Size-dependent Strength Research Articles

Size-dependent deformation mechanisms in two-phase γ-TiAl/α2-Ti3Al alloys

Polysynthetic twinned (PST) TiAl single crystals, consisting of alternating layers of γ-TiAl and α2-Ti3Al, exhibit excellent mechanical properties. However, size-dependent deformation mechanisms have not yet been fully elucidated. In this work, we investigated the deformation process of two-phase γ-TiAl/α2-Ti3Al alloys with different layered sizes via uniaxial tensile loading using molecular dynamics simulations. The results show that with the decreasing phase boundary (PB) spacing λ or domain boundary (DB) spacing d, the excess free volume at the intersection of DB and PB decreases, leading to increased yield stress. We found that a higher interface density (smaller λ or d) can accommodate more dislocations, and the size-dependent ultimate strength follows an approximate Hall-Petch relation. These findings offer an essential understanding for the size-dependent PST TiAl single crystals with high strength.

Twinning, slip and size effect of phase-transforming ferroelectric nanopillars

Ferroelectric materials are widely used in energy applications due to their field-driven multiferroic properties. The stress-induced phase transformation plays an important role in the functionality over repeated and consecutive operation cycles, especially at the micro/nanoscales. Here we report a systematic in-situ uniaxial compression tests on cuboidal Barium titanate (BaTiO3) nanopillars with size varying from 100 nm to 3000 nm, by which we explore the stress-induced transformation and its interplay with plastic deformation. We confirm the superelasticity achieved in pillars by martensitic phase transformation from tetragonal to orthorhombic. There exists a critical size, 330 nm, for the yield stress. Above 330 nm, martensitic phase transformation aids slip along the plane with a low Schmid factor, in turn, the pseudo-compatible twins form within the shear band. The scaling exponent of size-dependent yield strength is found to be exactly 1. For nanopillars smaller than 330 nm, no twins form, only slips with large Schmid factors are activated, and size effect vanishes. All pillars with sizes from 100 nm to 300 nm achieve the theoretical yield limit around 9 GPa. Our experimental results uncover the interplay between twins and slips in BaTiO3 nanopillars, which pave the way for the optimization of microstructure design of ferroelectric materials for microelectronic applications at small scales.

Genetically correlated leaf tensile and morphological traits are driven by growing season length in a widespread perennial grass.

Leaf tensile resistance, a leaf's ability to withstand pulling forces, is an important determinant of plant ecological strategies. One potential driver of leaf tensile resistance is growing season length. When growing seasons are long, strong leaves, which often require more time and resources to construct than weak leaves, may be more advantageous than when growing seasons are short. Growing season length and other ecological conditions may also impact the morphological traits that underlie leaf tensile resistance. To understand variation in leaf tensile resistance, we measured size-dependent leaf strength and size-independent leaf toughness in diverse genotypes of the widespread perennial grass Panicum virgatum (switchgrass) in a common garden. We then used quantitative genetic approaches to estimate the heritability of leaf tensile resistance and whether there were genetic correlations between leaf tensile resistance and other morphological traits. Leaf tensile resistance was positively associated with aboveground biomass (a proxy for fitness). Moreover, both measures of leaf tensile resistance exhibited high heritability and were positively genetically correlated with leaf lamina thickness and leaf mass per area (LMA). Leaf tensile resistance also increased with the growing season length in the habitat of origin, and this effect was mediated by both LMA and leaf thickness. Differences in growing season length may promote selection for different leaf lifespans and may explain existing variation in leaf tensile resistance in P. virgatum. In addition, the high heritability of leaf tensile resistance suggests that P. virgatum will be able to respond to climate change as growing seasons lengthen.

Microstructural and textural evolution of double stage cold rolled non-grain oriented electrical steel

Non-grain oriented electrical steels (NGOES) are typically used in electric applications with rotating magnetic fields and thus essential for the production of electric motors. The increasing number of electric vehicles results in a growing demand for electrical steel sheets used in the stacked laminations of rotor and stator components. E-mobility applications require the best possible magnetic properties for optimum performance and efficiency, especially at high frequencies. In addition, increased mechanical strength is necessary to withstand the centrifugal forces resulting from high revolution speeds. Chemical composition, microstructure and crystallographic texture strongly influence the magnetic properties, whereas the mechanical properties are mainly affected by the chemical composition and grain size. Optimizing the texture is a possible method for improving the magnetic properties without significantly compromising the mechanical strength. In this work a special processing route for the production of 3.25% Si NGOES sample material has been studied, using laboratory cold rolling and annealing facilities. Compared to the classical processing route of single stage cold rolling and annealing, this alternative method involves two cold rolling steps with an intermediate annealing treatment between the first and second rolling sequence and a final annealing treatment after the second rolling step. The samples were produced with different intermediate thicknesses, changing the amount of cold rolling deformation of each sample variation. The degree of deformation affects the recrystallization and grain growth behavior and thus the resulting microstructure and texture. The microstructural and textural evolution was investigated in the hot rolled, intermediate annealed and final annealed state using electron backscatter diffraction (EBSD). Finished samples were additionally examined using magnetic testing and tensile testing. The results indicate a correlation between the intermediate thickness and the final grain size of the steel samples. Furthermore, the highly grain size dependent mechanical strength and magnetic losses are influenced. EBSD-data were used to interpret the texture and to calculate a parameter describing the magnetic quality of the texture. The results show a strong improvement of magnetically favorable texture components along with increasing intermediate thickness, enabling significantly better polarization values in rolling direction and transversal direction. However, anisotropy of the magnetic properties increases as well due to the textural changes.

High-pressure studies of size dependent yield strength in rhenium diboride nanocrystals.

The superhard ReB2 system is the hardest pure phase diboride synthesized to date. Previously, we have demonstrated the synthesis of nano-ReB2 and the use of this nanostructured material for texture analysis using high-pressure radial diffraction. Here, we investigate the size dependence of hardness in the nano-ReB2 system using nanocrystalline ReB2 with a range of grain sizes (20-60 nm). Using high-pressure X-ray diffraction, we characterize the mechanical properties of these materials, including bulk modulus, lattice strain, yield strength, and texture. In agreement with the Hall-Petch effect, the yield strength increases with decreasing size, with the 20 nm ReB2 exhibiting a significantly higher yield strength than any of the larger grained materials or bulk ReB2. Texture analysis on the high pressure diffraction data shows a maximum along the [0001] direction, which indicates that plastic deformation is primarily controlled by the basal slip system. At the highest pressure (55 GPa), the 20 nm ReB2 shows suppression of other slip systems observed in larger ReB2 samples, in agreement with its high yield strength. This behavior, likely arises from an increased grain boundary concentration in the smaller nanoparticles. Overall, these results highlight that even superhard materials can be made more mechanically robust using nanoscale grain size effects.

Temperature- and internal structural size-dependent strength of nanotwinned face-centered cubic metals

The Nanotwin structure exhibits great potential as a strengthening medium, with its effectiveness influenced by both internal structural size and temperature. In this work, we developed a strength model that incorporates the dependence on temperature and internal structural size. This model can predict the strength of nanotwinned (NT) FCC metals with intracrystalline or intercrystalline twin boundaries featuring different internal structural sizes at varying temperatures at the inverse Hall-Petch stage. The proposed prediction model has significant importance for enhancing our understanding of the mechanical behavior exhibited by NT metals and facilitating the design of super-strong materials that can withstand extreme conditions.

Influence of Dislocation Substructure on Size-Dependent Strength of High-Purity Aluminum Single-Crystal Micropillars

In order to understand the influence of dislocation substructures on the size-dependent strength (smaller is stronger) of micron-sized metals, we have fabricated single-crystal cylindrical micropillars with various diameters approximately ranging from 1 to 10 μm, which were prepared on the surface of the fully annealed sample and the subsequently cold-rolled samples of high-purity aluminum (Al). The annealed micropillars exhibited a size dependence of the resolved shear stress required for slip. The shear stress (τi) normalized by shear modulus (G) and the specimen diameter (d) normalized by Burgers vector (b) followed the correlation of τi/G=0.33(d/b)−0.63. The size-dependent strength was reduced by cold-rolling, resulting in lower power-law exponents (0.26~0.31) for the correlation in the cold-rolled specimens. The fine dislocation substructures introduced by the cold-rolling could be associated with the reduced size-dependent strength, which can be rationalized using the stochastic model of the dislocation source length in an assumption of homogenously distributed dislocations existing in the experimental micropillars. The inhomogeneous dislocation substructure with various dislocation cell sizes would contribute to a variation in the measured strength depending on the location, likely due to the probability of exiting the dislocation cell walls (local variation in dislocation density) in the micropillars fabricated on the cold-rolled Al samples.

Size-Dependent Behaviour of Hard Rock Under Triaxial Loading

Understanding size effects is important to rigorously analyse the behaviour of rocks and rock masses at different scales and for different applications. A number of empirical and numerical studies have included size effects on the uniaxial compressive strength of different rocks, but only few have focussed on the triaxial compressive strength. In this study, several triaxial tests were conducted on granite samples at different confinements (from 0.2 to 15 MPa) and sizes (from 30 to 84 mm in diameter). The most relevant strength parameters were recovered including peak and residual strengths, orientation and frictional response of shear bands. Size effects were observed to be less dominant at high confining pressures for both peak and residual strengths. The resulting data were analysed in the context of size-dependent rock strength theories. For peak strength analyses, the unified size effect law (USEL) and the improved unified size law (IUSEL) were used, in which the double trends, ascending descending behaviours were observed. Size-dependent Hoek–Brown modified failure criteria based on USEL and IUSEL were fit to peak strengths exhibiting a good agreement between the models and the laboratory data. The brittle-ductile transition and the frictional behaviour of shear band under triaxial loading were also analysed. A clear brittle behaviour was particularly observed in samples with large-diameters tested at low confinements. Finally, in regards to frictional behaviour, the shear band angle found to be affected by both confinement and sample size.

Fracture and size effect analysis in concrete using 3-D G/XFEM and a CZM-LEFM correlation model: Validation with experiments

The existence of process zones at crack tips in quasi-brittle materials is responsible for the structural size-dependent fracture strength. Hence, accurate prediction tools should not only be capable of predicting the fracture propagation and its load–displacement attributes, but should render themselves capable of the size effect analysis as well. This paper applies a robust 3-D generalized/eXtended finite element method (G/XFEM) algorithm to fracture propagation in concrete and validates its capability to capture the size effect behavior based on the cohesive zone model (CZM). Equipped with the capability of mesh adaptivity, the framework utilized in discretizing the resulting system of equations allows the adoption of independent representation for the background solid mesh and the fracture surfaces without the need for conformity between the two. The fracture simulations on a series of geometrically similar concrete beams under three-point bending have shown very good agreement with available experimental results in terms of both load–displacement (peak load and post-peak) characteristics and size effect behavior. The study also models the experimental problems using Linear Elastic Fracture Mechanics (LEFM) to investigate the structure’s size threshold below which the applicability of LEFM diminishes. The effect of beam geometry and concrete material properties on the LEFM accuracy is assessed by calculating the deviations between LEFM and bilinear cohesive model solutions. The simulation results show that power functions best describe the effect of beam’s depth and tensile strength, and linear functions best fit the effect of elastic modulus and fracture toughness. Subsequently, the study presents and validates an empirical correlation model that modifies the LEFM solution to predict similar ultimate strength as the CZM in addition to capturing the concrete size effect law successfully.

Theoretical model for yield strength of monocrystalline Ni3Al by simultaneously considering size and strain rate

AbstractTo comprehensively describe the size and strain rate dependent yield strength of monocrystalline ductile materials, a theoretical model was established based on the dislocation nucleation mechanism. Taking Ni3Al as an example, the model firstly fits results of molecular dynamics simulations to extract material dependent parameters. Then, a theoretical surface of yield strength is constructed, which is finally verified by available experimental data. The model is further checked by available third part molecular dynamics and experimental data of monocrystalline copper and gold. It is shown that this model can successfully leap over the huge spatial and temporal scale gaps between molecular dynamics and experimental conditions to get the reliable mechanical properties of monocrystalline Ni3Al, copper and gold.

Hierarchical scaling model for size effect on tensile strength of polycrystalline rock

Here, we proposed an analytical model for quantifying the intriguing size-dependent tensile strength of polycrystalline rock, i.e. first ascending then descending with the increase of specimen size. The meso‑structure of polycrystalline rock was firstly degraded to a hierarchical arrangement of regularly cuboid mineral grains. The tensile strength distribution of mineral grain interface (GI) is modeled by Weibull distribution, and the stress state near the failed GI is analytically calculated. Then a probabilistic analysis of the failure evolution in hierarchical mineral grain sets (sets of sets) was performed by considering the meso crack initiation at the GI to their propagation at macro scale, so that the tensile strength distribution and the meso crack accumulation in the rock specimen can be derived. The consistency between the model predictions and experimental results demonstrates the proposed model is valid. In addition, the results revel that the size effect trend, ascending or descending, is determined by the dispersion degree of structure strength distribution.

Size-dependent microstructural evolution and mechanical properties of crystalline/amorphous high-entropy alloy nanostructured multilayers: Cu/FeCoCrNiBSi vs Ni/FeCoCrNiBSi

Magnetron sputtering technique was employed to synthesize crystalline/amorphous high-entropy alloy (AHEA) X/AHEA (X = Cu and Ni, AHEA = Fe20Co20Cr20Ni20B10Si10) nanostructured multilayers (CANMs) with equal layer thickness h ranging from 5 to 150 nm, aiming at systematically investigating their plastic deformation and microstructural evolution. Unlike traditional crystalline/crystalline multilayers often with shear banding at small h, the present X/AHEA CANMs exhibit h-independent homogeneous deformation via the thinning of both constituent layers, while associated with h-dependent deformation-induced devitrification in AHEA layers with thickness below 25 nm. This homogeneous plasticity of AHEA layers with the large incubation size for mature shear bands can be ascribed to the coupling between dislocations in X layers and shear transformation zones in AHEA layers. Meanwhile, the absorption of abundant dislocations emitted from X layers by AHEA layers with small thickness facilitates the occurrence of devitrification behavior, implying the microstructural instability under strong constraint conditions. Moreover, both of Cu/AHEA and Ni/AHEA CANMs manifest size-dependent hardness with the fashion that “smaller is stronger”, which is captured well by the rule-of-mixture, based on the size-dependent strength of X nanolayers and size-independent homogenous flow of AHEA nanolayers.

Size effect on compressive behavior of FRP-confined engineered cementitious composites (ECC)

• A first-ever experimental study on the size effect of GFRP- and LRS FRP-confined ECC columns was conducted. • The influences of specimen size, FRP confinement level, and FRP type were examined. • A new size-dependent ultimate stress model of FRP-confined ECC was established. The reliable design of the high-performance column made of fiber reinforced polymer (FRP)-confined engineered cementitious composites (ECC) necessitates a clear understanding of the size effect under axial compression. This paper presents the compressive behaviors of glass FRP (GFRP) and large rupture strain (LRS) polyethylene terephthalate (PET) FRP-confined ECC columns. The specimen size, confinement level, and FRP type were the variables. Five diameters of 100, 200, 300, 400, and 500 mm were designed to cover a wide size range. Results showed that both the compressive strength and ductility of ECC were substantially improved with FRP confinement. Compared with GFRP-confined ECC, PET FRP-confined ECC exhibited higher ductility. The key stresses, namely initial peak stress, post-peak ravine stress, and ultimate stress decreased with increasing specimen size. Nevertheless, the specimen size had a marginal influence on the key strains and dilation behavior. After evaluating the existing size-dependent ultimate strength models of FRP-confined concrete, a new expression for predicting the ultimate strength of FRP-confined ECC was introduced, which was shown to fit well with the test results.

Fracture and energetic strength scaling of epoxy-resins toughened with multi-walled carbon nanotubes

The paper studies the toughening effect of multi-walled carbon nanotubes (MWCNTs) as nanofiller on epoxy resins. We use the size-effect testing methodology to prepare geometrically similar epoxy specimens with varying MWCNT weight fractions. We tested 72 single-edge notched samples and 72 unnotched samples in tensile loading. The addition of MWCNTs resulted in a non-negligible fracture process zone (FPZ). A size-dependent strength is observed and is modeled using type-II energetic scaling law. The mode-I fracture toughness and the FPZ size increased with the MWCNT content, peaked at optimum weight fraction, and then decreased at higher weight fraction. Fractography showed the growth of nanoclusters with an increase in the MWCNT content. We speculate this reduction in the fracture toughness at higher weight fractions is due to failure occurring in the nanoclusters instead of the nanofiller-reinforced matrix.

Fluctuations in crystalline plasticity

Recently acoustic signature of dislocation avalanches in HCP materials was found to be long tailed in size and energy, suggesting critical dynamics. Even more recently, the intermittent plastic response was found to be generic for micro- and nano-sized systems independently of their crystallographic symmetry. These rather remarkable discoveries are reviewed in this paper in the perspective of the recent studies performed in our group. We discuss the physical origin and the scaling properties of plastic fluctuations and address the nature of their dependence on crystalline symmetry, system size, and disorder content. A particular emphasis is placed on the associated emergent behaviors, including the formation of dislocation structures, and on our ability to temper plastic fluctuations by alloying. We also discuss the "smaller is wilder" size effect that culminates in a paradoxical crack-free brittle behavior of very small, initially dislocation free crystals. We show that the implied transition between different rheological behaviors is regulated by the ratio of length scales $R=L/l$, where $L$ is the system size and $l$ is the internal length. We link this new size effect with other related phenomena like size dependence of strength ("smaller is stronger") and the size induced switch between different hardening mechanisms. One of the technological challenges in nanoscience is to tame the intermittency of plastic flow. We show that this task can be accomplished by generating tailored quenched disorder which allows one to control micro- and nano-scale forming and opens new perspectives in micro-metallurgy and structural engineering of ultra-small load-carrying elements. These results could not be achieved by conventional methods that do not explicitly consider the stochastic nature of collective dislocation dynamics.

Theoretical insight of strengthening and hardening behavior in ultrafine-grained metals under high pressure

The mechanism-based theoretical models are presented to provide the theoretical explanations for strengthening and pressure-induced hardening behaviors in ultrafine-grained metals under high pressure. The grain boundary deformation model is extended to construct the relationship among the critical stress for grain boundary deformation, pressure and the grain size. The pressure-dependent critical twinning stress is derived on the basis of dislocation theory to describe the pressure-induced hardening behavior. The classic Hall-Petch for the grain size-dependent yield strength is modified through involving the contribution of partial dislocations. The simulation results demonstrate that the proposed models provide good descriptions of the strengthening and hardening behaviors in ultrafine-grained metals with respect to the high pressure. The critical grain size for the transition of deformation mechanisms is sensitive to the pressure and the grain boundary thickness. The predicted grain size-dependent yield strength and flow stress under high pressure are agreeable well with the experimental tests. These findings could shed some lights into understanding the plastic deformations of ultrafine-grained metals under high pressure.

Switchable Electron Transfer in Single Thermoresponsive Core-Shell Plasmonic Hybrid Nanoelectrodes

Active control of electrochemical processes at the nanoscale is promising for applications in switchable electronics. It has been demonstrated that stimuli-responsive polymers can serve as logic gates to switch between “on” and “off” states in response to environmental changes at both the macro- and nanoscale. As the majority of these stimuli-responsive polymers are weak polyelectrolytes, metal ions or conductive monomers are often incorporated into the stimuli-responsive matrix for electrochemical applications. However, the incorporation of conductive components may reduce the gating efficacy of these stimuli-responsive materials. In this work, we investigated the efficacy of switchable electron transfer in nonconductive stimuli-responsive core-shell hybrid nanoelectrodes consisting of thermoresponsive poly(N-isopropylacrylamide) grafted from plasmonic gold nanoparticles, termed pNIPAM@AuNPs. Under applied electrochemical potentials, electron transfer to the plasmonic core can be monitored optically through changes in the linewidth and peak position of the longitudinal surface plasmon resonance. Using single-particle dark-field spectroelectrochemistry, we observed that expanded pNIPAM@AuNPs exhibited hindered electron transfer, but, upon polymer collapse, electron transfer substantially increased. We also determined that, although heterogeneous, the extent of electron transfer in pNIPAM@AuNPs was reversibly switched through temperature cycling. Furthermore, we established that the gating efficiency of the polymer is dependent on the core morphology as a result of the size and shape dependent strength of the plasmonic electric field. These results provide insight into reversibly gated electron transfer in stimuli-responsive hybrid nanoelectrodes and suggest that a conductive polymer matrix is not necessarily required to facilitate electron transfer.

Enhanced Hall-Petch strengthening in graphene/Cu nanocomposites

Grain size dependent strength, known as Hall-Petch relation, has been approved to be valid in crystalline metals and alloys. However, softening would eventually occur as grain size reduced into nanoscale that below a critical value. Hence, it is essential to find a way to break the strength limitation by avoiding the deformation mechanism transition from dislocation-mediated to grain-boundary-mediated processes. By replacing grain boundary (GB) of nanocrystalline Cu with graphene, in the present study, molecular dynamics simulations show that graphene-boundary (GrB) embedded GrB/Cu nanocomposites exhibit enhanced enlarged Hall-Petch slope with decreasing grain size. The absence of inverse-Hall-Petch relation and the extremely high strength derived at the GrB/Cu nanocomposites were interpreted by the high back stress and abundant dislocation activity that attributed from the high-degree of heterogeneous structure of the nanocomposites.

Micropillar compression deformation of single crystals of Fe3Ge with the L12 structure

The plastic deformation behavior of single crystals of Fe3Ge with the L12 structure has been investigated at room temperature as a function of crystal orientation by micropillar compression tests. In addition to slip on (010), slip on (111) is observed to occur in Fe3Ge for the first time. The CRSS (critical resolved shear stress) for (111)[101¯] slip, estimated by extrapolating the size-dependent strength variation to the ‘bulk’ size, is ~240 MPa, which is almost 6 times that (~40 MPa) for (010)[101¯] slip similarly estimated. The dissociation scheme for the superlattice dislocation with b=[101¯] is confirmed to be of the APB (anti-phase boundary)-type both on (010) and on (111), in contrast to the previous prediction for the SISF (superlattice intrinsic stacking fault) scheme on (111) because of the expected APB instability. While superlattice dislocations do not have any preferential directions to align when gliding on (010) (indicative of low frictional stress at room temperature), the alignment of superlattice dislocations along their screw orientation is observed when gliding on (111). This is proved to be due to thermally-activated cross-slip to form Kear-Wilsdorf locks, indicative of the occurrence of yield stress anomaly that is observed in many other L12 compounds such as Ni3Al. Some important deformation characteristics expected to occur in Fe3Ge (such as the absence of SISF-couple dissociation and the occurrence of yield stress anomaly) will be discussed in the light of the experimental results obtained (APB energies on (111) and (010) and CRSS values for slip on (111) and (010)).

Micropillar Compression Deformation of Single Crystals of Fe <sub>3</sub>Ge with the L1 <sub>2</sub> Structure

The plastic deformation behavior of single crystals of Fe3Ge with the L12 structure has been investigated at room temperature as a function of crystal orientation by micropillar compression tests. In addition to slip on (010), slip on (111) is observed to occur in Fe3Ge for the first time. The CRSS (critical resolved shear stress) for (111)[10‾1] slip, estimated by extrapolating the size-dependent strength variation to the ‘bulk’ size, is ~240 MPa, which is almost 6 times that (~40 MPa) for (010)[101] slip similarly estimated. The dissociation scheme for the superlattice dislocation with b=[10‾1] is confirmed to be of the APB (anti-phase boundary)-type both on (010) and on (111), in contrast to the previous prediction for the SISF (superlattice intrinsic stacking fault) scheme on (111) because of the expected APB instability. While superlattice dislocations do not have any preferential directions to align when gliding on (010) (indicative of low frictional stress at room temperature), the alignment of superlattice dislocations along their screw orientation is observed when gliding on (111). This is proved to be due to thermally-activated cross-slip to form Kear-Wilsdorf locks, indicative of the occurrence of yield stress anomaly that is observed in many other L12 compounds such as Ni3Al. Some important deformation characteristics expected to occur in Fe3Ge (such as the absence of SISF-couple dissociation and the occurrence of yield stress anomaly) will be discussed in the light of the experimental results obtained (APB energies on (111) and (010) and CRSS values for slip on (111) and (010)).