2012
DOI: 10.2355/isijinternational.52.1661
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An Analytical Model for the Kinetics of Strain-induced Precipitation in Titanium Micro-alloyed Steels

Abstract: This paper presents an analytical model to describe the precipitation kinetics during isothermal holding following high temperature deformation in Ti micro-alloyed steels. This model was based on the classical nucleation and growth theory (CNGT) and Avrami equation. Using this model, the precipitation-timetemperature (PTT) diagrams for the kinetics of precipitation were easily obtained, and results show a good agreement between the experimental observation and the predictions of the model in terms of the chara… Show more

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Cited by 26 publications
(10 citation statements)
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“…The activation energy of atomic diffusion along the dislocation pipe has not been precisely determined, and it is always assumed to be two‐thirds or 0.7–0.8 times of bulk diffusion activation energy. In the present model it is assumed that the nucleation is controlled by bulk diffusion and coarsening is controlled by the effective diffusion coefficient including dislocation diffusion effect .…”
Section: Calculation Results and Discussionmentioning
confidence: 99%
“…The activation energy of atomic diffusion along the dislocation pipe has not been precisely determined, and it is always assumed to be two‐thirds or 0.7–0.8 times of bulk diffusion activation energy. In the present model it is assumed that the nucleation is controlled by bulk diffusion and coarsening is controlled by the effective diffusion coefficient including dislocation diffusion effect .…”
Section: Calculation Results and Discussionmentioning
confidence: 99%
“…Similar to recrystallization, the strain induced precipitation occurring mostly during the time interval of the plateau can be supposed to obey Avrami's law, and the precipitated fraction ( X p ) can be expressed as: Xnormalp=1expln 0.95tt0.05n …”
Section: Resultsmentioning
confidence: 99%
“…22) A larger solubility product of VC in high Mn steel can result in a lower supersaturation degree of VC precipitation, which further leads to a smaller thermodynamic driving force for VC precipitation and a slower precipitation rate in comparison to low Mn steel. According to Yong's theory, 38,39) the relative precipitation-temperature-time (PTT) diagram for VC precipitation can be calculated by the following equation: where t 0.05da that corresponds to the fraction precipitated 5% is defined as the start time of precipitation, t 0da is an almost temperature independent parameter, d d * is the critical diameter of nucleus, ΔG * is the critical nucleation energy, Q is the activation energy for V atom in bulk, β is a parameter introduced in the model, k is the Boltzmann constant and T is the absolute temperature. The detailed description for this model and the parameters used for calculation can be referred to the literature.…”
Section: Vc Precipitation During Aging Treatment After Hot Rollingmentioning
confidence: 99%