Optimization of the johnson-mehl-avarami equation parameters for <Emphasis Type="Italic">α</Emphasis>-ferrite to <Emphasis Type="Italic">γ</Emphasis>-austenite transformation in steel welds using a genetic algorithm

A nonisothermal Johnson-Mehl-Avarami (JMA) equation with optimized JMA parameters is proposed to represent the kinetics of transformation of α-ferrite to γ-austenite during heating of 1005 steel. The procedure used to estimate the JMA parameters involved a combination of numerical heat-transfer and fluid-flow calculations, the JMA equation for nucleation and growth for nonisothermal systems, and a genetic algorithm (GA) based optimization tool that used a limited volume of experimental kinetic data. The experimental data used in the calculations consisted of phase fraction of γ-austenite measured at several different monitoring locations in the heat-affected zone (HAZ) of a gas tungsten arc (GTA) weld in 1005 steel. These data were obtained by an in-situ spatially resolved X-ray diffraction (SRXRD) technique using synchrotron radiation during welding. The thermal cycles necessary for the calculations were determined for each monitoring location from a well-tested three-dimensional heat-transfer and fluid-flow model. A parent centric recombination (PCX) based generalized generation gap (G3) GA was used to obtain the optimized values of the JMA parameters, i.e., the activation energy, pre-exponential factor, and exponent in the nonisothermal JMA equation. The GA based determination of all three JMA equation parameters resulted in better agreement between the calculated and the experimentally determined austenite phase fractions than was previously achieved.