Simulation of Inhomogeneous Materials Evolution in Hot Rolling Using a Layer Model

Abstract

A fast simulation of the inhomogeneous materials evolution during the deformation steps and its effect on subsequent processes is demanded for the development of new technologies for materials with a homogeneous microstructure. In the paper a layer model for flat hot and cold rolling is presented. A deepened understanding of the influence of inhomogeneities in material state and material flow on the whole process can be reached due to the introduction of a new computational concept for variable layer thickness distributions in the layer model. The concept will be explained and the additional information obtained concerning the influence of shear, local residual stresses as well as inhomogeneous stress and strain states in the roll gap on the microstructure evolution will be presented and discussed.

Fast Numerical Simulation of Symmetric Flat Rolling Processes for Inhomogeneous Materials Using a Layer Model − Part I: Basic Theory

“…In addition, in slab theory there is a need for an additional semi‐empirical equation, which describes the thickness variation of each individual layer during the deformation process. For this purpose, the model of Zhang for two layers was modified for an application in NS‐layer configurations with arbitrary hardness and thickness distributions . The layer thickness model depends on ratios of local yield stresses of each layer, friction, layer thickness ratio, as well as the strain history of the individual layer.…”

“…This layer thickness model of Equation was first rewritten as a differential equation . From several numerical investigation it was found, that this differential form shows a higher numerical stability, even for a larger number of layers NS.…”

“…For multi‐pass hot rolling additionally to the flow stress model, a model representing the softening kinetics, precipitation, and grain size development of the material during deformation and the interpass time has to be used . For a fast computation of the whole roll passes model approaches based on JMAK − theory are preferred …”

“…For this purpose, the model of Zhang for two layers [14] was modified for an application in NSlayer configurations with arbitrary hardness and thickness distributions. [15,16] The layer thickness model depends on ratios of local yield stresses of each layer, friction, layer thickness ratio, as well as the strain history of the individual layer.…”

“…The mechanical properties across the thickness are calculated based on the description of the material flow and the flow curves of the material. Due to the assumptions and simplifications made, a stiff set of first-order differential equations has to be solved, [15] which strongly depends on several internal parameters especially the individual position of the neutral line x Ni à for each layer. In general, a numerical solution has to be found by imposing an iteration for finding the neutral line position x Ni à .…”