**4. Design of energy absorbing and fracture control in shocked porous ceramics**

Pre-existing defects in ceramics induce shock wave compression fractures and may lead to the failure of designed functions. One traditional strategy for failure prevention has been by sintering "defect-free" ceramics (e.g., a large, perfect single-crystal sample). However, such treatment by sintering is difficult in practice and costly in expense, and more importantly, it only increases the critical emergence stress of shock fracture rather more than eliminating the probability of shock failure. Adopting an approach that is the opposite of creating defect-free ceramics, one may be able to control shock fracture and avoid the shock failure of ceramics by properly introducing defects. The control of shock fracture by introducing defects may seem counterintuitive. However, under quasi-static loading, there have already been many successful cases in which defects are introduced to avoid catastrophic fracture. In nature, highly mineralized natural materials owe their exceptional toughness and quasi-ductility to microscopic building blocks, weak interfaces and architecture [40–42]. In engineering, the fracture toughness of "hard and brittle" glass and metal glasses has been increased by properly introducing microcracks and voids [43–45]. These mechanisms can be summarized as crack shielding, deflection, and bridging, which effectively reduce the crack-driving force [46]. In shock applications, however, the difference is that a shock wave relates to a high-power pulse. The stress and the energy input are sufficient to vanquish various toughening strategies. Hence, numerous cracks nucleate and grow inevitably. In this case, strategies for toughening brittle materials cannot be duplicated. Instead, a novel approach in addressing shock fracture is proposed, i.e., modulating the propagation of crack network in shocked ceramics by deliberately adding pores.

#### **4.1. Control of the fractured region**

implies that the crack-driving force is very strong. The branching of numerous intergranular cracks from the main transgranular crack may be attributed to the need for more effective shock

A novel mechanism of slippage and rotation deformation, which contributes to and enhances inelastic deformation of the shocked brittle materials, has been revealed by this model. In shocked porous ceramic, numerous shear cracks are emitted during void collapse, forming a crack network. As a consequence, the media are comminuted into scattered tiny shatters by interlaced cracks. When the field of the relative velocity in these comminuted regions is drawn (**Figure 8**), the arrows (which indicated the relative velocities and directions of media) revealed complex vortex structures, showing that the shatters were slipping and rotating under shock [17]. The complex vortex structures indicate that the network composed of shear cracks takes a similar role to that of shear bands in high-strength high-toughness metallic glasses [32, 33]. They provide the precondition for relative slippages of media and irreversible

The rotational deformations of different types of materials have been reported in shock and static high-pressure investigations carried out by experiments and simulations [34–38]. For example, nickel nanoparticles were found to rotate in a diamond anvil cell when the pressure rose from 3 GPa to more than 38 GPa. When the particle sizes were various from 500 nm down to 3 nm, the measurements indicated that more active grain rotation occurs in the smaller nickel nanocrystals. Investigations here and in literatures about rotational deformation of various materials and loading conditions indicate that it becomes a universal and important deformation mechanism under high pressure to help the loaded systems to relieve shear stress and dissipate strain energy, when other usual deformations (e.g., dislocation, twinning)

energy dissipation.

210 Recent Advances in Porous Ceramics

deformation of the sample.

are absent or repressed [38, 39].

**Figure 8.** Slippage and rotation of shatters induced by extending shear cracks.

**3.3. Slippage and rotational deformation of shatters**

Mesoscopic damage and deformation evolutions (void collapse, shear fracture, and rotational deformation) induced significant stress relaxation, leading to macroscopic "plastic" response, although the model particles and springs did not contribute to plasticity (only a linear elastic interaction was set in springs of the model). Note that here plasticity is taken in its broadest sense; it is identified not by dislocation movements, but by the macroscopic stress-strain curve and irreversible deformations. **Figure 9** shows the correlation between macroscopic plasticity and mesoscopic damage evolution. Initially, a steep shock front is induced by the impact of the piston. The shock front broadens and splits into two waves during propagation inside a sample. The precursor wave is an elastic wave, which propagates with longitudinal acoustic speed. The second wave, which corresponds to an irreversible deformation, is usually termed the deformation wave (it is called plastic wave in ductile metals). The propagation speed of the deformation wave is slower than the elastic wave; thus, a plateau is produced between these two waves. After the deformation wave, the final equilibrium state, namely the Hugoniot state, is achieved. The deformation wave and the following plateau (the Hugoniot state) correspond to a "severely fractured state (SFS)," where shear fracture, void collapse, and rotational deformation of comminuted media are processed abundantly [10]. Note that the deformation wave and

porosity was therefore simulated; **Figure 10(c)** shows that its average degree of damage is reduced to ~0.1, but the damage is distributed throughout the sample. An alternative approach is worth looking for. Instead of sintering fully dense ceramics, a new idea is to make use of the pores. As shown in **Figure 10(b)**, voids are deliberately added in the ceramic; **Figure 10(d)** shows the degree of damage of a porous sample with 9.3% porosity (it is the porosity of PZT ceramics used in experiments) after sufficient evolvement: half of the porous sample has an average damage of ~0.4, and the other half of the sample is almost intact. A "shielded region" is acquired at the cost of severe fracture in the other parts of the sample (the "damaged region"). The design of controlling fractured region is based on the following mechanism: (1) the deformation wave would be slowed down by the deliberately increased porosity; (2) if the pulse is short compared with the thickness of the sample, then a rarefaction wave (the "trailing edge" of a stress pulse of shock) would catch up and unload the slow deformation wave; (3) the SFS would be frozen after the deformation wave vanishes, rather than sweep through the entire sample. After that, the ceramic will undergo elastic compression and stay in a mildly damaged state.

**Figure 11(a)** shows the configuration of the model to investigate whether voids can protect part of a sample away from the SFS. In one of the simulation runs, the porosity of the sample is

damage distribution after sufficient evolvement is shown in **Figure 11(b)**. Half of the sample is in the SFS, whereas the other half is basically intact. **Figure 11(c)** plots three shock wave profiles at three midterm times. At 130 ns after impact, an elastic wave-deformation wave-rarefaction wave structure has formed; at 240 ns, the rarefaction wave has caught the deformation wave; at 350 ns, the deformation wave has unloaded completely, and the SFS should be frozen at that time. Indeed, the boundary between the damaged region and shielded region at 800 ns in **Figure 11(b)** matches the position where the deformation wave vanished in **Figure 11(c)**.

**Figure 11.** Mechanism of earning a shielded region where the severely fractured state will not enter. (a) Configuration of the model. T refers to a very long momentum trap. (b) Damage distribution in the sample at 800 ns. (c) Stress wave

=300 m/s, which induces a ~5 GPa shock stress. The ultimate

Shock Compression of Porous Ceramics http://dx.doi.org/10.5772/intechopen.72246 213

**4.2. Validation by LSM simulation**

9.3% and the velocity of the flyer *vf*

evolution at three midterm times.

**Figure 9.** Comparison of (a) shock wave profiles and (b–d) damage distributions in dense, 5, and 12% porous ceramics, respectively.

the SFS propagate synchronously. If the deformation wave is unloaded, then, without enough energy to maintain damage evolution, the SFS would be "frozen." This is the foundation for modulating shock fracture.

**Figure 10** shows schematics of controlling shock fracture. A traditional strategy for doing it is sintering "fully dense" ceramics (**Figure 10(a)**). Evolution of a dense sample with only 0.5%

**Figure 10.** Schematic of short pulse evolutions in (a) dense ceramic (with 0.5% porosity) and (b) porous ceramic (with 9.3% porosity). Degrees of damage of (c) dense and (d) porous samples at 800 ns after impact.

porosity was therefore simulated; **Figure 10(c)** shows that its average degree of damage is reduced to ~0.1, but the damage is distributed throughout the sample. An alternative approach is worth looking for. Instead of sintering fully dense ceramics, a new idea is to make use of the pores. As shown in **Figure 10(b)**, voids are deliberately added in the ceramic; **Figure 10(d)** shows the degree of damage of a porous sample with 9.3% porosity (it is the porosity of PZT ceramics used in experiments) after sufficient evolvement: half of the porous sample has an average damage of ~0.4, and the other half of the sample is almost intact. A "shielded region" is acquired at the cost of severe fracture in the other parts of the sample (the "damaged region").

The design of controlling fractured region is based on the following mechanism: (1) the deformation wave would be slowed down by the deliberately increased porosity; (2) if the pulse is short compared with the thickness of the sample, then a rarefaction wave (the "trailing edge" of a stress pulse of shock) would catch up and unload the slow deformation wave; (3) the SFS would be frozen after the deformation wave vanishes, rather than sweep through the entire sample. After that, the ceramic will undergo elastic compression and stay in a mildly damaged state.

#### **4.2. Validation by LSM simulation**

**Figure 10.** Schematic of short pulse evolutions in (a) dense ceramic (with 0.5% porosity) and (b) porous ceramic (with 9.3%

the SFS propagate synchronously. If the deformation wave is unloaded, then, without enough energy to maintain damage evolution, the SFS would be "frozen." This is the foundation for

**Figure 9.** Comparison of (a) shock wave profiles and (b–d) damage distributions in dense, 5, and 12% porous ceramics,

**Figure 10** shows schematics of controlling shock fracture. A traditional strategy for doing it is sintering "fully dense" ceramics (**Figure 10(a)**). Evolution of a dense sample with only 0.5%

porosity). Degrees of damage of (c) dense and (d) porous samples at 800 ns after impact.

modulating shock fracture.

212 Recent Advances in Porous Ceramics

respectively.

**Figure 11(a)** shows the configuration of the model to investigate whether voids can protect part of a sample away from the SFS. In one of the simulation runs, the porosity of the sample is 9.3% and the velocity of the flyer *vf* =300 m/s, which induces a ~5 GPa shock stress. The ultimate damage distribution after sufficient evolvement is shown in **Figure 11(b)**. Half of the sample is in the SFS, whereas the other half is basically intact. **Figure 11(c)** plots three shock wave profiles at three midterm times. At 130 ns after impact, an elastic wave-deformation wave-rarefaction wave structure has formed; at 240 ns, the rarefaction wave has caught the deformation wave; at 350 ns, the deformation wave has unloaded completely, and the SFS should be frozen at that time. Indeed, the boundary between the damaged region and shielded region at 800 ns in **Figure 11(b)** matches the position where the deformation wave vanished in **Figure 11(c)**.

**Figure 11.** Mechanism of earning a shielded region where the severely fractured state will not enter. (a) Configuration of the model. T refers to a very long momentum trap. (b) Damage distribution in the sample at 800 ns. (c) Stress wave evolution at three midterm times.

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.

#### **4.3. Validation by soft recovery experiment**

**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 hemispheric shape.

sample. We attribute this "additional damage" in the shielded region of the recovered sample to two main reasons. First, there is roughness on the rear interface between the ceramic and the packet, which induced dynamic tensile stress after the shock wave has swept through and resulted in additional void damage. Second, the PZT ceramic is soft; a lot of grains are scaled off during polishing, which has a significant influence on the results counting. If one deducts the additional damage, then the experimental result is in good agreement with the simulation result.

**Figure 13.** Fracture character of porous ceramics in recovery experiments. (a) Voids evolution in the sample subjected to compression of 3.3 GPa. (b) Cross section of recovery sample. (c) Green circle represents basically intact void. (d) Red rectangle represents void which has collapsed. (e) Voids evolution in the sample subjected to compression of 1.4 GPa.

Shock Compression of Porous Ceramics http://dx.doi.org/10.5772/intechopen.72246 215

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 applica-

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

National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics,

**5. Conclusion**

**Author details**

Yin Yu and Hongliang He\*

tion upon shock wave loading.

integrally when one designs porous ceramics.

\*Address all correspondence to: honglianghe@caep.cn

CAEP, Mianyang, Sichuan, People's Republic of China

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

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

**Figure 13.** Fracture character of porous ceramics in recovery experiments. (a) Voids evolution in the sample subjected to compression of 3.3 GPa. (b) Cross section of recovery sample. (c) Green circle represents basically intact void. (d) Red rectangle represents void which has collapsed. (e) Voids evolution in the sample subjected to compression of 1.4 GPa.

sample. We attribute this "additional damage" in the shielded region of the recovered sample to two main reasons. First, there is roughness on the rear interface between the ceramic and the packet, which induced dynamic tensile stress after the shock wave has swept through and resulted in additional void damage. Second, the PZT ceramic is soft; a lot of grains are scaled off during polishing, which has a significant influence on the results counting. If one deducts the additional damage, then the experimental result is in good agreement with the simulation result.
