Research on the Nondestructive Measurement of Nonlinear Elastic Modulus by Using Ultrasonic Wave

The speed of sound in conventional linear elasticity is determined only by the elastic modulus and the density of the medium. In actuality, however, the speed of sound depends on the stress and this dependency becomes nonlinear as the stress increases. This paper explains such phenomena by introducing the nonlinear elastic modulus. Additionally, the relationship between nonlinear elastic modulus up to the fourth-order and the internal stress is discussed through computer simulations and experiments for an aluminum specimen. In the simulation, it is shown that the third-order elastic constant contributes to the slope of the sound speed vs stress curve and the fourth-order one determines the curvature. Experimental results shows good agreement with the expected result and the ratio of third- and fourth-order elastic constants present significant changes in magnitude and with sign inversion after the internal stress, becomes larger than the yielding stress. These results show that the measurement of nonlinear elastic constants may enable internal stress evaluation.