In order to investigate the properties of HEL
In order to investigate the properties of HEL of alumina under shocked loading, the HELs of tested alumina were plotted against the thicknesses of samples in Fig. 4. It is found that HEL of alumina decreases with the increase in sample thickness, which is termed as the elastic precursor decay. This phenomenon is considered to be similar to the phenomenon of size effect of other brittle materials, such as concrete and rock, namely the strength of brittle material decreases with the increase in its volume. However, the physical mechanism of this phenomenon is very complex and no complete satisfactory Tedizolid HCl exists presently. A simpler model has been proposed to describe the size effect of brittle materials under compressionwhere Y is the dynamic yield strength of material, D is the volume of sample, and A0, A1, and k are positive parameters. k is determined to be 0.4 for brittle materials . In the present paper, Y is related to σH through the well-known relationwhere D can be represented as πr2h. Because v and r are constants, Eq. (3) can be rewritten as A0 and B can be determined to be 3.04 and 3.84, respectively, by fitting the experimental data shown in Fig. 4. Murray et al.  studied this phenomenon in three grades of alumina through the stress–time measurements, and showed that the precursor decay effect was the greatest in the low purity aluminas. However, the further analysis  revealed that this phenomenon was probably a measurement artifact, resulting from the relatively slow response time of mangan in gauge. Obviously, the data obtained in our experiments did not support this point of view, which showed an apparent decay in HEL with the increase in sample thickness. VISAR is a non-contact technique without measurement errors existing in stress measurement, so it can be deduced that this phenomenon is an essential characteristic of the alumina under shock loading. The HEL is known as a point of transition from elastic response to inelastic response, so the phenomenon of elastic precursor decay should be studied combined with the failure mechanism of shocked alumina. The previous works reported that cracking, dislocation activity and twinning were observed in shock-loaded alumina, even when the peak-shock stress is less than the magnitude of HEL [21–27]. In authors\' opinion, the failure process occurring below HEL may play the dominant role in the phenomenon of elastic precursor decay. As is known to all, the evolution process of cracking or plasticity is an energy dissipation process essentially. In the region behind the elastic precursor wave, the preexisting microdetects act as stress concentrators and provide the nucleation sites for damage evolution, which dissipate the elastic energy. Thus, the longer distance the elastic wave passes through, the more elastic energy will be dissipated, which causes the amplitude of elastic wave decay. From the free surface velocity profiles, we can also observe the apparent recompressive wave signals which are marked by dashed line in Fig. 5. This phenomenon is interpreted as a failure wave. It follows from consideration of the time–distance diagram shown in Fig. 5 that the failure waves meet the unloading waves reflected from the free surfaces of the samples with different thicknesses at the distance and time , as determined by Eq. (5) Here, the longitudinal wave velocity cl in the sample is assumed to be a constant during wave propagation. The arrival time t1 of failure waves can be obtained from the free surface velocity profiles. The failure wave trajectories for the four samples with 4, 6, 8 and 10 mm in thickness are obtained by the Eq. (5) mentioned above as shown in Fig. 6. It can be seen from Fig. 6 that the four points locate just on a straight line in a good approximation, which can be fitted well by a linear equation between the time [t(µm)] and distance [x(mm)] as follows From Eq. (6), it can also be seen that there exists an initial delay time for the failure wave on the impact surface, which is about 0.105 µs. This delay failure mechanism is considered to be related to the evolution of microdetects under impact loading, such as microcracks growth and accumulation, etc., which was discussed in our earlier works .