Dislocation Density Gradient Research Articles

Study and development of the technology for hardening rope blocks by reeling

The study of the efficiency of hardening the parts working in spalling conditions through reeling with rollers were performed with the help of physical simulation and showed the high effect of hardening cast steels (a 10- to 14-fold increase in durability). The depth and degree of work hardening during plastic deformation of the surface layer were studied by the method of regression analysis. It was found that the 95-% confidence intervals for the depth of work hardening calculated from the results of measurements of yield strength make up 11‒36 % of the hardening depth and 32‒75 % by the hardness measurements. Electrography examination has shown that an increase in the degree of work hardening when reeling with a needle roller manifests itself in a higher dislocation density and cell size decrease in the substructure of ferrite grains. Diffusion of chemical elements in the surface layer in the process of surface deformation was studied with an analysis of the change of the surface microhardness. It was established that the content of Cr and C decreased by 20‒30 % in the transition zone and increased to 10‒15 % in the hardened layer. The main mechanism of diffusion during SFW is the dislocation density gradient. The process of the contact friction surface wear during reeling with consideration of slippage was investigated. It was proved that roughness of the friction surfaces affects the coefficient of friction and the rate of tribo-contact wear during reeling with slippage. For example, with a decrease in surface roughness after reeling with rollers, coefficient of friction for the lubricated surfaces decreases. A procedure for determining conditions of reeling with a wedge roller was developed. A method, technology, and a device for reeling the rope blocks with a wedge roller were developed to provide low roughness and high degree of work hardening of the surface. Optimal reeling conditions were found due to experiment planning using the steep convergence method. The obtained results of calculations will serve as initial data in designing working elements of the reeling devices and developing technological processes for strengthening parts. The conducted studies will find their future use in evaluation of the wear processes taking into account slippage of the «rope block – rope» friction couple.

Specific features of motion of molten zones in the field of silicon structural inhomogeneity

The formation and dynamics of molten Al–Si inclusions in silicon at temperatures of 1123–1273 K in the dislocation-density gradient field are investigated. It is established that the molten inclusion moves as a whole in accordance with the melting–crystallization mechanism: dissolution is observed at the front boundary in the region with a higher dislocation concentration and crystallization and on the back surface in the region with a lower one. The migration rates and activation energies are experimentally determined. It is demonstrated that the inclusion migration is limited by the melting–crystallization processes at the interfaces between the melt and matrix.

Dislocation-density based description of the deformation of a composite material

Composite materials consisting of hard particles in a ductile metallic matrix are of major interest since their strength and deformability can be dramatically changed by varying volume fraction, size and shape of the particles. Understanding dislocation motion in composite materials as the cause of plastic deformation therefore is an important task. Recently, advanced dislocation-based continuum theories of plasticity have been developed for performing meaningful averages over systems of straight and curved dislocation lines in a continuum approach. In this paper, we focus on a single slip heterogeneous microstructure and investigate how the dislocation interactions can be represented in an averaged dislocation density based continuum description. The representation of strong dislocation density gradients is discussed in the context of a formulation, which aims at a coarse-grained resolution. We introduce a set of dislocation density evolution equations which account for the formation and dissolution of dislocation dipoles. By applying the model to a composite structure, we demonstrate that the dislocation density based description can well describe the physical processes in the microstructure and a comparison to discrete dislocation dynamics simulations shows good agreement for the relaxation behavior of the considered composites.

Effect of Dislocation Density Gradient on Deformation Behavior of Pure Nickel Subjected to Torsion

Gradient hierarchical structures, including grain size gradient, twin density gradient, and texture gradient, are believed to broke up the long-standing dilemma-“strength-ductility trade-off” in materials science. Here we study the effect of dislocation density gradient on deformation behavior of pure nickel subjected to torsion. After applying torsion to cylindrical pure nickel samples, we find that Vickers hardness gradually decreased from surface to centre and the there is no obvious grain size gradient along the radial direction. The compression tests have been conducted on samples with different thickness of gradient layers. The results indicate that the yielding strength of the material can be three-times improved. Especially, the work-hardening rate “up-turn” phenomenon which was usually found in gradient nano-structures is presented in the torsion deformed pure nickel. Finally, the possible reasons and the effect of thickness of gradient structure are carefully discussed.

A new model for dynamic recrystallization under hot working conditions based on critical dislocation gradients

Abstract Dynamic recrystallization (DRX) occurs during hot working of metals and alloys with a sufficiently low stacking-fault energy. It is characterized by the nucleation and growth of new grains, which takes place concurrently to plastic deformation. DRX processes are used in industrial hot forming processes to control the microstructure and properties of the workpiece. Various models have been developed that consider the coupled evolution of microstructure and flow stress during hot deformation processes. It is widely accepted that the onset of DRX is characterized by an inflection point of the strain hardening rate as a function of stress. This so-called second-derivative criterion was derived by Poliak and Jonas in the 1990s using results from the thermodynamics of irreversible processes. Recent results show that models which use classical Avrami kinetics to describe the evolution of the recrystallized volume fraction violate the criterion if the Avrami exponent assumes a value of 3 or less. This inconsistency has its root in the assumptions made for the nucleation and growth of DRX nuclei and was shown to affect the accuracy of models used to design and control metal forming processes. This paper presents a new, consistent model for the nucleation of DRX. Typical nucleation models assume a constant dislocation density throughout the parent grains to derive a critical dislocation density for nucleation. However, it is clear from crystal plasticity that the dislocation density is higher at the grain boundaries than inside the grains. In order to involve dislocation gradients, coupled evolution equations for mobile and immobile dislocation densities are derived and solved under hot working conditions in this work. A new nucleation criterion is developed based upon the strain-dependent dislocation density gradient in parent grains. Once the critical gradient is reached, nucleation starts. The results of the newly developed criterion are compared with conventional models and experimental data. The comparison shows that the new criterion predicts more realistic critical dislocation densities in contrast to conventional models which over-estimate the critical dislocation density. As a consequence, more accurate predictions in the design and control of metal forming processes may be achieved with the new model.

A modified level set approach to 2D modeling of dynamic recrystallization

The macroscopic properties of metallic materials depend on the state of the grain microstructure. Recrystallization acts as one of the most important mechanisms in the evolution of the microstructure and hence also of the macroscopic properties. This paper presents a mesoscale model of microstructure evolution due to recrystallization, based on a level set formulation employed in a finite element setting. The use of level sets to represent grains and grain boundaries in polycrystal microstructures is a relatively recent development in computational materials science and the present contribution suggests new methodologies such as interface reconstruction, allowing for example boundary conditions to be prescribed along grain boundary interfaces and distinct localization and representation of grain boundary junctions. Polycrystal plasticity is modeled by considering the evolution of dislocation density in the individual crystals. The influence of grain boundaries on dislocation accumulation is captured in the model, causing the formation of dislocation density gradients within the grains. The model is used in simulations of dynamic recrystallization, taking pure copper as example material. It is shown that the proposed model captures the salient features of dynamic recrystallization during thermomechanical materials processing.

The Mechanics and Stability of Gold Nanoparticle-Oligo-Ligand-DNA Systems

ABSTRACTSystems in which DNA is adsorbed onto gold nanoparticles have the potential for applications in gene regulation therapies, drug delivery, sensing, and DNA scaffolding. However, the mechanical stability of gold nanoparticles (AuNPs) and interfacial behavior between the gold nanoparticles and thiol ligands are not well understood or quantified. The stability of DNA-AuNP) systems is, therefore, examined using a large-scale specialized finite-element approach with a dislocation-density based crystalline plasticity framework to model the AuNPs and an elastic description to model thiol ligands, DNA, and the ionic solution. For compressive loading conditions, the system exhibited morphological instabilities in the nanoparticles, as well as high stress and dislocation-density gradients at the thiol-nanoparticle attachment sites, which can affect system stability and attachment strength.

Microstructure evolution influenced by dislocation density gradients modeled in a reaction–diffusion system

Macroscopic properties of metallic materials are to a large extent dictated by the grain size and the presence and arrangement of grain boundaries. Plastic slip deformation will lead to the formation of dislocation pile-ups at grain boundaries, causing a heterogeneous distribution of dislocation density. This will on the macroscale manifest itself as a grain size dependence of the yield stress. Considering dynamic recrystallization, new grains will nucleate at sites of high stored energy. The existence of such favored nucleation sites is also largely due to a heterogeneous dislocation density distribution. To properly account for processes such as these in microstructure modeling, dislocation density gradients and grain boundary influence need to be considered. In the present contribution, the evolution of dislocation density is viewed as a reaction–diffusion system, involving mobile and immobile dislocations. Gradient effects are introduced by making the immobilization of mobile dislocations sensitive to the distance to grain boundaries. Through simulations in both single grains and polycrystals, it is shown that the present model provides a macroscopic yield stress behavior of Hall–Petch type, without explicitly incorporating a yield stress dependence on the grain size. In addition, the model is employed in a cellular automaton algorithm, allowing a polycrystalline microstructure to evolve due to dynamic recrystallization. It is shown that the introduced gradients provide important additions to recrystallization modeling.

Finite element investigation of size effects on the mechanical behavior of nickel single crystals

Abstract The influence of dimensions on the mechanical behavior of f.c.c. single crystals with dimensions larger than a few micrometers has been the topic of many experimental investigations and controversies during the 1970s and this question is still open. The objective of this article is to shed new light on this point by performing finite element simulations thanks to a strain gradient crystal plasticity model. Based on the model identification for nickel, several single crystal samples with various thicknesses and orientations were tested numerically in tension. The effect of dimensions was then analyzed considering the spatial distribution of dislocation densities. Near loading boundaries, dislocation density gradients appeared perpendicular to the Burgers vector direction of the primary activated slip system which modified the mechanical behavior. These gradients are discussed in terms of boundary conditions, crystal orientation and dislocation interactions with surfaces.

Modelling the combined effect of grain size and grain shape on plastic anisotropy of metals

Within each columnar grain of a metallic film, the resistance to dislocation glide varies in function of the orientation of the slip plane with regard to the grain long axis. Plastic slip is impeded across grain boundaries and this contributes to the anisotropy of the overall mechanical response. A simplified (Taylor-type) crystal plasticity model is proposed that accounts for such effect of grain shape on the slip system selection. Assuming that dislocation density gradients are normal to the grain boundaries, backstresses developed at the onset of plasticity are estimated based on two definitions of the effective grain boundary spacing “seen” by individual slip systems. The first one reduces to the mean area-to-perimeter ratio of cross-sections of the grain cut parallel to the slip plane. Closed-form expressions of the average backstresses developed inside grains with spheroidal shapes are introduced in the crystal hardening law. The model reproduces the very high plastic anisotropy of electro-deposited pure iron with a strong γ-fiber and a refined columnar grain structure [Yoshinaga, N., Sugiura, N., Hiwatashi, S., Ushioda, K., Kada, O., 2008. Deep drawability of electro-deposited pure iron having an extremely sharp 〈111〉//ND texture. ISIJ Int. 48, 667–670]. It also provides valid estimates of the texture development and the influence of grain size on the yield strength.

Studies about wafer bow of freestanding GaN substrates grown by hydride vapor phase epitaxy

Free-standing GaN wafers grown by hydride vapor phase epitaxy are typically concavely bowed. In situ and ex situ curvature measurements indicate that some strain developing at the very beginning of the epitaxial process or even in the template grown by metalorganic vapor phase epitaxy may be the origin of this bow. It can be only partly released by etching the defective back-side of the samples indicating that the strong dislocation density gradient is not the only reason for strain in free-standing GaN.

Microstructure Characterization of Hot Deformed Fe-32%Ni Alloy

Hot deformation behavior and microstructure evolution of Fe-32%Ni alloy were investigated when compressed at the temperature of 1000°C and a strain rate of 2×10-3s-1. The microstructures were analyzed using optical microscope (OM), electron back scatter diffraction (EBSD) and transmission electron microscope (TEM). The results show that the generation and development of dynamic recrystallization (DRX) can obviously refine the grains of Fe-32Ni% alloy and the DRX reached dynamic equilibrium when the strain was high. According to the TEM observations, the DRX microstructure can be categorized into three kinds: grains with low dislocation density, which are DRX nucleations; grains with low dislocation density around the grain boundary and high dislocation density in its interior which means that grains with dislocation density gradient and which are DRX grains in growth; grains with high dislocation density, which are fully work-hardened DRX grains.

The heterogeneous nature of slip in ice single crystals deformed under torsion

Ice single crystals were deformed under torsion and dislocation arrangements were analyzed by synchrotron topography at ESRF (European Synchrotron Radiation Facility). Profile analysis of the topographs revealed the scale-invariant character of the dislocation arrangement with long-range correlations. Dislocation density gradients are shown to be slightly anti-correlated as the intensity profile is similar to an anti-persistent random walk-like signal. This analysis reveals the influence of internal stresses on dislocation arrangement up to the sample scale. Similar observations in reversed torsion experiments, together with strong hardening behaviour, allow a mechanism of cross-slip of basal dislocations on prismatic planes to be suggested for interpretation of local dislocation interaction behaviour.

Mechanism of strain hardening and dislocation-structure formation in metals subjected to severe plastic deformation

The equations of dislocation kinetics are used to theoretically analyze the mechanism of strain hardening and the formation of fragmented dislocation structures in metals at large plastic strains. A quantitative analysis of the available data on aluminum and an aluminum-magnesium alloy shows that strain hardening at large plastic strains and the formation of fragmented dislocation structures are related to the interaction and self-organization of geometrically necessary dislocations (GNDs). On the microscale, the source of the GNDs is a locally nonuniform plastic deformation induced by a dislocation-density gradient in dislocation-cell boundaries.

On modelling of dynamic recrystallisation of fcc materials with low stacking fault energy

A model for dynamic recrystallisation is presented, which was developed for face-centred cubic materials with low stacking fault energies. The critical conditions for nucleation are derived and a nucleation model is used that defines the nucleation rate as the velocity determining factor and that is based on the thermal climb of edge dislocations. Stable nuclei grow in dependence on the grain boundary mobility, thus a grain size distribution can be derived. During deformation, a time-dependent dislocation density gradient develops in the recrystallised grains, which leads to a corresponding dislocation density over all recrystallised grains. If the recrystallised grain fraction meets the critical conditions for the onset of recrystallisation, a second cycle will start. The development of grain size and recrystallised fraction is compared with measured data.

Studies on age-hardening characteristics of ceramic particle/matrix interfaces in Al–Cu–SiCp composites using ultra low-load-dynamic microhardness measurements

Ultra low-load-dynamic microhardness testing facilitates the hardness measurements in a very low volume of the material and thus is suited for characterization of the interfaces in MMC's. This paper details the studies on age-hardening behavior of the interfaces in Al–Cu–5SiCp composites characterized using this technique. Results of hardness studies have been further substantiated by TEM observations. In the solution-treated condition, hardness is maximum at the particle/matrix interface and decreases with increasing distance from the interface. This could be attributed to the presence of maximum dislocation density at the interface which decreases with increasing distance from the interface. In the case of composites subjected to high temperature aging, hardening at the interface is found to be faster than the bulk matrix and the aging kinetics becomes progressively slower with increasing distance from the interface. This is attributed to the dislocation density gradient at the interface, leading to enhanced nucleation and growth of precipitates at the interface compared to the bulk matrix. TEM observations reveal that the sizes of the precipitates decrease with increasing distance from the interface and thus confirms the retardation in aging kinetics with increasing distance from the interface.

Dynamic recrystallization microstructures under hot working conditions

The characteristics of high temperature flow curves and evolution of new grain structures under conditions of dynamic recrystallization (DRX) are reviewed, together with the associated development of dislocation substructures. It is shown that the type of DRX taking place depends on the relative grain size D o/D s, where and D o and D s are the initial and stable dynamic grain sizes, and also on the nature of dispersion particles. These can be attributed to that dynamic nucleation occurs mainly at or near existing grain boundaries, and dynamic growth is controlled by not only the temperature corrected strain rate Z, but also dispersion particles. The work softening accompanied with DRX results from a change in the substructural nature from homogeneous. The dislocation substructures under full DRX are classified into the three categories: (i) DRX nuclei, (ii) growing DRX grains containing a dislocation density gradient, and (iii) large DRX grains with fairly homogeneous substructure. Finally, the metadynamic or post-dynamic restoration processes taking place in the DRX matrices are reviewed. The static softening-annealing time curve observed after DRX consists of three distinct stages with the respective inflection plateaus, followed by incomplete softening (stage 1,2 and 3). The rate of grain growth at stage 3 is much lower than that of normal grain growth. These can be caused by the stable existence of growing DRX grains having many-sided irregular shapes as well as high density dislocations.

Dislocation substructures developed during dynamic recrystallisation in polycrystalline nickel

AbstractThe dislocation substructures developed during dynamic recrystallisation (DRX) were studied by means of tensile tests and metallographic observations on polycrystalline nickel. The average cell size in the homogeneous substructures decreased rapidly with straining to about half the peak strain, whereupon DRX nuclei began to form. The average cell size then approached a constant value for increasing strain. Full DRX substructures were distributed heterogeneously throughout all areas, and were classifiable into three categories: (i) DRX nuclei, (ii) growing DRX grains containing a dislocation density gradient, and (iii) large DRX grains with a fairly homogeneous substructure. The average cell size in region (iii) could be expressed as a function of either the peak flow stress or the DRX grain size. The relationship between these microstructures and flow behaviour under DRX are discussed in detail.MST/1285

Influence of dislocation density and distribution on the aging behavior of 6061 Al [sbnd]SiC w composites

Precipitation hardening metal-matrix composites (MMCs) are known to age more rapidly than the unreinforced matrix alloys. It has been proposed that the accelerated aging is due to some dislocation defect mechanism which enhances nucleation, growth or both. Theoretical Avrami-type precipitation curves were generated assuming dislocation density dependent nucleation only and dislocation density dependent nucleation and growth. Curves were generated for both uniform dislocation density (to model cold work) and a dislocation density gradient (to model MMCs). These theoretical results were compared to precipitation curves generated by differential scanning calorimetry of unstrained and plastically strained unreinforced 6061 Al and 10 vol.% SiC whisker reinforced 6061 Al MMC. It was found on aging that β′ precipitation in the MMC initiates earlier and is completed later than in the unreinforced alloy with the same amount of plastic work as the composite. The reaction rate order for β′ precipitation was also determined from the calorimetric studies. These experimental results were interpreted in terms of the theoretical calculations. It is concluded that the matrix dislocation density distributions of metal-matrix composites can strongly influence macroscopically observed nucleation and growth rates.

Dissolution, solution transfer, diffusion versus fluid flow and volume loss during deformation/metamorphism

ABSTRACT Dissolution and solution transfer during deformation/metamorphism are controlled by the partitioning of deformation into progressive shearing and shortening components. Progressive shearing is readily accommodated by slip on the planar crystal structure of phyllosilicates and graphite without accumulating dislocation density gradients across grain boundaries.Progressive shortening is accommodated by the cores of most other minerals (including sulphides). These minerals develop strain, and hence dislocation density gradients, on their rims due to progressive shearing along grain boundaries. These gradients are particularly large when the mineral abuts phyllosilicate or graphite. The resulting chemical potential gradients between the core and rim drive dissolution, causing removal of the highly strained grain margins.Removal of dissolved material by solution transfer is aided by the geometry of shearing of phyllosilicates and graphite around other grains in an active anastomosing foliation. Interlayers and interfaces on boundaries lying at a low angle to the direction of shearing, and oriented relative to the sense of shear such that they can open, gape by small amounts. Water present in these interlayer spaces becomes destructured, considerably enhancing diffusion rates along the foliation.Penetrative volume loss, especially in deforming/metamorphosing pelitic rocks, is large at all metamorphic grades, increasing and becoming more penetrative with depth to at least the transition into granulite and eclogite facies. Transference of material by fluid flow from deep to high levels in the earth's crust is precluded because thousands to tens of thousands of rock volumes of fluid are required, necessitating continual recirculation of fluid from shallow to deep crustal levels in one large or several small sets of cells, unless some extremely large‐scale form of fluid channelling is possible. Reassessment of diffusion mechanisms, and hence rates, during deformation and pervasive foliation generation in large volumes of rock where fluid channeling cannot provide enough fluid, indicates that diffusion can proceed with sufficient rapidity that massive recirculation of fluid is no longer required. The amount of fluid can be reduced sufficiently to allow large volume losses by a one‐way flow of fluid to the earth's surface, in deforming/metamorphosing environments where the fluid pressure equals or exceeds the hydrostatic pressure.Deformation partitioning‐controlled dissolution progressively changes the bulk chemistry of a rock containing phyllosilicates or graphite during deformation/metamorphism because matrix minerals, other than phyllosilicates and graphite, are preferentially removed. The large size of porphyroblasts, if present, tends to preserve them from dissolution. Hence, the bulk chemistry operative during subsequent porphyroblast growth can have changed considerably from that operative when the first porphyroblasts grew, in rocks in which bedding is still well preserved.