UFM contrast theory

UFM detection is obtained by measuring the cantilever deflection as the ultrasound amplitude is modulated (Fig. 13.3). The ultrasonic excitation from a longitudinal wave transducer fixed to the bottom of the sample causes normal vibration of its surface. As the ultrasonic amplitude is increased, contact is eventually broken at the pull-off point (aI = hi), giving a discontinuity in the time-averaged displacement. We refer to this ultrasonic amplitude as the threshold amplitude, and the corresponding inflection in the displacement 

The force on the cantilever under normal sinusoidal vibration of amplitude a from an initial indentation hi is found by integrating over a vibration period (Kolosov and Yamanaka 1993)  

This description is based on the approximation that the cantilever has effectively infinite point mass. A fuller analysis of the cantilever takes into account its distributed mass and multiple vibration modes (Hirsekorn et al 1997). This allows a more rigorous description of the mode of operation of the UFM and the contrast in the images, and also provides the theoretical basis for using the cantilever as a waveguide through which vibrations can be introduced (Inagaki et al. 1998). For the applications to be described in this chapter, the key components of the UFM and the mechanical diode principle are  

The adhesion energy is 2y, and the mutual plane strain modulus and radius of curvature are 

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