Modelling of precipitation reactions in industrial processing

The present investigation is concerned with modelling of diffusion-controlled precipitation reactions in industrial processing, with particular emphasis on heat treatment. In the first part of the paper the components of the model are outlined and constitutive equations presented which allow the fraction transformed to be calculated as a function of time and temperature. The model uses a combination of chemical thermodynamics and kinetic theory to describe the microstructure evolution, with the particular feature of writing the Avrami equation in a differential form. In general, the solution of the differential equation requires stepwise integration in temperature-time space over a predetermined thermal cycle, but the mathematical treatment can largely be simplified if the additivity condition pertaining to an isokinetic reaction is satisfied. The theory is thus generic in the sense that it can be adopted to a wide spectrum of materials and heat treatment conditions, ranging from low and high alloy steels to aluminium alloys. In the second part of the paper this formalism has been applied to describe the quench sensitivity of AA6082 extrusions. The process model takes into account the thermal history of the base material and allows calculation of the peak strength following artificial ageing for a wide range of cooling conditions. The results show that the peak strength is both a function of the alloy composition, the homogenizing conditions and the cooling rate through the critical temperature range for beta'-Mg2Si precipitation, in agreement with general experience. It is concluded that the existing theoretical framework is sufficiently comprehensive to serve as a tool for alloy design and optimization of cooling schedules for AlMgSi extrusions and an illustration of this is given towards the end of the paper. Copyright (C) 1996 Acta Metallurgica Inc.