Roger W. Minich

Connectivity and percolation in simulated grain-boundary networks

Random percolation theory is a common basis for modelling intergranular phenomena such as cracking, corrosion or diffusion. However, crystallographic constraints in real microstructures dictate that grain boundaries are not assembled at random. In this work a Monte Carlo method is used to construct physically realistic networks composed of high-angle grain boundaries that are susceptible to intergranular attack, as well as twin-variant boundaries that are damage resistant. When crystallographic constraints are enforced, the simulated networks exhibit triple-junction distributions that agree with experiment and reveal the non-random nature of grain-boundary connectivity. The percolation threshold has been determined for several constrained boundary networks and is substantially different from the classical result of percolation theory; compared with a randomly assembled network, about 50-75% more resistant boundaries are required to break up the network of susceptible boundaries. Triple-junction distributions are also shown to capture many details of the correlated percolation problem and to provide a simple means of ranking microstructures.

Electrical conductivity of water compressed dynamically to pressures of 70–180 GPa (0.7–1.8 Mbar)

The electrical conductivity of water was measured at high pressures (70 to 180 GPa) and temperatures (4000 to 11 000 K) using a reverberating shock wave technique. The measured electrical conductivity of water varies from 39 to 200 Ω−1 cm−1 between 70 and 180 GPa. The relatively weak pressure dependence of the electrical conductivity is consistent with water being fully ionized chemically and the primary conduction mechanism is highly mobile protons. The results are in contrast to hydrogen, in which electrons are the dominant charge carriers.

Void growth by dislocation-loop emission

Experimental results from spall tests on aluminum reveal the presence of a dense dislocation structure in an annulus around a void that grew under the tensile pulse when a shock wave was reflected at the free surface of the specimen. The proposition is that dislocation emission from the void surface under load is a viable mechanism for void growth. To understand void growth in the absence of diffusive effects, the interstitial-loop emission mechanism under tensile hydrostatic stress is investigated. First, the micromechanics of pile-up formation when interstitial loops are emitted from a void under applied macroscopic loading is reviewed. Demand for surface energy expenditure upon void-surface change is taken into consideration. It is demonstrated that in face-centered cubic metals loop emission from voids with a radius of ∼10 nm is indeed energetically possible in the hydrostatic stress environment generated by shock loading. On the other hand, the levels of hydrostatic stress prevalent in common structu...

The Structure of the Cubic Coincident Site Lattice Rotation Group

This work is intended to be a mathematical underpinning for the field of grain-boundary engineering and its relatives. The inter-relationships within the set of rotations producing coincident site lattices in cubic crystals are examined in detail. Besides combining previously established but widely scattered results into a unified context, the present work details newly developed representations of the group structure in terms of strings of generators (based on quaternionic number theory, and including uniqueness proofs and rules for algebraic manipulation) as well as an easily visualized topological network model. Important results that were previously obscure or not universally understood (e.g. the Sigma combination rule governing triple junctions) are clarified in these frameworks. The methods also facilitate several general observations, including the very different natures of twin-limited structures in two and three dimensions, the inadequacy of the Sigma combination rule to determine valid quadruple nodes, and a curious link between allowable grain-boundary assignments and the four-color map theorem. This kind of understanding is essential to the generation of realistic statistical models of grain-boundary networks (particularly in twin-dominated systems) and is especially applicable to the field of grain-boundary engineering.

The α→ϵ phase transition in iron at strain rates up to ∼109 s−1

We have used a table-top scale laser to dynamically compress iron at strain rates in excess of 109 s−1. Using an embedded ultrafast interferometer, we have measured corresponding free surface histories with a time resolution of approximately 10 ps. We have analyzed the surface histories using a method that accounts for nonsteady wave propagation and time-dependent material behavior. We show that at these strain rates, the α→ϵ polymorphic transition begins within 100 ps after an initial very large (∼10 GPa) and mostly elastic compression and appears largely complete within a similar time thereafter. The corresponding deviatoric stress before the transition begins can exceed 3 GPa, while the transition stress itself is up to 25 GPa, nearly twice the value measured at low strain rates. We use these results to propose a systematic variation with loading time of the normal-stress/relative-volume curve followed by iron during rapid compression.

A unified approach for extracting strength information from nonsimple compression waves. Part II. Experiment and comparison with simulation

We apply general thermodynamics-based wave analysis methods to a gas-gun-driven plate impact experiment designed to derive strength information from tantalum at pressures of 10–25 GPa. The analysis provides estimates of the complete deformation paths in terms of the coupled evolution of mean stress, deviatoric stress, plastic strain, and plastic strain rate, yielding detailed information for direct comparison to strength models. This inverse analysis (deriving estimates of strength behavior directly from the measurements, with no strength model assumed) is compared to forward analysis (hydrodynamic simulations with specific strength models, in general adjusting parameters to optimally match the experiment). This comparison fulfills three goals. (1) To determine the parameter sensitivity and overall stability of the inverse analysis by analyzing simulated data as if it were experimental data. We find that, in reasonably favorable cases, precision to ∼10% is possible for the flow curve during loading and ∼3...

Scaling, Microstructure and Dynamic Fracture

The relationship between pullback velocity and impact velocity is studied for different microstructures in Cu. A size distribution of potential nucleation sites is derived under the conditions of an applied stochastic stress field. The size distribution depends on flow stress leading to a connection between the plastic flow appropriate to a given microstructure and nucleation rate. The pullback velocity in turn depends on the nucleation rate resulting in a prediction for the relationship between pullback velocity and flow stress. The theory is compared to observations of Cu on Cu gas-gun experiments (10-50 GPa) for a diverse set of microstructures. The scaling law is incorporated into a 1D finite difference code and is shown to reproduce the experimental data with one adjustable parameter that depends only on a nucleation exponent, {Lambda}.

A unified approach for extracting strength information from nonsimple compression waves. Part I: Thermodynamics and numerical implementation

We describe a comprehensive method of extracting estimates of the complete plastic deformation behavior, including full deviatoric-stress/plastic-strain (τ − ψ) curves, from one-dimensional dynamic compression experiments at moderate pressures (up to ∼50 GPa). The method combines and extends selected aspects of previous approaches and features a second-order velocity interpolation function designed to accommodate highly rate-dependent phenomena. Assumptions, and the expected limitations thereof, are made explicit and kept to a minimum. In particular, we do not assume any particular plasticity model, nor do we assume that the wave propagation is either simple or steady. Instead, we allow the data themselves to constrain any such behavior. We develop generalizations of standard equation-of-state analyses that account for the effects of rate-dependent relaxation on wave speeds and paths through thermodynamic space and show the potential to extract a great deal of strength information from the details of wave propagation.

Grain Size and Pressure Effects on Spall Strength in Copper

We are executing a systematic study to quantify the effects of specific microstructural features on the spall behavior of 99.999% copper. Single crystals with [100] orientation, polycrystals with three grain sizes, and internally oxidized single crystals are shocked with Cu flyers at velocities from 300 to 2000 m/s using a 35‐mm single/two‐stage light gas gun. VISAR measurements of the free surface velocity are used to characterize the spall pullback signal and details of the ringing. The high purity single crystals exhibit the highest spall strength followed by the large, medium and small grain size polycrystalline samples. Cu − 0.15 wt.% Si single crystals have been internally oxidized to produce a fine dispersion of 350 nm silica particles. These samples exhibit the lowest spall strength, a factor of two and greater below the high purity single crystals.

FREE SURFACE VELOCIMETRY CORRECTIONS FOR LOW PRESSURE SHOCKS

We consider how to interpret measured free surface velocities to estimate what a relatively weak shock (with an elastic‐plastic two‐wave structure, ∼5–30 GPa) would have looked like in an infinite sample. Hysteresis and nonlinear wave interactions introduce effects (inexact velocity doubling and the delay, partial reflection, and reverberation of waves) whose magnitudes can be estimated with simple models. We argue, and demonstrate in a simulated test case, that these estimates can eliminate most of the systematic error introduced by the free surface during loading.