of the evolution in the silicone oil target free-surface velocity as a function of time for a plate-impact experiment.[]{data-label="fig:freesurfacevelocityschematic"}](freesurfacevelocityschematic.pdf){width="0.9\columnwidth"}

From Fig. \[fig:wavediagram\](a), it can be seen that cavitation is expected to initiate at the intersection of the tail of the rear free-surface expansion front (line (2)-(3)) with the forward-moving characteristic where the critical tension is first reached (line (3)-(4)-(5)). Therefore, in the acoustic approximation, the spall strength can be evaluated from the velocity pullback ($\Delta u_\mathrm{fs}=u_\mathrm{max}- u_\mathrm{min}$) recorded on the free surface-velocity trace using the following expression [@Antoun2003]

$$\label{eq:1}
P_\mathrm{s} =\frac{1}{2}\rho_0c_0\Delta u_\mathrm{fs},$$

where $\rho_0$ and $c_0$ are the ambient density and speed of sound of the liquid. Similarly, the strain rate is inferred by fitting a linear slope to the free-surface velocity pullback signal ($\dot{u}_\mathrm{fs}$) [@Sheng2009]

$$\label{eq:2}
\dot{\epsilon}=\frac{-\dot{u}_\mathrm{fs}}{2c_0}.$$

It is also of interest to estimate the maximum pressure experienced by the liquid target as it is shock compressed prior to unloading. The particle velocity behind the shock wave ($u_\mathrm{p}$) can be estimated from the maximum free-surface velocity during shock-up using the following relation [@Walsh1955]

$$\label{eq:3}
u_ {\mathrm{p}}\approx \frac{1}{2}u_ {\mathrm{max}}.$$

From the conservation of mass and momentum across a shock wave, the post-shock pressure ($P_\mathrm{h}$) can be expressed as

$$\label{eq:4}
P_ 