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Research Papers

# The Role of Homogeneous Nucleation in Planar Dynamic Discrete Dislocation Plasticity

[+] Author and Article Information
Benat Gurrutxaga-Lerma

Department of Mechanical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: bg310@imperial.ac.uk

Daniel S. Balint

Department of Mechanical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: d.balint@imperial.ac.uk

Daniele Dini

Department of Mechanical Engineering,
Imperial College London,
London SW7 2AZ, UK
e-mail: d.dini@imperial.ac.uk

Daniel E. Eakins

Department of Physics,
Imperial College London,
London SW7 2AZ, UK
e-mail: d.eakins@imperial.ac.uk

Department of Physics,
Imperial College London,
London SW7 2AZ, UK
e-mail: a.sutton@imperial.ac.uk

A filter that excludes from the average all sampled values of stress, which are outside the $[m-1.5σ,m+1.5σ]$ interval, where m is the statistical mean, and σ is the standard deviation. (A $6σ$ filter would be insufficient).

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 1, 2014; final manuscript received January 29, 2015; published online June 3, 2015. Assoc. Editor: Erik van der Giessen.

J. Appl. Mech 82(7), 071008 (Jul 01, 2015) (12 pages) Paper No: JAM-14-1551; doi: 10.1115/1.4030320 History: Received December 01, 2014; Revised January 29, 2015; Online June 03, 2015

## Abstract

Homogeneous nucleation of dislocations is the dominant dislocation generation mechanism at strain rates above 108s−1; at those rates, homogeneous nucleation dominates the plastic relaxation of shock waves in the same way that Frank–Read sources control the onset of plastic flow at low strain rates. This article describes the implementation of homogeneous nucleation in dynamic discrete dislocation plasticity (D3P), a planar method of discrete dislocation dynamics (DDD) that offers a complete elastodynamic treatment of plasticity. The implemented methodology is put to the test by studying four materials—Al, Fe, Ni, and Mo—that are shock loaded with the same intensity and a strain rate of 1010s−1. It is found that, even for comparable dislocation densities, the lattice shear strength is fundamental in determining the amount of plastic relaxation a material displays when shock loaded.

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## Figures

Fig. 1

Linear superposition scheme, after Lubarda et al. [28]

Fig. 2

The geometry of the sample used in the D3P simulations of shock loading; 1×10μm wide, with a continuous load of 20 GPa applied on the top surface. Both lateral surfaces are free, while the bottom surface is reflective; the simulation is halted when the shock front reaches the reflective boundary.

Fig. 3

Number of dislocations nucleated each time step by the two possible mechanisms. Homogeneously nucleated dislocations outnumber dislocations generated by Frank–Read sources by two orders of magnitude.

Fig. 4

Positions of the dislocations in a small section of the left end of the sample, at t = 80 ps and t = 82 ps. The gray lines are the traces of the two principal slip planes (the 0 deg plane is a τ≈0 plane, so it barely has any activity), shown as a visual aid for identifying queues and pile-ups. (Note the difference in the x and y scales).

Fig. 5

Close-up view of the σxx stress field due to the dislocations in the simulation. As can be seen, there exists a strong heterogeneity of the stress fields. The magnitude of σxx is predominantly positive, suggesting that the dislocations tend to relax the highly compressive shock wave, in the sense of tending to make the overall σxx less compressive. (Note the difference in the x and y scales).

Fig. 6

Close-up view of the σyy stress field due to the dislocations in the simulation. As can be seen, there exists a strong heterogeneity of the stress fields. The magnitude of σyy is predominantly negative, suggesting that as a result of dislocation activity, the medium opposes lateral elongations. This is in fact the case; at the free surfaces at the top and the bottom the shock wave tends to produce a lateral elongation associated with the shear wave, which the dislocations tend to oppose in their σyy. (Note the difference in the x and y scales).

Fig. 7

Close-up view of the σxy stress field due to the dislocations in the simulation. As can be seen, there exists a strong heterogeneity of the stress fields. (Note the difference in the x and y scales).

Fig. 8

Evolution of the total dislocation density of a 1×10μm wide film over time

Fig. 9

This figure shows the position of the front at t = 65 ps, and some of the averaging sections behind the front, which are evenly spaced by Δx=1/15·cl/ɛ·, superimposed with the σxx stress field shown in Fig. 5; stress fields of the dislocations are calculated at 60–120 sampling points per section, as shown in Fig. 10. The mean is calculated over each section, and the standard error (deviation) of the mean is used as a measure of the statistical fluctuations introduced by the (random) dislocation distribution. The resulting data are collected in relaxation curves such as that provided in Fig. 11.

Fig. 10

σxx component of stress across a transverse section of the shock front. Alongside the average stress, the standard deviation of the mean is shown.

Fig. 11

Evolution of the plastic relaxation (the dislocations' σxx component of stress) averaged over the same transverse section as time advances. The average was obtained employing a 3σ filter. The points are accompanied by the corresponding standard deviation of the sample (not the standard error). In this specific example, the standard deviation shows a tendency to increase over time.

Fig. 12

Evolution of the plastic relaxation (the dislocations' σxx component of stress) at the shock front for nickel and aluminum

Fig. 13

Normalized plastic relaxation at the front for nickel and aluminum

Fig. 14

Dislocation density for aluminum and nickel

Fig. 15

Evolution of the plastic relaxation (the dislocations' σxx component of stress) for molybdenum, iron, and aluminum. Aluminum is shown for comparative purposes.

Fig. 16

Normalized σxx relaxation at the front for iron and molybdenum. Aluminum is shown for comparative purposes.

Fig. 17

Evolution of the dislocation density for molybdenum, iron, and aluminum

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