# Effect of Holes on Dynamic Crack Propagation under Impact Loading
## 2 Experiment
### Test System and Specim  
The Split-Hopkinson pressure bar test system applied in the experiment is shown in Figure 1, and the bars' parameters are listed in Table 1.  
The strain gauges were glued on the surface of the bars, and the voltage signal of the gauges could be collected using an ultra-dynamic strain amplifier, before being stored in the computer. With Equation (1) [23], one can gain the strain signals. \[\varepsilon\ =\ \frac{4U_{0}}{nE_{g}K}, \tag{1}\]  
where \(\varepsilon\) is the strain, \(U_{0}\) is the voltage recorded by the strain gauges, \(Eg\) is the bridge voltage, \(K\) is the sensitivity coefficient of the strain gauges, and \(n\) is the gain coefficient of the amplifier. Then, the loads acting on the top and bottom of the specimen could be calculated using Equation (2). \[ \begin{array}{rcl}P_{i}(t)&=&A_{i}E_{d}\big{[}\varepsilon_{i}(t)+\varepsilon_ {r}(t)\big{]}\\ P_{t}(t)&=&A_{i}E_{d}\varepsilon_{t}(t)\end{array} , \tag{2}\]  
where \(\varepsilon_{i}(t)\) and \(\varepsilon_{r}(t)\) are the strains of the incident bar caused by the incident wave and reflected wave, respectively. Moreover, \(\varepsilon_{t}(t)\) is the strain of the transmitted bar induced by the transmitted wave, \(P_{i}(t)\) is the load on top of the specimen, and \(P_{t}(t)\) is the load on the bottom of the specimen. A single-cleavage semi-circle specimen with a pre-crack and two empty holes is proposed to investigate the holes' effect on extending the crack, as shown in Figure 1. The length of the pre-crack was 25 mm with its tip sharpened by a thin blade, and the diameter of the semi-circle was 22 mm. There were two empty holes deployed symmetrically along the axis with two variables designed: D for distance from the crack tip to the middle point of the holes and B for distance between two holes. A total of nine types of specimens were investigated, as listed in Table 2. The initiation of the pre-crack under impact loading could be realized easily using the semi-circle on the top of the specimen, and sufficient space for crack propagation was left. The fracture behavior and characteristics of propagation \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Name** & **Material** & **Length** & **Diameter** & \(\rho\) & **E\({}_{\text{d}}\) (GPa)** & **\(\mathbf{v_{d}}\)** \\  & & **(mm)** & **(mm)** & **(kg/m\({}^{3}\))** & **E\({}_{\text{d}}\) (GPa)** & **\(\mathbf{v_{d}}\)** \\ \hline Incident Bar & 40 CrmoV & 3000 & 80 & 7600 & 210 & 0.25 \\ Transmitted Bar & 40 CrmoV & 2000 & 80 & 7600 & 210 & 0.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material parameters of Split-Hopkinson pressure bar. Figure 1: Split-Hopkinson pressure bar (SHPB) test system and specimen geometry. could be detected elaborately, especially for the hole zone. Other geometric parameters were as follows: 145 mm in length, 70 mm in width, 30 mm in thickness, and 6 mm in diameter for an empty hole. Crack propagation gauges (CPGs) were employed in order to measure the crack propagation velocity, and a complete test system is shown in Figure 2. The CPG is a precise resistance gauge with resistance fine wires equally spaced on a glass-silk baseplate. Before CPGs were installed, the surface of the specimen was cleaned with ethyl alcohol. Then, superglue was used to tightly attach the CPG to the surface of the specimen, while the joints of the CPG were carefully connected to the wires. It is important to make sure that the resistance fine wires on the CPG are undamaged and that the CPG adequately covers the possible crack path; thus, all details were checked twice before collection. A step-by-step voltage signal could be collected by the oscilloscope as the fine resistance wire was fractured by the running crack. Thus, the exact time when the crack fractured each fine wire could be confirmed. Then, the average crack propagation velocity between the adjacent wires could be obtained as the distance divided by time, as the distance between adjacent fine wires was constant at 2 mm.