Bulk and coated materials shear modulus determination by means of torsional resonant method

This work presents new developments in resonant torsional tests in order to determine the shear modulus G of bulk and coated materials. For this purpose, two main problems are resolved: free vibrations in torsion mode are obtained on rectangular plate samples maintained elastically between crossed wires located along vibration node lines. Then an analytic expression of the shape factor in the vibration equation is proposed in the case of bulk materials. It is due to the identification of warping by the application of Hamiltonʹs principle minimizing potential and kinetic energies described by the Lagrangien of the vibrating system. It allows to build a composite model of vibration for layered materials and to deduce the shear modulus of coatings by differential measurements. ethod has been firstly validated by studying several bulk isotropic materials for which flexural and torsional tests allow to determine E, G and ν with a great accuracy and to follow their evolution in a wide temperature range. It has been then applied to the elastic characterization of NiO oxides grown on Ni substrates.