Laser-induced shock compression of monocrystalline copper: characterization and analysis
TL;DR: In this paper, a method for estimating dislocation densities is proposed, based on nucleation of loops at the shock front and their extension due to residual shear stresses behind the front.
About: This article is published in Acta Materialia.The article was published on 2003-03-14. It has received 219 citations till now. The article focuses on the topics: Slip (materials science) & Crystal twinning.
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TL;DR: A nonlinear anisotropic continuum framework for describing the thermoelastic-plastic response of single crystals shocked along arbitrary orientations has been developed in this article, which incorporates nonlinear elasticity, crystal plasticity, and thermodynamic consistency within an incremental tensor formulation.
Abstract: A nonlinear anisotropic continuum framework for describing the thermoelastic-plastic response of single crystals shocked along arbitrary orientations has been developed. Our modeling approach incorporates nonlinear elasticity, crystal plasticity, and thermodynamic consistency within an incremental tensor formulation. Crystal plasticity was incorporated by considering dislocation motion along specified slip planes. The theoretical developments presented here are sufficiently general to also accommodate other types of inelastic deformation mechanisms. As representative applications of the theoretical developments, numerical simulations of shock wave propagation in lithium fluoride (LiF) and copper single crystals are presented and compared to wave profile data for several crystal orientations. Simulations of shock wave propagation along low-symmetry directions, where data are not available, are also presented to examine the propagation of quasilongitudinal and quasishear waves in crystals undergoing elastic-plastic deformation. Temperature calculations for the shocked single crystals are discussed.
64 citations
TL;DR: In this article, the authors examined the time to activate Frank-Read sources in response to macroscopic strain rates ranging from 10 1 ǫs −1 to 10 10 s −1 in aluminium under athermal conditions.
Abstract: This article examines the time to activate Frank–Read sources in response to macroscopic strain rates ranging from 10 1 s −1 to 10 10 s −1 in aluminium under athermal conditions. We develop analytical models of the bowing of a pinned dislocation segment as well as numerical simulations of three dimensional dislocation dynamics. We find that the strain rate has a direct influence on both the activation time and the source strength of Frank–Read sources at strain rates up to 10 6 s −1 , and the source strength increases in almost direct proportion to the strain rate. This contributes to the increase in the yield stress of materials at these strain rates. Above 10 6 s −1 , the speed of the bowing segments reaches values that exceed the domain of validity of the linear viscous drag law, and the drag law is modified to account for inertial effects on the motion of the dislocation. As a result the activation times of Frank–Read sources reach a finite limit at strain rates greater than 10 8 s −1 , suggesting that Frank–Read sources are unable to operate before homogeneous nucleation relaxes elastic stresses at the higher strain rates of shock loading. Elastodynamic calculations are carried out to compare the contributions of Frank–Read sources and homogeneous nucleation of dislocations to plastic relaxation. We find that at strain rates of 5×10 7 s −1 homogeneous nucleation becomes the dominant generation mechanism.
62 citations
TL;DR: In this paper, a general dislocation evolution equation is derived for a wide range of strain rates and it is found that there is a transitional strain rate (∼10 3 ǫ s −1 ) over which the phonon drag effects play a dominant role in dislocation generation resulting in a significant raise in the dislocation density and flow stress.
58 citations
TL;DR: In this paper, the effects of shock compression on [001] and [221] monocrystals were modeled using molecular dynamics simulations, and the formation of a two-wave structure was analyzed.
Abstract: Molecular dynamics (MD) simulations were used to model the effects of shock compression on [001] and [221] monocrystals. We obtained the Hugoniot for both directions, and analyzed the formation of a two-wave structure for the [221] monocrystal. We also analyzed the dislocation structure induced by the shock compression along these two crystal orientations. The topology of this structure compares extremely well with that observed in recent transmission electron microscopy (TEM) studies of shock-induced plasticity in samples recovered from flyer plate and laser shock experiments. However, the density of stacking faults in our simulations is 102 to 104 times larger than in the experimental observations of recovered samples. The difference between experimentally observed TEM and calculated MD results is attributed to two effects: (1) the annihilation of dislocations during post-shock relaxation (including unloading) and recovery processes and (2) a much shorter stress rise time at the front in MD (<1 ps) in comparison with flyer-plate shock compression (∼1 ns).
57 citations
TL;DR: In this article, the relationship between spall damage and local microstructure was investigated in multicrystalline copper samples via impact tests conducted with laser-driven plates at low pressures (2-6 GPa).
Abstract: Correlations between spall damage and local microstructure were investigated in multicrystalline copper samples via impact tests conducted with laser- driven plates at low pressures (2-6 GPa). The copper samples had a large grain size as compared to the thickness, which was either 200 or 1000mm, to isolate the effects of microstructure on the local response. Velocity interferometry was used to measure the bulk response of the free-surface velocity of the samples to monitor traditional spall tensile failure and to examine heterogeneities on the shock response due to microstructure variability from sample to sample. The shock pressure, dynamic yield strength and spall strength were determined from the measured velocity history via standard hydrodynamic approximations, while the effect of strength was explored via 1D hydrocode calculations. Electron Backscattering Diffraction, both in-plane and through-thickness, was used to relate crystallography to the presence of porosity around microstructural features such as grain boundaries and triple points. It was found that the dynamic yield strength measured from velocity histories in different samples correlated well with the crystallographic dependence reported for the dynamic yield strength in single crystals. Transgranular damage dominated in thin specimens with 230mm grain size, where porosity appeared close to, but not exactly at, grain boundaries. However, a transition to dominant intergranular damage was
57 citations
References
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27 Sep 1994
TL;DR: In this paper, the authors present a method to produce dynamic deformation at high strain rates by using Shear Bands (Thermoplastic Shear Instabilities) and dynamic fracture.
Abstract: Dynamic Deformation and Waves. Elastic Waves. Plastic Waves. Shock Waves. Shock Waves: Equations of State. Differential Form of Conservation Equations and Numerical Solutions to More Complex Problems. Shock Wave Attenuation, Interaction, and Reflection. Shock Wave-Induced Phase Transformations and Chemical Changes. Explosive-Material Interactions. Detonation. Experimental Techniques: Diagnostic Tools. Experimental Techniques: Methods to Produce Dynamic Deformation. Plastic Deformation at High Strain Rates. Plastic Deformation in Shock Waves. Shear Bands (Thermoplastic Shear Instabilities). Dynamic Fracture. Applications. Indexes.
2,609 citations
"Laser-induced shock compression of ..." refers background or methods in this paper
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...The dislocation density can be expressed as a function of pressure, P, through one of the equations obtained directly from the Rankine–Hugoniot equations and the equation of state [22]:...
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...In a similar manner, the residual temperature, TR, can be obtained from [22]:...
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TL;DR: An improved description of copper and ironcylinder impact (Taylor) test results has been obtained through the use of dislocation-mechanics-based constitutive relations in the Lagrangian material dynamics computer program EPIC•2.
Abstract: An improved description of copper‐ and iron‐cylinder impact (Taylor) test results has been obtained through the use of dislocation‐mechanics‐based constitutive relations in the Lagrangian material dynamics computer program EPIC‐2. The effects of strain hardening, strain‐rate hardening, and thermal softening based on thermal activation analysis have been incorporated into a reasonably accurate constitutive relation for copper. The relation has a relatively simple expression and should be applicable to a wide range of fcc materials. The effect of grain size is included. A relation for iron is also presented. It also has a simple expression and is applicable to other bcc materials but is presently incomplete, since the important effect of deformation twinning in bcc materials is not included. A possible method of acounting for twinning is discussed and will be reported on more fully in future work. A main point made here is that each material structure type (fcc, bcc, hcp) will have its own constitutive beha...
1,718 citations
TL;DR: In this article, a constitutive expression for the twinning stress in BCC metals is developed using dislocation emission from a source and the formation of pile-ups, as rate-controlling mechanism.
1,366 citations
TL;DR: In this paper, a periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip, which allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack.
Abstract: Dislocation nucleation from a stressed crack tip is analyzed based on the Peierls concept. A periodic relation between shear stress and atomic shear displacement is assumed to hold along the most highly stressed slip plane emanating from a crack tip. This allows some small slip displacement to occur near the tip in response to small applied loading and, with increase in loading, the incipient dislocation configuration becomes unstable and leads to a fully formed dislocation which is driven away from the crack. An exact solution for the loading at that nucleation instability is developed via the J -integral for the case when the crack and slip planes coincide, and an approximate solution is given when they do not. Solutions are also given for emission of dissociated dislocations, especially partial dislocation pairs in fcc crystals. The level of applied stress intensity factors required for dislocation nucleation is shown to be proportional to √γ us , where γ us , the unstable stacking energy, is a new solid state parameter identified by the analysis. It is the maximum energy encountered in the block-like sliding along a slip plane, in the Burgers vector direction, of one half of a crystal relative to the other. Approximate estimates of γ us are summarized and the results are used to evaluate brittle vs ductile response in fcc and bcc metals in terms of the competition between dislocation nucleation and Griffith cleavage at a crack tip. The predictions seem compatible with known behavior and also show that in many cases solids which are predicted to first cleave under pure mode I loading should instead first emit dislocations when that loading includes very small amounts of mode II and III shear. The analysis in this paper also reveals a feature of the near-tip slip distribution corresponding to the saddle point energy configuration for cracks that are loaded below the nucleation threshold, as is of interest for thermal activation.
1,320 citations
01 Jan 1940
TL;DR: In this paper, the size of a dislocation and critical shear stress for its motion were calculated for a single dislocation with respect to the size and motion of the dislocation.
Abstract: Calculations are made of the size of a dislocation and of the critical shear stress for its motion.
1,226 citations