Determination of the Temperature-Dependent Thermal Material Properties in the Cooling Process of Steel Plates

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.