## 4 Result and Discussion
### Failure Prediction and Damage Propagation Feature  
In general, multi-material structures such as metal/fiber-reinforced hybrids may exhibit complex failure modes when subjected to load, such as metal fracture, buckling, fiber fracture, matrix cracking, and delamination. Depending on the stacking configuration and operational conditions, these failure modes can occur singly or in combination. Consequently, finite element analysis is necessary to accurately assess the failure of laminates. Both [PERSON] and [PERSON]'s models use two damage variables to describe hybrid material damage. The post-processing module's state that SDV1 represents the fiber damage variable, and SDV2 represents the matrix damage variable. The predicted damage of laminates is illustrated in Figures 9-12. For failure analysis, both three-dimensional constitutive models used in this paper can predict the progressive failure mode of hybrids in laminates. The failure mechanism layers are divided into two regions. The region above the neutral layer is the compression region, and the region below the neutral layer is the stretching region. Figure 8: Longitudinal stress contours of 3/2 FMLs and 3/2 FMLs patch after failure (**a**) 3/2 FMLs, (**b**) 3/2 FMLs patch. (On the left is the [PERSON] criterion and on the right is the Hashin criterion). Figure 9: Damage of each CFRP layer in 2/1 FMLs. As shown in Figure 9, for 2/1 FMLs, fiber breakage may begin at the 0\({}^{\circ}\) fiber layer above the neutral layer due to the relatively low compressive strength of carbon fiber than its tensile strength. The simulation results show that fiber fracture occurred in the CFRP1 layer above the neutral layer, while no damage is observed in the CFRP2 layer in the remaining tension area. The Linde criterion is stricter than the Hashin criterion, and thus causes more obvious fiber failure. Both criteria accurately simulate the matrix failure less result. The SEM images of microstructure of the side-section of FMLs specimens after three-point bending are provided in Figure 9. First, the hybrid Al and CFRP structures can be seen clearly. Except for local fiber fractures, no obvious damage is observed in the flexural specimen, which is consistent with the simulated results. Figure 11: Damage of each CFRP layer in 3/2 FMLs. Figure 10: Damage of each CFRP layer in 2/1 FMLs patch. As can be seen from Figure 10, since the 2/1 FMLs patch CFRP layer is far away from the neutral layer and directly contacts the loading head during the test, its fiber fracture failure and matrix failure are relatively obvious. Both simulation criteria show that the fiber fracture in the CFRP1 layer located in the compression zone is obvious, and the matrix fracture characteristics are typical. However, the CFRP2 layer below the neutral layer was not damaged. By comparing the real photos and the finite element analysis results, the damage condition is the same, and the failure prediction of the finite element model of 2/1 FMLs and 2/1 FMLs patch under a three-point bending condition is verified. For 3/2 FMLs and 3/2 FMLs patch structures, the damage situation is more complex than usual. As seen in Fig. 11, the damage presented in the specimen of 3/2 FMLs structure is concentrated in the compression area at the upper part of the specimen. The fiber fracture failure and matrix fracture failure in the CFRP1 layer are predicted to be the same; however, the Hashin criterion suggests a different outcome for the matrix fracture failure in the CFRP2 layer. Linde criterion shows that the matrix failure is widespread around the matrix damage in the upper CFRP1 layer. Thus, the damage position predicted is in line with that of the CFRP1 layer, whereas the Hashin criterion predicts that the matrix failure in the CFRP2 layer is concentrated in the middle of the specimen, rather than at the edges. By SEM observations, matrix cracking and fiber fracture are observed in the CFRP-1 (upper) in 3/2 FMLs specimens, which is caused by the excessive bending displacement.