Ryan Austin

Numerical simulation of shock wave propagation in spatially-resolved particle systems

The shock compression of spatially-resolved particle systems is studied at the mesoscale through a series of finite element simulations. The simulations involve propagating shock waves through aluminium–iron oxide thermite systems (Al+Fe2O3) composed of micron-size particles suspended in a polymer binder. Shock-induced chemical reactions are not considered in this work; the particle systems are modelled as inert mixtures. Eulerian formulations are used to accommodate the highly dynamic nature of particulate shock compression. The stress–strain responses of the constituent phases are modelled explicitly at high strain rates and elevated temperatures. Dynamic behaviour of the model system is computed for a set of mixtures (20% and 50% epoxy content by weight) subjected to a range of loading conditions (particle velocities that span 0.300–1.700 km s−1). Spatial profiles of pressure and temperature obtained from the numerical simulations provide insight into thermomechanical responses at the particle level; such resolution is not available in experiments. Finally, Hugoniot data are calculated for the particle mixtures. Stationary pressure calculations are in excellent agreement with experiments, while shock velocity calculations exhibit larger deviations due to the 2D approximation of the microstructure.

Plasticity-Related Microstructure-Property Relations for Materials Design

Design has traditionally involved selecting a suitable material for a given application. A materials design revolution is underway in which the classical materials selection approach is replaced by design of material microstructure or mesostructure to achieve certain performance requirements such as density, strength, ductility, conductivity, and so on. Often these multiple performance requirements are in conflict in terms of their demands on microstructure. Computational plasticity models play a key role in evaluating structure-property relations necessary to support simulation-based design of heterogeneous, multifunctional metals and alloys. We consider issues related to systems design of several classes of heterogeneous material systems that is robust against various sources of uncertainty. Randomness of microstructure is one such source, as is model idealization error and uncertainty of model parameters. An example is given for design of a four-phase reactive powder metal-metal oxide mixture for initiation of exothermic reactions under shock wave loading. Material attributes (e.g. volume fraction of phases) are designed to be robust against uncertainty due to random variation of microstructure. We close with some challenges to modeling of plasticity in support of design of deformation and damage-resistant microstructures.

EQUATION OF STATE OF ALUMINUM-IRON OXIDE - EPOXY COMPOSITE

We report on the measurements of the shock equation of state (Hugoniot) of an Al∕Fe2O3/epoxy composite, prepared by epoxy cast curing of powder mixtures. Explosive loading, with Baratol, trinitrotoluene (TNT), and Octol, was used for performing experiments at higher pressures, in which case shock velocities were measured in the samples and aluminum, copper, or polymethyl methacrylate (PMMA) donor material, using piezoelectric pins. The explosive loading of the metal donors (aluminum and copper) will be discussed. Gas gun experiments provide complementary lower pressure data in which piezoelectric polyvinylidene fluoride (PVDF) stress gauges were used to measure the input and propagated stress wave profiles in the sample and the corresponding shock propagation velocity. The results of the Hugoniot equation of state are compared with mesoscale finite-element simulations, which show good agreement.

Mesoscale simulation of shock wave propagation in discrete Ni/Al powder mixtures

A numerical model is developed to simulate shock wave propagation in discrete Ni/Al powder mixtures. The model is used to investigate the particle-level deformation, heating, and mixing of two distinct Ni/Al powders, as mixing intensity dictates whether or not shock ignition is achieved in these reactive material systems. The main innovations of this work are (1) use of a rate-dependent, dislocation-based model of particle flow stress in the shock simulations and (2) quantitative analysis of the Ni/Al interfaces that are formed during wave propagation. An experimental powder, which is composed of micron-scale spherical Ni and Al particles, is simulated to validate the numerical model. An additional powder, composed of smaller particles, is simulated to investigate the effects of particle size on constituent deformation and mixing under shock wave loading. The simulations indicate that a reduction in particle size leads to increased Ni/Al interface temperature and dislocation density, as well as increased ...

The deformation and mixing of several Ni/Al powders under shock wave loading: effects of initial configuration

The shock wave initiation of ultra-fast chemical reactions in inorganic powder mixtures requires the reactants to be blended within the shock front or shortly behind it. As such, the details of particle deformation are crucial to understanding the sequence of events leading up to the shock initiation of these systems. It is known that the initial configuration of a powder (i.e. the mixture composition and particle morphology) can have a significant effect on the degree of mixing that is achieved under shock wave loading. However, it is difficult to fully resolve this mixing behaviour in shock compression experiments due to the time and length scales involved. In this work, the shock wave deformation and mixing of six distinct Ni/Al powders are studied at the particle level using finite element simulation. Attention is focused on the Ni/Al interfaces that are formed since overall mixture reactivity depends on the specific amount of reactant interfacial area and on conditions induced at those interfaces. The analysis reveals (i) a rank ordering of the powders based on reactant interfacial area formation, (ii) a scaling relation for the rate of Ni/Al interface production and (iii) the distributed nature of Ni/Al interface temperature and dislocation density over a range of shock stress. Finally, it is shown that particle velocity differentials tend to develop across Ni/Al interfaces when the compacted powders are reshocked by reflection waves. The velocity differentials stem from the heterogeneity of the aggregates and are hypothesized to drive fragmentation processes that enable ultra-fast reactions on a sub-microsecond time scale.

An Approach for Robust Micro-Scale Materials Design under Unparameterizable Variability

In this paper, we propose a method for the robust design of materials involving processes that are computationally intensive and selectively random. The material system considered is a Reactive Powder Metal Mixture (RPMM) composed of Al and Fe2O3. Shock simulations of discrete energetic particle mixtures are performed to predict the systems mechanical and thermal behavior that will be used by a designer of the mixture to achieve robust reaction initiation. The method proposed in this paper is the Robust Concept Exploration Method with Error Margin Indices (RCEM-EMI), which employs error margin indices as metrics to determine satisfying design specifications for given performance requirement ranges. An error margin index is a mathematical construct indicating the location of mean system performance and the spread of the performance considering both variability in design variables and models of the system. Variability in responses of a model may be due to system variation that cannot be easily parameterized as noise factors. Furthermore, lack of data, due to the cost of simulations and experiments, leads to uncertain parameters in empirical models. System response variability and parameter uncertainty in a response surface model are estimated in a computationally efficient manner to formulate the error margin indices, which are then leveraged to search for ranged sets of design specifications. Finally, the use of the proposed robust design method is illustrated by the design of a RPMM.

Temperature dependence of dynamic deformation in FCC metals, aluminum and invar

Laser-driven shock experiments were performed on fcc metals, aluminum and invar, at a range of initial temperatures from approximately 120-800 K to explore the effect of initial temperature on dynamic strength properties at strain rates reaching up to 107 s−1. In aluminum, velocimetry data demonstrated an increase of peak stress of the elastic wave, σE, with initial temperature. Alternatively, for invar, σE exhibits little-to-no decrease over the same initial temperature range. Aluminum’s unusual deformation behavior is found to primarily be due to anharmonic vibrational effects. Differences in the magnetic structure of aluminum and invar can account for discrepancies in high rate deformation behavior.

Equation of State of Aluminum — Iron Oxide (Fe2O3) — Epoxy Composite: Modeling and Experiment

We report on the investigation of the equation of state of an 2Al+Fe2O3+ 50 wt.% epoxy composite in the 2–23 GPa pressure range. An explosive loading technique, with piezoelectric pins to measure the shock velocity in the sample and in a donor material, was used for experiments exceeding 5 GPa. Gas gun experiments were performed on the same composites at lower pressures, using PVDF stress gauges to record the input and propagated stresses and the shock velocity based on the time of travel through the sample thickness. The experimental results are compared to numerical simulations of shock compression in discrete particle models. Model results are in agreement with experimental results.

Grain-Scale Simulation of Shock Initiation in Composite High Explosives

Many of the safety properties of solid energetic materials are related to microstructural features. The mechanisms coupling microstructural features to safety, however, are difficult to directly measure. Grain-scale simulation is a rapidly expanding area which promises to improve our understanding of energetic material safety. In this chapter, we review two approaches to grain-scale simulation. The first is multi-crystal simulations, which emphasize the role of multi-crystal interactions in determining the response of the material. The second is single-crystal simulations, which emphasize a more detailed treatment of the chemical and physical processes underlying energetic material safety.

Ultrafast dynamic response of single crystal β-HMX

We report results from ultrafast compression experiments conducted on β-HMX single crystals. Results consist of nominally 12 picosecond time-resolved wave profile data, (ultrafast time domain interferometry –TDI measurements), that were analyzed to determine high-velocity wave speeds as a function of piston velocity. TDI results are used to validate calculations of anisotropic stress-strain behavior of shocked loaded energetic materials. Our previous results derived using a 350 ps duration compression drive revealed anisotropic elastic wave response in single crystal β-HMX from (110) and (010) impact planes. Here we present results using a 1.05 ns duration compression drive with a 950 ps interferometry window to extend knowledge of the anisotropic dynamic response of β-HMX within eight microns of the initial impact plane. We observe two distinct wave profiles from (010) and three wave profiles from (010) impact planes. The (110) impact plane wave speeds typically exceed (010) impact plane wave speeds at t...