Low Energy Dislocation Structure Research Articles

In-situ TEM investigation of structural transformation from LEDS to twin in fatigued Cu single crystal during annealing

ABSTRACT Low-energy dislocation structure is one classical self-organised dislocation pattern, among which persistent slip band (PSB) ladders is the most representative. Periodically distributed PSB ladders consist of two phases: matrix phase and pattern phase. In the new two-phase model, the appearance of pattern phase results in the softening of PSBs with lower elastic constant. The formation of PSB ladders reflects two kinds of dynamic equilibriums: (i) bowing out and annihilation between unlike screw dislocations; (ii) multiplication and annihilation between unlike edge dislocations in the rung. Subsequently, in-situ annealing experiments indicate that most of the dislocations are annihilated and a few dislocations rearrange to result in the nucleation and growth of the twin. In a word, both the evolution of dislocation patterns and the transition from LEDS to twin structures are the process of energy redistribution. Controlling the stored energy per unit area will effectively improve the formation of distribution of defects, which will benefit to design the metallic materials based on the defect-engineering strategy.

INVESTIGATIONS ON THERMAL STABILITY OF FATIGUE DISLOCATION STRUCTURES IN CONJUGATE AND CRITICAL DOUBLE-SLIP-ORIENTED Cu SINGLE CRYSTALS

It is well known that the cyclic deformation behavior and dislocation structures of Cu single crystals with different orientations have been systematically investigated and understood. However, there is as yet no general and unequivocal knowledge of the thermal stability of fatigue-induced dislocation structures in Cu single crystals, which is particularly significant for the further improvement of low energy dislocation structure (LEDS) theory. In previous work, the thermal stability of fatigue dislocation structures in [4 18 41] single-slip and [233] coplanar doubleslip Cu single crystals have been reported. For deeply understanding the orientationdependent *国家自然科学基金项目51071041, 51231002, 51271054和51571058,以及高等学校博士学科点专项科研基金博导类项目20110042110017资助 收到初稿日期: 2015-11-09,收到修改稿日期: 2016-01-20 作者简介:郭巍巍,女,蒙古族, 1985年生,博士生 DOI: 10.11900/0412.1961.2015.00572 第761-768页 pp.761-768

Low-Energy Dislocation Structure (LEDS) character of dislocation boundaries aligned with slip planes in rolled aluminium

For the specific slip geometry of two sets of coplanar systems (a total of four systems) in fcc metals, the range of dislocation networks in boundaries aligned with one of the two active slip planes is predicted from the Frank equation for boundaries free of long-range elastic stresses. Detailed comparison with experimental data for eight dislocation boundaries in cold-rolled aluminium grains of the 45° ND rotated Cube orientation is conducted. It is concluded that the boundaries are Low-Energy Dislocation Structures, which are in good agreement with the Frank equation while also lowering the energy by dislocation reactions. Cross slip plays a role in the boundary formation process.

Effects of residual stress and interface dislocations on the ionic conductivity of yttria stabilized zirconia nano-films

The effects of residual stress and interface dislocations on the ionic conductivity of yttria stabilized zirconia (YSZ) polycrystalline nano-films deposited onto quartz substrate via pulsed-DC magnetron sputtering are systematically studied. The residual stress of YSZ film is evaluated by a cos2αsin2ψ method. The X-ray diffraction data indicates that a peening-induced compressive residual stress develops in the as-deposited film, increases with film thickness, and decreases the ionic conductivity. On the other hand, a thermal-mismatch-induced tensile residual stress develops in the annealed film, increases with annealing temperature, decreases with film thickness, and enhances the ionic conductivity. Ionic conductivities higher than the YSZ bulk are measured in both the as-deposited and annealed YSZ nano-films, indicating the existence of interface enhancement effect on the ionic conductivity. A type of low-energy dislocation structure forms next to the interface by sputtering, which hinders oxygen ion diffusion along the interface and lowers the ionic conductivity.

Equal Channel Angular Pressing of Al Alloy AA2219

Severe plastic deformation processes (SPD) are gaining importance as advanced materials processing techniques and hold immense potential in obtaining ultra fine-grained high strength materials. Among the SPD techniques, Equal channel angular pressing (ECAP) has its own merits to produce materials with ultra fine grains in bulk with better mechanical properties. The material deforms with high level of plastic strain inside the channel resulting in grain refinement of the output material with improvement in mechanical properties. A very viable die configuration was conceptualized and die was made with 1200 channel angle. Processing of 25 mm dia. of Al alloy AA2219 at room temperature was successfully carried out and grain refinement was observed. The mechanism of grain refinement has been studied using optical and transmission electron microscopy (TEM). It was observed that low energy dislocation structure (LEDS) forms concurrently with sub-grain structure due to dislocation rearrangements, which provide stability to the evolving sub-grain structure. Dislocation mobility is hindered by the presence of precipitates and / or intermetallic dispersoids present in the matrix and results in presence of dislocations in grain interiors. The pile up of dislocations at intermetallic dispersoids was confirmed from the dark field TEM micrographs. Present paper describes the experimental procedure and followed to attain severe plastic deformation through ECAP. Increase in hardness as well as refinement in the grain size after 5-passes have been discussed in light of extensive optical and TEM. The mechanisms of grain refinement to achieve nano-grained structure and strengthening accrued from the grain refinement through ECAP has been discussed.

Microstructure and texture evolution during ECAP of an AlMgSi alloy: Observations, mechanisms and modeling

Deformation banding and accompanying texture component rotations towards more stable orientations played an important role to grain sub-division and during the development of new high angle grain boundaries. The low energy dislocation structure (LEDS) approach predicted deformation band size in close correspondence to the present observations, and the proposed grain refinement mechanism. Formation of twin boundaries seemed to play an important role at strains beyond two.

Irradiation-Induced Recrystallization of Cellular Dislocation Networks in Uranium-Molybdenum Alloys

ABSTRACTWe developed a rate-theory-based model to investigate the nucleation and growth of interstitial loops and cavities during low-temperature in-reactor irradiation of uranium-molybdenum alloys. Consolidation of the dislocation structure takes into account the generation of forest dislocations and capture of interstitial dislocation loops. The theoretical description includes stress-induced glide of dislocation loops and accumulation of dislocations on cell walls. The loops accumulate and ultimately evolve into a low-energy cellular dislocation structure. Calculations indicate that nanometer-size bubbles are associated with the walls of the cellular dislocation structure. The accumulation of interstitial loops within the cells and of dislocations on the cell walls leads to increasing values for the rotation (misfit) of the cell wall into a subgrain boundary and a change in the lattice parameter as a function of dose. Subsequently, increasing values for the stored energy in the material are shown to be sufficient for the material to undergo recrystallization. Results of the calculations are compared with SEM photomicrographs of irradiated U- 10Mo, as well as with data from irradiated UO2.

Deformation bands, the LEDS theory, and their importance in texture development: Part II. Theoretical conclusions

The facts regarding “regular” deformation bands (DBs) outlined in Part I of this series of articles are related to the low-energy dislocation structure (LEDS) theory of dislocation-based plasticity. They prompt an expansion of the theory by including the stresses due to strain gradients on account of changing selections of slip systems to the previously known dislocation driving forces. This last and until now neglected driving force is much smaller than the components considered hitherto, principally due to the applied stress and to mutual stress-screening among neighbor dislocations. As a result, it permits a near-proof of the LEDS hypothesis, to wit that among all structures which, in principle, are accessible to the dislocations, that one is realized which has the lowest free energy. Specifically, the temperature rises that would result from annihilating the largest DBs amount to only several millidegrees Centigrade, meaning that they, and by implication the entire dislocation structures, are close to thermodynamical equilibrium. This is in stark contrast to the assumption of the presently widespread self-organizing dislocation structures (SODS) modeling that plastic deformation occurs far from equilibrium and is subject to Prigogine’s thermodynamics of energy-flow-through systems. It also holds out promise for future rapid advances in the construction of constitutive equations, since the LEDS hypothesis is the principal basis of the LEDS theory of plastic deformation and follows directly from the second law of thermodynamics in conjunction with Newton’s third law. By contrast, all other known models of metal plasticity are in conflict with the LEDS hypothesis. In regard to texture modeling, the present analysis shows that Taylor’s criterion of minimum plastic work is incorrect and should be replaced by the criterion of minimum free energy in the stressed state. Last, the LEDS hypothesis is but a special case of the more general low-energy structure (LES) hypothesis, applying to plastic deformation independent of the deformation mechanism. It is thus seen that plastic deformation is one of nature’s means to generate order, as a byproduct of the entropy generation when mechanical work is largely converted into heat.

Does plastic deformation proceed near thermodynamic equilibrium? The case made for shear-strained lamellar diblock copolymers

Observations on kink bands in lamellar diblock copolymers (SEP 40–70), caused by unidirectional or oscillatory shear strain, are interpreted in terms of the low-energy structure (LES) hypothesis, to wit: “In a material subject to mechanical stresses, that structure will be approached which has the lowest free energy among all structures which are in equilibrium with the tractions and are accessible to the system.” This is the generalization of the low-energy dislocation structure (LEDS) hypothesis applicable to dislocation structures in crystalline materials. In agreement with the LES hypothesis, moderate fatigue cycling of initially disordered material establishes an order such that the plane of the lamellae is parallel to the plane of shear stress application, being the orientation of lowest shear modulus and, hence, for fixed fatigue amplitude, of lowest strain energy. At fatigue strain amplitudes above about 40% the material develops kink bands on account of the compressive stress along the body diagonal of the samples. The geometry of these kink bands shows that the plane parallel to the lamellae serves as preferred slip plane with the lowest resistance against sliding among all possible directions. Also the kink band morphology conforms with the LES hypothesis. Specifically, on average the ratio of kink band length (L) to the square of kink band width (W), i.e., L/W2, is nearly constant as expected from the minimization of kink band boundary energy and the elastic strain energy on account of the strain discontinuity at the ends of the bands. Subsequent experiments on a different copolymer in a range of temperatures additionally verify the LES hypothesis through establishing that, throughout, large-amplitude cycling causes the lamella orientation of lowest shear modulus.

The theory of dislocation-based crystal plasticity

Abstract An overview of the low-energy dislocation structure (LEDS) theory of low-temperature, that is non-creep, dislocation-based crystal plasticity is presented, as systematically developed over the past 35 years. It is ultimately based on G. I. Taylor's 1934 theory of work hardening wherein he assumed that stress application causes the essentially instantaneous athermal generation of dislocation structures which are in equilibrium with the applied stress and which on stress release and reversal are stable up to the previously highest stress magnitude. As will be shown, at least in principle even though many details are still lacking, the following phenomena of crystal plasticity are readily explained by means of the LEDS theory: (1) the four stages of work hardening; (2) the shape of the stress-strain curve; (3) the temperature dependence of work hardening; (4) the low-temperature strain rate dependence of the flow stress; (5) the difference between ‘planar’ and ‘wavy’ glide materials (as exemplified by α-brass and copper respectively); (6) the empirical relationship D = KGb/T between dislocation cell size and flow stress; (7) grain-boundary hardening; (8) alloy hardening including solid-solution, precipitation and phase-boundary hardening; (9) slip lines and slip bands; (10) the evolution of the dislocation structures from stages I to IV; (11) deformation texture evolution; (12) work softening; (13) the thermodynamics of dislocation storage; (14) recovery, creep and recrystallization; (15) the development of dislocation structures in fatigue. All these are explained effortlessly on the basis of only the known properties of glide dislocations and the second law of thermodynamics, as expressed in the LEDS hypothesis, to wit that, among the structures which are in equilibrium with the applied tractions and accessible to the dislocations, those are formed which most nearly minimize the stored energy. (See Note added in proof at end of this paper.) The alternative ‘self-organizing dislocation’ model of crystal plasticity assumes plastic deformation to be due to individual thermally activated processes, which are treatable by the thermodynamics of energy-flow-through systems. It can be traced back to the early theory by R. Becker in 1925 and 1926 and still has to yield significant results.

The theory of dislocation-based crystal plasticity

Abstract An overview of the low-energy dislocation structure (LEDS) theory of low-temperature, that is non-creep, dislocation-based crystal plasticity is presented, as systematically developed over the past 35 years. It is ultimately based on G. I. Taylor's 1934 theory of work hardening wherein he assumed that stress application causes the essentially instantaneous athermal generation of dislocation structures which are in equilibrium with the applied stress and which on stress release and reversal are stable up to the previously highest stress magnitude. As will be shown, at least in principle even though many details are still lacking, the following phenomena of crystal plasticity are readily explained by means of the LEDS theory: (1) the four stages of work hardening; (2) the shape of the stress-strain curve; (3) the temperature dependence of work hardening; (4) the low-temperature strain rate dependence of the flow stress; (5) the difference between ‘planar’ and ‘wavy’ glide materials (as exemplified by α-brass and copper respectively); (6) the empirical relationship D = KGb/T between dislocation cell size and flow stress; (7) grain-boundary hardening; (8) alloy hardening including solid-solution, precipitation and phase-boundary hardening; (9) slip lines and slip bands; (10) the evolution of the dislocation structures from stages I to IV; (11) deformation texture evolution; (12) work softening; (13) the thermodynamics of dislocation storage; (14) recovery, creep and recrystallization; (15) the development of dislocation structures in fatigue. All these are explained effortlessly on the basis of only the known properties of glide dislocations and the second law of thermodynamics, as expressed in the LEDS hypothesis, to wit that, among the structures which are in equilibrium with the applied tractions and accessible to the dislocations, those are formed which most nearly minimize the stored energy. (See Note added in proof at end of this paper.) The alternative ‘self-organizing dislocation’ model of crystal plasticity assumes plastic deformation to be due to individual thermally activated processes, which are treatable by the thermodynamics of energy-flow-through systems. It can be traced back to the early theory by R. Becker in 1925 and 1926 and still has to yield significant results.

Some observations on deformation banding and correlated microstructures of two aluminum alloys compressed at different temperatures and strain rates

In compressed samples of high-purity aluminum alloys, without (Al–0.5 wt% Cu) and with hard precipitates (Al–0.5 wt% Cu–1.0 wt% Si), a variety of deformation band patterns has been observed, including occasional exquisite detailed structuring. According to the present preliminary results, the banding does not significantly depend on strain rates between 0.05 and 100%/s, nor on temperature from ambient to cryogenic (−193°C). However, it is greatly decreased by the presence of precipitates in the Al–Cu–Si alloy and was barely if at all visible at and above 200°C. The banding is due to changing selections of operating slip systems, falling short of the five required in the Taylor model of homologous deformation in polycrystals. The occasional exquisite detail in the banding pattern is accepted as virtual proof of the low-energy dislocation structure (LEDS) hypothesis, the basic tenet from which the LEDS theory of crystal plasticity follows without further assumptions. In agreement with this interpretation, also the underlying dislocation cell structure, which did not reveal any evident correlation with the deformation banding, as well as the observed workhardening features as dependent on strain rate and temperature are in accord with the LEDS theory.

Comparison of beginning and ending microstructures in metal shaped charges as a means to explore mechanisms for plastic deformation at high rates

Optical metallography and transmission electron microscopy (TEM) observations were made of a variety of forged or sputtered copper, molybdenum, and tantalum shaped charge components. The beginning shaped charge liner grain sizes and sub-structures were compared with those observed in residual (ending), recovered and corresponding jet fragments and slugs. The wide range of microstructures and evolutionary features of observed microstructures can be characterized by low-energy dislocation structure (LEDS) principles which are altered because the shaped charge deformation corresponds to hot working, and dynamic recovery and recrystallization play a prominent role. There is a prominent relationship between the starting liner grain size, Do, and the ratio Do/Ds, where Ds is the ending (slug or jet), steady-state grain size. As a consequence of this relationship, it appears that the volumetric stored energy, which depends upon the grain size and dislocation density (or degree of deformation), is the critical issue in controlling shaped charge jet stability.

Long-range stresses associated with boundaries in deformed materials

The deviation from a perfect low energy dislocation structure (LEDS) for the boundaries in deformed polycrystals is described. For polycrystals with approximately equiaxed grains it is argued that the existence of the grain boundaries introduces a population of geometrically necessary dislocations around the boundaries, a population which, because of the long-range stresses associated, does not represent a perfect LEDS, but the deviation is moderate. For polycrystals with flat grains and for polycrystals with the grains subdivided into flat bands the geometrically necessary dislocations may remain in the (grain or band) boundaries, but they still represent a certain, moderate deviation from LEDS. A distinction is made between two contributions from the geometrically necessary dislocations to hardening: conservative hardening which is associated with long-range stresses and frictional hardening which is associated with the dislocation density

Effects of low energy dislocation structures on crack tip shielding in ionic crystals

Dislocation structures near the tip of a crack and its effect on the local stress intensity factor in NaCl crystals are investigated by using the etch pit technique and the photoelastic method. In the early stage of slip activity, shielding-type dislocations are introduced from a crack tip and their arrangement indicates the presence of a dislocation-free zone. By using the photoelastic method, it is surely corroborated that those dislocations cause crack tip shielding to raise the value of fracture toughness in the early stage of dislocation generation. On the other hand, when slip activities are increased around the crack tip, dislocations of antishielding type as well as shielding type are introduced to produce slip bands consisting of high density dislocations and the dislocation-free zone disappears, suggesting that the increase in the activity of dislocations does not necessarily contribute to raising the value of fracture toughness in NaCl crystals. Neighboring dislocations of shielding and antishielding type mutually screen their long-range stress fields, so that their introduction indicates the formation of a low energy dislocation structure (LEDS). Thus, LEDS formation may have a marked influence on fracture behavior in NaCl crystals.

Work softening and Hall-Petch hardening in extruded mechanically alloyed alloys

Mechanically alloyed and extruded aluminum alloys developed for service at temperatures up to 500°C in aerospace applications exhibit work softening, as is typical for alloys with grain or subgrain sizes of about 1 μm and below. Experimental evidence is presented and compared with a recent theory of work softening based on the low energy dislocation structure (LEDS) concept. It is concluded that the observed work softening stems from a reduction in the τ 0 part of the flow stress, i.e. that part which does not depend on the density of trapped dislocations. In the present alloys, τ 0 is dominated by Hall-Petch grain boundary strengthening. Transmission electron microscopy evidence suggests that the softening arises, because plastic strain weakens what appears to be a continuous layer of “grain boundary substance” (perhaps carbon, Al 4C 3, or otherwise carbon-enriched substance) at which the boundaries are strongly anchored. With the boundaries thus immobilized, the relative lattice rotations among neighboring grains caused by the strain are accomodated by “geometrically necessary” dislocation rotation boundaries formed from reaction products of glide dislocations directly at the film surfaces. This is a new form of LEDS never previously reported. It contributes to, although does not necessarily dominate, the high recrystallization and service temperatures of the alloys.

The lattice dynamical mean field criterion for low energy dislocation structure formation in shape memory alloys

The low energy dislocation structure (LEDS) predicted by the lattice-variant shear theory consists of transformation dislocations created by two lattice-variant shears: a primary shear on a system with degenerate stress,sense, and a habit plane shear for which the variants self-accommodate. Two correlations (microscopic and macroscopic), analogous to amplitudon and phason soft mode branches of phenomenological theories, are required in order to maintain the mean field: (i) the high energy dislocation structure (HEDS) at each source (transformation dislocations of one sign) correlates with the opposite-sign HEDS at other sources to cancel their long-range stress fields; (ii) the primary shear at each source periodically alternates its direction on a system with degenerate stress sense. The macroscopic correlation of fluctuating LEDS (domain wall motion) gives rise to critical behavior and diverging physical properties. LEDS motion is characterized by a soliton or sliding mode phason which, when the domains are narrow, modulates the wavevector of the microscopic soft phonon mode and gives rise to an electron-phonon interaction for a possible electronic transition.

Determining subsurface stress distributions in tribological samples from dislocation cell sizes in low energy dislocation structures

The stress distribution that caused any observable low energy dislocation structure can be inferred from the scale thereof. For dislocation cells, the empirical formula τ ≈ 10 Gb/ L, with τ the resolved shear stress, L the average dislocation cell diameter, G the shear modulus and b the Burgers vector, is especially useful in this regard. As an example, it was applied to the subsurface dislocation cell size distribution underneath the wear scar on a copper foil 0.1 mm thick that had been glued onto a steel rod and then tested in a crossed-rods apparatus. The result confirms the theoretical expectation that the minimum required thickness, when foils are used to simulate the tribological behavior of bulk material, is at least twice, and more safely three times, the average contact spot diameter.

Problems in evaluating the dislocation densities in heavily deformed Cu-Nb composites

The dislocation density of the Cu matrix in a heavily cold-rolled Cu-20%Nb composite is evaluated as a function of deformation strain. The methods and problems involved in this analysis are described and discussed in detail. The maximum dislocation density was found to be 10 10-10 11 cm -2 at all strains investigated. Dislocations were not uniformly distributed but rather had a low energy dislocation structure. The effects of sample preparation, specifically ion-thinning, were evaluated and found to have little effect on the dislocation population of worked Cu but actually introduced defects into annealed Cu.

Deformation structures in lightly rolled pure aluminium

The dislocation structure of lightly rolled aluminium is free of substantial long-range stresses and thus is a low-energy dislocation structure (LEDS). It consists of ordinary cell walls, dense dislocation walls (DDWs) and microbands (MBs) which are stretched out along DDWs and are composed of small pancake-shaped cells. In one particular sample studied, MBs were found in the orientation of shear bands, although they are not observed macroscopically. Since the DDWs and MBs appear together as if forming one general feature they have been dubbed DDW-MBs. The structure can be explain on two hypotheses: (i) All volume elements enclosed by DDWs, including MBs, are blocks of dislocation cells sharing the same combination of active glide systems which, however, are fewer in number than would be needed to satisfy the Taylor condition fully, for the reason that the rate of work hardening increases with increasing number of simultaneously activated glide systems. (ii) MBs are formed later than the DDWs on which they are situated. They complement the deformation due to the earlier cell blocks towards a better approximation of the Taylor condition. It is considered that MBs assume the orientation of shear bands when the strain in them leads to geometrical softening.