BibTeX
@ARTICLE{
         Bambach2015Oio,
       title = "On instabilities of force and grain size predictions in the simulation of multi-pass
         hot rolling processes",
       journal = "Journal of Materials Processing Technology",
       pages = "95--113",
       year = "2015",
       doi = "10.1016/j.jmatprotec.2014.07.018",
       url = "http://www.sciencedirect.com/science/article/pii/S0924013614002775",
       author = "M. Bambach and S. Seuren",
       keywords = "Stability",
       abstract = "In multi-pass rolling processes such as plate rolling, accurate predictions of roll
         force and torque over all roll passes are desired, so that the pre-calculated roll pass schedule can
         be put into practice without exceeding the limits of the roll stand. In this context, the grain size
         has two roles; the final grain size determines the product properties, and the evolution of grain
         size influences the force predictions. Since the grain size predicted after each roll pass enters
         the recrystallization kinetics and grain size evolution equations of the subsequent pass, a
         feed-back loop for the grain size calculation is created, which may become unstable so that the
         computed roll force and grain size become very sensitive to small variations in the input
         parameters. Although models for the evolution of grain size in multi-stage hot rolling have been
         applied in the industry for decades, their mathematical stability has not been given much attention,
         which poses difficulties for force and grain size predictions in cases subject to partial
         recrystallization. In this paper, the stability of a common semi-empirical model for static
         recrystallization and grain growth is investigated. The conditions under which instabilities occur
         are analyzed both for an industrial plate rolling pass schedule and for idealized load cycles. It is
         shown that complete recrystallization between roll passes leads to a stable grain size evolution,
         and that some states of partial recrystallization are unstable and hence problematic for force and
         grain size predictions. Instabilities in force and grain size predictions of an industrial pass
         schedules are analyzed by computing sensitivities using automatic differentiation of the model,
         showing that large amplification factors may occur if the states of partial recrystallization are
         treated by average strains and grain sizes. The instabilities are an inherent property of the
         closed-form equations for microstructure evolution for some states of partial recrystallization.
         However, the side effects of the instabilities can be reduced if the microstructure is not
         represented by average values of grain size and accumulated strain but by substructures generated by
         partial recrystallization. This way, the accuracy of roll force predictions can be considerably
         improved.",
       volume = "216",
       ad_area = "Metal Forming",
       ad_tools = "ADiMat"
}