Determination of third-order elastic moduli to measure stressed-strained states in metal structural components of nuclear power plants
The article presents theoretically derived third-order elastic moduli. Data on the values of the third-order elastic moduli are required for measuring stressed-strained states  in metal structural components of NPPs. The values of the second-order elastic moduli obtained by different methods are found in the reference books [2, 3]. The third-order elastic moduli were obtained only by an acoustic method and there is a large scatter of numerical data, reaching several orders of magnitude [4 – 8]. The accuracy in determining stressed states by acoustic methods depends on the adequacy of an ultrasonic wave propagation velocity model and the accuracy in determining ultrasonic velocities. Therefore, it is necessary to develop methods for determining third-order elastic moduli without using acoustic methods. The author presents such a method based on experimental data on all-round compression, using a differential equation connecting the stress tensor with the strain tensor. The third order elastic constants were determined by the equations for the all-round, uniaxial and biaxial compression-tension. To determine the third-order elastic moduli in alloys used in nuclear power engineering, it is necessary to have data on the all-round compression of these materials [9 – 13]. Then, using the above procedure, it is possible to determine the values of these moduli. The experimentally obtained values of stresses with a negligible error coincide with the values of stresses calculated from the formulas.
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