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The formulas for the evaluation of the internal friction and shear elastic modulus of a film deposited on a cylindrical substrate using the torsion pendulum method are derived in this article. The internal friction and the shear modulus of the film, especially their variation with temperature, can be easily deduced by measuring the internal friction and the resonance frequency of the pendulum with the bare substrate and with the composite, respectively. As an example, the shear modulus and the internal friction of a TiN/Ti(C,N) multilayer film deposited on a Mo wire are measured in the temperature range from room temperature to 400 °C.
Li et al. (2003) studied this question.