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Academic literature on the topic 'Modified Avrami approach'
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Journal articles on the topic "Modified Avrami approach"
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Luo, Hai Wen, Lian Zi An, and Hong Wei Ni. "A New Approach to Model Heterogonous Recrystallization Kinetics Based on the Natural Inhomogeneity of Deformation." Materials Science Forum 558-559 (October 2007): 1139–44. http://dx.doi.org/10.4028/www.scientific.net/msf.558-559.1139.
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The classical JMAK equation was modified by combination with distribution density of the rate parameter k, which was deduced from a normal distribution of local strain. The modified equation is able to calculate the JMAK plots and the average Avrami exponent to characterize the entire heterogeneous recrystallization process. This new extension can successfully describe the relevant experimental observations, such as a smaller exponent than the basic JMAK theory predicts, and a decreasing slope of JMAK plots with the proceeding recrystallization. Moreover, it reveals that the Avrami exponent observed experimentally should significantly decrease with the increasing standard deviation of local strain distribution. In addition, it has a great potential to explain why most of experimentally observed values of Avrami exponents are less than 2 and why the Avrami exponent is insensitive to temperature and deformation conditions when the real standard deviation of local strain distribution in deformed metals is known.
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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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Gao, Song, Kun Yan Sui, Zhi Ming Wu, Wen Wen Wu, and Yan Zhi Xia. "Functionalization of Multiwalled Carbon Nanotubes by Poly (Ethlylene Glycol) and Non-Isothermal Crystallization Kinetic Study." Materials Science Forum 688 (June 2011): 127–34. http://dx.doi.org/10.4028/www.scientific.net/msf.688.127.
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Multi-walled carbon nanotubes (MWNT) were successfully chemically modified (MWNT-COOH) and reacted with polyethylene glycol (PEG) to prepare nanocomposites. As- prepared kinds of functionalized MWNT (MWNT-g-PEG) were characterized with FTIR, TGA and TEM. Nonisothermal crystallization kinetics of MWNT-g-PEG composites was investigated by differential scanning calorimeter (DSC). The kinetics was analyzed using the Ozawa and Avrami equation modified by Jeziorny. The results showed that the Ozawa approach failed to describe the crystallization behavior of nanocomposites, whereas the modified Avrami analysis could explain the behavior of MWNT-g-PEG nanocomposite only. It is observed that the presence of MWNT hindered the mobility of PEG chains and decreased the overall crystallization rate. It was found that the crystallization behavior of MWNT-g-PEG nanocomposite was strongly affected by the incorporation of MWNT. The data for the nonisothermal crystallization could be analyzed properly by the Avrami equation modified by Jeziorny. The results showed that the presence of MWNT decreased the overall nonisothermal crystallization rate of the PEG chains which were grafted onto the MWNT due to MWNT might act as physical hindrances retarding the mobility of PEG chains and decreased the crystallinity.
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Vyazovkin, Sergey, and Andrey Galukhin. "Problems with Applying the Ozawa–Avrami Crystallization Model to Non-Isothermal Crosslinking Polymerization." Polymers 14, no. 4 (2022): 693. http://dx.doi.org/10.3390/polym14040693.
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Ozawa has modified the Avrami model to treat non-isothermal crystallization kinetics. The resulting Ozawa–Avrami model yields the Avrami index (n) and heating/cooling function (χ(T)). There has been a number of recent applications of the Ozawa–Avrami model to non-isothermal crosslinking polymerization (curing) kinetics that have determined n and have used χ(T) in place of the rate constant (k(T)) in the Arrhenius equation to evaluate the activation energy (E) and the preexponential factor (A). We analyze this approach mathematically as well as by using simulated and experimental data, highlighting the following problems. First, the approach is limited to the processes that obey the Avrami model. In cases of autocatalytic or decelerating kinetics, commonly encountered in crosslinking polymerizations, n reveals a systematic dependence on temperature. Second, χ(T) has a more complex temperature dependence than k(T) and thus cannot produce exact values of E and A via the Arrhenius equation. The respective deviations can reach tens or even hundreds of percent but are diminished dramatically using the heating/cooling function in the form [χ(T)]1/n. Third, without this transformation, the Arrhenius plots may demonstrate breakpoints that leads to questionable interpretations. Overall, the application of the Ozawa–Avrami model to crosslinking polymerizations appears too problematic to be justified, especially considering the existence of well-known alternative kinetic techniques that are flexible, accurate, and computationally simple.
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Harshad, R. Patil, A. Parikh Parimal, and V. P. Murthy Z. "Study on nucleation and crystallization kinetics of polypropylene using bisphenol-A disodium as nucleating agent." Journal of Indian Chemical Society Vol. 88, Nov 2011 (2011): 1751–58. https://doi.org/10.5281/zenodo.5791768.
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Department of Chemical Engineering, Sardar Vallabhbhai National Institute of Technology, Surat-395 007, Gujarat, India <em>E-mail</em>: zvpm2000@yahoo.com, zvpm@ched.svnit.ac.in Fax: 91-261-2227334, 2228394 Reliance Industries Limited, Hazira Manufacturing Division, Surat-394 510, Gujarat, India <em>Manuscript received 29 December 2010, revised 29 March 2011, accepted 30 March 2011</em> Salt of bisphenol-A is explored for polypropylene nucleation and crystallization. Synthesized compound, sodium salt of bisphenoi-A (SBPA), showed nucleation efficiency as indicated by 2.6 and 6.4°c improvement in crystallization temperature (0.4 and 1 wt% loading of SBPA, respectively) of polypropylene (PP) by differential scanning calorimetry (DSC), lower spherulite size and increase of transmittance of PP film by UV-Visible spectrophotometer. The nucleation performance results of SBPA were compared with PP nucleated by commercial nucleating agent, sodium benzoate (SB), which has single aromatic ring structure. Wide angle X-ray diffraction (WAXD) and crystallite study of pp nucleated by SBPA and SB revealed possible explanation for correlating structure of nucleating agent with pp nucleation and crystallization. The nucleation effect of SBPA for PP was further substantiated by non-isothermal crystallization study by modified Avrami approach and was compared with PP without nucleating agent. SBPA was evaluated through Fourier transform infrared (FTIR) spectroscopy and energy dispersive X-ray (EDX) analysis for confirmation.
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Xu, Guoyong, and Qingren Zhu. "Studies on Crystallization and Melting Behaviors of UHMWPE/ MWNTs Nanocomposites with Reduced Chain Entanglements." Polymers and Polymer Composites 25, no. 6 (2017): 495–506. http://dx.doi.org/10.1177/096739111702500609.
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The nonisothermal crystallization and melting behavior of UHMWPE (ultra-high molecular weight polyethylene)/ MWNTs (multi-walled carbon nanotubes) nanocomposites with reduced chain entanglements was studied using differential scanning calorimetry (DSC) technique. The Ozawa approach failed to describe the crystallization behavior of nanocomposites, whereas the modified Avrami analysis could explain the behavior of UHMWPE/ MWNTs nanocomposite to some extent. A novel kinetic model by Liu et al. was able to satisfactorily describe the crystallization behavior of UHMWPE/MWNTs nanocomposites. The Dobreva and Kissinger methods failed to calculate the nucleation activity and activation energy, respectively, for the UHMWPE/MWNTs systems. Also the Vyazovkin model-free kinetic method was applied to nonisothermal crystallization to evaluate the dependence of the effective activation energy on conversion and temperature.
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Churyumov, Alexander Yu, Svetlana V. Medvedeva, Olga I. Mamzurina, Alena A. Kazakova, and Tatiana A. Churyumova. "United Approach to Modelling of the Hot Deformation Behavior, Fracture, and Microstructure Evolution of Austenitic Stainless AISI 316Ti Steel." Applied Sciences 11, no. 7 (2021): 3204. http://dx.doi.org/10.3390/app11073204.
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Hot deformation is one of the main technological stages of products made from metallic materials. It is strictly required to decrease the costs of developing optimized technologies at this stage without a significant decrease in the products’ quality. The present investigation offers an algorithm to unite three different models to predict the hot deformation behavior, fracture, and microstructure evolution. The hot compression and tension tests of the AISI 316Ti steel were conducted using the thermomechanical simulator Gleeble 3800 for the models’ construction. The strain-compensated constitutive model and the Johnson–Mehl–Avrami–Kolmogorov (JMAK)-type model of the grain structure evolution show a satisfactory accuracy of 4.38% and 6.9%, respectively. The critical values of the modified Rice and Tracy fracture criteria were determined using the experimental values of the relative cross-section reduction and finite element calculation of the stress triaxiality. The developed models were approved for the stainless AISI 316Ti steel by the hot torsion with tension test.
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Savelyev, Evgeniy, Andrey Akhmatkhanov, Mikhail Kosobokov, et al. "Abnormal Domain Growth during Polarization Reversal in Lithium Niobate Crystal Modified by Proton Exchange." Crystals 13, no. 1 (2023): 72. http://dx.doi.org/10.3390/cryst13010072.
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The results of an experimental study of the abnormal domain structure kinetics in lithium niobate single crystals with a surface layer modified by soft proton exchange are presented. Domain switching in a wide field range allowed two qualitatively different types of domain structure evolution to be revealed: (1) the traditional growth of hexagonal domains in fields higher than 21.5 kV/mm and (2) the abnormal growth of stripe domains oriented along the Y crystallographic directions in the field range from 3.8 to 21.5 kV/mm. The stripe domains had a width up to 4 µm and depth up to 30 µm. It was shown that the time dependence of the total length of stripe domains could be analyzed in terms of the modified Kolmogorov–Avrami approach, taking into account the transition from the one-dimensional β-model to the one-dimensional α-model. The possibility of the controllable creation of a quasi-periodic structure of stripe domains with an average period of 5 µm by a two-stage polarization switching process was demonstrated. The formation and growth of stripe domains were considered in terms of the kinetic approach to the evolution of the domain structure as a result of the domain walls’ motion under inefficient screening conditions caused by the presence of a modified surface layer. The abnormally low threshold fields were attributed to a presence of a “built-in” field facilitating switching, created by a composition gradient induced by soft proton exchange.
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Sethy, Sucharita, Saroj Kumar Samantaray, and Bhabani K. Satapathy. "Dynamic crystallization behavior of PA-12/PP-MWCNT nanocomposites: non-isothermal kinetics approach." Journal of Polymer Engineering 42, no. 2 (2021): 87–99. http://dx.doi.org/10.1515/polyeng-2021-0195.
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Abstract The effect of multi-walled carbon nanotubes (MWCNT) loading on the crystallization behavior of matrix polyamide 12 (PA-12), in PA-12/polypropylene-MWCNT (PP-MWCNT)-based nanocomposites were analyzed for their non-isothermal crystallization behavior at various cooling rates of 2.5–20 °C/min in differential scanning calorimetry (DSC). Several kinetic models such as Jeziorny (modified-Avrami), Mo and Tobin models were employed to analyze the crystallization behavioral trend with respect to time and temperature of the nanocomposites. The crystallization rate increased half-time of crystallization with MWCNT content as estimated from the Jeziorny theory. The linear agreement between Jeziorny model and experimental relative crystallinity outperforms the Tobin analysis where the coefficient of linear regression was found to be considerably trailing behind and off the satisfactory mark. The Mo model accounts for the percentage crystallinity and thereby successfully explained the crystallization behavior of PA-12 where the kinetic parameters increased with crystallinity indicating higher cooling rate for higher crystallinity. The MWCNT induced crystallization (nucleation activity) values were close to zero irrespective of MWCNT loading which reiterates the enhanced crystallization (rate) of PA-12 in the nanocomposites. Estimations based on Friedman approach showed inter-relationship between activation energy and crystallinity where the later was found to be governed by major (matrix) PA-12 phase.
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Lee, Jong K. "Understanding Dynamic Recrystallization Behavior through a Delay Differential Equation Approach." Materials Science Forum 558-559 (October 2007): 441–48. http://dx.doi.org/10.4028/www.scientific.net/msf.558-559.441.
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During hot working, deformation of metals such as copper or austenitic steels involves features of both diffusional flow and dislocation motion. As such, the true stress-true strain relationship depends on the strain rate. At low strain rates (or high temperatures), the stress-strain curve displays an oscillatory behavior with multiple peaks. As the strain rate increases (or as the temperature is reduced), the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value. It is understood that dynamic recovery is responsible for the stress-strain behavior with zero or a single peak, whereas dynamic recrystallization causes the oscillatory nature. In the past, most predictive models are based on either modified Johnson-Mehl-Avrami kinetic equations or probabilistic approaches. In this work, a delay differential equation is utilized for modeling such a stress-strain behavior. The approach takes into account for a delay time due to diffusion, which is expressed as the critical strain for nucleation for recrystallization. The solution shows that the oscillatory nature depends on the ratio of the critical strain for nucleation to the critical strain for completion for recrystallization. As the strain ratio increases, the stress-strain curve changes from a monotonic rise to a single peak, then to a multiple peak behavior. The model also predicts transient flow curves resulting from strain rate changes.
Conference papers on the topic "Modified Avrami approach"
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Waryoba, D. R., and P. N. Kalu. "Quantification of Recrystallization Kinetics in Heavily Drawn OFHC Copper Wires by Microhardness Technique." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42251.
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Mechanical properties of materials are inherently dependent on the microstructures that evolve during processing. The microstruture of heavily drawn and annealed OFHC copper is inhomogeneous, and as such it is difficult to assess its recrystallization kinetics by conventional methods. In this article, restoration kinetics of static recrystallization of heavily drawn oxygen free high conducting (OFHC) copper wires has been investigated by microhardness technique. The investigation was carried out on two cold drawn wires deformed to a true strain of 2.31 and 3.10 and annealed at 250°C for annealing times ranging from 10 s to 1 hr. The physical phenomena during annealing were characterized and analyzed using optical microscopy and measurement of microhardness. A unified approach, through the use of microhardness data, for the analysis of the restoration kinetics of recovery, recrystallization, and grain growth has been proposed. In this approach, a JMAK (Johnson-Mehl-Avrami-Kolmogrov) model was expressed in terms of microhardness data, and the results showed that the modified model linked the different restoration kinetics and provided the critical time for the transition from recovery to recrystallization, and to grain growth. The model compared favorably with conventional models, which treat the different restoration kinetics separately. Exponents of about 0.4 for recovery, 4.0 for recrystallization, and 0.5 for grain growth, were obtained. The results also showed that the JMAK exponent, n, is of the same order of magnitude as the grain growth exponent, 1/p.