# Experimental and Numerical Study on the Low Velocity Impact Behavior of ABR Pipe
## 4 Numerical Modeling
### Failure Model of Pipes  
Figure 9 shows the Mises stress nephogram of specimen M1-H1, for low impact energy. At the moment of initial contact between the drop hammer and the specimen, the impact force increases rapidly, the stress transfer speed is fast along the axial direction, the stress area is oval, and the surface of the top of the tube suffers local depression. In the process after 1.80 ms as shown in Figure 10a, the specimen and the drop hammer fall synchronously, the kinetic energy of the drop hammer decreases, the kinetic energy of the specimen increases, and the velocity of stress transfer along the circumferential direction increases. Starting from 2.5 ms, with the continuous transmission of stress in the contact \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{\(\mathbf{F_{\text{max}}}\)} & \multicolumn{2}{c}{\(\mathbf{T_{s}}\)} & \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{\(\mathbf{F_{\text{max}}}\)} & \multicolumn{2}{c}{\(\mathbf{T_{s}}\)} \\ \cline{2-2} \cline{5-10}  & **FE(kN)** & & & & & & & & \\ \hline M1-H1 & 6.448 & 1.001 & 3.05 & 0.953 & M3-H1 & 7.917 & 0.985 & 3.80 & 0.974 \\ M1-H2 & 9.151 & 1.029 & 3.00 & 0.938 & M3-H2 & 11.094 & 0.991 & 3.75 & 1.042 \\ M1-H3 & 12.660 & 1.006 & 3.00 & 0.909 & M3-H3 & 15.108 & 1.013 & 3.85 & 0.975 \\ M1-H4 & 15.059 & 1.005 & 3.00 & 0.909 & M3-H4 & 18.172 & 1.005 & 3.95 & 0.940 \\ M1-H5 & 17.051 & 0.998 & 3.00 & 0.909 & M3-H5 & 20.486 & 0.985 & 4.10 & 0.988 \\ M2-H1 & 7.371 & 1.037 & 3.45 & 0.945 & M4-H1 & 8.534 & 1.006 & 4.30 & 0.989 \\ M2-H2 & 10.423 & 0.993 & 3.45 & 0.945 & M4-H2 & 11.918 & 0.987 & 4.30 & 1.024 \\ M2-H3 & 14.261 & 1.032 & 3.45 & 0.885 & M4-H3 & 16.324 & 0.984 & 4.80 & 1.200 \\ M2-H4 & 16.849 & 1.062 & 3.45 & 0.932 & M4-H4 & 19.486 & 0.965 & 4.85 & 0.915 \\ M2-H5 & 18.890 & 1.032 & 3.55 & 0.986 & M4-H5 & 22.017 & 0.996 & 4.85 & 0.924 \\ Mean value & & & & & & 1.006 & & 0.964 \\ Std. dev. & & & & & & 0.023 & & 0.069 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of simulation results. Figure 9: Comparison between the test and the FEM results. area, the stress area on the top surface of the pipe gradually extends lengthwise, and the stress in the contact area of the pipe decreases when the drop hammer falls. Until the drop hammer springs back and disconnects from the pipe at the moment of 3.05 ms, the stress on the top surface of the pipe is striped, as shown in Figure 10b. With the increase of impact energy, the stress concentration area on the surface of the pipe top expands and the yield area of the pipe increases. The deformation velocity of the specimen impact contact area is greater than the falling speed of the drop hammer. After the specimen is separated from the drop hammer, the drop hammer will keep the falling speed moving for a distance, and the first impact process of the drop hammer ends at that point. In the subsequent process, the elastic strain of the specimen gradually recovered, the deformation in the contact area of the specimen first increased and then decreased, and it contacted the drop hammer again. In the subsequent process, the pipe and the drop hammer deformed synchronously until the drop hammer bounced back and separated from the specimen. Figure 11 shows the Von Mises nephogram of specimen M4-H5, for small impact energy. The impact force increases rapidly at the initial contact moment of the drop hammer with the specimen, and local depression appears on the surface of the tube top and rapidly expands to the surrounding area. When the time reaches 1.35 ms as shown in Figure 11a, the overall surface of the top of the tube moves downward with the impact process. During the subsequent process, the specimen descends synchronously with the drop weight. At 2.15 ms, with the continuous transfer of stress in the contact area, the development of pipeline stress reached its limit, and the impact reaction force of specimen reached its peak. In the subsequent process, however, the drop hammer and the impact area of the pipe will move downward.