Size-dependent Strain Research Articles

Size-dependent atomic strain localization mechanism in Nb/amorphous CuNb nanolayered composites

Experiments have shown that crystalline–amorphous nanolayered composites show a strong size dependence in strength and plasticity. However, the underlying mechanism remains unknown. Here, the layer thickness (h)-dependent compressive strength and plastic deformation of Nb/amorphous CuNb nanolayered composites with h ranging from 2.8 to 20 nm have been studied by molecular dynamics simulations. It is found that the strength increases monotonically with the decrease of h, which can be well captured by the refined confined layer slip model. Furthermore, the shear banding-induced strain localization was analyzed in detail based on the evolution of the von Mises strain distribution with the applied strain and a strain localization parameter that represents the deviation of the specific atomic Mises strain from the average one of all atoms. The results show that the strain localization of the composite shows a significant size dependence and its magnitude increases with the decrease in the layer thickness. The prevention of shear band propagation in thicker layer samples is attributed to that the amorphous phase is capable of forming an atomic vortex to alleviate the strain concentration caused by dislocation absorption. The thicker amorphous layers accommodate enhanced homogeneous plasticity than the thinner ones by forming a larger vortex. Note that the above size dependence of strength and strain localization in the composite agrees well with existing experimental measurements and observations in the layer thickness range considered. As a result, the present work gives a deeper insight into the understanding of the size-dependent strengthening and strain localization mechanism in the amorphous/crystalline composites.

Anomalous size dependent softening behaviors and related deformation mechanisms of Zr/Mo multilayers

As a representative of hcp/bcc metallic multilayers, the correlation between microstructures and mechanical properties of nanostructured Zr/Mo multilayers with were studied. Zr/Mo multilayers with different layer thicknesses were prepared by magnetron sputtering method. XRD and TEM analyses revealed that Zr/Mo multilayers have Zr (0002) and Mo (110) out-of-plane crystalline texture. The nanoindentation hardness of Zr/Mo multilayers is in the range of ∼9.9–10.8 GPa at h ≤ 10 nm, while decreases with reducing layer thickness at larger h, which is on the contrary of the common rule - smaller is stronger. The aforementioned strengthening mechanism applicable in multilayers, i.e., dislocation bowing-out in nanolayers is not suitable to explain this size dependent softening behavior, while the IBS model fits well with the measured hardness at h = 10 nm. This anomalous softening behavior at large layer thickness scales may be caused by its special structures and deformation mechanisms. Dislocations interact with the grain boundaries, instead of the interfaces, and grains rotation/grain boundaries sliding are the dominant deformation mechanism at large layer thickness scales. The size-dependent strain rate sensitivity and activation volume were also explored, to revealing the rate dependent deformation mechanisms.

Experimental and analytical studies of size effects on compressive ductility response of Ultra-High-Performance Fiber-Reinforced concrete

Ultra-high-performance fiber-reinforced concrete (UHPFRC) has gained a great deal of increasing interest in structural engineering applications, particularly where high ductility, strength, and high impact resistance are of prime concern. This study focuses primarily on the size effects ductility characteristics of UHPFRC with varying fiber concentrations subjected to uniaxial compressive load. It shows how to process the data from compression cylinder tests to extract the size-dependent strain at peak stress to provide a generic size-dependent stress–strain analytical model. For a slenderness factor of 2, the predicted peak stress from the analytical model deviated 0.34%, 0.26%, and 10.5% from the experimental peak stress results for a fiber concentration of 1%, 2%, and 3%, respectively, indicating good estimate of the analytical model with the experimental results. Furthermore, a numerical flexural segmental moment-rotation approach is applied to incorporate an analytical model to quantify apparently disparate UHPFRC member strength and ductility. Tests have shown that it is not the enhancement in the material concrete compressive strength but the phenomenal brittle ductility nature, observed as a result of increasing the slenderness of the specimen; in contrast, a substantial increase in ductility was achieved after crushing of concrete due to the addition of fibers. A size-dependent analytical approach has estimated good fit with the experimental and other published results. Finally, numerical simulation using a segmental approach at the ultimate limit state of rotation dealing with flexural ductility is significantly influenced by the increase in slenderness factor of the specimens and fiber concentrations.This is evident as the rotation capacity decreased by 62% and 75% for a slenderness factor of 3 and 4, respectively, compared to the slenderness factor 2, when the fiber concentration was 1%. Furthermore, for 2% fiber concentration, the decrease was 54%, and 80%, and for 3% fiber concentration, the decrease was found to be 49%, and 79% for the slenderness factor of 3 and 4, respectively in comparison to the slenderness factor 2, suggesting both slenderness factor and fiber concentration have a significant impact on the flexural ductility.

Gold nanoparticles aggregation on graphene using Reactive force field: A molecular dynamic study.

We examine the aggregation behavior of AuNPs of different sizes on graphene as function of temperature using molecular dynamic simulations with Reax Force Field. In addition, the consequences of such aggregation on the morphology of AuNPs and the charge transfer behavior of AuNP-Graphene hybrid structure are analyzed. The aggregation of AuNPs on graphene is confirmed from the center of mass distance calculation. The simulation results indicate that the size of AuNPs and temperature significantly affect the aggregation behavior of AuNPs on graphene. The strain calculation showed that shape of AuNPs changes due to the aggregation and the smaller size AuNPs on graphene exhibit more shape changes than larger AuNPs at all the temperatures studies in this work. The charge transfer calculation reveals that, the magnitude of charge transfer is higher for larger AuNPs-graphene composite when compared with smaller AuNPs-graphene composite. The charge transfer trend and the trends seen in the number of Au atoms directly in touch with graphene are identical. Hence, our results conclude that, quantity of Au atoms directly in contact with graphene during aggregation is primarily facilitates charge transfer between AuNPs and graphene. Our results on the size dependent strain and charge transfer characteristics of AuNPs will aid in the development of AuNPs-graphene composites for sensor applications.

Ultrastrong colloidal crystal metamaterials engineered with DNA.

Lattice-based constructs, often made by additive manufacturing, are attractive for many applications. Typically, such constructs are made from microscale or larger elements; however, smaller nanoscale components can lead to more unusual properties, including greater strength, lighter weight, and unprecedented resiliencies. Here, solid and hollow nanoparticles (nanoframes and nanocages; frame size: ~15 nanometers) were assembled into colloidal crystals using DNA, and their mechanical strengths were studied. Nanosolid, nanocage, and nanoframe lattices with identical crystal symmetries exhibit markedly different specific stiffnesses and strengths. Unexpectedly, the nanoframe lattice is approximately six times stronger than the nanosolid lattice. Nanomechanical experiments, electron microscopy, and finite element analysis show that this property results from the buckling, densification, and size-dependent strain hardening of nanoframe lattices. Last, these unusual open architectures show that lattices with structural elements as small as 15 nanometers can retain a high degree of strength, and as such, they represent target components for making and exploring a variety of miniaturized devices.

Assessing Strain Rate Sensitivity of Nanotwinned Al–Zr Alloys through Nanoindentation

Nanotwinned metals have exhibited many enhanced physical and mechanical properties. Twin boundaries have recently been introduced into sputtered Al alloys in spite of their high stacking fault energy. These twinned Al alloys possess unique microstructures composed of vertically aligned Σ3(112) incoherent twin boundaries (ITBs) and have demonstrated remarkable mechanical strengths and thermal stability. However, their strain rate sensitivity has not been fully assessed. A modified nanoindentation method has been employed here to accurately determine the strain rate sensitivity of nanotwinned Al–Zr alloys. The hardness of these alloys reaches 4.2 GPa while simultaneously exhibiting an improved strain rate sensitivity. The nanotwinned Al–Zr alloys have shown grain size-dependent strain rate sensitivity, consistent with previous findings in the literature. This work provides insight into a previously unstudied aspect of nanotwinned Al alloys.

Fracture universality in amorphous nanowires

Crystalline nanowires exhibiting a wide range of size-dependent fracture and failure modes have been extensively studied, yet the fracture behaviors of amorphous materials and their size dependence remain elusive. Here extensive atomistic simulations are performed to reveal the deformation and fracture behaviors in a broad class of amorphous nanowires with varying sizes, including CuZr, CuZrAl, FeP, Si, and a ductile Lennard-Jones system. It is found that the fracture strain ɛf increases with nanowire length L but decreases with diameter D, which exhibits a linear relationship with the diameter-to-length ratio as ɛf∝D/L, —a scaling law valid in these five distinct glassy systems understudied. We develop a theoretical model, capturing the size of plastic zone at plastic yielding and its vital role in governing the final fracture strain, which shows an agreement with the simulation data. By taking into account the intrinsic atomic-level ideal strain, remarkably, all the size-dependent fracture strain data collapse, signifying the universality of fracture nature in a broad range of glassy materials.

Size and Strain of Zinc Sulfide Nanoparticles Altered by Interaction with Organic Molecules.

Nanosized zinc sulfides (nano-ZnS) have size-dependent and tunable physical and chemical properties that make them useful for a variety of technological applications. For example, structural changes, especially caused by strain, are pronounced in nano-ZnS < 5 nm in size, the size range typical of incidental nano-ZnS that form in the environment. Previous research has shown how natural organic matter impacts the physical properties of nano-ZnS but was mostly focused on their aggregation state. However, the specific organic molecules and the type of functional groups that are most important for controlling the nano-ZnS size and strain remain unclear. This study examined the size-dependent strain of nano-ZnS synthesized in the presence of serine, cysteine, glutathione, histidine, and acetate. Synchrotron total scattering pair distribution function analysis was used to determine the average crystallite size and strain. Among the different organic molecules tested, those containing a thiol group were shown to affect the particle size and size-induced strain most strongly when added during synthesis but significantly reduced the particle strain when added to as-formed nano-ZnS. The same effects are useful to understand the properties and behavior of natural nano-ZnS formed as products of microbial activity, for example, in reducing environments, or of incidental nano-ZnS formed in organic wastes.

Study on PN heterojunctions associated bending coupling in flexoelectric semiconductor composites considering the effects of size-dependent and symmetry-breaking

Under bending deformation, size-dependent and structure-associated strain gradients can occur at the interface of a flexoelectric semiconductor (FS) PN heterojunction. Consequentially, a giant flexoelectric coupling will be induced to significantly enhance the flexoelectric effect of FS structures. To better understand the strain gradient–enhanced modulation performance and also reveal some other new phenomena, in this work, we theoretically and numerically study a beam shaped FS laminated composite subjected to pure bending loads. We first establish a one-dimensional theoretical model and then numerically explore the mechanical behaviors of the selected FS beam laminate. During analysis, structural symmetry breaking and size effect are considered by tuning the beam structural size and material parameters. We find that different from piezoelectric semiconductors whose mobile charges are driven by the piezo-potential, the mobile charges of FS composites induced by the flexo-potential are deterministically associated with strain gradients. Moreover, the strain gradients can exhibit a strong size-dependent effect and are quite sensitive to structural asymmetry and material parameters. We believe that our work can provide a new way to tune the carrier transport and electromechanical characteristics of a PN junction and thus can be useful to guide the next-generation flexotronic device designs.

Size-dependent strain rate sensitivity and interface structure influenced deformation mechanisms in Ti/Ta and Ti/Zr multilayers

The nanostructured Ti/Ta and Ti/Zr multilayers with equal layer thicknesses h ranging from 2.5 to 150 nm were prepared by using magnetron sputtering technique. Their rate dependent deformation behaviors were explored by nanoindentation. With reducing h, the strain rate sensitivity m of Ti/Ta multilayers decreased from a positive value to negative at the critical h* of ~ 20 nm, at which the hardness is insensitive to strain rate. While the m of Ti/Zr multilayers decreased as the decreasing of h. This evolution of strain rate sensitivity in multilayers was interpreted in terms of the heterogeneously interfacial structure, i.e., the constituent interlayer coherent interfaces and phase boundaries in nanolayers. The deformation morphologies after nanoindentation were observed and discussed to further examine plastic deformation and dislocation activities of multilayers.

Transverse free vibration of nanobeams with intermediate support using nonlocal strain gradient theory

In the present study, the transverse free vibration of intermediately supported nanobeams is investigated in the framework of size-dependent nonlocal strain gradient theory. Unlike the classical elasticity theory, nonlocal strain gradient theory considers the micro/nano scale effects in mechanical analysis of size-dependent structures. The potential and kinetic energies have been derived for the nanobeam model and the Ritz method has been used to determine the natural frequencies of intermediately supported nanobeams. A cantilever nanobeam model with intermediate support is considered in the analysis. By changing the position of the intermediate support, dimensionless vibration frequencies of the nanobeam model have been obtained. Obtained results from the present nonlocal strain gradient theory showed that hardening or softening material responses have been observed according to the classical elasticity theory depending on the magnitude of the material length scale parameter and nonlocal scale parameter. This mechanical behavior can provide an advantage to designers while modeling the micro/nanostructures. Present results can be used for the design of nano-sensors, nanotube-based resonators, and oscillators.

Nonlinear Large-Amplitude Oscillations of PFG Composite Rectangular Microplates Based Upon the Modified Strain Gradient Elasticity Theory

In this research work, the nonlinear large-amplitude free vibration characteristics of composite microplates made of a porous functionally graded (PFG) material are addressed numerically in the presence of different size-dependent strain gradient tensors as microscale. Accordingly, for the first time, the effect of each microstructural tensor is analyzed separately on the nonlinear free oscillations of PFG microplates with and without a central cutout. In order to fulfill this goal, the isogeometric computation approach is engaged to integrate the finite element approach into the nonuniform B-spline-based computer aided design tool. Accordingly, the geometry of the microplate with a central cutout is modeled smoothly to verify C−1 continuity based upon a refined higher-order plate formulations. In this regard, the microstructural-dependent frequency responses associated with the nonlinear free oscillations of microplates are traced. In both the cases of simply supported and clamped boundary conditions, it was revealed that the fundamental frequency is enhanced about 1.20% by considering only the symmetric rotation gradient tensor, about 3.27% by taking only the dilatation gradient tensor, and 9.43% by considering only the deviatoric stretch gradient tensor. On the other hand, the anisotropic character of PFG composite microplates results in an unsymmetrical frequency response curve, as the nonlinear frequencies associated with negative oscillation amplitudes are a bit higher than those of positive ones.

Kinetics and energetics of room-temperature microstructure in nanocrystalline Cu films: The grain-size dependent intragrain strain energy

The fast kinetics of the low-temperature microstructure evolution in nanocrystalline metals requires an additional driving force from the excess intragrain energy in addition to the driving forces from the grain boundary energy, surface or interface energy, and thermal strain energy. If the excess volume of the grain boundary induces lattice distortions in grain interiors, the intragrain energy is the elastic-strain energy and can be determined from a grain-size-dependent strain model. Considering the available intragrain strain energy, we use transmission electron microscopy, x-ray diffraction line-broadening analysis, and theoretical models to investigate the kinetics and energetics of room-temperature nanostructure relaxation and abnormal grain growth in electroplated nanocrystalline Cu films devoid of thermal strains and high-density dislocations. The experimental data of grain sizes and microstrains are consistent with the theoretical size-dependent strain model. The limited nanostructure relaxation of Cu occurs with the grain boundary width reduction and intragrain strain release, which cannot alter the structural anisotropy and intrinsic high-energy state of nanograins. Based on quantitative descriptions of the variations in grain size, microstrain, and transformed fraction during abnormal grain growth, the possible driving forces and grain boundary mobility were systematically evaluated. The results indicate that the size-dependent intragrain strain energy provides a crucial driving force for rapid nanograin growth and texture transition, whereas the low nanograin boundary mobility in Cu films is probably correlated with the strained-lattice migration and faceted-boundary migration.

Nonlinear Stability Characteristics of Porous Graded Composite Microplates Including Various Microstructural-Dependent Strain Gradient Tensors

In this study, the nonlinear buckling and postbuckling characteristics of composite microplates made of a porous functionally graded (PFG) material are scrutinized in the presence of different size-dependent strain gradient tensors as microscale. Accordingly, for the first time, the effect of each microstructural tensor is analyzed separately on the nonlinear stability of PFG microplates with and without a central cutout. In order to fulfill this goal, the isogeometric computation approach is engaged to integrate the finite element approach into the nonuniform B-spline-based computer aided design tool. Accordingly, the geometry of the microplate with a central cutout is modeled smoothly to verify [Formula: see text] continuity based upon a refined higher-order plate formulations. In this regard, the microstructural-dependent load-deflection paths associated with the nonlinear stability of axially compressed microplates are traced.

Effect of point defects and nanopores on the fracture behaviors in single-layer MoS2 nanosheets

Point defects and nanopores are inevitable and particularly noticeable in single-layer (SL) MoS2. Molecular dynamics (MD) simulations have been done to comprehensively study the influences of point defects and nanopores on tensile deformation behaviors of SLMoS2 nanosheets, and the dependences of fracture properties on defect type and concentration, pore size, temperature and strain rate are discussed. The formation energy of S vacancy (VS) is the lowest one, but that of VMoS6 is the highest one, corresponding to the highest and lowest fracture stress, respectively. The local stress concentration around point defects and nanopores might lead to the early bond breaking and subsequent nucleation of cracks and brittle fracture upon tensile loading. A modified Griffith criterion is proposed to describe the defect concentration and pore size dependent fracture stress and strain. These findings provide us an important guideline for the structural design of 2D materials in future applications.

Size-dependent strain-engineered nanostructures in MoS2 monolayer investigated by atomic force microscopy

The strain has been employed for controlled modification of electronical and mechanical properties of two-dimensional (2D) materials. However, the thermal strain-engineered behaviors of the CVD-grown MoS2 have not been systematically explored. Here, we investigated the strain-induced structure and properties of CVD-grown triangular MoS2 flakes by several advanced atomic force microscopy. Two different kinds of flakes with sharp-corner or vein-like nanostructures are experimentally discovered due to the size-dependent strain behaviors. The critical size of these two kinds of flakes can be roughly estimated at ∼17 μm. Within the small flakes, the sharp-corner regions show specific strain-modified properties due to the suffering of large tensile strain. While in the large MoS2 flakes, the complicated vein-like nanoripple structures were formed due to the interface slipping process under the larger tensile strain. Our work not only demonstrates the size-specific strain behaviors of MoS2 flakes but also sheds light on the artificial design and preparation of strain-engineered nanostructures for the devices based on the 2D materials.

A novel size-dependent nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite nanoplates

The paper presents a novel nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates. To observe the length scale and size-dependency effects of nanostructures, the nonlocal strain gradient theory (NSGT) is considered. The present model is efficient to capture both nonlocal effects and strain gradient effects in nanoplate structures. In addition, the material properties of the FG-CNTRC are assumed to be graded in the plate thickness direction. Based on the higher order shear deformation theory (HSDT), the weak form of the governing equations of motion of the nanoplates is presented using the principle of virtual work. Afterward, the natural frequency and deflection of the nanoplates are made out of isogeometric analysis (IGA). Thanks to higher order derivatives and continuity of NURBS basic function, IGA is suitable for the weak form of NSGT which requires at least the third-order derivatives in approximate formulations. Effects of nonlocal parameter, strain gradient parameter, carbon nanotube (CNT) volume fraction, distributions of CNTs and length-to-thickness ratios on deflection and natural frequency of the nanoplates are examined and discussed in detail. Numerical results are developed to show the phenomenon of stiffness-softening and stiffness-hardening mechanisms of the present model.

Size-dependent strain in fivefold twins of gold

Multiple twinned structures are common in low-dimensional materials. They are intrinsically strained due to the geometrical constraint imposed by the non-crystallographic fivefold symmetry. In this study, the strain distributions in sub-10 nm fivefold twins of gold have been analyzed by combining aberration-corrected transmission electron microscopy and first-principles calculations. Bending of atomic planes has been measured by both experiments and calculations, and its contribution to the filling of the angular gap was shown to be size-dependent.

Buckling Analysis of Intermediately Supported Nanobeams via Strain Gradient Elasticity Theory

Buckling of axially loaded cantilever nanobeams with intermediate support have been studied in the current study. Higher order size dependent strain gradient theory has been utilized to capture the scale effect in nano dimension. Minimum total potential energy formulation has been used in modeling of nanobeam. Approximate Ritz method has been applied to the energy formulation for obtaining critical buckling loads. Position of the intermediate support has been varied and its effect on the critical buckling load has been investigated in the analysis. Mode shapes in critical buckling loads have been shown for various intermediate support positions. Present results could be useful in design of carbon nanotube resonators.

Nonlinear vibration of fluid conveying cantilever nanotube resting on visco‐pasternak foundation using non‐local strain gradient theory

Frequency analysis and forced vibration response of fluid conveying viscoelastic nanotubes that resting on nonlinear visco-pasternak foundation under magnetic field using size-dependent non-local strain gradient theory are considered in this study. It is supposed that the nanotube is modelled as cantilever type beam and subjected to a harmonic load. The material property of the nanotube is modelled by Kelvin-Voigt viscoelastic constitutive relation and slip boundary conditions of nanotube conveying fluid are taken into account. Extended Galerkin method is used to obtain the nonlinear differential equation of the motion and the multiple time-scales method is utilised to investigate the primary vibration resonance of the nanotube. Firstly, the frequency analysis is performed on the linear system and the effects of foundation coefficients on the natural frequency are investigated at several flow velocities. Moreover, the resonance properties of the system are solved in closed form and analysed from the frequency-response curves, and then the effects of the non-local parameter, length scale parameter and magnetic field are fully investigated. In this case, non-local parameter, length scale parameter and foundation coefficients are highly influential on the frequency response of the considered system.