# Energy Dissipation and Stress Equilibrium Behavior of Granite under Dynamic Impact
## 4 Dynamic Behavior
### Peak Strength  
Under dynamic impact conditions, size effect and strain rate effect are coupled. In the SHPB text, the size effects of granite specimens were discussed in a similar strain rate range using a controlled loading rate method [13]. The prerequisite for using SHPB to obtain the intrinsic characteristics of rocks is to obtain measurements when the rock is in stress equilibrium, and to ensure that the stress equilibrium is maintained long enough to obtain valid data. Additionally, the change of the length-diameter ratio changes the rock stress wave single propagation time, which affects the stress equilibrium process. At the same time, rocks are internally anisotropic and the fracture damage strain of brittle materials such as rocks is generally only a few parts per thousand, as shown in Figure 12. This also leads to the existence of inhomogeneity in rock deformation under impact loading.  
Figure 11: Impact fracture morphology of granite samples under 156.8 s\({}^{-1}\) stain rate ((**a**–**e**) for different length–diameter ratios, 0.6 to 1.4).  
Figure 10: Stress-strain curve and stress history curve with different length–diameter ratios ((**a**–**e**) for 0.6\(\sim\)1.4).  
According to the stress history curve of granite specimens with different length-diameter ratios and loading strain rate (Figure 11), the time of the peak strength can be seen in Table 3. With the increasing load strain rate, the peak strength time is achieved earlier and peak strength id increased with loading strain rate. The granite with lower loading strain rate can maintain longer complete stage before the peak strength and can obtain a longer stress equilibrium time.  
The incident energy is basically closed under the same impact load, but the change of the granite length-diameter ratio changes the strength of the rock. From Figure 13, the strain rate of the specimen increases with decreasing length-diameter ratio at the same strain rate. The previously mentioned 0.6 aspect ratio specimen provides more time to maintain the stress equilibrium period. However, specimens with a length-diameter ratio of 0.6 are only able to exhibit this property during the first period of stress equilibrium and are not able to sustain the stress equilibrium time. The strain rate of a length-diameter ratio of 0.6 granite was as high as 160.46 s\({}^{-1}\), which is nearly 30% higher than the strain rate of 0.8 and 1.0 aspect ratio granite.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Length–Diameter** & \multirow{2}{*}{\(\sigma_{\text{max-time}}\)} & \(\sigma_{\text{max}}\) & **Length–Diameter** & \multirow{2}{*}{\(\sigma_{\text{max-time}}\)} & \(\sigma_{\text{max}}\) \\
**Ratio** & & & & & \\ \hline \multirow{4}{*}{0.6} & 160 & 76.33 & & 175 & 76.17 \\  & 139 & 96.05 & & 156 & 79.42 \\  & 136 & 95.99 & & 135 & 77.56 \\  & 106 & 88.33 & & 125 & 128.08 \\  & 146 & 60.21 & & 163 & 78.95 \\  & 130 & 83.64 & & 143 & 97.88 \\  & 139 & 91.09 & & 139 & 70.23 \\  & 114 & 113.82 & & 121 & 114.6 \\  & 179 & 71.15 & & & \\  & 145 & 101.13 & & & \\  & 136 & 102.18 & & & \\  & 129 & 121.56 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Peak strength data.  
Figure 12: Stress (**a**) and strain (**b**) time history curve.  
For the rock of same size, the strain rate curve of the specimen fluctuates sharply with increasing loading strain rate. According to the stress equilibrium time data, it can be seen that the time corresponding to the maximum value of the strain rate coincides with the equilibrium end time.  
The strain rate waveform is stable within the period before the maximum strain rate, and the corresponding time is consistent with the stress equilibrium time of the granite specimen. The strain rate time curve can also basically reflect the duration of stress equilibrium. Additionally, after the maximum value of the strain rate, the rock is damaged internally by the uneven distribution of stress, resulting in a sudden drop in the strain rate, and the strain rate curve loses efficacy after the specimen is broken.