Thermal wave scattering in composites with functionally grade interface and non-steady effective thermal conductivity pp.967-990
Authors: (Xue-Qian Fang, Dao-Bin Wang, Department of Engineering Mechanics, Shijiazhuang Railway Institute, P.R. China)
Abstract: With the wide application of polymer composites in aerospace, automotive industries, and other high temperature situations, functionally graded interface between the fibers and the matrix has been introduced in the design of composite to minimize thermal stresses and enhance thermal properties. In high temperature situations, the solving method in the steady state becomes inaccurate. The non-steady state method is an efficient way of predicting the effective thermal conductivity of composites under high temperature situations. Due to the complexity of non-steady loading, there are few calculations on the effective thermal conductivity in these materials under modulated conditions. Due to its noncontact, nondestructive, and highly sensitive nature, photo-thermal technique has become very powerful tools for the thermo-physical characterization and nondestructive evaluation of a wide variety of composites. Photo-thermal wave techniques are based on the generation and detection of thermal waves in the sample under study. In this chapter, thermal wave method is applied to investigate the non-steady effective thermal conductivity of composites with functionally graded interface in composites, and the analytical solutions of the problem are obtained. The two cases of dilute and dense fibers are considered. The Fourier heat conduction law is applied to analyze the propagation of thermal waves in the fibrous composite. The scattering and refraction of thermal waves by cylindrical fibers with non-homogeneous interface layer in the matrix are expressed by using wave functions expanded method, and the expanded mode coefficients are determined by satisfying the boundary conditions of the layers. The addition theorem for Bessel functions is used to accomplish the translation between different coordinate systems. In the case of dilute fibers, the theory of Waterman and Truell is used to analyze the scattering of thermal waves. In the case of dense fibers, the theory of quasicrystalline approximation and conditional probability density function are employed to treat the multiple scattering of thermal waves from the dense fibers. The effective propagating wave number and non-steady effective thermal conductivity of composites are obtained. As an example, the effects of the material properties of the coating on the effective thermal conductivity of composites are graphically illustrated and analyzed. Analysis shows that the non-steady effective thermal conductivity under higher frequencies is quite different from the steady thermal conductivity. Comparisons with the steady thermal conductivity obtained from other methods are also presented.