Size-dependent Strength Research Articles

Size-dependent strength and interface-dominated deformation mechanisms of Cu/Zr multilayer nanofilms

Abstract Molecular dynamics (MD) simulations are performed in this study to investigate the mechanical properties of Cu/Zr multilayer nanofilms (MNFs) during tensile and compression tests. The results reveal slip behavior in the tensile test and the phase transformation process in the compression test, where the former only occurs in the Cu film during the tensile test and the latter only occurs in the Zr film during the compression test. In addition, the effects of temperature, growth orientation, and layer number are investigated.

Uniaxial compression of silicon nanoparticles: An atomistic study on the shape and size effects

Molecular dynamics simulations were carried out to investigate the mechanical properties of silicon nanoparticles during uniaxial compression by a flat-punch indenter. We considered a large set of systems, with dimensions in the range 10 nm–50 nm, and various shapes like cubic (perfect and blunt), spherical, truncated spherical, and Wulff-shaped, as well as two compression orientations and two temperatures. Thorough analyses of the simulations first revealed that the relation between nanoparticle size and strength, usually termed as ’smaller is stronger’, is critically dependent on the nanoparticle shape, at least for the investigated size range. For instance, a significant and size-dependent strength decrease is determined for facetted Wulff-like nanoparticles, but not for cubic or spherical systems for compression along <100>. We also found that the nanoparticle shape greatly influences plasticity. Several original plasticity mechanisms are obtained, among which the nucleation of half-loop V-shaped dislocation contained in two different {111} planes, dislocations gliding in unusual {110} planes, or the nucleation of partial dislocations in shuffle {111} planes. Our investigations suggest that plasticity properties are mainly governed by the localization of shear stress build up during elastic loading, and the geometry of surfaces in contact with indenters, these two characteristics being intimately related to the nanoparticle shape.

Nucleation-Controlled Plasticity of Metallic Nanowires and Nanoparticles.

Nanowires and nanoparticles are envisioned as important elements of future technology and devices, owing to their unique mechanical properties. Metallic nanowires and nanoparticles demonstrate outstanding size-dependent strength since their deformation is dislocation nucleation-controlled. In this context, the recent experimental and computational studies of nucleation-controlled plasticity are reviewed. The underlying microstructural mechanisms that govern the strength of nanowires and the origin of their stochastic nature are also discussed. Nanoparticles, in which the stress state under compression is nonuniform, exhibit a shape-dependent strength. Perspectives on improved methods to study nucleation-controlled plasticity are discussed, as well the insights gained for microstructural-based design of mechanical properties at the nanoscale.

Nanomechanical studies of high-entropy alloys

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Additive Manufacturing and size-dependent mechanical properties of three-dimensional microarchitected, high-temperature ceramic metamaterials

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Size-dependent compressive strength properties of hard rocks and rock-like cementitious brittle materials

Rock engineering projects have always been constructed on different (from micro to macro) scales. This makes understanding rock behaviour at different scales essential. In previous statistical studies on igneous hard rocks, the correlation of uniaxial compressive strength (UCS) values in different diameters with estimations of specimen size effect models was weak. In view of this knowledge gap, the present research proposed a model of appropriate size effect in igneous hard rocks. This research also aimed at discussing the effect of specimen size and grain size on the UCS of concrete specimens. To achieve these aims, studies were conducted in parallel on the previous and new experimental data. Non-linear regression analysis on igneous hard rocks indicated that there is a better agreement between the outputs of the multi-fractal scaling model and the specimen size effect model using the fracture energy theory and the results of previous laboratory tests. In addition, in the experimental study, the grain size effect on the predictions of specimen size effect models was exhibited. The results of this research can be used for designing engineering projects at different scales.

Shear localization and size-dependent strength of YCd6 quasicrystal approximant at the micrometer length scale

Mechanical properties of materials are strongly dependent of their atomic arrangement as well as the sample dimension, particularly at the micrometer length scale. In this study, we investigated the small-scale mechanical properties of single-crystalline YCd6, which is a rational approximant of the icosahedral Y-Cd quasicrystal. In situ microcompression tests revealed that shear localization always occurs on {101} planes, but the shear direction is not constrained to any particular crystallographic directions. Furthermore, the yield strengths show the size dependence with a power law exponent of 0.4. Shear localization on {101} planes and size-dependent yield strength are explained in terms of a large interplanar spacing between {101} planes and the energetics of shear localization process, respectively. The mechanical behavior of the icosahedral Y-Cd quasicrystal is also compared to understand the influence of translational symmetry on the shear localization process in both YCd6 and Y-Cd quasicrystal micropillars. The results of this study will provide an important insight in a fundamental understanding of shear localization process in novel complex intermetallic compounds.

Effect of nodal mass on macroscopic mechanical properties of nanoporous metals

The current work investigates the effect of the nodal mass on the macroscopic mechanical behavior of nanoporous metals using the Finite Element Method. A nodal corrected beam modeling concept is introduced that allows local incorporation of the effective elastoplastic mechanical behavior of the nodal mass in the nodal area of a representative volume element (RVE). The calibration to the corresponding Finite Element solid model is achieved by integrating additional geometry and material parameters to the so-called nodal areas in the beam model. With this technique an excellent prediction can be achieved over a large range of deformation for different types of RVEs. From the results of the nodal corrected beam model, modified leading constants are determined in the scaling laws for Young's modulus and yield strength. The effect of the nodal correction is also studied with respect to various randomization levels. Finally, the ligament size dependent strength is analyzed by applying the proposed model to experimental data. It could be shown that the nodal correction improves the overall agreement with literature data, particularly for such data points that are related to samples with a high solid fraction.

Role of dislocation pile-ups in nucleation-controlled size-dependent strength of Fe nanowires

We studied the strength of Fe faceted nanowires under diametrical compression using molecular dynamics simulations. We show that a series of consecutive events of dislocation nucleations occurs at the vertices of the nanowire, and two edge dislocation pile-ups are formed before a catastrophic event occurs, previously named a cross-split of edge dislocations. The compressive stress at which dislocations are nucleated depends on the specimen's size and obeys a power-law, with an exponent that depends on the number of dislocations already nucleated into the pile-up. The role of the dislocation pile-up is discussed and, on the basis of classical nucleation theory, we examine the contribution of the dislocation pile-up to the nucleation conditions at the vertices of the nanowire. We found that three contributions need to be accounted for: the stress gradient at the vertices, the back stress from the nucleated pile-up, and the image stresses due to the confined volume of the nanowire. In addition, the proposed model agrees with the distribution of the dislocations inside the pile-up. We ratify that cross-splitting occurs at the head of the pile-up when the distance between the two leading dislocations is about twice their Burgers vectors. Considering this value as the limit for dislocation core coalescence, the results of our model and molecular dynamic simulations for the stresses needed for cross-splitting were in excellent agreement. Based on these results, we found the dependency of the critical stress needed for cross-splitting on the size. Finally, we extend the discussion to the general role of dislocation pile-ups in nucleation-controlled plasticity.

Size effects on the mechanical properties of nanocrystalline NbMoTaW refractory high entropy alloy thin films

The newly-surged high-entropy alloys (HEAs), in particular the refractory HEAs, manifest excellent properties for practice applications. In this work, we systematically investigated the plastic deformation characteristics (including the hardness, strain rate sensitivity (SRS), and activation volume) of nanocrystalline (NC) equiatomic NbMoTaW body-centered cubic (BCC) high-entropy alloy films (HEAFs) with thicknesses spanning from 100 to 2000 nm at room temperature. The BCC NbMoTaW HEAFs exhibited the strongest grain size ∼10 nm with the hardness of ∼16.0 GPa, above which the hardness decreases with increasing the grain size or film thickness, while below this critical size the material softening occurs. Given the friction stress and the source activation stress cannot be additive because they don't appear under the same circumstances, the size-dependent ultra-high strength in BCC HEAFs was discussed in terms of the solid solution hardening, the boundary dislocation density and the source strength. It was unveiled that above a critical grain size of ∼40 nm, the solid solution hardening becomes the predominant strengthening mechanism, while below this critical size the source strengthening becomes the predominant one in BCC NbMoTaW HEAs. Also, the strong size-dependence of SRS is emerged, which monotonically increased with decreasing thicknesses (just opposite to the activation volume). A thermally activated model based on the depinning process of bowed-out dislocations was employed to quantitatively account for the size-dependent SRS of the NbMoTaW HEAFs. Our findings not only provide deep insight into understanding the mechanical behavior of the NC BCC NbMoTaW HEAFs, at least in the studied size-range, also offer some clues for the metastability engineering strategy to design high performance HEAFs at small-scales.

Specimen size and shape dependent yield strength in micropillar compression deformation of Mo single crystals

The deformation behavior of [1¯25]-oriented Mo micropillars with rectangular cross-sections having the [111] primary slip direction parallel to one of the two orthogonal side-surfaces has been investigated as a function of specimen size and shape (with varying ratios for two side-edge lengths of the cross-section). Micropillars with square-shaped cross-sections exhibit a size dependence of the critical resolved shear stress τCRSS approximated by τCRSS∝L−m with a power-law exponent of m ∼0.5 (L: cross-section side length). For a series of micropillars with a fixed length for the side-edge perpendicular to [111] (CE series), the CRSS also exhibit a power-law relationship with a relatively small exponent of m = 0.3. In contrast, an unexpected size-dependence is observed with two strength plateaus being connected by a strongly size dependent region (m ∼ 1) for a series of micropillars having a fixed length for the other cross-section side (CS series). The observed specimen size and shape dependence of CRSS of Mo micropillars is discussed based on the stochastic dislocation source length model and the dislocation kinetics model.

Size dependent fracture strength and cracking mechanisms in freestanding polycrystalline silicon films with nanoscale thickness

The size dependent fracture strength and fracture mechanisms of polycrystalline silicon films are investigated by analyzing a wide range of specimen lengths and widths with thicknesses equal to 240 and 40nm. An on-chip method is used to deform the films and to determine the strength. The strength increases with decreasing external surface area. The thinnest films exhibit the lowest strength and a weaker size effect. The crack path changes from transgranular to intergranular with decreasing thickness. These results are related to differences in microstructure and surface roughness characteristics of the films as controlled by the fabrication process and thickness.

Experimental investigations on the failures of woven textile sandwich panels

To reveal the deformation, strength, and failure modes of woven textile sandwich composites (WTSCs), test methods suggested by national standards were referenced and discussed to carry out flatwise and edgewise compression experiments, uniaxial stretching experiments, and three-point bending experiments according to the structural characteristics of WTSC. Strength and failure modes of WTSCs in flatwise compression and uniaxial tension were acquired. Anisotropy and size dependency of strength and failure modes of WTSC panels in edgewise compression were revealed. Strength of weft-compressed panels has few variations when the length is smaller than 60 mm and then decreases obviously when the length is over 60 mm, accompanying with the failure modes turning from crushing, fracture to buckling. Progressive crushing and bending fracture are two observed post-failure modes. Two competing shear failure modes and facesheet failure were observed in three-point bending experiments. Shear strength of the woven core of WTSC was deduced by beam flexure. To acquire facesheet failure mode by long beam flexure, the span should be above 36 times the thickness of the panel.

Interplay between sample size and grain size: Single crystalline vs. ultrafine-grained chromium micropillars

To gain insights into the influence of the microstructure on the strengthening behaviour in confined volumes, single crystalline (sxx) and ultrafine-grained (ufg) Cr micropillars were investigated using in-situ scanning electron microscope microcompression tests. Post-compression images of the sxx pillars indicate crystallographic slip, while the ufg pillars reveal a bulk-like deformation behaviour and an emergence of grains from the sample surface. Stress-strain curves of sxx samples show intermittent flow and a scaling behaviour agreeing well with other bcc metals investigated previously. Also for ufg samples a size-dependent strength with a reduced but non-negligible scaling exponent is determined. This latter ufg size effect contributes to an increasing influence of near-surface grains controlling plastic flow with decreasing pillar diameter. While for micron-sized pillars the strength differs between the two microstructures, the two scaling trends converge for sub-micron pillars with diameters close to the grain size, indicative of a transition from boundary-mediated to single crystal plasticity.

Interpreting anomalous low-strength and low-stiffness of nanoporous gold: Quantification of network connectivity

The strength and elastic modulus of macroscopic nanoporous Au samples are much lower than that predicted by using Gibson-Ashby scaling laws. Here we attribute this discrepancy to a lowered network connectivity in nanoporous structure, and propose to modify the scaling equations (for both strength and stiffness) by introducing a concept of effective relative density. It is presented that the effective relative density can be determined by measuring the elasticity of nanoporous Au; under this scenario, the corrected strengths of Au nano-ligaments agree (on the order of magnitude) well with the previous data for similar-sized Au nanowires or nanopillars, which confirms our hypotheses. This study also revealed a low power-law exponent of size-dependent strength for Au nano-ligaments (β = −0.34) compared with that of Au submicron-pillars machined by focused ion beam (FIB) (β = −0.61), which may be related to the critical roles of surface defects played in deformation. A ratio between effective relative density and relative density is suggested to quantify the network connectivity in nanoporous structure, which decreases rapidly during structure coarsening – it explains why most previous nanoporous Au samples, which more or less experienced coarsening, were unexpectedly soft. Current study also leads to some general strategies for syntheses of strong and stiff nanoporous metals.

Time-dependent deformation of Sn micropillars

In this study, time-dependent plastic deformation of micropillars fabricated from low melting point metal Sn (~505K) was investigated at room temperature. Size-dependent strength was first evaluated and creep tests were then performed on the micropillars having diameters of 1 and 5μm. Sn pillars showed significant creep deformation, and creep rate was independent of pillar size. Creep stress exponent was determined to be ~1, and negligible effect of e-beam irradiation on creep rate confirmed that the lattice diffusion must be the predominant creep mechanism. Creep deformation of Sn micropillars, therefore, differs from the dislocation-climb based creep in bulk Sn.

Effect of surface energy upon size-dependent yield strength of single-crystalline hollow micro- and nanopillars

The physical nature of the size-dependent yield strength of micro- and nanopillars is still an open issue, where the surface energy may be one factor that influences the size effect of these pillars, especially for hollow pillars. In this study, the influence of the surface energy and surface elasticity upon the size-dependent yield strength of single-crystalline hollow micro- and nanopillars is considered quantitatively. An analytical expression of the size-dependent yield strength is established that considers the surface energy and the inner defects by the principle of minimum potential energy. The predicted yield strength of our model as a function of the pillar size is more precise than that of the well-known single arm source model when comparing the predictions with the experimental results of pillars made of Al or Ni. According to the surface elasticity, the surface energy can be determined by the thickness of the hollow pillars, the surface modulus and the surface strain, where the latter two are related to the external damages.

Recoverable Slippage Mechanism in Multilayer Graphene Leads to Repeatable Energy Dissipation.

Understanding the deformation mechanisms in multilayer graphene (MLG), an attractive material used in nanodevices as well as in the reinforcement of nanocomposites, is critical yet challenging due to difficulties in experimental characterization and the spatiotemporal limitations of atomistic modeling. In this study, we combine nanomechanical experiments with coarse-grained molecular dynamics (CG-MD) simulations to elucidate the mechanisms of deformation and failure of MLG sheets. Elastic properties of graphene sheets with one to three layers are measured using film deflection tests. A nonlinear behavior in the force vs deflection curves for MLGs is observed in both experiments and simulations: during loading/unloading cycles, MLGs dissipate energy through a "recoverable slippage" mechanism. The CG-MD simulations further reveal an atomic level interlayer slippage process and suggest that the dissipated energy scales with film perimeter. Moreover, our study demonstrates that the finite shear strength between individual layers could explain the experimentally measured size-dependent strength with thickness scaling in MLG sheets.

A Study of Disorder Shell Effects on the Mechanical Properties of SiC Nanowires

The mechanical properties of SiC nanowires were investigated using molecular dynamics simulation method. The results show that the disorder shell layer reduced the elastic modulus of SiC nanowires. This reduction mainly depends on the thickness and the atomic type of the disorder shell. Thicker C and Si disorder layers can strengthen and weaken the nanowires, respectively. Also, the core-shell wires have size-dependent strength, which can be understood by examining the variation of Young’s modulus and the volume fraction of the isolated core and isolated shell. Furthermore, the disorder coating was found to facilitate the brittle-ductile transition in the SiC core. The simulation results are expected to help the design and manufacturing of complex nanoscale architectures with desired mechanical properties.

Surface States and Band Gap Correlation in Silicon Nanoclusters

Tuning the visible emission of Si nanomaterials by modifying their size and shape is one of the key issue in optoelectronics. The observed optical gain in Si-nanoclusters (NCs) has given further impulse to nanosilicon research. We develop a phenomenological model by combining the effects of surface passivation, exciton states and quantum confinement (QC). The size and passivation dependent band gap, oscillator strength, radiative lifetime and photoluminescence (PL) intensity for NCs with diameter ranging from 1.0 to 6.0 nm are presented. By controlling a set of fitting parameters, it is possible to tune the optical band gap, PL peak and intensity. In case of pure clusters, the band gap is found to decrease with increasing NC size. Furthermore, the band gap increases on passivating the surface of the cluster with hydrogen and oxygen respectively in which the effect of oxygen is more robust. Both QC and surface passivation in addition to exciton effects determine the optical and electronic properties of silicon NCs. Visible luminescence is due to radiative recombination of electrons and holes in the quantum-confined NCs. The role of surface states on the band gap as well as on the HOMO-LUMO states is also examined and a correlation is established. Our results are in conformity with other observations. The model can be extended to study the light emission from other nanostructures and may contribute towards the development of Si based optoelectronics.