Dynamic Response of Advanced Ceramics by Ghatu Subhash

Author:Ghatu Subhash [Subhash, Ghatu]
Language: eng
Format: epub
Published: 2021-05-01T22:10:53+00:00

5.2.2 Beyond Plastic Waves: Development of Shock Waves

In the previous example, the medium of wave propagation was a slender rod subjected to an applied load that produced stress in excess of its yield strength, resulting in plastic deformation progressing along the bar and the material flowing in a lateral (radial) direction (Poisson's effect). With time, the energy dissipates, and the amplitude of plastic wave decreases. However, upon application of high amplitude shock loading, the material point is compressed axially in one direction and undergoes significant volume compression. A high pressure (compressive) wave now travels through the material depending on the stress amplitude. This means that the plastic front will not spread as depicted in Figure 5.2b, but with increasing pressure, it will become steep and sharp, rising as much as 50–100 times the flow stress of the material depending on the impact velocity. Such a situation often occurs in ballistic impact or high‐energy explosive loading where the material is subjected to high‐amplitude shock loading.

At these high pressures, metals do not deform by the traditional dislocation‐based (shear driven) plasticity but flow without any resistance to shear, similar to a Newtonian fluid. The stress state can thus be deemed hydrostatic, and the shear stress is assumed negligible. Shock loading can therefore be analyzed using a hydrodynamic treatment. The derivation of shock equations often begin with the ideal gas law. To illustrate the process, consider a piston rapidly compressing gas molecules inside a cylinder as illustrated in Figure 5.3. The ideal gas law for an isentropic process (adiabatic and reversible) is given by:

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