Hierarchical Microstructural Features of Cu-Alloys under Solidification

Zhiheng Huang¹*, Xiaodong Xiang², Yuezhong Meng¹, Huatay Lin³, Hui Yan⁴ and Yunfei Du^1,4

¹Sun Yat-sen University;

²Southern University of Science and Technology;

³Guangdong University of Technology;

⁴National Supercomputer Center in Guangzhou

ABSTRACT:  C.S. Smith pointed out that microstructures are structural-hierarchy systems. However, most works conducted up-to-date focus on establishing direct relationships between process and performance or utilizing simple and crude microstructural measures. The digital age of materials calls for more advanced and systematic framework for microstructural measures. S.R. Kalidindi put forward descriptors based on the two-point correlation function in 2015, but the coherence among statistical descriptors and extreme value analyses remain untouched. Mallat scattering transform (MST) emerges from mathematical research on mechanisms underlying deep convolution neural networks. Based on the MST framework, this study investigates the hierarchical microstructural features of Cu alloys under solidification and phase transformations during subsequent heat treatments. Results suggest that a logarithmic transform can constrain the hierarchical measures in certain ranges and each microstructure exhibits its unique features. Figure 1 shows the pseudo-color plot of the correlation coefficient matrix of the hierarchical features of 51 microstructures. 2D MST extracts translation invariances only, while 3D MST captures both translation and rotation invariances. As the 0^th order feature showing the average value of microstructure, the 1^st order features vary systematically according the scale and orientation of the analysis wavelet, and the 2^nd order features supply lost information for the 1^st order. The number of hierarchical features of a standard microstructure with 512 pixels ´ 512 pixels can be controlled around 200, and quantitative microstructure-property relationships can be then established based on such feature series.

 Figure 1. Pseudo-color plot of the correlation coefficient matrix of 51 microstructural images of Cu alloys characterized by hierarchical features.

Keywords: Cu-alloy; solidification; microstructure; hierarchical feature