**5. Conclusion**

Damage evolutions of dense, 5, and 12% porous ceramics have been further simulated and their ultimate damage distributions after the flyer impact at 300 m/s are compared. **Figure 12** plots the void collapse ratio *rcollapse* for all samples. The samples are divided into segments; the *rcollapse* is calculated from the ratio of the number of collapsed voids to the total number of voids in each segment. The boundary between the damaged region and shielded region corresponds to a rise of *rcollapse* from 0 to 1. For the same shock stress and the pulse width, as the porosity increases, the thickness of the shielded region increases accordingly. The dense ceramic has no shielded region, whereas the 12% porous ceramic has a shielded region of about 1 mm.

**Figure 13(a)** and **(e)** shows the fracture characteristics of the sample subjected to a compression of 3.3 GPa and that of 1.4 GPa, respectively. Each image is composed of 19 SEM frames, which are successively scanned along the "scanned area" marked in **Figure 13(b)**. The image has a width of 766 μm and a length of nearly 8 mm. The direction of the shock wave propagation is from the left of the image to the right. The green circles represent the voids that are basically intact. **Figure 13(c)** shows that they are concavities that are almost hemispheric and show no sign of collapse. The red rectangles represent the voids that have collapsed. **Figure 13(d)** shows that they are hollows that are believed to have been voids, but no longer retains their

For the sample loaded by a 3.3 GPa shock wave, an elastic wave-deformation wave structure emerged once, then the deformation wave is unloaded. The shield ratio should be *rshield*≈0.76, which means that ~1/4 of the sample would stay in the SFS and the other ~3/4 of the sample would be shielded. In **Figure 13(a)**, all the voids close to the impact surface have collapsed; but in the other half of the sample, there are numerous voids that are basically intact. While the distribution of the collapsed voids in the experimental samples is not as ideal as that in the modeled sample, this sample can still be divided distinctly into a damaged region and a shielded one. However, for a fully dense (0.5%-porous) sample, the simulation showed that a shielded region did not form under the same condition. For the sample loaded by a 1.4 GPa shock wave, only one elastic wave (which would not cause void collapse) emerged. And in

The results obtained from simulations and experiments have a similar trend, except that about 40% of the voids were identified as collapsed void in the shielded region of the experimental

**Figure 12.** Comparison of collapse ratios of dense and porous samples with different porosities under the same shock

**Figure 13(e)**, basically intact voids can be found throughout the sample.

**4.3. Validation by soft recovery experiment**

stress and pulse width. *rcollapse* represents collapse ratio.

hemispheric shape.

214 Recent Advances in Porous Ceramics

With the lattice-spring model simulation and the shock recovery experiment, mechanisms of damage evolution, including void collapse, shear fracture, and rotational deformation, are illuminated, and their contributions to the damage toleration of the shocked porous ceramics are demonstrated, which would be beneficial to the understanding of porous ceramics in application upon shock wave loading.

Here, adding pores deliberately does not mean to fabricate "foam ceramic." As the porosity increases, the length of the shielded region increases accordingly, and it should be considered integrally when one designs porous ceramics.
