Size-dependent Mechanical Properties Research Articles

Investigation of the size effect for photonic crystals

Three types of photonic crystal (PC) thin films have been prepared for the investigation of their deformation behaviors by nanoindentation tests at the microscale and nanoscale. Each type of PC thin film was composed of poly(methyl methacrylate) (PMMA) nanoparticles with a uniform size. Another type of thin film was prepared by assembling nanoparticles with three different sizes. It was exciting to observe that the hardness and Young’s modulus were significantly improved (more than 15 times) in well-ordered PC thin films than disordered ones. Furthermore, size-dependent mechanical properties were observed for the three types of PCs. Such a size effect phenomenon can be attributed to the special polycrystalline material having a periodical face-centered cubic structure of PC thin films. Furthermore, the indentation size effect that shows that the indentation hardness decreases with an increasing indentation depth has also been observed for all four types of thin films. It is conjectured that the application of the PC structure to other functional materials may enhance their mechanical properties.

Interface failure modes explain non-monotonic size-dependent mechanical properties in bioinspired nanolaminates.

Bioinspired discontinuous nanolaminate design becomes an efficient way to mitigate the strength-ductility tradeoff in brittle materials via arresting the crack at the interface followed by controllable interface failure. The analytical solution and numerical simulation based on the nonlinear shear-lag model indicates that propagation of the interface failure can be unstable or stable when the interfacial shear stress between laminae is uniform or highly localized, respectively. A dimensionless key parameter defined by the ratio of two characteristic lengths governs the transition between the two interface-failure modes, which can explain the non-monotonic size-dependent mechanical properties observed in various laminate composites.

On the elongated domains in electrospun nanofibers of polyamide-6 blends

We report analysis of electrospun polymer nanofibers fabricated from blends of semicrystalline polyamide-6 (PA-6) and fully amorphous polyamide-6 (PA-6I) in the narrow diameter range of 200–250 nm. The combined differential scanning calorimetry and wide angle x-ray scattering results show the presence of α- and γ-phase crystals in PA-6 nanofibers. Simultaneous small- and wide-angle x-ray scattering investigations confirmed the existence of small elongated domains which were formed during the electrospinning process due to stretching of polymer chains. The Debye–Bueche analysis determined a cross-sectional width of elongated domains in the range of 10.8–16 Å. Additionally, analysis by Ruland’s method revealed a decrease in the length of elongated domains with increasing crystalline phase content in the blends. Evaluation of Herman’s orientation function suggested that the domains possessed higher molecular anisotropy along the c-axis in PA-6I compared to PA-6 nanofibers. These investigations and the suggested role of the amorphous phase in molecular stretching of polymer chains in electrospun nanofibers, may have broad implications for the size-dependent mechanical properties.

Size-dependent piezoelectric and mechanical properties of electrospun P(VDF-TrFE) nanofibers for enhanced energy harvesting

Dimensional reduction of electrospun P(VDF-TrFE) increases crystallinity (DOC), electroactive phase content (EA), Young’s modulus (E) and piezoelectric coefficient (d33), collectively leading to enhanced piezoelectric energy harvesting efficiency.

Analytical Couple-stress Solution for Size-dependent Large-amplitude Vibrations of FG Tapered-nanobeams

In this paper, analytical couple-stress solution for size-dependent large-amplitude vibrations of FG (functionally-graded) tapered-nanobeams is presented. Using the modified couple-stress theory, the small scale effects are accounted for. Employing the Homotopy-Pade Analysis Method, efficient and accurate analytical expressions for the deflection and non-linear frequencies of the both single and double tapered nanobeam are presented. Very good agreement is observed between the present work results and some available results reported in the literature. This study may be helpful to investigate the size-dependent mechanical properties of MEMS\NEMS. Therefore, the proposed analytical solution can be used as an efficient tool for the material or geometrical parametric studies of small scale devices consisting of beams for their design and optimization which involves a large number of simulations.

An experimental investigation on the tangential interfacial properties of graphene: Size effect

The size-dependent mechanical properties and the edge effect of the tangential interface between graphene and a polyethylene terephthalate substrate (PET) are investigated. The interfacial mechanical parameters of graphene with seven different lengths are measured by in-situ Raman spectroscopy experiments. New phenomena are observed, such as the existence of the edge effect in the interfacial stress/strain transfer process, and the length of the edge of the interface can be affected by the size of graphene. Additionally, the interfacial shear stress exhibits a size effect, with its value significantly decreasing with an increase of the length of graphene. However, the ultimate stiffness and failure strength of the interface are size-independent as they are constant regardless of the length of graphene.

Size-dependent mechanical properties of Mg nanoparticles used for hydrogen storage

Magnesium (Mg) hydride is a promising hydrogen storage material, yet its application has been limited by the slow hydrogen sorption kinetics. Recently, Mg nanoparticles have shown significant improvement of hydrogen storage properties in terms of dimensional stability upon cycling with the trend that the smaller the particle, the better the sorption kinetics. Since the volume change during sorption generates stress, leading to plastic deformation, the fundamentals of the mechanical deformation of the Mg particles are a significant issue. By using in situ transmission electron microscope compression tests and atomistic simulations on Mg nanoparticles, it was observed that deformation in the larger particles was dominated by the nucleation of ⟨a⟩-type dislocations from stress concentrations at the contact surface, while the smaller particles deformed more homogeneously with greater distribution of multiple types of dislocation sources. Importantly, this improvement of plastic deformation with decrease in size is orientation-independent. First-principles calculations suggest that this improved plasticity can be explained by the nearly-isotropic ideal shear strength for Mg, which becomes more important in smaller nanoparticles. As a result, the smaller Mg nanoparticles demonstrated better plastic stability to accommodate volume change upon hydrogen storage cycling.

Size-dependent mechanical properties in AA6082 tailor welded specimens

AA6082 tailor welded blanks (TWBs) produced using laser welding and friction stir welding were studied in this paper. The nominal mechanical properties of welded AA6082 under uniaxial tension conditions were characterised by evaluating the local properties of the base material, heat affected zone (HAZ) and weld zone. Tensile specimens were machined in the way that the weld line lies perpendicular to the loading axis. Three standard-sized specimens containing varying ratios of weld in the gauge region of the specimen were used to determine the size-dependent properties of welded AA6082 in the TWBs. A post-weld strength prediction (PWSP) model, based on the theories of plasticity, has been developed to estimate the post-weld properties of the tailor welded specimens. The model can be used to predict the post-weld yield strength and the global tensile behaviour of welded AA6082 specimens. Good agreements between the modelling and the experimental results have been obtained, with the yield strength deviation less than 6%. It was found that the yield strength increased with increasing dimensions of the tensile specimens. The size-dependent phenomenon was studied and the complex plastic deformation mechanisms have been found to cause the size-dependent phenomenon.

Size-dependent mechanical properties of axial and radial mixed AlN/GaN nanostructure

In this paper, continuum multiscale models are proposed to describe the size-dependent mechanical properties of two kinds of heterogeneous nanostructures: radially heterogeneous nanowires and longitudinally heterogeneous nanolaminates. In both cases, the continuum models involve additional surface/interface energies, which allow capturing size effects. Several models of imperfect interface models, like coherent and spring-layer ones, are shown to respectively capture the size effects, which are reported by first-principles calculations performed on heterogeneous nanostructures. In each case, a procedure is proposed to identify the parameters of the surface/interface model in the continuum framework, based on first-principles calculations performed on slab systems. The obtained continuum models allow avoiding full computations on atomistic models, which are not affordable for large sizes (diameters, layer thickness). An increase of the overall stiffness for both kinds of heterogeneous AlN/GaN nanostructures with the decrease of the dimensions is evidenced. The continuum models are then compared with full first-principles calculations to demonstrate their accuracy and their ability to capture size effects.

Molecular statics simulations of the size-dependent mechanical properties of copper nanofilms under shear loading

Molecular statics simulations are conducted on single-crystal copper nanofilms subjected to shear loading to examine the effect of thickness on the mechanical properties of nanofilms. Simulation results show that not only the yield strength but also the shear modulus increases with decreasing film thickness. In order to better relate the yield strength of a copper nanofilm to its thickness, a Hall–Petch-like fitting function is proposed to predict the variation of yield strength with film thickness. The initial yield is found to be associated with the nucleation of dislocations. The energy required for the first nucleation of dislocations is calculated and plotted as a function of film thickness to elucidate the origin of the thickness effect on yield strength. In addition, the production of vacancy clusters is also found to depend on film thickness and three new patterns of vacancy clusters are observed in our simulations.

In situ cracking of silica beads in the SEM and TEM — Effect of particle size on structure–property correlations

Stöber Fink Bohn (SFB) silica is a well-known colloidal system: monodisperse spherical particles are readily obtained by this wet chemical synthesis route. Despite the frequent application of SFB silica, its mechanical properties are not comprehensively understood. Within this account, size dependent mechanical properties of single SFB particles are systematically investigated using in situ SEM and TEM techniques: particle properties are addressed in the size range of 1.5μm down to 200nm. Both, untreated particles and heat treated particles densified at 1000°C are investigated. Structural characterization by vibrational spectroscopy, by solid state nuclear magnetic resonance spectroscopy, by scanning electron microscopy and by focused ion beam machining allows correlating mechanical properties and the internal particle structure. For untreated particles comprised of a weakly cross-linked silica network a high degree of plasticity associated with low Young's moduli and hardness values is found. At large strains only cracking without full fracture of the particles occurs, whereby the crack path is clearly linked to the synthesis conditions: for larger particles obtained from a multistep growth process cracks propagate along weak intraparticle interfaces and are deflected around an inner core structure. After the thermal treatment cross-linking of the silica network is significantly enhanced and Young's moduli comparable to vitreous silica accompanied by increased hardness values are found. Only the smallest particles exhibit cracking; fracture into two or more pieces is distinguished for particles above 500nm. It is found by SEM imaging that the relative occurrence of cracking into several pieces is increasing with size — a behaviour associated with the brittle to ductile transition of silica. By testing a large quantity of particles, statistical significance is ensured.

Recent Simulation Study on Precise Positioning of Carbon Nanotubes by Dielectrophoresis

Carbon nanotubes (CNTs) have been widely studied for their unique size-dependent electrical, mechanical, and chemical properties. However, CNTs need to be precisely positioned in complex device structures. Dielectrophoresis (DEP) is an effective and practical method for precise assembly of CNTs. In this paper, the researches on simulation of precise positioning of CNTs by DEP are reviewed. Single electrode pairs include those with round, triangle, and rectangular tip shapes and electrode arrays such as comb electrodes are also taken accounted. The moving trajectories of CNTs during DEP from the selected literature are introduced. The effect of floating electrodes on precise manipulation of CNTs is examined as well.

Finite element study for conical indentation of elastoplastic micropolar material

Numerous experiments have repetitively shown that the material behavior presents effective size dependent mechanical properties at scales of microns or submicrons. In this paper, the size dependent behavior of micropolar theory under conical indentation is studied for different indentation depths and micropolar material parameters. To illustrate the effectiveness of the micropolar theory in predicting the indentation size effect (ISE), an axisymmetric finite element model has been developed for elastoplastic contact analysis of the micropolar materials based on the parametric virtual principle. It is shown that the micropolar parameters contribute to describe the characteristic of ISE at different scales, where the material length scale regulates the rate of hardness change at large indentation depth and the value of micropolar shear module restrains the upper limit of hardness at low indentation depth. The simulation results showed that the indentation loads increase as the result of increased material length scale at any indentation depth, however, the rate of increase is higher for lower indentation depth, relative to conventional continuum. The numerical results are presented for perfectly sharp and rounded tip conical indentations of magnesium oxide and compared with the experimental data for hardness coming from the open literature. It is shown that the satisfactory agreement between the experimental data and the numerical results is obtained, and the better correlation is achieved for the rounded tip indentation compared to the sharp indentation.

Prediction of mechanical properties of microstructures through a nonlocal stress field theory

The gradient type of nonlocal stress field theory has been one of the most popular theoretical approaches to study some size-dependent mechanical properties of microstructures. In this work, the nonlocal elasticity field theory is employed to investigate transverse bending vibration of the microbeams subjected to a pair of initial axial tensions, and the dynamical responses of such microstructures are determined and discussed in detail. The governing equation of motion containing a small length–scale parameter is derived according to the mechanical model constructed at microscale. Subsequently, two different methods, including the method of separation of variables and the multiple-scales analysis, are applied in the equation of motion to reveal the nonlocal elastic effects in vibrational behaviors of microstructures. It shows that the results by the two methods are in good agreement. Furthermore, the critical axial tension is also obtained, and it is observed to decrease with an increase in microscale parameter, which means an increase in nonlocal elastic effects causes the critical axial tension to decrease. By comparing with the results provided by the classical continuum vibration theory, inherent frequencies of the microbeams are lower or the bending stiffness is weakened in such a nonlocal stress model presented in this article.

Size-dependent mechanical properties of 2D random nanofibre networks

The mechanical properties of nanofibre networks (NFNs) are size dependent with respect to different fibre diameters. In this paper, a continuum model is developed to reveal the size-dependent mechanical properties of 2D random NFNs. Since such size-dependent behaviours are attributed to different micromechanical mechanisms, the surface effects and the strain gradient (SG) effects are, respectively, introduced into the mechanical analysis of NFNs. Meanwhile, a modified fibre network model is proposed, in which the axial, bending and shearing deformations are incorporated. The closed-form expressions of effective modulus and Poisson's ratio are obtained for NFNs. Different from the results predicted by conventional fibre network model, the present model predicts the size-dependent mechanical properties of NFNs. It is found that both surface effects and SG effects have significant influences on the effective mechanical properties. Moreover, the present results show that the shearing deformation of fibre segment is also crucial to precisely evaluate the effective mechanical properties of NFNs. This work mainly aims to provide an insight into the micromechanical mechanisms of NFNs. Besides, this work is also expected to provide a more accurate theoretical model for 2D fibre networks.

Sensitive determination of the Young's modulus of thin films by polymeric microcantilevers

A method for the highly sensitive determination of the Young's modulus of TiO2 thin films exploiting the resonant frequency shift of a SU-8 polymer microcantilever (MC) is presented. Amorphous TiO2 films with different thickness ranging from 10 to 125 nm were grown at low temperature (90 °C) with subnanometer thickness resolution on SU-8 MC arrays by means of atomic layer deposition. The resonant frequencies of the MCs were measured before and after coating and the elastic moduli of the films were determined by a theoretical model developed for this purpose. The Young's modulus of thicker TiO2 films (>75 nm) was estimated to be about 110 GPa, this value being consistent with the value of amorphous TiO2. On the other hand we observed a marked decrease of the Young's modulus for TiO2 films with a thickness below 50 nm. This behavior was found not to be related to a decrease of the film mass density, but to surface effects according to theoretical predictions on size-dependent mechanical properties of nano- and microstructures.

Role of surface on the size-dependent mechanical properties of copper nano-wire under tensile load: A molecular dynamics simulation

In this study we have used atomistic simulations to investigate the role of surface on the size-dependent mechanical properties of nano-wires. In particular, we have performed computational investigation on single crystal face-centered cubic copper nano-wires with diameters ranging from 2 to 20nm. The wire axis for all the nano-wires are considered along the [001] direction. Characterization of the initial optimized structures revealed clear differences in interatomic spacing, stress, and potential energy in all the nano-wires. The mechanical properties with respect to wire diameter are evaluated by applying tension along the [001] direction until yielding. We have discussed the stress–strain relationships, Young's modulus, and the variation in potential energy from surface to the center of the wire for all the cases. Our results indicate that the mechanical response (including yield strain, Young's modulus, and resilience) is directly related to the proportion of surface to bulk type atoms present in each nano-wire. Thus the size-dependent mechanical properties of single crystal copper nano-wire within elastic region are attributed to the surface to volume ratio (surface effect). Using the calculated response, we have formulated a mathematical relationship, which predicts the nonlinear correlation between the mechanical properties and the diameter of the wire.

Origin of Size Dependency in Coherent-Twin-Propagation-Mediated Tensile Deformation of Noble Metal Nanowires

Researchers have recently discovered ultrastrong and ductile behavior of Au nanowires (NWs) through long-ranged coherent-twin-propagation. An elusive but fundamentally important question arises whether the size and surface effects impact the twin propagation behavior with a decreasing diameter. In this work, we demonstrate size-dependent strength behavior of ultrastrong and ductile metallic NWs. For Au, Pd, and AuPd NWs, high ductility of about 50% is observed through coherent twin propagation, which occurs by a concurrent reorientation of the bounding surfaces from {111} to {100}. Importantly, the ductility is not reduced with an increase in strength, while the twin propagation stress dramatically increases with decreasing NW diameter from 250 to 40 nm. Furthermore, we find that the power-law exponent describing the twin propagation stress is fundamentally different from the exponent describing the size-dependence of the yield strength. Specifically, the inverse diameter-dependence of the twin propagation stress is directly attributed to surface reorientation, which can be captured by a surface energy differential model. Our work further highlights the fundamental role that surface reorientations play in enhancing the size-dependent mechanical behavior and properties of metal NWs that imply the feasibility of high efficiency mechanical energy storage devices suggested before.

Size-Dependent Mechanical Properties in Ni–Al Intermetallic Nano-particles Studied Using Embedded Atom Method

The energy and elastic constants C11, C12, and C44 as a function of particle size for Ni–Al intermetallic nano-particles are investigated by using embedded-atom method. We find that for nano-particles of large size, the size-dependent change in C12 is slightly different from those in C11 and C44, which is attributed to the internal strains. We also find that for the nanoparticles of size larger than 2.5 nm, the calculated C11, C12, and C44 of 1.52, 0.88 and 0.77 eV/A3 are in agreement with the available experimental results.

An experimental study on the stiffness of size-isolated microbubbles using atomic force microscopy

To fully assess contrast-enhanced acoustic bioeffects in diagnostic and therapeutic procedures, the mechanical properties of microbubbles need to be considered. In the present study, direct measurements of the microbubble stiffness were performed using atomic force microscopy by applying nanoscale compressions (up to 25 nN/s) on size-isolated, lipidcoated microbubbles (diameter ranges of 4 to 6 μm and 6 to 8 μm). The stiffness was found to lie between 4 and 22 mN/m and to decrease exponentially with the microbubble size within the diameter range investigated. No cantilever spring constant effect was found on the measured stiffness. The Young's modulus of the size-isolated microbubbles used in our study ranged between 0.4 and 2 MPa. Microstructures on the surface of the microbubbles were found to influence the overall microbubble elasticity. Our results indicated that more detailed theoretical models are needed to account for the size-dependent microbubble mechanical properties to accurately predict their acoustic behavior. The findings provided useful insights into guidance of cavitation-induced drug and gene delivery and could be used as part of the framework in studies on the shear stresses induced on the blood vessel walls by oscillating microbubbles.