Abstract
The velocity of an ultrasonic wave propagating in the uniformly deformed isotropic solid was analysed by the Eulerian viewpoint. The pseudo elastic coefficient (PEC) was used to solve the equation of motion of the elastic wave under finite deformation. The infinitesimal displacement gradients are connected to the stress increments by the PEC. Using the PEC and the partial differential equation of motion, the velocity of ultrasonic wave was quantitatively related to applied stress, moreover, the stress dependence on longitudinal and transverse wave velocities propagating in the direction parallel or perpendicular to the uniaxial tensile direction could be cleared. Consequently, the Murnaghan's third order elastic constants can be calculated by precisely measuring the uniaxial tensile stress and ultrasonic wave velocity.
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