## 3 Results and Discussion
### Hugoniot Elastic Limit and Spall Strength  
In these experiments, the Hugoniot elastic limit, \(\sigma_{\rm HEL}\), and spall strength, \(\sigma_{\rm spall}\), of the HSLA were determined by the measured free surface velocity data, which can be expressed as:  
\[\sigma_{\rm HEL}=\frac{1}{2}\rho_{0}c_{L}u_{\rm e} \tag{1}\]  
\[\sigma_{\rm spall}=\frac{1}{2}\rho_{0}c_{0}\Delta u_{fs} \tag{2}\]  
where the density \(\rho_{0}\) and sound speeds \(c_{L}\) and \(c_{0}\) are known, and \(u_{e}\) and \(\Delta u_{fs}\) can be calculated according to the measured HEL and pullback velocity. The calculated HEL and spallation strengths are listed in Table 3. As is shown in Figure 5, the stress at the HEL of the HSLA is estimated to be in the range of 1.32-1.50 GPa, presenting a similar HEL when compared with that of other conventional crystalline alloys [24; 25], such as mild steel (1.75 GPa), austenitic stainless steel (1.40 GPa) and HY80 naval armor steel (1.70 GPa). Figure 4: Rear free surface velocity vs. time for all specimens at flyer impact velocities from 194 to 938 m/s. (**a**) measured curves; (**b**) zone A; (**c**) zone B. The above analysis shows that the HSLA will be pulled by the rarefaction wave from the free surface of the specimen and OFHC, generating a pullback zone on the free surface velocity curve. Two important characteristics of this stage are the pullback speed and pullback amplitude: the former is related to the tensile strain rate, while the latter directly determines the peeling strength of the HSLA. The tensile strain rate can be calculated using Equation (3):  
\[\frac{d\epsilon}{dt}=\frac{1}{2}\frac{du_{fs}}{c_{0}dt} \tag{3}\]  
Table 3 shows the calculated values of the tensile strain rate at the impact velocities from 194 m/s to 938 m/s, which are in the range of 33.2 \(\times\) 10\({}^{3}\)-120.2 \(\times\) 10\({}^{3}\)s\({}^{-1}\), as shown in Figure 6. It is observed that the HSLA has high spallation strength (1.88-3.32 GPa) when compared with other steels [24; 26], such as Armco iron (1.07 GPa) and 09G2S steel (0.7-1.4 GPa). Below the phase-transition stress, the spallation strength first increased and then decreased with increasing shock stresses. This trend is attributed to the accumulation of damage within the HSLA as the initial shock-induced compression wave propagates, revealing that larger shock stress leads to a larger damage magnitude. Generally speaking, the spalling strength is related to the microstructure, the propagation of the impact pulse and the damage to the material. Differences in the time-sensitivity of damage initiation and propagation may cause variations in spall strength: when the material is loaded at higher strain rates, dynamic loading does not have enough time to induce internal defects in the material, resulting in a decrease in the spallation strength. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test No. **} & \(u_{\text{\emph{pfs}}}\) & \(U_{\text{\emph{s}}}\) & \(u_{\text{\emph{e}}}\) & \(\sigma_{\text{\emph{HEL}}}\) & \(\sigma_{\text{\emph{peak}}}\) & \(\Delta u_{\text{\emph{fs}}}\) & \(\sigma_{\text{\emph{spall}}}\) & \(\dot{\epsilon}\) \\  & **(m/s)** & **(m/s)** & **(m/s)** & **(GPa)** & **(GPa)** & **(m/s)** & **(GPa)** & **(10\({}^{3}\)s\({}^{-1}\))** \\ \hline
001 & 168 & 4023 & 74.0 & 1.50 & 3.04 & 120.0 & 1.88 & 33.2 \\
002 & 384 & 4179 & 73.8 & 1.49 & 6.53 & 147.5 & 2.31 & 66.6 \\
003 & 382 & 4273 & 65.5 & 1.32 & 6.65 & 147.8 & 2.31 & 78.1 \\
004 & 574 &When the impact stress is increased to the \(\alpha\)\(\rightarrow\)\(\varepsilon\) transformation stress, an increase in the rate of increase in spallation strength is observed. In general, the phase transformation of the alloy occurs before the spallation behavior, and the microstructure produced by the phase transformation will directly affect the subsequent tensile fracture of the material.