Global Journal of Science Frontier Research, A: Physics and Space Science, Volume 23 Issue 11

c) Standing wave According to the spallation model, a necessary condition for the formation of LSBs is the presence of at least two free surfaces, which are sources of unloading waves.It is of interest to reveal specific features of LSBs formation when the free surfaces are solid and smooth faces of the sample. A thick-walled hollow cylinder is used as a sample. Dynamic loading was carried out by an impact by the plate on the sample edge. Figure 6 shows that the impact loading of the sample with two free surfaces results in the formation of a system of annular bands of localization strain (circumferential spall damage). The shock wave passing through the sample sets in motion the lateral inner and outer surfaces of the hollow cylinder. The emerging counter propagating waves interact with each other and with the free faces of the sample, which leads to the oscillation of the sample in the standing wave mode [18]. Reflection of waves on the free surface, where the incident wave interacts with its reflected wave, leads to a change in the character of the reflected waves: the unloading wave becomes a compression wave and vice versa. The process of reflection on the free surface is a necessary oscillation mechanism, since it changes the direction of the velocity of the sample faces to the opposite one. The node of a standing wave is the point where the waves collide, and the mass velocity is zero. The deformation of the material in the compression-tension unit is explained by the periodic formation of interference zones of compression waves and unloading waves, which predetermines the origin and development of LSBs at the nodes of a standing wave. The antinodes are the faces themselves where the pressure is zero, and the length of the standing wave is equal to the doubled thickness between the sample faces. Damageability of Metals under Impulse Loading 1 Year 2023 25 Frontier Research Volume XXIII Issue ersion I VXI ( A ) Science © 2023 Global Journals Global Journal of Figure 5 shows the transformation of spall cracks into localized strain bands in the sample depth, and many of the LSBs are represented by a chain of pores. It should be noted that the exit of a perturbed shock wave onto a free surface always leads to radial spall damage in the form of spall cracks or LSBs between folds of the surface relief. Fig. 6: System of annular localized strain bands in a thick-walled hollow cylinder made of two-phase titanium obtained as a result of the end impact by a plate. Each band is the harmonic node of the standing wave A specific feature of a standing wave is the formation of energetically closed “compartments” (between the antinode and the node, where the distance is equal to ¼ of the wavelength) in which the energy is conserved and not exchanged with neighboring regions resulting in the oscillation continuing after the shock wave attenuation without the action of external forces until dissipative losses would lead to oscillation damping. Another feature of a standing wave is the formation of new natural oscillations (overtones (harmonics)) as shown in Fig. 6.The main natural vibration with the wavelength equal to the doubled distance between the sources of unloading waves 2 δ is formed, as a rule, in the central part of the sample. In a symmetrical standing wave, particles of the medium periodically approach or move away from the node. During the deformation process, additional new LSBs with intrinsic wavelengths are formed around the fundamental harmonic in which the relationship between the thickness of the sample and the overtone wavelength is described by the equation 2⁄ = 4⁄ , where n = 1, 3, 5. The case n = 1 refers to the fundamental intrinsic overtone . The LSBs arising at the nodes of standing waves have a coaxial annular shape, which is circumferential spall damage. A necessary condition for the formation of a standing wave is the presence of at least two free surfaces. The same condition is necessary for LSBs. The result of the experiment proved to be unexpected. It was assumed previously [11-14, 28, 32] that a standing wave is a consequence of the strain localization , but it turned out that LSBs are a consequence of oscillation and should reflect all the features of standing waves. The condition that the stress in the wave interference zone should not exceed the spall strength is preserved. It is also true that it is the tension in the interference zone