Dynamics of Heterogeneous Materials

Impulse propagation in granular (particular) materials due to the loading under impact or contact explosion is of practical interest for many applications. For example, granular bed from iron shot is used for the damping of contact explosions during technological operations in explosive chambers. It effectively prevents the chamber wall from the high-amplitude shock wave. The propagation and reflection of nonlinear waves with large amplitudes in sand or soil is important for the detection of foreign objects. The nature of waves in these materials is also of general interest because they represent the collective dynamic response strongly effected by mesostructure. At the same time, these materials pose some fundamental questions which demand reconsideration of the basic foundation of wave dynamics including shock-wave propagation and shock dynamics particularly.

Intense dynamic loading of porous, granular materials results in a completely new class of phenomena, in comparison with their behavior considered in the previous chapter. It includes a complex geometry of plastic flow, as well as fracture and melting. The mechanical deformation (shock loading, plastic flow) of heterogeneous porous materials has an essentially multiscale nature. For example, the hierarchy of scales includes:

Impulse transformation in laminates and porous materials has important practical applications connected with impact and blast mitigation. The investigation of strong shock-wave dynamics in laminar media is focused mainly on two important aspects. One is wave transformation, for example, attenuation or amplification of the shock amplitude as a function of the laminar system structure. Zababakhin [1965], [1970] predicted that as the layer thickness continuously decreased with distance for a one-dimensional system of alternating materials with different densities, the phenomenon of unlimited cumulation of the shock wave could be obtained. This was a first demonstration of unrestricted cumulation which is not related to the centripetal motion of matter. Later, this tendency was numerically and experimentally confirmed (Kozyrev, Kostyleva, and Ryazanov [1969]; Ogarkov, Purygin, and Samylov [1969]; Fowles [1979]). The successful application of this idea was demonstrated by the launching of the thin titanium plate to velocities of 16 km/s using a multiply graded-density impactor with increasing shock impedance from the impact surface in sequence TPX-plastic, magnesium, aluminum, titanium, copper, and tantalum (Chhabildas, Kmetyk, Reinhard, and Hall [1996]). This system tailors the time-dependent stress pulse to launch the flier plate intact by using a precisely controlled thickness of each layer.

Shear localization plays an important role in the process of high-speed metal cutting, armor resistance to high-velocity impact, and in the break-up of penetrators. The high-strain-rate plastic flow of fractured ceramics during the ballistic impact of ceramic armor plays an important role in governing the depth of penetration, as was shown in the model calculations by Curran, Seaman, Cooper, and Shockey [1993]. Another example is initiation by shear bands of energetic materials under high-strain-rate plastic flow, which is unstable at high strains for most materials.

Nonequilibrium heat release in powders under shock loading is strongly coupled with viscoplastic nonuniform material flow during the densification process (see Chapter 2). At the same time, the essential difference in time scales for mechanical and thermodynamical equilibrium for relatively large particles makes possible the decoupling of mechanical processes on the stage of compaction and the subsequent phenomena connected with heat diffusion. This is also possible due to the weak dependence of shock macroparameters on the details of energy release.

The shock treatment of powders, for example, to increase defect density and activate sintering, or to density them to solid density has a relatively long history of application attempts in the area of advanced materials. Nevertheless, the scale of industrial fabrication is very small in comparison, not only with the traditional powder technology methods, but even in comparison with the explosive forming, welding, or explosive hardening, which use the same type of loading. There are two main reasons for this.