Research status and prospects of the fractal analysis of metal material surfaces and interfaces

As a mathematical analysis method, fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties. Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions. Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces. However, fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials. From the perspective of two-dimensional planes and three-dimensional curved surfaces, this paper reviews the current research status of the fractal analysis of metal precipitate interfaces, metal grain boundary interfaces, metal-deposited film surfaces, metal fracture surfaces, metal machined surfaces, and metal wear surfaces. The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized. Starting from three perspectives of fractal analysis, namely, research scope, image acquisition methods, and calculation methods, this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed. It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.