Scalable, continuous variable, cellular automaton model for grain growth during homogenisation of vacuum arc remelted Inconel* 718

Abstract

A scalable, continuous variable, cellular automaton (CA) model for the quantitative simulation of normal grain growth is presented. The CA model is based on a discrete solution of the classical Turnbull rate equation for grain boundary motion on a mesoscopic scale. The domain is discretised using a regular cubic lattice considering the first and second nearest neighbourhoods. CA rules were usedto determine the state of each cellbased on the local driving force. The effects of both the boundary curvature and the misorientation of grains were incorporated. The driving force was used to determine the direction of the movement of each boundary cell, forming the basis of a continuous variable cell transition rule. The use of experimental grain boundary characteristics (e.g. energy and mobility) allows one to make predictions on industrially applicable spatial and temporal scales. The model was applied to quantitatively predict grain growth during the homogenisation heat treatment of vacuum arc remelted Inconel 718.