《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_fiber127

J.Am. Ceram.Soc.,901005-1018(2007) DO:10.l111551-2916.2007.01515.x c 2007 The American Ceramic Society urna Dynamic Fracture of Ceramics in Armor Applications Weinong w. chent AAE and MSE Schools, Purdue University, West Lafayette, Indiana 47907-2023 U.S. Army Research Office, Research Triangle Park, North Carolina 27709-2211 Bo Song and Xu Nie AAE and MSE Schools, Purdue University, West Lafayette, Indiana 47907-2023 Ceramic materials have been extensively used in armor appli of possibilities of defeating the threats. The fracture and pulver cations for both personnel and vehicle protection. As the types of ization of the ceramic material are also effective ways to dissi- threats have diversified recently, e.g., improvised explosive de- pate part of the kinetic energy(ke) generated by the projectile vices and explosively formed projectiles, a proper set of ceramic Further, the flow motion of the hard ceramic fragments around material selection criteria is needed to design and optimize cor- the projectile erodes the tip or even the entire length of the pro- responding mitigating structures. However, the dynamic frac- jectile, which further dissipates energy and spreads the impact ture and failure behavior of engineering ceramics is still not well area. This layered armor concept has been used in many vehicle understood Using examples of thin ceramic plates and confined and personnel armor designs. Because of their critical roles in thick ceramics subjected to kinetic energy projectile impact, this layered armors, ceramics have attracted considerable attention article provides a brief summary on the current understanding of for the determination of their mechanical responses and failure dynamic failure processes of ceramics under dynamic penetra- behavior under impact and thermal loadings. Among different tion loading conditions. Laboratory examination of dynamic structural ceramics, some types of oxide ceramics(mostly alumi- fracture of ceramics is conducted using split Hopkinson bars na ceramics) and non-oxide ceramics(mostly carbides, nitrides, with various loading rates, stress states, and loading histories. borides) are commonly used for ballistic protection. A signifi- cant improvement in the cost/performance ratio of silicon carbide ceramics has increased their popularity in recent armor applica- tions relative to more established materials such as alumin The development of armor systems depends on the threats to hen faster and harder hostile threats are encountere be defeated. The anti-armor threats have become more diversi- adding a ceramic plate on top of a metal plate has been fied recently. For example, improvised explosive devices (Ied known to enhance significantly the ballistic protection over the ing both blast and fragment loading on armor systems from monolithic metal armor since the 1960s and 1970s. A ceramic close range and pose significant challenges in protection con- plate on a woven/roven backing also exhibited similar ballistic cepts. An effective armor design is an optimized solution to enhancement on light armors for aircraft protection. Upon im- op a specific threat within the design constrains such as area pact, the ceramic plate surrounding the impact area may be density, cost, and schedule. To achieve high efficiency in armor ractured, pulverized, and ejected depending on different impact development, it is important to have the capability for predicting onditions. However, the dynamic failure processes of the cer- the armor performance before the product is made. With the aid amics effectively extend the time of impact loading and spread of high-speed computers and design software, the possibility the impact load over a larger area on the backing structures. developing such predictive capabilities has become realisticg- Both the loading time extension and the impact area increase However, realistic numerical simulations require accurate con- reduce the stress on the backing structures, thus enhancing the stitutive and failure models for all the materials involved in the impact event. This in turn requires reliable experimental results D. Green-contributing editor and the understanding of the deformation and failure processes of these materials under such extreme loading conditions. How ever, this desired understanding on the impact response of ma- terials is far from comprehensively developed. Many research december 4. 2006. partially supported by the U.S. Army Research Office under Grant No. efforts have been invested to develop a better understanding of different aspects in ceramic fracture and failure under dynamic Author to whom correspondence should be addressed. e-mail: when Feature

Dynamic Fracture of Ceramics in Armor Applications Weinong W. Chenw AAE and MSE Schools, Purdue University, West Lafayette, Indiana 47907-2023 A. M. Rajendran U.S. Army Research Office, Research Triangle Park, North Carolina 27709-2211 Bo Song and Xu Nie AAE and MSE Schools, Purdue University, West Lafayette, Indiana 47907-2023 Ceramic materials have been extensively used in armor appli￾cations for both personnel and vehicle protection. As the types of threats have diversified recently, e.g., improvised explosive de￾vices and explosively formed projectiles, a proper set of ceramic material selection criteria is needed to design and optimize cor￾responding mitigating structures. However, the dynamic frac￾ture and failure behavior of engineering ceramics is still not well understood. Using examples of thin ceramic plates and confined thick ceramics subjected to kinetic energy projectile impact, this article provides a brief summary on the current understanding of dynamic failure processes of ceramics under dynamic penetra￾tion loading conditions. Laboratory examination of dynamic fracture of ceramics is conducted using split Hopkinson bars with various loading rates, stress states, and loading histories. I. Introduction WHEN faster and harder hostile threats are encountered, adding a ceramic plate on top of a metal plate has been known to enhance significantly the ballistic protection over the monolithic metal armor since the 1960s and 1970s.1 A ceramic plate on a woven/roven backing also exhibited similar ballistic enhancement on light armors for aircraft protection.2 Upon im￾pact, the ceramic plate surrounding the impact area may be fractured, pulverized, and ejected depending on different impact conditions. However, the dynamic failure processes of the cer￾amics effectively extend the time of impact loading and spread the impact load over a larger area on the backing structures. Both the loading time extension and the impact area increase reduce the stress on the backing structures, thus enhancing the possibilities of defeating the threats. The fracture and pulver￾ization of the ceramic material are also effective ways to dissi￾pate part of the kinetic energy (KE) generated by the projectile. Further, the flow motion of the hard ceramic fragments around the projectile erodes the tip or even the entire length of the pro￾jectile, which further dissipates energy and spreads the impact area. This layered armor concept has been used in many vehicle and personnel armor designs.3,4 Because of their critical roles in layered armors, ceramics have attracted considerable attention for the determination of their mechanical responses and failure behavior under impact and thermal loadings.4–8 Among different structural ceramics, some types of oxide ceramics (mostly alumi￾na ceramics) and non-oxide ceramics (mostly carbides, nitrides, borides) are commonly used for ballistic protection.8 A signifi- cant improvement in the cost/performance ratio of silicon carbide ceramics has increased their popularity in recent armor applica￾tions relative to more established materials such as alumina. The development of armor systems depends on the threats to be defeated. The anti-armor threats have become more diversi- fied recently. For example, improvised explosive devices (IED) bring both blast and fragment loading on armor systems from close range and pose significant challenges in protection con￾cepts.4 An effective armor design is an optimized solution to stop a specific threat within the design constrains such as area density, cost, and schedule. To achieve high efficiency in armor development, it is important to have the capability for predicting the armor performance before the product is made. With the aid of high-speed computers and design software, the possibility of developing such predictive capabilities has become realistic.9–11 However, realistic numerical simulations require accurate con￾stitutive and failure models for all the materials involved in the impact event. This in turn requires reliable experimental results and the understanding of the deformation and failure processes of these materials under such extreme loading conditions. How￾ever, this desired understanding on the impact response of ma￾terials is far from comprehensively developed. Many research efforts have been invested to develop a better understanding of different aspects in ceramic fracture and failure under dynamic loading conditions. Feature D. Green—contributing editor This work was partially supported by the U.S. Army Research Office under Grant No. W911-05-1-0218 to Purdue University. w Author to whom correspondence should be addressed. e-mail: wchen@purdue.edu Manuscript No. 22256. Received September 17, 2006; approved December 4, 2006. Journal J. Am. Ceram. Soc., 90 [4] 1005–1018 (2007) DOI: 10.1111/j.1551-2916.2007.01515.x r 2007 The American Ceramic Society

In this paper, we use two typical ceramic armor summarize briefly the current understanding on the ceramic fracture and failure processes when subject to impact loading. he first case is the ceramic plate in a thin-layered armor syst Ceramic plate to resist impacts by hard objects such as armor-piercing bullets Partially damaged The other case is a confined thick ceramic target subjected to a long-rod penetration. Then, we present the dynamic fracture behavior of brittle materials, which is an important aspect in the processes of ceramic armor failure, under various conditions in loading rates. stress states, and loading histories. A recent effort in determining the dynamic fracture toughness for ceramics un- der valid testing conditions is also introduced. Most of the re- search on this topic described in this paper comes from various Back plate modified split Hopkinson bar experiments. We intend to present Fig 1. Illustration of a short projectile impacting a thin ceramic armor the main concepts and results on these aspects in an attempt to system. illustrate the physical mechanisms behind the failure phenome na, but not an exhaustive review on this subject. For example details related to failure waves, terminal velocities of dynamic the back surface to the impact surface. When the damaged acks, and spalling are not discussed in this paper Modeling zone reaches the projectile and the damaged area is comparable d simulation aspects are discussed only when they are directly to the projectile cross section, the ceramic tile fails. Before the related to the experimental results presented damaged zone reaches the projectile, the projectile is unable to penetrate. This time of non-penetration is known as dwell. If the projectile is short, this damage development time may be suffi- IL. Failure of Ceramics Under Impact ciently long, such that the projectile has completely deformed Upon impact by a KE projectile, the failure process onditierial impact surface. In this case, no penetration occurs. which is in a ceramic plastically or shattered before the damaged zone reaches the properties, geometry, confinement, and interfacial called interface defeat. However. such dwell or interface defe To discuss the failure processes, we take two common ccurs only when the projectile impacting velocity is below cer here: a thin ceramic plate backed by a ductile substrate ain critical values. Detailed numerical analysis also reveals thick ceramic target confined by metal jackets. Thin-plate armor that the damaged zone is conical in shape, pointing to the pro- jectile. Therefore, even the ceramic tile is damaged; the dam- vehicle protection systems, are primarily for defeating projectiles aged or cracked material still piles in the shape of a spreading from small arms and machine guns. Confined ceramic packets, one, which helps to redistribute the impact load to a larger area seen mostly in heavy vehicle armors, are designed to stop heavy n the surface of the backing plate. However, once the projectile metal, long rod, KE projectiles. Multiple layers of either of these velocity is beyond the critical value, the ceramic tile will be per ystems are also seen in some vehicle-protection forated either by a longer projectile and or a higher striking velocity. The prediction of the penetration process and the crit ical impact velocity clearly depends on the accurate modeling of (1) Failure of Ceramic Tiles the material responses and failure under impact conditions, both a typical thin-layered system consists of a ceramic plate and a for the target and the projectile. From the target side, damage is metal or textile backing plate bound together with a thin adhe most likely formed by a series of dynamic fracture processes sive layer, as shown schematically in Fig. 1. The work reported under multiaxial loading conditions. n a series of documents by wilkins et al. 2-6 and Landringham and Casey is probably the earliest systematic description of the dynamic failure in the ceramic plate when impacted by a KE (2) Failure of Confined Thick Ceramics projectile. Using computer simulations, which became powerful When a ceramic armor is subjected to the impact of a long rod tools in the study of ceramic failure under impact loading in the Ke projectile, which is usually made of a heavy metal, the it has been shown that the failure initiated jectile confers high energy density on the impact area over a from the back side of the ceramic tile. Upon impact, high- much longer duration. The efficiency of these projectiles ceramic tile and in the projectile. In the ceramic tile, the com- ensively deformed or damaged, the remaining undamaged por pressive stresses propagate along the thickness. When the waves tion of the long rod will continue to carry on the penetration reach the back surface, which is in contact with the backing process. In this case, the primary defeat mechanism is errosion, 3 plate, portions of the waves are transmitted into the backing plate. The rest of the waves are reflected back into the ceramic which requires a much thicker ceramic layer than the tiles de- scribed in the previous section. Furthermore, Hauver et al. ile. The mechanical impedance of the backing plate is typically and Malaise et al25 found that confined ceramics were much less than that of the ceramic tile; due to the intrinsically lower more efficient in defeating the penetrator. When the ceramic is wave speeds and the necessary low density, the reflected stresses confined, for example by a heat-shrunk metal cover, it takes become tensile As ceramic materials are typically much weaker higher impact load and a longer time to shatter the cerami under tensile loading as compared with their compressive re- Even after the ceramic is shattered the broken ceramic rubble is sponses, failure initiates where the tensile stress exceeds a critical still contained inside the ductile metal cover and can furthe alue. Further upon the point impact load, the target ma erode the projectile during the later stages of the penetration erial just ahead of the projectile deforms more in the out-of process. Both the extended time to shatter and the ability to lane direction than the material away from the impact zone due rode the penetrator contribute to the possible defeat of the to inertia effects. This causes the ceramic tile to bend which also long-rod generates a high tensile stress on the back surface of the tile just As shown schematically in Fig. 2, when a confined thick piece ahead of the projectile. However, this bending effect is unlikely of ceramic is impacted by a long rod, the ceramic materia to be a dominant factor wilkins et al. o observed that initial xtensively cracked as observed by Shockey and marchand racks in ceramic tiles do not significantly affect the penetration Even though the impact event occurs at very high rates of esistance of the target as long as the projectile does not impact deformation, the crack pattern resembles those observed in y close to the cracks. Numerical simulations reveal that brittle materials when subjected to a concentrated indentation time for the cracked or damaged zone to develop from load. If the long rod penetrates into the ceramic target, the

In this paper, we use two typical ceramic armor cases to summarize briefly the current understanding on the ceramic fracture and failure processes when subject to impact loading. The first case is the ceramic plate in a thin-layered armor system to resist impacts by hard objects such as armor-piercing bullets. The other case is a confined thick ceramic target subjected to a long-rod penetration. Then, we present the dynamic fracture behavior of brittle materials, which is an important aspect in the processes of ceramic armor failure, under various conditions in loading rates, stress states, and loading histories. A recent effort in determining the dynamic fracture toughness for ceramics un￾der valid testing conditions is also introduced. Most of the re￾search on this topic described in this paper comes from various modified split Hopkinson bar experiments. We intend to present the main concepts and results on these aspects in an attempt to illustrate the physical mechanisms behind the failure phenome￾na, but not an exhaustive review on this subject. For example, details related to failure waves, terminal velocities of dynamic cracks, and spalling are not discussed in this paper. Modeling and simulation aspects are discussed only when they are directly related to the experimental results presented. II. Failure of Ceramics Under Impact Upon impact by a KE projectile, the failure process in a ceramic target depends on many parameters that describe the material properties, geometry, confinement, and interfacial conditions. To discuss the failure processes, we take two common examples here: a thin ceramic plate backed by a ductile substrate and a thick ceramic target confined by metal jackets. Thin-plate armor systems, commonly seen in body armors and aircraft or light vehicle protection systems, are primarily for defeating projectiles from small arms and machine guns. Confined ceramic packets, seen mostly in heavy vehicle armors, are designed to stop heavy metal, long rod, KE projectiles. Multiple layers of either of these systems are also seen in some vehicle-protection systems. (1) Failure of Ceramic Tiles A typical thin-layered system consists of a ceramic plate and a metal or textile backing plate bound together with a thin adhe￾sive layer, as shown schematically in Fig. 1. The work reported in a series of documents by Wilkins et al. 12–16 and Landringham and Casey17 is probably the earliest systematic description of the dynamic failure in the ceramic plate when impacted by a KE projectile. Using computer simulations, which became powerful tools in the study of ceramic failure under impact loading in the years up to now,18–20 it has been shown that the failure initiated from the back side of the ceramic tile. Upon impact, high￾amplitude compressive stress pulses are generated both in the ceramic tile and in the projectile. In the ceramic tile, the com￾pressive stresses propagate along the thickness. When the waves reach the back surface, which is in contact with the backing plate, portions of the waves are transmitted into the backing plate. The rest of the waves are reflected back into the ceramic tile. The mechanical impedance of the backing plate is typically less than that of the ceramic tile; due to the intrinsically lower wave speeds and the necessary low density, the reflected stresses become tensile. As ceramic materials are typically much weaker under tensile loading as compared with their compressive re￾sponses, failure initiates where the tensile stress exceeds a critical value. Furthermore, upon the point impact load, the target ma￾terial just ahead of the projectile deforms more in the out-of￾plane direction than the material away from the impact zone due to inertia effects. This causes the ceramic tile to bend, which also generates a high tensile stress on the back surface of the tile just ahead of the projectile. However, this bending effect is unlikely to be a dominant factor. Wilkins et al. 16 observed that initial cracks in ceramic tiles do not significantly affect the penetration resistance of the target as long as the projectile does not impact on or very close to the cracks. Numerical simulations reveal that it takes time for the cracked or damaged zone to develop from the back surface to the impact surface.20 When the damaged zone reaches the projectile and the damaged area is comparable to the projectile cross section, the ceramic tile fails. Before the damaged zone reaches the projectile, the projectile is unable to penetrate. This time of non-penetration is known as dwell. If the projectile is short, this damage development time may be suffi- ciently long, such that the projectile has completely deformed plastically or shattered before the damaged zone reaches the impact surface. In this case, no penetration occurs, which is called interface defeat. However, such dwell or interface defeat occurs only when the projectile impacting velocity is below cer￾tain critical values.20,21 Detailed numerical analysis also reveals that the damaged zone is conical in shape, pointing to the pro￾jectile.20 Therefore, even the ceramic tile is damaged; the dam￾aged or cracked material still piles in the shape of a spreading cone, which helps to redistribute the impact load to a larger area on the surface of the backing plate. However, once the projectile velocity is beyond the critical value, the ceramic tile will be per￾forated either by a longer projectile and/or a higher striking velocity. The prediction of the penetration process and the crit￾ical impact velocity clearly depends on the accurate modeling of the material responses and failure under impact conditions, both for the target and the projectile. From the target side, damage is most likely formed by a series of dynamic fracture processes under multiaxial loading conditions. (2) Failure of Confined Thick Ceramics When a ceramic armor is subjected to the impact of a long rod KE projectile, which is usually made of a heavy metal, the pro￾jectile confers high energy density on the impact area over a much longer duration. The efficiency of these projectiles comes from the fact that even if the front end of the projectile is ex￾tensively deformed or damaged, the remaining undamaged por￾tion of the long rod will continue to carry on the penetration process. In this case, the primary defeat mechanism is errosion,3 which requires a much thicker ceramic layer than the tiles de￾scribed in the previous section. Furthermore, Hauver et al. 22–24 and Malaise et al. 25 found that confined ceramics were much more efficient in defeating the penetrator. When the ceramic is confined, for example by a heat-shrunk metal cover, it takes a higher impact load and a longer time to shatter the ceramic. Even after the ceramic is shattered, the broken ceramic rubble is still contained inside the ductile metal cover and can further erode the projectile during the later stages of the penetration process. Both the extended time to shatter and the ability to erode the penetrator contribute to the possible defeat of the long-rod projectile. As shown schematically in Fig. 2, when a confined thick piece of ceramic is impacted by a long rod, the ceramic material is extensively cracked as observed by Shockey and Marchand.26 Even though the impact event occurs at very high rates of deformation, the crack pattern resembles those observed in brittle materials when subjected to a concentrated indentation load.27,28 If the long rod penetrates into the ceramic target, the Partially damaged Failed Projectile Ceramic plate Back plate Fig. 1. Illustration of a short projectile impacting a thin ceramic armor system. 1006 Journal of the American Ceramic Society—Chen et al. Vol. 90, No. 4

April 2007 Fracture of Ceramics in Armor racture of Ceramics Under Uniaxial Ceramic Target letal confinement Dynamic compressive stress-strain responses of ceramics have been studied extensively. Split Hopkinson pressure bars(SHPB are commonly used tools to generate families of stress-strain curves at controlled strain rates. SHPB, orginally developed by Kolsky, has been modified to determine the dynamic consti- Comminuted material tutive behaviors of a variety of brittle materials including con crete and ceramics. The details of SHPB and its working inciple are well described. However, the focus of these ex perimental investigations is typically on the dynamic stress- strain response, which is another important aspect of ceramic pact response, rather than on dynamic fracture behavior. Re- cently, with improved high-speed imaging systems, dynami fracture processes are more accessible by diagnostic instrument Paliwal et al. imaged the dynamic fracture initiation and prop- Fig. 2. Illustration of a long rod penetrating a thick and confined ation inside a transparent ceramic specimen loaded using an ceramic armor system. he shPb experiments described below were on a silicon carbide(Sic-N) ceramic with a modified SHPb us- ceramic material must make room for the long rod to enter. Conceptually, the material in front of the tip of the projectile SHPB setup(Fig 3)used in this research consisted of a must be compressed by a very high pressure. 8. g T he hr tress. bars, with a density of 8100 kg/m, Young,s modulus of 200 sure, high shear loading turns the ceramic into an extensively GPa, and an elastic bar wave speed of 4969 m/s The bars had a cracked, but still interlocked state commonly known as a com- common diameter of 19.0 mm. The incident and transmission into the ceramic target, fine ceramic fragments ahead of the from strain gauges mounted on the bars were recorded using a penetrator flow radially around the nose of penetrator and are high-speed digital storage oscilloscope through differential pre- then ejected backwards along the shank of penetrator, and thus erode the penetrator. As the penetration process proceeds To minimize the stress concentrations in the brittle specimen the rapidly flowing ceramic fragments continue to erode the due to grip rigidity and alignment, two modifications were i penetrator until the penetrator disappears or the ceramic is per- troduced to the SHPB's testing section, as shown schematically forated. This penetration process will leave a tunnel with a in Fig 3. To prevent the ceramic specimen from indenting into diameter larger than the projectile diameter. The comminuted bar-end faces and thus causing stress concentrations along spec- zone in the ceramic target is rather concentrated around the imen edges, a pair of laterally confined, high-stiffness tungsten projectile. The resistance to comminution has been identified as carbide platens(0 12.7 mm x 6.35 mm) with mechanical im- significant factor governing the ballistic performance of a amic material.37 pedance matching with the bars were placed between the spec- imen and the bars. Ceramic specimens are very sensitive to he descriptions of these two ceramic armor penetration cas stress concentrations due to misalignment of the loadin es indicate that the ceramic failure processes are very compli To correct any slight misalignment, a simplified universal joint cated. The stress state varies from highly confined just ahead of consisted of a pair of hardened tool steel disks with a spherical the projectile to almost stress free on the surfaces away from the joining surface in between was placed between the tungsten striking point. The front surface near the impact area may spall bide platen and the transmission bar(Fig. 3). The disks have off by the tensile stresses during the wave reflections in the tar- the same diameter as the bars, thus introducing no impedance get, forming impact craters. The stress amplitude just ahead of mismatch to wave propagation through the disks. High-vacuum grease was applied on the curved contacting surfaces to minim- ceramic may be possible. The stress on the surface away from ize friction the impact zone is associated only with elastic waves. The rates The surface fracture and failure process in the ceramic spec- of deformation in the ceramic material corresponding to the imen was recorded by a digital high-speed camera synchronized the penetration process, the portion of the intact piece of ce- of the incident bar to generate incident pulses olli end various loading conditions also cover a wide spectrum. During with the SHPB setup. a pulse shaper was used at the uted rubbles that are subsequently rejected back toward the response at constant strain rate projectile direction. The rest of the ceramic target is extensively The dimensions of Sic-N cylindrical specimen used in this cracked. Thus, dynamic fracture ses are associated with esearch were 6.35 mm in diameter and 6. 35 mm in length. The all aspects of the target behavior during penetration. It SIC-N mens were core drilled from a 100 mm 100 ortant to develop a fundamental understanding of the dynamic mm x 50 mm block supplied by U.S. Army Research Labora- fracture behavior of ceramic materials. However, the research tory and then cut to 6.35 mm in length, with both ends precision accumulation on this aspect is still limited and so is the under- ground to within 0.005 mm perpendicularity from the central anding. For example, the processes of comminution of ceram- axis base. The cylindrical surface from core drilling was then ics under a high pressure at high rates are still not well ground to 6.350 mm diameter within 0.005 mm cylindricity. understood. In the following sections, we summarize some of We show two experiments under identical loading conditions the experimental efforts that were designed to develop a better One experiment was performed on a nearly perfect cylindrical understanding of the dynamic fracture behavior of ceramics and pecimen, and the other on a specimen with a small pre-existing the behavior of damaged ceramics. Under uniaxial tensi urface defect. Figure 4 shows the sequential images of the fra here the stress state is one-dimensional (1-D)stress or I-D ture and failure processes of the first specimen. Figure 5 shows strain, the resultant crack runs perpendicular to the tensile load the corresponding positions on the loading history where the g. which will not be discussed here. The stress states in the mages shown in Fig 4 were taken. The loading was provided by cases described below are more complicated of deformation are mostly limited to those ack aiehabpeh with sabes a 203-mm long striker impacting on the incident bar through a composite pulse shaper consisting of a 6.35 mm x 1.57 mm Hopkinson bars annealed copper disk and a 10.31 mm x 0.51 mm mild steel

ceramic material must make room for the long rod to enter. Conceptually, the material in front of the tip of the projectile must be compressed by a very high pressure. High shear stresses are also present in this high-pressure region.28,29 This high pres￾sure, high shear loading turns the ceramic into an extensively cracked, but still interlocked state, commonly known as a com￾minuted state or a Mescall zone.26,30–35 As the striker penetrates into the ceramic target, fine ceramic fragments ahead of the penetrator flow radially around the nose of penetrator and are then ejected backwards along the shank of penetrator, and thus erode the penetrator.34,36 As the penetration process proceeds, the rapidly flowing ceramic fragments continue to erode the penetrator until the penetrator disappears or the ceramic is per￾forated. This penetration process will leave a tunnel with a diameter larger than the projectile diameter. The comminuted zone in the ceramic target is rather concentrated around the projectile. The resistance to comminution has been identified as a significant factor governing the ballistic performance of a ce￾ramic material.37 The descriptions of these two ceramic armor penetration cas￾es indicate that the ceramic failure processes are very compli￾cated. The stress state varies from highly confined just ahead of the projectile to almost stress free on the surfaces away from the striking point. The front surface near the impact area may spall off by the tensile stresses during the wave reflections in the tar￾get, forming impact craters. The stress amplitude just ahead of the projectile is so high that a brittle–ductile transition in the ceramic may be possible. The stress on the surface away from the impact zone is associated only with elastic waves. The rates of deformation in the ceramic material corresponding to the various loading conditions also cover a wide spectrum. During the penetration process, the portion of the intact piece of ce￾ramic where the projectile passes through turns into commin￾uted rubbles that are subsequently rejected back toward the projectile direction. The rest of the ceramic target is extensively cracked. Thus, dynamic fracture processes are associated with all aspects of the target behavior during penetration. It is im￾portant to develop a fundamental understanding of the dynamic fracture behavior of ceramic materials. However, the research accumulation on this aspect is still limited and so is the under￾standing. For example, the processes of comminution of ceram￾ics under a high pressure at high rates are still not well understood. In the following sections, we summarize some of the experimental efforts that were designed to develop a better understanding of the dynamic fracture behavior of ceramics and the behavior of damaged ceramics. Under uniaxial tension, where the stress state is one-dimensional (1-D) stress or 1-D strain, the resultant crack runs perpendicular to the tensile load￾ing, which will not be discussed here. The stress states in the cases described below are more complicated, although the rates of deformation are mostly limited to those achievable with split Hopkinson bars. III. Dynamic Fracture of Ceramics Under Uniaxial Compression Dynamic compressive stress–strain responses of ceramics have been studied extensively. Split Hopkinson pressure bars (SHPB) are commonly used tools to generate families of stress–strain curves at controlled strain rates. SHPB, originally developed by Kolsky,38 has been modified to determine the dynamic consti￾tutive behaviors of a variety of brittle materials including con￾crete and ceramics.39–50 The details of SHPB and its working principle are well described.51 However, the focus of these ex￾perimental investigations is typically on the dynamic stress– strain response, which is another important aspect of ceramic impact response, rather than on dynamic fracture behavior. Re￾cently, with improved high-speed imaging systems, dynamic fracture processes are more accessible by diagnostic instruments. Paliwal et al. 52 imaged the dynamic fracture initiation and prop￾agation inside a transparent ceramic specimen loaded using an SHPB. The SHPB experiments described below were conducted on a silicon carbide (SiC–N) ceramic with a modified SHPB us￾ing ramp-loading pulses. The SHPB setup (Fig. 3) used in this research consisted of a C-350 maraging steel elastic striker, incident and transmission bars, with a density of 8100 kg/m3 , Young’s modulus of 200 GPa, and an elastic bar wave speed of 4969 m/s. The bars had a common diameter of 19.0 mm. The incident and transmission bars were 2835 and 1371 mm long, respectively. The signals from strain gauges mounted on the bars were recorded using a high-speed digital storage oscilloscope through differential pre￾amplifiers. To minimize the stress concentrations in the brittle specimen due to grip rigidity and alignment, two modifications were in￾troduced to the SHPB’s testing section, as shown schematically in Fig. 3. To prevent the ceramic specimen from indenting into bar-end faces and thus causing stress concentrations along spec￾imen edges, a pair of laterally confined, high-stiffness tungsten carbide platens (+12.7 mm
6.35 mm) with mechanical im￾pedance matching with the bars were placed between the spec￾imen and the bars.53,54 Ceramic specimens are very sensitive to stress concentrations due to misalignment of the loading axis. To correct any slight misalignment, a simplified universal joint consisted of a pair of hardened tool steel disks with a spherical joining surface in between was placed between the tungsten car￾bide platen and the transmission bar (Fig. 3).55 The disks have the same diameter as the bars, thus introducing no impedance mismatch to wave propagation through the disks. High-vacuum grease was applied on the curved contacting surfaces to minim￾ize friction. The surface fracture and failure process in the ceramic spec￾imen was recorded by a digital high-speed camera synchronized with the SHPB setup. A pulse shaper was used at the impact end of the incident bar to generate incident pulses of linear ramps, which was necessary to deform the specimen with a nearly linear response at constant strain rates.56,57 The dimensions of SiC–N cylindrical specimen used in this research were 6.35 mm in diameter and 6.35 mm in length. The SiC–N specimens were core drilled from a 100 mm
100 mm
50 mm block supplied by U.S. Army Research Labora￾tory and then cut to 6.35 mm in length, with both ends precision ground to within 0.005 mm perpendicularity from the central axis base. The cylindrical surface from core drilling was then ground to 6.350 mm diameter within 0.005 mm cylindricity. We show two experiments under identical loading conditions. One experiment was performed on a nearly perfect cylindrical specimen, and the other on a specimen with a small pre-existing surface defect. Figure 4 shows the sequential images of the frac￾ture and failure processes of the first specimen. Figure 5 shows the corresponding positions on the loading history where the images shown in Fig. 4 were taken. The loading was provided by a 203-mm long striker impacting on the incident bar through a composite pulse shaper consisting of a +6.35 mm
1.57 mm annealed copper disk and a +10.31 mm
0.51 mm mild steel Ceramic Target Projectile Ejecta Metal confinement Comminuted material Fig. 2. Illustration of a long rod penetrating a thick and confined ceramic armor system. April 2007 Dynamic Fracture of Ceramics in Armor 1007

Journal of the American Ceramic Society--Chen et al. Vol. 90. No 4 computer tigger signal striker fse shape stran gages incident bar transmission bar 松)— stainless steel s Wheatstone bridge Wheatstone bridge universal joint digital osciloscope pre-amplifier specimen assembly Fig 3. Schematic illustration of the experimental setup for dynamic fracture(one-dimensional stress compression) disk. The loading rate of the resulting ramp pulse in the incident the specimen was loaded very evenly because of the precautions bar was 9.76x 10 MPa/s. The first image shows the SiC-N took in the ent design and setup. However, the ejec- specimen sandwiched between two platens in the testing section ion of material also indicates the possible limitation of using of an SHPB. The second image was taken 40 us after the arrival cylindrical specimens to obtain compressive material properti of the front tip of the ramp loading pulse, when the load was of ceramics. At 75 us into the loading, surface cracks just be- only about 10% of the eventual failure load (position I in came visible as shown in the third image. The overall compre Fig 5). Even at this low loading level, fine powder was noticed sive loading reached about 83% of the eventual peak stress to eject from the edges of both ends of the cylindrical specimen. (Fig. 5). The cracks were initiated from the edges and propa- The ejected powder is believed to be the fine particles created by gated approximately along the specimen axial direction. Such the concentrated stresses at the specimen edges, mixed with cracks were populated very quickly. The next image was taken 5 some lubricant. Even though the overall compressive stress was us later, and many cracks had become visible on the cylindrical very low, the local concentrated and multi-axial stresses were surface. Fine particles were ejected in the radial directions from apparently sufficient enough to pulverize the ceramic materials the middle of the specimen, in addition to those ejected from the at the edges. The even pattern of the ejection also verifies that edges. The specimen diameter increased slightly. Another 5 us Unit: microsecond T=0 T T=80 T=85 T=90 Fig 4. Dynamic fracture and failure process of a SiC-N specimen under uniaxial compression

disk. The loading rate of the resulting ramp pulse in the incident bar was 9.76
106 MPa/s. The first image shows the SiC–N specimen sandwiched between two platens in the testing section of an SHPB. The second image was taken 40 ms after the arrival of the front tip of the ramp loading pulse, when the load was only about 10% of the eventual failure load (position 1 in Fig. 5). Even at this low loading level, fine powder was noticed to eject from the edges of both ends of the cylindrical specimen. The ejected powder is believed to be the fine particles created by the concentrated stresses at the specimen edges, mixed with some lubricant. Even though the overall compressive stress was very low, the local concentrated and multi-axial stresses were apparently sufficient enough to pulverize the ceramic materials at the edges. The even pattern of the ejection also verifies that the specimen was loaded very evenly because of the precautions we took in the experiment design and setup. However, the ejec￾tion of material also indicates the possible limitation of using cylindrical specimens to obtain compressive material properties of ceramics. At 75 ms into the loading, surface cracks just be￾came visible as shown in the third image. The overall compres￾sive loading reached about 83% of the eventual peak stress (Fig. 5). The cracks were initiated from the edges and propa￾gated approximately along the specimen axial direction. Such cracks were populated very quickly. The next image was taken 5 ms later, and many cracks had become visible on the cylindrical surface. Fine particles were ejected in the radial directions from the middle of the specimen, in addition to those ejected from the edges. The specimen diameter increased slightly. Another 5 ms Fig. 3. Schematic illustration of the experimental setup for dynamic fracture (one-dimensional stress compression). T = 0 T = 40 T = 75 T = 80 T = 85 T = 90 T = 95 T = 100 Unit: microsecond Fig. 4. Dynamic fracture and failure process of a SiC–N specimen under uniaxial compression. 1008 Journal of the American Ceramic Society—Chen et al. Vol. 90, No. 4

April 2007 Fracture of Ceramics in Arm the corresponding stress history in this spec The first was taken before the arrival of the loading pulse. At 15 the arrival of the loading pulse front, when the load in the imen was very low as marked by position I in Fig. 7, an inclined urface crack was already visible as circled in Fig. 6. As the 苏es specimens and the testing conditions were nominally the same, this inclined crack was considered to initiate from a pre-existing urface defect on the specimen. The inclined crack grew as the 3000 loading was increased, as shown in the next two images At 45 us into the loading, when the specimen stress was less than half of its peak level, the inclined crack tip turned into the axial direc- tion. This crack tip behavior is very similar to the well-docu- mented wing cracks observed under quasi-static loading condition Under the dynamic loading in this study, be fore the wing crack could extend through the specimen, other axial cracks were initiated and propagated in the axial direction as seen in the following images taken at 5-us intervals. The Time(microsecond) loading, when the sample had been extensively cracked, as can be seen in the images. Because of the small surface defect, the Fig. 5. Axial compressive stress history in the specimen corresponding ultimate strength of this specimen was much lower than the to the images in fig. 4 previous case(3.3 vs 5.3 GPa), which is an indication that small urface defects can drastically alter the specimen response, lead ing to a scattered nature of the ceramic failure data later, the specimen had been divided into thin axial columns by The images presented in Figs. 4 and 6 reveal some of the many axial cracks. Some of the columns started to colla fundamental aspects associated with the dynamic crack initi- both ends of the specimen. At this point, the axial cor ation and propagation in brittle materials under uniaxial com- tress reached its peak value(position 5 in Fig. 5). The pression. The cracks initiate from stress-concentrated features in became unstable as the load-bearing columns along the axial the specimen, where the features are the specimen edges in the direction became less and less as the columns further collapsed. case of Fig 4, and a surface defect and then edges in the case of Figure 6 shows the images of the fracture and failure pro- Fig. 6. Once the cracks are initiated, they eventually propagate cesses in a specimen with a surface defect under the identical roughly along the compressive loading axis. Before a dominant loading conditions as the previous experiment. Figure 7 shows crack can run through the specimen, many other cracks form 015 Fig. 6. Dynamic fracture and failure process of another SiC-N specimen under uniaxial compression

later, the specimen had been divided into thin axial columns by many axial cracks. Some of the columns started to collapse near both ends of the specimen. At this point, the axial compressive stress reached its peak value (position 5 in Fig. 5). The specimen became unstable as the load-bearing columns along the axial direction became less and less as the columns further collapsed. Figure 6 shows the images of the fracture and failure pro￾cesses in a specimen with a surface defect under the identical loading conditions as the previous experiment. Figure 7 shows the corresponding stress history in this specimen. The first image was taken before the arrival of the loading pulse. At 15 ms after the arrival of the loading pulse front, when the load in the spec￾imen was very low as marked by position 1 in Fig. 7, an inclined surface crack was already visible as circled in Fig. 6. As the specimens and the testing conditions were nominally the same, this inclined crack was considered to initiate from a pre-existing surface defect on the specimen. The inclined crack grew as the loading was increased, as shown in the next two images. At 45 ms into the loading, when the specimen stress was less than half of its peak level, the inclined crack tip turned into the axial direc￾tion. This crack tip behavior is very similar to the well-docu￾mented wing cracks observed under quasi-static loading conditions.58–60 Under the dynamic loading in this study, be￾fore the wing crack could extend through the specimen, other axial cracks were initiated and propagated in the axial direction, as seen in the following images taken at 5-ms intervals. The specimen became unstable at 65–70 ms after the beginning of loading, when the sample had been extensively cracked, as can be seen in the images. Because of the small surface defect, the ultimate strength of this specimen was much lower than the previous case (3.3 vs 5.3 GPa), which is an indication that small surface defects can drastically alter the specimen response, lead￾ing to a scattered nature of the ceramic failure data. The images presented in Figs. 4 and 6 reveal some of the fundamental aspects associated with the dynamic crack initi￾ation and propagation in brittle materials under uniaxial com￾pression. The cracks initiate from stress-concentrated features in the specimen, where the features are the specimen edges in the case of Fig. 4, and a surface defect and then edges in the case of Fig. 6. Once the cracks are initiated, they eventually propagate roughly along the compressive loading axis. Before a dominant crack can run through the specimen, many other cracks form Fig. 5. Axial compressive stress history in the specimen corresponding to the images in Fig. 4. 0 15 30 40 45 50 55 60 65 70 75 µs Fig. 6. Dynamic fracture and failure process of another SiC–N specimen under uniaxial compression. April 2007 Dynamic Fracture of Ceramics in Armor 1009

1010 Journal of the American Ceramic Society--Chen et al. Vol. 90. No. 4 3500 7 2500 1500 Fig 8. Schematic illustration of an inclined specimen for compression- hear loadi elopment in a ceramic material under uniaxial compression Although the loading provided by stress waves in an SHPB is dynamic, the uniaxial stress state is very simple. The stress states encountered by a ceramic target when subjected to ke projectile npacts can be very complicated. It is therefore important to Time(microsecond) study the dynamic fracture behavior under more complicated stress states at high rates Fig. 7. Axial compressive stress history in the specimen corresponding Before the onset of damage in the the deviation from a uniaxial stress state may be indicated by the maximum shear stress which is half of the difference between the two ex and propagate simultaneously. It takes a higher load to drive treme principal stresses, normalized by the maximum axial com- multiple cracks at the same time, which is one of the mechanisn pressive stress. The normalization expresses the shear stress for higher compressive strength at higher loading rates. As relative to the axial compression, which is a clear indication of crack is formed with a pair of newly formed surfaces with space he deviation from the uniaxial stress state. The normalized (even only a small amount)in between, the specimen volume shear stress may be controlled to decrease or increase. The main must increase to accommodate the cracks. as we have observed approach to decrease the normalized shear stress component is most of the cracks run along the axial direction where the com- to apply lateral confinement on the specimen while the specimen axially compressed. Hydrostatic confinement has been adopt- pressive loading is applied. The increase in specimen volume is ed from quasi-static tri-axial testing techniques. For example mainly through the increases in its radial and circumferentia dimensions, which we also observed in the high-speed images Frew combined a hydrostatic compression chamber with This volume increase, commonly termed as dilatancy or bulki oulse-shaped SHPB to determine the effects of strain rates the dynamic stress-strain behavior and brittle-ductile transition compression. 3 It is noted that, once the cracks initiate the on a lime stone. Other methods of lateral confinement include was also observed in rocks subjected to quasi-static uniaxial The increase in specimen is no longer homogeneous and isotropic, even at the macroscopic scales. As can be examined from the stress histories stress state that needs to be explored. Nie et al. 69 used an in- in Figs. 5 and 7, the axial load in the specimen continues to in- clined specimen in a pulse-shaped SHPB to explore the dynamic visible on the specimen surface. However, the specimen response fracture initiation and development during compression/shear in the directions perpendicular to the axial direction may be very loading on a borosilicate glass specimen. Here, we briefly pres- ent the fracture behavior in brittle materials under a compres different.Take position 7 in Fig. 7 as an example: the image in sion/shear loading and under a multiaxial compression loading initiation of loading. The specimen has been extensively cracked The experiment on a borosilicate glass under compression/ in the axial direction. However it would take about 20% more shear loading was conducted on a modified SHPB. The exper- axial stress before the specimen reached its peak stress. In other Fig. 3. Instead of a right cylindrical specimen, prismatic speci- load even cracked extensively. In the transverse directions, how- men geometry with its axis inclining at an angle from the loading axis was used to introduce additional shear stress in the speci- ever, it is clear that the specimen has disintegrated and can no men(Fig. 8). The loading was provided by a 254-mm long longer bear any load, especially tensile load. Therefore, even Ne8 damage or cracking and the load was controlled to be copper pulse shaper with a dimension of ( 8.7 mm x1.69 mm striker impacting at the incident bar end through an anneale homogeneous and isotropic before the uniaxial compression, when the load is beyond a critical value The loading rate of the resulting ramp pulse in the incident bar the resultant damage is highly anisotropic. Owing to the crack vas4.2×10°MPa/s The specimens were borosilicate glass, provided by U.s neous. It is thus very challenging to properly model the damage Poissons ratio v=0.19, longitudinal wave speed CL=5508 nificant research effort. For example, Wells and Wells et al. m/s, and shear wave speed Cs= 3417 m/s. The cuboid samples presented recent progresses in the 3-D visualization of interior were cut from a glass plate and then ground to specified dimen- ballistic damage in armor ceramics and provided further re- sions. The specimens were 9 mm by 9 mm in cross section and search directions in this area. The direct visualization of surface 2.5 mm in length. For the experiment presented here, the spec- crack initiation and propagation during dynamic axial compres- imen axis was tilted 7 from the compressive loading axis. This sion presented in this paper with quantitative measurements in ngle introduces an additional shear component in the specimen stress, strain, and time of events supplies extensive information luring axial compression, although the tilting also causes the to validate analytical and numerical models for dynamic events. stress distribution on the specimen end faces to be non-uniform, ind numerical tools are needed to determine the failure stres- IV. Dynamic fracture of Ceramics Under multiaxial Stresses between the glass specimen and Hopkinson bar ends. The dynamic compressive loading from the SHPB had a lin The cases presented in the previous section give visual ear ramp shape, which deformed the brittle specimen at a nearly constant average strain rate under a dynamically equilibrated

and propagate simultaneously. It takes a higher load to drive multiple cracks at the same time, which is one of the mechanisms for higher compressive strength at higher loading rates.61 As a crack is formed with a pair of newly formed surfaces with space (even only a small amount) in between, the specimen volume must increase to accommodate the cracks. As we have observed, most of the cracks run along the axial direction where the com￾pressive loading is applied. The increase in specimen volume is mainly through the increases in its radial and circumferential dimensions, which we also observed in the high-speed images. This volume increase, commonly termed as dilatancy or bulking, was also observed in rocks subjected to quasi-static uniaxial compression.62,63 It is noted that, once the cracks initiate, the specimen is no longer homogeneous and isotropic, even at the macroscopic scales. As can be examined from the stress histories in Figs. 5 and 7, the axial load in the specimen continues to in￾crease even significantly after the initiation of the first cracks visible on the specimen surface. However, the specimen response in the directions perpendicular to the axial direction may be very different. Take position 7 in Fig. 7 as an example; the image in Fig. 6 corresponding to this position was taken 60 ms after the initiation of loading. The specimen has been extensively cracked in the axial direction. However, it would take about 20% more axial stress before the specimen reached its peak stress. In other words, the specimen was still able to bear further increased axial load even cracked extensively. In the transverse directions, how￾ever, it is clear that the specimen has disintegrated and can no longer bear any load, especially tensile load. Therefore, even though the specimen was homogeneous and isotropic before the onset of damage or cracking and the load was controlled to be uniaxial compression, when the load is beyond a critical value, the resultant damage is highly anisotropic. Owing to the crack propagation and interaction, the damage is also non-homoge￾neous. It is thus very challenging to properly model the damage status quantitatively. Damage quantification also attracted sig￾nificant research effort. For example, Wells64 and Wells et al. 65 presented recent progresses in the 3-D visualization of interior ballistic damage in armor ceramics and provided further re￾search directions in this area. The direct visualization of surface crack initiation and propagation during dynamic axial compres￾sion presented in this paper with quantitative measurements in stress, strain, and time of events supplies extensive information to validate analytical and numerical models for dynamic events. IV. Dynamic Fracture of Ceramics Under Multiaxial Stresses The cases presented in the previous section give visual and quantitative descriptions on dynamic fracture initiation and de￾velopment in a ceramic material under uniaxial compression. Although the loading provided by stress waves in an SHPB is dynamic, the uniaxial stress state is very simple. The stress states encountered by a ceramic target when subjected to KE projectile impacts can be very complicated. It is therefore important to study the dynamic fracture behavior under more complicated stress states at high rates. Before the onset of damage in the specimen, the deviation from a uniaxial stress state may be indicated by the maximum shear stress, which is half of the difference between the two ex￾treme principal stresses, normalized by the maximum axial com￾pressive stress. The normalization expresses the shear stress relative to the axial compression, which is a clear indication of the deviation from the uniaxial stress state. The normalized shear stress may be controlled to decrease or increase. The main approach to decrease the normalized shear stress component is to apply lateral confinement on the specimen while the specimen is axially compressed. Hydrostatic confinement has been adopt￾ed from quasi-static tri-axial testing techniques. For example, Frew66 combined a hydrostatic compression chamber with a pulse-shaped SHPB to determine the effects of strain rates on the dynamic stress–strain behavior and brittle–ductile transition on a lime stone. Other methods of lateral confinement include electromagnetic67 and mechanical collars.53,68 The increase in the normalized shear is less common but is also an important stress state that needs to be explored. Nie et al. 69 used an in￾clined specimen in a pulse-shaped SHPB to explore the dynamic fracture initiation and development during compression/shear loading on a borosilicate glass specimen. Here, we briefly pres￾ent the fracture behavior in brittle materials under a compres￾sion/shear loading and under a multiaxial compression loading. The experiment on a borosilicate glass under compression/ shear loading was conducted on a modified SHPB. The exper￾imental setup was very similar to the one schematically shown in Fig. 3. Instead of a right cylindrical specimen, prismatic speci￾men geometry with its axis inclining at an angle from the loading axis was used to introduce additional shear stress in the speci￾men (Fig. 8). The loading was provided by a 254-mm long striker impacting at the incident bar end through an annealed copper pulse shaper with a dimension of F8.7 mm
1.69 mm. The loading rate of the resulting ramp pulse in the incident bar was 4.2
106 MPa/s. The specimens were borosilicate glass, provided by U.S. Army Research Laboratory, with a density r 5 2.21 g/cm3 , Poisson’s ratio n 5 0.19, longitudinal wave speed CL 5 5508 m/s, and shear wave speed CS 5 3417 m/s. The cuboid samples were cut from a glass plate and then ground to specified dimen￾sions. The specimens were 9 mm by 9 mm in cross section and 12.5 mm in length. For the experiment presented here, the spec￾imen axis was tilted 71 from the compressive loading axis. This angle introduces an additional shear component in the specimen during axial compression,70 although the tilting also causes the stress distribution on the specimen end faces to be non-uniform, and numerical tools are needed to determine the failure stres￾ses.69 Polished steel cylinders are used as platens and placed in between the glass specimen and Hopkinson bar ends. The dynamic compressive loading from the SHPB had a lin￾ear ramp shape, which deformed the brittle specimen at a nearly constant average strain rate under a dynamically equilibrated Fig. 7. Axial compressive stress history in the specimen corresponding to images in Fig. 6. α Fig. 8. Schematic illustration of an inclined specimen for compression￾shear loading. 1010 Journal of the American Ceramic Society—Chen et al. Vol. 90, No. 4

pril 2007 fracture of Ceramics in Arm Fig9. Dynamic fracture process in a glass specimen under compression/shear. stress state. Figure 9 shows the high-speed images of the dy- base at one of the flat faces of the specimen. The apex of the namic fracture and failure processes in the glass specimen, cone was located at or very close to the center of the specimen whereas Fig. 10 shows the corresponding average axial stress axis. Inside the cone, the crack density was much lower than the history in the specimen. As the loading was increased, the stress- crack density outside the cone. The crack density outside the concentrated corners of the specimen first cracked. The conical region decreased with increasing confining pressure. cracked /damaged areas in a glass specimen can easily be seen in Furthermore, a thin annular region of powdered material, which the optical images as bright regions since the crack surfaces re- was observed on the bottom of the confined specimen where the flect light much better. With increasing axial loading, the con- base of the cone was located, indicates a very high local crack sequent crack propagation was approximately along the density. In fact, the annular region is a cross section of a layer of specimen axis, rather than the compressive loading direction. ceramic rubble formed on the conical surface, which implies that Detailed stress analysis showed that the cracks ran along the there was severe sliding motion across the conical fault in the principal direction with maximum compressive stress and per- dynamic deformation process. The conical surface formed pendicular to the tensile stress in the transverse direction. Owing conically shaped fault. After the fault was formed, further de- to the introduction of the shear stress by tilting the specimen, the formation of the specimen was accommodated by relative slid- maximum compression direction was along the specimen axis, ing of the material across the fault. The resistance of the material ot the loading direction along the SHPB loading axis. Fur- against the sliding became the load-bearing capacity of the spec- ther numerical simulation using a continuum damage mechanics imen after the peak load. As the resistance to the sliding was the glass specimen would propagate along the specimen arte >n much lower than the compressive strength of the material, the model for material description also indicated that the cracks To reduce the shear component during axial compression. radial confinement is commonly used as mentioned earlier. Chen and Ravichandran 44, 45 and Chen2 used mechanical confine- 1000 ment, in the form of shrink-fit metal jackets on the cylindrical 6 surface of the ceramic specimen, to examine the failure mode of a machinable glass ceramic (MACOR) and a hot-pressed alu- minum nitride(AIN). Figure ll shows a specimen section con- taining the axis of a MACOR specimen with a thin metal jacket for minor confinement. The loading axis is vertical in the figure The specimen was loaded past its compressive axial strength in n SHPB experiment. The fractured specimen was retained by 方400 le thin metal jacket. The specimen material has a white color Red dye was used to reveal the crack pattern. Top and bottom 200 views of the specimen (not shown) show that the initially circular cross sections of the specimens have become slightly irregular in shape. This implies that the deformation of the specimen became non-homogeneous after damage was initiated. A common fea- 020406080100120 ure was observed on all the recovered ceramic specimens on Time(us) cross section cutting through the specimen axis: in each of the Fi opressive stress history recovered specimens, there was a conical-shaped region with its corre

stress state. Figure 9 shows the high-speed images of the dy￾namic fracture and failure processes in the glass specimen, whereas Fig. 10 shows the corresponding average axial stress history in the specimen. As the loading was increased, the stress￾concentrated corners of the specimen were first cracked. The cracked/damaged areas in a glass specimen can easily be seen in the optical images as bright regions since the crack surfaces re- flect light much better. With increasing axial loading, the con￾sequent crack propagation was approximately along the specimen axis, rather than the compressive loading direction. Detailed stress analysis showed that the cracks ran along the principal direction with maximum compressive stress and per￾pendicular to the tensile stress in the transverse direction. Owing to the introduction of the shear stress by tilting the specimen, the maximum compression direction was along the specimen axis, not the loading direction along the SHPB loading axis.69 Fur￾ther numerical simulation using a continuum damage mechanics model for material description also indicated that the cracks in the glass specimen would propagate along the specimen axis.71 To reduce the shear component during axial compression, radial confinement is commonly used as mentioned earlier. Chen and Ravichandran44,45 and Chen72 used mechanical confine￾ment, in the form of shrink-fit metal jackets on the cylindrical surface of the ceramic specimen, to examine the failure mode of a machinable glass ceramic (MACOR) and a hot-pressed alu￾minum nitride (AlN). Figure 11 shows a specimen section con￾taining the axis of a MACOR specimen with a thin metal jacket for minor confinement. The loading axis is vertical in the figure. The specimen was loaded past its compressive axial strength in an SHPB experiment. The fractured specimen was retained by the thin metal jacket.44 The specimen material has a white color. Red dye was used to reveal the crack pattern. Top and bottom views of the specimen (not shown) show that the initially circular cross sections of the specimens have become slightly irregular in shape. This implies that the deformation of the specimen became non-homogeneous after damage was initiated. A common fea￾ture was observed on all the recovered ceramic specimens on a cross section cutting through the specimen axis: in each of the recovered specimens, there was a conical-shaped region with its base at one of the flat faces of the specimen. The apex of the cone was located at or very close to the center of the specimen axis. Inside the cone, the crack density was much lower than the crack density outside the cone. The crack density outside the conical region decreased with increasing confining pressure. Furthermore, a thin annular region of powdered material, which was observed on the bottom of the confined specimen where the base of the cone was located, indicates a very high local crack density. In fact, the annular region is a cross section of a layer of ceramic rubble formed on the conical surface, which implies that there was severe sliding motion across the conical fault in the dynamic deformation process. The conical surface formed a conically shaped fault. After the fault was formed, further de￾formation of the specimen was accommodated by relative slid￾ing of the material across the fault. The resistance of the material against the sliding became the load-bearing capacity of the spec￾imen after the peak load. As the resistance to the sliding was much lower than the compressive strength of the material, the 1 23 4 5 6 Fig. 9. Dynamic fracture process in a glass specimen under compression/shear. 0 20 40 60 80 100 120 0 200 400 600 800 1000 Stress (Mpa) Time (us) 1 4 3 5 6 2 Fig. 10. Axial average compressive stress history in the specimen corresponding to images in Fig. 9. April 2007 Dynamic Fracture of Ceramics in Armor 1011

Journal of the American Ceramic Society--Chen et al. Vol. 90. No. 4 the specimen axis to reveal the crack / damage patterns inside the specimen. Various stages of the conical fault formation process were revealed by tion of the crack/fault patterns on the cross sections. The results on both ceramics under light confine ment are summarized by the schematics shown in Fig. 12.44.4At the onset of loading, the local tensile stresses were not sufficient to cause any microcracks to nucleate or propagate, implying that the defect density inside the specimen remains undisturbed by loading. Thus, the stress-strain behavior was essentially lin- ear during the initial stage as shown in Fig. 12(a). After the load was sufficiently large to cause the initial flaws/microcracks to propagate under the action of local tensile stresses, the crack density increased continuously as loading and deformation pro- essed. This would account for the decrease in the slope of the stress-strain curve until the compressive strength was reached as shown in Fig. 12(b). Even though the applied principal stresses of different magnitudes were compressive, local tensile stresses developed near inhomogeneties and crack tips within the spec- imen. It is noted that, due to the high-rate loading, many cracks can propagate inside the specimen simultaneously, rather Fig. 11. Dynamic faulting in a machinable glass ceramic specimen than a critical crack running across the specimen. As the axial stress approached the compressive strength, the crack density in the specimen reached a critical value, where the cracks begin to fault was expected to form before or when the compressive interact at or near stress concentrations In the case of the cy- trength in the specimen was reached. If the shape of the conical lindrical specimens, the highest stress concentrations occur at fault is locally irregular, and/or the cracks outside the cone are the right corners, although in some cases internal defects were not evenly distributed, sliding across the fault will cause the also found to initiate cracks such as those shown in Fig. 6 and specimen to have an irregular shape after loading those found in transparent brittle materials. However, be- The discussion above indicates that the formation of the con- fore the internal-filaw-initiated cracks could propagate through ical fault plays a critical role in determining the compressive the sample, cracks were found to initiate from the corners. The strength of the ceramic specimen. It is of significant interest to cracks initiated at the corners interact to form macroscopic investigate the process of conical fault formation. To do this, the cracks, which then penetrate into the specimen as shown in axial loading should be terminated at us times just before Fig. 12(c). One pair of the cracks will prevail to form a conical and just after the peak stress is reached in the specimen. This fault within the specimen. The onset of fault formation presum- level of load control is not achievable in most testing facilities. ably corresponds to the bifurcation or peak point on the stress- However, using a modified split Hopkinson pressure bar, with strain curve. After the formation of the fault, the stress-strain the single loading feature and the control over the shape, mag- behavior became unstable, and the specimen began to deform at nitude, and duration of the loading pulse, it is feasible to ter- a very high strain rate. The sliding of the fragments across the minate the axial loading at various stages after the peak, making faults became the dominant deformation mechanism in the post it possible to reveal the process of the conical fault formation. failure stage as shown in Fig. 12(d). In the sliding process, grains SHPB experiments were conducted on specimens confined by located on the opposite surfaces of the fault were deformed and/ metal sleeves with a 26-mm long striker. As the failure strain or pulled out from the bulk material. It is expected that a sub- the ceramic specimen was very small, a short striker was neces- stantial amount of energy from impact loading will be dissipated sary to terminate the load near the peak stress. The recovered during this process. This dynamic crack initiation and propaga specimens were then sliced along a cross section that contained tion process has been numerically simulated using an improved G Fig 12. Schematic of the dynamic process of the fault formation under compression

fault was expected to form before or when the compressive strength in the specimen was reached. If the shape of the conical fault is locally irregular, and/or the cracks outside the cone are not evenly distributed, sliding across the fault will cause the specimen to have an irregular shape after loading. The discussion above indicates that the formation of the con￾ical fault plays a critical role in determining the compressive strength of the ceramic specimen. It is of significant interest to investigate the process of conical fault formation. To do this, the axial loading should be terminated at various times just before and just after the peak stress is reached in the specimen. This level of load control is not achievable in most testing facilities. However, using a modified split Hopkinson pressure bar, with the single loading feature and the control over the shape, mag￾nitude, and duration of the loading pulse, it is feasible to ter￾minate the axial loading at various stages after the peak, making it possible to reveal the process of the conical fault formation. SHPB experiments were conducted on specimens confined by metal sleeves with a 26-mm long striker. As the failure strain in the ceramic specimen was very small, a short striker was neces￾sary to terminate the load near the peak stress. The recovered specimens were then sliced along a cross section that contained the specimen axis to reveal the crack/damage patterns inside the specimen. Various stages of the conical fault formation process were revealed by inspection of the crack/fault patterns on the cross sections. The results on both ceramics under light confine￾ment are summarized by the schematics shown in Fig. 12.44,45 At the onset of loading, the local tensile stresses were not sufficient to cause any microcracks to nucleate or propagate, implying that the defect density inside the specimen remains undisturbed by loading. Thus, the stress–strain behavior was essentially lin￾ear during the initial stage as shown in Fig. 12(a). After the load was sufficiently large to cause the initial flaws/microcracks to propagate under the action of local tensile stresses, the crack density increased continuously as loading and deformation pro￾gressed. This would account for the decrease in the slope of the stress–strain curve until the compressive strength was reached as shown in Fig. 12(b). Even though the applied principal stresses of different magnitudes were compressive, local tensile stresses developed near inhomogeneties and crack tips within the spec￾imen.73 It is noted that, due to the high-rate loading, many cracks can propagate inside the specimen simultaneously, rather than a critical crack running across the specimen. As the axial stress approached the compressive strength, the crack density in the specimen reached a critical value, where the cracks begin to interact at or near stress concentrations. In the case of the cy￾lindrical specimens, the highest stress concentrations occur at the right corners, although in some cases internal defects were also found to initiate cracks such as those shown in Fig. 6 and those found in transparent brittle materials.52,69 However, be￾fore the internal-flaw-initiated cracks could propagate through the sample, cracks were found to initiate from the corners. The cracks initiated at the corners interact to form macroscopic cracks, which then penetrate into the specimen as shown in Fig. 12(c). One pair of the cracks will prevail to form a conical fault within the specimen. The onset of fault formation presum￾ably corresponds to the bifurcation or peak point on the stress– strain curve. After the formation of the fault, the stress–strain behavior became unstable, and the specimen began to deform at a very high strain rate. The sliding of the fragments across the faults became the dominant deformation mechanism in the post failure stage as shown in Fig. 12(d). In the sliding process, grains located on the opposite surfaces of the fault were deformed and/ or pulled out from the bulk material. It is expected that a sub￾stantial amount of energy from impact loading will be dissipated during this process. This dynamic crack initiation and propaga￾tion process has been numerically simulated using an improved Fig. 11. Dynamic faulting in a machinable glass ceramic specimen under confinement. Fig. 12. Schematic of the dynamic process of the fault formation under compression. 1012 Journal of the American Ceramic Society—Chen et al. Vol. 90, No. 4

April 2007 Fracture of Ceramics in Arm Johnson-Holmqul lode for the material-constitutive and nts has gained more attention recently to develop a better failure behavior description. noted that understanding of the fracture behavior and the formation of the ical fault existed in specimens loaded both dynamically comminuted zone in the ceramic targ the mechanica quasi-statically avior of the comminuted ceramic is still rarely known Chen and luo 54, 93 Luo et al. 94 and Chen and luo? con- ducted an experimental research into the behavior of the com- As described in the case of thick ceramic penetration, the ce. ental data for developing material models that were needed ramic material just in front of the projectile must be disinte- design and simulations. In this research, to create a comminuted grated into fine pieces such that they can fow around the ceramic and then determine its impact response. a recently de deformed tip of the projectile and be ejected backward. The eloped load/reloading SHPB technique was used to load an disintegrated fine ceramic fragments will initially interlock to intact ceramic specimen with two consecutive loading pulses in a each other under high pressure, leaving minimum amount of single dynamic experiment. The first pulse crushed/pulverized pen space. This state of the ceramic is commonly called com- the intact specimen into a comminuted state after characterizing minuted. The eventual rejection of the pulverized ceramic the intact material. The extent of the impact-induced damage akes the room for the projectile to advance. Furthermore, was controlled by tailoring the profile of the first loading pulse his comminuted/pulverized state of the ceramic material is the After unloading of the first pulse, a second pulse loaded the nly material that is in direct contact with the surface of the specimen. The response of the specimen to the second loading projectile over the entire duration of the penetration process. gave the dynamic constitutive behavior of the ceramic damaged Thus, an accurate and quantitative understanding of formation to a known level at a desired strain rate. 93, 94 Controlled pulse of the comminuted ceramic and the mechanical responses of shaping on both loading pulses ensured that the specimen de- he damaged ceramic under impact is important in order formed at nearly constant strain rates under dynamic stress to model and simulate the penetration process accuratel quilibrium during both of the loading stages Although extensive research efforts have been invested in dete One of the challenges in the experimental design for commin- understanding t ponse of bulk materials,5,40-50,77-84 little is known on the impact response of to those encountered during penetration. If the damaged spec- Even though dislocations imen is prepared before conducting subsequent dynamic SHPB have been identified as the evidence of plastic flow associated testing for properties of the damaged ceramics, it is very difficult to handle or machine the d d ceramic powder has been explored by plate-impact type of ex- disturbing the damage states. It is thus desired to conduct periments, . the formation of the comminuted zone still needs two consecutive SHPB experiments within a rather short time. to be understood. It has been postulated that the comminuted One experiment is to pulverize the intact ceramic and the other zone is formed through a series of dynamic cracking events, se- to characterize the comminuted ceramic quentially, ring cracks, radial cracks, and lateral cracks." La- A schematic of the experimental setup modified from an Salvia presented very clear evidence of the existence of a SHPB is shown in Fig 13. One of the modifications is the two comminuted zone in a titanium diboride ahead of a sphere- im- strikers and the associated pulse shapers to load the intact and pacted zone where the shear component in the stress was the pulverized ceramic at a nearly constant strain rate under d most severe. However, the detailed comminuted zone formation namic equilibrium. Another modification is the test-section plat process under impact loading is very difficult to observe. Indir en and universal joint system to minimize stress concentrations in the specimen. The damage in the specimen is controlled by terials or ceramics indicate that shear-dominant deformation adjusting the first loading pulse. The loading rate on the dam- also occurs underneath the indenter. The deformation mecha- aged ceramic is controlled by the amplitude of the second load isms include slip and twinning within the grains, grain boun ing pulse. The lateral confinement on the specimen is controlled ary sliding.. Static and dynamic indentation tests were foun by the choice of material and wall thickness of the metal jackets around the ceramic specimens. which is consistent with the fact that the crack/damage patterns Figures 14 and 15 show example experimental results that in the specimens recovered from both dynamic and quasi-static reveal the damage effects on the compressive stress-strain re- loadings were similar. Although the indentation type of ex- sponses of SiC-N ceramic In the experiments, the amplitude of Aluminum striker Steel striker Incident bar Specimen assembly Transmission bar for e Springs Copper pulse shaper Strain gauge Axial Strain Transveral strain gauge Steel sleeve metal sleeve Wheatstone Bridge Wheatstone Bridge Wheatstone Bridge Pre-amplifier Pre-amplifier Fig 13. Schematic of the modified split Hopkinson pressure bars setup for loading/unloading experiments

Johnson–Holmquist model for the material-constitutive and failure behavior description.74,75 It was also noted that the con￾ical fault existed in specimens loaded both dynamically and quasi-statically.72 V. Dynamic Behavior of Damaged/Comminuted Ceramics As described in the case of thick ceramic penetration, the ce￾ramic material just in front of the projectile must be disinte￾grated into fine pieces such that they can flow around the deformed tip of the projectile and be ejected backward. The disintegrated fine ceramic fragments will initially interlock to each other under high pressure, leaving minimum amount of open space. This state of the ceramic is commonly called com￾minuted.76 The eventual rejection of the pulverized ceramic makes the room for the projectile to advance. Furthermore, this comminuted/pulverized state of the ceramic material is the only material that is in direct contact with the surface of the projectile over the entire duration of the penetration process. Thus, an accurate and quantitative understanding of formation of the comminuted ceramic and the mechanical responses of the damaged ceramic under impact is important in order to model and simulate the penetration process accurately. Although extensive research efforts have been invested in deter￾mining and understanding the impact response of bulk ceramic materials,35,40–50,77–84 little is known on the impact response of pulverized/damaged ceramics.30,85 Even though dislocations have been identified as the evidence of plastic flow associated with comminuted ceramics,34,84 and the impact response of the ceramic powder has been explored by plate-impact type of ex￾periments,30,36 the formation of the comminuted zone still needs to be understood. It has been postulated that the comminuted zone is formed through a series of dynamic cracking events, se￾quentially, ring cracks, radial cracks, and lateral cracks.26 La￾Salvia86 presented very clear evidence of the existence of a comminuted zone in a titanium diboride ahead of a sphere-im￾pacted zone where the shear component in the stress was the most severe. However, the detailed comminuted zone formation process under impact loading is very difficult to observe. Indir￾ect observations by indentation techniques on transparent ma￾terials or ceramics indicate that shear-dominant deformation also occurs underneath the indenter. The deformation mecha￾nisms include slip and twinning within the grains, grain bound￾ary sliding.87,88 Static and dynamic indentation tests were found to generate a similar damage pattern in the ceramic targets,89,90 which is consistent with the fact that the crack/damage patterns in the specimens recovered from both dynamic and quasi-static loadings were similar.72 Although the indentation type of ex￾periments has gained more attention recently to develop a better understanding of the fracture behavior and the formation of the comminuted zone in the ceramic target,91,92 the mechanical be￾havior of the comminuted ceramic is still rarely known. Chen and Luo,54,93 Luo et al.,94 and Chen and Luo95 con￾ducted an experimental research into the behavior of the com￾minuted ceramics as a function of damage levels, strain rates, and confinement levels to provide physical insights and exper￾imental data for developing material models that were needed in design and simulations. In this research, to create a comminuted ceramic and then determine its impact response, a recently de￾veloped load/reloading SHPB technique was used to load an intact ceramic specimen with two consecutive loading pulses in a single dynamic experiment. The first pulse crushed/pulverized the intact specimen into a comminuted state after characterizing the intact material. The extent of the impact-induced damage was controlled by tailoring the profile of the first loading pulse. After unloading of the first pulse, a second pulse loaded the specimen. The response of the specimen to the second loading gave the dynamic constitutive behavior of the ceramic damaged to a known level at a desired strain rate.93,94 Controlled pulse shaping on both loading pulses ensured that the specimen de￾formed at nearly constant strain rates under dynamic stress equilibrium during both of the loading stages. One of the challenges in the experimental design for commin￾uted ceramic properties is to create comminuted ceramics similar to those encountered during penetration. If the damaged spec￾imen is prepared before conducting subsequent dynamic SHPB testing for properties of the damaged ceramics, it is very difficult to handle or machine the damaged ceramic specimens without disturbing the damage states.68,96 It is thus desired to conduct two consecutive SHPB experiments within a rather short time. One experiment is to pulverize the intact ceramic and the other to characterize the comminuted ceramic. A schematic of the experimental setup modified from an SHPB is shown in Fig. 13. One of the modifications is the two strikers and the associated pulse shapers to load the intact and pulverized ceramic at a nearly constant strain rate under dy￾namic equilibrium. Another modification is the test-section plat￾en and universal joint system to minimize stress concentrations in the specimen. The damage in the specimen is controlled by adjusting the first loading pulse. The loading rate on the dam￾aged ceramic is controlled by the amplitude of the second load￾ing pulse. The lateral confinement on the specimen is controlled by the choice of material and wall thickness of the metal jackets around the ceramic specimens. Figures 14 and 15 show example experimental results that reveal the damage effects on the compressive stress–strain re￾sponses of SiC–N ceramic. In the experiments, the amplitude of Incident bar Specimen assembly Transmission bar Wheatstone Bridge Pre-amplifier Oscilloscope Pre-amplifier Wheatstone Bridge Axial Strain gauge Transveral strain gauge Strain gauge for εi and εr Strain gauge for εt Springs Copper pulse shaper Aluminum striker Steel striker WC platen Ceramics Universal Joint Specimen assembly Steel sleeve metal sleeve Wheatstone Bridge Pre-amplifier Fig. 13. Schematic of the modified split Hopkinson pressure bars setup for loading/unloading experiments. April 2007 Dynamic Fracture of Ceramics in Armor 1013

Journal of the American Ceramic Society--Chen et al. Even though it is well known that dynamic fracture of ceramics lays a critical role in the t response of ceramic target accurate determination of dynamic fracture toughness at high loading rates remains a challenge. There still does not exist a standard experimental procedure to determine the dynamic frac ture toughness as a function of loading rates. Many dynamic echniques have been proposed over the past two decades, which can be approximately categorized into three groups: high rate #100504,326s bending, high rate tension, and dynamic wedging. The theoret 芹110204,358s…1165s cal background and many experimental techniques in dynamic #110202,392s-1175s fracture were reviewed by Ravi-Chandar. Owing to the na #110102,3308…1022s ture of impact loading, if the crack does not propagate during the first pass of the loading stress wave, the loading conditions at the crack tip are very complicated. Bohme and Kalthoff pro- vided a clear example that illustrated the situation. They used a three-point bending configuration with a drop weight impacting Fig 14. Incident bar pulses from experiments of Sic-n damaged to t the loading point, and measured the load histories at the loading point and the two supporting points, the displacement histories between the supports and the specimen, and the crack tip stress-intensity factor history. The results showed that the the first loading pulse was adjusted, while the second pulse re- load history recorded from the loading point neither synchro nained nearly identical. Figure 14 shows the incident-bar pulses ized with the load histories at the supports nor with the crack tip for such a series of dynamic experiments under 104 MPa con- stress-intensity factor history. Their results also showed that the finement pressure. As the damage was very sensitive to the first loading rate at the crack tip was far from constant during the loading pulses, variation in the peak loading does not appear to entire loading process. There is evidence that significant vibra be significant in the figure. However, subtle differences in load- on/ resonance is coupled with the bending deformation of the ing pulse produced significantly different results. Figure I specimen. The detailed information revealed by Bohme and shows the corresponding dynamic compressive stress-strair Kalthoff's experiments indicates that the crack tip stress-inten- curves that display the effects of specimen damage on the me- sity factor does not synchronize with far-field load measure- chanical responses. The results in Fig. 15 show that when the ments for these dynamic bending experiments. Quasi-static ceramic specimen is damaged below a critical level, the specimen equations relating the far-field peak loading to fracture tough- remains nearly elastic under the second loading. When the spec- ness are therefore no longer valid. Essential remedies are neces imen is damaged beyond the critical level, the specimen flows sary to obtain valid d ic fracture toughness under compression of the second loading pulse Compressed by Weerasooriya et al. modified an SHPB facility with a spe- formed only at a strain rate of 166s-I, whereas the specimen and a pulse-shaping technique for dynamic equilibrium and damaged most extensively deformed at a strain rate six times constant loading rate. Dynamic equilibrium is necessary to re- higher. The results indicate that the effects of damage on the late far-field measurements to crack-tip behavior. A constant mechanical response of the ceramic are not gradual, but rather loading rate is convenient for reporting fracture toughness data abrupt. The ceramic specimen may maintain a very high load a function of loading rate. The specimen configurat bearing capacity even when already damaged. The capacity sud selected to be astm standard Chevron notched beams for denly declines when the damage reaches a critical level. The more consistent manufacturing quality of brittle specimens and three stress-stain curves in Fig. 15 for extensively damaged for facilitating comparison with quasi-static results Four-point specimens also indicate that, once beyond a critical damage bending loading was chosen to minimize the data scattering due level, further damage to the ceramic does not significantly affect to slight misalignment. Annealed copper pulse shapers were the load-bearing capacity anymore. Such load-reload experi- used to generate ramp incident pulses and to stop the dynamic ments have also been conducted at higher strain rates, where loading at a desired instant, for example, just before fracture they were called shock-reshock experiments 97-100 The experi- As the experiment is designed in such a way that the specimen ments at lower strain rates using Hopkinson bars provide more deforms under dynamic equilibrium at a nearly constant loading details on loading and deformation histories rate, the AsTM quasi-static standard method can therefore be used to relate the peak loading on the specimen to the fracture 6000 toughness at the crack tip in data reduction. A schematic of the experimental setup is shown in Fig. 16. Using this method, dy namic experiments were conducted to determine the dynamic fracture toughness for a silicon carbide(SiC-N). The results esented in Fig. 17. The dynamic fracture toughness of 8-12 MPa. n #110204,358s-11655 significantly higher than the quasi-static toughness #110202,392s-1175s #110102,330s-->1022 toughness of this ceramic material VI. Research Challenges Dynamic fracture of ceramic materials in armor applications is till a very rich field for scientific exploration. We illustrated two specific armor failure cases in Section Il of this article. There are 0 0000.050.100.150.2 0.30 any other examples where dynamic fracture and failure ar 0.25 critical factors. For Strain ments were conducted in ceramic targets. The penetration Fig 15. Dynamic stress-strain curves of Sic-n damaged to different process was found to be approximately steady state. So the re- sults were described by the classical Tate equation. It would re-

the first loading pulse was adjusted, while the second pulse re￾mained nearly identical. Figure 14 shows the incident-bar pulses for such a series of dynamic experiments under 104 MPa con- finement pressure. As the damage was very sensitive to the first loading pulses, variation in the peak loading does not appear to be significant in the figure. However, subtle differences in load￾ing pulse produced significantly different results. Figure 15 shows the corresponding dynamic compressive stress–strain curves that display the effects of specimen damage on the me￾chanical responses. The results in Fig. 15 show that when the ceramic specimen is damaged below a critical level, the specimen remains nearly elastic under the second loading. When the spec￾imen is damaged beyond the critical level, the specimen flows under compression of the second loading pulse. Compressed by identical second pulses, the specimen damaged the least de￾formed only at a strain rate of 166 s1 , whereas the specimen damaged most extensively deformed at a strain rate six times higher. The results indicate that the effects of damage on the mechanical response of the ceramic are not gradual, but rather abrupt. The ceramic specimen may maintain a very high load￾bearing capacity even when already damaged. The capacity sud￾denly declines when the damage reaches a critical level. The three stress–stain curves in Fig. 15 for extensively damaged specimens also indicate that, once beyond a critical damage level, further damage to the ceramic does not significantly affect the load-bearing capacity anymore. Such load–reload experi￾ments have also been conducted at higher strain rates, where they were called shock–reshock experiments.97–100 The experi￾ments at lower strain rates using Hopkinson bars provide more details on loading and deformation histories. VI. Dynamic Fracture Toughness Even though it is well known that dynamic fracture of ceramics plays a critical role in the impact response of ceramic targets, accurate determination of dynamic fracture toughness at high loading rates remains a challenge. There still does not exist a standard experimental procedure to determine the dynamic frac￾ture toughness as a function of loading rates. Many dynamic techniques have been proposed over the past two decades, which can be approximately categorized into three groups: high rate bending, high rate tension, and dynamic wedging. The theoret￾ical background and many experimental techniques in dynamic fracture were reviewed by Ravi-Chandar.101 Owing to the na￾ture of impact loading, if the crack does not propagate during the first pass of the loading stress wave, the loading conditions at the crack tip are very complicated. Bo¨hme and Kalthoff102 pro￾vided a clear example that illustrated the situation. They used a three-point bending configuration with a drop weight impacting at the loading point, and measured the load histories at the loading point and the two supporting points, the displacement histories between the supports and the specimen, and the crack tip stress-intensity factor history. The results showed that the load history recorded from the loading point neither synchron￾ized with the load histories at the supports nor with the crack tip stress-intensity factor history. Their results also showed that the loading rate at the crack tip was far from constant during the entire loading process. There is evidence that significant vibra￾tion/resonance is coupled with the bending deformation of the specimen. The detailed information revealed by Bo¨hme and Kalthoff’s experiments indicates that the crack tip stress-inten￾sity factor does not synchronize with far-field load measure￾ments for these dynamic bending experiments.97 Quasi-static equations relating the far-field peak loading to fracture tough￾ness are therefore no longer valid. Essential remedies are neces￾sary to obtain valid dynamic fracture toughness. Weerasooriya et al. 103 modified an SHPB facility with a spe￾cially designed gauge section for dynamic fracture experiments and a pulse-shaping technique for dynamic equilibrium and constant loading rate. Dynamic equilibrium is necessary to re￾late far-field measurements to crack-tip behavior. A constant loading rate is convenient for reporting fracture toughness data as a function of loading rate. The specimen configuration was selected to be ASTM standard Chevron notched beams for more consistent manufacturing quality of brittle specimens and for facilitating comparison with quasi-static results. Four-point bending loading was chosen to minimize the data scattering due to slight misalignment. Annealed copper pulse shapers were used to generate ramp incident pulses and to stop the dynamic loading at a desired instant, for example, just before fracture.104 As the experiment is designed in such a way that the specimen deforms under dynamic equilibrium at a nearly constant loading rate, the ASTM quasi-static standard method can therefore be used to relate the peak loading on the specimen to the fracture toughness at the crack tip in data reduction. A schematic of the experimental setup is shown in Fig. 16. Using this method, dy￾namic experiments were conducted to determine the dynamic fracture toughness for a silicon carbide (SiC–N). The results are presented in Fig. 17. The dynamic fracture toughness of 8–12 MPa m1/2 is significantly higher than the quasi-static toughness of 4–6 MPa m1/2, indicating the rate sensitivity on the fracture toughness of this ceramic material. VII. Research Challenges Dynamic fracture of ceramic materials in armor applications is still a very rich field for scientific exploration. We illustrated two specific armor failure cases in Section II of this article. There are many other examples where dynamic fracture and failure are critical factors. For example, high-speed penetration experi￾ments were conducted in ceramic targets.105 The penetration process was found to be approximately steady state. So the re￾sults were described by the classical Tate equation. It would re- 0 200 400 600 800 1000 −50 0 50 100 Voltage (mV) Time (µs) Fig. 14. Incident bar pulses from experiments of SiC–N damaged to different levels under confinement. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 2000 4000 6000 Stress (MPa) Strain Fig. 15. Dynamic stress–strain curves of SiC–N damaged to different levels under confinement. 1014 Journal of the American Ceramic Society—Chen et al. Vol. 90, No. 4