Modelling of non-isothermal transformations in alloys containing a particle distribution Original Research Article

A framework for modelling coupled nucleation, growth and coarsening in diluted alloys is presented, based on the method of finite differences. According to the assumptions, the particle distribution is divided into a series of discrete size classes, each represented by a control volume. By applying a standard procedure for discretization of the governing evolution equation, the flux of particles in and out of the control volumes can be calculated at each time step during thermal cycling. The essential features of the model are illustrated in various numerical examples and case studies, where the memory of a past process step is likely to have an effect on the overall transformation behaviour. These include simulation of up-quenching and linear heating of age hardening Al–Mg–Si alloys under idealized conditions, assuming spherical particles with uniform thermodynamic properties.