ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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17. “Standard Test Methods for the Determination of Fracture Toughness of Advanced Ceramics at

Ambient Temperature,” PS 070-97, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1998

18. “Standard Test Methods for the Determination of Fracture Toughness of Advanced Ceramics at

Ambient Temperature,” C 1421-99, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999

19. “Testing Methods for the Fracture Toughness of High Performance Ceramics,” JIS R1607-90, Japanese

Industrial Standards Committee, Tokyo, Japan, 1990

20. G. Anstis, P. Chantikul, B. Lawn, and D. Marshall, A Critical Evaluation of Indentation Techniques for

Measuring Fracture Toughness I: Direct Crack Measurements,” J. Am. Ceram. Soc., Vol 64 (No. 9),

1981, p 533–538

21. C.B. Ponton and R.D. Rawlings, Dependence of the Vickers Indentation Fracture Toughness on the

Surface Crack Length, Br. Ceram. Trans. J., Vol 88, 1989, p 83–99

22. “Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics)—Test Method for Fracture

Toughness of Monolithic Ceramics at Room Temperature by Single Edge Pre-Cracked Beam (SEPB)

Method,” ISO DIS15732, Geneva, Switzerland, 1999

23. “Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics)—Test Method for Fracture

Toughness of Monolithic Ceramics at Room Temperature by Surface Crack in Flexure (SCF) Method,”

ISO TC206/WG16, Geneva, Switzerland, 1999

24. “Advanced Technical Ceramics—Monolithic Ceramics—Test Methods for Determination of Apparent

Fracture Toughness,” CEN TC184, Brussels, Belgium, 1999 (draft, prENV)

25. A. Ghosh, M.G. Jenkins, A.S. Kobayashi, K.W. White, and R.C. Bradt, The Fracture Resistance of a

Sintered Silicon Carbide Using the Chevron-Notch Bend Bar, Silicon Carbide '87, Ceramic

Transactions, Vol 2, J.D. Crawley and C.E. Semler, Ed., The American Ceramic Society, Inc.,

Westerville, Ohio, 1989, p 241–251

26. H. Awaji and Y. Sakaida, V-Notch Technique for Single-Edge Notched Beam and Chevron Notch

Methods, J. Am. Ceram. Soc., Vol 73 (No. 11), 1990, p 3522–3523

27. J. Kübler, Fracture Toughness of Ceramics Using the SEVNB Method, Ceram. Eng. Sci. Proc., Vol 20

(No. 4), 1999

28. “Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperatures,” C

1161-94, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999

29. P. Chantikul, G. Anstis, B. Lawn, and D. Marshall, A Critical Evaluation of Indentation, Techniques for

Measuring Fracture Toughness II: Strength Methods, J. Am. Ceram. Soc., Vol 64 (No. 9), 1981, p 539–

543

30. B.J. Pletka, E.R. Fuller, Jr., and B.G. Koepke, An Evaluation of Double Torsion Testing: Experimental,

STP 678, Fracture Mechanics Applied to Brittle Materials, S.W. Frieman, Ed., ASTM, 1979, p 19–37

31. E.R. Fuller, Jr., An Evaluation of Double Torsion Testing: Analysis, STP 678, Fracture Mechanics

Applied to Brittle Materials, S. Frieman, Ed., ASTM, 1979, p 3–18

32. J.A. Salem and J.L. Shannon, Jr., Fracture Toughness of Si

Measured with Short Bar Chevron

Notched Specimens, J. Mater. Sci., Vol 22 (No. 1), 1987, p 321–324

33. J.J. Mecholvsky and S.W. Frieman, Determination of Fracture Mechanics Parameters Through

Fractographic Analysis of Ceramics, STP 678, Fracture Mechanics Applied to Brittle Materials, S.W.

Frieman, Ed., ASTM, 1979, p 136–150

34. R.W. Rice, Fractographic Determination of K

and Effects of Microstructual Stresses in Ceramics,

Fractography of Glasses and Ceramics, V. Frechette and J. Varner, Ed., Vol 17, Ceramic Transactions,

American Ceramic Society, 1991

35. “Standard Practice for Fractography and Characterization of Fracture Origins in Advanced Ceramics,”

C 1322-96, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999

36. H. Awaji, J. Kon, and H. Okuda, “The VAMAS Fracture Toughness Round Robin on Ceramics,”

VAMAS report 9, JFCC, Nagoya, Japan, 1990

37. G.D. Quinn, R.J. Gettings, and J.J. Kübler, “Fracture Toughness of Ceramics by the Surface Crack in

Flexure (SCF) Method, A VAMAS Round Robin,” VAMAS report 17, NIST, Gaithersburg, Maryland,

1994

38. G.R. Irwin, Fracture Mechanics, Mechanical Testing, Vol 8, ASM Handbook, ASM International, 1985,

p 439–464

39. R.A. Schmidt and T.J. Lutz, K

and J

of Westerly Granite-Effects of Thickness and In-Plane

Dimensions, STP 678, Fracture Mechanics Applied to Brittle Materials, S.W. Frieman, Ed., ASTM,

1979

40. R. Steinbruch, R. Kehands, and W. Schaarnwächter, Increase of Crack Resistance during Slow Crack

Growth in Al

Bend Specimens, J. Mater. Sci., Vol 18, 1983, p 265–270

41. J.C. Hay and K.W. White, Grain-Bridging Mechanisms in Monolithic Alumina and Spinel, J. Am.

Ceram. Soc., Vol 76 (No. 7), 1993, p 1849–1854

42. J.C. Hay and K.W. White, Crack Face Bridging Mechanisms in Monolithic MgAl

Spinel

Microstructures, Acta Metall. Mater., Vol 40 (No. 11), 1992, p 3017–3025

43. J.A. Salem, J.L. Shannon, Jr., and R.C. Bradt, Crack Growth Resistance of Textured Alumina, J. Am.

Ceram. Soc., Vol 72 (No. 1), 1989, p 20–27

44. J.A. Salem, J.L. Shannon, Jr., and M.G. Jenkins, Some Observation on Fracture Toughness and Fatigue

Testing with Chevron-Notched Specimens, STP 1172, Chevron-Notch Fracture Test Experience:

Metals and Non-Metals, K.R. Brown and F.I. Baratta, Ed., ASTM, 1992, p 9–25

45. M.G. Jenkins, A.S. Kobayashi, K.W. White, and R.C. Bradt, A 3-D Finite Element Analysis of a

Chevron-Notched, Three-Point Bend Fracture Specimen for Ceramic Materials, Int. J. Fract., Vol 34,

1987, p 281–295

46. R.F. Krause, Jr., Rising Fracture Toughness from the Bending Strength of Indented Alumina Beams, J.

Am. Ceram. Soc., Vol 71 (No. 5), 1988, p 338–343

47. J.E. Ritter, Crack Propagation in Ceramics, Ceramics and Glasses, Vol 4, Engineering Materials

Handbook, ASM International, 1991, p 694–699

Fracture Resistance Testing of Brittle Solids

Michael Jenkins, University of Washington; Johnathan Salem, NASA-Glenn Research Center

Fracture Toughness and R-Curve Testing at Elevated Temperature

Decreasing mechanical properties and performance with increasing temperature are consistently observed for

most materials. Complications of tests at elevated temperature include temperature control, environmental

effects (both material and test apparatuses), and time-dependent behavior (e.g., creep or oxidation).

In fracture testing, a particularly troubling complication is the effect of material and/or environmental

interactions on the crack-tip conditions. A good example of this is crack-tip blunting, which may more easily

occur after the trouble of introducing an atomistically sharp precrack in fracture testing specimens.

At this time, no standardized test methods exist for fracture testing at elevated temperature (for metals or

nonmetals). As the need increases for such standards, they will no doubt be introduced, not without much

controversy and complication.

Test Methods for Fracture Toughness at Elevated Temperature

At this time there are no specific elevated-temperature standards for fracture toughness testing. Apparently, it is

assumed that ambient temperature standards will be implemented with due care taken to ensure proper use at

elevated temperatures. In most cases, this is a reasonable approach. However, complications that have been

noted are crack healing and blunting in those methods that rely on precracking prior to fracture testing.

An early report of this “flaw healing” in SCF tests showed that fracture strength of indented flexure bars made

of a silicon carbide increased by a factor of three after annealing in air. This implies that the increase in strength

is due to the reduction in the effect of the SCF precrack on the susceptibility to fracture. Annealing in a vacuum

caused a similar, but somewhat reduced, effect (Ref 48).

Special caution is advised in extending methods that start with a sharp crack introduced at ambient temperature.

These methods include SEPB, SCF, IS, and precracked methods such as SENB and DCB. Methods that form

cracks in situ will probably not experience the “flaw healing” phenomenon. These methods include all the

chevron notched test specimens (CNB, CNSB, CNSR), SEVNB, and DT. Given the difficulties of properly

performing and analyzing the IF method at ambient temperature, it appears doubtful that it could be successful

at elevated temperatures.

Examples of Elevated-Temperature Fracture Toughness Test Data

“Flaw healing” can be a particular problem at elevated temperatures for precracked fracture test methods.

However, even methods such as the CNB may exhibit difficulties in initiating and propagating cracks under

certain conditions (e.g., very high temperatures). An in situ toughened silicon nitride (SN251, Kyocera

Corporation, Kyoto, Japan 1990 vintage) was fracture tested using CNB, SEPB, and fine notched (50 μm

thickness) SENB (Ref 44). The load-displacement curves for the CNB tests are shown in Fig. 25. The stable

curves at 25 and 1200 °C (77 and 2200 °F) provide valid test results according to ASTM C 1421. However, the

highly nonlinear behavior at 1371 °C (2500 °F), although stable and valid according to the standard, was ruled

an invalid test because a crack initiated and grew only part way before stopping at the tip of the chevron.

Instead, the highly nonlinear behavior shown in Fig. 25 was attributed to “plastic hinging” (Ref 44).

Fig. 25 Load displacement curves for stable fracture in chevron notched beam (CNB) fracture tests of an

in situ toughened silicon nitride. The test at 1370 °C is an invalid test because a crack never initiated at

the tip of the chevron, and plastic hinging occurred. Source: Ref 44

Comparison of fracture toughness results from CNB, SEPB, and sharp notch SENB are presented in Fig. 26.

Note that under the proper conditions at 1371 °C (2500 °F) (fast heat up and short hold times), the SEPB

method, despite the sharp precrack, gives results similar to the sharp notch SENB method. The CNB method at

1371 °C (2500 °F) under these test conditions tends to overestimate fracture toughness as expected from the

nonlinear loading curve shown in Fig. 25.

Fig. 26 Comparison of fracture toughness for in situ toughened silicon nitride (SN251) as functions of

temperature for chevron notched beam (CNB), single-edge precracked beam (SEPB), and single-edge V-

notch beam (SEVNB) fracture test methods

In a demonstration of the diversity of application of the CNB method, fracture toughness for seven advanced

ceramics (from aluminum oxide to silicon carbide to silicon nitride) and eight temperatures (from 20–1400 °C

or 68–2600 °F) in ambient air are plotted with error bars in Fig. 27. With the exception of the nonlinear

behavior of the in situ toughened silicon nitride, all results are predictable and consistent (Ref 49).

Fig. 27 Fracture toughness results as functions for temperature for seven advanced ceramic materials.

Source: Ref 49

R-Curve Testing at Elevated Temperature

Temperature-dependent mechanical properties and performance are consistently observed for most materials.

At elevated temperatures complications of fracture testing include temperature control, environmental effects

(both material and test apparatuses), and time-dependent behavior.

In R-curve fracture testing, the complication of materials and/or environmental interactions on the crack-tip

conditions is of concern. For example, crack-tip blunting can occur after an atomistically sharp precrack is

introduced in fracture test specimens. Even methods that are successful at in situ crack initiation can exhibit

problems with “flaw healing” as the crack propagates through the material during R-curve testing.

At this time, no dominant test methods exist for R-curve testing at elevated temperature (for metals or

nonmetals). If the need develops for such test methods, they will no doubt be introduced, but not without much

controversy and complication.

Test Methods for R-Curve Testing at Elevated Temperature. Currently, there are no specific elevated

temperature standards for R-curve testing. Apparently, it is assumed that ambient temperature standards will be

implemented with due care taken to ensure proper use at elevated temperatures. In most cases, this is a

reasonable approach. However, complications that have been noted are crack healing and blunting in those

methods that rely on precracking prior to fracture testing.

One successful method promoted as characterizing the complete fracture history (crack initiation to stable crack

propagation to final fracture) of a brittle material in a single test used to CNB test specimen (Ref 49). This

method used a monotonic load history combined with a laser-based apparatus to measure CMOD, and it used a

compliance method to determine crack length, fracture toughness, R-curve, and work of fracture for a range of

monolithic and composite advanced ceramics.

Special caution is advised in extending methods that start with a sharp crack introduced at ambient temperature.

These methods include SEPB, SCF, IS, and precracked methods such as SENB and DCB. Methods that form

cracks in situ will probably not experience the “flaw healing” phenomenon. These methods include other

chevron notched test specimens (CNB, CNSB, CNSR), SEVNB, and DT. Given the difficulties of properly

performing and analyzing the IF method at ambient temperature, it appears doubtful that it could be successful

at elevated temperatures.

Examples of Elevated-Temperature R-Curve Test Data. The use of the CNB method to characterize the

complete fracture history of a single test specimen (Ref 45) is an excellent demonstration of the information

available to characterize fracture behavior of brittle materials. For example, flat R-curves for three materials are

shown at two temperatures (20 and 1200 °C, or 68 and 2200 °F) in Fig. 28(a). Nonlinear R-curves are shown

for four materials in Fig. 28(b). Keep in mind that it has been shown that R-curves are not material properties

and are highly dependent on test conditions, including test specimen geometry. Thus, the R-curves shown in

Fig. 28 indicate material response and “toughening mechanisms” in the presence of cracks. However, the

information is of questionable use for design purposes.

Fig. 28 R-curves for materials tested at room and elevated temperature usign the chevron notch beam

(CNB) method. (a) Flat R-curves. (b) Nonlinear R-curves. Source: Ref 49

References cited in this section

44. J.A. Salem, J.L. Shannon, Jr., and M.G. Jenkins, Some Observation on Fracture Toughness and Fatigue

Testing with Chevron-Notched Specimens, STP 1172, Chevron-Notch Fracture Test Experience:

Metals and Non-Metals, K.R. Brown and F.I. Baratta, Ed., ASTM, 1992, p 9–25

45. M.G. Jenkins, A.S. Kobayashi, K.W. White, and R.C. Bradt, A 3-D Finite Element Analysis of a

Chevron-Notched, Three-Point Bend Fracture Specimen for Ceramic Materials, Int. J. Fract., Vol 34,

1987, p 281–295

48. J.J. Petrovic and M.C. Mendiratta, Fracture from Controlled Surfaces Flows, Fracture Mechanics

Applied to Brittle Materials, STP 678, S.W. Frieman, Ed., ASTM, 1992, p 83–102

49. M.G. Jenkins, M.K. Ferber, A. Ghosh, J.T. Peussa, and J.A. Salem, Chevron-Notched, Flexure Tests for

Measuring the Elevated Temperature Fracture Resistance of Structural Ceramics, STP 1172, Chevron-

Notch Fracture Test Experience: Metals and Non-Metals, K.R. Brown and F.I. Baratta, Ed., ASTM,

1992, p 159–177

Fracture Resistance Testing of Brittle Solids

Michael Jenkins, University of Washington; Johnathan Salem, NASA-Glenn Research Center

Summary

The fracture of theoretical brittle solids, while conceptually (and mathematically) rather simple and

straightforward, is far from simple in practice. “Real” materials often contain residual stresses, microstructures,

and geometric features that can complicate test methods intended to extract what appears to be a fundamental

material property: fracture resistance in the form of fracture toughness. Further complicating test methods are

differences in fracture behavior because of the type of flaw: intrinsic flaws (i.e., microcracks) often provide

information on intrinsic fracture resistance behavior; that is, fundamental behavior without influence of

microstructure or history of crack propagation (i.e., R-curve) fracture resistance. In contrast, extrinsic flaws

(i.e., induced cracks) can be used to measure either the intrinsic or the steady-state fracture resistance, but can

also lead to apparently large scatter (actually, differences) in the results if the influence of the microstructure

and history of crack propagation are not accounted for.

Standardized test methods for fracture of brittle solids (specifically, advanced ceramics) developed to date (e.g.,

ASTM C 1421, JIS R1607, and ISO DIS15732) have concentrated on maximizing repeatability and

reproducibility of the fracture resistance measurements at the onset of brittle fracture. Minimizing the effects of

R-curve behavior, environmentally assisted crack growth and variability in testing are primary concerns.

Although R-curve behavior is recognized as having a strong influence on the fracture behavior of

polycrystalline brittle solids, no standardization activities are currently underway to develop standard test

methods. Several reasons may be responsible for this lack of activity:

• Research in this area is still quite active and no dominant methods have emerged.

• It is not clear how to deal with the issue of intrinsic fracture resistance versus steady-state fracture

resistance and how this relates to the design methodologies that include probabilistic methods and

statistical strength distributions.

• R-curve behavior is not a material property because it is dependent on component (i.e., test specimen)

geometry, crack shape, crack propagation history, stress levels, and test parameters.

At elevated temperature, methods that involve the creation of sharp precracks at room temperature may become

unusable at certain elevated temperatures as crack healing and crack-tip blunting negate the effects of

precracks. Methods that use either in situ crack formation or very sharp notches seem to provide better ways to

measure either fracture toughness or R-curve behavior at elevated temperatures.

For brittle solids, it is clear that the driver behind methods to determine fracture resistance is not necessarily for

its use in determining the resistance of the material or design to extrinsic flaws. Instead, the need is to

accurately and precisely determine the fracture resistance of brittle solids for use in relative comparison indices

for evaluation of material performance in fracture-resistance related (but not fracture-resistance driven)

applications.

Fracture Resistance Testing of Brittle Solids

Michael Jenkins, University of Washington; Johnathan Salem, NASA-Glenn Research Center

References

1. G.D. Quinn, Strength and Proof Testing, Ceramics and Glasses, Vol 4, Engineering Materials

Handbook, ASM International, 1991, p 585–598

2. A.A. Griffith, The Phenomena of Rupture and Flow in Solids, Philos. Trans. R. Soc. (London) A, Vol

221, 1920, p 163–198

3. B. Lawn, Fracture of Brittle Solids, Cambridge University Press, 1993

4. K.E. Amin, Toughness, Hardness, and Wear, Ceramics and Glasses, Vol 4, Engineered Materials

Handbook, S.J. Schneider, J., Ed., ASM International, 1991, p 599–609

5. G.R. Irwin, Fracture I, Handbuch der Physik, Vol 6, Springer-Verlag, Berlin, Germany, 1958, p 558–

590

6. “Standard Test Method for Plane Strain Fracture Toughness of Metallic Materials,” E 399-90, Annual

Book of ASTM Standards, Vol 03.01, ASTM, 1998

7. STP 678, Fracture Mechanics Applied to Brittle Materials, S.W. Freiman, Ed., ASTM, 1979

8. T. Fujii and T. Nose, Evaluation of Fracture Toughness of Ceramic Materials, IJIS Int., Vol 29 (No. 9),

1989, p 717–725

9. G.D. Quinn, M.G. Jenkins, J.A. Salem, and I. Bar-On, Standardization of Fracture Toughness Testing of

Ceramics in the United States, Kor J. Ceram., Vol 4 (No. 4), 1998, p 311–322

10. M. Sakai and R.C. Bradt, Fracture Toughness Testing of Brittle Materials, Int. Mater. Rev., Vol 38 (No.

2), 1993, p 53–58

11. J. Larsen-Basse, Abrasive Wear of Ceramics, Friction and Wear of Ceramics, S. Jahanmir, Ed., Marcel

Dekker, Inc., New York, 1994, p 99–118

12. A. Evans and D. Marshall, Wear Mechanisms in Ceramics, Fundamentals of Friction and Wear of

Materials, D. Rigney, Ed., American Society for Metals, 1981, p 439–452

13. J. Ritter, Erosion Damage in Structural Ceramics, Material Sci. Eng. Vol 71, 1985, p 195–201

14. J.B. Quinn and G.D. Quinn, Hardness and Brittleness of Ceramics, Ceram. Eng. Sci. Proc., Vol 17 (No.

3), 1996, p 59–68

15. J.B. Quinn and G.D. Quinn, Indentation Brittleness of Ceramics: A Fresh Approach, J. Mater. Sci., Vol

32, 1997, p 4331–4346

16. “Standard Test Method for Measurement of Fracture Toughness,” C 1820-96, Annual Book of ASTM

Standards, Vol 3.01, ASTM, 1999

17. “Standard Test Methods for the Determination of Fracture Toughness of Advanced Ceramics at

Ambient Temperature,” PS 070-97, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1998

18. “Standard Test Methods for the Determination of Fracture Toughness of Advanced Ceramics at

Ambient Temperature,” C 1421-99, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999

19. “Testing Methods for the Fracture Toughness of High Performance Ceramics,” JIS R1607-90, Japanese

Industrial Standards Committee, Tokyo, Japan, 1990

20. G. Anstis, P. Chantikul, B. Lawn, and D. Marshall, A Critical Evaluation of Indentation Techniques for

Measuring Fracture Toughness I: Direct Crack Measurements,” J. Am. Ceram. Soc., Vol 64 (No. 9),

1981, p 533–538

21. C.B. Ponton and R.D. Rawlings, Dependence of the Vickers Indentation Fracture Toughness on the

Surface Crack Length, Br. Ceram. Trans. J., Vol 88, 1989, p 83–99

22. “Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics)—Test Method for Fracture

Toughness of Monolithic Ceramics at Room Temperature by Single Edge Pre-Cracked Beam (SEPB)

Method,” ISO DIS15732, Geneva, Switzerland, 1999

23. “Fine Ceramics (Advanced Ceramics, Advanced Technical Ceramics)—Test Method for Fracture

Toughness of Monolithic Ceramics at Room Temperature by Surface Crack in Flexure (SCF) Method,”

ISO TC206/WG16, Geneva, Switzerland, 1999

24. “Advanced Technical Ceramics—Monolithic Ceramics—Test Methods for Determination of Apparent

Fracture Toughness,” CEN TC184, Brussels, Belgium, 1999 (draft, prENV)

25. A. Ghosh, M.G. Jenkins, A.S. Kobayashi, K.W. White, and R.C. Bradt, The Fracture Resistance of a

Sintered Silicon Carbide Using the Chevron-Notch Bend Bar, Silicon Carbide '87, Ceramic

Transactions, Vol 2, J.D. Crawley and C.E. Semler, Ed., The American Ceramic Society, Inc.,

Westerville, Ohio, 1989, p 241–251

26. H. Awaji and Y. Sakaida, V-Notch Technique for Single-Edge Notched Beam and Chevron Notch

Methods, J. Am. Ceram. Soc., Vol 73 (No. 11), 1990, p 3522–3523

27. J. Kübler, Fracture Toughness of Ceramics Using the SEVNB Method, Ceram. Eng. Sci. Proc., Vol 20

(No. 4), 1999

28. “Standard Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperatures,” C

1161-94, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999

29. P. Chantikul, G. Anstis, B. Lawn, and D. Marshall, A Critical Evaluation of Indentation, Techniques for

Measuring Fracture Toughness II: Strength Methods, J. Am. Ceram. Soc., Vol 64 (No. 9), 1981, p 539–

543

30. B.J. Pletka, E.R. Fuller, Jr., and B.G. Koepke, An Evaluation of Double Torsion Testing: Experimental,

STP 678, Fracture Mechanics Applied to Brittle Materials, S.W. Frieman, Ed., ASTM, 1979, p 19–37

31. E.R. Fuller, Jr., An Evaluation of Double Torsion Testing: Analysis, STP 678, Fracture Mechanics

Applied to Brittle Materials, S. Frieman, Ed., ASTM, 1979, p 3–18

32. J.A. Salem and J.L. Shannon, Jr., Fracture Toughness of Si

Measured with Short Bar Chevron

Notched Specimens, J. Mater. Sci., Vol 22 (No. 1), 1987, p 321–324

33. J.J. Mecholvsky and S.W. Frieman, Determination of Fracture Mechanics Parameters Through

Fractographic Analysis of Ceramics, STP 678, Fracture Mechanics Applied to Brittle Materials, S.W.

Frieman, Ed., ASTM, 1979, p 136–150

34. R.W. Rice, Fractographic Determination of K

and Effects of Microstructual Stresses in Ceramics,

Fractography of Glasses and Ceramics, V. Frechette and J. Varner, Ed., Vol 17, Ceramic Transactions,

American Ceramic Society, 1991

35. “Standard Practice for Fractography and Characterization of Fracture Origins in Advanced Ceramics,”

C 1322-96, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999

36. H. Awaji, J. Kon, and H. Okuda, “The VAMAS Fracture Toughness Round Robin on Ceramics,”

VAMAS report 9, JFCC, Nagoya, Japan, 1990

37. G.D. Quinn, R.J. Gettings, and J.J. Kübler, “Fracture Toughness of Ceramics by the Surface Crack in

Flexure (SCF) Method, A VAMAS Round Robin,” VAMAS report 17, NIST, Gaithersburg, Maryland,

1994

38. G.R. Irwin, Fracture Mechanics, Mechanical Testing, Vol 8, ASM Handbook, ASM International, 1985,

p 439–464

39. R.A. Schmidt and T.J. Lutz, K

and J

of Westerly Granite-Effects of Thickness and In-Plane

Dimensions, STP 678, Fracture Mechanics Applied to Brittle Materials, S.W. Frieman, Ed., ASTM,

1979

40. R. Steinbruch, R. Kehands, and W. Schaarnwächter, Increase of Crack Resistance during Slow Crack

Growth in Al

Bend Specimens, J. Mater. Sci., Vol 18, 1983, p 265–270

41. J.C. Hay and K.W. White, Grain-Bridging Mechanisms in Monolithic Alumina and Spinel, J. Am.

Ceram. Soc., Vol 76 (No. 7), 1993, p 1849–1854

42. J.C. Hay and K.W. White, Crack Face Bridging Mechanisms in Monolithic MgAl

Spinel

Microstructures, Acta Metall. Mater., Vol 40 (No. 11), 1992, p 3017–3025

43. J.A. Salem, J.L. Shannon, Jr., and R.C. Bradt, Crack Growth Resistance of Textured Alumina, J. Am.

Ceram. Soc., Vol 72 (No. 1), 1989, p 20–27

44. J.A. Salem, J.L. Shannon, Jr., and M.G. Jenkins, Some Observation on Fracture Toughness and Fatigue

Testing with Chevron-Notched Specimens, STP 1172, Chevron-Notch Fracture Test Experience:

Metals and Non-Metals, K.R. Brown and F.I. Baratta, Ed., ASTM, 1992, p 9–25

45. M.G. Jenkins, A.S. Kobayashi, K.W. White, and R.C. Bradt, A 3-D Finite Element Analysis of a

Chevron-Notched, Three-Point Bend Fracture Specimen for Ceramic Materials, Int. J. Fract., Vol 34,

1987, p 281–295

46. R.F. Krause, Jr., Rising Fracture Toughness from the Bending Strength of Indented Alumina Beams, J.

Am. Ceram. Soc., Vol 71 (No. 5), 1988, p 338–343

47. J.E. Ritter, Crack Propagation in Ceramics, Ceramics and Glasses, Vol 4, Engineering Materials

Handbook, ASM International, 1991, p 694–699

48. J.J. Petrovic and M.C. Mendiratta, Fracture from Controlled Surfaces Flows, Fracture Mechanics

Applied to Brittle Materials, STP 678, S.W. Frieman, Ed., ASTM, 1992, p 83–102

49. M.G. Jenkins, M.K. Ferber, A. Ghosh, J.T. Peussa, and J.A. Salem, Chevron-Notched, Flexure Tests for

Measuring the Elevated Temperature Fracture Resistance of Structural Ceramics, STP 1172, Chevron-

Notch Fracture Test Experience: Metals and Non-Metals, K.R. Brown and F.I. Baratta, Ed., ASTM,

1992, p 159–177