Influence of Size on the Fractal Dimension of Dislocation Microstructure
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 (<inline-formula> <math...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-04-01
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| Series: | Metals |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-4701/9/4/478 |
| Summary: | 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 (<inline-formula> <math display="inline"> <semantics> <msub> <mi>n</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula>) is found to be consistent with experimental results gleaned from transmission electron microscopy images. The value of <inline-formula> <math display="inline"> <semantics> <msub> <mi>n</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula> 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 (<inline-formula> <math display="inline"> <semantics> <msub> <mi>n</mi> <mn>3</mn> </msub> </semantics> </math> </inline-formula>) is determined. The analysis here shows that (<inline-formula> <math display="inline"> <semantics> <msub> <mi>n</mi> <mn>3</mn> </msub> </semantics> </math> </inline-formula>) is significantly smaller than (<inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>+</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>) of 2D projected dislocations in all considered sizes. |
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| ISSN: | 2075-4701 |