# Investigation of Mixed-Mode I/II Fracture under Impact Loading Using Split-Hopkinson Pressure Bar
## 1 Introduction  
Construction building materials are a significant component of civil engineering, which is shown to be increasingly crucial in dominating the structure strength and project safety. However, there are many inherent or induced discontinuities, such as natural defects, flaws, and micro-cracks, which can be found in general materials, such as concrete and rock. When the material is subjected to dynamic loading, the defects of material will develop and result in crack initiation as well as propagation. Consequently, the propagating crack might cause immense engineering disasters. Therefore, much attention has been attracted to this hot point, the dynamic fracture of constructionbuilding materials. Numerous laboratory investigations have been conducted to understand the crack propagation behavior and fracture mechanism [1; 2; 3; 4; 5; 6]. The pure mode I crack propagation behavior with initiation, propagation, and arrest detected was illuminated by [PERSON] [7] in the series work, while [PERSON] [8] proposed a universal function method with which the dynamic stress intensity factor (DSIF) of mode I fracture can be calculated accurately. Then, the loading rate effect on crack propagation behavior was discussed [9; 10], and the methods to determine the dynamic crack fracture toughness of mode I cracks were given by [PERSON] [11] and [PERSON] [12; 13] with Split-Hopkinson pressure bar involved. Up to now, the majority of efforts have been mainly concentrated on the mode I crack, which of course enriches the knowledge of the dynamic fracture and crack propagation. However, the dynamic fracture of mixed-mode I/II crack has not been studied extensively at present. Actually, in practical applications, the mixed-mode I/II fracture can be found in most cases due to varied impact orientations and it is the dominator in controlling the damage of construction building materials, as well as structure stability. For mixed-mode I/II crack, abundant achievements under static loading conditions have been made by researchers [14; 15; 16; 17; 18]. Several classic specimen configurations have been proposed to study the crack propagation behavior and fracture growth in brittle materials, such as the single edge notched three-point-bend (SENB) [19], the asymmetric four-point-bend (AFPB) [20], the Brazilian disk (BD) [21], and the semi-circular bends (SCB) [22], as shown in Figure 1.  
Figure 1: Different specimens in the mixed-mode fracture testing. (**a**) Single edge notched three-point-bend (SENB). (**b**) Asymmetric four-point-bend (AFPB). (**c**) Brazilian disk (BD) under static loads. (**d**) Semi-circular bends (SCB) under static loads. (**e**) Brazilian disk (BD) under dynamic loads. Those specimen configurations were widely applied in the vast fracture toughness measuring and behavior detecting. Furthermore, fracture models such as the maximum tangential stress (MTS) [23; 24], the maximum tangential strain [25], and the maximum energy release [26] were also employed to evaluate mixed-mode crack trajectory. Moreover, to investigate the mixed-mode fracture problems under static loading conditions, multiple numerical methods have been given in recent years with various applications [27; 28; 29; 30; 31]. However, the investigation on mixed-mode fracture under dynamic loading has been conducted very scarcely, as it might be impeded by the complexity of dynamic material properties, wave propagation, and rate effect. So far, only limited literature can be found related to dynamic mixed-mode I/II fracture investigation. Among them, the Brazilian disk (BD) in Figure 1d was used by [PERSON] [32] to measure dynamic stress intensity factors with SHPB and the semi-circular bend (SCB) specimen in Figure 1e was mentioned in a famous review paper [33]. However, when it comes to the investigation of mixed-mode crack propagation, especially in a complete process including initiation, propagation, and arrest, a comprehensive investigation method with appropriate specimen remains unknown.