# Experimental and Numerical Study on the Low Velocity Impact Behavior of ABR Pipe
## 2 Experimental Specimens and Theories
### Methods and Theories  
The test system consists of a 3.2 m high bracket, steel guide rails, V-shaped fixtures, test components, drop hammer and data acquisition systems, as shown in Figure 2. According to GB/T14152-2001 [32] and ASTM D7136 [33], D90 type drop hammer with multiple quality grades and a steel V-shaped fixture with an included angle of 120\({}^{\circ}\) were selected for the test. The drop hammer head did not deform after repeated impacts in the test. The fixture and bracket are bolted to the ground to ensure the stability of the structure. The use of a pressure rod fixed pipeline prevented pipeline rebound. Lubricant is coated inside the guide rail to eliminate the friction effect of the inner wall of the guide rail on the drop \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen** & \begin{tabular}{c} **Height** \\ **(H/m)** \\ \end{tabular} & \begin{tabular}{c} **Mass** \\ **(M/kg)** \\ \end{tabular} & \begin{tabular}{c} **Energy** \\ **(E/J)** \\ \end{tabular} & \begin{tabular}{c} **Specimen** \\ **(H/m)** \\ \end{tabular} & \
\begin{tabular}{c} **Height** \\ **(M/kg)** \\ \end{tabular} &
\begin{tabular}{c} **Mass** \\ **(E/J)** \\ \end{tabular} \\ \hline M1-H1 & 0.25 & 5.20 & 12.74 & M3-H1 & 0.25 & 10.20 & 24.99 \\ M1-H2 & 0.50 & 5.20 & 25.48 & M3-H2 & 0.50 & 10.20 & 49.98 \\ M1-H3 & 1.00 & 5.20 & 50.96 & M3-H3 & 1.00 & 10.20 & 99.96 \\ M1-H4 & 1.50 & 5.20 & 76.44 & M3-H4 & 1.50 & 10.20 & 149.94 \\ M1-H5 & 2.00 & 5.20 & 101.92 & M3-H5 & 2.00 & 10.20 & 199.92 \\ M2-H1 & 0.25 & 7.80 & 19.11 & M4-H1 & 0.25 & 12.90 & 31.605 \\ M2-H2 & 0.50 & 7.80 & 38.22 & M4-H2 & 0.50 & 12.90 & 63.21 \\ M2-H3 & 1.00 & 7.80 & 76.44 & M4-H3 & 1.00 & 12.90 & 126.42 \\ M2-H4 & 1.50 & 7.80 & 114.66 & M4-H4 & 1.50 & 12.90 & 189.63 \\ M2-H5 & 2.00 & 7.80 & 152.88 & M4-H5 & 2.00 & 12.90 & 252.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of specimens. Figure 1: The material tensile test of ABR pipes. hammer. During the test, the drop hammer is connected with the decoupling device and pulled up to the specified height. When the drop hammer stabilizes, showing no obvious shaking, the drop hammer is released through the decoupling device to make it fall freely and impact on the axial midpoint and circumferential highest point of the specimen. An acceleration sensor is installed at the hammer head to measure the acceleration time-history curve of the falling hammer in the impact process, and the data acquisition frequency is 20 kHz. The upper frequency of the acquisition instrument is set at 800 Hz, in order to filter the influence of higher frequency signals. Using the acceleration time-history curve data collected by the test accelerometer, the impact force time-history curve is calculated according to ASTM D7136/D7136M-12 [33], and the vertical displacement of the drop hammer during the impact load can be obtained by quadratic integration of the acceleration curve. The formula is given by  
\[F=ma \tag{1}\]  
\[v=v_{0}+gt-\int_{0}^{t}adt \tag{2}\]  
Figure 2: Impact test apparatus. \[u=\int_{0}^{t}vdt \tag{3}\]  
where \(F\) is the impact force, \(m\) is the mass of drop hammer, \(a\), \(v\) and \(u\) are the acceleration, velocity, displacement of drop hammer, \(v_{0}\) is the impactor velocity at time of initial contact, \(t\) is the time during impactor drop and impact event, \(g\) is the acceleration due to gravity. In the initial conditions of the experiment, the height \(H\) and mass m of the falling hammer were pre-set. The initial velocity of the hammer at the moment of impact can be calculated using Formula (4). The experimental curves obtained through the tests provide temporal data \(t\) and acceleration \(a\). At this point, Formula (1) is transformed into Formula (5). The corresponding velocity and displacement temporal data can be calculated using Formulas (6) and (7) respectively. These calculations are derived from the experimental data curves.