Multifractal Characteristics of Gain Structures: A Universal Law of Polycrystalline Strain-Hardening Behaviors
Abstract
:1. Introduction
2. Method and Experiment
2.1. Correlation Dimension of Polycrystalline Materials
2.2. Results of Al Tensile Experiment
- (1)
- def load_and_preprocess_image (image_path): Load the EBSD image and convert it to a binary image using Otsu’s binarization method;
- (2)
- def find_grain_centers (binary_image): Identify the geometric centers of the grains using the skimage.measure library;
- (3)
- def count_grains_within_radius (centers, scan_points, radius): Use KDTree to calculate the mean number of grain geometric centers within a specified radius r for each scan point;
- (4)
- def plot_grains_and_scan (centers, scan_points, radius, counts, image): Plot the geometric centers of the grains and the scan results on the EBSD image using matplotlib;
- (5)
- Calculate the grain correlation dimension D using Equation (3).
3. Verification
4. Discussion
4.1. Relationship between the Pointwise Dimension and Material Manifold
4.2. The Equivalence Relationship between the Correlation Dimension of the Strength Coefficient Field and Grains
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Fu, M.; Chen, J.; Huang, Z.; Chen, B.; Hu, Y.; Wang, B. Multifractal Characteristics of Gain Structures: A Universal Law of Polycrystalline Strain-Hardening Behaviors. Fractal Fract. 2024, 8, 504. https://doi.org/10.3390/fractalfract8090504
Fu M, Chen J, Huang Z, Chen B, Hu Y, Wang B. Multifractal Characteristics of Gain Structures: A Universal Law of Polycrystalline Strain-Hardening Behaviors. Fractal and Fractional. 2024; 8(9):504. https://doi.org/10.3390/fractalfract8090504
Chicago/Turabian StyleFu, Maoqing, Jiapeng Chen, Zhaowen Huang, Bin Chen, Yangfan Hu, and Biao Wang. 2024. "Multifractal Characteristics of Gain Structures: A Universal Law of Polycrystalline Strain-Hardening Behaviors" Fractal and Fractional 8, no. 9: 504. https://doi.org/10.3390/fractalfract8090504