Microstrain-level measurement of third-order elastic constants applying dynamic acousto-elastic testing

Abstract

The nonlinear elasticity of solids at the microstrain level has been recently studied by applying dynamic acousto-elastic testing. It is the analog of conventional quasi-static acousto-elastic experiments but the strain-dependence (or stress-dependence) of ultrasonic wave-speed is measured with an applied strain ranging from 10−7 to 10−5 and produced by a stationary elastic wave. In conventional quasi-static acousto-elastic experiments, the strain is applied in a quasi-static manner; it exceeds 10−4 and can reach 10−2. In this work, we apply dynamic acousto-elastic testing to measure the third-order elastic constants of two isotropic materials: polymethyl methacrylate and dry Berea sandstone. The peak amplitude of the dynamic applied strain is 8 × 10−6. The method is shown to be particularly suitable for materials exhibiting large elastic nonlinearity like sandstones, since the measurement is performed in the domain of validity of the third-order hyperelastic model. In contrast, conventional quasi-static acousto-elastic experiments in such materials are often performed outside the domain of validity of the third-order hyperelastic model and the stress-dependence of the ultrasonic wave-speed must be extrapolated at zero stress, leading to approximate values of the third-order elastic constants. The uncertainty of the evaluation of the third-order elastic constants is assessed by repeating multiple times the measurements and with Monte-Carlo simulations. The obtained values of the Murnaghan third-order elastic constants are l = −73 GPa ± 9%, m = −34 GPa ± 9%, and n = −61 GPa ± 10% for polymethyl methacrylate, and l = −17 000 GPa ± 20%, m = −11 000 GPa ± 10%, and n = −30 000 GPa ± 20% for dry Berea sandstone.