Parameter estimation in multi-axial thermal diffusivity experiments

Thermomechanical analysis requires quantifying the thermophysical properties of thermal conductivity (or diffusivity) and specific heat. The extended flash method allows simultaneous measurement of multiple components of the thermal diffusivity tensor. The locations of the temperature sensors in such an experiment have an affect on the ability to accurately estimate the desired components of the diffusivity tensor. Here, D-optimization is applied to a simulated extended flash diffusivity experiment to improve the accuracy of the experiment through optimization of the inter-sensor distance. Results indicate that the optimal inter-sensor distance increases with an increasing ratio of inplane to out-of-plane diffusivity. The analytically determined optimal sensor positioning for an isotropic material is validated via experimental measurements on AISI 304 stainless steel, where it is shown that the accuracy of the estimated parameters improves for data sampled at the optimized locations.; When modeling the anisotropic thermal response of materials, the material may be rotated such that the physical axes coincide with the principal axes of the thermal diffusivity tensor, resulting in thermal orthotropy. During measurements of such a tensor, however, the principal axes may be unknown, requiring a method to determine principal values and the orientation of the principal directions while simultaneously measuring the diffusivity. An analytical study was performed where the four non-zero components of the diffusivity tensor alpha were estimated for a material possessing random in-plane anisotropy on the order of certain manufactured or mechanically loaded elastomers. Results indicate that a four-sensor array allows sufficient sampling of the material response to permit estimation of alpha to within 1% of the reference values. When orthotropy is assumed for a material exhibiting random in-plane anisotropy, the estimated values of alphaii are resolved to within 0.4% of the reference values when the magnitude of the anisotropy is on the order of that seen in common deformed or machined elastomers. It is shown that the specimen orientation affects the amount of information obtained concerning the estimated parameters; skew orientations may improve the accuracy of the experiment, if orientation information is known prior to experimentation.