Mathematical model of influence of rapid induction heating on nucleation and growth of precipitates

Abstract

A mathematical model of the influence of rapid induction heating on the nucleation and growth of secondary phases in diffusion controlled processes has been developed. The total stress produced by the electromagnetic field and acting on the volume V of a specimen was derived and added to other external stresses applied to the system. Then, the total effective stress was introduced into mathematical equations of diffusion controlled nucleation and growth processes. In addition, the effect of rapid induction heating on the age hardening treatment of a selected cast nickel base superalloy, IN738LC, was investigated experimentally. For this purpose, two types of rapid aging with equal heating rates were applied: one treatment was induction aging and the other was salt bath aging. Microstructural characteristics of γ′ precipitates and hardening behaviour were studied by means of scanning electron microscopy (SEM), electron image analysis, transmission electron microscopy (TEM), and hardness testing. According to the results obtained, although the rates of heating in induction and salt bath aging were equal, the rates of nucleation and growth of γ′ precipitates in induction aging were much faster than those obtained in salt bath aging, especially in the first minutes of the aging process. Furthermore, the characteristics of γ′ precipitates with induction aging were more favorable than those with salt bath and normal aging. It was observed that the growth rate of γ′ in induction aging deviated considerably from the t1/3 growth law of the standard modified Lifshitz, Slyozov, and Wagner (MLSW) theory. The remarkable improvement of microstructural characteristics obtained with induction aging can be attributed to the existence of the external electromagnetic force produced by rapid induction heating.