## 4 Test Result
### Crack Cracking Mechanism  
To investigate the mechanisms underlying crack formation, this paper employs cohesive elements to identify the types of cracks that arise based on the damage they exhibit. The Mixed-Mode Index for Damage Evolution Measurement (MMIXDME) is utilized to determine the damage type within the cohesive elements by characterizing the proportion of fracture modes during the damage evolution process. Specifically, when the MMIXDME value falls within the range of 0 to 0.5, the cohesive elements are primarily subject to tensile damage, leading to the formation of tensile cracks. Within the range of 0.5 to 1, the cohesive elements are dominated by splitting damage (splitting cracks). When this value reaches 1, the cohesive elements undergo shear forces but do not result in damage to the cohesive elements themselves.  
Figure 9 provides a detailed illustration of the influence of fracture inclination angle on the crack initiation mechanism. Upon overall observation, when the specimen undergoes failure, the primary cracks interconnect through the prefabricated holes and fractures, forming a crack network that spans the entire specimen. During this process, the specimen primarily undergoes tensile failure, manifested by the gradual propagation of cracks under tensile stress, ultimately leading to the fracture of the specimen. Additionally, small-scale shear failure occurs at both ends of the prefabricated fracture due to stress concentration and the action of shear stress.  
Further analysis reveals that the angle of the prefabricated fracture has a significant impact on the crack initiation and propagation patterns. As the angle of the prefabricated fracture increases, the shear stress at the fracture ends also rises, resulting in an increase  
Figure 9: Crack initiation mechanisms influenced by crack angle: (**a**) \(0^{\circ}\), (**b**) \(15^{\circ}\), (**c**) \(60^{\circ}\), (**d**) \(90^{\circ}\), (**e**) \(150^{\circ}\).  
in the number of shear cracks generated at these ends. This phenomenon is particularly evident when the fracture inclination angle is 90\({}^{\circ}\), at which point the fracture is nearly perpendicular to the tensile direction, causing the shear stress at the fracture ends to reach its maximum value, thereby promoting the generation and propagation of shear cracks.  
Figure 10 presents a detailed examination of the influence of fracture length on the crack initiation mechanism. When the fracture length is 20 mm, the specimen primarily undergoes tensile failure during loading, manifested by the gradual propagation of cracks under tensile stress. In the vicinity of the hole, due to the stress concentration effect, small-scale shear failure zones emerge. Simultaneously, around the prefabricated fracture, the presence of the fracture leads to significant stress concentration, which further exacerbates the generation and propagation of cracks.  
As the fracture length increases to 28 mm and 40 mm, tensile cracks dominate the failure mode of the specimen. This is because, with the increase in fracture length, the specimen is more prone to forming continuous tensile stress zones during loading, thereby facilitating the initiation and propagation of tensile cracks. In contrast, the occurrence of shear cracks becomes relatively infrequent, possibly because, as the fracture length increases, the specimen tends to form a global tensile fracture mode upon failure rather than localized shear failure.