# Multiscale Damage Evolution Analysis of Aluminum Alloy Based on Defect Visualization
## 1 Introduction  
Fatigue fracture is one of the most common failure modes for engineering structures, and 80-90% of failures fall into this category [1; 2; 3]. Therefore, fatigue failure of metals has been the subject of study by many researchers. However, the understanding of fatigue mechanisms for evaluation of fatigue damage accumulation and fatigue life is still a challenging task up to now. With the development of theory and framework of the continuum damage mechanics (CDM), probably first presented by [PERSON] [4], and the advance in technique for micro-observation of interior structure of steel materials, such as scanning electron microscopy [5], different methods and theories have been employed to study the evolution law of fatigue damage processes, such as the number of cycle load to failure, dissipated energy, and degradation in mechanical properties [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. In recent years, more and more scholars have devoted to the study of fatigue damage processes. On the one hand, many researchers pay attention to the continuous average damage variable to describe the degradation of material on a larger macro-scale, which is easy for engineering applicationsdue to its simplicity and effectiveness. Since [PERSON] expressed this concept in the description of fatigue damage accumulation in 1945 [17], the cumulative fatigue damage theories have been developed increasingly, including the works of [PERSON] and [PERSON] [18], [PERSON] [19], [PERSON] [20], [PERSON] [21], [PERSON] [22], and many others. As a result, many different fatigue damage models have been developed based on the concept of CDM developed by [PERSON], [PERSON] [23], [PERSON] [24], and many others. However, most of the methods for macroscopic fracture are short for a deep and comprehensive understanding of microscopic damage mechanics theory in the study of the macro-scale fatigue process. On the other hand, the methods of microscopic fatigue analysis, which are used to describe the microscopic defects initiation and growth behavior, are studied by some researchers, e.g., [PERSON] [25], [PERSON] [26], and [PERSON] [27], among many others. [PERSON] [28] and [PERSON] and [PERSON] [29] have studied the nucleation, growth, and coalescence of cylindrical and spherical voids related to the fracture theory. [PERSON] et al. [30] developed a micro-scale fatigue model, which was able to characterize the effect of many micro-structural entities (cracks, voids, grains, etc.) on high cycle fatigue response of metallic materials. [PERSON] et al. [31] used the computed tomography for detecting the distribution of voids in Ti-6 Al-4V samples manufactured by selective laser melting. More recently, [PERSON] [32] analyzed the fatigue crack growth process in the material by using synchrotron X-ray micro-computed tomography. However, such attempts providing insight into the fatigue damage process have built-in complexities, which require accurate and detailed knowledge of microstructural features. Both of the above research methods are based on the study of fatigue damage evolution in a single macro-scale or microscale. On the macro-scale, using a macro-variable to describe the continuous average fatigue damage accumulation extent cannot be explained by the fatigue failure mechanisms viewed from a smaller microscale. Nevertheless, the micro-analysis of microscopic defect behavior, focusing on only a few single cracks or voids, cannot evaluate average fatigue damage extent in a larger macro-scale. It has long been regarded as a very important issue to establish the micro-macro relationship for the fatigue accumulation process because such a relationship can enhance our understanding of the fundamental nature of fatigue mechanisms, but it is still a challenging task up to now. There are few scholars who have studied multiscale fatigue damage evolution process and models. For instance, [PERSON] et al.