## 3 Results and Discussion  
### Gauge Trace Analyses  
Regarding the free surface velocity distribution, some typical characteristics should be noted: When the elastic precursor wave reaches the free surface of the sample, the free surface particle velocity increases sharply to a certain value, which can be used to calculate the HEL value; when damage or spalling occurs in the sample, the sparse waves are reflected as compressional waves in damaged or denuded regions, resulting in an early pullback of the free surface velocity, which can be used to estimate spall strength under the assumption of an acoustic approximation; the Hugoniot relationship of the specimen can be determined from particle velocity, impact velocity, and impact stress. Figure 3 shows the free surface velocity of test sample No. 004 monitored by DISAR. To illustrate shock wave propagation more clearly, a graph of Lagrangian distance versus time is shown and the timescale of the \(x\)-axis is canceled in Figure 3. The specimen was initially impacted by the OFHC flyer at time \(t_{0}\), producing an elastic precursor (dashed line) and a shock wave (solid line) in the specimen and flyer. It is assumed that the elastic precursor propagates at the longitudinal speed of sound \(c_{\mathrm{L}}\), which is faster than the speed of the shock wave. Therefore, the precursor wave reaches the rear free surface of the specimen at time \(t_{1}\), resulting in a rapid increase in particle velocity in a very short time (a measurement value less than 15 ns). It is clear from the free surface velocity curve that the particle velocity increases linearly with HEL. The HEL is followed by distortion of the elastic-plastic yielding and free-surface velocity data due to the time period during which the elastic precursor reflects back to the oncoming shock wave and the interaction that occurs between the different stress pulses. Thereafter, the shock wave, propagating at the velocity \(U_{\mathrm{s}}\), reached the free surface at the rear of the specimen at time \(t_{2}\). The arrival of the shock wave caused the free surface velocity to rapidly increase to a peak value. Once the shock wave reached the flyer and the free surface of the specimen, it was reflected back as a rarefaction wave. It is well known that the head of the release wave also propagated at the longitudinal sound speed, while the tail of the release wave propagated at the bulk sound speed. Measurements of the above parameters for the HSLA are given in Table 1. When the rarefaction waves from the free surface of the specimen and OFHC met at time \(t_{3}\), a tensile stress was generated. When the tensile stress exceeds its spall strength, a free surface appears on the spall surface, and a pulse propagating at the longitudinal speed of sound is generated on the surface. The pulse reached the rear free surface of the specimen at time \(t_{4}\), resulting in a reduction in velocity. A new pulse arrived at time \(t_{5}\) and caused a characteristic pullback in the velocity, which is further evidence of the occurrence of spallation. The change in free surface velocity between the peak and the first minimum is called the pullback velocity, which is used to calculate the spalling strength of the material. As shown in Figure 3, the smaller peak after the free surface velocity maximum is due to the spallation pulse propagating back and forth within the surface after failure.