Analytical model of pass-by-pass strain in rod (or bar) rolling and its applications to prediction of austenite grain size

Rod rolling is a process where the deformation state of the workpiece between the work rolls is quite different from the strip rolling process. However, in most microstructure evolution models, the simple area strains (natural logarithm of the area reduction ratio) multiplied by a constant have been used to compute pass-by-pass evolution of austenite grain size (AGS) in rod (or bar) rolling, without any verification. The strains at a given pass play a crucial role in determining the recrystallization behavior (static or dynamic). In this study, an analytical model that calculates the pass-by-pass strain and strain rate in rod rolling has been developed and verified by conducting four-pass (oval–round) bar and plate rolling experiments. Numerical simulations have then been carried out for the four-pass rolling sequence using the area strain model and the new analytical model, focusing on the effect of the method for calculating the strain on the recrystallization behavior and evolution of AGS. The AGS predicted was compared with those obtained from hot torsion tests. It is shown that the analytical model developed in this study is more appropriate in the analysis of bar (or rod) rolling. It was found that the recrystallization behavior and evolution of AGS during this process were influenced significantly by the calculation method for the deformation parameters (strain and strain rate). The pass-by-pass strain obtained from the simple area strain model is inadequate to be used as an input to the equations for recrystallization and AGS evolution under these rolling conditions.