Application of Kolmogorov–Johnson–Mehl–Avrami equations to non-isothermal conditions

A temperature domain form of the standard Kolmogorov–Johnson–Mehl–Avrami (KJMA) equation is presented which can be used simulate phenomena such as phase transformation and recrystallization kinetics under non-isothermal conditions. This form of the KJMA equation relies on a parameterized temperature–time history based on either a quadratic polynomial or shape preserving quadratic spline, and can be solved using a Gauss–Legendre quadrature scheme with low computational cost and algorithmic complexity. Sample calculations are included for the case of non-isothermal static recrystallization in a hot deformed C–Nb steel, and comparison is made with results obtained by conventional time domain schemes.