Multiphysically coupled thermal–acoustic axisymmetric wave propagation for electron acoustic nondestructive observations

Abstract

The nondestructive observation using thermoelastic–piezoelectric couplings by the chopped electron beam in the commercial-based scanning electron microscope has been proposed as a scanning electron-induced acoustic microscope (SEAM). Our own-built SEAM has successfully provided some nondestructive observations of micro-defects such as micro-voids, cracks and delamination. In order to investigate the thermal–acoustic wave properties as the principle of observation in SEAM, an axisymmetric thermoelastic–piezoelectric computational model was proposed. Three kinds of governing equations in three dimensions multiphysically coupled among non-Fourier heat conduction, dynamic elasticity and piezoelectricity were first derived and then reduced to the axisymmetric two-dimensional and finally to the one-dimensional equations. The thermal wave and thermal stress wave observed in a monolayer cylinder with the thermal relaxation were first analyzed for both the cases with an almost circular vacancy-like inclusion and without it. The results were in agreement with the analytical prediction, and it was observed that the delay of traveling waves was increased due to the longer transport path as the inclusion radius. A three-multilayer model corresponding to the real measurement system of SEAM was employed to estimate the piezoelectromotive output to the cyclic temperature change on one end face. Fast Fourier transformation of that wave gives us the clear resonance frequencies driven by the thermal-induced disturbance, and thus, the estimated eigenfrequency of the measurement system will be utilized for the higher resolution of the electron acoustic image of SEAM.