## 3 Analysis
### Dynamic Stress-Strain Curves  
Different impact air pressures can be selected to obtain different strain rates, while the size of the impact air pressure influences the rupture and crushing morphology of the specimen. If the chosen air pressure is low, the specimen cannot be damaged in the dynamic load test, and thus the Weibull distribution model cannot be used to quantitatively characterize the degree of hard coal crushing. If the air pressure is too high, there will be little variation in the degree of fragmentation of the specimen. The test specimens were test-punched before the test, and three impact air pressures of 0.15 MPa, 0.2 MPa, and 0.3 MPa were selected to obtain different strain rates. The impact test of three specimens were tested under the same conditions. Among them, seven groups of three specimens were used to obtain valid data. The velocity that was obtained by impact bullet was 2.538-5.011 m/s. The maximum strain rate of the tested coal specimens ranged from 67.465 to 99.879 s\({}^{-1}\), while the compressive strength ranged from 25.999 to 43.743 MPa. The impact compression test results of hard coal are shown in Table 2. The stress-strain curve of a typical hard coal specimen is shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Specimen** & **Impact Pressure** & **Impact Velocity** & **Maximum Strain Rate** & **Peak Stress** & **Peak Strain** & **Destruction** \\
**No.** & **/MPa** & **/(m-s\({}^{-1}\))** & **/s\({}^{-1}\)** & **/MPa** & **/(10\({}^{-3}\))** & **Destruction** \\ \hline
1 & 0.15 & 2.675 & 90.090 & 25.999 & 14.718 & broken \\
2 & 0.15 & 3.275 & 97.434 & 30.152 & 17.588 & broken \\
3 & 0.2 & 3.574 & 67.465 & 40.135 & 21.165 & broken \\
4 & 0.2 & 4.024 & 99.879 & 43.743 & 22.558 & broken \\
5 & 0.3 & 4.804 & 93.168 & 33.425 & 29.227 & broken \\
6 & 0.3 & 4.819 & 83.046 & 19.864 & 21.187 & broken \\
7 & 0.3 & 5.011 & 94.704 & 37.268 & 26.966 & broken \\ \hline \end{tabular}
\end{table} 
Table 2: Impact test results of hard coal specimens. The stress-strain curve change process that is shown in Figure 5 can be divided into three stages. In the initial stage, the specimen and the end of the pressure bar are gradually compacted. The internal pores and cracks of the specimen are tightly closed in a very short time after close contact. The initial inelastic deformation stage is not obvious: when the curve enters the elastic deformation stage, it increases almost linearly. When the stress reaches about 80% of the peak stress, the curve grows slowly and enters the elastoplastic phase. As the stress increases, the microcracks gradually expand and form new cracks. After the peak stress, the stress decreases rapidly with the increase in the strain and enters the plastic softening stage. At this time, the crack inside the specimen is further expanded and penetrates with the main crack, eventually breaking the specimen. The peak stress increases with the increase in the strain rate. This is because in response to an external load, when the strain rate is low, the largest internal defect of hard coal specimens will bear the stress and deformation that is attached to other defects. In this case, the specimen will only fail along its own internal defect. With a further increase in the strain rate, when the crack propagation rate in the specimen is greater than the overall stress and deformation rate of the material, other small defects and sub-defects in the material will be activated, and the force that is exerted on the material as a whole will be shared by all defects in the material and the surrounding area. In this case, the specimen exhibits stress enhancement and strain rate effect. However, based on the test results, the results of some specimens do not conform to the overall law, which may be due to the existence of a certain discrete type of different hard coal specimen. Compared with rock specimens, the overall homogeneity of coal specimens is poor, and the existence of primary cracks in some coal specimens is large.