Analysis of soft impingement in nonisothermal precipitation

Abstract

The effects of soft impingement on precipitation are considered. A physically realistic analytical treatment of soft impingement has been developed for solid-state precipitation in a nonisothermal heating/cooling process following the basic assumptions (i.e., a two-stage transformation including site saturation of nucleation, isotropic growth and linear approximation for a concentration gradient in front of the precipitate/matrix interface). Furthermore, both one-and three-dimensional precipitations have been described using a compact expression which is analogous to Zener's model but with a temperaturedependent growth coefficient. A detailed description for the model parameters has been given for the model application. Good agreement with published experimental data, for example, the decomposition of austenite in a 0.038-0.30wt%Mn plain carbon steel, has been achieved.

Deduction of activation energy for diffusion by analyzing soft impingement in non-isothermal solid-state precipitation

“…1 Actually, a value of f at maximum transformation rate, f k , follows from d 2 f/ dt 2 = 0 and thus, f k = 1 À RT k 2 (df/dT) k /Q D , which is independent of F, but, analogous to the value of f z , is dependent of the initial condition of the alloy system such as x, etc. This will be studied in our further work [18]. presented in Fig.…”

“…Upon transformation in heating process, the soft impingement starts before the transformationrate maxima, which may be ascribed to the relative contributions from effects due to soft impingement and due to diffusion. Further study [18] is needed for a detailed explanation. Upon transformation in cooling process, only if the cooling rate is sufficiently small, the transformation rate maxima coincide with the initiating points of soft impingement; otherwise, the soft impingement starts after the transformation-rate maxima (Fig.…”

“…In Ref. [18], deduction of the activation energy for diffusion is shown by analyzing soft impingement in isothermal precipitation. In the present work, an analogous approach for non-isothermal precipitation will be derived.…”

“…Deduction of activation energy for diffusion upon non-isothermal cooling case Analogously, according to Eq. (18), the corresponding transformation rate at the initiating point of soft impingement is given as df dT…”

Deduction of activation energy for diffusion by analyzing soft impingement in isothermal solid-state precipitation

“…[20], the deduction of activation energy for diffusion is shown by analyzing soft impingement in non-isothermal precipitation, based on the treatment dealing with soft impingement in non-isothermal solid-state precipitation [21]. On this basis, an analogous approach for isothermal precipitation will be derived.…”