# Study on Dynamic Splitting Properties of S-PP Hybrid Fiber Concrete after High Temperatures
## 2 Test Materials and Methods
### Dynamic Splitting Test  
This test was completed by \(\Phi\)50 mm SHPB test device (Figure 4), which is composed of a launching power device, incident bar, transmission bar, absorption bar, and dynamic strain test system. The bar is made of a high-strength alloy with a density of 7850 kg/m\({}^{3}\), an elastic modulus of 210 GPa, a Poisson's ratio of 0.3, a longitudinal wave velocity of 5173 m/s, an incident bar length of 2 m, and a transmission bar length of 2 m. In the test, a spindle-shaped bullet is used to generate a half-sine loading wave. Regarding the impact load effect caused by the explosion, the impact speed is selected as 6.6 m/s, and the average strain rate of the specimen is around 102 s\({}^{-1}\).  
The dynamic splitting test follows the static elastic mechanics theory in terms of splitting strength. Brittle materials such as concrete are in a central two-way tensile compressive stress state under impact load. Most failure forms of the samples meet the conditions for the center of the flattened Brazilian disc to crack so that the splitting strength can be used as its tensile strength [21]. To ensure the central crack initiation condition required by the test as much as possible, according to the requirements of document [22], the loading angle of the platform is controlled by the cushions to satisfy the requirement (\(2a\geq 20^{\text{o}}\)). This method also improves the phenomenon of stress concentration at the loading part. The picture of specimen installation is shown in Figure 5. The force on the flattened Brazilian disc is shown in Figure 6, and the calculation formula of the central tensile stress of the specimen is as follows.  
\[\sigma_{st,d}=n\frac{2F(t)}{\pi d\textit{h}} \tag{1}\]  
where \(F(t)\) represents the force at both ends of the test piece, \(d\) represents the diameter of the test piece, \(h\) represents the thickness of the test piece, \(n\) represents the correlation coefficient of loading angle, the loading angle of this test is 22\({}^{\circ}\), and \(n\) is taken as 0.95.  
Figure 4: Schematic diagram of the SHPB device for the dynamic splitting test.  
Figure 5: The picture of specimen installation.  
The test process is based on the assumption of one-dimensional stress and uniformity. After the bullet hits the incident bar, the incident wave will propagate along the bar, and the transmitted wave and reflected wave will be generated when encountering the Brazilian disc specimen. The incident wave, reflected wave, and transmitted wave on the bar are collected by pasting strain gauges on the incident bar and transmission bar and combining them with the super dynamic strain gauge. According to the force reaction theorem, the force on both ends of the test piece can be expressed as Equation (2).  
\[F(t)=\frac{\pi D^{2}}{8}E(\varepsilon_{i}(t)+\varepsilon_{r}(t)+\varepsilon_{t }(t)) \tag{2}\]  
where \(\varepsilon_{i}\), \(\varepsilon_{r}\), and \(\varepsilon_{t}\) represent the strain of the incident wave, reflected wave, and transmitted wave, respectively, \(D\) represents the diameter of the pressure bar, and \(E\) represents the elastic modulus of the pressure bar.  
To sum up, the dynamic splitting strength of concrete specimens can be expressed as Equation (3).  
\[f_{st,d}=1.9\frac{F(t)_{\max}}{\pi d\hbar} \tag{3}\]  
where \(f_{st,d}\) represents the dynamic splitting strength of concrete specimens, and \(F(t)_{\max}\) represents the maximum load acting on both ends of the specimen.