Slip band formation and mobile dislocation density generation in high rate deformation of single fcc crystals

The mechanisms for the nucleation, thickening, and growth of crystallographic slip bands from the sub-nanoscale to the microscale are studied using three-dimensional dislocation dynamics. In the simulations, a single fcc crystal is strained along the [111] direction at three different high strain rates: 10⁴, 10⁵, and 10⁶?s^??1. Dislocation inertia and drag are included and the simulations were conducted with and without cross-slip. With cross-slip, slip bands form parallel to active (111) planes as a result of double cross-slip onto fresh glide planes within localized regions of the crystal. In this manner, fine nanoscale slip bands nucleate throughout the crystal, and, with further straining, build up to larger bands by a proposed self-replicating mechanism. It is shown that slip bands are regions of concentrated glide, high dislocation multiplication rates, and high dislocation velocities. Cross-slip increases in activity proportionally with the product of the total dislocation density and the square root of the applied stress. Effects of cross-slip on work hardening are attributed to the role of cross-slip on mobile dislocation generation, rather than slip band formation. A new dislocation density evolution law is presented for high rates, which introduces the mobile density, a state variable that is missing in most constitutive laws.     

Plastic deformation at high strain rates

In the present paper a new method, an original testing device and techniques for the study of plastic deformation in materials at high strain rates up to 2×10⁴ s^–1 achieved with the use of very short stress pulses (length within 10–20 s) are described. The suggested method of yieldpoint determination respects the effects of delayed plastic deformation in the yield point at loading by very short intensive stress pulses. The investigations were carried out in polycrystalline ARMCO-iron and low-alloyed steel, and besides on the specimens irradiated by neutrons with integral dose 1·35×10¹⁹ ncm^–2. The experimental results obtained are interpreted from the point of view of the present knowledge of the process of plastic deformation in bcc metals.     

Extended planar boundary inclinations in fcc single crystals and polycrystals subjected to plane strain deformation

When fcc single crystals with high-symmetry crystal orientations are deformed to moderate strains by rolling, tension or channel die compression, long dislocation boundaries inclined to the extension axis form. Similarly, long dislocation boundaries are often found in grains embedded in polycrystals deformed in the same manner. These extended planar boundaries (EPBs) are characteristically -30-40° from the extension direction and contain the transverse specimen axis. The objective of the present article is to demonstrate that EPBs formed during plane strain deformation are parallel to equivalent slip planes, a pair of hypothetical slip systems used for analyses of the strain and crystal rotation components in place of the larger number of physical slip systems. The coincidence of EPBs and equivalent slip plane inclinations is shown to account for persistent observations of EPBs in the angle range -30-40° from the rolling direction, in rolled single crystals of various initial orientations. The tendency of EPBs towards tilt or twist boundary character can also be rationalized on the basis of the equivalent slip system concept and consideration of the dislocation types available to be incorporated into EPBs.     

Dislocational kinetics in the intense deformation of fcc single crystals

The stability of the dislocational subsystem of fcc single crystals deformed in dynamic conditions is investigated. It is shown that, depending on the deformational conditions, the system may have one or two steady states, one of which is ρ _s ⁽¹⁾ . When the system has one trivial steady state, it may be stable or unstable. In some conditions, a second unstable point ρ _s ⁽²⁾ appears; in this case, ρ _s ⁽¹⁾ is stable. Tomsk State Architectural and Building Academy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 43–48, August, 1997.     

Modeling of the evolution of a dislocation structure and development of microplastic deformation in single crystals of fcc substitutional solid solutions

An analysis is made of evolution of a dislocation structure during the initial stage of plastic deformation and the stress-strain diagrams are derived theoretically for single crystals of fcc substitutional solid solutions. The example of Cu-Al alloys is used to confirm the theoretically predicted relationship between the stress and strain, and also between the flow stress and the resistance to the motion of a single dislocation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 93–97, July, 1980.     

High temperature deformation and extended plasticity in Mg single crystals

The high temperature deformation behavior of Mg single crystals was precisely investigated using orientation imaging microscopy. For this purpose, Mg single crystals of various orientations were tensile tested in vacuum at temperatures between 473 and 673?K. A strain rate of 4.2?×?10^?4?s^?1 was employed. The elongations to fracture depended strongly on crystal orientation, the lowest fracture strains being associated with multiple slip. Single crystals in which single slip was activated exhibited extended ductilities corresponding to more than 1.5 in true strain. The strong orientation dependence of the ductility can also be correlated with the ease of occurrence of dynamic recrystallization (DRX), which took place in the multiple-slip specimens. The role of twinning in the initiation of DRX is also discussed.     

Shear localization in dynamic deformation of copper single crystals

Dynamic deformation of copper single crystals, especially of fatigued copper single crystals with different orientations, was conducted on a split-Hopkinson pressure bar apparatus. The strain rates were in the range 2???9?×?10³?s^?1. After dynamic deformation, the adiabatic shear bands (ASBs) were examined in a light microscope and SEM. The width and spacing of ASBs formed under different strain rates in a fatigued copper single crystal were measured and the spacing of ASBs is one-order of magnitude smaller than the theoretical predictions. The possible reasons for the discrepancy were discussed. The critical strains for the ASB formation in four different orientated single crystals at stain rate of about 4?×?10³?s^?1 were determined by examining the post-deformation specimens and dynamic stress–strain curves. It is clearly indicated that the critical strains for the ASB formation are orientation-dependent in copper single crystals. A simple microscopic mechanism for ASB formation in fatigued single crystals was proposed.     

Mechanoluminescence induced by elastic and plastic deformation of coloured alkali halide crystals at fixed strain rates

Mechanoluminescence (ML) emission from coloured alkali halide crystals takes place during their elastic and plastic deformation. The ML emission during the elastic deformation occurs due to the mechanical interaction between dislocation segments and F-centres, and the ML emission during the plastic deformation takes place due to the mechanical interaction between the moving dislocations and F-centres. In the elastic region, the ML intensity increases linearly with the strain or deformation time, and in this case, the saturation region could not be observed because of the beginning of the plastic deformation before the start of the saturation in the ML intensity. In the plastic region, initially the ML intensity also increases linearly with the strain or deformation time, and later on, it attains a saturation value for large deformation. When the deformation is stopped, initially the ML intensity decreases at a fast rate; later on, it decreases at a slow rate. The decay time for the fast decrease of the ML intensity gives the relaxation time of dislocation segments or pinning time of the dislocations, and the decay time of the slow decrease of the ML intensity gives the diffusion time of holes in the crystals. The saturation value of the ML intensity increases linearly with the strain rate and also with the density of F-centres in the crystals. Initially, the saturation value of the ML intensity increases with increasing temperature, and for higher temperatures the ML intensity decreases with increasing temperature. Therefore, the ML intensity is optimum for a particular temperature of the crystals. From the ML measurements, the relaxation time of dislocation segments, pinning time of dislocations, diffusion time of holes and the energy gap between the bottom of the acceptor dislocation band and interacting F-centre level can be determined. Expressions derived for the ML induced by elastic and plastic deformation of coloured alkali halide crystals at fixed strain rates indicates that the ML intensity depends on the strain, strain rate, density of colour centres, size of crystals, temperature, luminescence efficiency, etc. A good agreement is found between the theoretical and experimental results.     

Multiphysical simulation analysis of the dislocation structure in germanium single crystals

To grow high-quality germanium crystals is one of the most important problems of growth industry. The dislocation density is an important parameter of the quality of single crystals. The dislocation densities in germanium crystals 100 mm in diameter, which have various shapes of the side surface and are grown by the Czochralski technique, are experimentally measured. The crystal growth is numerically simulated using heat-transfer and hydrodynamics models and the Alexander–Haasen dislocation model in terms of the CGSim software package. A comparison of the experimental and calculated dislocation densities shows that the dislocation model can be applied to study lattice defects in germanium crystals and to improve their quality.     

Effect of stacking-fault energy on the development of a dislocation substructure,strain hardening,and plasticity of fcc solid solutions

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 35–46, March, 1991.     

Relaxation processes in metals at high strain rates

Mathematical modeling is used for experiments involving the loading of plates by plane shock waves to study the relaxation of shear stresses during the high-rate deformation of metallic materials. It is established that the characteristic relaxation times vary broadly — from fractions of a nanosecond to several microseconds. Such variation is indicative of a change in the mechanism responsible for relaxation. As a result, there is a difference between the quasi-equilibrium shear stresses in the elastic precursor and the same stresses behind the shock front. Metallic materials remain capable of resisting plastic deformation behind the front. Structural irregularities created by high-rate deformation result in localization of plastic flow at the microscopic level, which in turn causes the parameters of the stress-strain state at this level to differ from the corresponding parameters on the macroscopic scale.Siberian Physico-Technical Institute, affiliated with Tomsk University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 82–90, August, 1995.     

Plastic shear response of a single asperity: a discrete dislocation plasticity analysis

We investigate the plastic shear response during static friction of an asperity protruding from a large FCC single crystal. The asperity is in perfectly adhesive contact with a rigid platen and is sheared by tangentially moving the platen. Using discrete dislocation plasticity simulations, we elucidate the plastic shear behaviour of single asperities of various size and shape, in search for the length scale that controls the plastic behaviour. Since plasticity can occur also in the crystal, identification of the length scale that controls a possible size-dependent plastic behaviour is far from being trivial. It is found that scaling down the dimensions of an asperity results in a higher contact shear strength. The contact area is dominant in controlling the plastic shear response, because it determines the size of the zone, in and below the asperity, where dislocation nucleation can occur. For a specific contact area, there is still a dependence on asperity volume and shape, but this is weaker than the dependence on contact area alone.     

Supersonic dislocation stability and nano-twin formation at high strain rate

Improved understanding of the plastic deformation of metals during high-strain-rate shock loading is key to predicting their resulting material properties. This paper presents the results of molecular-dynamics simulations which address two fundamental questions related to materials deformation: the stability of supersonic dislocations and the mechanism of nano-twin formation. The results show that aluminium plastically deforms by the subsonic motion of edge dislocations when subjected to applied shear stresses of up to 600?MPa. Although higher applied stresses initially drive transonic dislocations, this motion is transient, and the dislocations decelerate to a sustained subsonic saturation velocity. Slowing of the transonic dislocation is controlled by the interaction with excited Rayleigh waves. 800?MPa marks a critical shear stress at which dislocation glide gives way to nano-twin formation via the homogeneous nucleation of Shockley partial dislocation dipoles. At still higher applied stresses, additional dislocation dipole nucleation produces a mid-stacking fault transformation of the twinned material.     

Modelling plasticity of Ni3Al-based L12 intermetallic single crystals. II. Two-step ( T 1 and T 2) deformation behaviour

The two-step (T ₁ and T ₂) deformation behaviour of Ni₃Al-based single crystals was modelled under the framework of a new constitutive model proposed by Y.S. Choi, D.M. Dimiduk, M.D. Uchic, et al. [Phil. Mag. 87 1939 (2007)]. A new set of formulations and criteria, which identify thermally reversible and irreversible components of the constitutive variables and define the relative significance of those components, was developed and implemented within the new constitutive framework. The simulation results well captured the general qualitative trends of the flow behaviour upon re-straining at T ₂ after pre-straining at T ₁ for both T ₁?>?T ₂ and T ₁?<?T ₂. Modelling results suggested that the dislocation substructures generated at T ₁ need to be treated as partially or fully transferable to plastic flow at T ₂, at least through the early stage of re-straining, to capture all major pre-strain effects. In particular, the large strengthening effect at T ₂ for even a few percent of pre-strain at T ₁ was obtainable only by controlling the availability of mobile dislocations and sources at T ₂.     

A quantum field theory of lattice dynamics and melting in fcc crystals

Phonons in crystals are constructed by particle-hole excitations of ion cores. The Ward-Takahashi relations play an essential role in constructing the lattice dynamics and determining the melting temperature. The phonon dispersion and the melting temperature in fcc crystals are presented. In principle, our theory covers metallic, covalent and molecular crystals.     

Study of the atomic structure of bcc and fcc crystals upon instantaneous plastic deformation

The evolution of the atomic structure of face-centered cubic (fcc) and body-centered cubic (bcc) crystals under the conditions of pulsed external loads and large plastic strains is investigated on the basis of computer experiments. The crystals are strained in steps to 32%. After each deformation step (2%), the system is relaxed by molecular dynamics to a new equilibrium state at 300 K. The results of the computer experiments show that plastic deformation can take place under instantaneous external loads either as a result of the motion of partial dislocations, twinning, or the turning and displacement of atomic planes, depending on the stage of the process. The laws governing the variation of the potential energy of the system and the rotation angle of the atomic planes as functions of the degree of plastic strain of the crystal are found. Zh. Tekh. Fiz. 67, 100–102 (December 1997)     

Localized strain autowaves at the initial stage of plastic flow in single crystals

Plastic strain localization in single crystals of pure metals and alloys is studied on the yield plateau and at the easy glide stage with a zero or small strain hardening coefficient. The difference between localization patterns in the two cases is explained, and strain localization mechanisms are suggested. At these stages of plastic deformation, various types of autowaves are observed.