変形結晶中の超音波の伝搬速度と応力の関係

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The ultrasonic wave propagations in a deformed crystal with symmetry in whatever respect have been theoretically investigated by a method similar to that of Thurston^2). A weak ultrasonic wave deformation has been superposed on a statically deformed state of the crystal. Substituting the general anisotropic linear stress-strain relation (4) and the assumed plane wave solution (16) into the equation of motion (15), the rotationless propagation condition(20) proposed by Truesdell^7) is specified by the statically deformed state for a given propagation direction, and the propagation velocities are determined by the eigenvalues of the acoustical tensor (19). The static deformation is so small that the second and higher order of the displacement gradient are to be neglected, and effect of the applied stress is regarded as perturbation. The acoustical tensor is then explicitly expressed by the stress in the first-order approximation (23). The characteristics equation (28) obtained from the propagation condition (20) is reduced to the relation (31) which gives the perturbations of the eigenvalues of the acoustical tensor (33) and (34). This method is restricted to the non-degenerate case with respect to the propagation velocities of the natural state. The velocity difference of two quasitransverse waves is calculated, which indicates the acoustical birefringence and consists of the intrinsic anisotropy of a crystal and the effect of the applied stress. The formulae thus obtained are applied to the orthorhombic system, and the results show that the acoustical birefringence for the waves propagating along a crystal axis depends on the three normal stresses along the crystal axes.
社団法人日本材料学会の論文
1969-08-15

変形結晶中の超音波の伝搬速度と応力の関係

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