# Investigation of Mixed-Mode I/II Fracture under Impact Loading Using Split-Hopkinson Pressure Bar
## 2 Experiment
### Specim and Experimental System  
The propagation behavior of mixed-mode I/II crack is more complicated than mode I with its crack path developing irregularly, which means the propagating crack is hard to track. To make a quantitative investigation of mixed-mode I/II crack propagation, the variable angle single cleavage semi-circle (VASCSC) specimen was chosen as the basic configuration, and the pre-crack could be designed with different angles. Thanks to the VASCSC specimen configuration, sufficient space was available behind the pre-crack which made mixed-mode crack propagate adequately, and the fracture initiation was easily realized due to the semi-circle in the top of the specimen. In addition, with the variable angle of pre-crack, which controlled the loading direction, the crack initiation could perform a mixed-mode fracture. The geometric parameters of the specimen are shown in Figure 2. The length of the specimen was 100 mm, the width was 70 mm, and the thickness was 25 mm. Besides, the diameter of the semi-circle was 26 mm, and the pre-crack was designed with a length of 20 mm, and its tip was sharpened by the laser technique. The angle (\(\theta\)) between the pre-crack and specimen symmetrical axis could be varied. To reduce the random error induced by material heterogeneity, polymethyl methacrylate (PMMA) was used to make the specimens. PMMA is usually applied in investigating the dynamic fracture mechanism of brittle material, it shows similar fracture characteristics under impact loading to concrete and rock [34; 35]. The measured material parameters of PMMA are shown in Table 1.  
The Split-Hopkinson pressure bar (SHPB) system and Crack Propagation Gauge (CPG) system were coordinated together with synchronization to detect dynamic stress condition and crack extending velocity, shown in Figure 3. The material parameters of the incident bar and transmitted bar are listed in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & \(\mathbf{C_{d}}\) **(m/s)** & \(\mathbf{C_{s}}\) **(m/s)** & \(\mathbf{\rho}\) **(kg/m\({}^{3}\))** & \(\mathbf{E_{d}}\) **(GPa)** & \(\mathbf{k}\) **(GPa)** & \(\mathbf{v_{d}}\) \\ \hline PMMA & 2382 & 1305 & 1187 & 5.61 & 4.35 & 0.28 \\ \hline \hline \end{tabular} In this table, \(C_{d}\) denotes the longitudinal wave velocity, \(C_{S}\) denotes the transverse wave velocity, \(E_{d}\) denotes the dynamic elastic modulus, \(v_{d}\) denotes [PERSON]’s ratio, \(k\) denotes the bulk modulus and \(\rho\) denotes the density.  
\end{table} 
Table 1: Material parameters of polymethyl methacrylate (PMMA) in the experiment. Figure 3: Split-Hopkinson pressure bar (SHPB) system and Crack Propagation Gauge (CPG) system. Figure 2: Variable angle single cleavage semi-circle (VASCSC) specimen geometry. The voltage signal was collected by the ultra-dynamic strain amplifier from the strain gauges glued on the midpoint of the incident bar and transmitted bar. The strain signals can be obtained by Equation (1). \[\varepsilon=\frac{4U_{0}}{nE_{g}K}, \tag{1}\]  
where \(\varepsilon\) denotes the strain, \(U_{0}\) denotes the voltage, \(Eg\) denotes the voltage of the bridge, \(K\) denotes the sensitivity coefficient of the strain gauges, and \(n\) denotes the gain coefficient of the amplifier. Then, with Equation (2), one can calculate the dynamic loading on the top and bottom of the sample. \[ \begin{gathered} P_{i}(t)=A_{i}E_{d}[\varepsilon_{i}(t)+ \varepsilon_{r}(t)]\\ P_{t}(t)=A_{i}E_{d}\varepsilon_{t}(t)\end{gathered}  \tag{2}\]  
where \(P_{i}(t)\) and \(P_{t}(t)\) are the load on the top and bottom of the sample, respectively. \(\varepsilon_{i}(t)\), \(\varepsilon_{r}(t)\), and \(\varepsilon_{i}(t)\) denote incident strain, reflected strain, and transmitted strain, respectively. \(A_{i}\) and \(A_{t}\) are the cross-section area of the incident bar and transmitted bar, respectively. In the experiment, sixteen specimens with two groups were impacted with a constant speed of 7.5 m/s which corresponds to high loading rate testing.