Extension of the Freiberg Layer Model by Means of Elastic–Plastic Material Behavior

Abstract

For development of new materials and improvement of material properties today simulation of the production processes is essential. The understanding of the processes' mechanics and thermodynamics give the ability of tuning the process toward property improvement and efficiency. Flat rolling is one of the main processes used for production of flat metal semiproducts such as sheets, strips, and plates. In simulation of flat rolling today, two main approaches are used. The first is the elementary theory of plasticity, also known as strip or slab method, which was the first theoretical approach to describe the conditions within the roll gap. The second one is the finite element method, which offers a general approach for complex problems.The elementary theory was established by von Kármán. [1] Well-known contributors are Ford et al., [2][3][4] Orowan, [5] and Alexander. [6] In recent years, only few new contributions to this topic were published, for example, Kim et al., [7] Schmidtchen and Kawalla, [8] and Freshwater. [9,10] This approach's main benefit is the fast computation speed due to 1D differential equation formulation.The finite element theory is actively developed since the 1980s, for example, by Hwu and Lenard, [11] Jamal et al., [12] Jiang and Tieu, [13] Rout et al., [14] and Kainz et al. [15] . It provides a general approach for complex problems in two or three dimensions and offers the high accuracy of the simulation results. The main disadvantage is the high computational effort in solving the equation systems, increasing rapidly with nonlinearity of the base equations and resolution of the problem space. Therefore, this method has grown along with the development of high-performance computer systems in the past decades. However, fast methods are needed for use in control systems or production scheduling. Some authors try to combine the slab method with partial finite element solutions to achieve a decrease in computation time, for example, Kim et al. [7] . Another approach was shown by Schmidtchen and Kawalla [8] in extending the elementary theory by dividing the strip element into a number of discrete layers. This turns the 1D resolution of the elementary theory into a 2D one. Nevertheless, this model only requires 1D differential equation solving, which can be done fast and easy with common numerical methods. Due to this 1D formulation, it can be easily coupled with microstructure and precipitation models. The model is currently used in industry for online-simulation and controlling of direct input steel plants, including microstructure and precipitation simulation. Due to the layering, it is suitable for inhomogeneity determined processes, such as block rolling and direct input, were conventional slab method fails. However, it is only able to describe the layers as in plastic or rigid state. This work has the aim to extend it by elastic-plastic material behavior. The influence of the elastic behavior should be investigated in comparison with the rigid-plastic layer model as well as to FEM simulatio...

Extension of the Freiberg Layer Model by Means of Solidification for Roll Casting

“…This approach is similar to the model described in Schmidtchen and Kawalla, [ 8 ] Schmidtchen, [ 43 ] and Weiner, Schmidtchen, and Prahl. [ 40 ] The changes to the model there are as follows: 1) As viscosities of the melt are typically low, the heat generation due to friction can be neglected; 2) The term of heat generation by deformation is not applicable here and removed; 3) A term describing the solidification heat is included.…”

“…This is one main benefit of the current model in comparison to former approaches, where the solid region is modeled by viscose material laws too. Here, for the solid region, the elastic–plastic program from the authors’ previous work in Weiner, Schmidtchen, and Prahl [ 40 ] was plugged in. To make the transition possible, two transition conditions must be fulfilled by both model parts: [label=()].…”

“…In the classic elementary theory of rolling, is the point, where the velocities of the rolling material and the roll surfaces are equal. See Weiner, Schmidtchen, and Prahl [ 40 ] for further information. is heavily influenced by the position of the point of full solidification .…”

Integrated Process Simulation of Non-Oriented Electrical Steel

“…Several a-priori unknown parameters are included in the layer model. Consequently, a complex iteration structure is needed as described in [30].…”

“…By an extrapolation of the three magnetization curves used to parameterize the model and the elliptical approach, the magnetization behavior up to full saturation can be described in the entire sheet plane. In Figure 19b, three exemplary magnetization curves are displayed, which are modeled with Equation (30). The modeled as well as the measured behavior are displayed.…”