Transformation kinetics of alloys under non-isothermal conditions

TL;DR

This paper develops a differential equation model to describe the kinetics of solid-to-solid phase transformations in alloys under non-isothermal conditions, incorporating thermal history and phase equilibrium considerations.

Contribution

It introduces a novel differential equation approach that accounts for phase equilibrium, relaxation times, and complex thermal paths in modeling alloy transformation kinetics.

Findings

Model accurately predicts phase transformation under heating and cooling.

Incorporates both additive and non-additive transformation processes.

Uses path integral concept to consider all thermal histories.

Abstract

The overall solid-to-solid phase transformation kinetics under non-isothermal conditions has been modeled by means of a differential equation method. The method requires provisions for expressions of the fraction of the transformed phase in equilibrium condition and the relaxation time for transition as functions of temperature. The thermal history is an input to the model. We have used the method to calculate the time/temperature variation of the volume fraction of the favored phase in the alpha-to-beta transition in a zirconium alloy under heating and cooling, in agreement with experimental results. We also present a formulation that accounts for both additive and non-additive phase transformation processes. Moreover, a method based on the concept of path integral, which considers all the possible paths in thermal histories to reach the final state, is suggested.