Considering the nonlocal small-scale effect and surface effect, we perform the size-dependent vibration analysis of carbon nanotube (CNT). The modified governing equations for CNT’s vibration behaviors are derived by using the nonlocal Euler–Bernoulli and Timoshenko beam models, together with the consideration of surface tension and surface elasticity. According to the numerical experiments, both small-scale effect and surface effect make a substantial difference. For flexural vibration, size effect for CNT’s vibration behaviors weakens with the increase of its diameter, but strengthens with the increase of the length–diameter ratio; for shear vibration with constant length–diameter ratio, a nonlinear correlation between size effect and CNT’s diameter exists, suggesting that there is a typical diameter for CNTs, which corresponds to the “strongest” size effect. In addition, the effects of elastic substrate modulus, temperature change, and axial preloading on the vibration behaviors and their size-dependence are analyzed, respectively.

The effects of specimen size, Hall–Petch (H-P) grain or subgrain size, particle size plus spacing, and crack size on the yield strength, plastic deformation, and fracturing properties of crystalline materials are described on a dislocation mechanics basis. The size effects are assessed at relevant macro- and/or micro-and/or nano-scale dimensions; in the latter case, at the upper-limiting strength levels. The description is applied mostly to face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) metals but also involves grain size/particle size–dependent (composite) steel material behaviors. Competition is described for the role of dislocation pile-ups versus hole-joining mechanisms for ductile failure. Grain size–dependent microhardness and strain rate sensitivity measurements are presented for nano-grain size strengthening and grain size weakening, respectively. An intrinsic size effect is demonstrated for silicon crystal nano-indentation hardness testing, which, on microscale loading, leads to evaluation of crack size dependence and, for polycrystalline alumina, to associated H-P behavior for the fracture mechanics stress intensity.

Theoretical models for the strength and ductility of high-order hierarchically nanotwinned metals are developed, and especially analytical expressions of mechanical parameters with various influencing factors are deduced. Furthermore, the size effect on mechanical properties is analyzed based on these mechanism-based plasticity models, wherein the effects of twin spacing and grain size on the strength and ductility are discussed systemically. Related analysis demonstrates that the twin spacing plays an important role. Through adjusting the twin spacing of the primary layer of twin lamellae and optimizing the combination of twin spacing of the high-order layers, expected mechanical properties with high strength and high ductility could be achieved. Besides, the grain size also has a significant effect, and the reduction in grain size still induces a positive effect on the strength, whereas a negative effect on the ductility. Finally, a material design approach for the optimization of comprehensive mechanical properties is suggested.

Utilizing the experimental and modeling approaches, the Gamma radiation effects on stress responses of the silicon rubber foam under quasistatic compression are investigated. In the experimental work, the samples of the silicon rubber and the silicon rubber foams are quasistatically compressed before and after the Gamma radiation (a dose of 500 kGy and a dose rate of 100 Gy/min). The data reveal that the Gamma radiation obviously increases the material hardness, e.g., the compressive stresses of the silicon rubber and the silicon rubber foams both increase over 5 times as the strain is 20%. In the simulation work, a multiscale method combined with finite element method is developed to numerically predict the compressive stress of the silicon rubber foams. The microscale models are first constructed based on the real microstructures of the silicon rubber foams. The compressive stress and strain relation before and after the Gamma radiation is then simulated and obtained utilizing the phenomenological constitutive models based on the testing data of the silicon rubber. The simulation reveals that the Gamma radiation strongly affects the compressive response of the microscale models. The stress responses of the microscale models are then transferred into the macroscale models. The results also prove that the Gamma radiation obviously increases the hardness of the macroscale models. Data comparison shows that the numerical results agree with the testing data well, which verifies the developed method. The present work develops a new method to predict the radiation effects on mechanical properties of rubber foams.

This article reports on the growth kinetics of cerium oxide (CeO2) nanoparticles prepared via a sintering method. By varying the sintering temperatures and periods of time, particle size of CeO2 nanoparticles was tuned from 11 to 100 nm. Ostwald ripening mechanism prevails in the growth process, and the growth kinetics is determined to follow an equation, D5 = 16.25 + 3.6 × 1020 exp(−344.20/RT) in the temperature range of 700 to 1000°C. After dispersing Pt on CeO2 nanoparticles, the size effect for the catalytic performance of the CO oxidation reaction was researched. When temperature and period of time are set at 700 °C and 2 h, respectively, dispersion of Pt onto CeO2 nanoparticles led to the largest quantity of chemisorbed oxygen species on the surface and the best catalytic performance. The findings reported here would provide a feasible path for the preparation of advanced catalysts in the future and moreover to discover novel size-dependent supports for many catalytic applications.

The stability of dynamic fracture is a fundamental and challenging problem in the field of materials science. The grain size effect on dynamic fracture instability in polycrystalline graphene under tear loading is explored via theoretical analysis and molecular dynamics simulations. The fracture stability phase diagram in terms of grain size and crack propagation velocity is obtained, and three regions of crack propagation are identified: stable, metastable, and unstable. For grain size above 2 nm, there exists a critical velocity beyond which fracture instability occurs, and this critical velocity depends linearly on grain size. Decreasing grain size leads to reduced characteristic time for correction of crack path deflection, which plays a dominant role in dynamic fracture instabilities. However, when grain size is below 2 nm, there does not exist a critical velocity for steady propagation of cracks due to discontinuous effects. Our results also provide a valuable insight into dynamic fracture of polycrystalline graphene as well as other 2D and quasi-2D materials.

Nanocrystalline and nanolaminated materials show enhanced radiation tolerance compared with their coarse-grained counterparts, since grain boundaries and layer interfaces act as effective defect sinks. Although the effects of layer interface and layer thickness on radiation tolerance of crystalline nanolaminates have been systematically studied, radiation response of crystalline/amorphous nanolaminates is rarely investigated. In this study, we show that irradiation can lead to formation of nanocrystals and nanotwins in amorphous CuNb layers in Cu/amorphous-CuNb nanolaminates. Substantial element segregation is observed in amorphous CuNb layers after irradiation. In Cu layers, both stationary and migrating grain boundaries effectively interact with defects. Furthermore, there is a clear size effect on irradiation-induced crystallization and grain coarsening. In situ studies also show that crystalline/amorphous interfaces can effectively absorb defects without drastic microstructural change, and defect absorption by grain boundary and crystalline/amorphous interface is compared and discussed. Our results show that tailoring layer thickness can enhance radiation tolerance of crystalline/amorphous nanolaminates and can provide insights for constructing crystalline/amorphous nanolaminates under radiation environment.

Reactions in Ni/Al nanolaminates exhibit high combustion temperatures and wave speeds that are customizable through changes to nanostructure. Nanolaminates fabricated via vapor deposition exhibit columnar grains with average diameters on the order of the individual layer thickness; yet, their role on nanolaminate combustion has not been previously investigated. The current work uses molecular dynamics simulations to elucidate the effect of grain size on reaction rates and combustion temperatures in Ni/Al nanolaminates. Decreasing grain size is shown to increase reaction rates as well as increase peak temperatures consistent with the excess enthalpy of smaller grain sizes. Additionally, grain boundaries provide heterogenous nucleation sites for the diffusion-restricting B2–NiAl phase. Focusing on Ni diffusion into liquid Al, an effective diffusion coefficient is computed as a function of grain size, which may be used in thermodynamic models for this stage of the reaction.

Irradiation resistance of metallic nanostructured multilayers is determined by the interactions between defects and phase boundaries. However, the dose-dependent interfacial morphology evolution can greatly change the nature of the defect–boundary interaction mechanisms over time. In the present study, we used atomistic models combined with a novel technique based on the accumulation of Frenkel pairs to simulate irradiation processes. We examined dose effects on defect evolutions near zirconium–niobium multilayer phase boundaries. Our simulations enabled us to categorize defect evolution mechanisms in bulk phases into progressing stages of dislocation accumulation, saturation, and coalescence. In the metallic multilayers, we observed a phase boundary absorption mechanism early on during irradiation, while at higher damage levels, the increased irradiation intermixing triggered a phase transformation in the Zr–Nb mixture. This physical phenomenon resulted in the emission of a large quantity of small immobile dislocation loops from the phase boundaries.

Dislocation-mediated plasticity in stable nanocrystalline metals, where grain boundary motion is suppressed, is revisited in the context of dislocation elastodynamics. The effect of transient waves that emanate from the generation and motion of dislocations is quantified for an idealized Cu–10 at.% Ta system with grain sizes on the order of 50 nanometers. Simulations indicate that for this material, as dislocation velocities approach 0.6–0.8 times the shear wave speed, grains several grain diameters away from the initial glide event experience a large transient shear stress for a finite duration. These transient shear stresses increase with increasing glide velocity and can activate nucleation sites far from the original nucleation event. These considerations are used to explain recent experimental observations of a lack of increase in flow stress with increasing loading rate, as well as localization resistance, in this class of stable nanocrystalline metals.

The effect of grain size on the flow strength of FCC polycrystals was analyzed by means of computational homogenization. The mechanical behavior of each grain was dictated by a dislocation-based crystal plasticity model in the context of finite strain plasticity and takes into the account the formation of pile-ups at grain boundaries. All the model parameters have a clear physical meaning and were identified for different FCC metals from dislocation dynamics simulations or experiments. It was found that the influence of the grain size on the flow strength of FCC polycrystals was mainly dictated by the similitude coefficient K that establishes the relationship between the dislocation mean free path and the dislocation density in the bulk. Finally, the modeling approach was validated by comparison with experimental results of the effect of grain size on the flow strength of Ni, Al, Cu, and Ag.

Amorphous/crystalline (A/C) nanolayers provide an effective model system to study the mechanical behavior and size effects of metallic glasses and crystalline metals in confined geometries. In this work, we experimentally investigated the structure–property relationship in A/C nanolayers containing HCP crystalline layers. CuTi/Ti and CuZr/Zr nanolayers were prepared by magnetron sputtering with layer thicknesses in the range 10–100 nm. The hardness values of the CuTi/Ti and CuZr/Zr nanolayers were close to those of the monolithic CuTi and CuZr, respectively. The hardness remained virtually the same for different layer thicknesses as opposed to CuTi/Cu amorphous/FCC crystalline nanolayers, which exhibit increasing strength with decreasing layer thickness. Confined layer slip model predicts that the effective flow stress of HCP crystalline layers is higher than that of the amorphous layers. As a result, the strength and size effects are governed by the mechanical behavior of the softer amorphous layer.

Metal matrix composites (MMCs) have great potential to replace monolithic metals in many engineering applications due to their enhanced properties, such as higher strength and stiffness, higher operating temperature, and better wear resistance. Despite their attractive mechanical properties, the application of MMCs has been limited primarily due to their high cost and relative low fracture toughness and reliability. Microstructure determines material fracture toughness through activation of different failure mechanisms. In this paper, a 3D multiscale modeling technique is introduced to resolve different failure mechanisms in MMCs. This approach includes 3D microstructure generation, meshing, and cohesive finite element method based failure analysis. Calculations carried out here concern Al/SiC MMCs and focus on primary fracture mechanisms which are correlated with microstructure characteristics, constituent properties, and deformation behaviors. Simulation results indicate that interface debonding not only creates tortuous crack paths via crack deflection and coalescence of microcracks but also leads to more pronounced plastic deformation, which largely contributes to the toughening of composite materials. Promotion of interface debonding through microstructure design can effectively improve the fracture toughness of MMCs.

Thermal conductivity of uranium dioxide (UO2) is an important nuclear fuel performance property. Radiation- and fission-induced defects and microstructures, such as xenon (Xe) gas bubbles, can degrade the thermal conductivity of UO2 significantly. Here, molecular dynamics simulations are conducted to study the effect of Xe bubble size and pressure on the thermal conductivity of UO2. At a given porosity, thermal conductivity increases with Xe cluster size, then reaches a nearly saturated value at a cluster radius of 0.6 nm, demonstrating that dispersed Xe atoms result in a lower thermal conductivity than clustering them into bubbles. In comparison with empty voids of the same size, Xe-filled bubbles lead to a lower thermal conductivity when the number ratio of Xe atoms to uranium vacancies (Xe:VU ratio) in bubbles is high. Detailed atomic-level analysis shows that the pressure-induced distortion of atoms at bubble surface causes additional phonon scattering and thus further reduces the thermal conductivity.

In this work, we investigate misfit dislocations in PbTe/PbSe heteroepitaxial systems using the concurrent atomistic–continuum (CAC) method. A potential model containing the long-range Coulombic interaction and short-range Buckingham potential is developed for the system. By considering the minimum potential energy of relaxed interface structures for various initial conditions and PbTe layer thicknesses, the equilibrium structure of misfit dislocations and the dislocation spacings in PbTe/PbSe(001) heteroepitaxial thin films are obtained as a function of the PbTe layer thicknesses grown on a PbSe substrate. The critical layer thickness above which misfit dislocations inevitably form, the structure of the misfit dislocations at the interfaces, and the dependence of average dislocation spacing on PbTe layer thickness are obtained and discussed. The simulation results provide an explanation for the narrowing of the spread of the distribution of misfit dislocation spacing as layer thickness increases in PbTe/PbSe(001) heteroepitaxy.

A rigorous analysis of yield strength of pure iron over a wide grain size scale, using an extensive compilation of experimental data, indicates that the common Hall–Petch relationship is not obeyed with large deviations at the extremes of grain size. The author proposes here a phenomenological exponential function to represent the grain size effect on strength over multiple length scales. It is shown that the exponential function describes the grain size dependence of strength remarkably well, on the basis of a large set of experimental data for pure Fe. A nonlinear regression analysis indicated that the function provided a very high degree of correlation of data. The validity of the function is also supported by its conformation to physical boundary conditions at the extremes of grain size, that is, by asymptotically reaching the limiting stress for dislocation nucleation at infinitesimal grain size, and, the strength of single crystal at infinite grain size. The exponential form is a significant improvement over the Hall–Petch relationship and may be used as a guide to develop a reliable theory of grain size strengthening of iron.

Intrinsic size effects in nanoglass plasticity have been connected to the structural length scales imposed by the interfacial network, and control over this behavior is critical to designing amorphous alloys with improved mechanical response. In this paper, atomistic simulations are employed to probe strain delocalization in nanoglasses with explicit correlation to the interfacial characteristics and length scales of the amorphous grain structure. We show that strength is independent of grain size under certain conditions, but scales with the excess free volume and degree of short-range ordering in the interfaces. Structural homogenization upon annealing of the nanoglasses increases their strength toward the value of the bulk metallic glass; however, continued partitioning of strain to the interfacial regions inhibits the formation of a primary shear band. Intrinsic size effects in nanoglass plasticity thus originate from biased plastic strain accumulation within the interfacial regions, which will ultimately govern strain delocalization and homogenous flow in nanoglasses.

Several experiments and molecular dynamics calculations have reported anomalous mechanical behaviors of nanoporous materials that may be attributed to capillary effects. For example, nanoporous gold exhibits a tension–compression asymmetry in yield strength with the material being stronger in compression than tension. In addition, some molecular dynamics calculations have reported a spontaneous collapse of pores in nanoporous gold with nanometer-sized ligaments. Despite these perplexing observations, there are few theoretical models capable of shedding light on such capillary phenomena, particularly under general stress states. Here, we utilize a physics-based model to explore the implications of high surface energies on the mechanical response of dislocation-starved nanoporous materials subject to general stress states. For low stress triaxialities, we report an anomalous size effect and an anomalous temperature-dependence of dislocation-starved nanoporous materials with sufficiently large surface energies. Additionally, we provide an analytic criterion for spontaneous pore collapse in nanoporous materials with nanometer-sized ligaments.

The extrinsic indentation size effect (ISE) is utilized to analyze the depth-dependent hardness for Berkovich indentation of non-uniform dislocation distributions with one and two dimensional deformation gradients and is then extended to indentation results at grain boundaries. The role of the Berkovich pyramid orientation and placement relative to the grain boundary on extrinsic ISE is considered in terms of slip transmission at yield and plastic incompatibility during post-yield deformation. The results are interpreted using a local dislocation hardening mechanism originally proposed by Ashby, combined with the Hall–Petch equation. The Hall–Petch coefficient determined from the extrinsic ISE of the grain boundary is found to be consistent with the published values for pure Fe and mild steel. A simple, linear continuum strain gradient plasticity model is used to further analyze the results to include contributions from a non-uniform distribution in plastic strain and dislocation density.