Atomistic simulation of the stacking fault energy and grain shape on strain hardening behaviours of FCC nanocrystalline metals

ABSTRACT

Ultra-fine grained copper with nanotwins is found to be both strong and ductile. It is expected that nanocrystalline metals with lamella grains will have strain hardening behaviour. The main unsolved issues on strain hardening behaviour of nanocrystalline metals include the effect of stacking fault energy, grain shape, temperature, strain rate, second phase particles, alloy elements, etc. Strain hardening makes strong nanocrystalline metals ductile. The stacking fault energy effects on the strain hardening behaviour are studied by molecular dynamics simulation to investigate the uniaxial tensile deformation of the layer-grained and equiaxed models for metallic materials at 300?K. The results show that the strain hardening is observed during the plastic deformation of the layer-grained models, while strain softening is found in the equiaxed models. The strain hardening index values of the layer-grained models decrease with the decrease of stacking fault energy, which is attributed to the distinct stacking fault width and dislocation density. Forest dislocations are observed in the layer-grained models due to the high dislocation density. The formation of sessile dislocations, such as Lomer–Cottrell dislocation locks and stair-rod dislocations, causes the strain hardening behaviour. The dislocation density in layer-grained models is higher than that in the equiaxed models. Grain morphology affects dislocation density by influencing the dislocation motion distance in grain interior.     

Dislocation emission by pores in nanocrystalline metals

A theoretical model is proposed to describe the emission of lattice and grain-boundary dislocations from pores in nanocrystalline metals during mechanical loading. In this model, dislocation emission occurs via an ideal nanoshear. A dislocation nucleates at a finite distance from a pore, and the modulus of its Burgers vector increases continuously from zero to the modulus of the Burgers vector of a lattice or grain-boundary dislocation. The applied stress and the critical pore-dislocation distance at which dislocation emission via an ideal nanoshear in nanocrystalline Ni, Al, and Cu becomes an energetically favorable and barrier-free process are determined.     

具有室温超塑延展性的纳米晶体铜

卢柯等人用电沉积法合成的高纯度、高致密度的纳米晶体铜的体材可以在室温经过冷轧延伸到５０倍以上而不出现应变硬化效应、力学性能测试与微结构研究表明,这种超塑延展性来源于晶界主导的塑性形变机制,而不是晶格位错机制。同时这种室温超塑延展性的纳米晶体铜材料具有广阔的工业应用前景。     

The effect of size on dislocation cell formation and strain hardening in aluminium

The formation of dislocation cells has a significant impact on the strain hardening behaviour of metals. Dislocation cells can form in metals with a characteristic size defined by three-dimensional tangles of dislocations that serve as “walls” and less dense internal regions. It has been proposed that inhibiting the formation of dislocation cells could improve the strain hardening behaviour of metals such as Al. Here we employ in situ scanning electron microscope compression testing of pure Al single crystal pillars with physical dimensions larger, close to and smaller than the reported cell size in Al, respectively, to investigate the possible size effect on the formation of dislocation cell and the consequent change of mechanical properties. We observed that the formation of dislocation cells is inhibited as the pillar size decreases to a critical value and simultaneously both the strength and the strain hardening behaviour become strongly enhanced. This phenomenon is discussed in terms of the effect of dimensional restriction on the formation of dislocation cells. The reported mechanism could be applied in polycrystalline Al where the tunable physical dimension could be grain size instead of sample size, providing insight into Al alloy design.     

Structural states and specific features of the deformation behavior of metals and alloys with mixed nano-and micrograin structure

A classification of the structural states of materials with a mixed nano-and microcrystalline structure is proposed. Theoretical analysis of the structural mechanisms and peculiarities of plastic flow of singlephase and two-phase nanostructured metals and alloys with a bimodal size distribution of grains and phases is performed. The effect of grain-boundary and dislocation mechanisms of plastic flow on the specific features of the deformation behavior and plasticity of nanocrystalline materials is analyzed. A microstructural model of strain hardening of a material with two-scale nano-and micrograin structure is proposed and the condition for the loss of plastic flow stability of such a material is investigated. The dependence of the yield strength and uniform strain of nanocrystalline materials with a two-scale structure on the grain size and the ratio of the volume fractions of the nano-and microstructural components is calculated.     

Description of primary creep by means of the stochastic model

Feltham's stochastic model is used to describe dislocation hardening during primary creep in metals which contain a three-dimensional irregular network of dislocations. The original stochastic equation is modified so as to fulfil a condition of volume conservation. The modified differential equation is then solved and a time-dependent distribution function of dislocation segment lengths is obtained. Since the creep strain is given by a summation of strain contributions from individual dislocation segments, the time dependence of the creep strain, i.e. the creep curve, can also be obtained.     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

The effects of the finest grains on the mechanical behaviours of nanocrystalline materials

This article proposes a new constitutive model to account for effects of the finest grains, with sizes ranging from 2 to 4 nm, on the mechanical behaviours of nanocrystalline (NC) materials. In this model, the normal nanograins (ranging from 20 to 100 nm) were treated as though they were composed of a grain interior (GI) and a grain boundary (GB) affected zone (GBAZ). The finest grains were considered to be part of the GBAZ, denoted as super triple junctions (STJs). For the initial plastic deformation stage of the NC materials, a phenomenological constitutive equation was suggested to predict the deformation behaviours of the GBAZ. The formation of GB dislocation (GBD) pileups provides dramatic strain hardening in deformed NC materials and thereby enhances their ductility. Then, the constitutive equations to describe the plastic deformation of the GI and the GBAZ lattice region were established. In this stage, the GBAZ are already saturated with GBD pileups, and GI deformation is the dominant mechanism. Finally, the mechanical model for the NC materials with the finest grains was built using the self-consistent method, and an overall moderate “work hardening,” sustained over a long range of plastic strain, was predicted. The effects of TJs/STJs on the deformation mechanism were quantitatively analysed. The analysis demonstrated that the existence of the finest grains will simultaneously lead to good strength and good ductility.     

Dislocation density-based constitutive model for the mechanical behaviour of irradiated Cu

Performance degradation of structural steels in nuclear environments results from the formation of a high number density of nanometre-scale defects. The defects observed in copper-based alloys are composed of vacancy clusters in the form of stacking fault tetrahedra and/or prismatic dislocation loops that impede the motion of dislocations. The mechanical behaviour of irradiated copper alloys exhibits increased yield strength, decreased total strain to failure and decreased work hardening as compared to their unirradiated behaviour. Above certain critical defect concentrations (neutron doses), the mechanical behaviour exhibits distinct upper yield points. In this paper, we describe the formulation of an internal state variable model for the mechanical behaviour of such materials subject to these (irradiation) environments. This model has been developed within a multiscale materials-modelling framework, in which molecular dynamics simulations of dislocation–radiation defect interactions inform the final coarse-grained continuum model. The plasticity model includes mechanisms for dislocation density growth and multiplication and for irradiation defect density evolution with dislocation interaction. The general behaviour of the constitutive (homogeneous material point) model shows that as the defect density increases, the initial yield point increases and the initial strain hardening decreases. The final coarse-grained model is implemented into a finite element framework and used to simulate the behaviour of tensile specimens with varying levels of irradiation-induced material damage. The simulation results compare favourably with the experimentally observed mechanical behaviour of irradiated materials.     

Strain mapping in nanocrystalline grains simulated by phase field crystal model

In recent years, the phase field crystal (PFC) model has been confirmed as a good candidate to describe grain boundary (GB) structures and their nearby atomic arrangement. To further understand the mechanical behaviours of nanocrystalline materials, strain fields near GBs need to be quantitatively characterized. Using the strain mapping technique of geometric phase approach (GPA), we have conducted strain mapping across the GBs in nanocrystalline grains simulated by the PFC model. The results demonstrate that the application of GPA in strain mapping of low and high angles GBs as well as polycrystalline grains simulated by the PFC model is very successful. The results also show that the strain field around the dislocation in a very low angle GB is quantitatively consistent with the anisotropic elastic theory of dislocations. Moreover, the difference between low angle GBs and high angle GBs is revealed by the strain analysis in terms of the strain contour shape and the structural GB width.     

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.     

Effect of grain size dispersion on the strength and plasticity of nanocrystalline metals

The effect of the dispersion of the grain size distribution on the yield stress, ultimate stress, and uniform strain of nanocrystalline metals is analyzed theoretically. It is shown that, as the grain size dispersion increases, the degree of grain boundary hardening (Hall-Petch effect) of nanocrystalline materials decreases, the onset of the grain boundary softening (inverse Hall-Petch effect) shifts to smaller nanograin sizes, and the uniform strain at which necking occurs increases.     

Dislocation and defect density-based micromechanical modeling of the mechanical behavior of fcc metals under neutron irradiation

A rate-independent dislocation and defect density-based evolution model is presented that captures the pre- and post-yield material behavior of fcc metals subjected to different doses of neutron radiation. Unlike previously developed phenomenological models, this model is capable of capturing the salient features of irradiation-induced hardening, including increase in yield stress followed by yield drop and non-zero stress offset from the unirradiated stress–strain curve. The key contribution is a model for the critical resolved slip resistance that depends on both dislocation and defect densities, which are governed by evolution equations based on physical observations. The result is an orientation-dependent non-homogeneous deformation model, which accounts for defect annihilation on active slip planes. Results for both single and polycrystalline simulations of OFHC copper are presented and are observed to be in reasonably good agreement with experimental data. Extension of the model to other fcc metals is straightforward and is currently being developed for bcc metals.     

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.     

Atomic-scale study of dislocation–stacking fault tetrahedron interactions. Part I: mechanisms

Stacking fault tetrahedra (SFTs) are formed under irradiation in fcc metals and alloys. The high number density of SFTs observed suggests that they should contribute to radiation-induced hardening and, therefore, be taken into account when estimating mechanical property changes of irradiated materials. The key issue in this is to describe the interaction between a moving dislocation and an individual SFT, which is distinguished by a small physical size of the order of ～1–10?nm. We have performed atomistic simulations of edge and screw dislocations interacting with SFTs of different sizes at different temperatures and strain rates. Five possible interaction outcomes have been identified, involving either partial absorption, or shearing or restoration of SFTs. The mechanisms that give rise to these processes are described and their dependence on interaction parameters, such as SFT size, dislocation–SFT geometry, temperature and stress/strain rate are determined. Mechanisms that help to explain the formation of defect-free channels cleared by gliding dislocations, as observed experimentally, are also discussed. Hardening due to the various mechanisms and their dependence on loading conditions will be presented in a following paper (Part II).     

A crossover from hardening to softening in nanocrystalline Ni by annealing and rolling

Two similar crossover behaviors from hardening to softening were revealed in both annealed and rolled nanocrystalline (NC) Ni by nanoindentation tests, which is totally different from that in coarse-grained samples. X-ray diffraction and transmission electron microscopy results show that the dislocation density continuously decreases with the increment of annealing temperature, whereas it first increases and then decreases with the increased rolling strain. The change of rate sensitivity in annealed NC Ni is different from that of the rolled sample. The crossover from hardening to softening by annealing is attributed to grain-boundary relaxation, while dislocation accumulation and annihilation is responsible for the crossover behavior in rolled NC Ni.     

A multiscale gradient-dependent plasticity model for size effects

The mechanical behaviour of polycrystalline material is closely correlated to grain size. In this study, we investigate the size-dependent phenomenon in multi-phase steels using a continuum dislocation dynamic model coupled with viscoplastic self-consistent model. We developed a dislocation-based strain gradient plasticity model and a stress gradient plasticity model, as well as a combined model, resulting in a theory that can predict size effect over a wide range of length scales. Results show that strain gradient plasticity and stress gradient plasticity are complementary rather than competing theories. The stress gradient model is dominant at the initial strain stage, and is much more effective for predicting yield strength than the strain gradient model. For larger deformations, the strain gradient model is dominant and more effective for predicting size-dependent hardening. The numerical results are compared with experimental data and it is found that they have the same trend for the yield stress. Furthermore, the effect of dislocation density at different strain stages is investigated, and the findings show that the Hall–Petch relation holds for the initial strain stage and breaks down for higher strain levels. Finally, a power law to describe the size effect and the transition zone between the strain gradient and stress gradient dominated regions is developed.     

Achieving large uniform tensile ductility in nanocrystalline metals

Synchrotron x-ray diffraction and high-resolution electron microscopy revealed the origin of different strain hardening behaviors (and dissimilar tensile ductility) in nanocrystalline Ni and nanocrystalline Co. Planar defect accumulations and texture evolution were observed in Co but not in Ni, suggesting that interfacial defects are an effective passage to promote strain hardening in truly nanograins. Twinning becomes less significant in Co when grain sizes reduce to below ~15 nm. This study offers insights into achieving excellent mechanical properties in nanocrystalline materials.     

Softening caused by profuse shear banding in a bulk metallic glass

By controlling the specimen aspect ratio and strain rate, compressive strains as high as 80% were obtained in an otherwise brittle metallic glass. Physical and mechanical properties were measured after deformation, and a systematic strain-induced softening was observed which contrasts sharply with the hardening typically observed in crystalline metals. If the deformed glass is treated as a composite of hard amorphous grains surrounded by soft shear-band boundaries, analogous to nanocrystalline materials that exhibit inverse Hall-Petch behavior, the correct functional form for the dependence of hardness on shear-band spacing is obtained. Deformation-induced softening leads naturally to shear localization and brittle fracture.