# Fatigue Damage Evaluation of Aviation Aluminum Alloy Based on Strain Monitoring
## 2 Crystal Plasticity Modeling and Numerical Implementation
### Crystal Plasticity Finite Element Model of 7075-T6 Aluminum Alloy  
This paper presents a polycrystalline model using Voronoi tessellation [49]. The study utilizes the finite element sub-model technique to investigate the impact of microstructure near the crack tip on crack tip deformation. The sub-model, located in the vicinity of the crack tip, consists of approximately 100 grains with random orientations, as shown in Figure 1. The loading method is determined based on the local displacements obtained from the analytical results of the global model. The validity of this sub-model analysis method has been confirmed in previous literature [50]. Displacements are used as boundary conditions in this paper to ensure a balance of strain energy between the global model and sub-model boundary conditions.  
The sub-model in this study follows the crystal plasticity principle mentioned earlier. On the other hand, the global model is an elastoplastic model that takes into account isotropic and kinematic hardening variables throughout the transient and saturation phases of the cyclic response [51]. To implement both the sub-model and the global model, the researchers used the ABAQUS v2021 finite element software.  
To ensure reasonable macroscopic mechanical properties of the simplified model and moderate computational cost, this paper selects 125 grains(generated using Neper 4.5.4-1) to determine material parameters, as shown in Figure 2a. Experimental studies have demonstrated that there is almost no difference in the stress-strain curves for different Euler angle parameters, as depicted in Figure 2d for uniaxial tensile results with various grain orientations. Some studies have indicated that both experiments and simulations show the evident influence of grain size [52]. Therefore, this paper determines the average grain size of the material using EBSD and provides the grain size for finite element simulations based on EBSD experiments. Moreover, when the number of grains exceeds 100, its impact on the macroscopic response becomes very weak [53]. To align with the actual complex machining process, this paper randomly sets the grain orientation, resulting in overall isotropy. The simplification of the model significantly reduces the computational cost, enabling the adoption of the trial-and-error method in this paper to determine material parameters more quickly and meet the requirements.  
Figure 1: Establishment of polycrystalline model: (**a**) main model and its loading method, (**b**) location of sub-model, (**c**) crystal plasticity model.  
Figure 2: Uniaxial stretching polycrystal model: (**a**) setting of boundary conditions; (**b**) comparison between uniaxial tensile test and simulation; (**c**) comparison of fatigue cyclic loading experiment and simulation; (**d**) the effect of different grain orientations on the model.  
The boundary conditions, as shown in Figure 2a, include constraining the displacement in the Z-axis direction of the XBY plane, constraining the displacement in the X-axis direction of the XAB plane, and applying a specified displacement in the ZAC plane (Zeiss SIGMA 500, Jena, Germany). The selected cell type is C3D8R-Enhanced, which is used to simulate static and cyclic tension, following the approach described in paper [53]. Table 1 presents the material parameters of the intrinsic model for 7075-T6 aluminum alloy, which were determined through the trial-and-error method. The theoretical calculations, as depicted in Figure 2b, show a remarkable agreement between the model simulations and the experimental data. The material parameters used in this study demonstrate their capability to accurately predict the mechanical properties of 7075-T6 aluminum (Murphy and Nolan Inc., Syracuse, NY, USA) alloy.