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. 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. 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. 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.

中文翻译：

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钢的三阶弹性常数和应力相关系数的测量

到目前为止，文献中对钢的三阶弹性常数的讨论很少。在这项研究中，精确测量了多晶钢在绝热和等温条件下的二阶和三阶弹性常数。为了测量与拉伸应力相对应的弹性波传播时间的微小变化，对均质和各向同性的试样进行了高精度处理，对测量仪器进行了严格的校准，并使测量室的温度保持恒定。作者提出了一个获得钢的三阶弹性常数的实验公式。该公式中与应力有关的系数αij对于获得三阶弹性常数是绝对必要的。所获得的应力相关系数清楚地表明，应力方向与弹性波振荡方向之间存在特殊关系。当弹性波的频率方向与施加应力的方向匹配时，αij变为较大的负值。对于四种钢，分别获得了Lamè常数和Murnaghan的三阶弹性常数ℓ，m，n。绝热条件下的二阶和三阶弹性常数小于等温条件下的二阶和三阶弹性常数。晶格的振荡是非线性的，这被观察为三阶弹性常数。因此，可以获得有关材料的内应力和热性能的知识。