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Research Papers

Scaling Laws in the Ductile Fracture of Metallic Crystals

[+] Author and Article Information
M. I. Baskes

Bagley College of Engineering,
Mississippi State University,
Mississippi, MS 39762
Jacobs School of Engineering,
University of California, San Diego,
La Jolla, CA 92093
Los Alamos National Laboratory,
Los Alamos, NM 87545

M. Ortiz

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

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 1, 2015; final manuscript received March 29, 2015; published online June 3, 2015. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 82(7), 071003 (Jul 01, 2015) (5 pages) Paper No: JAM-15-1002; doi: 10.1115/1.4030329 History: Received January 01, 2015; Revised March 29, 2015; Online June 03, 2015

We explore whether the continuum scaling behavior of the fracture energy of metals extends down to the atomistic level. We use an embedded atom method (EAM) model of Ni, thus bypassing the need to model strain-gradient plasticity at the continuum level. The calculations are performed with a number of different 3D periodic size cells using standard molecular dynamics (MD) techniques. A void nucleus of a single vacancy is placed in each cell and the cell is then expanded through repeated NVT MD increments. For each displacement, we then determine which cell size has the lowest energy. The optimal cell size and energy bear a power-law relation to the opening displacement that is consistent with continuum estimates based on strain-gradient plasticity (Fokoua et al., 2014, “Optimal Scaling in Solids Undergoing Ductile Fracture by Void Sheet Formation,” Arch. Ration. Mech. Anal. (in press); Fokoua et al., 2014, “Optimal Scaling Laws for Ductile Fracture Derived From Strain-Gradient Microplasticity,” J. Mech. Phys. Solids, 62, pp. 295–311). The persistence of power-law scaling of the fracture energy down to the atomistic level is remarkable.

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Figures

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Fig. 1

Periodic unit cell of infinite slab of thickness H deforming under prescribed opening displacements δ on its surface. The deformations localize to a band of thickness a, which further subdivides into ~L2/a2 cubes of size a. A void nucleates from the center of every cube and then expands to accommodate the volume increase of the band.

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Fig. 2

Energy relative to the unstrained cell normalized by the (111) surface area versus cell displacement scaled by the z-direction cell size of the basic cell (~6Å) for various cell sizes denoted by the number of basic cells in each direction

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Fig. 3

Number of periods in the cell with the lowest energy as a function of the scaled displacement

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Fig. 4

Lowest energy as a function of the scaled displacement

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Fig. 5

Energy relative to the unstrained cell normalized by the (111) surface area versus cell displacement scaled by the z-direction cell size of the basic cell (~6Å) for N = 6. CNA was performed at the points indicated by circles.

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Fig. 6

CNA at (a) the peak energy, (b) after the energy drop, and (c) after fracture. Fcc atoms are denoted as green, hcp (stacking fault) as red, bcc as blue, and unknown (dislocation core, vacancy, and free surface) as white.

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Fig. 7

Surfaces at (a) after the energy drop and (b) after fracture as indicated by the circles in Fig. 5

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