Quick and repeatable shear modulus measurement based on torsional resonance using a piezoelectric torsional transducer.

Shear modulus is one of the fundamental mechanical properties of materials, while its quick and accurate measurement is still a challenge. Here we proposed a method for shear modulus measurement based on torsional resonance using a piezoelectric torsional transducer bonded on a cylindrical specimen. Firstly, the torsional transducer was introduced which consists of two thickness poled, thickness shear (d15) piezoelectric half-rings. Secondly, the equivalent circuit of the transducer-cylindrical specimen system is derived and the shear modulus can be explicitly obtained using the torsional resonance frequency. The internal friction can also be obtained, which is calculated by using an approximate formula. Then, shear modulus and internal friction measurement on four materials including 1045 steel, 6061 aluminum, quartz glass and PMMA were conducted. Results indicate that all the measured shear moduli are consistent with the reference values in literatures. The repeatable error in shear modulus measurement is within 0.2%, which is very desirable. Finally, shear modulus measurement scheme under high (or low) temperature is proposed using a frequency-match quartz glass bar as the thermal insulator. Measurement results on the 6061 aluminum indicates that from room temperature to 500 °C, the shear modulus decreases from 26.8 GPa to 16.6GPa. The proposed method is very reliable and quite convenient, which can be widely used in near future.