On evolutional and catastrophic regimes of meso-macro energy exchange in dynamically loaded media

Abstract

Study of the role of velocity fluctuations in processes of energy exchange between mesoscopic and macroscopic scale levels represents an important stage in the development of our knowledge about the shockwave behavior of heterogeneous materials. In the case of dynamic deformation, the concept of mesoparticle has much wider meaning as applied to quasistatic processes, in which mesoparticles are specific structural defects such as dislocation groups, vortex structures, shear bends, and other structural formations of scale 0.1‐10 μ m [1]; they represent field structures, the only distinct feature of which is the presence of a velocitycorrelated group of medium points. This means that a mesoparticle is a space formation, the internal points of which have identical or close velocities. The lifetime of these structures is determined by the duration of the dynamic deformation process. Each mesoparticle, as a separate structural formation, has its own overall velocity. In a heterogeneous medium, a dynamically deformed structure is characterized by velocity scattering. Therefore, mesoparticle velocity fluctuations can remove a considerable part of momentum and energy transferred to the medium. According to recent experiments [2], the generally accepted opinion that 90% of plastic work is immediately transformed into heat is erroneous. It is found that, in the microsecond range of dynamic loading, only 30‐ 35% of plastic work is transformed into heat, while the rest of the work is spent on the formation of the mesostructure. The main mechanism of structure formation is large-scale velocity fluctuations, the quantitative characteristic of which is the standard deviation of the mesoparticle velocities. Analysis of the experimental data on shock loading of materials reveals two regimes of energy exchange between mesoscales and macroscales of dynamic deformation—smooth or evolutional and catastrophic regimes. The latter regime implies that the mean particle velocity decreases suddenly at a certain strain rate, while the standard deviation of velocities increases. This statement was verified by impact tests of two sets of 30XH4M steel targets subjected to different thermal treatments. As an example, Fig. 1 shows the time profiles of the mean velocity and standard deviation of velocities as obtained upon plane impact loading of two targets with velocities of 324 and 320 m/s. The profiles were recorded using a two-channel velocity interferometer [3]. Although the impact velocities are close to each other in these experiments, the time profiles of the mean velocity and standard deviation of velocities are significantly different. In the first case, the mean velocity increases gradually up to 310 m/s, while in the second case, the break of the mean velocity occurs at a velocity of 160 m/s (point B in Fig. 1b). The behavior of the standard deviation of velocities is opposite: its increase rate is much higher in the second case. The second case corresponds to the catastrophic regime of energy exchange between the mesoscale and macroscale. To deduce a criterion for the transition from the evolutional to catastrophic regime of energy exchange between the mesoscopic and macroscopic scales of dynamic deformation, we consider the one-dimensional propagation of an elastoplastic wave in a medium characterized by mesoscopic velocity fluctuations. The equations of momentum and mass conservation have the form