Size-dependent elasticity of nanowires: Nonlinear effects

Liang, Haiyi; Upmanyu, Moneesh; Huang, Hanchen

doi:10.1103/physrevb.71.241403

Cited by 333 publications

(294 citation statements)

References 18 publications

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“…11,33 The observed size effect on elasticity of Ag NWs is generally a result of their large surface area to volume ratio, 34 more specifically, surface elasticity 35 and/or bulk nonlinear elasticity (due to surface stress). 36,37 Though our results are in good agreement with other experimental results, 11,33 we do note that there is a substantial gap between the experiments and the atomistic simulations in terms of the critical diameter where the elasticity size effect becomes marked. 14 One significant reason is the difference in aspect ratio (length/diameter).…”

Section: Resultssupporting

confidence: 81%

Size effects on elasticity, yielding, and fracture of silver nanowires:In situexperiments

et al. 2012

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This paper reports the first quantitative measurement of a full spectrum of mechanical properties of five-fold twinned silver (Ag) nanowires (NWs) including Young's modulus, yield strength and ultimate tensile strength. In situ tensile testing of Ag NWs with diameters between 34 and 130 nm was carried out inside a scanning electron microscope (SEM). Young's modulus, yield strength and ultimate tensile strength all increased as the NW diameter decreased. The maximum yield strength in our tests was found to be 2.64 GPa, which is about 50 times the bulk value and close to the theoretical value of Ag in the <110> orientation. The size effect in the yield strength is attributed to the increase in the Young's modulus. Yield strain scales reasonably well with the NW surface area, which reveals that yielding of Ag NWs is due to dislocation nucleation from surface sources. Pronounced strain hardening was observed for most NWs in our study. The strain hardening, which has not previously been reported for NWs, is mainly attributed to the presence of internal twin boundaries. KEYWORDSfive-fold twin, size effect, Young's modulus, yield strength, ultimate tensile strength, strain hardening

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Section: Resultssupporting

confidence: 81%

Size effects on elasticity, yielding, and fracture of silver nanowires:In situexperiments

et al. 2012

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“…Since this study is limited to small amplitude rippling we further simplify the edge as a spring with constant stress. This composite approximation is similar in principle to the core-shell framework often invoked to describe elastic behavior of nanowires and thin films [44][45][46] . For a system so structured strain compatibility and force equilibrium require that the elastic Hamiltonian that maps the initially flat ribbon to its deformed state, R ≡ (x, y, 0) → R ′ ≡ (x + u x , y + u y , ζ), satisfies the generalized Föppl-von Kármán (F-vK) equations 43 .…”

Section: Stability Analysis Of Periodic Ripplesmentioning

confidence: 99%

Rippling instabilities in suspended nanoribbons

Wang

Upmanyu

2012

Phys. Rev. B

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Morphology mediates the interplay between the structure and electronic transport in atomically thin nanoribbons such as graphene as the relaxation of edge stresses occurs preferentially via outof-plane deflections. In the case of end-supported suspended nanoribbons that we study here, past experiments and computations have identified a range of equilibrium morphologies, in particular for graphene flakes, yet a unified understanding of their relative stability remains elusive. Here, we employ atomic-scale simulations and a composite framework based on isotropic elastic plate theory to chart out the morphological stability space of suspended nanoribbons with respect to intrinsic (ribbon elasticity) and engineered (ribbon geometry) parameters, and the combination of edge and body actuation. The computations highlight a rich morphological shape space that can be naturally classified into two competing shapes, bending-like and twist-like, depending on the distribution of ripples across the interacting edges. The linearized elastic framework yields exact solutions for these rippled shapes. For compressive edge stresses, the body strain emerges as a key variable that controls their relative stability and in extreme cases stabilizes co-existing transverse ripples. Tensile edge stresses lead to dimples within the ribbon core that decay into the edges, a feature of obvious significance for stretchable nanoelectronics. The interplay between geometry and mechanics that we report should serve as a key input for quantifying the transport along these ribbons.

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“…It is also significant that theory [41] as well as experiment [42] points toward nonlinear bulk elasticity as relevant for the effective elastic response of nanomaterials. Ngô et al [25] have pointed out that the most obvious phenomenon in the latter context is the shear instability at the points of inflection of the generalized stacking-fault energy function.…”

Section: Stiffening By Surface Excess Elasticity Softening By Shear mentioning

confidence: 99%

Nanoporous Gold—Testing Macro-scale Samples to Probe Small-scale Mechanical Behavior

Mameka¹,

Wang

Markmann

et al. 2015

Materials Research Letters

120

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Nanoporous gold made by dealloying exemplifies how the exciting mechanical properties of nanoscale objects can be exploited in designing materials from which macroscopic things can be formed. The homogeneous microstructure and the possibility of adjusting the ligament size, L, between few and few hundred nm, along with the high deformability and reproducible mechanical behavior predestine the material for model studies of small-scale plasticity using reliable macroscopic testing schemes on mm-or cm-size samples. Such experiments tend to agree with the Gibson-Ashby scaling relation for strength versus solid fraction, while suggesting an essentially L −1 scaling of the local strength of the ligaments. By contrast, the elastic compliance is dramatically enhanced compared to the Gibson-Ashby relation for the stiffness. Contrary to intuition, the anomalously compliant behavior of the nanomaterial goes along with a trend for more stiffness at smaller L. This article discusses surface excess elasticity, nonlinear elastic behavior and specifically shear instability of the bulk, network connectivity, and the surface chemistry as relevant issues which deserve further study.

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Size-dependent elasticity of nanowires: Nonlinear effects

Cited by 333 publications

References 18 publications

Size effects on elasticity, yielding, and fracture of silver nanowires:In situexperiments

Size effects on elasticity, yielding, and fracture of silver nanowires:In situexperiments

Rippling instabilities in suspended nanoribbons

Nanoporous Gold—Testing Macro-scale Samples to Probe Small-scale Mechanical Behavior

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