Dennis E. Grady

The spall strength of condensed matter

Two conditions are proposed which place constraints on the processes of dynamic spall in condensed media, and determine inequalities which bound the spall strength, fragment size, and failure time. Spall is defined as rupture within a body due to stress states in excess of the tensile strength of the material. The first is a horizon condition which establishes a domain of communication, consistent with the time to failure, within which spall must be independent of the surrounding environment. The second is an energy condition which requires that the potential and kinetic energy associated with the tensile loading process exceed the fracture energy of the material. Equality in the relations established from these conditions corresponds to energy-limited spall and provides specific analytic expressions for the spall properties. Inequality implies flaw-limited spall and requires more detailed material property information before spall can be characterized. Energy-limited spall is determined by the material fracture toughness in brittle solids and the material flow stress in ductile solids. Calculated spall properties, assuming energy-limited spall, compare well with experimental spall data for various materials. Under certain conditions, a transition from brittle to ductile spall (definition in text) with increasing strain rate is predicted. Comparison is made with spall data on 6061-T6 aluminum for which a brittle-to-ductile transition is predicted to occur at a critical strain rate of approximately 4 × 105 s−1. Energy-limited spall in liquids within their range of Newtonian fluid behavior is governed by surface energy and viscosity. Spall is predicted to be dominated by surface energy at low strain rates and viscous dissipation at high rates. Examples of each appear to exist within the scant experimental spall data available for liquids.

Local inertial effects in dynamic fragmentation

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.

Shock viscosity and the prediction of shock wave rise times

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 η=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.

Geometric statistics and dynamic fragmentation

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 distr...

The growth of unstable thermoplastic shear with application to steady-wave shock compression in solids*

Abstract T he catastrophic growth of unstable thermoplastic shear following the transition from homogeneous deformation to heterogeneous localized deformation through distributed shear banding is studied through approximate analytic and computational methods. The calculations provide expressions for shear band widths, spacing, catastrophic growth times and the rate of stress communication between shear bands. The optimum shear band width and spacing are found to be consistent with a minimum work principle. The model predicts that the product of the energy dissipated and the localization time in the shear localization process is invariant with respect to changes in the driving strain rate. Such behavior has been noted in the steady-wave shock compression of a number of solids. The calculations are applied to heterogeneous shear localization observed in the shock compression of aluminum.

Spall fracture properties of aluminum and magnesium at high temperatures

Measurements of the dynamic tensile strength of aluminum and magnesium have been carried out by investigations of the spall phenomena over a wide range of temperatures, shock‐wave intensities, and load durations. Free‐surface velocity profiles were recorded with VISAR and used to provide the spall strength measurements. The initial temperature of samples was varied from room temperature to near the melting point. The peak compressive pressure in the shock waves was varied from 5 to 50 GPa for aluminum and from 2 to 10 GPa for magnesium. The load duration was varied by more than one order of magnitude. The free‐surface velocity measurements showed a precipitous drop in the spall strength of preheated samples as temperatures approached the melting point. No significant influence of the peak pressure on the spall strength was observed. The strain‐rate dependencies of the spall strength could be represented as power functions with a power index of 0.060 for aluminum and 0.072 for magnesium. Unexpectedly large...

An experimental investigation of shock wave propagation in periodically layered composites

In heterogeneous media, scattering due to interfaces/microstructure between dissimilar materials could play an important role in shock wave dissipation and dispersion. In this work, the influence of interface scattering on finite-amplitude shock waves was experimentally investigated by impacting flyer plates onto periodically layered polycarbonate/6061 aluminum, polycarbonate/304 stainless steel and polycarbonate/glass composites. Experimental results (obtained using velocity interferometer and stress gage) show that these periodically layered composites can support steady structured shock waves. Due to interface scattering, the effective shock viscosity increases with the increase of interface impedance mismatch, and decreases with the increase of interface density (interface area per unit volume) and loading amplitude. For the composites studied here, the strain rate within the shock front is roughly proportional to the square of the shock stress. This indicates that layered composites have much larger shock viscosity due to the interface/microstructure scattering in comparison with the increase of shock strain rate by the fourth power of the shock stress for homogeneous metals. Experimental results also show that due to the scattering effects, shock propagation in the layered composites is dramatically slowed down and the shock speed in composites can be lower than that either of its components.

Dynamic fracture growth and interaction in one dimension

Abstract The present study considers concepts relating fracture energy and fracture dynamics. Analyses of Mott are expanded to explicitly account for energy dissipation during the fracture process. Expressions are obtained for the nominal fragment size, fracture time, and dynamic fracture strain. It is shown that communication between growing fractures is relatively slow. Numerical analysis is used to examine the interaction of ductile fractures and the conditions that may lead to arrest or completion of growing fractures.

Plate impact response of ceramics and glasses

Soft‐recovery plate impact experiments have been conducted to study the evolution of damage in polycrystalline Al2O3 samples. Examination of the recovered samples by means of scanning electron microscopy and transmission electron microscopy has revealed that microcracking occurs along grain boundaries; the cracks appear to emanate from grain‐boundary triple points. Velocity‐time profiles measured at the rear surface of the momentum trap indicate that the compressive pulse is not fully elastic even when the maximum amplitude of the pulse is significantly less than the Hugoniot elastic limit. Attempts to explain this seemingly anomalous behavior are summarized. Primary attention is given to the role of the intergranular glassy phase which arises from sintering aids and which is ultimately forced into the interfaces and voids between the ceramic grains. Experiments are reported on the effects of grain size and glass content on the resistance of the sample to damage during the initial compressive pulse. To fu...

Particle size statistics in dynamic fragmentation

Condensed matter, when subjected to intense disrupting forces through impact or radiation deposition, will break up into a randomly distributed array of fragments. An earlier analysis of random fragmentation is extended to account for fragmentation in bodies which are finite in extent and for bodies within which the minimum fragment size is bounded. The statistical fragment size relations are compared with molecular dynamic simulations of dynamic fragmentation, with fragmentation caused by the high‐energy collision of nuclear particles, and with the distribution of galaxies in the universe which are assumed to be fragment debris from the primordial Big Bang.