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: In this article, a continuum model is developed to analytically predict the force-depth curve by coupling the classical Hertzian solution for elastic field and the evolution of dislocation density by considering multiple slip systems.
22 citations
TL;DR: In this article, it was shown that the plastic deformation of metallic crystals under intense shock wave loading is determined by the power-law pressure dependence of the density of geometrically necessary dislocations generated at the shock wave front ρ ∼ P3.
Abstract: The plastic deformation of metallic crystals under intense shock wave loading has been theoretically investigated. It has been experimentally found that the plastic strain rate \(\dot \varepsilon \) and the pressure in the wave P are related by the empirical expression \(\dot \varepsilon \) ∼ P4 (the Swegle-Grady law). The performed dislocation-kinetic analysis of the mechanism of the origin of this relationship has revealed that its power-law character is determined by the power-law pressure dependence of the density of geometrically necessary dislocations generated at the shock wave front ρ ∼ P3. In combination with the rate of viscous motion of dislocations, which varies linearly with pressure (u ∼ P), this leads to the experimentally observed relationship \(\dot \varepsilon \) ∼ P4 for a wide variety of materials with different types of crystal lattices in accordance with the Orowan relationship for the plastic strain rate \(\dot \varepsilon \) = bρu (where b is the Burgers vector). In the framework of the unified dislocation-kinetic approach, it has been theoretically demonstrated that the dependence of the pressure (flow stress) on the plastic strain rate over a wide range from 10−4 to 1010 s−1 reflects three successively developing processes: the thermally activated motion of dislocations, the viscous drag of dislocations, and the generation of geometrically necessary dislocations at the shock wave front.
22 citations
TL;DR: In this paper, a dynamic discrete dislocation plasticity (D3P) method is proposed to simulate dislocations under weak shock loading and high strain rate, which is a two-dimensional method of discrete dislocations dynamics aimed at the study of plastic relaxation processes in crystalline materials subjected to weak shockloading.
Abstract: This chapter concerns with dynamic discrete dislocation plasticity (D3P), a two-dimensional method of discrete dislocation dynamics aimed at the study of plastic relaxation processes in crystalline materials subjected to weak shock loading. Traditionally, the study of plasticity under weak shock loading and high strain rate has been based on direct experimental measurement of the macroscopic response of the material. Using these data, well-known macroscopic constitutive laws and equations of state have been formulated. However, direct simulation of dislocations as the dynamic agents of plastic relaxation in those circumstances remains a challenge. In discrete dislocation dynamics (DDD) methods, in particular the two-dimensional discrete dislocation plasticity (DDP), the dislocations are modeled as discrete discontinuities in an elastic continuum. However, current DDP and DDD methods are unable to adequately simulate plastic relaxation because they treat dislocation motion quasi-statically, thus neglecting the time-dependent nature of the elastic fields and assuming that they instantaneously acquire the shape and magnitude predicted by elastostatics. This chapter reproduces the findings by Gurrutxaga-Lerma et al. (2013) , who proved that under shock loading, this assumption leads to models that invariably break causality, introducing numerous artifacts that invalidate quasi-static simulation techniques. This chapter posits that these limitations can only be overcome with a fully time-dependent formulation of the elastic fields of dislocations. In this chapter, following the works of Markenscoff & Clifton (1981) and Gurrutxaga-Lerma et al. (2013) , a truly dynamic formulation for the creation, annihilation, and nonuniform motion of straight edge dislocations is derived. These solutions extend the DDP framework to a fully elastodynamic formulation that has been called dynamic discrete dislocation plasticity (D3P). This chapter describes the several changes in paradigm with respect to DDP and DDD methods that D3P introduces, including the retardation effects in dislocation interactions and the effect of the dislocation’s past history. The chapter then builds an account of all the methodological aspects of D3P that have to be modified from DDP, including mobility laws, generation rules, etc. Finally, the chapter explores the applications D3P has to the study of plasticity under shock loading.
20 citations
28 Mar 2019-Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
TL;DR: In this paper, the effects of pulse duration (plateau width) and strain rate (rising edge slope), and associated twin strengthening were investigated under quasi-isentropic compression (IC) and shock compression (SC) to about 12 GPa.
Abstract: Deformation twinning in a mild steel is investigated under quasi-isentropic compression (IC) and shock compression (SC) to about 12 GPa, as regards the effects of pulse duration (plateau width) and strain rate (rising edge slope), and associated twin strengthening. The pulse duration ranges from 80 ns to 790 ns; and two rise times are explored, approximately 30 ns for SC and 300 ns for IC. Free-surface velocity histories are measured to obtain strain and strain rate. The postmortem samples are characterized with electron backscatter diffraction, and the yield strengths of the samples pre-deformed by impact are examined with a materials testing system. For SC, twin density and size increase with pulse duration up to 580 ns. At longer pulse durations, the increase in twin density is stagnated as a result of deviatoric stress relaxation, while twin size continues growing. For IC (410 ns), twin density and size are much larger than the SC counterpart, as a result of shallower rising edge. Increased deformation time can compensate the effects of reduced strain rate or applied stress for deformation twinning. Twin strengthening effect is strong in postmortem samples, depends on twin density instead of area fraction, and follows the empirical Hall–Petch relationship.
20 citations
TL;DR: In this paper, multiple shots of femtosecond laser-driven shock pulses changed coarse crystalline iron grains with a size of 140 μm into nanocrystals with a high density of dislocations, which had never been observed in conventional shock processes.
Abstract: We found that multiple shots of femtosecond laser-driven shock pulses changed coarse crystalline iron grains with a size of 140 μm into nanocrystals with a high density of dislocations, which had never been observed in conventional shock processes. We performed metallurgical microstructure observations using transmission electron microscopy (TEM) and hardness measurements using nanoindentation on cross-sections of shocked iron. TEM images showed that grains with sizes from 10 nm through 1 μm exist within 2 μm of the surface, where the dislocation density reached 2 × 10{sup 15 }m{sup −2}. Results of the hardness measurements showed a significant increase in hardness in the nanocrystallized region. We suggest that the formation of a high density of dislocations, which is produced by a single shock, induces local three-dimensional pile-up by the multiple-shocks, which causes grain refinement at the nanoscale.
20 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