There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Review of experimental techniques for high rate deformation and shock studies

The dynamic tensile strength of materials at load durations of a few microseconds or less is studied by analyzing the spall phenomena under shock pulse loading. The paper is devoted to discussing the methodology and capabilities of the technique to measure spall strength, its error sources, spall fracture of materials of different classes and the factors governing the high-rate fracture of metals and alloys under such conditions.

Spall fracture: methodological aspects, mechanisms and governing factors

Microscopic mechanisms of photomechanical spallation are investigated in a series of large-scale molecular dynamics simulations performed for molecular and metal targets. A mesoscopic breathing sphere model is used in simulations of laser interaction with molecular targets. A coupled atomistic-continuum model that combines a molecular dynamics method with a continuum description of the laser excitation and subsequent relaxation of the conduction band electrons is used for metal targets. Similar mechanisms of the laser-induced photomechanical spallation are observed for molecular and metal targets. For both target materials, the relaxation of compressive stresses generated under conditions of stress confinement is found to be the main driving force for the nucleation, growth and coalescence of voids in a subsurface region of an irradiated target at laser fluences close to the threshold for fragmentation. The mechanical stability of the region subjected to the void nucleation is strongly affected by the laser heating and the depth of the spallation region in bulk targets is much closer to the surface as compared with the depth where the maximum tensile stresses are generated. Two stages can be identified in the evolution of voids in laser spallation, the initial void nucleation and growth, with the number of voids of all sizes increasing, followed by void coarsening and coalescence, when the number of large voids increases at the expense of the quickly decreasing population of small voids. The void volume distributions are found to be relatively well described by the power law N(V)∼V-τ, with exponent gradually increasing with time. Comparison of the simulation results obtained for Ni films of two different thicknesses and bulk Ni targets suggests that the size/shape of the target plays an important role in laser spallation. The reflection of the laser-induced pressure wave from the back surface of a film results in higher maximum tensile stresses and lower threshold fluence for spallation. As the size of the film increases, the locations of the spallation region and the region of the maximum tensile stresses are splitting apart and the threshold fluence for spallation increases.

Photomechanical spallation of molecular and metal targets: molecular dynamics study

High Rates and Impact Experiments

This article presents experimental results of the dynamic yield strength and dynamic tensile strength (“spall strength”) of aluminum single crystals at shock-wave loading as a function of temperature. The load duration was ∼40 and ∼200 ns. The temperature varied from 20 to 650 °C which is only by 10 °C below the melting temperature. A linear growth of the dynamic yield strength by more than a factor of 4 was observed within this temperature range. This is attributed to the phonon drag effect on the dislocation motion. High dynamic tensile strength was maintained over the whole temperature range, including the conditions at which melting should start in a material under tension. This could be an indication of the existence of superheated states in solid crystals.

Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point

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 amplitudes for the Hugoniot elastic limit of both aluminum and magnesium were observed at temperatures approaching the melting point.

Spall fracture properties of aluminum and magnesium at high temperatures

We review the latest results of investigations into polymorphous transformations, the deformation, and the fracture of solids in different structural states subjected to shock waves of submicrosecond duration. The problem of attaining the ideal strength of a condensed material is discussed. An anomalous rise in dynamic yield stress as the in test temperature increases was discovered for high-purity metals. The effects of superheating in the crystal state and premelting under tension, as well as failure waves in shock-compressed glasses, were also discovered.

https://iopscience.iop.org/article/10.1070/PU2007v050n08ABEH006327/pdf

Shock waves in condensed-state physics

Spall strength measurements for commerical grade molybdenum and molybdenum single crystals were made in a wide range of load durations (∼10−9 s – 10−6 s) and intensities (∼5 – 100 GPa). Resistance to fracture of pure single crystals was found to exceed two times the spall strength of polycrystalline molybdenum and to increase with shorter load duration. The value of the shock wave amplitude does not influence the spall strength of single crystals. The largest spall strength obtained under nanosecond load duration amounts to 30% of the ultimate theoretical strength.

S. V. Razorenov

Papers

Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point

Spall fracture properties of aluminum and magnesium at high temperatures

Shock waves in condensed-state physics

Spall strength of molybdenum single crystals

Simulation of spall fracture of aluminum and magnesium over a wide range of load duration and temperature