compressive stress of ~15.4 GPa, which is significantly higher than the reported range for the spall strength of WHA. The free surface velocity (FSV) profiles were measured using Photon Doppler Velocimetry (PDV) [4] single-point probes. Following impact, all samples were soft recovered by decelerating them into low-density foam. 26.4 Free Surface Velocity Profiles The free surface velocity (FSV) profiles for the experiments reported herein are shown in Fig. 26.3a. These measurements were performed at the sample back free surface. Key parameters and calculated values are listed in Table 26.1. The peak free surface velocities are 0.375 and 0.377 mm/μs, corresponding to peak compressive stresses of ~15.4 GPa (calculated using the Hugoniot parameters for tungsten: Co ¼4.022mm/μs and s ¼1.26). Both loading profiles exhibit a slight inflection in the shock front at ~0.1 mm/μs, potentially indicative of the Hugoniot elastic limit (HEL). Although the long pulse profile exhibits some rounding and increases slightly with time, the stress pulse remains within 95 % of the peak stress for ~0.5μs, before starting to release. In contrast, the short pulse profile exhibits a sharp transition at peak stress and remains within 95 % of the peak stress for less than 0.05 μs. Upon release both profiles exhibit a classic pull-back signal and ringing, generally indicative of spall or dynamic fracture occurring within the sample [5, 6]. A more detailed view of the pull-back regions are shown in Fig. 26.3b. The drops in the free surface velocity (ΔFSV) from the peak states to the minima are 0.056 and 0.067 mm/μs for the long and short pulse profiles respectively. From these results, the spall strengths (σspall) for the two experiments can be determined using the relationships proposed by Novikov [7] and the correction proposed by Kanel [8]: σspall ¼ 1 2 ρ0cB ΔFSVþδ ð Þ; (26.1) where ρo is the ambient density (19,260 kg/m3), c B is the bulk sound speed (4.022 mm/μs), and ΔFSV is the observed pull-back signal (as shown in Fig. 26.3b). The accuracy of the spall strength is improved by correcting for the ΔFSV in Eq. 26.1 [8] δ ¼h 1 CB 1 CL _u1 _u2 j j _u1 j jþ _u2 ; (26.2) where h is the thickness of the spalled region (measured in optical micrographs as ~1.75 mm for profile L and 0.4 mm for profile S), CL is the longitudinal sound speed (5.22 mm/μs), and are the unloading and re-compression rates calculated as Fig. 26.3 (a) Traces of the free surface velocity showing shock loading with long (L) and short (S) pulse durations. The curves are plotted such that the drop from the peak state starts at similar times for both experiments. (b) Region of the free surface velocity highlighting the pull-back signal, indicative of spall plane formation 212 E.N. Brown et al.
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