# Energy Dissipation and Stress Equilibrium Behavior of Granite under Dynamic Impact
## 3 Energy Dissipation and Stress Equilibrium Time
### Stress Equilibrium Time
#### 3.1.2 Stress Equilibrium Factor Curve  
The stress balance factor curves of granite specimens with a length-diameter ratio of 0.6 shown as Figure 3a under different strain rates are taken as examples. According to the above-mentioned stress equilibrium time (Table 2) when the strain rate is 63.8 s\({}^{-1}\), the stress balance factor waveform of 0-46 \(\upmu\)s fluctuates sharply and is in a state of stress disorder. The stress difference between the two ends of the specimen is very large, resulting in uneven internal stress distribution. The stress balance factor waveform of 46-151 \(\upmu\)s is close to the stable state and in the stress balance period. After 151 \(\upmu\)s, the waveform rises rapidly and appears irregular, which is caused by the deformation failure at both ends of the specimen. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Length–Diameter** & **Strain Rate (s\({}^{-1}\))** & **Initial Time (\(\upmu\)s)** & **End Time (\(\upmu\)s)** & **Duration (\(\upmu\)s)** \\ \hline \multirow{4}{*}{0.6} & 63.8 & 46 & 151 & 105 \\  & 109.8 & 55 & 139 & 84 \\  & 156.8 & 86 & 156 & 70 \\  & 253.2 & 96 & 133 & 37 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Stress equilibrium time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Length–Diameter** & \multirow{2}{*}{**Strain Rate (s\({}^{-1}\))**} & \multirow{2}{*}{**Initial Time (\(\mu\)s)**} & \multirow{2}{*}{**End Time (\(\mu\)s)**} & \multirow{2}{*}{**Duration (\(\mu\)s)**} \\
0.8 & & 63.8 & 36 & 174 & 138 \\  & & 109.8 & 50 & 175 & 125 \\  & & 156.8 & 69 & 170 & 101 \\  & & 253.2 & 73 & 134 & 61 \\  & & 63.8 & 108 & 185 & 77 \\  & & 109.8 & 66 & 133 & 67 \\
1.0 & & 156.8 & 122 & 175 & 53 \\  & & 253.2 & 136 & 173 & 37 \\  & & 63.8 & 82 & 148 & 66 \\
1.2 & & 109.8 & 79 & 136 & 57 \\  & & 156.8 & 85 & 131 & 46 \\  & & 253.2 & 136 & 162 & 26 \\  & & 63.8 & 75 & 138 & 63 \\
1.4 & & 109.8 & 106 & 140 & 34 \\  & & 156.8 & 141 & 172 & 31 \\  & & 253.2 & 150 & 174 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 3: Stress equilibrium factor curve with different strain rates includes length–diameter ratio of 0.6 (a), 0.8 (b), 1.0 (c), 1.2 (d), and 1.4 (e). Under the same impact load, the granite specimens with a length-diameter ratio from 0.8 to 1.4 are in the stress equilibrium period of 46-151 \(\upmu\)s, 36-174 \(\upmu\)s, 108-185 \(\upmu\)s, 82-148 \(\upmu\)s, and 75-138 \(\upmu\)s, respectively. By comparison, the waveform of stress balance factor with a length-diameter ratio of 0.8 is the most stable. Figure 4 shows the stress equilibrium time and correlation equations for each combination of impact velocities and equilibrium time with length-diameter ratios of 0.6-1.4. The initial time of the stress equilibrium with the length-diameter ratio of 0.8 occurs at 36 \(\upmu\)s; for a length-diameter ratio of 1.0, this is 108 \(\upmu\)s. Figure 5 shows that the duration of stress equilibrium with a length-diameter ratio of 0.8 is up to 138 \(\upmu\)s. The time to maintain the stress equilibrium state for a length-diameter ratio of 1.4 is 63 \(\upmu\)s, which is the shortest duration between five length-diameter ratios of granite specimen. The granite specimen with a length-diameter ratio of 0.8 has the most favorable stress equilibrium initial time and duration among the five length-diameter specimens. Additionally, the duration of stress equilibrium is more than twice as long compared to that of the granite specimen with a length-diameter ratio of 1.4, which can provide a reference for subsequent studies on the effect of the length-diameter ratio on stress uniform. Figure 4: Initial time of stress equilibrium. Figure 5: Duration of stress equilibrium. In general, according to the degree of waveform fluctuation, the stress state of the specimen is divided into three stages: stress disorder, stress equilibrium, and stress imbalance.