Thermo-acoustical waves in thermo-plastic materials

The propagation velocities and the variation of the amplitudes of thermo-acoustical waves in thermo-plastic materials are theoretically investigated. The constitutive equations of anisotropic thermo-plastic materials are derived from the concept of imaginary decomposition of the deformation rate tensor into the elastic and plastic contributions and from that of the plastic potential. From generalized Vernotte's heat conduction law the propagation condition of the jumps of the velocity gradients and of the temperature rate is obtained. In isotropic materials and in the case of a normal stress vector on the wave front we have two purely mechanical transverse waves and two thermo-longitudinal coupled waves. Formulae for the velocities and amplitudes are quite similar with those for thermo-elastic materials. The variation of the amplitude is discussed. There are, in general, three effects on the variation, that is, the non-planar, heat conduction and plastic flow effects. The transverse waves are subjected only to the non-planar effect, while the thermo-longitudinal waves may grow or decay according to the above three effects.