Research status and prospect of fractal analysis of surface and interfaces of metal materials

As a mathematical analysis method, fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties. It has been applied to shape characterization at various scales and dimensions in metal materials. Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics of surface and interfaces and properties in the study of metal materials. However, fractal analysis can quantitatively describe the shape characteristics of metal materials and then establish the quantitative relationship between these 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 fractal analysis in 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 dimension of the surface and interface and the properties of metal materials is summarized. Starting from three perspectives of fractal analysis, which are the research scopes, image acquisition methods and calculation methods, this paper points out the direction of research on fractal analysis of surface and interfaces of metal materials that need to be developed. It is believed that revealing the deep mechanism between the fractal dimension of the surface and interface and the properties of metal materials will be the key research direction of fractal analysis of metal materials in the future.