Thermal wave scattering in functionally graded materials containing a spherical inclusion

• Based on the hyperbolic equation of heat conduction.
• Utilizing the wave function expansion method.
• A general solution of the scattered fields of thermal waves is obtained.
• The subsuface defect is taken as a spherical inclusion in the modeling.
• Non-destructive evaluation for functionally graded materials.

In this paper, based on the law of non-Fourier heat conduction, using the wave function expansion method, the thermal wave scattering and temperature distributions of semi-infinite functionally graded materials containing a spherical inclusion were presented. According to the hyperbolic equation of heat conduction, a general solution of scattered fields of thermal waves was obtained. In addition, a matrix formulation to determine mode coefficients of scattered waves were used. Taking into account the engineering background, the incidence of thermal waves excited by the periodically modulated laser and the subsurface defect was treated as a spherical inclusion in the modeling. Numerical simulation was graphically presented and analyzed. It is shown that the influence of the spherical inclusion on the thermal wave scattering and temperature distributions in functionally graded materials are related to the depth of buried spherical inclusion, the nonhomogeneous parameters and the thermal relaxation time. The paper is expected to provide data references of the inverse problem for infrared thermal wave nondestructive evaluation of functionally graded materials.