Abstract
Accelerated cooling (ACC) is a key technology in producing thermomechanically controlled processed (TMCP) steel plates. In a TMCP process, hot plates are subjected to a strong cooling resulting in a complex microstructure leading to increased strength and fracture toughness. The microstructure, residual stresses, and flatness deformations are strongly affected by the temperature evolution during the cooling process. Therefore, the full control (quantification) of the temperature evolution is essential regarding plate design and processing. It can only be achieved by a thermophysical characterization of the material and the cooling system. In this paper, the focus is on the thermophysical characterization of the material properties which govern the heat conduction behavior inside of the plates. Mathematically, this work considers a specific inverse heat conduction problem (IHCP) utilizing inner temperature measurements. The temperature evolution of a heated steel plate passing through the cooling device is modeled by a 1D nonlinear partial differential equation with temperature-dependent material parameters which describe the characteristics of the underlying material. Usually, the material parameters considered in IHCPs are often defined as functions of the space and/or time variables only. Since the measured data (the effect) and the unknown material properties (the cause) depend on temperature, the cause-to-effect relationship cannot be decoupled. Hence, the parameter-to-solution operator can only be defined implicitly. By proposing a parametrization approach via piecewise interpolation, this problem can be resolved. Lastly, using simulated measurement data, the presentation of the numerical procedure shows the ability to identify the material parameters (up to some canonical ambiguity) without any a priori information.
Highlights
Accelerated cooling (ACC) is a key technology in producing thermomechanically controlled processed (TMCP) steel plates
In a TMCP process, hot plates are subjected to a strong cooling resulting in a complex microstructure leading to increased strength and fracture toughness. e microstructure, residual stresses, and flatness deformations are strongly affected by the temperature evolution during the cooling process. erefore, the full control of the temperature evolution is essential regarding plate design and processing
This work considers a specific inverse heat conduction problem (IHCP) utilizing inner temperature measurements. e temperature evolution of a heated steel plate passing through the cooling device is modeled by a 1D nonlinear partial differential equation with temperature-dependent material parameters which describe the characteristics of the underlying material
Summary
This paper is motivated in the modeling of a MULPIC (MULti-Purpose Interrupted Cooling, cf. [21, 22]) laminar cooling process for cooling low-alloy heavy plates (C-content about 0.10%C) with typical start and end cooling temperatures between 750 and 850°C and 400 and 550°C respectively. In order to gather the main heat conduction information, measured temperatures at different depths with respect to the thickness of the heavy plate are needed. By applying cooling water evenly on top (z > L) and bottom surface (z < 0) of the heavy plate, one can assume that, for some fixed depth 0 < z < L, the temperatures are equal with respect to width at any time. E exact dependence of the temperature on space and time is highly affected by the material parameters In the following, these material parameters will be determined as a solution of an inverse heat conduction problem, where the measured temperatures ut and ub are used for the Dirichlet boundary conditions of the PDE model. These material parameters will be determined as a solution of an inverse heat conduction problem, where the measured temperatures ut and ub are used for the Dirichlet boundary conditions of the PDE model. e measured core temperature uc is left to be the data, see Section 4 and 5
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