**3. Mechanisms of damage and deformation in shocked porous ceramics**

A shock wave relates to a high-power pulse, in which stress and the energy are sufficient to vanquish toughness of ceramics. It would activate pre-existing defects (e.g., microvoids, cracks, and grain boundaries), extends cracks, and breaks media. Mechanical, electrical, and optical properties of ceramics are severely affected by shock waves [28–30], and consequently, it may deteriorate the designed functions of ceramics. Hence, revealing the mechanisms of damage and deformation in shocked porous ceramics would be a foundation for modulation of shock behavior and enhancement of robustness of the porous ceramics involving shock applications. In this section, the effects of voids and grain boundaries on the mesoscopic deformation features of shocked porous ceramics have been explored and compared with shock experiments with the recovery of shocked porous ceramics. Microscope photographs of voids in the recovered sample have been analyzed and compared with computational results. A novel mechanism of slippage and rotation deformation has been revealed, which contributes to and enhances inelastic deformation of the shocked brittle materials. As the pressure increases, the rotational deformation becomes a universal and important mechanism for relieving shear stress and dissipating strain energy.

the voids in sintered ceramics have diameters of ~50 μm. Bulk density of the samples is determined using the Archimedes method, and the sample porosity is calculated from the ratio of

**Figure 4.** Mesoscopic mechanisms of shock plasticity in porous brittle material. (a) Distribution of the maximum resolved shear stress when shock wave has just swept through a void. (b) A snapshot of shear cracks extension around the void after

shock wave has swept through. (c) Relative slippage and rotational deformation revealed in post-shocked region.

In the recovery experiment, one wants to recover porous ceramic that contains shock compression fracture, and this fracture should only be produced by high-speed impact between the flyer and the target. Therefore, a momentum trap (**Figure 5(b)**), which has the same shock impedance as the ceramic, is needed to bear the intense dynamic tension produced by rarefaction waves and to fly away alone carrying most of the momentum input by the flyer. **Figure 5(c)** shows an incised sample: an integral recovered ceramic (yellow) is conserved in a brown brass packet. Samples are polished and acid etched before scanning electron microscopy (SEM) studies.

**Figure 6** shows comparison of void collapse features observed in the model with an isolated void and recovered porous ceramics. Long-distance extended cracks that are emitted from voids are an important feature in the model (**Figure 6(a)**). **Figure 6(b)** shows representative

**Figure 5.** (a) Microscopic observation of a void in initial porous lead zirconate titanate ceramic. (b) A schematic of the

shock experiment with recovery of the shocked porous ceramics. (c) Cross section of a recovered sample.

= 8010 kg/m3

). The sample porosity is 9.3%.

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the bulk density to the theoretical density (*ρ*<sup>0</sup>

#### **3.1. Void collapse under shock wave compression**

Simulations reveal that void collapse is initiated from severe shear stress concentrations around the void after the shock sweeps through. When media far from the void experience a mild shear stress, media in four corners around the void achieve the fracture criterion. **Figure 4** shows an isolated void that swept by a shock wave. Four shear cracks extend from the void, and broken fragments fill into void along shear cracks and occupy the free volume.

To validate the computational results, shock experiments with the recovery of shocked porous ceramics have been implemented [31]. The lead zirconate titanate (PZT) ceramic has been used, which is a ferroelectric ceramic and generates megawatts of electrical power in a short period of time via a ferroelectric-to-antiferroelectric phase transformation driven by the shock wave from a high-explosive. Unpoled samples have been used, which have no bound charge and charge releasing under the shock experiments. Voids in the ceramics were introduced during fabrication by adding spherical polymethyl methacrylate particles. As shown in **Figure 5(a)**,

**3. Mechanisms of damage and deformation in shocked porous** 

**Figure 3.** Schematic of the shock wave compression model for porous ceramics.

relieving shear stress and dissipating strain energy.

**3.1. Void collapse under shock wave compression**

fragments fill into void along shear cracks and occupy the free volume.

A shock wave relates to a high-power pulse, in which stress and the energy are sufficient to vanquish toughness of ceramics. It would activate pre-existing defects (e.g., microvoids, cracks, and grain boundaries), extends cracks, and breaks media. Mechanical, electrical, and optical properties of ceramics are severely affected by shock waves [28–30], and consequently, it may deteriorate the designed functions of ceramics. Hence, revealing the mechanisms of damage and deformation in shocked porous ceramics would be a foundation for modulation of shock behavior and enhancement of robustness of the porous ceramics involving shock applications. In this section, the effects of voids and grain boundaries on the mesoscopic deformation features of shocked porous ceramics have been explored and compared with shock experiments with the recovery of shocked porous ceramics. Microscope photographs of voids in the recovered sample have been analyzed and compared with computational results. A novel mechanism of slippage and rotation deformation has been revealed, which contributes to and enhances inelastic deformation of the shocked brittle materials. As the pressure increases, the rotational deformation becomes a universal and important mechanism for

Simulations reveal that void collapse is initiated from severe shear stress concentrations around the void after the shock sweeps through. When media far from the void experience a mild shear stress, media in four corners around the void achieve the fracture criterion. **Figure 4** shows an isolated void that swept by a shock wave. Four shear cracks extend from the void, and broken

To validate the computational results, shock experiments with the recovery of shocked porous ceramics have been implemented [31]. The lead zirconate titanate (PZT) ceramic has been used, which is a ferroelectric ceramic and generates megawatts of electrical power in a short period of time via a ferroelectric-to-antiferroelectric phase transformation driven by the shock wave from a high-explosive. Unpoled samples have been used, which have no bound charge and charge releasing under the shock experiments. Voids in the ceramics were introduced during fabrication by adding spherical polymethyl methacrylate particles. As shown in **Figure 5(a)**,

**ceramics**

206 Recent Advances in Porous Ceramics

**Figure 4.** Mesoscopic mechanisms of shock plasticity in porous brittle material. (a) Distribution of the maximum resolved shear stress when shock wave has just swept through a void. (b) A snapshot of shear cracks extension around the void after shock wave has swept through. (c) Relative slippage and rotational deformation revealed in post-shocked region.

the voids in sintered ceramics have diameters of ~50 μm. Bulk density of the samples is determined using the Archimedes method, and the sample porosity is calculated from the ratio of the bulk density to the theoretical density (*ρ*<sup>0</sup> = 8010 kg/m3 ). The sample porosity is 9.3%.

In the recovery experiment, one wants to recover porous ceramic that contains shock compression fracture, and this fracture should only be produced by high-speed impact between the flyer and the target. Therefore, a momentum trap (**Figure 5(b)**), which has the same shock impedance as the ceramic, is needed to bear the intense dynamic tension produced by rarefaction waves and to fly away alone carrying most of the momentum input by the flyer. **Figure 5(c)** shows an incised sample: an integral recovered ceramic (yellow) is conserved in a brown brass packet. Samples are polished and acid etched before scanning electron microscopy (SEM) studies.

**Figure 6** shows comparison of void collapse features observed in the model with an isolated void and recovered porous ceramics. Long-distance extended cracks that are emitted from voids are an important feature in the model (**Figure 6(a)**). **Figure 6(b)** shows representative

**Figure 5.** (a) Microscopic observation of a void in initial porous lead zirconate titanate ceramic. (b) A schematic of the shock experiment with recovery of the shocked porous ceramics. (c) Cross section of a recovered sample.

**Figure 6.** (a) Shear cracks emit from the void because of shear stress concentrations after the exposure to a shock wave. (b) Long-distance extended cracks and (c) thick cranny are observed representative mesoscopic deformation features. (d) Minor crack advances along GBs.

long cracks in the recovery sample subjected to 3.3 GPa compression. The extended crack directions deviate from those around the modeled isolated void (**Figure 6(a)**), and only two cracks are emitted. In **Figure 6(c)**, no long crack exists around this void; instead, a thick crevice forms at the top left corner of the void. It can be deduced that numerous grains in this area were damaged by multicracks and were scaled off during polishing to form such a feature. Many cracks that advance along GBs of porous PZT ceramic have been observed (**Figure 6(d)**). Hence, a more complex model, including multivoid and GBs, would be needed to reproduce these damaged features.

#### **3.2. Characters of shear cracks around collapsing voids**

Features of void collapse and shear fracture obtained from the polycrystalline model containing multivoid have been analyzed. In **Figure 7(a)**, fragments of grains fill a damaged void, and long shear cracks extend from the void. All fragments have been removed in **Figure 7(b)** to compare with experimental observations (**Figure 7(c)**). In **Figure 7(d)**, a wide area on the bottom left corner of the void has been damaged during crack evolution. When all fragments have been removed, a thick crevice is visible (**Figure 7(e)**), which is comparable with the deformation feature observed experimentally (**Figure 7(f)**). **Figure 7(g**–**i)** compares damage features between two voids. A few minor cracks, which are similar to the intergranular crack in **Figure 6(d)**, exist around all the voids in the polycrystalline model.

value that cannot support transgranular fractures. This fracture mode is termed "transgranularto-intergranular crack mode." However, intergranular cracks branch from the main transgranular crack during main crack propagation to form thick crevices. This fracture mode is termed "main (transgranular) crack and branching (intergranular) cracks mode." Media in a wide area will be damaged in this fracture mode, and a thick crevice becomes visible after fragments have

**Figure 7.** Comparison of deformation features observed in the polycrystalline model and recovery sample. (a)–(c) Representative long-distance extended shear cracks. (d)–(f) Representative thick crevices. (g)–(i) Crack transfixion between

Shock Compression of Porous Ceramics http://dx.doi.org/10.5772/intechopen.72246 209

What is the dominant factor that leads to these two different fracture modes? As shown in **Figure 7(d)**, the main crack comminutes media in a wide area during its propagation. The thickness of the main transgranular crack is ~10 μm. The violent extension of the main crack

been removed.

two voids.

The polycrystalline model also reveals the evolution of long cracks and thick crevices. For long cracks, an initially transgranular crack translates into an intergranular cracks after a certain propagation range. The translation should occur when the crack-driving force is decreased to a

long cracks in the recovery sample subjected to 3.3 GPa compression. The extended crack directions deviate from those around the modeled isolated void (**Figure 6(a)**), and only two cracks are emitted. In **Figure 6(c)**, no long crack exists around this void; instead, a thick crevice forms at the top left corner of the void. It can be deduced that numerous grains in this area were damaged by multicracks and were scaled off during polishing to form such a feature. Many cracks that advance along GBs of porous PZT ceramic have been observed (**Figure 6(d)**). Hence, a more complex model, including multivoid and GBs, would be needed to reproduce

**Figure 6.** (a) Shear cracks emit from the void because of shear stress concentrations after the exposure to a shock wave. (b) Long-distance extended cracks and (c) thick cranny are observed representative mesoscopic deformation features. (d)

Features of void collapse and shear fracture obtained from the polycrystalline model containing multivoid have been analyzed. In **Figure 7(a)**, fragments of grains fill a damaged void, and long shear cracks extend from the void. All fragments have been removed in **Figure 7(b)** to compare with experimental observations (**Figure 7(c)**). In **Figure 7(d)**, a wide area on the bottom left corner of the void has been damaged during crack evolution. When all fragments have been removed, a thick crevice is visible (**Figure 7(e)**), which is comparable with the deformation feature observed experimentally (**Figure 7(f)**). **Figure 7(g**–**i)** compares damage features between two voids. A few minor cracks, which are similar to the intergranular crack in **Figure 6(d)**, exist

The polycrystalline model also reveals the evolution of long cracks and thick crevices. For long cracks, an initially transgranular crack translates into an intergranular cracks after a certain propagation range. The translation should occur when the crack-driving force is decreased to a

these damaged features.

Minor crack advances along GBs.

208 Recent Advances in Porous Ceramics

**3.2. Characters of shear cracks around collapsing voids**

around all the voids in the polycrystalline model.

**Figure 7.** Comparison of deformation features observed in the polycrystalline model and recovery sample. (a)–(c) Representative long-distance extended shear cracks. (d)–(f) Representative thick crevices. (g)–(i) Crack transfixion between two voids.

value that cannot support transgranular fractures. This fracture mode is termed "transgranularto-intergranular crack mode." However, intergranular cracks branch from the main transgranular crack during main crack propagation to form thick crevices. This fracture mode is termed "main (transgranular) crack and branching (intergranular) cracks mode." Media in a wide area will be damaged in this fracture mode, and a thick crevice becomes visible after fragments have been removed.

What is the dominant factor that leads to these two different fracture modes? As shown in **Figure 7(d)**, the main crack comminutes media in a wide area during its propagation. The thickness of the main transgranular crack is ~10 μm. The violent extension of the main crack 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 energy dissipation.

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

gation of crack network in shocked ceramics by deliberately adding pores.

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

**4.1. Control of the fractured region**

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 propa-

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**porous ceramics**

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

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 deformation of the sample.

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) are absent or repressed [38, 39].

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