Research Papers

Sensitive Material Behavior: Theoretical Model and Experiment for Compression Collapse of Gold Particles at Submicron Scale

[+] Author and Article Information
J. Q. Hu, Y. N. Cui

Applied Mechanics Laboratory,
School of Aerospace,
Tsinghua University,
Beijing 100084, China

Z. L. Liu

Applied Mechanics Laboratory,
School of Aerospace,
Tsinghua University,
Beijing 100084, China
e-mail: liuzhanli@tsinghua.edu.cn

Z. J. Wang, Z. W. Shan

Center for Advancing Materials Performance
from the Nanoscale (CAMP-Nano)
& Hysitron Applied
Research Center in China (HARCC),
State Key Laboratory for
Mechanical Behavior of Materials,
Xi'an Jiaotong University,
Xi'an 710049, China

Z. Zhuang

Applied Mechanics Laboratory,
School of Aerospace,
Tsinghua University,
Beijing 100084, China
e-mail: zhuangz@tsinghua.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 14, 2014; final manuscript received June 23, 2014; accepted manuscript posted June 27, 2014; published online July 3, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(9), 091007 (Jul 03, 2014) (9 pages) Paper No: JAM-14-1214; doi: 10.1115/1.4027916 History: Received May 14, 2014; Revised June 23, 2014; Accepted June 27, 2014

Recent in situ TEM experiments observed that single crystalline gold particles with diameter ranging from 300 to 700 nm suddenly collapse, accompanying numerous dislocations escaping from the free surface during a flat punch pushing toward the particle. This collapse is catastrophic for the microdevices in service. In this work, we numerically and theoretically analyze the collapse mechanisms of this kind of “sensitive material.” First, by carrying out molecular dynamics (MD) simulations and finite element (FEM) analysis, we conclude that the strong strain burst in the collapse is derived from the robust emissions of plentiful pile-up dislocations in a particular area. Then, on the basis of numerical analyses, a theoretical model based on the virtual work principle is developed to predict the load–displacement curve during the indentation and reveal the energy dissipation and transformation before the particle collapse. Furthermore, a micromechanics-based dislocation pile-up model is established to quantitatively interpret the mechanism of particle collapse. Based on these studies, we propose the dislocation avalanche at the microscale depends not only on the peak stress but also on the stress gradients. The research is helpful for the design of reliable microdevices.

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Greer, J. R., and De Hosson, J. T. M., 2011, “Plasticity in Small-Sized Metallic Systems: Intrinsic Versus Extrinsic Size Effect,” Prog. Mater. Sci., 56(6), pp. 654–724. [CrossRef]
Kim, J.-Y., Jang, D., and Greer, J. R., 2012, “Crystallographic Orientation and Size Dependence of Tension–Compression Asymmetry in Molybdenum Nano-Pillars,” Int. J. Plast., 28(1), pp. 46–52. [CrossRef]
Gu, R., and Ngan, A. H. W., 2013, “Dislocation Arrangement in Small Crystal Volumes Determines Power-Law Size Dependence of Yield Strength,” J. Mech. Phys. Solids, 61(6), pp. 1531–1542. [CrossRef]
Greer, J. R., Oliver, W. C., and Nix, W. D., 2005, “Size Dependence of Mechanical Properties of Gold at the Micron Scale in the Absence of Strain Gradients,” Acta Mater., 53(6), pp. 1821–1830. [CrossRef]
Heyer, J. K., Brinckmann, S., Pfetzing-Micklich, J., and Eggeler, G., 2014, “Microshear Deformation of Gold Single Crystals,” Acta Mater., 62, pp. 225–238. [CrossRef]
Argon, A. S., 2013, “Strain Avalanches in Plasticity,” Philos. Mag., 93(28–30), pp. 3795–3808. [CrossRef]
Wang, Z.-J., Li, Q.-J., Shan, Z.-W., Li, J., Sun, J., and Ma, E., 2012, “Sample Size Effects on the Large Strain Bursts in Submicron Aluminum Pillars,” Appl. Phys. Lett., 100(7), p. 071906. [CrossRef]
Gu, R., and Ngan, A. H. W., 2012, “Effects of Pre-Straining and Coating on Plastic Deformation of Aluminum Micropillars,” Acta Mater., 60(17), pp. 6102–6111. [CrossRef]
Kiener, D., Hosemann, P., Maloy, S. A., and Minor, A. M., 2011, “In Situ Nanocompression Testing of Irradiated Copper,” Nature Mater., 10(8), pp. 608–613. [CrossRef]
Zaiser, M., Schwerdtfeger, J., Schneider, A. S., Frick, C. P., Clark, B. G., Gruber, P. A., and Arzt, E., 2008, “Strain Bursts in Plastically Deforming Molybdenum Micro- and Nanopillars,” Philos. Mag., 88(30–32), pp. 3861–3874. [CrossRef]
Suresh, S., Nieh, T.-G., and Choi, B. W., 1999, “Nano-Indentation of Copper Thin Films on Silicon Substrates,” Scr. Mater., 41(9), pp. 951–957. [CrossRef]
Gouldstone, A., Kon, H.-J., Zeng, K.-Y., Giannakopoulos, A. E., and Suresh, S., 2000, “Discrete and Continuous Deformation During Nanoindentation of Thin Films,” Acta Mater., 48(9), pp. 2277–2295. [CrossRef]
Uchic, M. D., Dimiduk, D. M., Florando, J. N., and Nix, W. D., 2004, “Sample Dimensions Influence Strength and Crystal Plasticity,” Science, 305(5686), pp. 986–989. [CrossRef] [PubMed]
Nix, W. D., Greer, J. R., Feng, G., and Lilleodden, E. T., 2007, “Deformation at the Nanometer and Micrometer Length Scales: Effects of Strain Gradients and Dislocation Starvation,” Thin Solid Films, 515(6), pp. 3152–3157. [CrossRef]
Csikor, F. F., Motz, C., Weygand, D., Zaiser, M., and Zapperi, S., 2007, “Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale,” Science, 318(5848), pp. 251–254. [CrossRef] [PubMed]
Li, H., Ngan, A. H. W., and Wang, M. G., 2011, “Continuous Strain Bursts in Crystalline and Amorphous Metals During Plastic Deformation by Nanoindentation,” J. Mater. Res., 20(11), pp. 3072–3081. [CrossRef]
Zhou, C., Biner, S., and Lesar, R., 2010, “Simulations of the Effect of Surface Coatings on Plasticity at Small Scales,” Scr. Mater., 63(11), pp. 1096–1099. [CrossRef]
Ispánovity, P. D., Groma, I., Györgyi, G., Csikor, F. F., and Weygand, D., 2010, “Submicron Plasticity: Yield Stress, Dislocation Avalanches, and Velocity Distribution,” Phys. Rev. Lett., 105(8), p. 085503. [CrossRef] [PubMed]
Gerberich, W. W., Mook, W. M., Chambers, M. D., Cordill, M. J., Perrey, C. R., Carter, C. B., Miller, R. E., Curtin, W. A., Mukherjee, R., and Girshick, S. L., 2006, “An Energy Balance Criterion for Nanoindentation-Induced Single and Multiple Dislocation Events,” ASME J. Appl. Mech., 73(2), pp. 327–334. [CrossRef]
Li, J., Vliet, K. J. V., Zhu, T., Yip, S., and Suresh, S., 2002, “Atomistic Mechanisms Governing Elastic Limit and Incipient Plasticity in Crystals,” Nature, 418(18), pp. 307–310. [CrossRef] [PubMed]
Tsuru, T., Shibutani, Y., and Kaji, Y., 2010, “Nanoscale Contact Plasticity of Crystalline Metal: Experiment and Analytical Investigation Via Atomistic and Discrete Dislocation Models,” Acta Mater., 58(8), pp. 3096–3102. [CrossRef]
Van Vliet, K., Li, J., Zhu, T., Yip, S., and Suresh, S., 2003, “Quantifying the Early Stages of Plasticity Through Nanoscale Experiments and Simulations,” Phys. Rev. B, 67(10), p. 104105. [CrossRef]
Xu, S., Guo, Y. F., and Ngan, A. H. W., 2013, “A Molecular Dynamics Study on the Orientation, Size, and Dislocation Confinement Effects on the Plastic Deformation of Al Nanopillars,” Int. J. Plast., 43, pp. 116–127. [CrossRef]
Weinberger, C. R., and Cai, W., 2010, “Plasticity of Metal Wires in Torsion: Molecular Dynamics and Dislocation Dynamics Simulations,” J. Mech. Phys. Solids, 58(7), pp. 1011–1025. [CrossRef]
Ng, K. S., and Ngan, A. H. W., 2008, “A Monte Carlo Model for the Intermittent Plasticity of Micro-Pillars,” Modell. Simul. Mater. Sci. Eng., 16(5), p. 055004. [CrossRef]
Li, S., Ren, B., and Minaki, H., 2014, “Multiscale Crystal Defect Dynamics: A Dual-Lattice Process Zone Model,” Philos. Mag., 94(13), pp. 1414–1450. [CrossRef]
Cui, Y. N., Lin, P., Liu, Z. L., and Zhuang, Z., 2014, “Theoretical and Numerical Investigations of Single Arm Dislocation Source Controlled Plastic Flow in FCC Micropillars,” Int. J. Plast., 55, pp. 279–292. [CrossRef]
Wang, Z.-J., Shan, Z.-W., Li, J., Sun, J., and Ma, E., 2012, “Pristine-to-Pristine Regime of Plastic Deformation in Submicron-Sized Single Crystal Gold Particles,” Acta Mater., 60(3), pp. 1368–1377. [CrossRef]
Chuang Deng, F. S., 2009, “Near-Ideal Strength in Gold Nanowires Achieved Through Microstructural Design,” ACS Nano, 3(10), pp. 3001–3008. [CrossRef] [PubMed]
Ogata, S., Li, J., Hirosaki, N., Shibutani, Y., and Yip, S., 2004, “Ideal Shear Strain of Metals and Ceramics,” Phys. Rev. B, 70(10), p. 104104. [CrossRef]
Gall, K., Diao, J., and Dunn, M. L., 2004, “The Strength of Gold Nanowires,” Nano Lett., 4(12), pp. 2431–2436. [CrossRef]
Volkert, C. A., and Lilleodden, E. T., 2006, “Size Effects in the Deformation of Sub-Micron Au Columns,” Philos. Mag., 86(33–35), pp. 5567–5579. [CrossRef]
Plimpton, S., 1995, “Fast Parallel Algorithms for Short-Range Molecular Dynamics,” J. Comput. Phys., 117(1), pp. 1–19. [CrossRef]
Foiles, S., Baskes, M., and Daw, M., 1986, “Embedded-Atom-Method Functions for the FCC Metals Cu, Ag, Au, Ni, Pd, Pt, and Their Alloys,” Phys. Rev. B, 33(12), pp. 7983–7991. [CrossRef]
Gerberich, W. W., 2006, “An Energy Balance Criterion for Nanoindentation-Induced Single and Multiple Dislocation Events,” ASME J. Appl. Mech., 73(2), pp. 327–334. [CrossRef]
Akarapu, S., and Hirth, J. P., 2013, “Dislocation Pile-Ups in Stress Gradients Revisited,” Acta Mater., 61(10), pp. 3621–3629. [CrossRef]


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Fig. 1

Process design for compression in situ experiment of gold particle in TEM [28]: (a) silicon wedge substrate; (b) a thin SiO2 layer is deposited; (c) thin Au film is deposited on the surface of the thin SiO2 layer; and (d) Au particles are formed after high-temperature annealing and for in situ TEM compression test

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Fig. 2

(a) Compressive force versus displacement of Au particle with diameter 300 nm; (b) TEM images during the burst process; and (c)–(f) experiment data and TEM images for particles with diameter 400 nm and 500 nm, respectively. Experimental data from Wang et al. [28].

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Fig. 3

(a) Compressive force versus displacement results of two simulations and experiment in 500 nm diameter particle; (b) Mises stress distribution in 500 nm diameter particle for ideally elastic–plastic model

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Fig. 4

(a) MD model of gold hemisphere particle compression; (b) dislocation structures under different compressive displacement and radius ratio, blue atoms with CSD > 7 while red atoms with CSD from 3 to 7

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Fig. 5

(a) Shear stress distribution along the radius in a section plane of the hemisphere; (b) two regions divided by dislocation densities

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Fig. 6

The theoretical load–displacement curve is compared with the experiment data and FEM result of the particle with diameter 500 nm

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Fig. 7

Three distinct energy forms versus displacement from theoretical model

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Fig. 8

(a) Two coordinate systems in a gold hemisphere. (b) Local resolved shear stress distribution along O1A.

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Fig. 9

(a) Linear stress distribution along a slip direction. (b) Plot of the normalized dislocation distribution as a function of location.

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Fig. 10

Stress distribution along the slip direction under different compressive displacement in sample with diameter 500 nm

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Fig. 11

Configuration of dislocations on a slip plane and the emission process at critical state at the collapse point




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