# Effect of Holes on Dynamic Crack Propagation under Impact Loading
## 3 Numerical Method
### Discussion of Mechanism  
To discuss the holes' effect on the propagating crack, the specimen named B16-D30 was focused on, and its velocity vector contour is plotted in Figure 13.  
During the stress wave propagation in the specimen, the particles were motivated by the stress wave with varying velocity. When the stress wave encountered the surfaces of the holes, the particles on the free surface were without constraint and moved forward, which caused deformation of the holes. Together with the extending of the crack tip, the velocity of the particles between the holes and crack tip changed in terms of both magnitude and direction. Thus, the state motion of the particles in the crack tip was influenced and the crack propagation behavior responded. From Figure 13b, it can be observed that the particles in the running crack tip were restrained when the crack rushed into the holes' zone, lasting until the crack escaped the zone. This could explain the velocity curve in Figure 12b, where the crack propagating velocity firstly decreased in the holes' zone then increased.  
The contour plots of maximum principal stress and compressive stress are illustrated in Figure 14. Figure 14 clearly shows that a compression area was formed between the two holes. In particular, in Figure 14b, the stress \(\sigma_{\mathrm{yy}}\) was obtained by numerical simulation, in which \"+\" denotes compressive stress and \"\(-\)\" denotes tensile stress. When t = 288.3 \(\mu\)s, a compressive stress field already existed between the holes before the crack initiation with typical features. When t = 261.5 \(\mu\)s, the propagating crack approached the holes' zone, whereas the particles between the crack tip and the holes encountered each other, thereby reshaping the whole compressive field. When the crack tip in the central zone of the connection line was between two holes, the overlay effect of the stress field was more prominent, and this was also the specific time at which the crack arrest phenomenon occurred. Therefore, the effect of the holes was dependent on the compressive stress field caused by the particle movement during the crack propagation process.  
Figure 13: Numerical (ATUODYN) results of the B16-D30 specimen. (**a**) Velocity vector contour in the central zone of the connection line between two holes. (**b**) Particle velocity vector on the crack tips.  
To quantitatively reveal the relationship between the holes' effect and the compressive stress field, the maximum compressive stress curves with different distance B and D are illustrated in Figure 15. The maximum compressive stress in the holes' zone was larger than that in other areas, except for the pre-crack tip. An extreme value appeared in the central zone of the connection line between the two holes, with values of 24.12 MPa, 28.64 MPa, and 27.27 MPa for the specimens with constant distance B = 12 mm but different D. When distance D = 15 mm, where the holes were close to the pre-crack tip, the holes had an influence on crack initiation, and the maximum compressive in the central zone of the connection line between the two holes increased as distance B decreased. When distance D = 30 or D = 45, the holes' influence on the pre-crack tip was limited, and the maximum compressive stress slightly increased. Thus, the compressive stress was sensitive to the two holes' locations, especially distance B, while the maximum compressive stress in the central zone of the connection line between the two holes was a crucial index in determining the holes' influence.