Analysis of the strain-rate sensitivity of flow stresses in nanocrystalline FCC and BCC metals

The dependence of the strain-rate sensitivity coefficient of flow stresses S = dlnσ/dln\(\dot \varepsilon \) on temperature, strain rate, and grain size in nanocrystalline (NC) metals is analyzed quantitatively in terms of the dislocation-kinetics approach taking into account the properties of grain boundaries as sources, sinks, and barriers for moving dislocations. The interaction of moving dislocations with a dislocation forest in nanograin boundaries is shown to be responsible for the fact that the values of this coefficient in NC fcc metals (Cu, Ni) are an order of magnitude greater than those in coarse-grained metals and for the strong dependence of the coefficient S on the above factors. This dependence is largely caused by the annihilation of lattice dislocations in grain boundaries controlled by the activation energy of grain boundary diffusion. The values of the coefficient S in NC bcc metals (α-Fe) are an order of magnitude lower than those in coarse-grained samples, because dislocations move in a Peierls relief in nanograins     

Generation of glide split-dislocation half-loops by grain boundaries in nanocrystalline Al

A three-dimensional model for the generation of split dislocations by grain boundaries in nanocrystalline A1 is proposed. In terms of this model, rectangular glide split-dislocation half-loops nucleate at glide lattice dislocation loops pressed to grain boundaries by an applied stress. The level of the applied stress and the grain size at which the emission of such dislocation half-loops becomes energetically favorable are determined. The dependences of the stacking-fault width on the grain size and the applied stress are found. The anomalously wide stacking faults experimentally detected in nanocrystalline A1 are shown to be caused by high internal stresses forming in the stages of preparation, treatment, or local loading of nanocrystalline samples.     

Strength and plasticity of nanocrystalline metals with a bimodal grain structure

Using dislocation-kinetics equations, the structural factors are discussed that determine the strength and plastic properties of nanocrystalline metals with a bimodal grain structure containing not only nanograins but also a certain volume fraction of micron-sized grains. It is found that the plasticity (uniform strain) of nanocrystalline metals with a bimodal structure is significantly higher than that of a unimodal structure and the strength remains at the same high level. This improvement can be attained for a certain combination of factors, such as the relation between the grain sizes, the ratio of the volume fractions of nano-and micrograins in the bimodal structure, and the parameter determining the efficiency of grain boundaries as dislocation sources.     

Dislocation cross-slip in nanocrystalline fcc metals

Constant strain rate molecular dynamics simulations of nanocrystalline Al demonstrate that a significant amount of dislocations that have nucleated at the grain boundaries, exhibit cross-slip via the Fleischer mechanism as they propagate through the grain. The grain boundary structure is found to strongly influence when and where cross-slip occurs, allowing the dislocation to avoid local stress concentrations that otherwise can act as strong pinning sites for dislocation propagation.     

Influence of coherent nanoinclusions on stress-driven migration of low-angle grain boundaries in nanocomposites

A theoretical model that effectively describes stress-driven migration of low-angle tilt grain boundaries in nanocomposites with nanocrystalline or ultrafine-grained metallic matrices containing ensembles of coherent nanoinclusions has been developed. Within this model, low-angle tilt boundaries have been considered as walls of edge dislocations that, under the influence of stress, slip in the metallic matrix and can penetrate into nanoinclusions. The dislocation dynamics simulation has revealed three main regimes of the stress-driven migration of low-angle grain boundaries. In the first regime, migrating grain boundaries are completely retarded by nanoinclusions and their migration is quickly terminated, while dislocations forming grain boundaries reach equilibrium positions. In the second regime, some segments of the migrating grain boundaries are pinned by nanoinclusions, whereas the other segments continue to migrate over long distances. In the third regime, all segments of grain boundaries (except for the segments located at the boundaries of inclusions) migrate over long distances. The characteristics of these regimes have been investigated, and the critical shear stresses for transitions between the regimes have been calculated.     

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.     

Yield stress of nanocrystalline materials: role of grain-boundary dislocations,triple junctions and Coble creep

A theoretical model is suggested which describes the strengthening of nanocrystalline materials due to the effects of triple junctions of grain boundaries as obstacles for grain-boundary sliding. In the framework of the model, a dependence of the yield stress characterizing grain-boundary sliding on grain size and triple-junction angles is revealed. With this dependence we have found that, in as-fabricated nanocrystalline materials, the yield stress depends upon a competition between conventional dislocation slip and grain-boundary sliding. On the other hand, yield stress dependence on grain size in heat-treated nanocrystalline materials is described as that caused by a competition between conventional dislocation slip and Coble creep. Grain-size and triple-junction angle distributions are incorporated into the consideration to account for distributions of grain size and triple-junction angles, occurring in real specimens. The results of the model are compared with experimental data from as-fabricated and heat-treated nanocrystalline materials and shown to be in good agreement.     

Elliptic nanopores in deformed nanocrystalline and nanocomposite materials

A theoretical model is suggested which describes the nucleation of nanoscale pores (nanopores) of elliptic shape in deformed nanocrystalline and nanocomposite materials. In the framework of the model, elliptic nanopores in nanocrystalline and nanocomposite materials nucleate at interfaces in the stress fields of interfacial edge dislocations with large Burgers vectors. When elliptic nanopores nucleate, they remove the cores of interfacial dislocations. The stress field and energy of such dislocated elliptic nanopores are calculated, and their equilibrium sizes and shape parameters are revealed. It is theoretically shown that the elliptic shape of nanopores is due to the effects of interfaces (grain and interphase boundaries) on fracture processes at the nanoscale level.     

Emission of partial dislocations by grain boundaries in nanocrystalline metals

A theoretical model is proposed to describe the emission of partial dislocations by grain boundaries in nanocrystalline materials during plastic deformation. Partial dislocations are assumed to be emitted during the motion of grain-boundary disclinations, which are carriers of rotational plastic deformation. The ranges of the parameters of a defect structure in which the emission of partial dislocations by grain boundaries in nanocrystalline metals are energetically favorable are calculated. It is shown that, as the size of a grain decreases, the emission of partial dislocations by its boundary becomes more favorable as compared to the emission of perfect lattice dislocations.     

On the annealing of junction disclinations in deformed polycrystals

The kinetics of relaxation of disclination quadrupoles formed within triple junctions of grains during plastic deformation are studied. The calculations are made using the discrete dislocation model for disclinations by simulating the climb of dislocations. Exponential relationships are obtained for the relaxation of the strength and elastic energy of disclination quadrupoles with a characteristic time proportional to the cube of grain size. The distribution of vacancy fluxes along grain boundaries (GBs) during the relaxation of a disclination quadrupole is studied in detail. The relation between continuum and discrete dislocation approaches to a study of the GB recovery process is considered. Characteristics of each relaxation stage are studied. A hierarchy of characteristic relaxation times for dimerent grain size ranges is constructed and it is show that in nanocrystalline materials the spreading time of trapped lattice dislocations can depend on the grain size.     

Modelling and simulation of dynamic recrystallisation based on multi-phase-field and dislocation-based crystal plasticity models

ABSTRACT

The mechanical properties of metals used as structural materials are significantly affected by hot (or warm) plastic working. Therefore, it is industrially important to predict the microscopic behaviour of materials in the deformation process during heat treatment. In this process, a number of nuclei are generated in the vicinity of grain boundaries owing to thermal fluctuation or the coalescence of subgrains, and dynamic recrystallisation (DRX) occurs along with the deformation. In this paper, we develop a DRX model by coupling a dislocation-based crystal plasticity model and a multi-phase-field (MPF) model through the dislocation density. Then, the temperature dependence of the hardening tendency in the recrystallisation process is introduced into the DRX model. A multiphysics simulation for pure Ni is conducted, and then the validity of the DRX model is investigated by comparing the numerical results of microstructure formation and the nominal stress–strain curve during DRX with experimental results. The obtained results indicate that in the process of DRX, nucleation and grain growth occur mainly around grain boundaries with high dislocation density. As deformation progresses, new dislocations pile up and subsequent nucleation occurs in the recrystallised grains. The influence of such microstructural evolution appears as oscillation in the stress–strain curve. From the stress–strain curves, the temperature dependence in DRX is observed mainly in terms of the yield stress, the hardening ratio, and the change in the hardening tendency after nucleation occurs.     

Hydrogen-induced softening in nanocrystalline Ni investigated by nanoindentation

The influence of hydrogen on the plastic deformation of nanocrystalline nickel was analysed by recourse to nanoindentation on the uncharged and hydrogen-charged samples. It was revealed that, in nanocrystalline Ni, hydrogen significantly decreases hardness but does not alter the strain rate sensitivity. Through thermal desorption spectroscopy measurement, charged hydrogen was expected to reside in face-centred cubic lattice, grain boundaries (GBs) and vacancies rather than dislocations. The hydrogen-induced softening behaviour is discussed in terms of the possible roles of hydrogen in GB-assisted dislocation flow mechanism.     

Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

A thermally activated dislocation-based constitutive flow model of nanostructured FCC metals involving microstructural evolution

Abstract

Due to their interface and nanoscale effects associated with structural peculiarities of nanostructured, face-centered-cubic (FCC) ultrafine-grained/nanocrystalline (UFG/NC) metals, in particular nanotwinned (NT) metals exhibit unexpected deformation behaviours fundamentally different from their coarse-grained (CG) counterparts. These internal boundaries, including grain boundaries and twin boundaries in UFG/NC metals, strongly interact with dislocations as deformation barriers to enhance the strength and strain rate sensitivity (SRS) of materials on the one hand, and play critical roles in their microstructural evolution as dislocation sources/sinks to sustain plastic deformation on the other. In this work, building on the findings of twin softening and (de)twinning-mediated grain growth/refinement in stretched free-standing NT–Ni foils, a constitutive model based on the thermally activated depinning process of dislocations residing in boundaries has been proposed to predict the steady-state grain size and simulate the plastic flow of NT–Ni, by considering the blocking effects of nanotwins on the absorption of dislocations emitted from boundaries. It is uncovered that the stress ratio (η_stress) of effective-to-internal stress can be taken as a signature to estimate the stability of microstructures during plastic deformation. This model not only reproduces well the plastic flow of the stretched NT–Ni foils as well as reported NT–Cu and the steady-state grain size, but also sheds light on the size-dependent SRS and failure of FCC UFG/NC metals. This theoretical framework offers the opportunity to tune the microstructures in the polycrystalline materials to synthesise high performance engineering materials with high strength and great ductility.     

High strength and superplasticity of nanocrystalline materials

The part played by grain boundaries in nanocrystalline materials produced by equal-channel angular pressing is considered. The tensile strength and tensile and compressive yield stresses of various materials and alloys were studied over a broad low-temperature range. It was found that, at close-to-liquid helium temperatures, the strength is the highest possible for the given material and that strain localization is better pronounced than in conventional materials. The results obtained are interpreted in terms of the influence of boundaries, which act as the dominant hardening factor increasing the resistance to dislocation motion. By contrast, experiments conducted at elevated temperatures showed the boundaries to become mobile, thus imparting superplasticity to materials in some cases. The actual maximum tensile and torsional shears are compared. It is demonstrated that, despite the closeness between the tensile-and torsional-deformation activation energies, the stress-strain curves and the shears differ strongly, which implies that these characteristics are affected by the actual type of deformation involved.     

Crack-stimulated generation of deformation twins in nanocrystalline metals and ceramics

A theoretical model is proposed that describes the generation of deformation twins near brittle cracks of mixed I and II modes in nanocrystalline metals and ceramics. In the framework of the model, a deformation twin nucleates through stress-driven emission of twinning dislocations from a grain boundary distant from the crack tip. The emission is driven by both the external stress concentrated by the pre-existent crack and the stress field of a neighbouring extrinsic grain boundary dislocation. The ranges of the key parameters, the external shear stress, τ, and the crack length, L, are calculated within which the deformation-twin formation near pre-existent cracks is energetically favourable in a typical nanocrystalline metal (Al) and ceramic (3C-SiC). The results of the proposed model account for experimental data on observation of deformation twins in nanocrystalline materials reported in the literature. The deformation-twin formation is treated as a toughening mechanism effectively operating in nanocrystalline metals and ceramics.     

Plastic deformation behaviour of layer-grained silver polycrystalline from atomistic simulation

Two types of nanocrystalline polycrystalline silver models in bulk, film and nanowire forms were constructed with layer-grained or equiaxed grain morphologies and average grain sizes of ~7.8 and ~14.7 nm. Uniaxial tensile deformation was performed to investigate the effect of grain morphology and free surface on the plastic deformation behaviour under the strain rate of 5 × 10⁸ and 10⁷ s^?1 at 0.1 K. Grain Boundary (GB) orientation and dimensions in layer-grained morphology promoted the formation of sessile dislocation structures. Some dislocations interacted with each other and some dislocations got obstructed by stacking faults. However, the resulting configurations did not last long enough to cause strain hardening. Strain softening was observed in all models except for the layer-grained models in bulk form, where steady plastic flow was observed after yield. The location and orientation of free surfaces with respect to GBs imposed geometric constraints on the deformation mechanisms (GB sliding and formation of sessile dislocations) which produced asymmetric stress states that influenced the elastic as well as plastic response of the material. The yield stress and flow stress were much smaller at lower strain rate simulations. The proportion of perfect dislocations increased as the strain rate decreased from 5 × 10⁸ to 10⁷ s^?1 due to the decrease of applied stress. Dislocations were mainly emitted from grain boundaries or triple junctions at both high and low strain rate deformations. These results provided insights into the understanding of layer-grained nanocrystalline materials and the synthesis of materials with both high strength and ductility.     

非对称倾侧亚晶界的晶体相场法研究

采用晶体相场法研究非对称倾侧亚晶界结构及其在应力作用下的微观运动机制.分别从温度、倾斜度角以及应力施加方向等方面对其结构及迁移过程进行分析和讨论.结果表明,非对称倾侧亚晶界由符号相同的一排刃型位错等距排列,部分出现由两个相互垂直排列的刃型位错构成的位错组;在应力作用下,非对称倾侧亚晶界迁移的微观机制包括位错的滑移和攀移、位错组分解、单个位错与位错组反应、单个位错分解以及位错湮灭;温度降低和倾斜度增大都会阻碍亚晶界的迁移过程;应力方向改变导致位错运动方向改变,从而改变晶界迁移形式.     

Dislocation dynamics in nanocrystalline nickel

It is believed that the dynamics of dislocation processes during the deformation of nanocrystalline materials can only be visualized by computational simulations. Here we demonstrate that observations of dislocation processes during the deformation of nanocrystalline Ni with grain sizes as small as 10 nm can be achieved by using a combination of in situ tensile straining and high-resolution transmission electron microscopy. Trapped unit lattice dislocations are observed in strained grains as small as 5 nm, but subsequent relaxation leads to dislocation recombination.     

Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al

The interaction of dislocations with grain boundaries (GBs) determines a number of important aspects of the mechanical performance of materials, including strengthening and fatigue resistance. Here, the coupled atomistic/discrete-dislocation (CADD) multiscale method, which couples a discrete dislocation continuum region to a fully atomistic region, is used to study screw-dislocations interacting with Σ3, Σ11, and Σ9 symmetric tilt boundaries in Al. The low-energy Σ3 and Σ11 boundaries absorb lattice dislocations and generate extrinsic grain boundary dislocations (GBDs). As multiple screw dislocations impinge on the GB, the GBDs form a pile-up along the GB and provide a back stress that requires increasing applied load to push the lattice dislocations into the GB. Dislocation transmission is never observed, even with large GBD pile-ups near the dislocation/GB intersection. Results are compared with experiments and previous, related simulations. The Σ9 grain boundary, composed from a more complex set of structural units, absorbs screw dislocations that remain localized, with no GBD formation. With increasing applied stress, new screw dislocations are then nucleated into the opposite grain from structural units in the GB that are nearby but not at the location where the original dislocation intersected the boundary. The detailed behaviour depends on the precise location of the incident dislocations and the extent of the pile-up. Transmission can occur on both Schmid and non-Schmid planes and can depend on the shear stresses on the GB plane. A continuum yield locus for transmission is formulated. In general, the overall dissociation and/or transmission behaviour is also determined by the Burgers vectors and associated steps of the primitive vectors of the grain boundary, and the criteria for dislocation transmission formulated by Lee et al . [Scripta Metall. 23 799 (1989); Phil. Mag. A 62 131 (1990); Metall. Trans. A 21 2437 (1990)] are extended to account for these factors.