Real-time visualization of impact damage in monolithic silicon carbide and fibrous silicon carbide ceramic composite

International Journal of Impact Engineering 129 (2019) 168–179

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International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng

Real-time visualization of impact damage in monolithic silicon carbide and fibrous silicon carbide ceramic composite

T

⁎

Nesredin Kedira, , Cody D. Kirkb, Guo Zheruib, Nicholas E. Kerschenc, Sun Taod, Kamel Fezzaad, Chen Weinonga,b,c a

Department of Materials Engineering, Purdue University, 701 W Stadium Ave, West Lafayette, IN, USA Department of Aeronautics and Astronautics, Purdue University, 701 W Stadium Ave, West Lafayette, IN, USA c Department of Mechanical Engineering, Purdue University, 701 W Stadium Ave, West Lafayette, IN, USA d Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA b

A R T I C LE I N FO

A B S T R A C T

Keywords: Spherical impact Real-time visualization Synchrotron X-ray source Monolithic ceramics Fibrous ceramic composites Silicon carbide Gas turbine materials

Impact resistance from foreign debris is a critical requirement for brittle ceramic and ceramic composite materials intended for use in the hot-section of gas turbine engines. A design to mitigate against such impact failures necessitates a detailed understanding of the driving failure mechanisms. The present study introduces a unique time-resolved experimental method which advances the latter effort. Specifically, a pulsed synchrotron X-ray source, in phase contrast imaging (PCI) configuration, is used as a medium, to visually characterize the evolution of damage inside the target materials during impact. As a proof of concept, two types of ceramic materials were tested: monolithic silicon carbide and fibrous silicon carbide composite. Impact was performed using a light-gas gun and 1.5 mm diameter spheres of partially stabilized zirconia (PSZ) and silicon nitride (Si3N4). The retrieved dynamic X-ray image sequences provided clear outlines of the damage features. In the case of the monolithic ceramic, the impact by a PSZ projectile initially produced a cone crack and complete failure resulted by extension of a median crack. By contrast, the fibrous composite deformed readily prior to cone crack formation. Nearly identical damage features were observed in the monolith for the Si3N4 projectile, with the exception of the added vertical tensile crack. For this same projectile, the fibrous ceramic showed very limited surface deformation and enhanced cone cracking and kinking of laminates along the crack path. The latter response is attributed to the change in projectile properties. Some of the target materials were recovered, and post-mortem analysis via scanning electron microscopy (SEM) showed correlation with observed X-ray damage profiles. Moreover, simple Hertzian contact was used to estimate damage for the elastic portion of impact. This approach was found to yield a reasonable match with experimental results for the surface displacement near the contact interface.

1. Introduction Advanced ceramic and ceramic matrix composites (CMCs) are enabling materials for the development of efficient gas turbine engines. The touted efficiency stems from higher turbine inlet temperatures that are achieved by replacing traditional metallic superalloy structures, in the hot-section of the engine, with uncooled high-temperature ceramics. Further gains, in engine performance and component life, are also achieved, due respectively to reduction in weight and improvement in creep resistance [1–4]. Over the past four decades, several technology transition efforts have been spurred to realize these benefits in-service. These efforts have yielded both dynamic and stationary prototypes ranging from silicon nitride (Si3N4) turbine nozzle guide vanes and ⁎

blades [1–3,5], to silicon carbide CMC (SiCf/SiC) turbine shrouds [4]. Still, these materials have demonstrated poor reliability under harsh engine operating environments, as they are prone to damage via oxidation [4,5] and impact by debris [1,6]. The former is currently being addressed through material processing efforts [1,4,5]. The issue of impact remains a challenge, as the fundamental attributes of the damage process have yet to be entirely elucidated. The response of brittle targets to impact by small particles has been considerably investigated. Initial studies were focused on glass, which examined the post-impact strength of targets [7,8]. The resulting damage features included ring, cone, radial and median cracks, in addition to localized inelastic fracture. A threshold velocity for rapid decay of strength was established and attributed to unstable propagation of

Corresponding author. E-mail address: [email protected] (N. Kedir).

https://doi.org/10.1016/j.ijimpeng.2019.01.012 Received 21 November 2018; Received in revised form 12 January 2019; Accepted 21 January 2019 Available online 13 March 2019 0734-743X/ © 2019 Published by Elsevier Ltd.

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discontinuous SiC fibers arranged in a cross-ply [0˚/90˚] layup. Details of the processing methodology for the composite have been previously reported [18]. Briefly, fibers are produced by melt spinning a mixture of SiC powder, sintering aids and thermoplastic polymer. The green fibers are arranged into sheets and coated with graphite slurry to create a low modulus carbon coating interface. The coated sheets of fiber are stacked in a cross-ply layup to form a 30 ply [0˚/90˚]15 panel. Transformation from a green state into a solid body is achieved via binder burnout at 800°C and sintering at 1900°C. The resulting microstructure is shown in Fig. 1a and consists of elongated fibers with hexagonal morphology. The composite architecture is designed for enhanced toughness and functionality at high-temperature, making it ideal for gas-turbine applications. Hexoloy SA SiC targets were also used, for comparison with the fibrous SiC composite. The monolithic ceramic is produced in plate form via pressureless sintering of submicron α-SiC powder. As shown in the micrograph of Fig. 1b, the sintered ceramic has a dense (≥98%) microstructure with retained porosity highlighted in dark. It is also noted to have fine grains (<10 μm) [17]. Its unique physical and thermomechanical properties include low density, high hardness, high thermal conductivity, low thermal expansion, and enhanced creep resistance. These properties make it an excellent candidate for wear, ballistic protection, and resistive heating applications. It is also often employed in studies as a model substrate material for gas turbine grade environmental barrier coatings (EBCs) [20]. The microstructure of the PSZ sphere is shown in Fig. 1c. This region is representative of the overall microstructure and highlights a large pore containing unsintered particles. From this observation, it is evidenced that fine PSZ particles compose the projectile and yield a porous microstructure. By contrast, the Si3N4 projectile is found to retain a highly dense microstructure, as shown in Fig. 1d. Additionally, the rareearth oxide boundary phases (bright spots, Fig. 1d) and elongated grains (dark streaks, Fig. 1d) are indicative of a toughened Si3N4 morphology [2,5,11]. The projectile properties in Table 1 also show that the Si3N4 spheres are light-weight, brittle and possess high hardness, in comparison to the PSZ spheres which retain moderate hardness, as well as a higher density and toughness. This difference in properties translates to a variation in the type of contact that is observed between the projectile and target during impact.

the cone or median crack vents [8]. Similar observations have also been made for impact in monolithic ceramics [9–11]. Unlike glass, however, radial and back-side cracks were also shown to activate and drive failure in microstructurally toughened ceramics. Despite their improved toughness, CMCs have also demonstrated a susceptibility to impact in the form of (front- and back- side) spallation and cone cracking [12,13]. However, their capacity to resist penetration is considerably higher for equivalent ranges of velocities. Across different target materials, target hardness, fracture toughness and microstructure have all been identified as critical material properties which control the ensuing fracture behavior. These investigations clearly showed that several fracture mechanisms operate during impact; hence, our understanding of damage is determined by our capability to accurately characterize each mechanism as it develops with time. Postmortem analysis is the most common method used for investigating impact damage in advanced ceramics and composites. The two predominant approaches in use are specimen cross-sectioning [12–14] and interface-bonded specimens [15]. In both cases, damage mechanisms are inferred by microscopic examinations. However, these methods are incapable of fully capturing the transient impact process. For instance, crushing of the surface due to continued impact loading erodes crack initiation markers. Secondary strikes by rebounding projectiles or projectile debris also alter the original damage features. Specific to cross-sectioning, loss of vital information occurs during the cutting and surface preparation stages. Similarly, interfacial bonds can absorb energy through sliding or break down during dynamic loading. Hence, a more appropriate method considers real-time observation. Chaudhri and Walley have successfully applied this approach in the form of high-speed photography for glass targets [16]. The opacity of ceramics and CMCs renders traditional optical methods of observation unfeasible. The objective of the present study is to introduce a novel method which enables in-situ characterization of impact on low density ceramics and CMCs. This method uses a pulsed polychromatic X-ray beam, from a high-energy synchrotron source, to probe the interior of the target material during the impact process and produce photographic records of the transient event. A limited set of monolithic SiC and fibrous SiC composite targets are used to perform a proof of concept study on the characterization method. In addition to the built-in variation in target microstructure, partially stabilized zirconia (PSZ) and Si3N4 projectiles are used to assess the effects of projectile density and hardness. A detailed analysis of the observed impact damage evolution is provided for the four target/projectile combinations with accompanying photographic evidence. A geometric analysis of elastic contact depth is performed and analytical Hertzian contact solutions are applied for comparison. The limited quantitative efforts aim to merely demonstrate the range of capabilities offered by the proposed real-time observation method.

2.2. Impact experiments Impact experiments were conducted using a single stage light-gas gun system integrated with a pulsed synchrotron X-ray source for realtime imaging. The X-ray in-situ visualization capability has previously been applied with a single-loading Kolsky bar device to study the dynamic mechanical behavior several material systems [21,22]. Alternatively, a gas gun enables much higher strain rates (>105 s−1) [23] than those achieved by the bar setup (102–105 s−1) [24]. The current effort utilizes a configuration that is subdivided into three components: gas gun, X-ray source, and triggering / synchronization system. A detailed schematic of the overall impact experimental facility is provided in Fig. 2. A single-stage, smooth bore, light-gas gun equipped with a custom barrel insert was used to perform the impact experiments. The gun barrel retains an internal diameter (I.D.) of 38.1 mm and a length of 1.83 m. High pressure helium gas is used to propel the projectile and nitrogen gas is used to actuate the fast switching spool valve. The fast actuation ensures reliability in timing the event between the fire and trigger signals. An insert containing a secondary barrel with an I.D. of approximately 1.5 mm and a length of 381 mm is used to guide the small projectiles. As shown in the bottom left of Fig. 2, the insert consists of a high-pressure tube (small barrel), a support tube, an endcap with an internal taper, and a flange fabricated from tool steel. The taper on the end-cap directs the gas flow through the orifice of the small barrel; while the flange, bolted to the inside of the chamber, prevents

2. Materials and methods 2.1. Target and projectile materials Experiments were conducted on a fibrous SiC composite and Hexoloy SA SiC (Saint-Gobain Advanced Ceramics, Niagara Falls, NY) materials. Targets for impact testing were obtained by sectioning panels of each material type using a low speed diamond saw. The target dimensions were 10.56 ± 0.17 mm × 4.01 ± 0.14 mm × 2.98 ± 0.23 mm and 14.84 ± 0.27 mm × 2.95 ± 0.12 mm × 1.6 ± 0.01 mm for the fibrous composite and Hexoloy ceramic respectively. Silicon nitride (CoorsTek, Golden, CO) and partially stabilized zirconia (MSE Supplies, Tucson, AZ) spheres with a diameter of 1.5 mm were used as projectile materials. The general microstructure of the targets and projectiles, and their corresponding material properties are respectively provided in Fig. 1 and Table 1. The fibrous composite has a unique architecture which consists of 169

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Fig. 1. Micrographs of the targets (top) and projectiles (bottom) retrieved using a scanning electron microscope (SEM) in back-scatter mode.

Advanced Photon Source (APS), beamline 32-ID-B, at US Argonne National Laboratory (ANL). The present study uses polychromatic Xrays in phase contrast Imaging (PCI) configuration. In comparison to attenuation based X-ray imaging, PCI utilizes the phase shift of transmitted X-rays. This shift results from the difference in thickness and refractive index between specimen features. Interference fringes from the phase shift enable enhanced visualization of edges / boundaries such as cracks in brittle materials. A detailed description of the operating methodology for PCI imaging has previously been presented [22] and will be reiterated here briefly. In standard operating mode, 24 electron bunches with a temporal spacing of 153 ns and duration of 100 ps orbit the circular synchrotron storage ring near relativistic speeds. The electron bunches are allowed to exit the ring along tangential corridors (beamlines) and enter experimental stations (or X-ray hutches). An insertion device (undulator or wiggler) imposes a periodic magnetic field of opposite polarity on the electrons causing them to oscillate with a narrow frequency band along its path. The accompanying deceleration results in energy losses which facilitate emissions of coherent X-rays of highbrilliance. In the current study, a U18 undulator with a period of 18 mm, length of 2.4 m and period of 133 ns was used at a gap of

displacement of the insert. In this arrangement, the spherical projectile is loaded into the small barrel from the chamber-side using a steel wire ramrod. As shown in the bottom right of Fig. 2, four linear motion shafts, 12.7 mm in diameter, are threaded to the tool steel flange and used to support the sample holder. Prior to installing the sample, four steel spacers with an I.D. of 12.83 mm and length of 25.4 mm are inserted to provide a reasonable standoff dance between the barrel-end and the sample holder. This separation distance aligns the impact surface of the specimen to the window of the chamber. The 25.4 mm thick steel sample holder retains a 3 mm by 1.5 mm vertical slot for positioning the sample and a 6 mm by 6 mm horizontal slot for passage of the incident X-ray beam. The latter yields a partially supported configuration (6 mm deep slot vs. a 1.5 mm deep channel for the specimen). Hence, a 6 mm by 4.5 mm aluminum insert placed into this horizontal slot served as a full support backing for the specimens. Once the sample holder is positioned, plastic spacers and wing nuts are used to secure the assembly. In the current work, all tests were performed under standard conditions with projectile velocities in the range of 200–260 m/s, a full support target configuration and a projectile vector normal on the surface plane of the target. The synchrotron X-ray imaging capability was provided by the

Table 1 Properties of the target and projectiles materials at standard temperature and pressure. Material

Target

Projectile

a b c d e f g

Hexoloy SiCa,b Fibrous SiC compositec,d PSZ (5.2% Y2O3)e Si3N4 (5 N)f

Elastic modulus, E (GPa)

Density, ρ (g/ cm3)

Longitudinal Wave Speed, CL (km/s)g

Poison's ratio, ν

Vickers hardness, H (GPa)

Fracture toughness, KIC (MPa m )

410 324

3.10 3.12

11.50 10.20

0.14 0.30

25.2 ± 0.8 1.72 ± 0.44

2.50 ± 0.10 10.70 ± 0.40

200 320

6.10 3.20

5.73 10.00

0.30 0.26

12.00 15.50

9.00 6.00

Modulus, density, and Poisons ratio – from Saint-Gobin Ceramics Hexoloy® SA sillicon carbide technical data sheet. Vickers hardness and fracture toughness – from reference [17]. Modulus, density, Vickers hardness, and fracture toughness – from reference [18]. Poisons ratio – assumed to be a unidirectional CMC fiber tow from reference [19]. All properties obtained from supplier data sheet (MSE Supplies LLC). All properties obtained from supplier data sheet (Coors Tek, Inc). Calculated directly assuming a 1-D wave and no lateral deformation, CL = E / ρ . 170

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Fig. 2. Schematics of the light gas-gun facility integrated with high-energy synchrotron Xray's for in-situ studies of impact in opaque materials. A side-view of the gas-gun with barrel and chamber cross-section as well as an outline of the control systems (Top). A sideview of the barrel insert cross-section and front views of the sample holder, and the chamber flange containing the break wire (Bottom Left). A top-view of the barrel insert and X-ray visualization setup during experiments (Bottom Right).

2.3. Post-impact analysis

11 mm. The resulting X-ray emission retained a pulse width of 33 ps and harmonic energy of ∼ 25 KeV. Prior to interacting with the sample, the beam was shaped by an adjustable slit into a rectangular spot with dimensions of ∼ 2500 × 1600 μm2. Photons transmitted through the sample were projected onto a 100 μm thick single crystal Lu3Al5O12: Ce scintillator (decay time: 70 ns, Crytur Ltd, Turnov, Czech Republic). The scintillator was used to convert the X-rays to visible light. The visible light was reflected off a 45˚ mirror where it was magnified by a 5x objective lens and tube lens before being captured by a high-speed camera (Shimadzu Hyper Vision HPV-X2, Kyoto, Japan). The approximate spatial resolution of the imaging setup was 6.4 µm/pixel. A total of 256 frames (400 × 250 px2) were captured with a frame rate and exposure time of 2 MHz and 200 ns, respectively. A multifaceted triggering system was used to capture the impact event. The experiment was initiated by a ‘fire’ signal from a control box to a delay generator (DG 535, Stanford Research Systems, Sunnyvale, CA). The delayed signal was subsequently relayed to a water cooled copper block “slow” X-ray shutter system, causing it to open starting from a fully closed state. The slow shutter fully opened within ∼53 ms and remained open for ∼33 ms before closing. Opening of the slow shutter also generated a secondary trigger signal which was sent to a separate DG. Again, a delayed trigger was sent out by the second DG, but this time to the “fast” X-ray shutter. Actuation of the fast shutter required 3 ms, with 1 ms in a fully opened state. Hence, a total of 1 ms capture window was made accessible by the latter triggering approach. A break-wire system functioning via a 5 V power supply was also used to independently trigger the recording process and time the closing of the fast shutter in the high-speed camera. In the present study, the wire was adhered to the flange of the barrel insert (see Fig. 2 bottom left). An oscilloscope (Tektronix MDO3014, Tektronix Inc, Beaverton, OR) was used to record the trigger signal generated by an open circuit in the break wire as it is ruptured by the projectile. This event also prompted an output signal from the oscilloscope to trigger the high-speed camera. The time between ‘fire’ and wire break (or function time) was also recorded by the oscilloscope. For the current study it was determined to be 72 ± 2 ms. This timing was critical in selecting appropriate DG settings for successful synchronization of the gas gun and imaging systems.

Subsequent to impact loading, recoverable debris of the failed samples were used to perform postmortem analysis. This was accomplished with the aid of a SEM (FEI Nova Nano 200, FEI Technologies Inc., Hillsboro, Oregon). Further, the open-source image analysis software, Fiji (ImageJ), was used to enhance the details of the captured high-speed X-ray image sequences, as well as to extract qualitative and quantitative data on the impact response. The qualitative information was used to highlight the observed damage mechanisms during impact. Further, the retrieved quantitative data on impact damage depth was compared against estimations from elastic Hertzian contact formulations. 3. Results and discussion 3.1. In-situ observations In this proof of concept study, a total of six experiments were performed. The experimental results revealed unique failure modes for the fibrous ceramic composite and monolithic ceramic, as well as for impact by Si3N4 and PSZ spheres. Details of these observations are provided in the proceeding sections 3.1.1. PSZ sphere – fibrous SiC composite Two successful experiments were performed for the case of a PSZ impactor and fibrous SiC composite target. Despite the similarity in the impact conditions, the two samples showed distinct impact behaviors. The X-ray image sequences for the first sample, impacted at ∼226 m/s, are shown in Fig. 3. Clear outlines of the intact composite laminate structure and PSZ sphere are observed in the first X-ray image (frame). Contact between the two bodies occurs between the first and second frame. The elapsed time after contact was estimated based on the projectile speed to be 0.25 µs (frame 2). With the exception of a slight change in intensity at the contact region, little damage is observed immediately after contact until t = 2.5 µs (not shown). Between t = 2.5 μs–2.75 μs, the projectile deforms the target without incurring any visible damage. Deformation of the target is characterized in the Xray images as a decrease in transmission intensity within the damage 171

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Fig. 3. X-ray image sequences depicting impact of 1.5 mm PSZ sphere on a fibrous SiC composite. Impact velocity ∼ 226 m/s and high-speed imagining at 2 M fps. Contact is followed by deformation (frame 3) and then rebound (frame 4–6). Target plumage, frame 4 arrow, and lateral cracking ensue during the rebound event.

a faint cone crack is observed at the bottom end of the contact region. A cone crack semi-apex angle of ∼27.43˚ is estimated for this sample using the features in frame 3. Continued loading results in visible deformation of the target and formation of minor laminate kinks along the pre-existing cone crack path (frame 4). After reaching a damage depth of ∼190 μm (frame 4), the projectile begins to rebound from the compacted surface with a measured velocity of ∼47 m/s. Concurrently, a median crack vent nucleates just below the compacted region and extends to the back surface of the sample (frame 5). In the final stages of damage (frame 6), near surface laminates are delaminated from the target and the remaining material is observed to fragment into two pieces along the median crack. It is also at this time that the projectile shows signs of cracking damage. In comparison to the first sample, the second sample showed three additional damage features: formation of a Hertzian cone crack, intralaminar kinks, and median crack. The formation of Hertzian crack as a precursor to large deformation suggests an initial response that is primarily elastic. Similar observations have been reported during spherical indentation and impact of brittle monolithic ceramics and glass [9–13,16,26]. Typically, such cone cracks occur due to a decaying radial tensile stress which develops a maximum in magnitude near the edge of contact [26]. The cone crack is followed by subsurface deformation and formation of structural kinks in the individual laminates. Akin to the impact response of thermal barrier coatings (TBCs) with columnar microstructures [6,27], it's reasonable to infer that the kink band in the composite forms to relieve the intralaminar shear stresses generated by the radial displacement of material during deformation. Further, the laminate kinks run along the preceding cone crack. This is likely owed to the weak crack boundary which enables sliding of the laminates. It is thus possible to infer that the lack of a cone crack in the first sample prevented the formation of laminate kinks despite the large level of deformation. Unlike the first sample, a median crack vent is observed, in addition to lateral cracking and material removal from

zone. The contact boundary is highlighted by a dotted line around the sphere. A maximum deformation depth of 264.41 μm was determined for this experiment using the third frame in Fig. 3. Projectile rebound occurred for t > 2.75 μs. The measured rebound velocity was ∼50 m/ s. During the rebound event, a confined plume of fine particles was ejected from the target (frame 4, Fig. 3). Damage accumulations in the form of cracking and material removal are also observed as the projectile starts to separate from the target surface. Throughout the impact event, the projectile is observed to remain intact with no discernable deformation or cracking. Compaction, cracking and material removal were the three primary damage modes observed for the first composite sample. The mode of compaction (or crushing) occurred during the initial stages, where ∼ 95% of the kinetic energy input was dissipated as work to drive the projectile into the target. Deformation of the target was expected, given the drastic difference in hardness between the sample and projectile (see Table 1). Fig. 4 shows magnified X-ray images from Fig. 3, at t = 5.75 μs and t = 6.25 μs. These images show faint cracks that traverse the entire length of the sample and around the deformation zone. The crack patterns near the surface resemble lateral crack vents which occur during indentation of brittle materials by a sharp object [25]. Such cracks are likely formed by the residual tensile stress that is generated from relaxation of the compacted zone during the unloading process (i.e., projectile rebound). Tensile release of the material around the lateral cracks also results in the observed material removal. Note that a median crack vent that typically runs ahead of the lateral cracks in brittle elastic materials was not evident from these images. Given the latter anomaly, additional samples would be needed to confirm the observed response. The X-ray image sequences depicting impact of the second composite sample at a velocity of ∼240 m/s are shown in Fig. 5. Again, the frame preceding contact shows the outlines of the target and projectile. The second frame depicts the moment of contact. After 0.5 μs (frame 3),

Fig. 4. Magnified sections of frames four and five from Fig. 3: Impact on fibrous SiC composite by 1.5 mm PSZ sphere at 226 m/s. The doted orange lines lie just below the lateral cracks which run across the thickness of the sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 5. X-ray image sequences depicting impact of 1.5 mm PSZ sphere on a fibrous SiC composite. Impact velocity ∼ 240 m/s and high-speed imagining at 2 M fps. Contact is followed by cone cracking (frame 3). Laminate kinks (green arrow), deformation zone (white arrow) and median crack vent (red arrow) are observed with continued loading per frame 4. Upon rebound, the median crack extends (white arrow, frame 5) to the back of the target. In the final stages (frame 6), near surface laminates are spalled, the samples separates along the median crack and cracks appear in the PSZ sphere (white arrow, frame6). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

this crack system develops due to a radial tensile stress at the edge of contact. Continued loading then induces a median crack and additional crack systems appear upon unloading. Similar impact behaviors have been reported for SiC ceramics by Shin and Maekawa [28] and Takahashi et al. [29]. These studies also used steel, SiC and Si3N4 projectiles at velocities ranging between 100 - 400 m/s. The findings suggest that impact crater size increases with projectile hardness and median crack formation occurs at higher impact velocities (>155 m/s). This compliments the current findings where a visible crater is not observed from impact by the compliant PSZ sphere and a median crack is observed due to the higher impact velocities. Further, the measured cone crack angle (∼ 47.6˚) in this work is in agreement with reported values which range between 47˚– 50˚ [28–30]. The value of this angle is also found to be independent of projectile material (or projectile properties). A drastic difference is observed in the impact response of the monolithic SiC and fibrous SiC composite materials for a PSZ projectile. Impact of the monolith resulted in target fracture and projectile deformation. In comparison, the fibrous composite experienced both deformation and cracking with no damage to the projectile. One explanation to this response is the relative difference in hardness between the three material systems. The brittle elastic SiC monolith retains the highest hardness and impact by a more compliant PSZ projectile will primarily yield fracture. Deformation of the PSZ projectile also results in continued loading of the ceramic producing multiple cracks in addition to extending the initial cone crack. In contrast, the fibrous composite behaves in an inelastic manner since it retains a lower hardness value relative to the PSZ sphere. As a result, it experiences both deformation and fracture during impact. Effects of projectile hardness on impact response have been highlighted previously in the

accumulated residual tensile stress. 3.1.2. PSZ sphere – hexoloy SiC monolith Homogeneous Hexoloy SiC samples were also examined under similar impact conditions, using a PSZ projectile. Two successful experiments were achieved for this case and both showed nearly equivalent failure modes. Fig. 6 depicts the sequence of dynamic X-ray images for one of the samples impacted at ∼ 211 m/s. The first frame shows the two bodies prior to contact. The sphere contacts the target surface before the next frame and the elapsed time is estimated to be 0.25 µs (frame 2). Initial damage is observed after 0.5 µs (frame not shown), in the form of a faint partially developed cone crack segment. A more distinct outline of the cone crack is shown in frame 3. Concurrent deformation and localized fracture of the projectile also result in the ejection of debris. The second segment of the cone crack is observed in frame 4, with continued loading by the projectile. An average semiapex angle of ∼ 47.6˚ is measured directly from the latter frame. As time progresses, a median crack vent initiates and propagates towards the back surface of the target. The PSZ projectile also experiences extensive deformation prior to complete fragmentation in frame 6. As the projectile breaks apart at the contact interface, the cone and median crack vents open-up rapidly resulting in complete fracture of the target. It's important to note that the cone crack initiation points were difficult to locate. This was overcome by the crack mouth openings in later stages which were used to trace back to the crack origins. The monolithic SiC target was observed to behave as a brittle elastic material when impacted by the PSZ projectile. Immediately after contact, the projectile deformed elastically until a critical contact area was attained for the initiation of a Hertzian cone crack. As noted previously,

Fig. 6. X-ray image sequences depicting impact of 1.5 mm PSZ sphere on a Hexoloy SiC ceramic. Impact velocity ∼ 211 m/s and highspeed imagining at 2 M fps. Contact is followed by a cone crack segment (green arrow) and ejection of projectile material (white arrow) per frame 3. The second segment of the cone crack appears (white arrow) in frame 4 and it is followed by a median crack (white arrow) in frame 5. In frame 6, the projectile fragments completely causing the cone and median cracks to open-up. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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visual of the internal structure for the two bodies is depicted in the first frame. The next frame captures the projectile which appears to be already in contact with the target surface. The elapsed time after contact is estimated to be 0.34 µs. At this time, a segment of the fully formed cone crack is observed in the target, in addition to several diametral cracks in the projectile. The semi-apex angle of the cone crack is determined to be ∼ 42.5˚. Continued loading primarily results in damage to the projectile in the form of diametral crack bifurcations (frame 3). As the projectile disintegrates into debris (frames 4), a ‘vertical’ crack perpendicular to the impact direction and a median crack vent are developed in the target. Separation of the projectile debris from the target surface causes the cone crack, median crack and vertical crack to open-up at their respective nucleation points (frames 5 and 6). In the final stages, the three crack vents intersect leading to complete fracture of the target. A generally consistent response, with some variation, was observed in the SiC substrate when subject to impact by either a PSZ or Si3N4 projectile. Under both impact conditions, a cone crack is initially formed followed by a delayed median crack. Further, the measured cone crack angles in both cases are similar, and within the range of reported values by previous investigations [28–30]. Still, a variation in the failure of the projectile was observed. The compliant PSZ sphere deforms considerably while the brittle Si3N4 sphere fractures immediately upon contact. This variation in fracture behavior affects the duration of loading on the target. The latter is observed as a delay in cone crack formation for impact by a PSZ sphere and a delay in median crack formation for impact by a Si3N4 sphere. Additionally, the high impact energy and longer loading duration for the PSZ projectile results in the formation of multiple crack vents after the formation of the median crack. Conversely, the shorter duration of loading by the Si3N4 projectile only produces median and vertical secondary cracks. The vertical crack is established as a tensile crack which results from interaction of the release pressure wave, generated by the fracture of the projectile, and the initial pressure wave of impact reflected off from the back surface of the target. The latter is confirmed by considering the impedance mismatch at the specimen/aluminum backing interface. For aluminum, CL ≈ 5050 m/s (with E =68.9 GPa and ρ= 2.7 g/cm3) and the resulting impedance (Z = ρCL ) is ∼ 2.5 times lower than that for monolithic SiC (see Table 1). This mismatch yields in an inversion of the incident compressive stress wave (from impact) to a tensile reflected wave at the interface. Differences in impact behavior were also observed between the SiC monolith and fibrous SiC composite targets. A juxtaposition of these materials under impact by the PSZ projectile was provided in section (ii). In regards to impact by the Si3N4 projectile, a reversed order in crack initiation is observed with a median crack occurring fist in the fibrous ceramic and a cone crack in the SiC monolith. Note, however, that this behavior only applies to the current experiment and additional experiments are need for confirmation. During contact, the SiC monolith experiences significant cracking and the Si3N4 sphere pulverizes into small fragments. This is not the case for the more compliant fibrous SiC target, where only a few cracks form prior to ejection of near surface laminates. Also, the projectile fragments into larger pieces as opposed to minute debris for the latter case. This behavior results in a longer contact time for the fibrous material which prevents the vertical tensile crack generated by a release pressure wave in the monolith. Finally, the architecture of the fibrous ceramic enables absorption of impact induced material displacement by kinking of the laminates. This is not the case in the homogeneous ceramic where impact energy is primarily dissipated by crack initiation and growth.

form of an elastic-plastic (E-P) parameter1 [31]. In this approach, a purely elastic response is generalized as having an E-P parameter of <<1 and a combined elastic – inelastic response is characterized by an E-P parameter of >1. Per the properties listed in Table 1, impact of the SiC monolith by PSZ appeals to the elastic condition with a minimum EP value of `0.5, while impact of the fibrous SiC composite by the same projectile renders an inelastic condition with a maximum E-P value of ∼7. 3.1.3. Si3N4 sphere – fibrous SiC composite In addition to PSZ, Si3N4 spheres were used to investigate the effects of projectile properties on the impact response of the fibrous SiC composite material. Only one sample was successfully loaded at a velocity of ∼259 m/s and the resulting dynamic X-ray image sequences are shown in Fig. 7. It is noted that the slightly higher impact velocity results from the reduction in inertia of the low density Si3N4 projectile. The initial image shows the internal structure of the target and sphere before contact. In this case, the target is observed to retain defects including cracks. These defects are likely induced during sample sectioning. Hence, they are contained on the cut faces and do not influence the initial contact behavior. Frame 2 shows the response immediately after contact (t = 0.25 µs) where a diametral and a median crack are observed to form in the projectile and target respectively. This is followed by a well-developed segment of a cone crack in the target near the perimeter of contact and surrounded by laminate kinks (frame 3). A value of ∼28.8˚ is obtained for the cone crack semi-apex angle from frame 3. Continued loading enhances the laminate kinks and extends the median crack in the target to the back surface (frame 4). After significant cracking, fragments of the projectile begin to rebound at an average velocity of ∼ 30 m/s and near surface laminates begin to delaminate from the bulk (frame 5). In the final stages (frame 6), the cone and median crack vents open-up and the delaminated segments are ejected from the bulk. Still, the remaining target material is contained through fiber tow bridging across the median crack interface. A slight difference in the impact response of the fibrous SiC composite was observed for the Si3N4 projectile, as compared to the PSZ projectile. First, impact by the Si3N4 sphere is found to result in a median crack immediately after contact while cone cracking occurs for a PSZ sphere. Since only one sample was successfully loaded for this proof of concept study, this result must be considered anomalous. Typically, a median crack forms independently or after the formation of a cone crack. Several factors could have affected the observed result including processing defects (cracks, porosity, etc.) and defects from sample prepration. It is also possible that early onset of fracture by the projectile could have played a role. Regardless, additional experiments are required to provide a more robust hypothesis. Other critical differences include the limited deformation and pronounced laminate kinks for impact by the Si3N4 projectile, in contrast to the PSZ projectile. This observation suggests that material displacement, for Si3N4 projectiles, is primarily elastic and accommodated by interlaminar shear instead of material crushing / compaction. It is also important to note that a much shorter loading duration is observed for Si3N4, which tended to fail via brittle fracture. Overall, the two projectile types were found to yield similar cone crack semi-apex angel values (∼ 28˚) for similar impact conditions. This finding reiterates the characteristic of the cone crack angle to be independent of the projectile properties. 3.1.4. Si3N4 sphere – hexoloy SiC monolith The impact behavior of the SiC monolithic ceramic was also assessed using a Si3N4 projectile. Similar to the fibrous SiC composite, only one sample was successfully impacted at a velocity of ∼256 m/s. The resulting dynamic X-ray image sequences are provided in Fig. 8. A

3.2. Impact damage morphology As was shown in the X-ray PCI images, nearly all of the projectiles and targets were fragmented into several pieces during the impact experiments. The fragmented pieces of the projectile were too small to be

1

Elastic-plastic parameter is defined as the ratio of projectile hardness to target hardness (i.e., Hp/Ht) [31]. 174

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Fig. 7. X-ray image sequences depicting impact of 1.5 mm Si3N4 sphere on a fibrous SiC composite. Impact velocity ∼ 259 m/s and high-speed imagining at 2 M fps. In frame 2, contact is followed by a diametral crack (white arrow) in the projectile and a median crack (green arrow) in the target. A segment of the cone crack (green arrow) appears in frame 3, coupled with crack branching in the projectile (white arrows). Visible laminate kinks (doted green boundary) are observed around the cone crack in frame 4. Additional cracks (white arrow) and pronounced kinks are observed in frame 5. In the last stages, frame 6, near surface laminates are spalled, as the cone and median crack open-up concurrent with rebound of the fragmented projectile. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 8. X-ray image sequences depicting impact of 1.5 mm Si3N4 sphere on a Hexoloy SiC ceramic. Impact velocity ∼ 256 m/s and highspeed imagining at 2 M fps. Contact (frame 2) is followed by a cone crack segment (green arrow) in the target and diametral cracks (white arrow) in the projectile. The diametral cracks bifurcate in frame 3. Projectile pulverization, median crack (white arrow) and a vertical tensile crack (green arrow) are formed in frame 4. The median, cone and vertical cracks open-up and cause complete fracture (frames 5 and 6). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 9. SEM micrographs of the impact morphology developed in fibrous SiC composite and monolithic SiC targets with a 1.5 mm diameter PSZ projectile at velocities ranging from 210–250 m/s. (a) shows the distinct damage layers on the surface of the fibrous SiC composites. (b1) shows the 3D cone geometry formed by a cone crack and (b2) shows a close-up of the contact surface for (b1).

a smaller circular region devoid of material and a perimeter highlighted by fiber fractures. Based on observations of dynamic X-ray images, the fiber damage occurred during impact loading and the void was created by delamination and breakaway of near surface material during unloading. The latter damage patterns are not observed in the top most surface, #4. Instead, a significant amount of material loss is shown with brittle fracture as the source. This is confirmed by the presence of welldefined and straight radial cracks and smooth fracture surfaces. The top surface thus behaves as a brittle coating which absorbs impact damage via radial and circumferential cracking. Note that the radial cracks were not observed in the 2D dynamic X-ray images since they are contained on the top surface and are unresolved at lower magnifications (5X). Electron micrographs of the recovered SiC monolith segment are shown in Fig. 9b(1 and 2). In the 2D dynamic X-ray visualizations, the Hertzain cracks were identified by the propagation of two angled

captured for post-mortem analysis. However, some remnants of the target impacted by PSZ spheres were retrieved and analyzed using SEM in secondary electron mode. The resulting SEM micrographs are shown in Fig. 9(a and b). A discussion of the observed damage features is offered next, starting with the fibrous composite target. The overall failure surface for a portion of the impacted fibrous SiC composite is shown in Fig. 9a. Note that the depth of damage extends to several plies. Overall, four distinct damage surfaces are identifiable. These surfaces are assigned numerical labels in ascending order, based on height. The two surfaces at the bottom (#1 and #2 in Fig. 9a) appear to retain little to no fiber damage at their center. However, they also encompass a semi-circular segment whose trace within the remainder of the composite is highlighted by circumferential cracking. This feature is most likely associated with the Hertzian cone crack observed in the dynamic X-ray images of Fig. 5. The next immediate surface, #3, retains 175

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cracks. In actuality, the cracks are three dimensional and encompass a conical volume, however, the path of the X-rays results in a 2D projection of the 3D fracture phenomena. Fig. 9b1 shows the resulting conical dome formed by impact from a PSZ sphere. Similar observations have been made for thinner Si3N4 disks impacted by steel projectiles [32]. Fig. 9b2 shows a close-up view of the dome surface. A key microstructural feature to note is the uninterrupted fracture morphology which suggests unstable crack growth after crack nucleation. Further, the region of contact shows signs of impression and/or friction induced damage. Past investigations have shown the damage depth to be slightly over ∼0.5 μm for a harder Si3N4 projectile at equivalent impact velocities [28]. Thus, significant inelastic damage from impact by a more compliant PSZ projectile is not expected and requires further investigation.

uz =

u ′z =

(1)

where R is the radius of the sphere and E* is the combined effective modulus. The latter material dependent parameter is explicitly expressed as: −1

(2)

In Eq. (2), the variables E′ and E are the moduli of the sphere and halfspace, and the variables ν′ and ν are the corresponding Poison's ratios. The applied normal load from Eq. (1) is distributed across the contact region and yields a maximum value of contact pressure at the center which is given by:

pM =

3 P 2 πa2

(1 − ν 2) E * a2 ⎡ r2 2 − 2 ⎤ r /a ≤ 1 ⎥ 2E′ R⎢ a ⎣ ⎦

(5)

The Hertzian approach was only applied to three of the four contact conditions which showed a discernable elastic regime: PSZ sphereHexoloy SiC, Si3N4 sphere-Hexoloy SiC and Si3N4 Sphere-Fibrous SiC. I all three cases, the sphere experienced the highest level of displacement. Measurements of the ‘relative’ displacement depth were thus performed on the sphere per the schematic in Fig. 10. The resulting depth profiles and their respective estimations, using Eq. (5), are shown in Fig. 11(a–c). The first condition considers the PSZ sphere in contact with a monolithic SiC substrate. As shown in Fig. 11a.1 and a.2, a reasonable fit is obtained for u ′z . The estimated Hertzian profiles are slightly larger across the region of contact, with the first (S1) and second (S2) experiments yielding approximate errors of 14% and 12% respectively for r = 0 (i.e., the point of maximum displacement). The error in the estimation primarily arises from the quasi-static nature of Hertzian contact which requires very limited energy loss. Additional factors include the low quantity of test specimens and the assumption of an idealized spherical displacement. Furthermore, the granular microstructure of the PSZ sphere (see Fig. 1c) has the potential to induce interparticle friction between grains during dynamic compaction [36] and hence restrict the level of deformation during impact. By contrast, a good fit is obtained between estimated and experimental displacement contours for impact of a Si3N4 sphere on a monolithic SiC substrate (Fig. 11b). The favorable result is attributed to the reduced compliance of Si3N4 which influenced a purely elastic–elastic contact condition with no observable compaction. A similar result is obtained for contact between Si3N4 sphere and fibrous SiC composite as shown in Fig. 11c. In the latter, the attendant experiment was off-center vertically on the viewing plane and as a result only half of the deformation profile is displayed. Overall, the maximum elastic displacements were similar ranging between 40.8 μm and 52.7 μm with the low end corresponding to the compliant PSZ sphere. The latter analysis on impact induced elastic displacement showed the soundness of the quasi-static Hertzian formulations. This realization enables us to determine other quantities of interest such as the contact load, which in the current case is considered as an impact force. A straight forward approach to accomplish this entails solving Eq. (1) for P. Additionally, we are able to estimate the maximum radial tensile stress acting at the edge of contact [34]. Analytically, this stress is related directly to the impact force by the following expression:

An all-encompassing analysis of impact damage in the SiC monolith and Fibrous SiC composite is quantitatively complex and beyond the scope of this study. Instead, a narrow application is offered where only the elastic damage regime is considered. This is performed using simple Hertzian contact formulations. Hertzian contact is quasi-static in nature and in order to be applicable for dynamic loading conditions the duration of contact must be assumed to be sufficient for the passage of several elastic pressure waves within the target and projectile [7,8,16,33].The latter holds in the current study due to an order of magnitude difference between the estimated longitudinal wave velocities (see Table 1) and the impact velocities. In the succeeding analysis, the Hertzian solution for displacement of the contact boundary is used to estimate the damage profile for a given impact condition. The resulting deformation contours are compared with direct measurements from the in-situ impact experiments. The latter is performed using a single camera frame near the transition point from elastic to inelastic damage. This selection allows for assessment of the maximum elastic response. Following the comparison, additional calculations are performed to estimate the impact (i.e., contact) force, maximum radial stress and loading duration. In Hertzian contact, the radius of the circular impression area resulting from the application of a normal load P on a rigid sphere in contact with an elastic half space is given by:

(1 − ν 2) (1 − ν ′2) ⎤ E* = ⎡ + ⎢ E E′ ⎥ ⎣ ⎦

(4)

where r is the location of a point in the contact region measured relative to the central axis of contact. A corresponding equation for the sphere, uz′, is formulated by replacing E and ν in Eq. (4) with their respective counterparts for the sphere. We now have the required equations to construct a purely geometric relation between u ′z and a. This is accomplished by first solving for P in Eq. (1) then substituting into Eq. (3) and finally plugging the result into Eq. (4) to eliminate pM.

3.3. Assessment of damage

3 PR 1/3 ⎞ a=⎛ ⎝ 4 E* ⎠

(1 − ν 2) πa ⎡ r2 pM 2 − 2 ⎤ r /a ≤ 1 ⎢ E 4 ⎣ a ⎥ ⎦

σm =

1 − 2ν′ P r /a = 1 2πa2

(6)

It was noted in a previous section that σm promotes the initiation of critical Hertzian cone cracks, which is indeed observed throughout the in-situ impact experiments. Lastly, the elastic loading duration can be approximated using the momentum based formulation of Timoshenko and Goodier [37],

(3) 2

This pressure distribution was shown by Hertz to induce surface displacement of the half-space (or sphere) [34] and the resulting axisymmetric displacement profile has the form,

5ρ′π ⎞2/5 R t = α⎛ 1/5 ⎝ 4E * ⎠ V ⎜

⎟

(7)

where α is a constant, ρ′ is the projectile density, and V is the impact velocity. Table 2 provides a summary of the impact force, radial stress and

2

The resulting pressure distribution was proposed by Johnson [35] and has the form, p (r ) = pm 1 − (r / a)2 . 176

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advanced. For impact force, we consider the contact diameter as the governing parameter and compare with available databases. In the case of impact by a PSZ sphere on a monolithic SiC substrate, a similar contact diameter has been reported previously by Akimune et al. under analogous impact conditions [31]. Hence, the determined impact force is deemed reasonable. Previous assessments of impact on monolithic SiC by Si3N4 sphere have also reported contact diameters which encompass the value obtained in the current work [28]. The case of impact by a Si3N4 sphere on a fibrous SiC composite has yet to be studied, and thus the impact force must be substantiated by additional testing. In terms of radial stress, we compare with numerical simulations. One of the applicable works is by Takahashi et al. [29], where an explicit

Fig. 10. Schematic view of the contact geometry showing the elastic deformation of the PSZ or Si3N4 sphere of radius R during impact. The doted circular boundary represents the expected range of projectile displacement uz′ for a given contact radius a.

Fig. 11. Measured elastic displacment profiles and their respective Hertzian estimations for impact of monollitic SiC target by a PSZ projectile (a.1 and a.2) and Si3N4 projectile (b), as well as impact of a fibrous SiC composite by a Si3N4 projectile (c). In the decription, f-SiC coresponds to fibrous SiC composite. Table 2 Summary of results for impact force, radial stress and loading duration under three distinct impact conditions. Impact condition

Impact force, P [kN]

Max. radial stress, σr [GPa]

Loading duration, tp [μs]

Loading duration, te [μs]b

PSZ - SiC Si3N4 - SiC Si3N4 - f-SiCa

3.31 4.86 6.71

3.36 6.24 6.61

1.45 0.98 1.02

1.08 0.62 0.69

a b

f-SiC: fibrous SiC composite. Loading duration is considered as the time elapsed between contact and rebound.

finite element model (FEM) was used to predict a maximum stress of ∼4 GPa for impact of a SiC monolith by a Si3N4 sphere at 100 m/s. Given that the radial stress increases with impact velocity (hence

elastic loading duration determined for the three impact conditions. Given the limited number of tests, a detailed comparison between the results is inconsequential. Instead, an individualized assessment is 177

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measurements. Still, the method of estimation is ideal and very limited in scope. More comprehensive approaches are needed for reliable determinations of impact damage.

impact force), a revision of the FEM is expected to render a stress near the values determined in the current work. A similar analysis for the PSZ sphere is not available; however, the lower impact force suggests a lower resultant radial stress. Finally, we consider the loading duration which is compared in Table 2 against values extracted from the in-situ experiments. Clearly, the prediction (tp) overestimates the observed loading duration (te). Chaudhri and Walley has shown similar overestimations by Eq. (7), for impact velocities >120 m/s [16]. The momentum based estimations then provide an upper bound for the elastic loading duration and by adjusting the constant α we can reduce the error. In the current work, α = 2 yields correlating values for t as compared with the typical value of 2.94 used to determine tp in Table 2. Despite the reasonable approximations, it is important to emphasize that the Hertzain formulations are limited in applicability for impact induced damage. More comprehensive estimations must include dynamic and frictional effects as well as inelastic deformations. The empirical side can also be bolstered by use of particle velocity tracking methods such as photon doper velocimetry (PDV) or high pressure stress/strain gauges. Coupled with the dynamic X-ray in-situ visualization method, a robust model can be developed to enable prediction of damage evolution during impact. This has practical consequences for the gas-turbine materials community where impact damage of ceramic hot-section components is a key obstacle for technology transition into service. A damage prediction capability would surely enable engineering of impact resistant ceramic material systems and/or protective coatings.

This initial study was successful in assessing the range of possibility for impact induced failure characterization via dynamic X-ray visualization method. Still, additional experiments are needed to gain a firm grasp of the observed impact responses for the specific material systems considered, especially the engine-grade inhomogeneous fibrous SiC composite. Acknowledgments The authors gratefully acknowledge support from the Office of Naval Research (ONR) through a Research Grant N00014-17-1-2711 (Program Manager: Dr. David Shifler). We also appreciate the generosity of Dr. Sung Choi of the Naval Air Warfare Center (NAVAIR) for generously donating material for this research. We are grateful for the aid of Alex Deriy, for technical and safety support in our experiments at beamline 32-IDB, APS. This research used resources of the Advanced Photon Source, a User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract no. DE-AC02-06CH11357. N. Kedir acknowledges the Purdue Doctoral Fellowship program for support. References

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The capability of a high-energy pulsed synchrotron X-ray source for visualizing damage in ceramic and ceramic composite materials during impact was investigated. An emphasis was placed on the ability to obtain time-resolved information of the individual damage mechanisms. Our observations and analysis have led to the following findings: (1) Impact damage features including deformation and cracking were visibly identified in the retrieved dynamic X-ray image sequences. This allowed for observation of the evolution of various damage mechanisms in real-time during the impact event. (2) Impact of the fibrous SiC composite by a PSZ sphere initially yielded inelastic deformation. In one of the two successful experiments, a cone crack and subsequent kinking of the laminates was observed. Unloading of the PSZ projectile resulted in the secondary median and lateral cracks systems which accommodated delamination and breakaway of the near surface laminates. The projectile showed little to no damage during the impact process. (3) Impact of monolithic SiC ceramic by a PSZ sphere resulted in a primary cone crack and a median crack. Extensive deformation resulted in the PSZ sphere and this enabled continued loading and formation of multiple secondary cracks in the target. (4) Impact by a Si3N4 sphere resulted in drastic changes to the failure mode of the fibrous composite and minor changes to the monolithic ceramic. Immediately after contact, the sphere initiated fracture via diametral crack networks. This reduced the level of target deformation and enhanced cone cracking and laminate kink formation in the fibrous composite. Unloading of the sphere fragments led to removal of material along the cone and median crack vents. In the SiC monolith, the primary difference was the activation of a vertical tensile crack from interaction of the release and reflected stress waves. (5) A purely geometric formulation of Hertzian contact was used to estimate the elastic surface displacement profile for a given contact radius. A similar profile, constructed using a selected frame from the dynamic X-ray images, was used for comparison. With the exception of contact between the fibrous composite and PSZ sphere, a reasonable match was determined between the estimations and 178

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