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Thermal wave scattering in composites with functionally grade interface and non-steady effective thermal conductivity pp.967-990 $100.00
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. 


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Thermal wave scattering in composites with functionally grade interface and non-steady effective thermal conductivity pp.967-990