PERFORMANCE TESTING AND STRENGTH PREDICTION OF CERAMIC-TO-METAL JOINTS

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1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y. 117 Gr c The Society shall not be responsible for statements or opinions advanced in G rj papers or discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Papers are available from ASME for 15 months after the meeting. Printed in U.S.A. Copyright 1993 by ASME 93-GT-412 PERFORMANCE TESTING AND STRENGTH PREDICTION OF CERAMIC-TO-METAL JOINTS J.H. Selverian and Dave A. ONeil OSRAM SYLVANIA INC. 6 Boston Street Salem, MA 197 Shinhoo Kang Valenite 1711 Thunderbird Troy, MI 4884 ABSTRACT Brazed joints were made between silicon nitride and Ni-based and Fe-based super alloys. Room temperature shear (torsion) strengths ranged from MPa for Si3N4-to-Incoloy 99 joints and from MPa for the Si3N4-to-Inconel 718 joints. At 5 C the joint strength was 12 MPa while at 65 C and 95 C the joints strengths were less than 2 MPa. These low strengths at 65 C and 95 C were attributed to a reduction in the shrink-fit and to low braze strength at these high temperatures. Finite element analysis (FEA) and a probabilistic failure theory (CARES) were used to predict the joint strengths. The predicted joint strengths agreed well with measured joint strengths in torsional loading at 2 C. Torsion tests were also performed at 65 C. Aspects of the material systems, residual stresses, mechanical behavior, and strength predictions are presented. Two new braze alloys based on the Au-Ni-Cr-Fe system were used to overcome the poor high temperature strength. Joints made with these brazes had good strength (85 MPa and 35 N-m) at 65 C. INTRODUCTION Ceramics are being considered for structural components in the development of advanced heat engines. A key issue is the problem of joining a ceramic rotor to a metal shaft to transmit power. Design concepts for ceramic-to-metal brazed joints were described in an earlier paper (Selverian et al 1992a). The major type of loading these joints will experience is torsional and thermal, therefore, the joints were evaluated with torsion, torsion fatigue, and thermal fatigue tests. The joints were tested at room temperature, 5 C, 65 C, and 95 C. The experimental results were linked to the predictions based on the residual stresses calculated by finite element analysis with simplifying assumptions. The goals of this work were to develop a ceramic-to-metal joint that could withstand 2.9 N-m (5 MPa) of torque at 65 C and 95 C and would have a 2 cm 2 brazed area, and to develop methods to predict joint performance. EXPERIMENTAL PROCEDURE For the 65 C application an Fe-based superalloy, Incoloy 99, was selected because of its low coefficient of thermal expansion (CTE) as well as its high-temperature properties. For the 95 C application a Ni-based superalloy, Inconel 718, was chosen solely for its high-temperature capabilities. The CTE of Inconel 718 is approximately 5% greater then that of Incoloy Presented at the International Gas Turbine and Aeroengine Congress and Exposition Cincinnati, Ohio May 24-27, 1993 This paper has been accepted for publication in the Transactions of the ASME Discussion of it will be accepted at ASME Headquarters until September 3,1993

2 99. In the remainder of the paper Incoloy 99 and Inconel 718 together were referred to as structural alloys. Silicon nitride (Si3N4+6%Y2O3) was selected as the structural ceramic material. The silicon nitride shaft was polished to a.1 µm surface finish. A 3-µm thick Ti-coating was electron beam evaporated onto one end of the silicon nitride shaft. This Ti-coating served to promote wetting and adhesion between the ceramic and braze alloy. Nickel and molybdenum were used as interlayer materials between the ceramic and the structural alloy, and a Au-5Pd-2Ni (in wt%) braze alloy was used. The two material systems studied were; Si3N4/Ni/Incoloy 99 as the 65 C system and Si3N4/Mo/Inconel 718 as the 95 C system. The Au-5Pd-2Ni braze alloy was used in both systems. Joint Geometry The joint consists of a 1.27 cm diameter silicon nitride rod brazed to a cm outer diameter metal shaft with a 2 cm 2 brazed area. The ceramic rod fits into a cup machined into the end of the metal shaft. A schematic of the ceramicto-metal joint geometry is shown in Figure 1. Finite element analysis showed that this type of cylindrical lap joint resulted in lower residual stress in the ceramic compared to other geometries (Selverian et al 1992a). EJ Ceramic Braze Interlayer Q Structural alloy Empty space Figure 1. Schematic of the ceramic-to-metal joint geometry. Brazing Process The entire ceramic-to-metal joint was placed in a graphite brazing fixture for alignment. A thermocouple was placed near the joint, and the brazing set-up was placed in a vacuum furnace. The furnace was raised to the brazing temperature, 118 C, in approximately 1 hour at which point the vacuum was 1-2 to 1-3 Pa. The joint was held at temperature for 1 minutes. After brazing the furnace power was turned off and the joints cooled to room temperature in approximately 3 hours. Testing of Brazed Joints Figure 2 shows a brazed joint between silicon nitride and Incoloy 99. This type of joint was used for the torsion and torsion fatigue tests. All of the mechanical testing of the brazed joints was carried out on a servo hydraulic axial/torsional machine. The top and bottom gripping axes were axially aligned to within 4-µm of one another. Figure 2. Brazed Si3N4/Ni/Incoloy 99 joint. Test sample for torsion and mechanical fatigue testing. The ceramic Is 1.27 cm In diameter and the metal Is cm in diameter. Torsion tests were run at a rate of.2 /sec and the axial load was controlled to within ±4.5 N of zero to maintain pure torsional loading. An induction furnace, with a SiC susceptor, was used to heat the joints for the elevated temperature tests. Torsion fatigue tests were carried out at minimum and maximum torques of N- m, N-m, or N-m, all with a 1.5 Hz loading frequency. Torques of N-m are typical values found in heat engines currently under development. The temperature versus time profile used for the 65 C thermal fatigue testing consisted of a maximum temperature of 65 C and a minimum 2

3 temperature of 335 C with a frequency of.7 Hz. The temperature versus time profile used for 95 C thermal fatigue testing consisted of a maximum temperature of 95 C and a minimum temperature of 545 C with a frequency of.11 Hz. The thermal fatigue conditions were also developed with the idea of simulating the stresses developed in a heat engine. All of the mechanical and thermal tests were conducted in air. :i*3i1l31:1 DIE'1&iell I *-9 [N1 The bending moment in the brazed joint, due to misalignment between the ceramic and metal parts of the joint, introduced additional stresses in the joint. There was no strong correlation between the bending moment and the shear stress of a joint for bending moments below approximately 25 N-m. Results from room temperature torsion tests of Si3N4/Ni/Incoloy 99 joints are shown in Table I. The measured shear strengths calculated according to Equation 1 were in the range of MPa at room temperature. The shear stress, 't, for an applied torque, MT, and a gauge diameter, D, was given by 16 MT ti = Eq. 1 It D 3 Table I. Results of the torsion tests of S13N4/Ni/Incoloy 99 brazed joints. Test Temp. ( C) Torque (N-m) Shear Strength (MPa) Bending Moment (N-m) Rotation ( ) * * * * * * * * # # # # ' broke in ceramic. # ceramic slipped in joint. Fracture started in the ceramic near the top of the interlayer. Away from the interlayer, the fracture surface formed an approximately 45 angle. Near the top of the interlayer, the angle of the fracture surface varied from 45. This suggested that the stress pattern near the interlayer was significantly different than in the bulk silicon nitride away from the interlayer. The initiation site of fracture was in agreement with the finite element prediction that the maximum residual stress would occur at the top of the interlayer (Selverian et al 1992a). Figure 3. Fracture surface of a S13N4/NI/Incoloy 99 joint fractured In a room temperature torsion test. The ceramic is 1.27 cm in diameter and the metal is cm in diameter. ;3

4 Table II. Results of the torsion tests of S13N4/Mo/inconel 718 brazed joints. Test Temp. ( C) Torque (N-m) Shear Strength (MPa) Bending Moment (N-m) Rotation ( ) *.38 Figure 4. S13N4/Mo/Inconel 718 joint fractured In a room temperature torsion test. The ceramic Is 1.27 cm In diameter and the metal Is cm in diameter * * * * # Results from the torsion tests at 65 C are also shown in Table I. In general, the strengths of these joints were very low ( MPa). During the torsion tests the ceramic would slip without fracturing. Auger analysis of the fracture surface indicated that the fracture path was complex and occurred in the silicon nitride, in the TiN reaction layer, and in the braze alloy. Titanium nitride has been commonly seen as a reaction layer forming between titanium and silicon nitride. For all of the torsion tests at all temperatures studied, the torque versus rotation plots were straight lines, indicating that yielding of the metal components did not occur before final fracture or slippage. Results from the room temperature torsion tests of the Si3N4/Mo/Inconel 718 joints are shown in Table II. The fracture behavior of these joints, Figure 4, was similar to the Si3N4/Ni/Incoloy 99 joints. However, the Si3N4/Mo/Inconel 718 joints were significantly weaker than the Si3N4/Ni/Incoloy 99 joints. The shear strengths of the Si3N4/Mo/Inconel 718 joints at room temperature ranged from 3 to 127 MPa. This difference in room temperature strength was largely attributed to the higher residual stresses developed in the Si3N4/Mo/Inconel 718 joints. The higher residual stresses were due to the higher CTE of Inconel 718 as compared to Incoloy 99, and due to the lower CTE and higher flow stress of molybdenum as compared to nickel. ' broke in ceramic. # ceramic slipped in joint. Fatigue Testing Thermal and mechanical fatigue tests were used to evaluate the effects of repeated thermal and mechanical loading on the long-term performance of the brazed joints. Braze joints were made for thermal fatigue tests at 65 C and 95 C. The same joint geometry was used as in Figure 2. The initial crack distribution in the joint was checked by microfocus x-ray. No cracks were detected in the silicon nitride. The apparent lack of cracks in the silicon nitride could be due to either no cracking or to the cracks being smaller than the 4 µ m detection limit of the x-ray equipment. The samples were reexamined by microfocus x-ray after 1, 1, and 1 cycles. The Si3N4/Ni/Incoloy 99 joints survived all 1 cycles without evidence of cracking. Severe oxidation of the molybdenum interlayer in the Si3N4/Mo/Inconel 718 joints prevented their complete testing. Several Si3 N 4 /Ni/Incoloy 99 and Si3N4/Mo/Inconel 718 joints were torsion fatigue tested at room temperature, Table III. A Si3N4/Ni/Incoloy 99 joint was first fatigued at room temperature for 13 cycles then fatigued at 4

5 room temperature for 1 6 cycles. All of the joints survived 1 6 fatigue cycles at a torque amplitude of N-m. The joints showed no signs of degradation; the rotation required to maintain these torques was unchanged at ±.32 from the start of the test. The torque amplitudes were increased to N-m and to N-m. One joint was tested at each torque level and joints survived 1 6 cycles, Table II. Table II. Room temperature fatigue tests of S13N4/NI/Incoloy 99 and S13N4/Mo/inconel 718 brazed joints. Joint Torque (N-m) Rotation ( ) Number of Cycles for Failure Si3N4/Ni/ X.31 > 13* Incoloy 99 :: ±.32 > 13 ±.31 > 1 3 * ±.32 > 13 * X.31 > > > 16 Si3N4/Mo/ > 13* Inconel 718 ±.26 > 13 * These samples were heated to 65-7 C, then gripped in the testing machine, and then cooled to room temperature before testing, to realign the sample. Effect of Shrink Fit For joints that failed in the joint region, the joint strength was broken down into 2 main parts. The first was the intrinsic strength of the metallurgical bonding across the ceramic/metal interface and the second was the shrink-fit force which was due to the compressive forces exerted on the ceramic by the surrounding metal. Of these two factors the shrink-fit was believed to be the most temperature sensitive. However, at high-temperatures the temperature dependant properties of the joint materials also played a role in the joint strength. Tables I and II showed that the joints were very weak at 65 C and 95 C. It was uncertain whether the low joint strength was due to a weakening of the braze alloy or due to a reduction in the shrink-fit due to the elevate temperature testing. Therefore, the amount of shrink-fit (radial stress) in the final joint geometry was calculated by finite element analysis (Selverian et al 1992a). The radial stresses were measured from the centroid of the 12 ceramic finite elements at the ceramic/metal interface. In Figure 5, these radial stresses were plotted as a function of distance along the ceramic/metal interface, for several temperatures. The radial stress distribution in the ceramic changed and became very complicated at temperatures above 2 C. ca a. E 5 25 Q) -25 C -5 N -75 Cl) 1 C 2 C 5 C 65 C -1 `^,.,` ' Distance From Top of Interlayer (mm) Figure 5. Centroid stresses in the ceramic at the ceramic/interlayer Interface as a function of temperature calculated by finite element analysis for a S13N4/NI/Incoloy 99 joint. The joint was initially cooled down to 2 C from the brazing temperature then reheated to the different temperatures. The stresses in Figure 5 were used to estimate the loss in joint strength as a result of an increase in temperature and the resultant 5

6 decrease in shrink-fit. For a shrink-fit joint, the torque (T) the joint can withstand without slipping was approximated by the following equation: n T=µ ra Pi Eq. 2 i=1 where µ was the coefficient of friction between the ceramic and metal (-.1), "r" was the radius of the ceramic (6.35 mm), "A" was the area of contact which was taken as the area/element in the FEA mesh (1.7 x 1-5 m2) times the number of elements (n) with a compressive stress, and Pi was the radial compressive stress in element "i" (Orr). Only compressive stresses were included in this analysis. The radial stresses along the ceramic/metal interface are shown in Figure 5. The calculated values of the torque due to the shrink-fit stresses were 122 N-m at 2 C, 25 N-m at 5 C, and 1.8 N-m at 65 C, corresponding to shear strengths of 34 MPa, 62 MPa, and 4 MPa, respectively. These torque values are for a shrink-fit joint and are only valid for joints that slipped at the ceramic/metal interface and did not break in the ceramic or fail by deformation of any of the metallic components of the joint. The total strength of a joint can be thought of as being comprised of two components; the shrinkfit, and the metallurgical bond. The metallurgical bond component is the chemical bonding and mechanical interlocking at the ceramic/metal interface, in this case between the Ti-coating and silicon nitride. The total joint strength is defined as; I, which is supported by the fact that at room temperature the ceramic broke and the joint did not slip, i.e., the joint was stronger than the ceramic. At 5 C the total joint strength is approximately 62 MPa + 85 MPa = 147 MPa, which compares favorably with the experimental value of 123 MPa after 1 cycles of fatigue testing, Table III. At 65 C the total joint strength is approximately 4 MPa + 85 MPa = 89 MPa. This value is significantly higher that the experimental value of approximately 1 MPa, Table I. This discrepancy is attributed to a weakening of the braze alloy at 65 C, indicating that at the higher temperatures the joint strength is controlled by the strength of the braze alloy. The mechanical properties of the braze alloy at elevated temperatures were expected to play an important role in determining the creep behavior of this joint. However, the creep requirements for this joint were not well defined and were not studied. Table IV. Results of the 5 C torsion tests of Si3N4/Ni/Incoloy 99 brazed joints. All of these joints were fatigued tested at room temperature before testing at 5 C. Torque Shear Previous Fatigue Fracture Strength Test Conditions Mode (N-m) (MPa) (cycles at stress) at slipped at cer. broke slipped 16 at total joint strength = shrink-fit + metallurgical bond Eq. 3 where the contribution of the metallurgical bond to the joint strength is approximately constant at 85 MPa for the temperature range studied (Table V in Selverian and Kang, 1992c). For the joints tested at room temperature the total joint strength is approximately 34 MPa + 85 MPa = 389 MPa. This strength is significantly higher than the measured joints strengths, Table Comparison Between FEA Predictions and Exnerlmental Results Finite element analysis was used to predict the residual stress for each joint component (Selverian et al, 1992a). The joints were assumed to have perfect bonding at every interface, the presence of voids in the braze was ignored. Further, the influences of metallurgical reactions due to processing was not accounted for in the analysis. Bulk properties were used for each material in the joint. Also, significant alloying was seen between the braze, interlayer, and 6

7 structural alloys. This alloying caused a change in the braze alloy's composition and hence in its properties (the most important was the flow stress). Such effects were not accounted for in the finite element analysis. The comparison between predictions and experimental results were made with a probabilistic approach to joint failure. For the probabilistic approach, the NASA CARES program (Nemeth et al, 1989a and 1989b) was used to calculate the probability of survival (Ps) of the joints and the result was presented in the form of a probability plot. In this approach, the predicted strength value was obtained by superimposing the distribution of an applied torque and the calculated residual stress. Probabilistic Ap row For this approach, an applied torque was superimposed with the calculated residual stress field as a shear stress. Figure 6 shows the torque distribution used to determine the shear stress. A stress concentration due to the change in cross-section at the joint was included as before. The stress concentration was 1.7 at the top of the joint and tapered off to 1. a distance of one ceramic diameter away from the joint. Selection of the stress concentration factor depended on the radius of the fillet formed by the braze alloy. A fillet radius of 1 mm was selected, however the fillet radius varied over the joint area. The stress concentration factor was estimated from Rourk (1971). The fraction of torque carried by the ceramic and metal components in the joint region was calculated based on the material properties and was also factored into the torque distribution shown in Figure 6. Once the torque was added to the residual stress field, the combined stress field was used as input to the CARES probabilistic failure computer code (Nemeth et al, 1989a and 1989b) to obtain the probability of survival for the joint at the applied torque level. This same procedure was performed at several different torques and the probability of failure (Pf) values were calculated as a function of applied torque. This probabilistic approach to joint strength, unlike the maximum principal stress approach, provided a method to estimate the strength distribution of a ceramic-to-metal brazed joint and can be used as a design aid d 1.4 C. O 1.2 I- 1. N.8.6 E.4 Z.2 Bottom N Interlavbr Top of interlayer Distance along Ceramic (mm) Figure 6. Plot of the torque distribution In the ceramic portion of the brazed joint. Torque values are normalized to the applied torque. Two failure theories were used to predict the behavior of the ceramic-to-metal joints for comparison. These were; 1) Shetty criterion, with c =.82, a penny-shaped crack, and a shearinsensitive Batdorf crack density coefficient, and 2) coplanar strain energy release rate, with a Griffith crack, and a shear-sensitive Batdorf crack density coefficient. For these failure theories the Weibull modulus (m v ), the normalized Weibull scale parameter (cr ov ), and the Batdorf crack density coefficient (kg V) were calculated from 4-point bend tests of the silicon nitride material used in the ceramic-to-metal brazed joints. Twenty-four samples were tested and I outlier was detected in the data (Selverian and Kang, 1992b). A Weibull modulus (m y ) of 21.2 and a normalized Weibull scale parameter (cr ow ) of MPa(m) 3/21. 2 were used for both failure theories. A shear-insensitive Batdorf crack density coefficient of 43.4 and a shear-sensitive Batdorf crack density coefficient of 22.2 were used for the Shetty and coplanar strain energy release rate theories, respectively. The maximum likelihood method was used to fit the experimental data. The constants described above were required as input variables by the 7

8 CARES program and are further described by Nemeth et al (1989a). Figure 8 and 9 show experimental and predicted results of torsion testing of the brazed joints. The predicted strength distributions surrounded the experimental values and intermediate values of Pf, where Pf = 1 - P s. However, at the low and high regions of the probability distributions the predictions deviated from the experimentally measured strengths. Also, the predicted probability distributions were much steeper (higher Weibull modulus) than the experimental probability distribution. The Weibull modulus decreased from 21.2 for the unbrazed ceramic to -4 for the S i 3 N 4 /Ni/Incoloy 99 brazed joints. A similar decrease in Weibull modulus was seen in shear testing of ceramic-to-metal lap joints (Selverian and Kang, 1992c) and in 4-point bend tests of ceramic-to-metal butt joints (Lugscheider and Tillmann, 199). The cause of the difference in the slopes (Weibull modulus) of the probability distributions was unknown. C) LL w a C). L. IL nn Shetty (C=.82) Penny-shaped crack Shear-insensitive Strain energy Griffith crack Shear-sensitive Torque (N-m) Figure 9. Predicted and experimental values of the brazed joint strength measured in torsion (S13N4/Mo/Inconel 718). Two failure theories were used: 1) Shetty criterion with c =.82, penny-shaped crack, and a shear-insensitive Batdorf crack density and 2) coplanar strain energy release rate, Griffith crack, and a shear-sensitive Batdorf crack density. 'I.- 1. IL LL.6._.5.4 ca I n Shetty (C=.82) Penny-shaped frack Shear-insensit' e I I. Strain energy Griffith crack Shear-sensitive Torque (N-m) Figure 8. Predicted and experimental values of the brazed Joint strength measured in torsion (S13N4/NI/IncoIoy 99). Two failure theories were used: 1) Shetty criterion with c =.82, penny-shaped crack, and a shear-insensitive Batdorf crack density and 2) coplanar strain energy release rate, Griffith crack, and a shear-sensitive Batdorf crack density. D evelopment of New High Temperature Braze Alloy The results in Tables I and II point out the need for new braze alloys for application temperature above 5 C to provide high-temperature creep strength as well as oxidation resistance. A FEA (finite element analysis) study (Selverian et al 1992a) indicated that the alloys need to have low yield strength, high ductility, and high ultimate strength at low temperature for optimum bonding performance. High ductility and high toughness values of the alloys are extremely important in producing braze foils by rolling. Many of these requirements are in conflict. Interactions between joining components sometimes cause compatibility problems. There is a limit in brazing temperatures to prevent silicon nitride substrates from decomposing, --12 C. Two new braze alloys were developed for high temperature use. These alloys are based on the Au-Ni-Cr-Fe-Mo system (SK-1) and the Au-Ni- Cr-Fe system (SK-2) (Kang et al 1992). The results of some preliminary mechanical tests of joints brazed with these alloys are given in Tables VI and VII and Figure 9. Joints made 8

9 with these new braze alloys exceed the goal of N-rn of torque at 65 C. Table V. Torsional strength of the PY6/NI/Incoloy 99 system brazed with SK-1 or SK-2 braze alloy at 11 C for 3 minutes. Braze Alloy Test Temp. C Torque N-m Bending Moment N-m Rotation SK * * * * * * * $ 29 SK * * * * * * $ 1 1# broke in ceramic. # ceramic slipped in joint. $ greater than 5% unbonded area. Table VI. Torsional rupture of PY6/Ni/Incoloy 99 joints with the SK-1 braze at 65 C for an applied torque of 2.9 N-m. Bending Maximum rtime to Creep Rate Moment Rotation Rupture ( /hr) N-m (hrs) x x >1* 8.8x > x1-3 * Experiment was stopped after 1 hours creep at 65 C due to a planned electrical shut-down. d Cu X 1..5 ^ Time (hours) Figure C creep behavior of ceramicmetal Joints brazed with the SK-1 alloy. SUMMARY AND CONCLUSIONS Material systems designed for 65 C and 95 C applications were evaluated in terms of torsion, torsion fatigue, and thermal fatigue. Si3N4/Ni/Incoloy 99 was selected as the 65 C system while Si3N4/Mo/Inconel 718 was selected as the 95 C system. The Au-5Pd-2Ni braze alloy was used in both systems. A cylindrical lap geometry with an interlayer was selected for these joints. Room temperature and 5 C torsion strengths of the 65 C system were measured in the range of 3-1 N-m with a 2 cm 2 brazed area while the strength at 65 C was significantly lower ( N-m). This was attributed to a reduction in the shrink-fit at 65 C. The Si3N4/Ni/Incoloy 99 joints showed excellent room temperature fatigue behavior. A similar trend was seen in the high-temperature strength of the Si3N4/Mo/Inconel 718 joints, which had lower strength than the Si3N4/Ni/Incoloy 99 joints due to the high CTE of Inconel 718. The strength predictions of the finite element analysis were compared with experimental results. Scatter in the measured strengths and the difference between measured and predicted strengths indicated the importance of processing effects and the probabilistic nature of ceramic failure on the fracture process. Fractographs of room temperature torsion specimens showed that the initiation sites for cracking coincided with U 9

10 those for maximum principal stress. This indicated that the maximum principal stress criterion should be a good estimate of the location of probable fracture. However, the probabilistic approach for the ceramic-to-metal brazed joints was a better method for comparing the performance of various brazed joints due to the statistical nature of ceramic failure, and it provided an estimate of the strength distribution of the joint for design considerations. Two new braze alloys were developed and demonstrated to be useful at 65 C. These alloys are based on the Au-Ni-Cr-Fe-Fe system and the Au-Ni-Cr-Fe system and resulted in joints with strengths of 85 MPa at 65 C. ACKNOWLEDGMENTS This research was sponsored, in part, by the U.S. Department of Energy, Assistant Secretary for Conservation and Renewable Energy, Office of Transportation Systems, as part of the Ceramic Technology for Advanced Heat Engines Project of the Advanced Materials Development Program, under contract DE-ACO5-84R214 with Martin Marietta Energy Systems, Inc. Special thanks go to M. Santella and D. R. Johnson at ORNL. The support of R. Schulz at the DOE is also appreciated. The authors wish to thank H. Kim for his support and E. Dunn for their contributions. The participation in the experimental program by D. Bazinet and G. McCloud is gratefully acknowledged. Assistance from K. Kim is appreciated. REFERENCES F. P. Beer and E.R. Johnston Jr., "Mechanics of Materials," McGraw-Hill, New York, p. 398, (1981). S. Kang, E.M. Dunn, J.H. Selverian, and H. Kim, Ceramic Bulletin, 68, p , (1989). S. Kang, J.H. Selverian, and D. ONeil, Oak Ridge National Laboratory, Final report, Subcontract No. 86X-SBO47C, (1992). D.H. Kim, S.H. Hwang, and S.S. Chun, Ceramics International, 16, p , (199). Nemeth, N.N., J.M. Mandersheid, and J.P. Gyekenyesi, "Ceramic Analysis and Reliability Evaluation of Structures (CARES) - Users Guide," NASA Technical Paper 2916, (1989a). Nemeth, N.N., J.M. Mandersheid, and J.P. Gyekenyesi, American Ceramic Society Bulletin, 68(12), p , (1989b). E. Lugscheider and W. Tillmann, J. American Welding Soc., 69(11), p. 416-s s, (199). R.J. Rourk, "Formulas for Stress and Strain," 4th edition, p , McGraw-Hill, New York, (1971). J.H. Selverian, D. O'Neil, and S. Kang, The American Ceramic Society Bulletin vol 71(9) (1992a). J.H. Selverian and S. Kang, The American Ceramic Society Bulletin vol 71(1) (1992b). J.H. Selverian and S. Kang, J. American Welding Soc., 71(1), (1992c). 1