Sung R. Choi

University of Toledo, Toledo, Ohio

David L. Krause

Glenn Research Center, Cleveland, Ohio

Assessments of Mechanical and Life

Limiting Properties of Two Candidate

Silicon Nitrides for Stirling Convertor

Heater Head Applications

NASA/TM—2006-214089

January 2006
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Sung R. Choi

University of Toledo, Toledo, Ohio

David L. Krause

Glenn Research Center, Cleveland, Ohio

Assessments of Mechanical and Life

Limiting Properties of Two Candidate

Silicon Nitrides for Stirling Convertor

Heater Head Applications

NASA/TM—2006-214089

January 2006

National Aeronautics and

Space Administration

Glenn Research Center
Acknowledgments

The authors are grateful to Ralph Pawlik for experimental work. Thermal conductivity and coefficient

of thermal expansion of both AS800 and SN282 silicon nitrides were determined by Dongming Zhu, RME.

This work was supported by Advanced Technology Development for Stirling Convertor, NASA Glenn

Research Center, Cleveland, Ohio.

Available from

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ideas from a technical peer group.

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Aeronautics and Space Administration.

Available electronically at http://gltrs.grc.nasa.gov
NASA/TM—2006-214089 1 

Assessments of Mechanical and Life Limiting Properties of 

Two Candidate Silicon Nitrides for Stirling Convertor 

Heater Head Applications 

Sung R. Choi 

University of Toledo 

Toledo, Ohio 43606 

David L. Krause 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

NASA Glenn Research Center is developing advanced technology for Stirling convertors with a 

target of significantly improving the specific power and efficiency of the convertor and overall generator 

for Mars rovers and deep space missions. One specific approach to the target has been recognized as the 

use of appropriate high-temperature materials. As a series of ceramic material approaches in Advanced 

Stirling Convertor Development Program in fiscal year 2005, two commercial, structural silicon nitrides 

AS800 and SN282 were selected and their mechanical and life limiting properties were characterized at 

1050 °C in air. AS800 exhibited both strength and Weibull modulus greater than SN282. A life limiting 

phenomenon was apparent in AS800 with a low slow crack growth parameter n = 15; whereas, a much 

increased resistance to slow crack growth was found in SN282 with n>100. Difference in elastic modulus 

and thermal conductivity was negligible up to 1200 °C between the two silicon nitrides. The same was 

true for the coefficient of thermal expansion up to 1400 °C. 

Introduction

NASA Glenn Research Center is developing advanced technology for Stirling convertors with a goal 

of substantially improving the specific power and efficiency of the convertor and overall generator. These 

advances could provide significant performance and mass benefits for Mars rovers and deep space 

missions and could be allow the use of Stirling radioisotrope power systems for radioisotrope electric 

propulsion and Venus missions (ref. 1). Performance and mass improvement targets have been 

established and tasks are underway to fulfill these targets. One of approaches to the targets is to use 

higher-temperature materials such as superalloys, refractory metal alloys, and ceramic materials (ref. 2). 

Structural analysis of Stirling Convertor heater heads using superalloys has been made focusing on 

durability, reliability, and performance (refs. 3 and 4). Of those candidate materials, ceramics offer a 

number of significant advantages over metal counterparts including lower density, higher-temperature 

strength, more creep and life-limiting resistances, a wide range of thermal conductivities, and more 

resistance to corrosive environments. Some previous work for Stirling convertors has also shown that 

ceramic materials exhibited a better resistance to helium permeability compared to nickel-based 

superalloy IN718 (ref. 1). A schematic showing a Stirling convertor is presented in figure 1 (ref. 5). The 

heater head is a component considered to be used with potential structural ceramics. 

In the fiscal year of 2005, a new work started to evaluate mechanical properties of two commercial 

candidate silicon nitrides AS800 and SN282 in Advanced Stirling Technology Program. The major effort 

was to generate important design data including basic mechanical properties, strength, life prediction 

parameters, and some other thermal properties such as thermal conductivity and coefficient of thermal 

expansion. This paper reports the recent results on these mechanical characterizations of the two 
NASA/TM—2006-214089 2 

Alternator

Piston Heater head

Displacer

Figure 1.—Schematic of Stirling convertor showing a heater head (ref. 5). 

candidate silicon nitrides at 1050 °C that was one of target temperatures set for Advanced Stirling 

convertors. The candidate advanced structural ceramics have been used in various propulsion programs at 

NASA Glenn for gas turbine engine applications at higher temperatures 1200 to 1371 °C (refs. 6 to 10). 

Experimental Procedures 

Materials 

Materials used in this work were commercially available silicon nitrides AS800 (Honeywell, 

Torrance, California, ’99 vintage, gel-cast) and SN282 (Kyocera, Vancouver, Washington, ’00 vintage). 

These two silicon nitrides, both gas-pressure sintered, are currently considered as strong candidate 

materials for gas-turbine applications in view of their substantially improved elevated-temperature 

properties (refs. 11 to 13). Both materials are toughened silicon nitrides with microstructures tailored into 

elongated grain structures. The degree of elongation and the size of grains were greater in AS800 than 

SN282, as shown in figure 2. The billets for each material were machined into flexure test specimens 

measuring 3.0 by 4.0 by 45.0 mm, respectively, in thickness, width, and length. The final finishing was 

completed in a longitudinal direction of test specimens with a no. 500 diamond grinding wheel under the 

specified conditions in accordance with ASTM standard C1211 (ref. 14). Prior to testing, all AS800 test 

specimens were annealed at 1200 °C in air for 2 hr to eliminate or minimize damage and/or residual 

stresses presumably associated with machining. All SN282 test specimens were annealed by the 

manufacturer prior to testing with proprietary annealing condition. 

Basic Mechanical and Physical Properties 

Basic ambient-temperature mechanical and physical properties including uniaxial and biaxial flexure 

strength, elastic modulus, Poisson’s ratio, density, Vickers hardness, fracture toughness, and R-curve 

have been determined from other programs. These basic properties and test methods related will be 

briefly described in the Results and Discussion section. 

Flexure Strength Testing 

Strength testing for both AS800 and SN282 flexure test specimens was performed at 1050 °C in air 

using a SiC four-point flexure fixture with 20-mm inner and 40-mm outer spans in accordance with 

ASTM C 1211 (ref. 14). An electromechanical test frame (Model 8562, Instron, Canton, Massachusetts) 

was used in load control with a load rate of 60 N/s which corresponds to a stress rate of 50 MPa/s. Each 

test specimen was held for about 20 min at 1050 °C for thermal equilibration before testing. A total of 

20 test specimens were tested for each material. A limited fractographic analysis was performed after 

strength testing to determine failure origin and flaw configuration, etc. 
NASA/TM—2006-214089 3 

(a) AS800 (b) SN282

Figure 2.—Microstructures of AS800 and SN282 silicon nitrides used in this work. 

Dynamic Fatigue (Life Prediction; Life Assessment) Testing 

Slow crack growth (SCG) behavior of brittle materials can be determined using dynamic fatigue (or 

called constant stress-rate) testing under a given environment/temperature condition. This test method, as 

specified in ASTM C 1368 (ref. 15) or C 1465 (ref. 16), determines flexure strengths with several 

different applied test rates. From the determined strength data as a function of applied test rate, slow crack 

growth or life prediction parameters of a material can be determined using an appropriate relation. 

Dynamic fatigue testing was performed in flexure at 1050 °C in air with both AS800 and SN282 silicon 

nitrides flexure test specimens. For AS800, three different test rates of 0.05, 0.005, and 0.0005 MPa/s 

were employed in load control of the electromechanical test frame (Model 8562, Instron, Canton, 

Massachusetts). A total of 20 test specimens were used at a test rate of 0.05 MPa/s while 10 test 

specimens were used at each of 0.005 and 0.0005 MPa/s. For SN282, two test rates of 0.05 and 

0.0005 MPa/s were used with 15 and 10 specimens at respective test rates. To save test time particularly 

at the lowest test rate of 0.0005 MPa/s in which typical time to failure was around 200 to 300 hr, a 

preload technique to accelerate testing was applied (refs. 14, 15, and 17 to 19). Preloads ranging from 

50 to 80 percent of the failure stress of the material determined at 0.0005 MPa/s were employed. Note that 

the flexure strength data obtained at 60 N/s (=50 MPa/s) from flexure strength testing were used as one 

set of the dynamic fatigue data for each material. The test specimen’s configuration and test fixture were 

the same as those used in flexure strength testing. Also, the thermal equilibration condition at dynamic 

fatigue testing was the same as that applied in flexure strength testing. Limited optical microscopy was 

conducted for fractographic analysis. 

Elastic Modulus Measurements 

Elastic modulus of both AS800 and SN282 silicon nitrides were determined as a function of 

temperature ranging from 25 to 1200 °C by the impulse excitation of vibration method, ASTM C 1259 

(ref. 20), using a flexure specimen configuration with nominal dimensions of 3 by 4 by 45 mm. Output 

information such as resonance frequency was continuously recorded as a function of temperature via data 

acquisition incorporated with an automatic excitation system (Model MK5, GrindoSonic, J.W. Lemmens, 

Belgium). The scatter in elastic modulus of these silicon nitrides was observed negligibly small, typically 

with a coefficient of variation less than 2 percent (refs. 7 and 8), so that only one specimen was used for 

each material. 
NASA/TM—2006-214089 4 

Thermal Properties: Thermal Conductivity and Coefficient of Thermal Expansion 

Thermal conductivity of both AS800 and SN282 silicon nitrides was determined at temperatures 

ranging from 300 to 1200 °C using a diffusion-cooled 3.5 kW CO2 laser high-heat flux rig (Type DC 035, 

Rofin, Hamburg, Germany). A disk specimen configuration was utilized, measuring 45 mm in diameter and 

2 mm in thickness. The specimen surface heating was provided by the laser beam and the back-side air 

cooling was used to maintain desired specimen temperatures. A uniform laser power distribution was 

achieved over 24 mm diameter aperture region of the specimen by using an integrating ZnSe lens combined 

with specimen rotation. The test rig systems and general procedures for the thermal conductivity 

measurements have been described elsewhere (ref. 21). Thermal conductivity was determined from the 

pass-through heat flux and the measured temperature gradient through the specimen thickness under the 

steady-state laser heating conditions using a one-dimensional heat transfer model (ref. 21). 

Thermal expansion experiments to determine the coefficient of thermal expansion (CTE) of two 

silicon nitrides were conducted using a dilatometer system (UNITHERM, ANTER Corp., Pittsburgh, 

Pennsylvania) in air at temperatures ranging from 25 to 1400 °C. The nominal dimensions of flexure test 

specimen were 3 by 4 by 25 mm (length). Longitudinal displacement of the specimen was continuously 

recorded during the heating/cooling cycle through a data acquisition system combined with an LVDT and 

temperature measuring devices (ref. 22). 

Results and Discussion 

Basic Mechanical and Physical Properties 

Basic ambient-temperature mechanical and physical properties of both AS800 and SN282 silicon 

nitrides such as elastic modulus, Poisson’s ratio, density, Vickers hardness, flexure (uniaxial and biaxial) 

strength, fracture toughness, and R-curve have been determined previously and are summarized in table 1 

together with test methods used. Note that the R-curve for both silicon nitrides was estimated by the 

indentation technique (ref. 26) and can be expressed (ref. 27) 

q KR = k [a] (1) 

where KR is fracture resistance (MPa m1/2), a is crack size (μm), and k and q are R-curve parameters. The 

values of k and q are listed in table 1. 

TABLE 1.—BASIC MECHANICAL AND PHYSICAL PROPERTIES OF AS800 AND SN282 SILICON NITRIDES AT 

AMBIENT TEMPERATURE (REFS. 7 AND 9) 

Flexure Strength4 R-curve 

Parameters6

Material 

Elastic 

modulus1

E (GPa)

Poisson’s 

ratio1

ν

Density2

ρ

(g/cm3

) 

Hardness3

H (GPa) Type of 

loading 

Mean 

strength 

(MPa)

Weibull 

modulus 

Characteristic 

strength 

(MPa) 

Fracture 

toughness5 

KIc

(MPa√m) k q 

AS800 Uniaxial 775(45) 21 795 

 Si3N4

309 0.27 3.27 13.6(1.4) Biaxial 678(45) 18 698 8.1(0.3) 3.02 0.13 

SN282 Uniaxial 595(64) 11 623 

 Si3N4

304 0.28 3.32 15.3 (0.2) Biaxial 426(60) 8 451 5.5(0.2) 2.56 0.10 

Notes: 

1. By the impulse excitation technique, ASTM C 1259 (ref. 20) 

2. By mass/volume method 

3. By Vickers microhardness indentation, ASTM C 1327 (ref. 23) 

4. Uniaxial testing: by four-point flexure with 20/40 mm spans with 3 by 4 by 45 mm bars, ASTM C 1161 (ref. 24) 

(Number of test specimens used: 20 for each material). Biaxial testing: by ring-on-ring configuration with 20/40 mm 

rings with 2-mm-thick and 45-mm-diameter disks (Number of test specimens used: 10 for AS800 and 21 for SN282). 

5. By single-edge-precracked-beam (SEPB) method, ASTM C 1421 (ref. 25). 

6. See the text for descriptions. 

The numbers in the parentheses indicate ±1.0 standard deviations. 
NASA/TM—2006-214089 5 

Flexure Strength 

The two-parameter Weibull plots of flexure strength of both AS800 and SN282 silicon nitrides 

determined at 1050 °C in air are shown in figure 3, where lnln[1/(1-F)] was plotted as a function of lnσf

with F and σf being failure probability and flexure strength, respectively. Weibull modulus m and 

characteristic strength σθ were m = 25 and σθ = 611 MPa for AS800. For SN282, m = 14 and 

σθ = 515 MPa. The mean strength was 598±28 MPa for AS800 and 496±43 MPa for SN282. The Weibull 

modulus for AS800 and SN282 (m = 25 and 14, respectively) at 1050 °C compares well with the values 

determined at ambient temperature (m = 18 to 21 and 8 to 11, respectively, see table 1) and at 1316 °C 

(m = 24 and 12, respectively) for AS800 and SN282 (ref. 28), all with the similar number ( = 20) of test 

specimens used at each test temperature. Failure origins of both silicon nitrides, in many cases, were 

associated with surface-related defects such as machining flaws, pores, and elongated grains. Typical 

examples of fracture surfaces are shown in figure 4. 

Figure 5 shows a summary of mean flexure strength as function of test temperature, combined with 

the previously determined strength data at different temperatures (refs. 6, 7, and 28). A general trend was 

observed for SN282 such that strength decreased monotonically with increasing temperature, as observed 

in many advanced ceramics. By contrast, AS800 exhibited a strength drop at 1050 °C, deviating from the 

trend in strength with regard to temperature. The reason is not clear yet; however, it is speculated that 

intermediate-temperature oxidation might have caused such a strength drop for AS800. It has been 

reported that intermediate-temperature oxidation around 700 to 1100 °C was responsible for both strength 

degradation and enhanced slow crack growth for some silicon nitride ceramics (ref. 29). 

ln [strength], ln [MPa]

5.6 5.8 6.0 6.2 6.4 6.6 6.8

lnln[1/(1-F)]

-5

-4

-3

-2

-1

0

1

2

m=14

m=25

σθ=611 MPa σθ=515 MPa

SN282 AS800

Flexure/1050o

C

Figure 3.—Weibull distributions of flexure strength determined at 

1050 °C in air for AS800 and SN282 silicon nitrides. m = Weibull 

modulus, σθ = characteristic strength and F = failure probability. 
NASA/TM—2006-214089 6 

(a) AS800 (b) SN282 

Figure 4.—Typical fracture surfaces of specimens tested at 50 MPa/s in flexure at 1050 °C in 

air: (a) AS800 and (b) SN282 silicon nitrides. Volume flaws located to the top surfaces were 

responsible for failure, with flaw origins indicated with arrows. Bars in 500 μm. 

Temperature, T [oC]

0 200 400 600 800 1000 1200 1400 1600

Flexure strength, 

σf [MPa]

0

200

400

600

800

1000

AS800

SN282

Flexure/Air

Figure 5.—Summary of flexure strength as a function of temperature for 

AS800 and SN282 silicon nitrides tested in air. Data, except for 

1050 °C, quoted from previous work (refs. 6, 7, and 28). 
NASA/TM—2006-214089 7 

Dynamic Fatigue 

Result of dynamic fatigue testing for AS800and SN282 silicon nitrides at 1050 °C in air are shown in 

figure 6, where flexure strength was plotted as a function of applied stress rate. For AS800, between 

applied stresses of 50 and 0.05 MPa/s, there was little strength degradation. However, at applied stress 

rates ≤0.05 MPa/s, strength degradation took place with further decreasing applied stress rate, showing a 

susceptibility to slow crack growth. By contrast, no appreciable strength degradation occurred for SN282, 

indicative of significant resistance to slow crack growth. 

Stress rate, [MPa/s]

10-5 10-4 10-3 10-2 10-1 100 101 102 103

Fracture stress, 

σf [MPa]

200

300

400

500

600

700

800

900

1000

n =15

n =168

AS800 Si3N4

Flexure/1050oC

σ

(a) AS800 silicon nitride 

Stress rate, [MPa/s]

10-5 10-4 10-3 10-2 10-1 100 101 102 103

Fracture stress, 

σf [MPa]

200

300

400

500

600

700

800

900

1000

n >200

SN282 Si3N4

Flexure/1050oC

σ

(b) SN282 silicon nitride 

Figure 6.—Summary of flexure strength as a function of applied stress 

rate, determined for AS800 and SN282 silicon nitrides in dynamic 

fatigue testing in flexure at 1050 °C in air. Slow crack growth 

parameter n is shown for each material. 
NASA/TM—2006-214089 8 

Weibull distributions of strength determined at different stress rates are shown in figure 7. Weibull 

modulus ranged from m = 14 to 26 for AS800 with a somewhat decrease at lower applied stress rates 

σ ≤0.005 MPa/s. Weibull modulus for SN282 ranged from m = 14 to 18, almost independent of test rate. 

Figure 8 shows typical fracture surfaces of AS800 specimens tested at 0.05 and 0.0005 MPa/s. At 

0.05 MPa/s, a region of fracture mirror including fracture origin was well defined; whereas, at 

0.0005 MPa/s, the fracture mirror region became significant, indicating the occurrence of extensive slow 

crack growth. No noticeable evidence of slow crack growth was observed from fracture surfaces of 

SN282 specimens tested at the lowest test rate of 0.0005 MPa/s. If a ceramic flexure specimen is 

susceptible to 

ln [strength], ln [MPa]

5.6 5.8 6.0 6.2 6.4 6.6 6.8

lnln[1/(1-F)]

-5

-4

-3

-2

-1

0

1

2

AS800

Flexure/1050o

C

0.0005 MPa/s 0.005 MPa/s

0.05 MPa/s

50 MPa/s

(a) AS800 silicon nitride 

ln [strength], ln [MPa]

5.8 6.0 6.2 6.4 6.6

lnln[1/(1-F)]

-5

-4

-3

-2

-1

0

1

2

SN282

Flexure/1050o

C

0.0005 MPa/s

50 MPa/s 0.05 MPa/s

(b) SN282 silicon nitride 

Figure 7.—Weibull distributions of flexure strength determined for 

AS800 and SN282 silicon nitrides in dynamic fatigue testing at 

1050 °C in air. 
NASA/TM—2006-214089 9 

(a) Tested at 0.05 MPa/s 

 

(b) Tested at 0.0005 MPa/s 

Figure 8.—Typical examples of fracture surfaces of specimens tested at 0.005 (a) and 0.0005 MPa/s 

(b) in dynamic fatigue testing for AS800 silicon nitride at 1050 °C in air. Bars in 500 μm. 

creep at elevated temperatures, creep deformation is typically observable at low stress rates 

≤0.05 MPa/s during testing (from load-time or displacement-time curve) or from the curvature of 

specimens tested. However, no noticeable creep deformation was observed for both AS800and SN282 

during testing or from specimens tested, indicating that creep was not an issue for the material at this 

temperature. In fact, creep of many advanced structural silicon nitrides has been known to be negligible 

below 1200 °C. Hence, slow crack growth can be a major consideration factor for AS800 than creep as 

far as component reliability/life is concerned. 

The basic formulation of slow crack growth (SCG) for advanced monolithic and composite 

(reinforced with particulates, platelets or whiskers) ceramics at elevated temperatures follows an 

empirical power-law form 

n v A KI KIc = [ / ] (2) 

where v, KI, and KIc are crack velocity, mode I stress intensity factor, and mode I fracture toughness, 

respectively. A and n are material/environment dependent SCG parameters. In case of dynamic fatigue 

loading, a constant stress rate ( σ ) is applied to a test specimen until the test specimen fails. The 

corresponding fracture strength (σf) can be derived from equation (2) as a function of applied stress rate 

( σ ) with some mathematical manipulations to give (ref. 15 and 16) 

D

n f log log 1

1 log σ +

+

σ =  (3) 

where D is another SCG parameter associated with A, n, and KIc, inert strength, and crack geometry 

factor. The SCG parameters n and D can be determined from the slope and intercept by a linear regression 

analysis when log (fracture strength) is plotted as a function of log (applied stress rate). Equation (3) is 

the basis commonly used in dynamic fatigue testing, which has been adopted to determine SCG or life 

prediction parameters of advanced ceramics in ASTM test standards at both ambient and elevated 

temperatures (refs. 15 and 16). 

The results shown in figure 6 were plotted according to equation (3) with units of MPa for σf and 

MPa/s for σ . For AS800, SCG parameters were found to be n = 15 and D = 699 between σ = 0.05 and 

0.0005 MPa/s, whereas n = 168 and D = 585 between σ = 50 and 0.05 MPa/s. Particularly, an enhanced 

susceptibility to SCG with a low SCG parameter n = 15 was noted at the region of lower applied stress 

rates, which would affect significantly a long term life/reliability of components made out of the material. 
NASA/TM—2006-214089 10

The inferior resistance to SCG at 1050 °C may be attributed to intermediate-temperature oxidation, as 

also observed from the strength test results (see fig. 5) and from other silicon nitride ceramics (ref. 29). 

More detailed microstructural analysis using SEM, TEM or any appropriate means is required to reveal 

the exact cause of enhanced SCG behavior of AS800 at 1050 °C. For SN282, SCG parameters were 

n = 16750 and D = 493. It is generally categorized that significant SCG occurred for n<30, intermediate 

SCG for 30<n<70, and insignificant SCG for n>70. Hence, virtually no slow crack growth occurred for 

SN282. 

A simplified life prediction diagram, stress rupture, can give a better interpretation of life prediction 

of brittle materials, which was constructed in figure 9 using the same geometrical and dimensional 

configurations of test specimens that were employed in dynamic fatigue testing. The prediction was made 

based on SCG and strength parameters estimated for AS800 and SN282 as a function of applied stress (σ) 

using a relation e.g., (ref. 30) 

t = f (m,σ ,n,D,F,σ) f i (4) 

where tf is life, F is the failure probability, and σi is the inert strength. Note that a new SCG parameter of 

n = 150, instead of n = 16750, was used for SN282 for the sake of a more realistic, conservative 

estimation of life. The prediction made in figure 9 is valid when the same failure mechanism is operative, 

irrespective of loading condition, either dynamic fatigue or constant stress (stress rupture). For simplicity, 

a failure probability of approximately F = 50 percent was used for both silicon nitrides. Of course, 

different levels of failure probability can be also incorporated. As can be seen from the figure, two 

different regions of life exist for AS800 because of a transition in the dynamic fatigue behavior shown in 

figure 6. Therefore, a significant drop in life for AS800 is expected to occur at lower applied stresses. 

This result prompts an initiation of stress rupture testing to verify the life prediction made based on this 

dynamic fatigue data. By contrast, as expected, SN282 exhibited a significant resistance to SCG, a very 

desirable feature of structural components. A detailed life prediction and reliability of ceramic Stirling 

convertor heater head components can be made using finite element modeling and an appropriate 

reliability tool such as the CARES/Life integrated computer code (ref. 31). Furthermore, accurate 

evaluation of applied mechanical/thermal stresses acting on the component in service must be exercised in 

order to better predict the resulting component reliability/life. 

n =168

Time to failure, tf [s]

100 101 102 103 104 105 106 107 108 109

Applied stress, 

σ [MPa]

200

300

400

500

600

700

800

900

1000

n =15

n =168

AS800

Flexure/1050o

C

n =150

SN282

Figure 9.—Simplified life prediction diagram, converted from the 

dynamic fatigue data for AS800 and SN282 silicon nitrides at 

1050 °C in air. 
NASA/TM—2006-214089 11

As mentioned in the Experimental Procedures section, preloads were applied to save test time at the 

lowest test rate of 0.0005 MPa/s in which most (≈ 80 percent) test times in dynamic fatigue testing are 

consumed. An analytical solution of fracture stress as a function of preload has been made and verified 

for many brittle materials at ambient or elevated temperatures (refs. 17 to 19). The resulting solution of 

fracture stress is expressed as 

( ) 1

1

* 1 1 + + σ = + αn n p (5) 

where *σ is the normalized fracture stress, in which the fracture stress with preload is normalized with 

respect to the fracture stress without preload, α p is preloading factor (0≤ α p ≤1), in which the applied 

preload stress is normalized with respect to the fracture stress without preload. Results of fracture stress 

as a function of preload, applied at 0.0005 MPa/s for AS800 and SN282, are depicted in figure 10. Also 

included is the theoretical prediction based on equation (5) together with values of n = 15 and 150, 

respectively for AS800 and SN282. There seems to exist a discrepancy or a good agreement between the 

data and the theory for AS800 and SN282. This is due to the fact that reliable strength data without 

preload were not obtained for both materials since only one test specimen was tested for each material 

without preload. Of course, more test specimens without preload are required. Nonetheless, the strength 

data with preload are believed reliable and accurate and can be regarded as representing values at 

0.0005 MPa/s, based on our long experience on this technique for various brittle materials. The important 

thing for this technique is that 50 to 80 percent saving of test time was achieved without changing 

inherent strength values. Note again that at the lowest stress rate the normal test time for one specimen 

without preload was approximately 200 to 300 hr (10 days). 

Elastic Modulus

Results of elastic modulus as a function of temperature for both AS800 and SN282 silicon nitrides are 

shown in figure 11. Elastic modulus of both materials decreased monotonically and linearly up to 

1200 °C. The values of elastic modulus at ambient temperature, 310 and 304 GPa for AS800 and SN282, 

respectively, are in an excellent agreement with those (309 and 304 GPa, respectively; see table 1) 

determined independently by using a different excitation/acoustic system (Type 2669, Brüel & Kjær, 

Denmark). The data in figure 11 can be formulated via a regression analysis as 

E = −0.013T + 310 for AS800 

(6) 

E = −0.012 T + 304 for SN282 

where E is elastic modulus in GPa and T is temperature in degree Celsius (°C). The correlation coefficient 

of regression was r

2

coef>0.996 for both curves. Elastic modulus degradation from 25 to 1200 °C was about 

5 percent for both AS800 and SN200. This negligible degradation in elastic modulus with regard to 

temperature is typical of many silicon nitrides (refs. 32 and 33). As a consequence, both shear modulus 

and Poisson’s ratio at ambient temperature are expected to remain almost unchanged up to 1200 °C as 

well. Also note that no appreciable difference in elastic modulus was found between the two materials in 

the temperature range studied. 
NASA/TM—2006-214089 12

Preload, αp [%]

0 20 40 60 80 100

Normalized fracture stress, 

σf

*

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

( =0.0005 MPa/s)

AS800 Si3N4

Flexure/1050oC

σ

Theoretical

(a) AS800 silicon nitride 

Preload, αp [%]

0 20 40 60 80 100

Normalized fracture stress, 

σf

*

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

( =0.0005 MPa/s)

SN282 Si3N4

Flexure/1050oC

σ

Theoretical

(b) SN282 silicon nitride

Figure 10.—Normalized fracture stress as a function of preload for 

AS800 and SN282 silicon nitrides in dynamic fatigue testing at 

1050 °C in air at the lowest stress rate of 0.0005 MPa/s. The 

theoretical prediction based on equation (5) is also presented. 
NASA/TM—2006-214089 13

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

0 200 400 600 800 1000 1200 1400

Temperature (C)

Youngs Modulus (Gpa)

(a) AS800 

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

0 200 400 600 800 1000 1200 1400

Temperature (C)

Youngs Modulus (Gpa)

(b) SN282 

Figure 11.—Elastic modulus as a function of temperature 

determined by the impulse excitation of vibration 

method (ref. 20): (a) AS800 and (b) SN282 silicon 

nitrides. 

Thermal Conductivity and Coefficient of Thermal Expansion 

Results of thermal conductivity measurements for both AS800 and SN282 silicon nitrides are 

summarized in figure 12, where thermal conductivity was plotted against temperature up to 1200 °C. Due 

to some limitations at lower temperatures inherent in the laser test methodology, it is suggested to utilize 

the data above 600 °C as valid ones. No difference in thermal conductivity between the two silicon 

nitrides was observed. 

Coefficient of thermal expansion (CTE) as a function of temperature is summarized for both silicon 

nitrides in figure 13. Thermal expansion data for each material are also included. The value of CTE for 

both materials increased from 2.5 to 4.6×10–6 mm/mm (by 80 percent) when temperature increased from 

200 to 1200 °C. Like elastic modulus and thermal conductivity, there was little difference in CTE for a 

given temperature between two materials, both lying in CTE = 2.5 to 4.6×10–6 mm/mm within the 

temperature range investigated. 
NASA/TM—2006-214089 14

Figure 12.—Thermal conductivity as a function of 

temperature determined by a laser high heat-flux method 

for AS800 and SN282 silicon nitrides. 

Figure 13.—Coefficient of thermal expansion (CTE) as a function 

of temperature determined by a dilatometer for AS800 and 

SN282 silicon nitrides. Thermal expansion data are also included. 

Implications 

AS800 silicon nitride exhibited better mechanical properties in fracture toughness and strength at 

ambient temperature than SN282 counterpart. For example, fracture toughness and flexure strength of 

AS800 are greater by 50 percent and 30 to 60 percent, respectively, as compared with those of SN282. 

The same is true for Weibull modulus and R-curve. Furthermore, fast-fracture strength (with no presence 

of slow crack growth) and Weibull modulus at elevated temperatures are greater for AS800 than for 

SN282. In terms of ambient-temperature mechanical properties and elevated-temperature fast-fracture 

strength, a preferable choice as a candidate structural material for a Stirling convertor heater head would 

be AS800 if one does not consider a life limiting phenomenon of the material at elevated temperatures. As 

seen from the results of this study (see figs. 6 and 9), however, the life limiting phenomenon was apparent 

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0

2.0

4.0

6.0

8.0

10.0

0 500 1000 1500

AS800

SN282

Average CTE-AS800

Average CTE-SN282

Thermal expansion, %

Average coefficient of thermal expansion

(CTE), ppm

Temperature, °C

CTE 

Thermal 

expansion 

0

20

40

60

80

100

200 400 600 800 1000 1200

SN 282

AS 800

Thermal conductivity, W/m-K

Temperature, °C
NASA/TM—2006-214089 15

Figure 14.—Stress rupture results of AS800 and SN282 

silicon nitrides tested at 1371 °C in air in flexure (ref. 28). 

for AS800 even at an intermediate temperature of 1050 °C in air. At temperatures ≥1316 °C in air, 

resistance to creep, slow crack growth, and environmental degradation (oxidation) has been observed all 

greater for SN282 than for AS800. One example of stress rupture of AS800 and SN282 previously 

determined at 1371 °C in air is depicted in figure 14, which shows a significant susceptibility to slow 

crack growth (or short long-term lives) for SN282, as compared with SN282 counterpart (ref. 28). More 

work is required in order to characterize life limiting properties of both AS800 and SN282 in different 

loading (stress rupture, flexure, tension, etc) and environmental (air, helium, vacuum, etc.) conditions. In 

addition, efforts to perform structural reliability/life prediction analysis together with non-destructive 

evaluation (NDE) are also required. 

Future Work 

Future work regarding materials’ characterization and basic component design may include following 

items: 

• Fractogractic analysis 

• Life assessment: stress rupture and creep for AS800 and SN282 

• Environmental effects (air, helium, vacuum) on life/durability 

• Non-destructive evaluation (NDE) of materials/components 

• Reliability/life prediction of prospective structural ceramic components using an appropriate 

integrated design code (CARES/life) 

Summary 

Strength and life assessment testing for two commercial silicon nitrides AS800 and SN282 were 

conducted at 1050 °C in air. Flexure strength and Weibull modulus of AS800 were greater than those of 

SN282. Susceptibility to slow crack growth that controls life of structural components was apparent for 

AS800 with a relatively low life prediction parameter n = 15, while SN282 exhibited a much increased 

resistance to life limiting phenomenon. No appreciable difference in elastic modulus or thermal 

TIME TO FAILURE, t

f [s]

100 101 102 103 104 105 106 107 108

APPLIED STRESS, 

σ [MPa]

200

300

400

500

600

700

800

900

100

1000

AS800

SN282

1371oC/air 1371 °C/air 
NASA/TM—2006-214089 16

conductivity was observed between the two silicon nitrides up to 1200 °C. The same was true for 

coefficient of thermal expansion up to 1400 °C. Although AS800 exhibited greater fast-fracture strength, 

higher fracture toughness, rising R-curve, and better Weibull modulus, it did not provide a guaranteed 

resistance to slow crack growth at 1050 °C. More testing and analysis are required to better understand 

materials’ life limiting behavior in different environments and thus to generate a reliable design database 

for Stirling convertor heater head applications. 

References 

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Gas Turbines,” Ceram. Eng. Sci. Proc., 22[3] 159–166 (2001). 

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Nitride,” Ceram. Eng. Sci. Proc., 22[3] 167–174 (2001). 

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AS800 Silicon Nitride from As-Processed Surface Regions,” Ceram. Eng. Sci. Proc., 22[3] 175–

182 (2001). 

14. ASTM C 1211, “Test Method for Flexural Strength of Advanced Ceramics at Elevated 

Temperatures,” Annual Book of ASTM Standards, Vol. 15.01, American Society for Testing & 

Materials, West Conshohocken, PA (2005). 
NASA/TM—2006-214089 17

15. ASTM C 1368, “Standard Test Method for Determination of Slow Crack Growth Parameters of 

Advanced Ceramics by Constant Stress-Rate Flexural Testing at Ambient Temperature,” Annual 

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Conshohocken, PA (2005). 

16. ASTM C 1465, “Standard Test Method for Determination of Slow Crack Growth Parameters of 

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Conshohocken, PA (2005). 

17. S.R. Choi and J.P. Gyekenyesi, “Fatigue Strength as a Function of Preloading in Dynamic Fatigue 

Testing of Glass and Ceramics,” Trans. of ASME, J. Eng. Gas Turbines & Power, 119 493–499 

(1997). 

18. S.R. Choi and J.A. Salem, “Preloading Technique in Dynamic Fatigue Testing of Glass and 

Ceramics with an Indentation Flaw System,” J. Am. Ceram. Soc., 79[5] 1228–1232 (1996). 

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Methodology in Constant Stress-Rate Testing for Advanced Structural Ceramics—A Preloading 

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New Orleans, Louisiana (2001). 

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22. D. Zhu and R.A. Miller, “Sintering and Creep Behavior of Plasma-Sprayed Zirconia-and HafniaBased Thermal Barrier Coatings,” Surf. Coat. Technol., 108–109 114–120 (1998). 

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versus SEVNB Methods,” Proceedings of the 11th International Conference on Fracture (ICF XI), 

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Ceramics—SEPB versus SEVNB Method,” NASA/TM—2006-214090, National Aeronautics and 

Space Administration, Glenn Research Center, Cleveland, OH (2006). 

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NASA/TM—2006-214089 18

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This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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24

Assessments of Mechanical and Life Limiting Properties of Two Candidate

Silicon Nitrides for Stirling Convertor Heater Head Applications

Sung R. Choi and David L. Krause

Advanced ceramics; High temperature mechanical properties; Life prediction;

Stirling engine

Unclassified -Unlimited

Subject Category: 07

Sung R. Choi, University of Toledo, 2801 W. Bancroft St., Toledo, Ohio 43606; and David L. Krause, NASA Glenn

Research Center. Responsible person, Sung R. Choi, organization code RXL, 216–433–8366.

NASA Glenn Research Center is developing advanced technology for Stirling convertors with a target of significantly

improving the specific power and efficiency of the convertor and overall generator for Mars rovers and deep space

missions. One specific approach to the target has been recognized as the use of appropriate high-temperature materials.

As a series of ceramic material approaches in Advanced Stirling Convertor Development Program in fiscal year 2005,

two commercial, structural silicon nitrides AS800 (Honeywell, Torrence, California) and SN282 (Kyocera, Vancouver,

Washington) were selected and their mechanical and life limiting properties were characterized at 1050 °C in air.

AS800 exhibited both strength and Weibull modulus greater than SN282. A life limiting phenomenon was apparent in

AS800 with a low slow crack growth parameter n = 15; whereas, a much increased resistance to slow crack growth

was found in SN282 with n>100. Difference in elastic modulus and thermal conductivity was negligible up to 1200 °C

between the two silicon nitrides. The same was true for the coefficient of thermal expansion up to 1400 °C.