Measurement of third-order elastic constants and stress dependent coefficients for steels

Abstract

Abstract Background There has been little discussion of the third-order elastic constants of steels in the literature until now. In this study, the precise second- and third-order elastic constants of polycrystalline steels were measured under adiabatic and isothermal conditions. Method To measure the minute change in the propagation time of the elastic wave corresponding to the tensile stress, the uniform and isotropic specimens were processed with high precision, the measuring instruments were strictly calibrated, and the temperature of the measurement chamber was kept constant. The author proposes an experimental formula to obtain the third-order elastic constants of steels. The stress dependent coefficients α ij in this formula are absolutely necessary to obtain the third-order elastic constants. Results The obtained stress dependent coefficients clearly indicated that there is a special relationship between the directions of stress and that of the oscillation of the elastic wave. When the frequency direction of the elastic wave matched the direction of the applied stress, α ij became a larger negative value. Lamè constants and Murnaghan’s third-order elastic constants ℓ,m,n were obtained for four types of steels. Conclusions The second- and third-order elastic constants under adiabatic conditions were smaller than those under isothermal conditions. Oscillation of crystal lattice is nonlinear and this is observed as the third-order elastic constants. Therefore, it is possible to obtain the knowledge on the internal stress and the thermal properties of the materials. This is also the basis of theoretical discussion of the thermal expansion coefficients.