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Influence of Size on the Fractal Dimension of Dislocation Microstructure

Department of Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, CA 90095, USA
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Metals 2019, 9(4), 478; https://doi.org/10.3390/met9040478
Received: 29 March 2019 / Revised: 19 April 2019 / Accepted: 20 April 2019 / Published: 25 April 2019
(This article belongs to the Special Issue Dislocation Mechanics of Metal Plasticity and Fracturing)
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Abstract

Three-dimensional (3D) discrete dislocation dynamics simulations are used to analyze the size effect on the fractal dimension of two-dimensional (2D) and 3D dislocation microstructure. 2D dislocation structures are analyzed first, and the calculated fractal dimension ( n 2 ) is found to be consistent with experimental results gleaned from transmission electron microscopy images. The value of n 2 is found to be close to unity for sizes smaller than 300 nm, and increases to a saturation value of ≈1.8 for sizes above approximately 10 microns. It is discovered that reducing the sample size leads to a decrease in the fractal dimension because of the decrease in the likelihood of forming strong tangles at small scales. Dislocation ensembles are found to exist in a more isolated way at the nano- and micro-scales. Fractal analysis is carried out on 3D dislocation structures and the 3D fractal dimension ( n 3 ) is determined. The analysis here shows that ( n 3 ) is significantly smaller than ( n 2 + 1 ) of 2D projected dislocations in all considered sizes. View Full-Text
Keywords: dislocation microstructure; fractal analysis; size effect dislocation microstructure; fractal analysis; size effect
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Cui, Y.; Ghoniem, N. Influence of Size on the Fractal Dimension of Dislocation Microstructure. Metals 2019, 9, 478.

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