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A general definition of dynamic fragmentation can encompass any impulsive process which partitions a body of material into discrete domains. Two examples are fragmentation due to brittle fracture under impact loading and fragmentation due to shear banding in shock-compression plastic deformation. In application, prediction of fragment size or shear band spacing is frequently either the objective, or else requisite to understanding the process. An approach is presented whereby surface or interface area created in the fragmentation process is governed by an equilibrium balance of the surface or interface energy and a local inertial or kinetic energy. Fragment size can be approximately related to surface or interface area. Relations provided by the analysis compare well with experimental dynamic fracture and shock-wave shear-band results.

The present study is focused on viscouslike behavior of solids during large-amplitude compressive stress-wave propagation. Maximum strain rate in the plastic wave has been determined for 30 steady- or near steady-wave profiles obtained with velocity interferometry methods. The materials include six metals, aluminum, beryllium, bismuth, copper, iron, and uranium, and two insulating solids, magnesium oxide and fused silica. A plot of Hugoniot stress versus maximum strain rate for each material is adequately described by η̇=aσmh. The exponent m is approximately 4 for all materials while the coefficient a is material dependent. A model is developed which incorporates the observed trends of the shock viscosity data in a three-dimensional framework. Finite-difference calculations using the model reproduce the experimental wave profile data.

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The present study is focused on the distributions in particle size produced in dynamic fragmentation processes. Previous work on this subject is reviewed. We then examine the one-dimensional fragmentation problem as a random Poisson process and provide comparisons with expanding ring fragmentation data. Next we explore the two-dimensional (area) and, less extensively, the three-dimensional (volume) fragmentation problem. Mott’s theory of random area fragmentation is developed, and we propose an alternative application of Poisson statistics which leads to an exponential distribution in fragment size. Both theoretical distributions are compared with analytic and computer studies of random area geometric fragmentation problems, including those suggested by Mott, the Voronoi construction, a variation of the Johnson–Mehl construction, and several methods of our own. We find that size distributions from random geometric fragmentation are construction dependent, and that a conclusive choice between the two distributions cannot be made. A tentative application of the maximum entropy principle to fragmentation is discussed. The statistical theory is extended to include a concept of statistical heterogeneity in the fragmentation process. Finally, comparisons are made with various, dynamic fragmentation data.

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In terms of shock-compression characteristics, minerals of geophysical interest are placed in a class of materials which, because of some rather unique Hugoniot and shock-compression properties, are classified as brittle solids. The physical processes responsible for these shock-wave properties are not yet well established. However, recent experimental observations and theories based on localized, nonhomogeneous shear deformation and a transient nonuniform thermal state appear to provide a reasonable qualitative picture. In the present work, some of the terminal and transient shock-compression features observed in brittle solids are reviewed with particular emphasis on Hugoniot release-wave measurements. The possibility of instabilities in the laws governing shear deformation leading to observed heterogeneous deformation is considered, and although an elementary model is treated, the method shows promise of predicting the material and kinematic properties governing occurrence, growth, and frequency of localized deformation features. Transient stress wave calculations in crystalline quartz demonstrate how the kinematic environment governing instability growth is established under shock-wave compression. In addition, the transient nonuniform thermal state resulting from heterogeneous deformation is shown to provide a possible explanation for the observation of both 'fluidlike' and 'solidlike' shock release waves depending on the competing properties of thermal diffusion, melting temperature, and degree of thermal localization. The analysis shows a striking difference between those minerals which do, and do not, undergo a shock-induced phase transition and leads to speculated similarities between the kinetics of shock-induced phase transformation in brittle solids and the kinetics of thermal detonation in explosives. INTRODUCTION Strong shock waves continue to provide a useful tool for investigating the physics of solids under conditions of extremepressure and temperature. Hugoniot equations of state have been determined for numerous materials of geophysical interest, and recent technical advances are providing methods for determining temperature, viscosity, electric and magnetic properties, crystal structure, and other physical properties at shock-wave pressures. Such methods are impressive considering the very brief span of time during which a region of the material can be maintained at a shocked state after passage of a strong shock wave. Unexplained features of the shock-compression process in minerals have persisted, however, and recent results have raised serious questions concerning thermodynamic equilibrium and the microstructural state of solids at Hugoniot pressures. How, for instance, does a mineral subjected to Hugoniot temperatures and pressures compare with a mineral at the same temperature and pressure achieved under conditions of static compression? Is pressure and temperature equilibrium achieved in the brief microsecond or less during which the shocked state persists? What are the microstructural f...