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

0 � = �− 0 2� � = �− 0 � � . Damageability of Metals under Impulse Loading © 2023 Global Journals 1 Year 2023 26 Frontier Research Volume XXIII Issue ersion I VXI ( A ) Science Global Journal of that determines the damageability of the material. The compression in the interference zones inhibits and slows down the destruction process. The opposite is also true. If LSBs are observed in the experiment, then the sample was in the process of oscillation. The model of strain localization under impulse loading remains to be the spallation one but requires substantial changes. Strain localization arises at the nodes of standing waves under long-term deformation conditions in the compression-tension mode after passing a shock wave, while the stress in the wave interference zone does not exceed the spall strength. Standing waves in samples of limited size are the result of the interference of counter propagating waves and their interaction with the sample faces. It should be noted that exceeding the load above the dynamic strength of the material leads to the fragmentation of the sample and formation of fragments in an amount approximately equal to the ratio of the pressure in the shock wave to the value of the spall strength. d) Attenuation of standing waves (reverberation) The question of oscillation damping under shock loads remains unstudied. It is possible to estimate. The damping coefficient α can be estimated using the geometric interpretation of the conservation laws as it was done in [5]. The specific energy converted into heat on the P-V diagram is equal to the surface area bounded by the Rayleigh-Michelson straight line and the load is entrope. The energy attenuation coefficient of a standing wave characterizes the fraction of energy converted into heat to the total energy of a unit mass. According to [5], the specific energy loss is equal to = � 1 3 � 0 02 2 , where ρ 0 is the density of the metal, ε is the degree of deformation equal to u 0 /c 0 , and c 0 and b are the adiabatic parameters; = 2 03 3 02 03 = 1 3 0 is the equation determining the energy fraction . When deriving this equation, the authors [5] replaced the is entrope by the adiabatic. For an ideal elastoplastic medium at relatively low pressures, the loss of a portion of the specific energy е depends on the dynamic elastic limit σ y and the degree of deformation corresponding to the Hugoniot elastic limit σ G : = 2 ( − ) 3 0 [19]. Taking into account that the strain localization arises at stresses slightly lower than the spall strength σ S , the equation for the fraction of dissipative energy takes the form = ( − ) 3 2 . The change in the energy over time, taking into account dissipation, is described by the expression � = − , which implies = 0 exp(- ατ ), here τ is the non dimensional time = 0 � = � , where с 0 is the sound speed , and T = δ /c 0 is half the period of the reverberation cycle . The amplitude of a standing wave decays with time according to an exponential law with the coefficient equal to half the attenuation coefficient of the specific internal energy α /2 Here T 0 is the total period of oscillation of the standing wave. The energy attenuation coefficient of the standing wave is equal to the fraction of energy converted into heat divided by the oscillation period Т 0 [20]. The attenuation of a standing wave is characterized by time t * during which the amplitude of the wave will change е - fold =2.718 , ∗ = 0 /α . During this time, the standing wave will complete N cycles , = ∗ 0 � = 1� . The distance passed by the shock wave and related to the thickness of the sample is ∗ � = 2� . The critical value of the mass velocity corresponding to the spall strength is u 0 = 0.112 mm/µs for a steel sample. In this work, the decay time of the standing wave was calculated by the direct determination of the surface areas on the P-V diagram ( δ = 7 mm; sample diameter 20 mm; speed of sound с 0 = 5 mm/ µs ; duration of the initial pulse Δ = 0.6 µs; pressure of the incoming shock wave 4.2 GPa; damping coefficient of the specific internal energy calculated from the P–V diagram α =0.019, T 0 = 2.8µs, t* = 147.4µs, x*=737mm, N = 53; ∗ ∆� = 245 . For comparison, the dissipative energy fraction in the specific energy is α G = 0.0108 [5], and α s = 0.086 [20], and t hese fractions may differ by 5-10 times. Thus, after the passage of the shock wave, the sample maintains the oscillatory mode for almost 150 µs more, which is almost 250 times longer than the duration of the initial impulse load. III. S pherical I mpactor This is another example of how ignoring the compressibility of solids makes difficult the solution of important practical problems. Spherical shock waves arising by the collapse of cavitation bubbles lead to hardening of the surface layer due to their multiple formation. However, experiments [21] showed the formation of needle-like aggregates in the surface layers at the initial stage of cavitation erosion. The model of erosive wear of a surface under the influence of a flow of spherical particles cannot explain the occurrence of needle-like damageability . Another model that explains damageability by the action of cumulative jets that arise during the asymmetrical collapse of a cavitation bubble cannot explain a sufficiently thick layer of hardened material. The consideration of solid body compressibility appeared as the formation of shock waves during impulse loading shows that it is the spherical impactor