Hall–Petch description of nanopolycrystalline Cu,Ni and Al strength levels and strain rate sensitivities

Strength and strain rate sensitivity measurements for nanopolycrystalline copper, nickel and aluminium materials are assessed on the basis of a Hall–Petch method of analysis. The H–P k_ε values are attributed to the need for cross-slip in the grain boundary regions. Transition of the H–P dependence to the stress for a single dislocation loop expanding against the grain boundary resistance provides an explanation of higher measurements for nanoscale aluminium material.     

Hardening and thermal stability of nanocrystalline AlMg4.8 powder

Ball milled nanocrystalline AlMg4.8 powder was investigated in terms of hardening and thermal stability. The validity of the Hall–Petch relation was confirmed down to the minimum grain size of ～44 nm. Prolonged milling in the range of the minimum grain size still increased the hardness. This development is discussed in terms of contamination effects and the influence of full and partial dislocations. Concerning thermal stability, recovery processes occur in the range of 100–230°C, whereas substantial grain growth starts at a temperature of ～250°C. The enthalpy release for recovery was detected to be ～39 J mol^?1 and ～208 J mol^?1 for grain growth. Dynamic strain ageing was indicated by an activation energy for recovery of Q?～?120 kJ mol^?1. The activation energy of grain growth was calculated by means of the Kissinger theory (Q?=?200–210 kJ mol^?1) and using the results of static grain growth (Q?=?204 kJ mol^?1).     

Dislocation structures. Part II. Slip system dependence

Part I established, via extensive transmission electron microscopy investigations, that the type of dislocation structure formed in metals of medium-to-high stacking fault energy upon deformation in tension or rolling to moderate strain levels (≤0.8) depends strongly on crystallographic grain orientation. This paper analyzes the grain orientation-dependent structures in terms of the active slip systems, focusing on the crystallographic plane of extended planar boundaries (geometrically necessary boundaries). The analysis establishes slip systems as the factor controlling the dislocation structure. Five fundamental slip classes, consisting of one to three active slip systems, have been identified. Multiple activation of these slip classes is also considered. The slip classes give rise to different types of dislocation structure, of which all except one contains geometrically necessary planar boundaries aligning with unique crystallographic planes (not necessarily slip planes). A slip class leads to the same type of structure, irrespective of the macroscopic deformation mode, as also demonstrated by successful predictions for shear deformation.     

Nanocrystalline gold with small size: inverse Hall–Petch between mixed regime and super-soft regime

ABSTRACT

Molecular dynamics simulations were used to study the atomic mechanisms of deformation of nanocrystalline gold with 2.65–18?nm in grain size to explore the inverse Hall–Petch effect. Based on the mechanical responses, particularly the flow stress and the elastic-to-plastic transition, one can delineate three regimes: mixed (10–18?nm, dislocation activities and grain boundary sliding), inverse Hall-Petch (5–10?nm, grain boundary sliding), and super-soft (below 5?nm). As the grain size decreases, more grain boundaries present in the nanocrystalline solids, which block dislocation activities and facilitate grain boundary sliding. The transition from dislocation activities to grain boundary sliding leads to strengthening-then-softening due to grain size reduction, shown by the flow stress. It was further found that, samples with large grain exhibit pronounced yield, with the stress overshoot decrease as the grain size decreases. Samples with grain sizes smaller than 5?nm exhibit elastic-perfect plastic deformation without any stress overshoot, leading to the super-soft regime. Our simulations show that, during deformation, smaller grains rotate more and grow in size, while larger grains rotate less and shrink in size.     

Flow stress/strain rate/grain size coupling for fcc nanopolycrystals

A Hall–Petch (H–P)-type dependence is demonstrated for reciprocal activation volume measurements for nanocrystalline and conventional grain size, strengthened Ni and Cu materials, consistent with predictions derived from the dislocation pile-up model. The observed H–P dependence indicates that the shear stress for cross-slip must be involved in the full grain size regime for transmission of plastic flow at the grain boundaries of fcc metals.     

Dimensional attributes in enhanced hardness of nanocrystalline Ta–V nanolaminates

The scaling of microstructure to the nanoscale is a well-known method of enhancing the physical properties of many materials. New findings reveal a 10-fold enhancement in the hardness of nanocrystalline Ta and V nanolaminates is attributable to grain size effects, more so than the layer pair spacing. A Hall–Petch relationship of hardness with grain size appears in these body-centred-cubic nanocrystalline structures.     

Establishing the microstructure-strengthening correlation in severely deformed surface of titanium

Surface nanostructuring of engineering materials can be utilised to enhance materials performance for various applications. The aim of this work was to investigate the evolution of microstructure and its correlation with strengthening mechanisms in nanocrystalline commercially pure titanium (cp-Ti) produced by surface mechanical attrition treatment (SMAT). The individual contributions of dislocation slip and twining as the deformation mechanisms during SMAT have been quantified using X-ray line profile analysis and corroborated with transmission electron microscopy and electron backscattered diffraction techniques. It is found that twining is operative only in the early stages of deformation. The absence of twin–twin intersections suggests that twining is not directly responsible for the initial refinement of grain size. Dislocation slip is the major deformation mode, which leads to the refinement of the microstructure by forming low-angle lamellar boundaries. Continuous dynamic recrystallisation is demonstrated to be the mechanism of nanocrystallisation in cp-Ti using detailed microscopic analysis. In contrast to previous studies, which have neglected the contribution of Taylor strengthening, it is observed that a combination of Hall–Petch and Taylor relationships can explain the strength only if separate set of parameters K (Hall–Petch constant) and α (geometrical factor in Taylor relationship) are used for the nanocrystalline surface and severely deformed sub-surface of cp-Ti. Taken together, this work provides new insights into the underlying mechanisms for engineering nanocrystalline materials.     

Size effects and magnetoelastic couplings: a link between Hall–Petch behaviour and coercive field in soft ferromagnetic metals

Size effects regarding Hall–Petch (HP) relation are studied in this work for cobalt, nickel and Fe–3wt.%Si (FeSi), from polycrystalline to multicrystalline states. The materials show a breakdown in HP plot for thickness (t) to grain size (d) ratio less than a critical value. This appears in the beginning of plasticity for cobalt and FeSi whereas a plastic strain threshold must be overcome for nickel. Measurements of the coercive field on strained samples are able to depict such modification for low t/d ratio. Values of the coercive field in the polycrystalline domain allow an estimation of the magnetocrystalline anisotropy energy, related to the grain volume fraction concerned by reversal mechanisms for magnetic domains. Multicrystalline samples of cobalt and FeSi becomes magnetically softer at the yield stress. This is linked to a delay of the maximum intergranular stress towards higher strains for FeSi. For cobalt, non-linear elasticity and strong basal texture modify the magnetoelastic effects in coarse grain samples. For nickel, size effect on the coercive field appears after a few per cent of plastic strain as for HP relationship. A mean internal stress can be captured by magnetic measurements on polycrystals, related to the intragranular part of the kinematic stress. The softening of the magnetic properties for strained nickel multicrystals is due to a competition between the apparition of dislocation cells, which increases the coercive field by mechanisms of magnetic domain wall pinning, and surface softening of multicrystals, which tends to decrease the value of H_c.     

Critical grain sizes of micro-and mezolevel polycrystals

The influence of size effects on the dislocation structure and parameter k of the Hall—Petch relation is considered. Three critical grain sizes, in the vicinity of which the mechanisms of polycrystal deformation and strengthening change, are shown to exist. These critical grain sizes are due mostly to the presence of geometrically essential dislocations.     

Inverse Hall–Petch like behaviour in a mechanically milled nanocrystalline Al5Fe2 intermetallic phase

In the present investigation, the indentation study on the high-energy ball-milled nanocrystalline Al₅Fe₂ intermetallic compound has established the inverse Hall–Petch (IHP) behaviour. The structural characterisation of the milled powder particles by X-ray diffraction (XRD) and transmission electron microscopy has shown the evolution of nanocrystalline phase. Micro-indentation measurements have revealed the increase in hardness with decreasing grain size, reaching to a maximum of 9.0 ± 0.3 GPa up to a grain size of 32 ± 4 nm, followed by a decrease. The decrease in hardness with further refinement, an indication of grain size softening, demonstrates the IHP-like behaviour. The deviation from the Hall–Petch behaviour has been discussed using various models based on the dislocations and grain boundary-mediated processes. From the analysis, it appears that the model based on mesocopic grain boundary sliding phenomena is more appropriate to account for the observed grain size softening.     

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.     

Formation of surface roughness on nanocrystalline aluminium samples under straining by molecular dynamics studies

The surface roughening of nanocrystalline aluminium samples was investigated by molecular dynamics simulations. Attention was focused on the fact that roughness increases with the grain size and the strain. The elastic–plastic transition was found at around 3.5% strain and a reverse Hall–Petch effect was observed under straining conditions. Then, different strain distributions in grains and grain boundaries at the sample surface were highlighted, yielding to the formation of local roughness. Finally, a linear relationship between the magnitude of roughness and the out-of-plane strain component was found.     

Collective Grain Interactions II. Non‐linear Collective Drag Force

It is found that the collective effects operating at large distances from the grain surface can produce substantial scattering of the ion flux and create an additional collective drag force dominant for large grain densities. The consideration is restricted to large grain charges β = Z_de ²a /T_iλ_Di ? 1 and T_i /T_e ? 1 (–eZ_d being the grain charge in units of electron charge, a being the grain size, λ_Di being the ion Debye radius and T_e,i being electron and ion temperatures, respectively). For present dusty plasma experiments β ≈ 10–50, the large charges of grains are screened non‐linearly and the ion scattering creates non‐linear drag force. The present investigation considers effects of scattering by collective grain fields at large distances from the grains. It is found that the physical reason of the importance of collective drag force, calculated in this paper, is related to presence of weakly screened collective field of grains outside the non‐linear screening distance depending on grain densities. The amplitude of this collective fields of the grains is determined by non‐linear screening at non‐linear screening radius. It is shown that for dust densities of present experiments the collective drag force related to this scattering can be of the order of the non‐linear drag force caused by scattering inside the non‐linear screening radius or even larger. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Grain refinement and strengthening of a Cu–0.1Cr–0.06Zr alloy subjected to equal channel angular pressing

Abstract

The grain refinement and mechanical properties of a Cu–0.1Cr–0.06Zr alloy subjected to equal channel angular pressing (ECAP) at a temperature of 673 K were examined. The microstructure evolution was characterised by the development of a large number of low-angle subboundaries at small strains. An increase in the true strain resulted in gradual transformation of low-angle subboundaries into high-angle grain boundaries that was assisted by the deformation micro-banding. The development of new ultra-fine grains was considered as a kind of continuous dynamic recrystallization, the kinetics of which was characterised by a sigmoid-type dependence on strain and could be expressed by a modified Johnson–Mehl–Avrami–Kolmogorov equation. ECAP led to significant strengthening of the alloy. The yield strength increased from 105 MPa in the initial state to 390 MPa after 8 ECAP passes. A modified Hall–Petch relationship was applied to analyse the contributions of grain refinement and dislocation density to the overall strengthening. In spite of significant strengthening, the electro-conductivity remained at a level of 80% IACS.     

Low-strain fatigue in AISI 316L steel surface grains: a three-dimensional discrete dislocation dynamics modelling of the early cycles I. Dislocation microstructures and mechanical behaviour

The early stages of the formation of dislocation microstructures in low-strain fatigue are analysed, using three-dimensional discrete dislocation dynamics modelling. Simulations under various conditions of loading amplitude and grain size have been performed. Both the dislocation microstructures and the associated mechanical behaviour are accurately reproduced in single-slip as well as in double-slip loading conditions. The microstructures thus obtained are analysed quantitatively, in terms of number of slip bands per grain, band thickness and band spacing. The simulations show the crucial role of cross-slip both for the initial spreading of strain inside the grain and for the subsequent strain localization in the form of slip bands. A complete and detailed scheme for the persistent slip band formation is proposed, from the observation of the numerical dislocation arrangements.     

Interaction of dislocation pile-up with a low-angle tilt boundary: a discrete dislocation dynamics study

Abstract

The pile-up of dislocations between two low-angle tilt boundaries (LATB) in an fcc crystal was simulated using three-dimensional discrete dislocation dynamics. The LATB was constructed using glissile edge dislocations stacked on each other. The dislocations in the pile-up were chosen such that their reactions with the dislocations in the LATB resulted in glissile junctions. Parallel pairs of dislocations were inserted to a maximum allowable value estimated from theoretical expressions. A resolved shear stress was applied and increased in steps so as to move the dislocations in the pile-up towards the boundaries. The shear stress required to break the lead dislocation from the wall was determined for varying spacings between the two boundaries. The shear stress and boundary spacing followed the Hall–Petch type relation. Dislocation pile-ups without a LATB were also simulated. The spacing of the dislocations in the pile-up with LATB was found to be closer (ie higher dislocation density) than that without LATB. It was shown through analytical expressions that LATB exerts an attractive force on the dislocations in the pile-up thereby creating a denser pile-up.     

Incipient plasticity and voids nucleation of nanocrystalline gold nanofilms using molecular dynamics simulation

In this study, the incipient plasticity and voids nucleation of nanocrystalline gold were investigated using a molecular dynamics simulation. The effects of mean grain size and temperature were evaluated in terms of the material's stress-strain diagram, Young's modulus, yield strength, common-neighbor analysis, slip vectors, and deformation behaviors. From the stress-strain diagram, at 300?K, the maximum stress value corresponding to a grain size of 3.2?nm was much lower and the stress curve was clearly different from those corresponding to other grain sizes. Young's modulus increased with increasing mean grain size. The inverse Hall–Petch relation was observed. The slip was the main deformation behavior at a mean grain size of 3.2?nm. Moreover, the internal stress was more pronounced with increasing temperature. At 700?K, the main deformation area range was concentrated in the lattice at the middle of the samples, resulting in an almost force–induced structural transformation phenomenon in the middle. Void damage occurred at the junction of three–grain boundaries during the tensile process. With decreasing mean grain size, the less internal differential slip was generated under the same temperature and strain conditions.