berggren equations resulted to be not suitables because of the activation energy values obtained.
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Bianchi, O., R. V. B. Oliveira, R. Fiorio, J. De N. Martins, A. J. Zattera, and L. B. Canto. "Assessment of Avrami, Ozawa and Avrami–Ozawa equations for determination of EVA crosslinking kinetics from DSC measurements." Polymer Testing 27, no. 6 (2008): 722–29. http://dx.doi.org/10.1016/j.polymertesting.2008.05.003.

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Levine, L. E., K. Lakshmi Narayan, and K. F. Kelton. "Finite size corrections for the Johnson–Mehl–Avrami–Kolmogorov equation." Journal of Materials Research 12, no. 1 (1997): 124–32. http://dx.doi.org/10.1557/jmr.1997.0020.

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The Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation is frequently used to describe phase transformations involving nucleation and growth. The assumptions used in the derivation of this equation, however, are frequently violated when making experimental measurements; use of the JMAK equation for analyzing such data can often produce invalid results. Finite-size effects are among the most serious of these problems. We present modified analytic JMAK equations that correct for the finite-size effects and are roughly independent of both the sample shape and the shape of the growing nuclei. A comparison with computer simulations shows that these modified JMAK equations accurately reproduce the growth behavior over a wide range of conditions.
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Martin, David. "Application of Kolmogorov–Johnson–Mehl–Avrami equations to non-isothermal conditions." Computational Materials Science 47, no. 3 (2010): 796–800. http://dx.doi.org/10.1016/j.commatsci.2009.11.005.

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Vyazovkin, Sergey, and Nicolas Sbirrazzuoli. "Nonisothermal Crystallization Kinetics by DSC: Practical Overview." Processes 11, no. 5 (2023): 1438. http://dx.doi.org/10.3390/pr11051438.

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Providing a minimum of theory, this review focuses on practical aspects of analyzing the kinetics of nonisothermal crystallization as measured with differential scanning calorimetry (DSC). It is noted that kinetic analysis is dominated by approaches based on the Avrami and Arrhenius equations. Crystallization kinetics should not be considered synonymous with the Avrami model, whose nonisothermal applications are subject to very restrictive assumptions. The Arrhenius equation can serve only as a narrow temperature range approximation of the actual bell-shaped temperature dependence of the crystallization rate. Tests of the applicability of both equations are discussed. Most traditional kinetic methods tend to offer very unsophisticated treatments, limited only to either glass or melt crystallization. Differential or flexible integral isoconversional methods are applicable to both glass and melt crystallization because they can accurately approximate the temperature dependence of the crystallization rate with a series of the Arrhenius equations, each of which corresponds to its own narrow temperature interval. The resulting temperature dependence of the isoconversional activation energy can be parameterized in terms of the Turnbull–Fisher or Hoffman–Lauritzen theories, and the parameters obtained can be meaningfully interpreted and used for kinetic simulations.
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Gough, Terry, and Reinhard Illner. "Modeling Crystallization Dynamics when the Avrami Model Fails." VLSI Design 9, no. 4 (1999): 377–83. http://dx.doi.org/10.1155/1999/38517.

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Recent experiments on the formation of crystalline CO2 from a newly discovered binary phase consisting of CO2 and C2H2 at 90° K fail to be adequately simulated by Avrami equations. The purpose of this note is to develop an alternative to the Avrami model which can make accurate predictions for these experiments. The new model uses empirical approximations to the distribution densities of the volumes of three-dimensional Voronoi cells defined by Poisson-generated crystallization kernels (nuclei). Inside each Voronoi cell, the growth of the crystal is assumed to be linear in diameter (i.e., cubic in volume) until the cell is filled by the CO2 crystals and the C2H2 (thought of as a waste product). The cumulative growth curve is computed by averaging these individual growth curves with respect to the distribution density of the volumes of the Voronoi cells. Agreement with the experiments is excellent.
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Ahmadi, R., Madaah Hosseini, and A. Masoudi. "Avrami behavior of magnetite nanoparticles formation in co-precipitation process." Journal of Mining and Metallurgy, Section B: Metallurgy 47, no. 2 (2011): 211–18. http://dx.doi.org/10.2298/jmmb110330010a.

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In this work, magnetite nanoparticles (mean particle size about 20 nm) were synthesized via coprecipitation method. In order to investigate the kinetics of nanoparticle formation, variation in the amount of reactants within the process was measured using pH-meter and atomic absorption spectroscopy (AAS) instruments. Results show that nanoparticle formation behavior can be described by Avrami equations. Transmission electron microscopy (TEM) and X-ray diffraction (XRD) were performed to study the chemical and morphological characterization of nanoparticles. Some simplifying assumptions were employed for estimating the nucleation and growth rate of magnetite nanoparticles.
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Dissertations / Theses on the topic "Avrami equations"

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Novotný, Igor. "Roubování VTMOS na PHB." Master's thesis, Vysoké učení technické v Brně. Fakulta chemická, 2018. http://www.nusl.cz/ntk/nusl-376859.

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Diploma thesis deals with the grafting of vinyltrimethoxysilane (VTMOS) onto poly(3–hydroxybutyrate)PHB. Subsequent characterization of the amount of grafted VTMOS and changes in the thermal properties associated with the rate of crystallization. The theoretical part deals with mechanism and the influences of grafting. In the experimental part VTMOS was grafted onto PHB without subjecting VTMOS to hydrolysis and subsequent crosslinking. By differential scanning calorimetry (DSC) and Avrami equation, the effect of grafted silane group on pure was studied. The MVR was used to compare the rheological properties of initial PHB, grafted PHB and crosslinked PHB by siloxane linkages.
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See, Marianna B. (Marianna Blackman). "Constrained and unconstrained growth : applying the Avrami Equation to the production of materials." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/80902.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Materials Science and Engineering, 2013.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (p. 51-52).<br>Production of materials which are limited by the amount available on the earth's surface follow a growth curve similar to the Avrami equation which governs the process of nucleation and growth. This thesis will analyze whether the product curve follows not only the same path but the same steps as the Avrami model: initially slow growth during an introductory period, accelerated growth during market acceptance, and declining growth following market saturation. This thesis will use two materials, steel and aluminum, as a case study to further understand the applicability of the Avrami model to production forecasts of materials available in finite or limited amounts. The aim of this project was to provide producers of various materials a model to use to predict when it would be profitable to invest in and enter a market and when not to do so. The framework developed provides a well-behaved model for the initial two stages, introduction and market acceptance, and forecasts the transition point between those two stages. However, due to lack of current data as neither aluminum nor steel have reached market saturation, a fit for the final stage and a forecast for the transition from market acceptance to market saturation has not yet been determined.<br>by Marianna B. See.<br>S.B.
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Pattanayak, Pratik. "Correlation between Vogel Fulcher Tamman & Avramov Equation for Glass Viscosity." Thesis, 2009. http://ethesis.nitrkl.ac.in/1118/1/PRATIK_THESIS.docx.

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Among many equations the VFT and Avramov equations can fit the glass viscosity data ranging from 101 to 1015 poise. The VFT equation needs 3 empirical constants (fitting parameter) to fit the viscosity data over a wide range. Whereas, Avramov equation is based on entropy – temperature correlation. When fitting a particular viscosity data over a wide range of viscosity it has been observed that both equation fall over each other with minimum deviation. So it would be logical to find out some correlation from that characteristic. In the present work an attempt has been made to find the origin of VFT constants by help of Avramov equation. Viscosity data of SiO2 based glass system has been taken in to account to find some correlations.
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Books on the topic "Avrami equations"

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Cantor, Brian. The Equations of Materials. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851875.001.0001.

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This book describes some of the important equations of materials and the scientists who derived them. It is aimed at anyone interested in the manufacture, structure, properties and engineering application of materials such as metals, polymers, ceramics, semiconductors and composites. It is meant to be readable and enjoyable, a primer rather than a textbook, covering only a limited number of topics and not trying to be comprehensive. It is pitched at the level of a final year school student or a first year undergraduate who has been studying the physical sciences and is thinking of specialising into materials science and/or materials engineering, but it should also appeal to many other scientists at other stages of their career. It requires a working knowledge of school maths, mainly algebra and simple calculus, but nothing more complex. It is dedicated to a number of propositions, as follows: 1. The most important equations are often simple and easily explained; 2. The most important equations are often experimental, confirmed time and again; 3. The most important equations have been derived by remarkable scientists who lived interesting lives. Each chapter covers a single equation and materials subject. Each chapter is structured in three sections: first, a description of the equation itself; second, a short biography of the scientist after whom it is named; and third, a discussion of some of the ramifications and applications of the equation. The biographical sections intertwine the personal and professional life of the scientist with contemporary political and scientific developments. The topics included are: Bravais lattices and crystals; Bragg’s law and diffraction; the Gibbs phase rule and phases; Boltzmann’s equation and thermodynamics; the Arrhenius equation and reactions; the Gibbs-Thomson equation and surfaces; Fick’s laws and diffusion; the Scheil equation and solidification; the Avrami equation and phase transformations; Hooke’s law and elasticity; the Burgers vector and plasticity; Griffith’s equation and fracture; and the Fermi level and electrical properties.
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Book chapters on the topic "Avrami equations"

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Gooch, Jan W. "Avrami Equation." In Encyclopedic Dictionary of Polymers. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_931.

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Cantor, Brian. "The Avrami Equation." In The Equations of Materials. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851875.003.0009.

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When materials are heated or cooled, their structure often changes. This is called a phase transformation. Phase transformations are used extensively to modify and control the final microstructure and properties of a material during manufacturing into its final product form. The Avrami equation describes the sigmoidal (S-shaped) way in which the amount of a new phase evolves, initially accelerating as particles of the new phase nucleate and grow, and then decelerating as the old phase becomes progressively exhausted. This chapter explains the development of new phases by nucleation and growth, the mechanisms of precipitation, eutectoid and martensite reactions, and the use of time–temperature–transformation curves to understand and control transformation behaviour. The Avrami equation was derived independently in the mid-20th century by Melvin Avrami at Columbia University, Robert Mehl and his student W. Johnson at Carnegie Tech, and Andrei Kolmogorov at Moscow State University. Avrami was horrified by the development of the atomic bomb at the end of the Second World War and dropped out of society to work as a caretaker on Orcas Island off the West Coast of America, before changing his name and returning as a physicist some years later; Mehl is known as one of the father figures of metallurgical science in the United States; and Kolmogorov made important advances in fields such as trigonometry, probability, topology, turbulence and genetics.
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"Avrami equation." In Encyclopedic Dictionary of Polymers. Springer New York, 2006. http://dx.doi.org/10.1007/978-0-387-30160-0_900.

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"The Calculating Experiments for Metal/Carbon Nancomposites Synthesis in Polymeric Matrixes with the Application of Avrami Equations." In Nanostructures, Nanomaterials, and Nanotechnologies to Nanoindustry. Apple Academic Press, 2016. http://dx.doi.org/10.1201/b16956-18.

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"Thermodynamics of Microstructure Change." In Thermodynamics of Microstructures. ASM International, 2008. http://dx.doi.org/10.31399/asm.tb.tm.t52320259.

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Abstract This chapter provides a classification of the types of microstructural changes and transformations and then reviews each type. It presents the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation and explains the thermodynamics of eutectic solidification and eutectoid transformation. An appendix covers growth of eutectoid structure in carburized pearlite.
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Low, I. M., and W. K. Pang. "Decomposition Kinetics of MAX Phases in Extreme Environments." In MAX Phases and Ultra-High Temperature Ceramics for Extreme Environments. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-4066-5.ch002.

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MAX phases are remarkable materials but they become unstable at elevated temperatures and decompose into binary carbides or nitrides in inert atmospheres. The susceptibility of MAX phases to thermal dissociation at 1300-1550 °C in high vacuum has been studied using in-situ neutron diffraction. Above 1400 °C, MAX phases decomposed to binary carbide (e.g., TiCx) or binary nitride (e.g., TiNx), primarily through the sublimation of A-elements such as Al or Si, which results in a porous surface layer of MXx being formed Positive activation energies were determined for decomposed MAX phases with coarse pores but a negative activation energy when the pore size was less than 1.0 µm. The kinetics of isothermal phase decomposition at 1550 °C was modelled using a modified Avrami equation. An Avrami exponent (n) of &lt; 1.0 was determined, indicative of the highly restricted diffusion of Al or Si between the channels of M6X octahedra. The role of pore microstructures on the decomposition kinetics is discussed.
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Kotake, Shigeo, Yasuyuki Suzuki, and Masafumi Senoo. "Monte Carlo simulation of inhomogeneous nucleation and crystal growth by Johnson-Mehl-Avrami equation." In Advanced Materials '93. Elsevier, 1994. http://dx.doi.org/10.1016/b978-0-444-81993-2.50069-x.

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Conference papers on the topic "Avrami equations"

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DINÇER, M. S. "Evolution of microstructure during hot incremental disk rolling of a nickel-based super-alloy." In Material Forming. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902479-72.

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Abstract. In the aerospace industry, the turbine disk plays a crucial role. Controlling the average grain size during the hot forming of nickel-based superalloys such as Inconel 718 is critical for turbine disk production. Recrystallization is primarily responsible for evolution of microstructure during a hot forming process. In the current study, Finite Element Method (FEM) is employed to assess grain size evolution during an incremental disk rolling process. FEM simulations are used to obtain temperature, strain and strain rate distributions. Then, utilizing these deformation distributions, recrystallization and consequent average grain size distributions are calculated using Johnson-Mehl-Avrami-Kolmogorov (JMAK) equations. Simulations are conducted for different spindle rates of the workpiece. This process is sensitive to the temperature and meta-dynamic recrystallization. Results show that temperature increases with the spindle rate due to the inelastic heat generation. Also a higher grain size variation through thickness is obtained for the simulation with lower spindle rate since meta-dynamic recrystallization fraction is higher.
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You, Haoxing, Mei Yang, Yishu Zhang, and Richard D. Sisson. "Austempering and Bainitic Transformation Kinetics of AISI 52100." In HT2021. ASM International, 2021. http://dx.doi.org/10.31399/asm.cp.ht2021p0203.

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Abstract AISI 52100 is a high carbon alloy steel typically used in bearings. One hardening heat treatment method for AISI 52100 is austempering, in which the steel is heated to above austenitizing temperature, cooled to just above martensite starting (Ms) temperature in quench media (typically molten salt), held at that temperature until the transformation to bainite is completed and then cooled further to room temperature. Different austempering temperatures and holding times will develop different bainite percentages in the steel and result in different mechanical properties. In the present work, the bainitic transformation kinetics of AISI 52100 were investigated through experiments and simulation. Molten salt austempering trials of AISI 52100 were conducted at selected austempering temperatures and holding times. The austempered samples were characterized and the bainitic transformation kinetics were analyzed by Avrami equations using measured hardness data. The CHTE quench probe was used to measure the cooling curves in the molten salt from austenitizing temperature to the selected austempering temperatures. The heat transfer coefficient (HTC) was calculated with the measured cooling rates and used to calculate the bainitic transformation kinetics via DANTE software. The experimental results were compared with the calculated results and they had good agreement.
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Luo, Min, Chun Xu, Bing Zhou, Yan-hui Guo, and Rong-bin Li. "Static Recrystallization Behavior of a Nitrogen Controlled Z2CN19-10 Austenitic Stainless Steel." In ASME 2017 12th International Manufacturing Science and Engineering Conference collocated with the JSME/ASME 2017 6th International Conference on Materials and Processing. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/msec2017-2746.

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In order to increase the hot workability and provide proper hot forming parameters for nitrogen controlled Z2CN19-10 austenitic stainless steel, the static recrystallization behavior was investigated by double-pass hot compression tests in the temperature range of 950–1100°C, initial grain size of 72μm–152μm, and the strain rates of 0.01, 0.1, 1, and 5 s−1. The tests were conducted with inter-pass times varying between 1 and 100 s after achieving a pass strain of 0.05, 0.1, 0.15 and 0.2 in the first pass on a Gleeble-1500 thermo-mechanical simulator. The static recrystallization fraction has been predicted by the 2 % offset stress method and verified by metallographic observations. The metallographic results indicate the crystallized grains generate at the cross of the prior austenite grain boundary and grow up. Also the kinetics of static recrystallization behavior for Z2CN19-10 steel are proposed. Experimental results show that the volume fraction of static recrystallization increases with the increase of deformation temperature, strain rates, pass strain and interval time, while it decreases with the increase of initial grain size. According to the present experimental results, the activation energy (Q) and Avrami exponent (n) was determined as 199.02kJ/mol and 0.69. The established equations can give a reasonable estimate of the static recrystallization behavior for Z2CN19-10 steel.
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Dong, Hongbo, Xianlong Wang, and Ming Gao. "Calculation of Recrystallization Kinetics of Mn-Nb-Cu-B Microalloyed Low-Carbon Steel Based on Avrami Equation." In 2023 International Seminar on Computer Science and Engineering Technology (SCSET). IEEE, 2023. http://dx.doi.org/10.1109/scset58950.2023.00127.

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VÁZQUEZ, J., P. VILLARES, and R. JIMÉNEZ-GARAY. "INTEGRATION OF THE AVRAMI TRANSFORMATION EQUATION AND CALCULATION OF THE KINETIC PARAMETERS USING NON-ISOTHERMAL TECHNIQUES: APPLICATIONS TO PRACTICAL CASES." In Proceedings of the Fifth International Workshop on Non-Crystalline Solids. WORLD SCIENTIFIC, 1998. http://dx.doi.org/10.1142/9789814447225_0056.

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Buchner, Christoph, and Wilhelm Schneider. "Explosive Crystallization in Thin Amorphous Layers on Heat Conducting Substrates." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22187.

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The self-sustaining process of transformation from an amorphous state to the crystalline state is considered. The crystallizing layer, which is mounted on a substrate, is assumed to be very thin. Thus the energy balance for the layer reduces to the equation of one-dimensional heat diffusion with a source term due to the local liberation of latent heat and a heat loss term due to thermal contact with the substrate. The crystallization rate is determined by a rate equation based on the crystallization theory due to A.N. Kolmogorov and M. Avrami. Heat conduction in the substrate is described by introducing a continuous distribution of moving heat sources at the interface. The problem is solved numerically with a collocation method. The propagation speed of the crystallization wave is obtained as an eigenvalue. Dual solutions are found below a critical value of a non-dimensional heat-loss parameter, whereas no solution exists above that value.
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Wu, Yujie, Qiang Yu, and Sven K. Esche. "Static Recrystallization Modeling With a Cellular Automata Algorithm." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82840.

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This paper reports on one part of a research project supported by NSF, which aims at developing a multi-scale methodology for systematic microstructure prediction in thermo-mechanical processing of metals. Based on combining mesoscopic microstructure models with macroscopic process formulations, the methodology is expected to provide universally applicable and accurate microstructure prediction capabilities. Cellular Automata (CA) models have been widely used in scientific studies of various microstructural phenomena. This paper discusses the modeling of the static recrystallization phenomenon by employing a regular CA algorithm. The recrystallization processes of single-phase systems under different nucleation conditions are simulated followed by the recrystallization kinetics analysis for 200 × 200 two-dimensional lattice. The performed simulations of static recrystallization confirm that the recrystallized volume fractions are time dependent. Furthermore, the simulated microstructures validate the following Johnson-Mehl-Avrami-Kolmogorov (JMAK) model according to which the recrystallized volume fraction is a sigmoidal function of time, and their evolution matches the JMAK equation with the expected exponents.
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Koch, Felix, Meinhard Kuna, Peter Hübner, and Marco Enderlein. "Residual Stress Analysis of In-Service Welded Gas Pipelines." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-97585.

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Maintenance work and extension of gas pipelines have to be done mostly with the pipeline being in operation to ensure continuous network coverage. Therefore, in-service welding operations are inevitable for both situations. The present paper focuses on a circumferential fillet weld connecting a high-pressure gas pipeline with a T-fitting, which is suitable for stoppling and the construction of connection branches. Against the background of safety assessment and process optimization the welding procedure is investigated by means of experiment and simulation. The simulation is based on the finite element method and predicts the temperature field as well as the evolution of the microstructure and the residual stresses during welding and cooling. The heat input during welding is modeled using the double ellipsoid heat source by Goldak, which is adapted to multi-pass welding and implemented in the commercial software ABAQUS. The microstructure evolution is analyzed by a phase transformation model based on the Avrami equation. A subsequent stress analysis provides results regarding the residual stresses. The simulation is validated by welding experiments dealing with a three-pass fillet weld. The experimental and numerical results are presented and compared by means of macrosections and thermocouple measurements.
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Guo, Xiao, Kai Xu, Xiaochun Lv, Peiyin Chen, Bo Chen, and Shubin Huo. "Investigation on Solidification Behavior of Deposited Metal by GTAW With ERNiCrFe-13 Wire." In 2021 28th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/icone28-63770.

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Abstract ERNiCrFe-13 was developed based on ERNiCrFe-7A with Nb and Mo addition with the aim of further improving ductility dip cracking. In addition, solidification cracking susceptibility may increase against a wide solidification temperature range due to Nb and Mo segregation. In this study, the solidification behavior of the deposited metal via gas tungsten arc welding (GTAW) with an experimental ERNiCrFe-13 wire was investigated using JMatPro solidification calculations, differential scanning calorimetry (DSC) analysis, in situ observations by laser confocal scanning microscopy, scanning electron microscopy (SEM), and energy-dispersive X-ray spectroscopy (EDS). Both Nb and Mo exhibited segregation toward the liquid phase during solidification, while Fe showed opposite tendency according to the calculated partition coefficients k at the initial solidification stage. The k based on both the solidification calculation and EDS tests showed that Nb had a stronger segregation tendency than Mo. The solidification temperature range (STR) tested by DSC was significantly narrower than the predicted STR, which can be attributed to the overestimated segregation based on the Scheil model. The in-situ observation results showed that the relationship between the liquid phase area fraction f and temperature T followed the Avrami equation well. The solidification process included three stages: initial nucleation stage, rapid growing-up stage, and final solidification stage with rates of 0.015 s−1, 0.15 s−1, and 0.015 s−1, respectively.
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10

Ghosh, Suhash, and Chittaranjan Sahay. "Modeling Phase Transformation Kinetics and Their Effect on Hardness and Hardness Depth in Laser Hardening of Hypoeutectoid Steel." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50175.

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Much research has been done to model laser hardening phase transformation kinetics. In that research, assumptions are made about the austenization of the steel that does not translate into accurate hardness depth calculations. The purpose of this paper is to develop an analytical method to accurately model laser hardening phase transformation kinetics of hypoeutectoid steel, accounting for non-homogeneous austenization. The modeling is split into two sections. The first models the transient thermal analysis to obtain temperature time-histories for each point in the workpiece. The second models non-homogeneous austenization and utilizes continuous cooling curves to predict microstructure and hardness. Non-homogeneous austenization plays a significant role in the hardness and hardness depth in the steel. A finite element based three-dimensional thermal analysis in ANSYS is performed to obtain the temperature history on three steel workpieces for laser hardening process with no melting; AISI 1030, 1040 and 1045 steels. This is followed by the determination of microstructural changes due to ferrite and pearlite transformation to austenite during heating and the subsequent austenite to martensite and other diffusional transformations during cooling. Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation is used to track the phase transformations during heating, including the effects of non-homogenous austenitization. The solid state nodal phase transformations during cooling are monitored on the material’s digitized Continuous Cooling Transformation (CCT) curve through a user defined input file in ANSYS for all cooling rates within the Heat Affected Zone (HAZ). Material non-linearity is included in the model by including temperature dependent thermal properties for the material. The model predictions for hardness underneath the laser and the HAZ match well with the experimental results published in literature.
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