Calibration of specific heat capacity and thermal conductivity for isotropic and anisotropic materials using full-field data

Abstract

Identified thermal material parameters are essential for reliable thermo-mechanical or purely thermal numerical simulations. For isotropic materials, specific heat capacity and thermal conductivity can be determined using established methods such as differential scanning calorimetry and laser-flash analysis. However, applying these methods to anisotropic materials requires significant effort in specimen preparation and may lead to questionable results. The advent of full-field measurement methods has significantly increased the availability of experimental data for model calibration. In this work, we utilize full-field temperature data from infrared thermography to calibrate the specific heat capacity and the thermal conductivity tensor of anisotropic composite material. The experimental data stems from a simple experimental setup comprising two heat plates. First, a suitable identification procedure is developed for isotropic material. Then, the proposed two-step calibration scheme is transferred to anisotropic composite material. The model calibration is performed using nonlinear least-squares and finite element simulations. Derivatives for the gradient-based optimization are computed via internal numerical differentiation rather than commonly applied difference quotients. Subsequently, validation is conducted using the first-order second-moment method taking into account various uncertain parameters. We demonstrate that the calibration of the specific heat capacity and the thermal conductivity tensor is feasible using full-field temperature data for isotropic and anisotropic materials. The identified parameters agree reasonably with reference values and show excellent agreement with validation experiments. Additionally, while internal numerical differentiation necessitates modifications to the finite element code, it offers significant rewards by substantially reducing the time required to compute gradients during optimization and uncertainty quantification with the first-order second-moment method. Especially the latter can be seamlessly integrated into the general finite element solution procedure.