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Research Papers

Mechanical Response of Hollow Metallic Nanolattices: Combining Structural and Material Size Effects

[+] Author and Article Information
L. C. Montemayor

Division of Engineering and Applied Science,
California Institute of Technology,
Pasadena, CA 91125

J. R. Greer

Division of Engineering and Applied Science,
California Institute of Technology,
Pasadena, CA 91125
e-mail: jrgreer@caltech.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 20, 2014; final manuscript received April 9, 2015; published online June 3, 2015. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 82(7), 071012 (Jul 01, 2015) (10 pages) Paper No: JAM-14-1531; doi: 10.1115/1.4030361 History: Received November 20, 2014; Revised April 09, 2015; Online June 03, 2015

Ordered cellular solids have higher compressive yield strength and stiffness compared to stochastic foams. The mechanical properties of cellular solids depend on their relative density and follow structural scaling laws. These scaling laws assume the mechanical properties of the constituent materials, like modulus and yield strength, to be constant and dictate that equivalent-density cellular solids made from the same material should have identical mechanical properties. We present the fabrication and mechanical properties of three-dimensional hollow gold nanolattices whose compressive responses demonstrate that strength and stiffness vary as a function of geometry and tube wall thickness. All nanolattices had octahedron geometry, a constant relative density, ρ ∼ 5%, a unit cell size of 5–20 μm, and a constant grain size in the Au film of 25–50 nm. Structural effects were explored by increasing the unit cell angle from 30 deg to 60 deg while keeping all other parameters constant; material size effects were probed by varying the tube wall thickness, t, from 200 nm to 635 nm, at a constant relative density and grain size. In situ uniaxial compression experiments revealed an order of magnitude increase in yield stress and modulus in nanolattices with greater lattice angles, and a 150% increase in the yield strength without a concomitant change in modulus in thicker-walled nanolattices for fixed lattice angles. These results imply that independent control of structural and material size effects enables tunability of mechanical properties of three-dimensional architected metamaterials and highlight the importance of material, geometric, and microstructural effects in small-scale mechanics.

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Figures

Grahic Jump Location
Fig. 1

Hierarchically structured materials combine structural and material size effects to enhance material properties and provide opportunities to create new materials that outperform current low-density materials. Material properties chart generated using CES SELECTOR (image courtesy of S. Das). (Figures reprinted with permission from Greer and De Hosson [20], Gu et al. [26], and Montemayor et al. [49]. Copyright 2011 by Elsevier Ltd. and 2012 by American Chemical Society, respectively.)

Grahic Jump Location
Fig. 2

(a) Schematic of relevant geometric parameters on a nanolattice unit cell and (b) TEM image showing columnar grain structure of tubes with grain size on the order of 50 nm (TEM courtesy of Z. Aitken, scale bar 100 nm)

Grahic Jump Location
Fig. 3

Representative images of the Au coating in a 60 deg nanolattice with a wall thickness of ∼661 nm. In the center region, the nanolattice walls are conformal; however, the coating is not conformal near the edges of the lattice as a result of the anisotropy of the sputtering process.

Grahic Jump Location
Fig. 4

SEM image of octahedron nanolattices with lattice angles from 30 deg to 60 deg, as well as representative stress–strain curve for each sample with an open circle showing the 0.2% yield stress of the structure. For the 30 deg lattice, it should be noted that the error bars are included but are small enough to be obscured by the data point itself (scale bar denotes 30 μm).

Grahic Jump Location
Fig. 5

Calculated yield stress and modulus values for lattices with angles ranging from 30 deg to 60 deg. The error bars were calculated by using the standard deviation of the data for yield stress and modulus (note: t = 352±87 nm for all samples).

Grahic Jump Location
Fig. 6

SEM image of 45 deg octahedron nanolattices with t ranging from 200 to 635 nm, as well as representative stress–strain curve for each sample with an open circle showing the 0.2% yield stress of the structure (scale bar denotes 20 μm)

Grahic Jump Location
Fig. 7

Calculated yield stress for both 45 deg and 60 deg octahedron nanolattices. The yield strength increases as (t/d) increases due to the material size effect.

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Fig. 8

(a) Modulus versus sine of lattice angle according to Eq. (4) and (b) yield stress versus sine of lattice angle according to Eq. (5)

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Fig. 9

TEM bright field image showing pores between grains as viewed through a section of a nanolattice wall, where the wall thickness is ∼200 nm

Grahic Jump Location
Fig. 10

(a) Ion channeling (sample at 52 deg tilt) and (b) TEM images of a ∼2 μm thin n-Au film showing columnar grain structure with multiple grains spanning the film thickness

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