Development of a Characterization Mold to Measure the Transverse Thermal Conductivity of a Composite Material by Inverse Analysis

Abstract

In the present work, the transverse thermal conductivity of a composite material is determined by inverse analysis of the heat conduction phenomenon. Knowing the evolution of boundary conditions in time, i.e., the bottom and top surface temperatures of a specific sample, the thermal conductivity can be deduced from transient temperature measurements at three given positions through the thickness of the part. Starting from an initial estimate of thermal conductivity, the inverse method begins by solving the direct problem, i.e., the heat equation. The solution gives the transient temperature field everywhere in the composite sample. Calculated temperatures are then compared with transient experimental measurements based on a criterion evaluating the integral in time of the square of the distance between the measured and predicted temperatures. Conductivity is modified iteratively so as to minimize this criterion until the desired accuracy is achieved. The inverse methodology is tested in this article for a composite part made out of unsaturated polyester resin and unidirectional glass fibers. A special multifunctional mold was designed to produce the composite test plates by the Resin Transfer Molding Process (RTM) and at the same time, measure the transverse thermal conductivity as a function of time and resin degree of polymerization. The mold has an adjustable cavity depth to accommodate various experimental configurations and allows easy testing of a series of different fiber volume contents. It is equipped with controlled heating and cooling devices. Numerical simulations were performed to determine the dimensions of the mold and to optimize the positions of temperature and pressure sensors.