Inverse Hall-Petch Effect Research Articles

Twin mechanical metamaterials inspired by nano-twin metals: Experimental investigations

By mimicking the geometrical relation of nano-twin crystals, we propose novel architected twin mechanical metamaterials (TMMs), which can impede local shearing band formation under external loading, thus avoiding global catastrophic failure. The effects of twin-space and twin angle on the mechanical performance of TMMs were also explored, such as: energy absorption, strength, and crack propagation resistance. The results showed that the twin topology design can not only significantly improve the energy-absorption efficiency but also remarkably improve the crack-propagation resistances of stretching-dominant mechanical metamaterials. We also studied the effect of twin-space and twin angle on the tensile strength of TMMs. This study is the first to report on the inverse Hall–Petch effect of TMMs. Our findings open an avenue for the design and fabrication of advanced materials with exceptionally tuneable mechanical properties.

Deformation mechanism and inverse Hall – Petch behavior in nanocrystalline materials

Abstract It is widely accepted that for the very smallest grain sizes (typically below 20 – 30 nm), dislocations play no significant role in the deformation of nanocrystalline materials. However, the grain-boundary mechanisms responsible for the reported decrease in strength with decreasing grain size in this regime (the ‘inverse Hall–Petch effect’) remain unclear. Here, we demonstrate by molecular-dynamics simulation that, in the absence of both grain growth and any dislocations, nanocrystalline fcc metals deform via a mechanism involving an intricate interplay between grain-boundary sliding and grain-boundary diffusion. By quantitatively reproducing the well-known Coble-creep formula for coarse-grained materials, we show that the ‘inverse Hall–Petch effect’ arises from sliding-accommodated grain-boundary diffusion creep. Previous, apparently contradictory, suggestions that GB sliding, on the one hand, or GB-diffusion creep, on the other, are responsible for this behavior can thus be reconciled as originating from one and the same deformation mechanism. We discuss the reasons why we believe that these simulations also capture the room-temperature deformation behavior of nanocrystalline fcc metals in the absence of dislocation nucleation and microcracking.

Ultra-high strength yet superplasticity in a hetero-grain-sized nanocrystalline Au nanowire

• Nanocrystalline nanowire always exhibits strength-ductility trade-off. Here, we provide in situ atomic-scale evidence that hetero-grain-sized nanocrystalline nanowires are simultaneously ultra-strong and ductile, with no strength-ductility trade-off. • The hetero-grain-sized nanocrystalline nanowire exhibits a super uniform elongation of ∼ 236% and high strength of ∼ 2.34 gigapascals at room temperature. • The in situ atomic-scale observations revealed that the dislocation activities, grain boundary plasticity, and surface atoms diffusion all contribute to the super elongation ability of hetero-grain-sized nanocrystalline nanowire. Nanocrystalline metals often display a high strength up to the gigapascal level, yet they suffer from poor plasticity. Previous studies have shown that the development of hetero-sized grains can efficiently overcome the strength-ductility trade-off of nanocrystalline metals. However, whether this strategy can lead to the fabrication of nanocrystalline nanowires exhibiting both high strength and superplasticity is unclear, similar to the atomistic deformation mechanism. In this paper, we show that ultra-small nanocrystalline Au nanowires comprising grains in both the Hall–Petch and inverse Hall–Petch grain-size regions can exhibit extremely high uniform elongation (236%) and high strength (2.34 gigapascals) at room temperature. In situ atomic-scale observations revealed that the plastic deformation underwent two stages. In the first stage, the super-elongation ability originated from the intergrain plasticity of small grains via mechanisms such as grain boundary migration and grain rotation. This intergrain plasticity caused the grains in the heterogeneous-structured nanowires to grow very large. In the second stage, the super-elongation ability originated from intragrain plasticity accompanied by the diffusion of surface atoms. Our results show that the hetero-grain-sized nanocrystalline nanowires, comprising grains with sizes both in the strongest Hall–Petch effect region and the inverse Hall–Petch effect region, were simultaneously ultra-strong and ductile. They displayed neither a strength-ductility trade-off nor plastic instability.

Delay of inverse Hall-Petch relationship of nanocrystalline Cu by modifying grain boundaries with coherent twins

In nanocrystalline metallic materials, with the decrease of grain size, the relationship between strength and grain size usually changes from the Hall-Petch (HP) to inverse Hall-Petch (IHP) relationship related to grain boundary (GB) characteristics. A series of nanocrystalline Cu samples with pre-specified grain orientations and different grain sizes were established, in which a part of GBs were replaced with coherent twin boundaries (CTBs). The mechanical behaviors of the samples with and without GB modification under tension were studied using molecular dynamics simulations. It was found that the HP and IHP relationships still work in the nanocrystalline Cu samples with GB modification, but the maximum strength is significantly improved, meanwhile the critical grain size for the transition from HP to IHP is reduced to 7.5 nm. The grain size effects on the flow stress were qualitatively analyzed based on the monitoring microstructure evolutions. The model dominated by GB was combined with that by intracrystalline CTB, which was further extended to quantitatively describe the grain size effect. It showed that the modification of GB could substantially delay the IHP effect, which provides a promising way for the design and optimization of the microstructure of high-performance nanocrystalline materials.

Deformation behaviors and inverse Hall-Petch effect in nanoindentation of silicon: An atomistic simulation study with experimental validation

In this research, the unique perspectives on deformation behaviors of monocrystalline and polycrystalline silicon materials in nanoindentation are studied by the atomistic simulation approach. First, the validity of molecular dynamics (MD) simulation model for nanoindentation is verified by comparing the indentation morphology and force of simulation with those of nanoindentation experiment on monocrystalline silicon using atomic force microscopy (AFM). Further simulation on nanoindentation of polycrystalline silicon reveals the intriguing phenomena such as phase transformation and the effect of grain size. The indentation force with respect to indentation depth is analyzed for the monocrystalline silicon and polycrystalline silicon with grain size ranging from 20.48 nm to 6.45 nm. Inverse Hall-Petch effect, which indicates that stress decreases with the decrease of grain size, is observed in the nanoindentation process of silicon. The grain boundary-induced stress during indentation process hardly affects the formation of bct-5 silicon significantly, but it is responsible for the reduced formation of β‑silicon. The amount of bct-5 silicon atoms at the maximum indentation depth is not significantly different among the polycrystalline cases. On the other hand, the amount of bct-5 atoms of monocrystalline silicon is 14–18% less than that of polycrystalline silicon. In addition, it is discovered that residual indentation morphology and residual phase transformation are not significantly affected by the grain size. As such, this research reflects the rare efforts that bring direct validation to atomistic simulation of nanomanufacturing and provide analysis on deformation and phase transformation under various grain sizes for silicon nanoindentation.

Molecular dynamic simulation of crack growth in Ti/TiN multilayer coatings

Three-dimensional molecular dynamics (MD) simulations were performed to investigate the crack growth in nanoscale multilayer Ti/TiN. The interatomic bonds were characterized using the second nearest-neighbor modified embedded-atom method. The models were built with an initial crack perpendicular to the interface in the ceramic layer under the uniaxial constant strain rate. First, simulations were conducted with two layer-numbers of Ti/TiN multilayers, including Ti(4 nm)/TiN(6 nm) and Ti(2 nm)/TiN(3 nm)/Ti(2 nm)/TiN(3 nm). The results showed that the crack in the TiN layer grew and reached the interface. The misorientation of the interface and the plastic deformation of the Ti layers can act as a barrier to crack growth and blunt crack tip at the interface. Also, Young's modulus and required stress for crack growth decreased by increasing the Ti layer thickness ratio at constant bilayer thickness. Furthermore, a decrease in the total thickness of the structure from 10 nm to 6 nm led to the inverse Hall–Petch effect. Increasing the strain rate has been shown to increase critical stress for crack growth, while Young's modulus remains unchanged. Also, at a higher strain rate, the structure toughness decreases. The results also revealed that increasing the temperature from 300 K to 700 K leads to a reduction in Young's modulus and critical stress.

Effects of cerium addition on microstructures and mechanical properties of CoCrNi medium entropy alloy films

In this work, the effects of rare-earth element Ce addition on the microstructures and mechanical properties of (CoCrNi)100-xCex (x = 0, 1.05, 2.61, 4.2, 5.96) medium entropy alloy films (MEAFs) were investigated. A series of (CoCrNi)100-xCex MEAFs was fabricated by radio frequency magnetron co-sputtering. The XRD and TEM results showed that the structure transformed from FCC to FCC + HCP at x = 2.61. Also, as Ni precipitated with Ce to form CeNi5 HCP phase, the localized depletion of Ni would encourage CoCrNi to transform from FCC to HCP phase. With the further increase in Ce content, Ce4.2 film became mixed nanocrystalline and amorphous structures and Ce5.96 film was fully amorphous. The nanoindentation and micro-pillar compression tests were conducted to study the mechanical properties of films. Both the hardness and Young's modulus showed an initial increase, reached the maxima of ~10 GPa and ~200 GPa, respectively, at x = 1.05, and then decreased with the increasing Ce content. The trends of yield strength and ultimate strength versus Ce content were similar to hardness. These results demonstrated that small amounts of Ce addition could strengthen CoCrNi MEAFs due to solid solution strengthening. However, excessive Ce addition would reduce the grain size to below ~10 nm and weaken the CoCrNiCe system due to the inverse Hall-Petch effect.

A Study of the Metallurgical and Mechanical Properties of Friction-Stir-Processed Cu

Friction stir processing (FSP), a severe plastic deformation process, was applied on pure Cu to obtain a stir zone with a very fine grain size. Yet, when FSP is used, the stir zone is as wide as the diameter of the shoulder at the upper surface of the weld and markedly narrower near its opposite surface. This property, as well as the differences between the advancing side and the retreating side, makes it impossible to obtain a uniform cross-section as far as the microstructure and mechanical properties are concerned. For these reasons, a new approach is proposed in which the material was processed on both sides, thus yielding a wider, rectangular and more homogenous stir zone from which all the specimens were machined out. Processing the material from both sides eliminated any microstructural difference between the upper and the lower side, at least within the gauge length’s cross-section of the creep specimens. Although grain refinement was detected, the mechanical properties of the friction-stir-processed (FSP’ed) material are inferior relative to those of the parent material. The TEM study reported in the current paper revealed the existence of nanosized grains in the FSP’ed material due to dynamic recrystallization (DRX) occurring during the processing stage. Because both X-ray inspection and fractography showed that the FSP’ed material was free of defects, the material may not comply with the Hall–Petch relation due to lower dislocation density caused by XRD occurring during FSP. The inverse Hall–Petch effect may also be considered as an assistive mechanism in mechanical property deterioration.

Constitutive modeling of size-dependent deformation behavior in nano-dual-phase glass-crystal alloys

Nano-dual-phase glass-crystal (NDPGC) metallic materials as the novel nanostructured materials have been proved experimentally to possess excellent mechanical properties, e.g. the nearly ideal strength. The present work is concerned with the constitutive analysis of size-dependent deformation behaviors in micropillars of a NDPGC alloy based on the micromechanics approach. The mechanism-based constitutive models are developed to explore the sample-size dependent mechanical behaviors of NDPGC pillars. An energy-based criterion for shear-band nucleation is employed to predict the diameter-dependent number of shear bands in large micropillars subjected to compression. The flow activation in metallic glass, grain reorganization, and grain refinement are involved in the proposed constitutive model for small micropillars. Numerical results demonstrate that the proposed theoretical model can describe the constitutive behaviors of the Mg-based NDPGC alloy. Good agreements between the theoretical and experimental results are achieved for the stress-strain relations and the diameter-dependent number of shear bands in large micropillars. It is found that the critical pillar diameter for generating shear bands increases with grain size and that the yield strength of NDPGC micropillars increases with the reduction in grain size (from 50 to 10 nm) without causing the inverse Hall-Petch effect. Therefore, a good combination of high yield strength and excellent plasticity can be achieved with small micropillars under compression. These findings show that the proposed model can be applied to optimize the mechanical performance of NDPGC alloys by controlling the microstructural size and sample (or feature) size.

From atomic-scale to mesoscale: A characterization of geopolymer composites using molecular dynamics and peridynamics simulations

A multiscale approach that couples molecular dynamics (MD) and peridynamics (PD) simulations was implemented to study the mechanical behavior of geopolymer composites (GC) consisting of geopolymer binder (GB), calcium silicate hydrate (CSH) and quartz. Using MD, intrinsic mechanical properties such as bulk modulus, shear modulus and strain energy release rates were determined for the constituent phases as well as the respective two-phase systems. The MD generated properties were then used to determine the input parameters for PD simulations. Both bond-based and state-based PD models were considered for simulating the GC. The first part of the PD study consisted of characterizing the properties of mesoscale porous GB. Interestingly, the predicted modulus of porous GB at porosities corresponding to experimental values compared well with experimental observations based on nanoindentation (NI). NI tests were also conducted using PD simulation to predict the hardness of GB, which was also consistent with experimental data. Finally, PD simulations of mesoscale GC consisting of multiple GB, CSH and quartz (010) domains showed that the presence of quartz (010) increases its strength. It was also observed that the strength of GC increased with increasing domain-sizes of the constituent phases, which can be compared to inverse Hall-Petch effects in nano-crystalline materials.

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.

Mechanical properties and microstructure evolution of Ti2AlC under compression in 25–1100 °C temperature range

This study investigates the effects of the initial grain size and temperature (ranging from room temperature to 1100 °C) on the mechanical properties and microstructure evolution of Ti2AlC MAX phase. A Hall-Petch like relationship is observed between compressive strength and the grain size below brittle-to-plastic transition temperature (BPTT). However, the compressive strength of fine-grained MAX phase decreases more rapidly with increasing temperature resulting in inverse Hall-Petch effect above BPTT. Results from postmortem EBSD analysis reveal complex microstructural evolution in both fine- and coarse-grained microstructures during loading at different temperatures. The pronounced drop in compressive strength for fine-grained microstructures at temperatures close to BPTT is attributed to creep induced grain boundary sliding resulting in texture development with more grains oriented for easy slip. In coarse-grained microstructures, no significant texture development is observed even though grain refinement occurs at all temperatures. A mathematical model has also been formulated to predict the experimentally observed grain size and temperature dependent variation in the compressive strength of Ti2AlC over a wide range of grain sizes and test temperatures. The mathematical model accounts for the competing effects of Hall-Petch strengthening and high temperature creep induced softening mechanisms.

Understanding surface and interface properties of modified Ti50Zr with nanotubes

The present work is a presentation of new results about the properties of nanostructures fabricated on Ti50Zr alloy surface in the context of the new trend in dentistry to extend Zr use as an alternative for Ti restorative works in the oral cavity. As a novelty, the present manuscript promotes a nanotubular Ti50Zr surface as a better choice than other TixZr alloys with and without modified nanostructured surfaces. The discussed modified nanostructured surfaces on Ti50Zr are mixtures of Ti and Zr nanotubes oxides fabricated via two steps anodizing and an ultrasonication stage between them leading to a nano cavities structure. The final surface nanotubes texture is able to improve mechanical properties and antibacterial effect. The surface characteristics were studied by scanning electron microscopy (SEM), X-ray diffraction (XRD), contact angle and atomic force microscopy (AFM) roughness determinations. Besides SEM and XRD characterization, the AFM extended investigation, developing more knowledge about adhesive and nano-mechanical properties, is a new approach, involving also the inverse Hall-Petch effect, in understanding surface and interface, able to introduce more performance in bio-applications.

Gradient structure regulated plastic deformation mechanisms in polycrystalline nanotwinned copper

Molecular dynamics simulations are performed to investigate the effects of grain size gradient and twin thickness gradient on uniaxial tensile deformation behaviors of gradient-structured polycrystalline copper. Simulation results reveal that there exist an inverse Hall–Petch effect and gradient structure regulated plastic deformation mechanisms. That is, the average flow stress of the gradient nanograined (GNG) model or the gradient nanotwinned (GNT) model decreases with decreasing the grain size or twin boundary (TB) spacing, exhibiting the breakdown in the Hall-Petch relationship when the grain size or TB spacing is smaller than a critical size. The dominant plastic deformation mechanism is found to transform from the grain boundary (GB)-mediated one to the dislocation-based counterpart with the increase of the applied strain in the GNG model. The TB migration and annihilation dominate the plastic deformation in the grains with small TB spacing; while in the grains with large TB spacing, the dislocation multiplication and cutting across TB are mainly responsible for accommodating the deformation in the GNT model. Furthermore, the gradient distribution of strain and incompatibility of deformation induced by GB or TB gradient distribution are observed by monitoring the microstructural evolution.

Nanomechanical and Material Properties of Fluorine-Doped Tin Oxide Thin Films Prepared by Ultrasonic Spray Pyrolysis: Effects of F-Doping.

Fluorine-doped tin oxide (FTO) thin films were deposited on glass substrates using ultrasonic spray pyrolysis (USP) at a fixed substrate temperature of 400 °C and various Fluorine/Tin (F/Sn) atomic ratios of 0, 0.1, 0.5, and 1.0. Effects of F/Sn atomic ratios on structural-morphological, compositional, electrical, optical, and nanomechanical properties of the FTO thin films were systematically studied. The FTO films exhibited a tetragonal structure with preferred orientations of (110), (200), and (211), and polycrystalline morphology with spear-like or coconut shell-like particles on the surfaces. The presence of F-doping was confirmed by XPS results with clear F1s peaks, and F-concentration was determined to be 0.7% for F/Sn = 0.1 and 5.1% for F/Sn = 0.5. Moreover, the resistivity of FTO films reduced remarkably from 4.1 mΩcm at F/Sn = 0 to 0.7 mΩcm at F/Sn = 1, primarily due to the corresponding increase of carrier concentration from 2 × 1020 cm−3 to 1.2 × 1021 cm−3. The average optical transmittance of the films prepared at F/Sn of 0–0.5 was over 90%, and it decreased to 84.4% for the film prepared at F/Sn = 1. The hardness (H) and Young’s modulus (E) of the FTO films increased when the F/Sn ratios increased from 0 to 0.5, reaching maximum values of H = 12.3 ± 0.4 GPa, E = 131.7 ± 8.0 GPa at F/Sn = 0.5. Meanwhile, the H and E reduced considerably when the F/Sn ratio further increased to 1.0, following the inverse Hall-Petch effect approximately, suggesting that the grain boundary effect played a primary role in manipulating the nanomechanical properties of the FTO films. Furthermore, favorable mechanical properties with large H/Ef and ratios were found for the FTO film prepared at F/Sn = 0.5, which possessed high crystallinity, large grain size, and compact morphology.

Influence of molybdenum on the mechanical properties, electrochemical corrosion and wear behavior of electrodeposited Ni-Mo alloy

In the present work, the influence of molybdenum (Mo) content on the grain size, hardness, corrosion and wear behavior of Ni-Mo alloy coatings electrodeposited from citrate electrolyte has been studied. Crack free Ni-Mo alloy with different Mo content (3, 5, 6, 9 and 12 at.%) was obtained using direct current and pulsed current electrodeposition. It was observed that the grain size of Ni-Mo alloy decreased with increase in Mo content. Hardness of the coatings increased with Mo content and decreased subsequently above 9 at.% Mo as per inverse Hall-Petch effect. Potentiodynamic polarization tests carried out in 2 N H2SO4 suggested increase in both corrosion current and passive current density with increase in Mo content. In addition, both friction coefficient and dry sliding wear rate of Ni-Mo coatings decreased with increase in Mo content. The results are rationalized based on grain size and Mo content in the coatings. Finally, Ni-Mo and Ni-W coatings were compared with hard chrome with respect to mechanical properties, wear and corrosion resistance. Results indicated that, Ni-Mo coatings exhibit least friction coefficient (0.2–0.3) amongst Ni-W and hard chrome coatings.

Atomic Simulations of Grain Structures and Deformation Behaviors in Nanocrystalline CoCrFeNiMn High-Entropy Alloy.

Using the molecular dynamics method, the melting character, mechanical properties, microstructures, and strain deformation mechanisms of nanocrystalline CoCrFeNiMn high-entropy alloy are systematically investigated in the present work. The simulation results suggest that the melting point in CoCrFeNiMn high-entropy alloy decreases with the grain size, decreasing from 3.6 to 2.0 nm. The grain size has a significant effect on shear and Young’s modulus compared to bulk modulus. The stress-strain simulation demonstrates that the ultimate tensile strength decreases with the decrease of the grain size, while the plastic deformation increases with the decrease in grain size. While the average grain size decreases to 2.0 nm, the amorphization induced by small grain size reduces plastic deformation. The common neighbor analysis shows that the face-centered cubic (FCC) composition of CoCrFeNiMn decreases gradually with decreasing grain size. For the sample with a grain size of 2.0 nm, the FCC composition is about 19% at a strain of 20%, accompanied by severe amorphization. The inverse Hall-Petch effect is observed for nanocrystalline CoCrFeNiMn high-entropy alloy in the present simulations. The atomic snapshot of CoCrFeNiMn with a grain size of 2.0 nm under the uniaxial strain confirms that the grain shape change, stacking fault formation, and amorphization are important mechanisms of plastic deformation in nanocrystalline high-entropy CoCrFeNiMn.

Dual-Phase Super-Strong and Elastic Ceramic.

Ceramic materials exhibit very high stiffness and extraordinary strength, but they typically suffer from brittleness. Amorphization and size confinement are commonly used to reinforce materials. However, the inverse Hall-Petch effect and the shear-band softening effect usually limit further improvement of their performance under a critical size. With an optimum structure design, we demonstrate that dual-phase zirconia nanowires (DP-ZrO2 NWs) with nanocrystals embedded in an amorphous matrix as a strengthening phase can overcome these problems simultaneously. As a result of this structure, in situ tensile tests demonstrate that the mechanical properties have been enormously improved in a way that does not follow both the inverse Hall-Petch effect and the shear band softening effect. The elastic strain approaches ∼7%, and the ultimate strength is 3.52 GPa, accompanied by a high toughness of ∼151 MJ m-3, making the DP-ZrO2 NW composite the strongest and toughest ZrO2 ever achieved. The findings provide a way to improve the mechanical properties of ceramics in a controllable manner, which may serve as a pervasive approach to be broadly applied to a variety of materials.

High-pressure torsion of iron with various purity levels and validation of Hall-Petch strengthening mechanism

Impurity atoms have a significant effect on the strength of metals processed by severe plastic deformation (SPD), but their strengthening mechanism is still under argument. To gain an insight into the strengthening mechanism, iron samples with different purity levels such as 99.96% (IF steel), 99.94% (Armco steel), 99.88% and 97.78% and with different initial states (bulk, powder and ball-milled) were processed by high-pressure torsion (HPT). The steady-state hardness and tensile strength for the materials with the micrometer and submicrometer grain sizes reasonably followed the Hall-Petch relationships reported earlier for pure iron and mild steels. However, the nanograined materials followed an inverse Hall-Petch relationship. It was shown that the occurrence of softening by the inverse Hall-Petch effect can be significantly avoided by stabilizing the grain boundaries using carbon atoms. These findings indicate that the extra hardening by impurity atoms is mainly due to the grain-boundary strengthening mechanism.

From metallic glasses to nanocrystals: Molecular dynamics simulations on the crossover from glass-like to grain-boundary-mediated deformation behaviour

Nanocrystalline metals contain a large fraction of high-energy grain boundaries, which may be considered as glassy phases. Consequently, with decreasing grain size, a crossover in the deformation behaviour of nanocrystals to that of metallic glasses has been proposed. Here, we study this crossover using molecular dynamics simulations on bulk glasses, glass–crystal nanocomposites, and nanocrystals of Cu64Zr36 with varying crystalline volume fractions induced by long-time thermal annealing. We find that the grain boundary phase behaves like a metallic glass under constraint from the abutting crystallites. The transition from glass-like to grain-boundary-mediated plasticity can be classified into three regimes: (1) For low crystalline volume fractions, the system resembles a glass–crystal composite and plastic flow is localised in the amorphous phase; (2) with increasing crystalline volume fraction, clusters of crystallites become jammed and the mechanical response depends critically on the relaxation state of the glassy grain boundaries; (3) at grain sizes ≥10nm, the system is jammed completely, prohibiting pure grain-boundary plasticity and instead leading to co-deformation. We observe an inverse Hall–Petch effect only in the second regime when the grain boundary is not deeply relaxed. Experimental results with different grain boundary states are therefore not directly comparable in this regime.