《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_j.1744-7402.2010.02588.x[1]

t.J. Appl Ceram. Technol.,8/2/308-316(2011) DO:10.I116.1744-7402.2010.02588 International Journal o pplied Ceramic TECHNOLOGY ceramic Product D Microstructure and Mechanical Properties of SiC and Carbon Hybrid Fiber Reinforced SiC Matrix Composite Shanhua Liu, Litong Zhang, Xiaowei Yin, Laifei Cheng, and Yongsheng Liu Naidongiy, a m, shanxi 710072, Pepl e composite Materials, Northwestern Polytechnical Silicon carbide(SiC) matrix composite reinforced by both SiC and carbon fibers([SiC-C]/pyrolytic carbon [Py C]/SiC) was fabricated by chemical vapor infiltration for reducing matrix microcracks. Microstructure, mechanical properties, and oxidation resistance of the composite were compared with those of C/PyC/SiC and C/PyCH /SiC composites in which PyC interphase was untreated and heat-treated at 1800.C in argon, respectively. Compared with the C/PyC/SiC C)/PyC/SiC composite shows considerable improvements in Flexural strength, fracture toughness, and oxidation resistance The different mechanical behaviors of the three composites were analyzed based on the He and Hutchinson's model Introduction vanced thermostructural materials for use in the aero- space industry, owing to their low density, excellent Silicon carbide(SiC)matrix composites reinforced thermal-shock resistance, and high mechanical proper with carbon fiber(C/SiC)and silicon carbide fiber(Sic/ ties at high temperatures . 2 Thermal residual stresses SiC)fabricated by chemical vapor infiltration( CVI)(TRS)are always generated in C/SiC composite during process have attracted considerable attentions as ad cooling from processing to room temperature due to an extensive mismatch of the coefficients of thermal This work was financially supported by The Centre for Foreign Talents Introduction and pansionCTEs)between fiber and matrix, which results cademic Exchange for Advanced Materials and Forming Technology Discipline and The in spontaneous cracking of the matrix. Using pyrolytic Research Fund of State Key Laboratory of Solidification Processing( Grant No. 44-QP. carbon(PyC) as an interphase between fiber and matrix 2009), Northwest Polytechnical University, Xi'an, China. can reduce the TRS of the C/SiC composite to some C 2010 The American Ceramic Society extent, which can be named as C/PyC/SiC composite

Microstructure and Mechanical Properties of SiC and Carbon Hybrid Fiber Reinforced SiC Matrix Composite Shanhua Liu, Litong Zhang, Xiaowei Yin,* Laifei Cheng, and Yongsheng Liu National Key Laboratory of Thermostructure Composite Materials, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, People’s Republic of China Silicon carbide (SiC) matrix composite reinforced by both SiC and carbon fibers ([SiC–C]/pyrolytic carbon [PyC]/SiC) was fabricated by chemical vapor infiltration for reducing matrix microcracks. Microstructure, mechanical properties, and oxidation resistance of the composite were compared with those of C/PyC/SiC and C/PyCHT/SiC composites in which PyC interphase was untreated and heat-treated at 18001C in argon, respectively. Compared with the C/PyC/SiC composite, (SiC– C)/PyC/SiC composite shows considerable improvements in flexural strength, fracture toughness, and oxidation resistance. The different mechanical behaviors of the three composites were analyzed based on the He and Hutchinson’s model. Introduction Silicon carbide (SiC) matrix composites reinforced with carbon fiber (C/SiC) and silicon carbide fiber (SiC/ SiC) fabricated by chemical vapor infiltration (CVI) process have attracted considerable attentions as ad￾vanced thermostructural materials for use in the aero￾space industry, owing to their low density, excellent thermal-shock resistance, and high mechanical proper￾ties at high temperatures.1,2 Thermal residual stresses (TRS) are always generated in C/SiC composite during cooling from processing to room temperature due to an extensive mismatch of the coefficients of thermal ex￾pansion (CTEs) between fiber and matrix, which results in spontaneous cracking of the matrix. Using pyrolytic carbon (PyC) as an interphase between fiber and matrix can reduce the TRS of the C/SiC composite to some extent, which can be named as C/PyC/SiC composite. Int. J. Appl. Ceram. Technol., 8 [2] 308–316 (2011) DOI:10.1111/j.1744-7402.2010.02588.x Ceramic Product Development and Commercialization r 2010 The American Ceramic Society This work was financially supported by The Centre for Foreign Talents Introduction and Academic Exchange for Advanced Materials and Forming Technology Discipline and The Research Fund of State Key Laboratory of Solidification Processing (Grant No. 44-QP- 2009), Northwest Polytechnical University, Xi’an, China. *yinxw@nwpu.edu.cn

wwceramics. org/ACT Properties of Sic Matrix Composite However, there still exists a great deal of matrix micro- Experimental Procedure cracks in the C/Py C/SiC composite. The microcracks in SiC matrix are regarded as one of the obstacles to the Preparation Process widespread use of C/SiC an inward diffuse through the matrix microcracks, Two kinds of fibers, Hi-Nicalon SiC fiber from fibers at 700oC, which led to the minimum strength carbon fiber from Japan Toray Tokyo, Japan)consist- retained ratio at the range of room temperature to 1250C. Therefore, it is necessary to reduce the ma- diameter of 14 and 7 um per-filament were used to pre trix microcracks of C/PyC/SiC composite for long-time pare fiber preforms using four-step three-dimensional wide temperature range. techniques by Nanjing Fiberglass Research and Design It is indicated that the trs can be controlled Institute, People's Republic of China. The major prop through the appropriate choice of the fiber-matrix erties of the raw materials are summarized in Table IIn pair. The TRS in C/PyC/SiC composite has been cal order to understand the effect of hybrid fibers on the ulated and measured in the previous work. compare mechanical properties of the composite, two types of with the C/PyC/SiC composite, the SiC/Py C/Sic preforms were braided. The first type contained both cause the Sic fiber has nearly the same CTE as the togethe arbon ibers, in which two iber tows were put composite yielded a negligible tRS (close to zero value) fiber bundles for braiding, and the sec- SiC matrix. The properties of fiber, interphase, ond one only contained carbon fiber. The volume frac- will occur or not when the compos under the preforms. PyC interphase and SiC matrix were depos- ited by CVI process. PyC interphase was deposited on Based on the above considerations, SiC matrix the surfaces of fibers by decomposition of C3H at composite reinforced by both SiC and carbon hybrid 900C for 144h at reduced pressure of 5kPa in fibers([SiC-CJ/Py C/SiC)using the PyC as the inter- CVI reactor, obtaining a thickness of 150 nm.One of phase may have a lower residual thermal stress and less the preforms only containing carbon fiber with the Pyc matrix cracks than C/PyC/SiC composite. Moreover, interphase was heat treated at 1800.C in argon for 1h heat treatment of the PyC interphase in C/Py C/SiC to increase the crystalline degree of PyC interphase. Sic composite may improve the crystalline degree of inter matrix was prepared at 1000C at a reduced pressure of phase, and the composite named as C/Pyc/SiC may using also have lower TRS and less matrix cracks than C/PyC/ with a molar ratio of 10 between H2 and MTS, which SiC composite. The major objectives of this work are to was carried by bubbling hydrogen in gas phase and have a knowledge on the microstructure and mechanical argon as the dilute gas to slow down the chemical re- action rate during deposition. For each CVI cycle, the oxidation behaviors at 700%C in air, which were com- deposition time was 80h. After CVI SiC for 6 cycles, pared with those of C/Py C/SiC and C/PyCHT/SiC the as-received composites were machined and polished ino3mm×4mm×40 mm samples. Consequently Table L. Properties of Raw Materials.11-16 Tensile Fracture Diameter Poisson's Modulus CTE strength energy onstituent ratio(v) (GPa) (X 10/K (GPa) T ( /m) Hi-Nicalon SiC fiber 2.74 14 4.6 20 T300 carbon fiber 0.3 1.12 8.6 0.23 Sic matrix 3.21 350

However, there still exists a great deal of matrix micro￾cracks in the C/PyC/SiC composite. The microcracks in SiC matrix are regarded as one of the obstacles to the widespread use of C/SiC composite. Oxidizing species can inward diffuse through the matrix microcracks, leading to the oxidation of PyC interphase and carbon fibers at 7001C, which led to the minimum strength retained ratio at the range of room temperature to 12501C.3–5 Therefore, it is necessary to reduce the ma￾trix microcracks of C/PyC/SiC composite for long-time use in a wide temperature range. It is indicated that the TRS can be controlled through the appropriate choice of the fiber–matrix pair.6 The TRS in C/PyC/SiC composite has been cal￾culated and measured in the previous work.7 Compared with the C/PyC/SiC composite, the SiC/PyC/SiC composite yielded a negligible TRS (close to zero value) because the SiC fiber has nearly the same CTE as the SiC matrix.8 The properties of fiber, interphase, and matrix decide whether the debonding of interphase will occur or not when the composite is under the loading. Based on the above considerations, SiC matrix composite reinforced by both SiC and carbon hybrid fibers ([SiC–C]/PyC/SiC) using the PyC as the inter￾phase may have a lower residual thermal stress and less matrix cracks than C/PyC/SiC composite. Moreover, heat treatment of the PyC interphase in C/PyC/SiC composite may improve the crystalline degree of inter￾phase, and the composite named as C/PyCHT/SiC may also have lower TRS and less matrix cracks than C/PyC/ SiC composite. The major objectives of this work are to have a knowledge on the microstructure and mechanical properties of the (SiC–C)/PyC/SiC composite and its oxidation behaviors at 7001C in air, which were com￾pared with those of C/PyC/SiC and C/PyCHT/SiC composites. Experimental Procedure Preparation Process Two kinds of fibers, Hi-Nicalon SiC fiber from Japan Nippon Carbon (Takauchi, Japan) and T300 carbon fiber from Japan Toray (Tokyo, Japan) consist￾ing of bundles of 500 and 1000 filaments with the diameter of 14 and 7 mm per-filament were used to pre￾pare fiber preforms using four-step three-dimensional techniques by Nanjing Fiberglass Research and Design Institute, People’s Republic of China. The major prop￾erties of the raw materials are summarized in Table I. In order to understand the effect of hybrid fibers on the mechanical properties of the composite, two types of preforms were braided. The first type contained both SiC and carbon fibers, in which two fiber tows were put together as one fiber bundles for braiding, and the sec￾ond one only contained carbon fiber. The volume frac￾tion of the fibers was approximately 40 vol% in both preforms. PyC interphase and SiC matrix were depos￾ited by CVI process. PyC interphase was deposited on the surfaces of fibers by decomposition of C3H6 at 9001C for 144 h at reduced pressure of 5 kPa in a CVI reactor, obtaining a thickness of 150 nm. One of the preforms only containing carbon fiber with the PyC interphase was heat treated at 18001C in argon for 1 h to increase the crystalline degree of PyC interphase. SiC matrix was prepared at 10001C at a reduced pressure of 5 kPa by using methyltrichlorosilane (MTS, CH3SiCl3) with a molar ratio of 10 between H2 and MTS, which was carried by bubbling hydrogen in gas phase and argon as the dilute gas to slow down the chemical re￾action rate during deposition. For each CVI cycle, the deposition time was 80 h. After CVI SiC for 6 cycles, the as-received composites were machined and polished into 3 mm 4 mm 40 mm samples. Consequently, Table I. Properties of Raw Materials7,11–16 Constituent Density (g/cm3 ) Diameter (lm) Poisson’s ratio (n) Modulus (GPa) CTE ( 106 /K) Tensile strength (GPa) Fracture energy C (J/m2 ) Hi-Nicalon SiC fiber 2.74 14 0.2 270 4.6 2.8 20 T300 carbon fiber 1.76 7 0.3 230 1.12 3.1 8.6 PyC 1.76 — 0.23 35 5.57 — 2–6 PyCHT 1.76 — 0.23 35 5.57 — 0–2 SiC matrix 3.21 — 0.21 350 4.6 — 6 www.ceramics.org/ACT Properties of SiC Matrix Composite 309

310 International Journal of Applied Ceramic Technolog-Liut, et al. Vol.8,No.2,2011 another two cycles of CVI SiC were essential for cov- followed by ion beam milling. The samples were exam- ering the porosity and the ends of fibers to form the final ined used field emission transmission electron micro- composites. Three kinds of composites were prepared. scope(Tecnai F30, FEI Company, Hillsboro, OR)with One was SiC matrix com posite reinforced with both an operated voltage of 300 kV SiC and carbon fibers([SiC-C]/Py C/SiC), which was named as hybrid composite and denoted as sample A C/PyC/SiC and C/PyC / SiC composites, denoted p The other two kinds of composites were named as Oxidation Tests Oxidation tests were conducted in static air in a samples B and C, respectively. The superscript HT tube furnace at 700C for 10h, and the weight changes means the PyC interphase was heat treated at 1800c of the samples were obtained by analytical balance(AG before the deposition of SiC matrix. It should be noted 204, Mettler Toledo, Schwerzenbach, Switzerland)and that PyC interphase in the hybrid composite was not be recorded as a function of oxidation time.Cumulative heat treated, because the strength of Hi-Nicalon SiC fi- weight change and the strength retained ratio of the ber deteriorate tes at temperatures exceeding 1400.C. samples were calculated according to the weight and flexural strength of the samples before and after oxida- tion tests, respectively Flexural Strength Tests and Microstructur Observation Results and Discussion Density and open porosity of the composites were btained by the archimedes method. The fexural Microstructure strength of the composites before and after oxidation was measured by the three-point Flexural method, and As shown in Table II, sample a had a higher den- the fracture toughness was determined by the single- sity than the other two kinds of composites. This result ge-notched-beam method using a fexural testing ma- was due to the significantly higher density of SiC fiber hine (SANS CMT 404, Sans Materials Testing, (2.74g/cm) than that of the carbon fiber(1.76g/cm) Shenzhen, China). The exural modulus was calculated Moreover, the diameter of SiC fber was larger than that using the slope of the load-displacement curves of the of carbon fiber, which made the spaces among the SiC composites according to the ASTM C1341-00 stan- fibers and SiC tows larger than those among carbon dard. The density, porosity, and Flexural strength of fibers and carbon tows, and hence it was easier for SiC the three kinds of the composites were measured after matrix to be deposited on the surfaces of SiC fibers and the sixth, seventh, and eighth cycles of CVI SiC matrix, SiC tows in the inner of the preform. As a result, the respectively. The microstructure of the composites and average value of open porosity the fracture surface morphologies of the tested samples lower than those of the other two kinds of composites, were analyzed by scanning electron microscopy (S- as shown in Table II 2700, Hitachi, Tokyo, Japan). For transmission elec The polished morphologies of SiC matrix in three on microscope (TEM) observation, the composites kinds of composites are shown in Fig. 1. There were were cut into samples with a thickness of 1000 um, no matrix microcracks found in sample A, as shown in and then mechanically thinned to a thickness of 30 um Figs. la and b. However, both samples B(Fig. Ic)and Table Il. Properties of the Three Kinds of Composites Flexural Fr acture Flexural ens porosity strengt modulus MPa) (MPam (GPa) ratio(%) A 6 530(16 175(2) 96(4.9) B 117(16) 33(0.5) 6(6.3) 18.6(1) 64(3.4 andard deviations are given in parentheses

another two cycles of CVI SiC were essential for cov￾ering the porosity and the ends of fibers to form the final composites. Three kinds of composites were prepared. One was SiC matrix composite reinforced with both SiC and carbon fibers ([SiC–C]/PyC/SiC), which was named as hybrid composite and denoted as sample A. The other two kinds of composites were named as C/PyC/SiC and C/PyCHT/SiC composites, denoted as samples B and C, respectively. The superscript HT means the PyC interphase was heat treated at 18001C before the deposition of SiC matrix. It should be noted that PyC interphase in the hybrid composite was not be heat treated, because the strength of Hi-Nicalon SiC fi- ber deteriorates at temperatures exceeding 14001C.9,10 Flexural Strength Tests and Microstructural Observation Density and open porosity of the composites were obtained by the Archimedes method. The flexural strength of the composites before and after oxidation was measured by the three-point flexural method, and the fracture toughness was determined by the single￾edge-notched-beam method using a flexural testing ma￾chine (SANS CMT 4304, Sans Materials Testing, Shenzhen, China). The flexural modulus was calculated using the slope of the load-displacement curves of the composites according to the ASTM C1341-00 stan￾dard.17 The density, porosity, and flexural strength of the three kinds of the composites were measured after the sixth, seventh, and eighth cycles of CVI SiC matrix, respectively. The microstructure of the composites and the fracture surface morphologies of the tested samples were analyzed by scanning electron microscopy (S- 2700, Hitachi, Tokyo, Japan). For transmission elec￾tron microscope (TEM) observation, the composites were cut into samples with a thickness of 1000 mm, and then mechanically thinned to a thickness of 30 mm followed by ion beam milling. The samples were exam￾ined used field emission transmission electron micro￾scope (Tecnai F30, FEI Company, Hillsboro, OR) with an operated voltage of 300 kV. Oxidation Tests Oxidation tests were conducted in static air in a tube furnace at 7001C for 10 h, and the weight changes of the samples were obtained by analytical balance (AG 204, Mettler Toledo, Schwerzenbach, Switzerland) and recorded as a function of oxidation time. Cumulative weight change and the strength retained ratio of the samples were calculated according to the weight and flexural strength of the samples before and after oxida￾tion tests, respectively. Results and Discussion Microstructure As shown in Table II, sample A had a higher den￾sity than the other two kinds of composites. This result was due to the significantly higher density of SiC fiber (2.74 g/cm3 ) than that of the carbon fiber (1.76 g/cm3 ). Moreover, the diameter of SiC fiber was larger than that of carbon fiber, which made the spaces among the SiC fibers and SiC tows larger than those among carbon fibers and carbon tows, and hence it was easier for SiC matrix to be deposited on the surfaces of SiC fibers and SiC tows in the inner of the preform. As a result, the average value of open porosity of hybrid composites was lower than those of the other two kinds of composites, as shown in Table II. The polished morphologies of SiC matrix in three kinds of composites are shown in Fig. 1. There were no matrix microcracks found in sample A, as shown in Figs. 1a and b. However, both samples B (Fig. 1c) and Table II. Properties of the Three Kinds of Composites Samples Density (g/cm3 ) Open porosity (%) Flexural strength (MPa) Fracture toughness (MPa m1/2) Flexural modulus (GPa) Strength retained ratio (%) A 2.56 6 530 (16) 17.5 (2) 96 (4.9) 99 B 2.23 10 117 (16) 3.3 (0.5) 66 (6.3) 67 C 2.25 9 505 (37) 18.6 (1) 64 (3.4) 78 Standard deviations are given in parentheses. 310 International Journal of Applied Ceramic Technology—Liu, et al. Vol. 8, No. 2, 2011

wwceramics. org/ACT Properties of Sic Matrix Composite 311 carbon fiber Sic fibe 150k13.0mm×500sE(M carbon fiber carbon fiber microcrack Fig. I. Scanning electron microscopic(SEM) images of polished cross-section morphologies of SiC matrix in three kinds of composites: (a) SiC matrix around carbon fiber bundle in sample A; (b) SiC matrix around SiC fiber bundle in sample A;(e) SiC matrix in sample B; and(d) SiC matrix in sample C. C(Fig. ld)had matrix microcracks. The TRS in the sample a decreased significantly. Compared with sam- ple B, the opening width of matrix microcracks in sam- ▲ Sample C le c decreased which indicated that the trs in sample C was lower than that in sample B. Mechanical Properties composites as a function of open porosity. As shown in Fig. 2, for samples A and C, when the porosity of the composites decreased from 15% and 16%to 6% and 9% he fexural strength increased from 385 and 359 MPa to 530 and 505 MPa. However, the fexural strength of sam ple b was nearly independent of the decrease of the Fig. 2. The flexural strength as a fuanction of the porosity for the porosity. As shown in Table Il, samples A, B, and C three kinds of composites

C (Fig. 1d) had matrix microcracks. The TRS in the sample A decreased significantly. Compared with sam￾ple B, the opening width of matrix microcracks in sam￾ple C decreased, which indicated that the TRS in sample C was lower than that in sample B. Mechanical Properties Figure 2 compares the flexural strength of the three composites as a function of open porosity. As shown in Fig. 2, for samples A and C, when the porosity of the composites decreased from 15% and 16% to 6% and 9%, the flexural strength increased from 385 and 359MPa to 530 and 505MPa. However, the flexural strength of sam￾ple B was nearly independent of the decrease of the porosity. As shown in Table II, samples A, B, and C SiC matrix a b c d carbon fiber SiC fiber SiC matrix microcrack carbon fiber microcrack carbon fiber Fig. 1. Scanning electron microscopic (SEM) images of polished cross-section morphologies of SiC matrix in three kinds of composites: (a) SiC matrix around carbon fiber bundle in sample A; (b) SiC matrix around SiC fiber bundle in sample A; (c) SiC matrix in sample B; and (d) SiC matrix in sample C. Fig. 2. The flexural strength as a function of the porosity for the three kinds of composites. www.ceramics.org/ACT Properties of SiC Matrix Composite 311

312 International Journal of Applied Ceramic Technolog-Liut, et al. Vol.8,No.2,2011 Sample B carbon fiber 0.00,2040608101 150kv128mn Fig 3. The load-displacement curves of the three kinds of chieved a flexural strength of 530, 117, and 504 MPa, and a fracture toughness of 17.5, 3.3, and 18.6 Mpa" respectively. The elastic modulus of SiC fiber(270 GPa) was higher than that of the carbon fiber(230 GPa)and the matrix porosity of sample a was smaller than those of samples B and C. As a result, the fexural modulus of sample A was 96GPa, much higher than those of sample arbon fiber B(66 GPa)and sample C Typical failure curves of three kinds of composites are shown in Fig 3. The Flexural curve of sample A was similar to that of SiC/Py C/SiC composite& The flexural 15owV 13.6mm x200 SE/(M) curve of sample A showed an initially linear elastic be- havior and then a nonlinear beh avioN th there existed debonding and sliding at the fiber/matrix nterphase zone, which led to the pullout of fibers However, there was no nonlinear stage in the fexural curve of sample B, which exhibited a brittle fracture behavior like monolithic ceramics, indicating that no debonding and sliding occurred at the interphase zone Flexural load-displacement curve of sample C showed early linear behavior with the increasing load, and then a noncatastrophic failure behavior was observed after the maximum loa nd 4 shows the fexural fracture surface mor phologies of three kinds of composites In sample A, SiC 15.0 fibers showed apparent pullout in the fiber bundle, while carbon fibers showed no pullout, as shown in Fig. 4a. These fracture features indicated that PyC works flexural fracture surface morphologies of three kinds of composites. (a) sample A showing SiC fibers were pulled out and no carbon on SiC fibers and not on carbon fibers. As a result, the fibers were pulled out;:(b)sample B showing no carbon fibers debonding and sliding of Py C interphase mainly occurred were pulled out; and(c)sample C showing carbon fibers were between SiC fiber and SiC matrix In sample B, the frac- pulled out. ture morphology of carbon fiber bundles was fat

achieved a flexural strength of 530, 117, and 504 MPa, and a fracture toughness of 17.5, 3.3, and 18.6Mpa m1/2, respectively. The elastic modulus of SiC fiber (270 GPa) was higher than that of the carbon fiber (230 GPa) and the matrix porosity of sample A was smaller than those of samples B and C. As a result, the flexural modulus of sample A was 96 GPa, much higher than those of sample B (66 GPa) and sample C (64 GPa). Typical failure curves of three kinds of composites are shown in Fig. 3. The flexural curve of sample A was similar to that of SiC/PyC/SiC composite.8 The flexural curve of sample A showed an initially linear elastic be￾havior and then a nonlinear behavior, indicating that there existed debonding and sliding at the fiber/matrix interphase zone, which led to the pullout of fibers. However, there was no nonlinear stage in the flexural curve of sample B, which exhibited a brittle fracture behavior like monolithic ceramics, indicating that no debonding and sliding occurred at the interphase zone. Flexural load-displacement curve of sample C showed nearly linear behavior with the increasing load, and then a noncatastrophic failure behavior was observed after the maximum load. Figure 4 shows the flexural fracture surface mor￾phologies of three kinds of composites. In sample A, SiC fibers showed apparent pullout in the fiber bundle, while carbon fibers showed no pullout, as shown in Fig. 4a. These fracture features indicated that PyC works on SiC fibers and not on carbon fibers. As a result, the debonding and sliding of PyC interphase mainly occurred between SiC fiber and SiC matrix. In sample B, the frac￾ture morphology of carbon fiber bundles was flat, as Fig. 3. The load–displacement curves of the three kinds of composites. a b c SiC fiber carbon fiber carbon fiber carbon fiber Fig. 4. Scanning electron microscopic (SEM) images of the flexural fracture surface morphologies of three kinds of composites: (a) sample A showing SiC fibers were pulled out and no carbon fibers were pulled out; (b) sample B showing no carbon fibers were pulled out; and (c) sample C showing carbon fibers were pulled out. 312 International Journal of Applied Ceramic Technology—Liu, et al. Vol. 8, No. 2, 2011

wwceramics. org/ACT Properties of Sic Matrix Composite 313 shown in Fig. 4b, which was consistent with its brittle E=E2(1-2) fracture behavior(Fig. 3). The low flexural strengt (117 MPa)and fracture toughness(3.3 MPam")are at- where subscripts f and m refer to the fber and the matrix, tributed to the brittle fracture behavior of sample B. The E" is the plane strain modulus for the phase x, Eand v are fect of heat treatment of PyC interphase on the fracture espective behavior of composites was studied. The fracture surface Phases, and longitudinal coordinate r is the ratio of frac- morphology of sample C showed that carbon fibers were ture energy of interphase to the adjacent fiber apparently pulled out, as shown in Fig. 4c, which implies Whether the interphase can be debonded or not that the heat-treated PyC interpahse can work on carbon depends on the characteristics(modulus and fracture fibers. As a result, the Flexural strength of sample C was energy) of the matrix, fiber, and interphase. The re- increased from 117 to 504 MPa compared with that of quired data for determining whether the interphase sample B, and the fracture toughness was increased from debonding or not in the present work are listed in Ta- 3.3 to 18.6MPam/2 ble I. The likely results were calculated and marked in In the present work, the difference in the failure Fig. 5. For SiC/PyC/SiC composite, asic/SiCm is behaviors and the fracture modes of the composites are -0.13, and the corresponding TPyc/sic is in the range attributed to the different properties of fibers and different of 0. 1-0.3, and hence a line segment Li is marked in interfacial bonding between fiber and matrix, in which Fig. 5. For CAPyC/SiC composite, ac /Sicm is-0. 23, PyC interphase plays a key role in the mechanical behav- and the corresponding I Pyc/c is in the range of 0.23- ior of a ceramic matrix composite. For two dissimilar 0.70, and hence a line segment L2 is marked in Fig. 5 elastic materials, the crack propagation behavior at th It can be found that most part of segment Li is in interphase has been studied by He and Hutchinson, the debonding region(below the cross-hatched curve) and a debonding diagram has been obtained, as shown in and Fig 6a shows the debonding of Py C interphase on Fig 5, which contains two regions showing the interphase SiC fiber in the sample A. It means that the PyC inter- debonding and fiber failure. Dundurs elastic mismatch phase can debond when the composites were during rameter o can be described as follows: loading. As a comparison, most part of segment L2 is on ES-Em the top of the cross-hatched line and the debonding of ig. 6b, which means the cracks will penetrate the n (1) PyC interphase was not found in sample B, as shown in However, carbon fibers were pulled out in the sample C (Fig. 4c), which indicates the heat-treated PyC inter- phase can be debonded when the composites were dur- ing loading, as shown in Fig. 6c. The reason for the result was that the heat treatment can improve the crys- L2 talline degree clear that crystallization degree of 0.5 heat-treated PyC(Fig. 7a) was higher than that of th untreated one(Fig. 7b),and the higher crystalline de gree of the heat-treated Py C interphase was beneficial Matrix for the pullout of carbon fibers. Meanwhile, it has been found that the fracture energy of PyC interphase can be reduced to by heat treatment owing to the improvement of the crystallization degree. The heat-treated PyC in- 0.5-0.23-0.130.0 templ er c ystalline degree had the lower Elastic mismatch a fracture energy(0-2J/m) than the untreated PyC Fig. 5. Comparison of the measured fra for ceramic interpahse(2-6]/m) /c. of C/ narx co mposite(CMC) Pyc /SiC composite was lowered in the range of 0- He and Hutchinson. 18 19 L, Ly and L, represent the calculated 0. 23, which is labeled as segment Ls in the debonding range ofI/ for SiG /RyC/SiC, C/l)yCSiC, and C/lyC"/SiC region of Fig. 5. As a result, carbon fibers in sample C mposites, respectively can be pulled out during loadi

shown in Fig. 4b, which was consistent with its brittle fracture behavior (Fig. 3). The low flexural strength (117MPa) and fracture toughness (3.3MPa m1/2) are at￾tributed to the brittle fracture behavior of sample B. The effect of heat treatment of PyC interphase on the fracture behavior of composites was studied. The fracture surface morphology of sample C showed that carbon fibers were apparently pulled out, as shown in Fig. 4c, which implies that the heat-treated PyC interpahse can work on carbon fibers. As a result, the flexural strength of sample C was increased from 117 to 504MPa compared with that of sample B, and the fracture toughness was increased from 3.3 to 18.6MPa m1/2. In the present work, the difference in the failure behaviors and the fracture modes of the composites are attributed to the different properties of fibers and different interfacial bonding between fiber and matrix, in which PyC interphase plays a key role in the mechanical behav￾ior of a ceramic matrix composite.16 For two dissimilar elastic materials, the crack propagation behavior at the interphase has been studied by He and Hutchinson,18,19 and a debonding diagram has been obtained, as shown in Fig. 5, which contains two regions showing the interphase debonding and fiber failure. Dundur’s elastic mismatch parameter a can be described as follows: a ¼ E f E m E f þ E m ð1Þ E x ¼ Ex ð1 v2 x Þ ð2Þ where subscripts f and m refer to the fiber and the matrix, E x is the plane strain modulus for the phase x, E and n are the elastic modulus and Poisson’s ratio for the respective phases, and longitudinal coordinate Gi Gf is the ratio of frac￾ture energy of interphase to the adjacent fiber. Whether the interphase can be debonded or not depends on the characteristics (modulus and fracture energy) of the matrix, fiber, and interphase. The re￾quired data for determining whether the interphase debonding or not in the present work are listed in Ta￾ble I. The likely results were calculated and marked in Fig. 5. For SiCf/PyC/SiC composite, aSiCf =SiCm is 0.13, and the corresponding GPyC=SiCf is in the range of 0.1–0.3, and hence a line segment L1 is marked in Fig. 5. For Cf/PyC/SiC composite, aCf =SiCm is –0.23, and the corresponding GPyC=Cf is in the range of 0.23– 0.70, and hence a line segment L2 is marked in Fig. 5. It can be found that most part of segment L1 is in the debonding region (below the cross-hatched curve), and Fig. 6a shows the debonding of PyC interphase on SiC fiber in the sample A. It means that the PyC inter￾phase can debond when the composites were during loading. As a comparison, most part of segment L2 is on the top of the cross-hatched line and the debonding of PyC interphase was not found in sample B, as shown in Fig. 6b, which means the cracks will penetrate the car￾bon fiber when the composites were during loading. However, carbon fibers were pulled out in the sample C (Fig. 4c), which indicates the heat-treated PyC inter￾phase can be debonded when the composites were dur￾ing loading, as shown in Fig. 6c. The reason for the result was that the heat treatment can improve the crys￾talline degree. It is clear that crystallization degree of heat-treated PyC (Fig. 7a) was higher than that of the untreated one (Fig. 7b), and the higher crystalline de￾gree of the heat-treated PyC interphase was beneficial for the pullout of carbon fibers. Meanwhile, it has been found that the fracture energy of PyC interphase can be reduced to by heat treatment owing to the improvement of the crystallization degree. The heat-treated PyC in￾terphase with higher crystalline degree had the lower fracture energy (0–2 J/m2 ) 16 than the untreated PyC interpahse (2–6 J/m2 ),12 and hence the GPyCHT =Cf of C/ PyCHT/SiC composite was lowered in the range of 0– 0.23, which is labeled as segment L3 in the debonding region of Fig. 5. As a result, carbon fibers in sample C can be pulled out during loading. Fig. 5. Comparison of the measured fracture energies for ceramic matrix composite (CMC) system with the debonding criterion of He and Hutchinson.18,19 L1, L2, and L3 represent the calculated range of Gi /Gf for SiCf /PyC/SiC, Cf /PyC/SiC, and Cf /PyC HT/SiC composites, respectively. www.ceramics.org/ACT Properties of SiC Matrix Composite 313

314 International Journal of Applied Ceramic Technolog-Liu, et al. Vol.8,No.2,2011 Sic matrix Pyc interphase debonding Fig. 7. The nages of py C interphase:(a) Untreate PyC interphase as received in sample A and B showing the poor crystalline degree (b) Heat-treated py C interphase in sample C showing the improvement in the crystalline degree. ferring load to the fiber, and hence the fexural strength of both samples A and C increased with the decrease of the open Fig. 6. Transmission electron microscopic images of the ryc porosity, as shown in Fig 3. However, the PyC inter showing the debonding in Sic noccmtetpa ec(a) sample A terphase morphologies of three kinds of compos Phase in C/PyC/SiC compos cannot be debonded B showing no debonding in Cr/By aSiC interphase zone; and (o under the loading, when the SiC matrix transferred the owing the debonding in Cr/lyc ASiC interphase a load to the interphase, and there was no debonding

The SiC matrix played a role in transferring the load to the fiber, and hence the flexural strength of both samples A and C increased with the decrease of the open porosity, as shown in Fig. 3. However, the PyC inter￾phase in C/PyC/SiC composite cannot be debonded under the loading, when the SiC matrix transferred the load to the interphase, and there was no debonding SiC fiber untreated PyC interphase a heat treated PyC interphase SiC matrix b Fig. 7. The HRTEM images of PyC interphase: (a) Untreated PyC interphase as received in sample A and B showing the poor crystalline degree; (b) Heat-treated PyC interphase in sample C showing the improvement in the crystalline degree. SiC fiber SiC matrix PyC interphase debonding a carbon fiber PyC interphase SiC matrix b c SiCmatrix carbon fiber PyC interphase debonding Fig. 6. Transmission electron microscopic images of the PyC interphase morphologies of three kinds of composites: (a) sample A showing the debonding in SiCf /PyC/SiC interphase zone; (b) sample B showing no debonding in Cf /PyC/SiC interphase zone; and (c) sample C showing the debonding in Cf /PyC HT/SiC interphase zone. 314 International Journal of Applied Ceramic Technology—Liu, et al. Vol. 8, No. 2, 2011

wwceramics. org/ACT Properties of Sic Matrix Composite 315 between the matrix and fiber, as a result, the fexural sample C, because of the larger opening width of crack strength of sample B did not increase apparently with(Fig. Ib)than that in sample C(Fig. Ic). In summary, the decrease of open porosity. the hybrid fibers can significantly improve the oxidation The brittle fracture mode of carbon fibers limits the resistance of Sic omposite when compared with strength and toughness of the hybrid composite. It is carbon-fiber-reinforced SiC matrix composites in air at supposed that the thickness of PyC interphase(150 nm) 700C in Cr/Py C/SiC composite was too thin to make the car- bon fiber be pulled out. To increase the thickness of PyC int only decrease the fract Conclusions nergy of PyC interphase but also reduce the roughness asperity interactions between the fber and matrix, Microstructure and mechanical properties of SiC which can make the Prc interphase debond during and carbon hybrid fibers reinforced SiC matrix com- posite were investigated, which were compared with thicknesses also can serve to accommodate residual ther- those of C/Py C/SiC and C/PyC/SiC mal mismatch stresses In a word, increasing the thick With the decrease of the open porosity, the fexural ness of PyC interphase may further improve the strength of the composites fitted the exponential func mechanical properties of the hybrid composite. tion. It was revealed that the ke the fracture behavior is the ratio of fracture energy of The Oxidation Behaviors of the Composite PyC interphase to the adjacent fiber. He and Hutchin- son's model that support these results are presented an The weight changes of the three kinds of compos- discussed in the present work. The oxidation properties ites as a function of oxidation time in air at 700C fe of the three kinds of composites were studied in air at 10h are shown in Fig. 8. The strength retention ratios 700 C for 10h. The main conclusions were as follows of the three kinds of composites were 99%, 67%, and (1)Both(SiC-C)/Py C/SiC hybrid composite and 78%,respectively, after oxidation for 10 h, as shown in C/PyCHT/SiC composite had higher flexural strength Table Il, Almost no weight change was found for sam- than C/PyC/SiC composite. With the decrease of th ple a after 10 h oxidation. However, there is an appar open porosity, the fexural strength of( SiC-C)/PyC/ ent weight loss for samples B and C, which were SiC and C/PyC /SiC composites exhibited the sig consistent with that of Cheng and colleagues. The nificantly incr nificantly increasing tendency but that of C/PyC/S microcracks in samples B and C acted as channels for was nearly independent on the open porosity xygen to diffuse into the interior of the composites. (2)(SiC-C)/PyC/SiC hybrid composite had th The weight loss of sample b was larger than that of less TRS-induced matrix microcracks compared with those in C/PyC/SiC composite and C/PyC /SiC composite. Compared with the C/PyC/SiC composite, the mechanical properties of hybrid composite were improved significantly by the pullout of SiC fibers due to a working PyC interphase. However, compared with the C/Py iC composite, the properties of hybrid -Sample C -Sample B composite at room temperature were not different ignificantl (3)The crystalline degree of the PyC interphase was modified by the heat treatment, which made the pullout of the carbon fibers possible for C/PyC/SiC (4)The fracture behaviors of the composites were supported by the He and Hutchinsons model. Whether Oxidation time(Hrs) the interphase can be debonded or not was mainly de rmined by the ratio of fracture of PyC inter phase to the adjacent fiber. Both higher fracture energy

between the matrix and fiber, as a result, the flexural strength of sample B did not increase apparently with the decrease of open porosity. The brittle fracture mode of carbon fibers limits the strength and toughness of the hybrid composite. It is supposed that the thickness of PyC interphase (150 nm) in Cf/PyC/SiC composite was too thin to make the car￾bon fiber be pulled out. To increase the thickness of PyC interphase may not only decrease the fracture energy of PyC interphase but also reduce the roughness asperity interactions between the fiber and matrix, which can make the PyC interphase debond during loading.6 Meanwhile, PyC interphase with increased thicknesses also can serve to accommodate residual ther￾mal mismatch stresses. In a word, increasing the thick￾ness of PyC interphase may further improve the mechanical properties of the hybrid composite. The Oxidation Behaviors of the Composites The weight changes of the three kinds of compos￾ites as a function of oxidation time in air at 7001C for 10 h are shown in Fig. 8. The strength retention ratios of the three kinds of composites were 99%, 67%, and 78%, respectively, after oxidation for 10 h, as shown in Table II, Almost no weight change was found for sam￾ple A after 10 h oxidation. However, there is an appar￾ent weight loss for samples B and C, which were consistent with that of Cheng and colleagues.3–5 The microcracks in samples B and C acted as channels for oxygen to diffuse into the interior of the composites. The weight loss of sample B was larger than that of sample C, because of the larger opening width of cracks (Fig. 1b) than that in sample C (Fig. 1c). In summary, the hybrid fibers can significantly improve the oxidation resistance of SiC matrix composite when compared with carbon-fiber-reinforced SiC matrix composites in air at 7001C. Conclusions Microstructure and mechanical properties of SiC and carbon hybrid fibers reinforced SiC matrix com￾posite were investigated, which were compared with those of C/PyC/SiC and C/PyCHT/SiC composites. With the decrease of the open porosity, the flexural strength of the composites fitted the exponential func￾tion. It was revealed that the key parameter to control the fracture behavior is the ratio of fracture energy of PyC interphase to the adjacent fiber. He and Hutchin￾son’s model that support these results are presented and discussed in the present work. The oxidation properties of the three kinds of composites were studied in air at 7001C for 10 h. The main conclusions were as follows: (1) Both (SiC–C)/PyC/SiC hybrid composite and C/PyCHT/SiC composite had higher flexural strength than C/PyC/SiC composite. With the decrease of the open porosity, the flexural strength of (SiC–C)/PyC/ SiC and C/PyCHT/SiC composites exhibited the sig￾nificantly increasing tendency but that of C/PyC/SiC was nearly independent on the open porosity. (2) (SiC–C)/PyC/SiC hybrid composite had the less TRS-induced matrix microcracks compared with those in C/PyC/SiC composite and C/PyCHT/SiC composite. Compared with the C/PyC/SiC composite, the mechanical properties of hybrid composite were improved significantly by the pullout of SiC fibers due to a working PyC interphase. However, compared with the C/PyCHT/SiC composite, the properties of hybrid composite at room temperature were not different significantly. (3) The crystalline degree of the PyC interphase was modified by the heat treatment, which made the pullout of the carbon fibers possible for C/PyC/SiC composite. (4) The fracture behaviors of the composites were supported by the He and Hutchinson’s model. Whether the interphase can be debonded or not was mainly de￾termined by the ratio of fracture energy of PyC inter￾phase to the adjacent fiber. Both higher fracture energy Fig. 8. The weight changes of the three kinds of composites in air at 7001C versus oxidation time. www.ceramics.org/ACT Properties of SiC Matrix Composite 315

316 International Journal of Applied Ceramic Technolog-Liut, et al. Vol.8,No.2,2011 of Sic fiber than that of carbon fiber and lower fracture 6. K.T. Faber, "Ceramic Composite Interfaces: Properties and Design, Anna. energy of heat-treated Py C interphase than that of un- 7. H. Mei, "Measurement and Calculation of Thermal Residual Stress in Fiber treated PyC interphase can make the interphase debond einforced Ceramic Matrix Composites, Compos. Sci. Technol., 68[15-16 during loading and consequently increase the strength 3285-3292(2008) 8. S.J. Wu, L F. Cheng. Q. Zhang L. T. Zhang, and Y. D. Xu,Thermo- ughness of the composites ()After oxidation in air at 700C for 10 h, the hmol,3l75-79(200) 9. M. Takeda, er ability of the Low-Oxygen-Conter posite was only 0. 26%, much Carbide Fiber lower than those of C/PyC/SiC and C/PyC/SiC 10. B. A Bender, J. S. Wallace, and D.J. Schrodt, " Effect of Thermochemical composites,4.23%, 2.53%, respectively. The strength on the Strength and Microstructure of SiC Fibres, ". Mater. Sci, etained ratio of hybrid composite was 99%, much 970-976(1991 I1. A. G. Evans and F. W. Zok, Review, the Physics and Mechanics of Fiber- higher than those of the other two composites, 67%, einforced Brittle Matrix Composites, " J. Mater. Sci., 29 [15]3857-3896 78%, ely 12. F. Rebaillat, ]. Lamon, and A G. Evans, Microcomposite Test Procedure for References 13. K Honjo, " Fracture Toughness of PAN-Based Carbon Fibers Estimated Lin,"Design, Preparation and Properties de cmcs 14. D. Wongs Modeling Failure Mechanism of Designed-to Fail Par 76 nd Nuclear Reactors: An Overview, Comp. Sci. 15. O. Nala. Bansal, and P. Narottam. ""In-PLane and Interlaminar Shear Influence of Interface Characteristics on the Mechanical Prop- trength of a Unidirectional Hi-Nicalon Fiber-Reinforced Celsian Matrix yranno-SA3 Fiber-Reinforced SiC/SiC Mini- omposites,Int / App. Ceram. Tecbomol, 7 291-303(2010). Three Dimensional C/SiC Composites in Air and Combustion Gas Envi- 17. ASTM 31 Standard Test Merhod面123286(9 meneS." Carbon,38[52103-2108(2000 nuous Fiber-Reinforced Advanced Ce Ku.Oxidation Behaviors ASTM Standards, Vol 15. 01, ASTM, We C/SiC in the Environments Contai M 8.M. Y. He and J. EgA,348[-2]47-53(2003) Dissimilar Elastic Materials, " Int./. 2591053-1067 5. C.Q. Tong. L F Cheng. X W. Yin, L T Zhang, and Y. D Xu, Oxidation ehavior of 2D C/SiC Composite Modified by SiB4 Particles in Inter-Bundle 19. M.Y. He and J. w. Hutchinson, "Kinking of a Crack Out of an Interface. ores,Compos. Sci. Technol, 68 3-4]602-607(2008) Appl Ma,56270-278(1989)

of SiC fiber than that of carbon fiber and lower fracture energy of heat-treated PyC interphase than that of un￾treated PyC interphase can make the interphase debond during loading and consequently increase the strength and toughness of the composites. (5) After oxidation in air at 7001C for 10 h, the weight loss of hybrid composite was only 0.26%, much lower than those of C/PyC/SiC and C/PyCHT/SiC composites, 4.23%, 2.53%, respectively. The strength retained ratio of hybrid composite was 99%, much higher than those of the other two composites, 67%, 78%, respectively. References 1. R. Naslain, ‘‘Design, Preparation and Properties of Non-Oxide CMCs for Application in Engines and Nuclear Reactors: An Overview,’’ Comp. Sci. Tech., 64 [2] 155–170 (2004). 2. C. Sauder, ‘‘Influence of Interface Characteristics on the Mechanical Prop￾erties of Hi-Nicalon Type-S or Tyranno-SA3Fiber-Reinforced SiC/SiC Mini￾composites,’’ Int. J. Appl. Ceram. Technol., 7 [3] 291–303 (2010). 3. L. F. Cheng, Y. D. Xu, L. T. Zhang, and X. W. Yin, ‘‘Oxidation Behavior of Three Dimensional C/SiC Composites in Air and Combustion Gas Envi￾ronments,’’ Carbon, 38 [15] 2103–2108 (2000). 4. X. W. Yin, L. F. Cheng, L. T. Zhang, and Y. D. Xu, ‘‘Oxidation Behaviors of C/SiC in the Oxidizing Environments Containing Water Vapor,’’ Mater. Sci. Eng. A, 348 [1–2] 47–53 (2003). 5. C. Q. Tong, L. F. Cheng, X. W. Yin, L. T. Zhang, and Y. D. Xu, ‘‘Oxidation Behavior of 2D C/SiC Composite Modified by SiB4 Particles in Inter-Bundle Pores,’’ Compos. Sci. Technol., 68 [3–4] 602–607 (2008). 6. K. T. Faber, ‘‘Ceramic Composite Interfaces: Properties and Design,’’ Annu. Rev., Mater. Sci., 27 499–525 (1997). 7. H. Mei, ‘‘Measurement and Calculation of Thermal Residual Stress in Fiber Reinforced Ceramic Matrix Composites,’’ Compos. Sci. Technol., 68 [15–16] 3285–3292 (2008). 8. S. J. Wu, L. F. Cheng, Q. Zhang, L. T. Zhang, and Y. D. Xu, ‘‘Thermo￾physical and Mechanical Properties of a Three-Dimensional Hi–Nicalon/SiC Composite,’’ Int. J. Appl. Ceram. Technol., 3 [1] 75–79 (2006). 9. M. Takeda, et al., ‘‘Thermal Stability of the Low-Oxygen-Content Silicon Carbide Fiber, Hi-Nicalont,’’ Compos. Sci. Technol., 59 813–819 (1999). 10. B. A. Bender, J. S. Wallace, and D. J. Schrodt, ‘‘Effect of Thermochemical Treatments on the Strength and Microstructure of SiC Fibres,’’ J. Mater. Sci., 26 970–976 (1991). 11. A. G. Evans and F. W. Zok, ‘‘Review, the Physics and Mechanics of Fiber￾Reinforced Brittle Matrix Composites,’’ J. Mater. Sci., 29 [15] 3857–3896 (1994). 12. F. Rebaillat, J. Lamon, and A. G. Evans, ‘‘Microcomposite Test Procedure for Evaluating the Interface Properties of Ceramic Matrix Composites,’’ J. Am. Ceram. Soc., 78 [2] 401–405 (1995). 13. K. Honjo, ‘‘Fracture Toughness of PAN-Based Carbon Fibers Estimated from Strength–Mirror Size Relation,’’ Carbon, 41 [5] 979–984 (2003). 14. D. Wongsawaeng, ‘‘Modeling Failure Mechanism of Designed-to Fail Par￾ticle Fuel,’’ Nucl. Eng. Technol., 41 [5] 715–722 (2009). 15. O¨ . U¨ nala, Bansal, and P. Narottam, ‘‘In-Plane and Interlaminar Shear Strength of a Unidirectional Hi-Nicalon Fiber-Reinforced Celsian Matrix Composite,’’ Ceram. Int., 28 [5] 527–540 (2002). 16. R. Naslain, ‘‘Fibre-Matrix Interphases and Interfaces in Ceramic Matrix Composites Processed by CVI,’’ Compos. Interfaces, 1 253–286 (1993). 17. ASTM ‘‘C 1341-00, Standard Test Method for Flexural Properties of Con￾tinuous Fiber-Reinforced Advanced Ceramic Composites,’’ Annual Book of ASTM Standards, Vol. 15. 01, ASTM, West Conshohocken, PA, 1–19, 2005. 18. M. Y. He and J. W. Hutchinson, ‘‘Crack Deflection at an Interface Be￾tween Dissimilar Elastic Materials,’’ Int. J. Solids Struct., 25 [9] 1053–1067 (1989). 19. M. Y. He and J. W. Hutchinson, ‘‘Kinking of a Crack Out of an Interface,’’ J. Appl. Mech., 56 270–278 (1989). 316 International Journal of Applied Ceramic Technology—Liu, et al. Vol. 8, No. 2, 2011