## 3 Results and Discussion
### Three Types of Stress Waves  
To aid in the interpretation of the stress profiles shown in Figure 4, some terminology is defined, first using the schematic of the flange/bar structure in Figure 5, which was originally prepared to illustrate the three stress waves (**B**, **E** and **R\({}_{\textbf{n}}\)**) proposed in this study. The term \"corner\" is the right angle between the impact surface on the flange and the outer surface of the bar. The \"reference plane\" refers to the imaginary radial plane that passes through the impact plane (see Figure 1a). The \"flange structure\" and \"incident bar\" are the structures on the left and right sides of the reference plane, respectively. The critical plane (\(p_{\text{c}}\)) is the nearest radial plane to the reference plane, after which a homogenised stress state appears. The concept of a critical plane is based on [PERSON]'s principle [53; 54].  
To interpret the monitored stress profiles in the incident bar, three types of stress waves are proposed, as follows. When the hollow striker impacts the flange, the particles on the flange surface (impact surface) move backwards and generate tensile stress on the right side of the reference plane (i.e., in the incident bar, particularly near the corner region). In this study, this generated wave is called the bar wave (**B** wave), as shown in Figure 5. The backward movement of flange particles also generates compressive stress--referred to as the flange wave (**F** wave)--on the left side of the reference plane (i.e., in the flange structure). According to [PERSON]'s principle, both the **B** and **F** waves are homogenised across the radial plane after travelling certain axial distances in the incident bar and flange structure, respectively; the schematic of their critical planes are shown in Figure 5 (\(p_{\text{c,B}}\) and \(p_{\text{c,F}}\), respectively).  
The compressive **F** wave is reflected at the rear end of the flange structure as a tensile wave, followed by its arrival at the reference plane. When the **F** wave arrives at the reference plane, the reverberation phenomenon is anticipated to occur as follows. If an elastic wave (e.g., the **F** wave) approaches a stress-free interface (e.g., the stress-free reference plane), due to the mismatch in general impedance [52; 55], only a part of the stress wave is transmitted to the incident bar, while the rest is reflected back to the flange structure. Accordingly, the residual **F** wave travels back and forth along the flange structure (reverberation takes place), causing it to enter the incident bar multiple times. For convenience, the magnitudes of transmitted waves into the incident bar in the first, second, and third instances of reverberation are denoted as **R\({}_{\textbf{1}}\)**, **R\({}_{\textbf{2}}\)**, and **R\({}_{\textbf{3}}\)**, respectively. These reverberation waves are simply denoted as **R\({}_{\textbf{n}}\)** waves. As shown in subsequent sections, there are cases where the **F** wave simply enters the incident bar without reverberation and propagates towards the strain gauge.  
Figure 5: **B**, **F**, and **R\({}_{\textbf{n}}\)** waves when the flange length is long (\(L_{\text{f}}>L_{\text{s}}\)). The solid arrows indicate the waves in the current moment, whereas the dashed arrows describe their trajectories. For simplicity, the **R\({}_{\textbf{n}}\)** waves in the flange structure are not shown (\(\Delta t\): pulse duration period, C: speed of sound, and SG: strain gage).