Fatigue fracture is one of the most common failure modes for engineering structures, and 80–90% of failures fall into this category [1
]. 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 Kachanov [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
]. 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 applications due to its simplicity and effectiveness. Since Miner 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 Marco and Starkey [18
], Henry [19
], Gatts [20
], Manson [21
], Chaboche [22
], and many others. As a result, many different fatigue damage models have been developed based on the concept of CDM developed by Chaboche, Manson [23
], Franke [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., Miller [25
], Angelova [26
], and Polák [27
], among many others. McClintock [28
] and Rice and Tracey [29
] have studied the nucleation, growth, and coalescence of cylindrical and spherical voids related to the fracture theory. McDowell 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. Leuders et al. [31
] used the computed tomography for detecting the distribution of voids in Ti–6Al–4V samples manufactured by selective laser melting. More recently, Hu [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, Desmorat et al. [33
] employed the Eshelby–Kröner scale transition law and used a double-scale model to describe the HCF (high-cycle fatigue) phenomenon in which damage occurred only at the microscopic scale. Wan et al. [34
] considered the phenomenon of building orientations and porosity in the additive manufacture structures and used the micro-scale damage-evolution equation to describe the damage evolution process at the macroscopic scale. However, such attempts focused on exploring the evolution process of micro-defect size and neglected the influence of microscopic defect shape and position distribution on fatigue damage. There is a paucity of modeling methods and fatigue damage evolution analyses based on micro-defects visualization processing and 3D reconstruction, considering aspects of the real random uniform micro-structural morphology. In this regard, this paper aimed to create a multiscale damage evolution model by an efficient and simple defect classification method and 3D reconstruction technology based on MCT (micro-computed tomography) scanning data. Firstly, fatigue specimens at different loading stages were scanned by MCT technology. The defect information for fatigue specimens was graded and simplified by the defect classification method, considering not only the micro-defect size but also the shape and position distribution on fatigue damage via AVIZO (3D visualization software, September 2, 2016, FEI SAS, Mérignac, France) visual processing. Then, 3D reconstruction was carried out. An equivalent simplified model was established by the ABAQUS subroutine. This model provided an effective tool to build a bridge between mesoscopic damage and macroscopic fracture, using the damage variable in macro-scale to characterize the mesoscopic damage evolution indirectly. At the same time, the residual fatigue life for engineering structures under unknown loading times could be predicted easily through the microstructure by nondestructive detection based on this methodological study.
5. Fatigue Life Prediction
Fatigue lives were predicted by establishing the relationship between the several important characteristic parameters: the damage Young’s modulus Ed, the damage variable D, and the number of cycles.
By the continuous damage mechanism (CDM) [35
] theory, the damage variable resulted from the initiation and growth of microvoids was often used to describe the degradation of material properties. For isotropic metal materials, the stiffness degradation represented by damage variable D is given by.
where E represents Young’s modulus of material without damage, and Ed
is the effective Young’s modulus with damage.
The damage variable D of each loading stage was calculated by Equation (7) based on the effective Young’s modulus Ed
of each fatigue specimen after static tensile test in ABAQUS. Consequently, the relationship between damage parameter D and fatigue life in the fatigue process could be obtained. The variation of the damage variable D and the damage Young’s modulus Ed
with the number of loading cycles N is, respectively, plotted in Figure 14
It could be seen from Figure 14
a,b that the damage variable D increased with the increase of the number of loading cycles N, and the damage Young’s modulus Ed
decreased gradually. However, the damage Young’s modulus Ed
decreased drastically if the damage degree D exceeded 0.1, resulting in a sharp degradation of material properties. Moreover, Figure 14
b shows that the damage parameter D of three groups of curves increased slowly in the early stage, which is the stable initiation stage of voids, and accounted for 10% to 80% of total life. After that, the damage parameter D increased rapidly in the unstable propagation stage of voids. However, no matter which damage stage the material was in, fatigue life could also be predicted conveniently based on the calculated damage variable D by the proposed multiscale damage evolution model for nondestructive detection.