Sung R. Choi

University of Toledo, Toledo, Ohio

John P. Gyekenyesi

Glenn Research Center, Cleveland, Ohio

Assessments of Fracture Toughness

of Monolithic Ceramics—SEPB Versus

SEVNB Methods

NASA/TM—2006-214090

January 2006
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Sung R. Choi

University of Toledo, Toledo, Ohio

John P. Gyekenyesi

Glenn Research Center, Cleveland, Ohio

Assessments of Fracture Toughness

of Monolithic Ceramics—SEPB Versus

SEVNB Methods

NASA/TM—2006-214090

January 2006

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

11th International Conference on Fracture

cosponsored by ICF, ESIS, and ASTM

Turin, Italy, March 20–25, 2005
Acknowledgments

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(UEET), NASA Glenn Research Center, Cleveland, Ohio.

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NASA/TM—2006-214090 1

Assessments of Fracture Toughness of Monolithic 

Ceramics—SEPB Versus SEVNB Methods 

Sung R. Choi

University of Toledo 

Toledo, Ohio 43606 

John P. Gyekenyesi 

National Aeronautics and Space Administration 

Cleveland, Ohio 44135 

Abstract 

Fracture toughness of a total of 13 advanced monolithic ceramics including silicon 

nitrides, silicon carbide, aluminas, and glass ceramic was determined at ambient 

temperature by using both single edge precracked beam (SEPB) and single edge v-notched 

beam (SEVNB) methods. Relatively good agreement in fracture toughness between the 

two methods was observed for advanced ceramics with flat R-curves; whereas, poor 

agreement in fracture toughness was seen for materials with rising R-curves. The 

discrepancy in fracture toughness between the two methods was due to stable crack growth 

with crack closure forces acting in the wake region of cracks even in SEVNB test 

specimens. The effect of discrepancy in fracture toughness was analyzed in terms of 

microstructural feature (grain size and shape), toughening exponent in R-curve, and stable 

crack growth determined using back-face strain gaging. 

1. Introduction 

There are several methods to determine fracture toughness of brittle materials such as 

glasses, glass ceramics, and advanced monolithic ceramics. These includes indentation 

techniques such as indentation fracture (IF) (ref. 1), indentation strength (IS) (ref. 2), 

surface crack in flexure (SCF) (ref. 3), chevron notch technique (ref. 3), single edge 

precracked beam (SEPB) technique (ref. 3), and single edge v-notched beam (SEVNB) 

technique (ref. 4). Both indentation fracture (IF) and indentation strength (IS) methods are 

based on the empirical calibration constants to determine fracture toughness; hence, they 

are less rigorous theoretically from a fracture-mechanics perspective than the other 

methods. 

The SEVNB technique (ref. 4) has been introduced recently, in which a final sharp vnotch with its radius ranging from 10 to 20 μm was introduced by polishing a pre-notched 

section with razor blade in conjunction with diamond paste. This technique has shown to 

be in good agreement with other techniques. A previous round robin on fracture toughness 

(ref. 4) was dedicated to use the SEVNB method to determine fracture toughness of five 
NASA/TM—2006-214090 2

Figure 1.—A typical example of a sharp v-notch 

produced in a SEVNB silicon nitride test 

specimen. 

different ceramic materials. It was shown that certain ceramics exhibited significant 

difference in fracture toughness between the SEVNB and SEPB methods: the SEVNB 

estimated lower fracture toughness than the SEPB. The plausible reason for this 

discrepancy was presumed to be attributed to R-curve behavior of the materials. 

This study, as motivated from the previous round robin, determined fracture toughness 

of a total of 13 advanced ceramics using both SEVNB and SEPB methods. The difference 

in fracture toughness between the two methods was carefully analyzed based on R-curve 

estimations and back-face strain measurements. The effect of major microstructural feature 

- grain size and its shape - was also taken into account. 

2. Experimental Techniques 

Flexure test specimens typically measuring b = 3.0 mm, W = 4.0mm, and L (length) = 

25 or 50 mm, were used in fracture toughness testing at room temperature in air. In the 

SEVNB method, a razor blade with diamond paste with grain size of 1 μm was used to 

generate a final sharp notch with a root radius ranging from 10 to 20 μm by tapering a saw 

notch (ref. 4). The final notch depth thus produced ranged from 1.0 to 2.0 mm. A typical 

example of a SEVNB test specimen thus v-notched is presented in figure 1. In the SEPB 

method (ref. 3), a starting indent crack was placed at the center of the 3.0 mm side of each 

test specimen. The indented test specimen was then placed onto a specially designed 

precracking fixture and then loaded via a test frame until the indent crack popped-in to 

form a sharp through-the-thickness precrack (refs. 3 and 5). The precrack size was 

typically around 2 mm. 

300μm
NASA/TM—2006-214090 3

A four-point flexure fixture with 20 (or 10) mm-inner and 40 (or 20) mm-outer spans 

was used to determine fracture load. A test rate of 0.5 mm/min was used via an 

electromechanical test frame (Model 8562, Instron) with a load cell with a capacity of 

1000 N. Crack sizes were optically determined from fracture surfaces of tested specimens. 

Typically, five test specimens were used for each material in each test method. Fracture 

toughness was calculated based on the formula by Srawley and Gross (ref. 6). Load versus 

back-face strain curves were also determined for some ceramics to better understand stable 

crack propagation. R-curve of each material was estimated using an indentation technique 

(ref. 7). A total of 13 advanced ceramics and glass ceramic were used: seven silicon 

nitrides (NC132, AS800 (’94), SN282, N3208, AS800 (’99), NCX34, and NKK), one 

silicon carbide (α-SiC; Hexoloy), four aluminas (AD998 (Coors), AD998 (VAMAS) 

(ref. 4), AD999 (VAMAS) (ref. 4), and 96% alumina), and one glass ceramic (Pyroceram 

9606). Many properties of these materials including strength and slow crack growth at 

elevated temperatures have been evaluated previously by the authors and others 

(refs. 8 and 13). Some properties such as density, elastic 1modulus and flexure strength at 

ambient temperature, together with fracture toughness values by SEPB and SEVNB 

methods determined in this work, are summarized in table 1. 

TABLE 1.—PROPERTIES AND FRACTURE TOUGHNESS OF 

CERAMIC MATERIAL USED IN THIS WORK 

Fracture toughness, 

KIc (MPa m1/2 Material ) a

Density 

(g/cm3) 

Elastic 

modulus, 

E (GPa) 

Flexure 

strengthc

(MPa) By SEPB By SEVNB 

NC132 Si3N4 (ref. 8) 

α-SiC (Hexoloy) (ref. 8) 

AS800 Si3N4 (’94) (ref. 8) 

SN282 Si3N4 (refs. 9 and 10) 

AD998 Al2O3 (ref. 8) 

N3208 Si3N4

b

 (ref. 4) 

Glass ceramic (Pyroceram) (ref. 11) 

AD998 Al2O3 (VAMAS)b (ref. 4) 

AS800 Si3N4 (’99) (ref. 9 and 10) 

NCX34 Si3N4 (ref. 8) 

NKK Si3N4 (ref. 12) 

96% Al2O3 (ref. 8) 

AD999 Al2O3 (VAMAS)b

 (ref. 4) 

3.20 

3.13 

3.27 

3.32 

3.85 

3.19 

2.59 

3.86 

3.27 

3.37 

3.26 

3.67 

3.97 

315 

415 

308 

304 

372 

297 

122 

386 

309 

296 

307 

309 

386 

1018(35) 

335(35) 

778(39) 

595(64) 

303(7) 

951(74) 

303(7) 

342 

775(45) 

805(50) 

774(38) 

344(15) 

350 

4.6(0.4) 

2.4(0.1) 

7.2(0.2) 

5.5(0.2) 

4.6(0.4) 

5.3(0.1) 

2.3(0.1) 

4.4(0.1) 

8.1(0.3) 

6.9(0.6) 

10.2(0.7) 

3.4(0.1) 

3.5(0.2) 

4.3(0.1) 

2.5(0.1) 

6.5(0.3) 

4.5(0.2) 

3.4(0.1) 

5.2(0.3) 

2.4(0.1) 

3.6(0.1) 

6.7(0.1) 

4.3(0.2) 

7.4 

3.1(0.1) 

3.6(0.2) a NC132, Norton Advanced Ceramics, Northboro, MA; α-SiC (Hexoloy), Saint-Gobain Advanced Ceramics, 

Niagara Falls, NY; AS800; Honeywell, Torrance, CA; SN282, Kyocera, Vancouver, WA; AD998, Coors, 

Golden, CO; N3208, Bayer-CFI, Germany; Pyroceram 9606, Corning, Corning, NY; AD998 (VAMAS) and 

AD999 (VAMAS), Metoxit, Switzerland; NCX34, Norton, Worcester, MA; NKK, NKK Corp., Japan; 96% 

Al2O3, General Electrical Ceramics, Laurens, SC. b Materials and their strength and density data from the VAMAS report (ref. 4). c

 Strength determined at ambient temperature in four-point flexure typically with 20 to 40 mm spans. The 

numbers in parentheses indicate ±1.0 standard deviation. 
NASA/TM—2006-214090 4

3. Results and Discussion 

Typical fracture surfaces of both SEPB and SEVNB silicon nitride specimens are 

shown in figure 2. Precracked or notched region is evident for each specimen. Note that the 

precrack front of the SEPB specimen is curved, which represents a unique feature of a popin event from a micro-indentation crack to form a precrack. A summary of fracture 

toughness of a total of 13 advanced ceramics used in this work by both SEVNB and SEPB 

methods is presented in figure 3 and table 1 as well. The figure compares the values of 

fracture toughness for each test material. As can be seen, agreement in fracture toughness 

between the two methods was good at lower fracture toughness, but poor at higher fracture 

toughness with a deviation becoming significant. This deviation can be seen more readily 

in terms of microstructural features -grain size and its shape- of test materials. Figure 4 

depicts KIc ratio [=(KIc by SEVNB)/(KIc by SEPB)] with respect to a range of grain size. 

Fine grained ceramics and glass ceramic, such as α-SiC, AD999 alumina, NC132 and 

N3208 silicon nitrides, and Pyroceram, exhibited little difference in fracture toughness 

with KIc ratio close to unity. By contrast, coarse grained and elongated grained ceramics 

exhibited consistently lower KIc ratio ranging from 0.6 to 0.9 with an average of about 0.8. 

This indicates clearly that the two methods are in good agreement for fine-grained 

materials but in poor agreement with coarse or elongated grained materials. 

It has been known that increase in fracture toughness for coarse or elongated grainstructured ceramics was due to mechanisms such as grain pullouts, grain bridging, and/or 

crack deflection, thereby generating crack closure stresses in the wake region of a crack. It 

has been also observed by the authors for a long time that these coarse and elongated 

grained ceramics revealed rising R-curve behavior with its degree depending on material. 

 

 (a) (b) 

Figure 2.—Typical fracture surfaces of silicon nitride specimens showing a precracked 

region by SEPB method (a) and a notched region by SEVNB method (b). 

Notched

Precracked region region

1 mm
NASA/TM—2006-214090 5

KIc by SEPB [MPa m1/2]

0 2 4 6 8 10 12 14

KIc by SEVNB [MPa m1/2]

0

2

4

6

8

10

12

14

1:1

NKK

AS800 ('99)

AS800('94)

NCX34

SN282

N3208

NC132

AD998

AD998 (V)

96%ALU

PYRO.

α-SiC

AD999

Figure 3.—Fracture toughness determined by SEVNB and 

SEPB methods for various ceramics. 

Range of average grain size [μm]

0 10 20 30 40

KIc ratio (KIc/SEVNB/KIc/SEPB)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Fine grain Coarse grain Elongated grain

Figure 4.—KIc ratio (=SEVNB/SEPB) with respect to range 

of grain sizes for various ceramics. 
NASA/TM—2006-214090 6

Figure 5.—A typical example of indent crack propagation in 

coarse grained NKK silicon nitride. A tortuous crack path 

with interactions such as grain bridging and pullout is noted. 

Crack size, [μm]

500 1000 1500 2000

Crack growth resistance,

K

R [MPa m1/2]

0

2

4

6

8

10

12

NKK

AS800

NC132

AD998

GLASS

Figure 6.—Crack growth resistance curves of some brittle 

materials, determined by indent techniques. 

A typical example showing a microstructural feature of a coarse and elongated grained 

NKK silicon nitride associated with tortuous indent crack propagation is shown in figure 5 

(ref. 12). Based on the authors’ experience, this material exhibited the highest value of 

fracture toughness (KIc = 10.2±0.7 MPam1/2) of monolithic ceramic materials and a rising 

R-curve as well (ref. 12). Typical examples of R-curves of some materials evaluated by the 

indentation technique (ref. 7), are shown in figure 6. Note that fine-grained NC132 silicon 

Indent

a 
NASA/TM—2006-214090 7

nitride (grain size <1 μm) and soda-lime glass showed flat R-curve behavior; whereas, 

coarse-grained AD998 alumina (grain size >10 μm) and elongated grained NKK and 

AS800 silicon nitrides (elongated grain size >20 μm) exhibited significant rising R-curves. 

The degree and size of grain elongation were greater in NKK than in AS800. The R-curve 

in figure 6 was formulated using the following expression (ref. 7) 

m KR = k[a] (1) 

where KR is crack growth resistance, a is crack size (crack extension), k is a parameter, and 

m is toughening exponent. With the estimated m parameter for each test material, KIc ratio 

was plotted as a function of m, as shown in figure 7. A clear trend can be seen from the 

figure such that KIc ratio remained close to unity for lower m values (m<0.02) but decreased 

appreciably (or dropped) at higher m values (m = 0.1 to 0.14), giving rise to a following 

approximation 

 KIc/SEVNB /KIc/SEPB ≈ –1.9 m + 1 (2) 

This, although not based on theoretical consideration, implies that the toughening exponent 

m could be an important parameter to quantify the degree of discrepancy in fracture 

toughness between the SEVNB and SEPB methods. 

Toughening exponent, m

0.00 0.05 0.10 0.15 0.20

KIc ratio (=KIc/VNB/KIc/PB)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

NCX34

AD998

96%ALU AS800('94)

NKK

SN282

α-SiC

PYRO.

N3208

AD998(V)

NC132

AS800('99)

Figure 7.—KIc ratio as a function of toughening exponent (m) 

for various ceramics. 
NASA/TM—2006-214090 8

Back face strain [microstrain]

0 200 400 600 800

Applied load, P [N]

0

20

40

60

80

100

120

140

160

180

AD998

AD999

AS800 SN

N3208 SN

SEVNB

Figure 8.—Typical examples of applied load-versus-strain 

curves, determined by back-face strain gaging. 

Typical load versus back-face strain curves of SEVNB test specimens of several 

ceramics are shown in figure 8 (Note that back-face strain was in compression but was 

expressed in tension for simplicity). Both fine-grained ceramics such as N3208 silicon 

nitride and AD998 alumina showed linearity in their load-versus-strain curves. However, 

the coarse-grained AD998 alumina and the elongated-grained AS800 silicon nitride 

exhibited nonlinearity at the region close to the final fracture, resulting in stable crack 

growth prior to instability. This stable crack growth was determined analytically in 

conjunction with the results of figure 8. The analytical solution was expressed as follows: 

1 [ ] ( , , , , ) 1/ 2 f L L b W E

d

dP o i

ε

α = − (3) 

where α = a/W with a and W being crack size and specimen depth, P is applied load, ε is 

backside strain, and the function f depends on fixture spans, and width and elastic modulus 

of test specimen. 

The crack growth resistance KR, corresponding to crack size (α) and applied load in the 

stable crack-growth region, was determined using equation (3) and the results are shown in 

figure 9. For N3208 and AD999 materials, no or negligible stable crack growth occurred. 

By contrast, AS800 material exhibited a significant stable crack growth, resulting in a 

considerable increase in fracture toughness by about 35 percent. Also, AD998 material 

resulted in fracture-toughness increase by about 25 percent. It is interesting to note from 

the figure that fracture toughness started from the values determined by the SEVNB 

method and ended up with the values determined by the SEPB method. This indicates that 

the discrepancy in fracture toughness between the two methods, particularly for coarse and 
NASA/TM—2006-214090 9

Crack extension, Δ [μm]

0 100 200 300 400

Crack growth resistance,

 KR [MPa m1/2]

0

2

4

6

8

10

SEVNB data

AS800 SN

N3208 SN

AD998(V)

AD999(V)

SEPB data

Figure 9.—Crack growth resistance curves determined by 

back-face strain gaging based on the results in figure 6. 

elongated grained ceramics, is due to the fact that the calculation of KIc in SEVNB 

specimens did not consider the stable crack growth in their final crack sizes, which is 

hardly discernable from fracture surfaces in many cases. Although this extension by sable 

crack growth is small in the order of a few hundred micrometers and the measurement 

imposes a great difficulty, the effect on fracture toughness is still significant. Stable crack 

growth occurring via grain bridging and pullouts together with crack closure stresses acting 

in the wake region is the most plausible, physical explanation for the discrepancy in 

fracture toughness between the two methods. 

4. Conclusions 

The discrepancy in fracture toughness between the SEVNB and SEPB methods was 

attributed to R-curve behavior of ceramic materials, in which stable crack growth through 

grain pullouts and/or bridging takes place, imposing crack closure forces in the wake 

region of a propagating crack even for SEVNB specimens. The discrepancy increased for 

materials with stronger rising R-curve and was quantified with a toughening exponent (m). 

It is recommended that both SEVNB and SEPB methods be used together to evaluate 

fracture toughness of any materials unknown in microstructural features and/or R-curve 

behavior. Any appropriate method to monitor stable crack growth in SEVNB specimens is 

also recommended. 

a 
NASA/TM—2006-214090 10

References 

1. P. Chantikul, G.R. Anstis, B.R. Lawn, and D.B. Marshall, “A Critical Evaluation of 

Indentation Techniques for Measuring Fracture Toughness: II. Strength method,” 

J. Am. Ceram. Soc., 64[9] 539–543 (1981). 

2. G.R. Anstis, P. Chantikul, B.R. Lawn, and D.B. Marshall, “A Critical Evaluation of 

Indentation Techniques for Measuring Fracture Toughness: I. Crack Size 

Measurements,” J. Am. Ceram. Soc., 64[9] 533–538 (1981). 

3. ASTM C 1421, “Test Methods for Determination of Fracture Toughness of Advanced 

Ceramics at Ambient Temperature,” Annual Book of ASTM Standards, Vol. 15.01,

ASTM, West Conshohocken, PA (2005). 

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Preliminary Results,” Ceram. Eng. Sci. Proc., 18[4] 155–162 (1997); (b) “Fracture 

Toughness of Ceramics Using the SEVNB Method; Round Robin,” VAMAS Report 

No. 37, EMPA, Swiss Federal Laboratories for Materials Testing & Research, 

Dübendorf, Switzerland (1999). 

5. S.R. Choi, A. Chulya, and J.A. Salem, “Analysis of Precracking Parameters for 

Ceramic Single-Edge-Precracked-Beam Specimens, pp. 73–88 in Fracture Mechanics 

of Ceramics, Vol. 10, Edited by R.C. Bradt, D.P.H. Hasselman, D. Munz, M. Sakai, 

and V. Ya. Shevchenko,” Plenum Press, New York, NY (1992). 

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Bending Forces,” pp. 559–579 in Cracks and Fracture, ASTM STP 601, American 

Society for Testing and Materials, Philadelphia. 1976. 

7. R.F. Krause, “Rising Fracture Toughness from the Bending Strength of Indented 

Alumina Beams,” J. Am. Ceram. Soc., 71[5] 338–343 (1988). 

8. S.R. Choi, J.M. Pereira, L.A. Janosik, and R.T. Bhatt, “Foreign Object Damage in 

Flexure Bars of Two Gas-Turbine Grade Silicon Nitrides,” Mat. Sci. Eng., A379 411–

419 (2004). 

9. S.R. Choi, J.M. Pereira, L.A. Janosik, and R.T. Bhatt, “Foreign Object Damage in 

Disks of Gas-Turbine Grade Silicon Nitrides by Steel Ball projectile at Ambient 

Temperature,” J. Mater. Sci., 39 6173–6182 (2004). 

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Ceramics at Elevated Temperatures: An Approach to High-Temperature ‘Inert’ 

Strength,” pp. 27–46 in Fracture Mechanics of Ceramics, Vol. 13, Edited by 

R.C. Bradt, D. Munz, M. Sakai, V. Ya. Shevchenko, and K. White, Kluwer 

Academic/Plenum Publishers, NY (2002). 

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Glass-Ceramic,” NASA/TM—2003-212487, National Aeronautics and Space 

Administration, Glenn Research Center, Cleveland, Ohio (2003). 

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Nitride,” J. Am. Ceram. Soc., 77[4] 1042–1046 (1994). 

13. S.R. Choi, various previous publications not quoted here. 
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16

Assessments of Fracture Toughness of Monolithic Ceramics—-SEPB Versus

SEVNB Methods

Sung R. Choi and John P. Gyekenyesi

Fracture toughness; Advanced monolithic ceramics; R-curve; SEPB and SEVNB methods

Unclassified -Unlimited

Subject Category: 07

Prepared for the 11th International Conference on Fracture cosponsored by ICF, ESIS, and ASTM, Turin,

Italy, March 20–25, 2005. Sung R. Choi, University of Toledo, 2801 W. Bancroft St., Toledo, Ohio 43606; and

John P. Gyekenyesi, NASA Glenn Research Center. Responsible person, Sung R. Choi, organization code RXL,

216–433–8366.

Fracture toughness of a total of 13 advanced monolithic ceramics including silicon nitrides, silicon carbide, aluminas,

and glass ceramic was determined at ambient temperature by using both single edge precracked beam (SEPB) and

single edge v-notched beam (SEVNB) methods. Relatively good agreement in fracture toughness between the two

methods was observed for advanced ceramics with flat R-curves; whereas, poor agreement in fracture toughness was

seen for materials with rising R-curves. The discrepancy in fracture toughness between the two methods was due to

stable crack growth with crack closure forces acting in the wake region of cracks even in SEVNB test specimens. The

effect of discrepancy in fracture toughness was analyzed in terms of microstructural feature (grain size and shape),

toughening exponent in R-curve, and stable crack growth determined using back-face strain gaging.