# Investigation of Mixed-Mode I/II Fracture under Impact Loading Using Split-Hopkinson Pressure Bar
## 4 Numerical Approach
### Numerical Result  
The crack propagation paths of specimens with different fracture modes are illustrated in Figure 12 with their initiation angle highlighted. Figure 11: Numerical (AUTODYN) model of the specimen-30\({}^{\circ}\). For specimen-0\({}^{\circ}\), the crack propagates with an initiation angle of zero forming a very perfectly straight line. For the numerical samples specimen-30\({}^{\circ}\), the intact crack propagation path is a curved line with a complicated variation trend associated with mixed-mode I/II fracture. Furthermore, there are several deflection points induced by crack deviation that could be observed in the experiment. However, some deflection points observed in the experiment are hard to be realized by the numerical approach. This is because the numerical method relies on the theoretical operation which sometimes cannot deduce exactly the same result as the experimental one which is controlled by a complex condition. When specimen-30\({}^{\circ}\) is compared with actual flaw patterns, the numerical results agree well with the experimental one. Especially, the initiation angle calculated by the numerical model does characterize the initiation fracture mode well. The initiation angle of specimen-30\({}^{\circ}\) is 60.22\({}^{\circ}\) which is nearly similar to the test result, 62.12\({}^{\circ}\), and the specimen-30\({}^{\circ}\) can be identified as mode I/II initiation. Furthermore, judging from the strained condition around the pre-cracks in Figure 12b, one can distinctly found that the specimen-30\({}^{\circ}\) should be a tensile-shear initiation where the tensile fracture is the dominator accompanied with shear fracture, and there is no closed crack being found during the crack propagation process. Meanwhile, the main deflection points of the crack appear in the approximate position as what was observed in the experiment, the points A and B in the numerical sample correspond to point A and B in the actual sample in Figure 6b. The crack trajectory is more irregular near the deflection point than in other areas. Especially in the initial propagation stage, the variation of the crack path is very complex and its propagation is unsteady, it looks like the extending crack is continuously adjusting fracture propagation direction. To confirm the crack propagation behavior discussed above, the fracture path in the numerical simulation was extracted in every 5.2 us with its length measured. Then the average crack extending velocity can be calculated and plotted in Figure 13 together with the experimental one. In addition, the horizontal displacement of the extending crack is defined as the benchmark to unify measurement for comparison purposes. Openly, the variation of both curves stays almost the same in Figure 13, and the crack deceleration at point A, B, and C can be detected clearly, even the amplitude of the decline of both are very similar. This implies that a very drastic deceleration event has occurred in the area near the deflection points leaving such trace before transform propagation direction, which matches the phenomenon in the experiment, too. One detail should be noticed, which is that the crack has a very low speed in the initial stage which cannot be recorded by crack propagation gauge in the experiment due to the too-short distance. Near the area C in Figure 13, the crack keeps a relatively low velocity before crack acceleration, and the speed is very fluctuant, which means the mixed-mode I/II crack propagation is a discontinuous process within the short period after initiation companies with high energy consumption. Moreover, this discontinuous process can be described as a  
Figure 12: Numerical (AUTODYN) crack propagation paths. (**a**) Crack path of the specimen-0\({}^{\circ}\). (**b**) Crack path of the specimen-30\({}^{\circ}\). deceleration-acceleration movement with unconsant extending speed.