ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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27. “Standard Test Method for J-Integral Characterization of Fracture Toughness,” ASTM E 1737, Annual
Book of Standards, Vol 03.01, ASTM, 1996
28. J.D. Landes and J.A. Begley, in Fracture Toughness, ASTM STP 560, 1974, p 170
29. S. Hashemi and J.G. Williams, Plast. Rubber Process. Appl., Vol 6, 1986, p 363
30. M.-L. Lu and F.-C. Chang, Polymer, Vol 36, 1995, p 2541
31. Z. Zhou, J.D. Landes, and D.D. Huang, Polym. Eng. Sci., Vol 34, 1994, p 128
32. M.-L. Lu, C.-B. Lee, and F.-C. Chang, Polym. Eng. Sci., Vol 35, 1995, p 1433
33. J.W. Hutchinson and P.C. Paris, in Elastic-Plastic Fracture, ASTM STP 668, 1979, p 37
34. I. Narisawa and M.T. Takemori, Polym. Eng. Sci., Vol 29, 1989, p 671
35. H. Swei, B. Crist, and S.H. Carr, Polymer, Vol 32, 1991, p 1440
36. C.-B. Lee, M.-L. Lu, and F.-C. Chang, J. Appl. Polym. Sci., Vol 47, 1993, p 1867
37. M.-L. Lu and F.-C. Chang, J. Appl. Polym. Sci., Vol 56, 1995, p 1065
38. B.M. Rimnac, T.W. Wright, and R.W. Klein, Polym. Eng. Sci., Vol 28, 1988, p 1586
39. B.D. Huang, in Toughened Plastics I: Science and Enginering, C.K. Riew and A.J. Kinloch, Ed., Vol
233, p 39, ACS Advances in Chemistry Series,, American Chemical Society, 1993
40. M.-L. Lu, K.-C. Chiou, and F.-C. Chang, Polymer, Vol 37, 1996, p 4289
41. K.J. Pascoe, in Failure of Plastics, W. Brostow and R.D. Corneliussen, Ed., Hanser Publishers, 1989, p
119
42. M.-L. Lu, K.-C. Chiou, and F.-C. Chang, Polym. Eng. Sci., Vol 36, 1996, p 2289
Fracture Resistance Testing of Plastics
Kevin M. Kit and Paul J. Phillips, University of Tennessee, Knoxville
References
1. N.G. McCrum, B.E. Read, and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids,
Wiley, 1967
2. I.M. Ward, Mechanical Properties of Solid Polymers, Wiley, 1983, p 15
3. E.H. Andrews, Cracking and Crazing in Polymeric Glasses, The Physics of Glassy Polymers, R.N.
Haward, Ed., Wiley, 1973, p 394
4. R. Natarajan and P.E. Reed, J. Polym. Sci. A, Polym. Chem., Vol 2 (No. 10), 1972, p 585
5. G.A. Bernier and R.P. Kambour, Macromolecules, Vol 1, 1968, p 393
6. E.H. Andrews, G.M. Levy and J. Willis, J. Mater. Sci., Vol 8, 1973, p 1000
7. L.E. Weber, The Chemistry of Rubber Manufacture, Griffin, London, 1926, p 336
8. K. Memmler, The Science of Rubber, R.F. Dunbrook and V.N. Morris, Ed., Reinhold, 1934, p 523
9. G.R. Irwin, in Encyclopaedia of Physics, Vol 6, Springer Verlag, 1958
10. N.G. McCrum, C.P. Buckley, and C.B. Bucknall, Principles of Polymer Engineering, Oxford University
Press, 1997, p 201
11. A.A. Griffith, Phil. Trans. R. Soc. (London) A, Vol 221, 1921, p 163
12. R.S. Rivlin and A.G. Thomas, J. Polym. Sci., Vol 10, 1953, p 291
13. R.P. Kambour, Appl. Polym. Symp., Vol 7, John Wiley & Sons, 1968, p 215
14. J.P. Berry, J. Polym. Sci. A, Polym. Chem., Vol 2, 1964, p 4069
15. E.H. Andrews, J. Mater. Sci., Vol 9, 1974, p 887
16. J.R. Rice, J. Appl. Mech. (Trans. ASME), Vol 35, 1968, p 379
17. J.R. Rice, Fracture, Vol 2, 1968, p 191
18. J.A. Begley and J.D. Landes, in Fracture Toughness, ASTM STP 514, 1972, p 1
19. J.D. Landes and J.E. Begley, in Fracture Toughness, ASTM STP 514, 1972, p 24
20. J.M. Hodgkinson and J.G. Williams, J. Mater. Sci., Vol 16, 1981, p 50
21. S. Hashemi and J.D. Williams, Polym. Eng. Sci., Vol 26, 1986, p 760
22. Y.W. Mai and P. Powell, J. Polym. Sci. B, Polym. Phys., Vol 29, 1991, p 785
23. M. Ouederni and P.J. Phillips, J. Polym. Sci. B., Polym. Phys., Vol 33, 1995, p 1313
24. “Standard Test Methods for Plane Strain Fracture Toughness and Strain Energy Release Rate of Plastic
Materials,” ASTM D 5045, Annual Book of Standards, Vol 08.03, ASTM, 1996
25. “Standard Test Method for Determining J-R Curves of Plastic Materials,” ASTM D 6068, Annual Book
of Standards, Vol 08.03, ASTM, 1996
26. “Standard Test Method for J
Ic
, A Measure of Fracture Toughness,” ASTM E 813, Annual Book of
Standards, Vol 03.01, ASTM, 1989
27. “Standard Test Method for J-Integral Characterization of Fracture Toughness,” ASTM E 1737, Annual
Book of Standards, Vol 03.01, ASTM, 1996
28. J.D. Landes and J.A. Begley, in Fracture Toughness, ASTM STP 560, 1974, p 170
29. S. Hashemi and J.G. Williams, Plast. Rubber Process. Appl., Vol 6, 1986, p 363
30. M.-L. Lu and F.-C. Chang, Polymer, Vol 36, 1995, p 2541
31. Z. Zhou, J.D. Landes, and D.D. Huang, Polym. Eng. Sci., Vol 34, 1994, p 128
32. M.-L. Lu, C.-B. Lee, and F.-C. Chang, Polym. Eng. Sci., Vol 35, 1995, p 1433
33. J.W. Hutchinson and P.C. Paris, in Elastic-Plastic Fracture, ASTM STP 668, 1979, p 37
34. I. Narisawa and M.T. Takemori, Polym. Eng. Sci., Vol 29, 1989, p 671
35. H. Swei, B. Crist, and S.H. Carr, Polymer, Vol 32, 1991, p 1440
36. C.-B. Lee, M.-L. Lu, and F.-C. Chang, J. Appl. Polym. Sci., Vol 47, 1993, p 1867
37. M.-L. Lu and F.-C. Chang, J. Appl. Polym. Sci., Vol 56, 1995, p 1065
38. B.M. Rimnac, T.W. Wright, and R.W. Klein, Polym. Eng. Sci., Vol 28, 1988, p 1586
39. B.D. Huang, in Toughened Plastics I: Science and Enginering, C.K. Riew and A.J. Kinloch, Ed., Vol
233, p 39, ACS Advances in Chemistry Series,, American Chemical Society, 1993
40. M.-L. Lu, K.-C. Chiou, and F.-C. Chang, Polymer, Vol 37, 1996, p 4289
41. K.J. Pascoe, in Failure of Plastics, W. Brostow and R.D. Corneliussen, Ed., Hanser Publishers, 1989, p
119
42. M.-L. Lu, K.-C. Chiou, and F.-C. Chang, Polym. Eng. Sci., Vol 36, 1996, p 2289
Fracture Toughness of Ceramics and Ceramic
Matrix Composites
J.H. Miller, Oak Ridge National Laboratory P.K. Liaw, The University of Tennessee, Knoxville
Introduction
CERAMICS are lightweight structural materials with much higher resistance to high temperatures and
aggressive environments than other conventional engineering materials. These characteristics of ceramics hold
promise in various applications for gas turbines, heat exchangers, combustors and boiler components in the
power generation systems, first-wall and high-heat-flux surfaces in fusion reactors, and structural components
in the aerospace industry (Ref 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
and 25). However, most of these engineering applications require high reliability and the improvement of
ceramic fracture toughness.
Monolithic ceramics are inherently brittle, making them highly sensitive to process- and service-related flaws.
Due to their low toughness, monolithic ceramics are prone to catastrophic failure and, thus, may be unsuitable
for engineering applications that require high reliability. Ceramic matrix composites (CMCs), however, can
provide significant improvement in fracture toughness and the avoidance of catastrophic failure (Ref 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
36, 37, 38, 39, 40, and 41). The fracture mechanisms in CMCs are identical to those found in monolithic
ceramics (brittle), but “plastic-like” behavior occurs in CMCs because of the toughening mechanisms of crack
bridging, branching, and deflection. The reinforcing particles, whiskers, or fibers that are present in the ceramic
matrix allow the bulk composite material to avoid unstable crack growth and the resulting catastrophic failure.
The toughness of CMCs comes from the fact that the reinforcement can provide crack bridges and cause cracks
to branch, deflect, or arrest. These issues are quite complicated, and they demonstrate the critical need for the
understanding of the fracture properties of ceramics and CMCs.
Much work has been done to develop methods for evaluating the fracture toughness of ceramic materials (Ref
42, 43, 44, 45, 46, 47, 48, 49, and 50). The concepts of both linear-elastic fracture mechanics (LEFM) and
elastic-plastic fracture mechanics (EPFM) are both of interest in regard to ceramic materials. Monolithic
ceramics, due to their brittle nature, behave in a linear-elastic manner. This fact has lead to the successful use of
LEFM methods for monolithic ceramics. Many CMCs, on the other hand, have an elastic-plastic fracture
behavior. This fact has lead researchers to attempt to use EPFM methods to evaluate the fracture toughness of
CMCs.
This article briefly introduces LEFM and EPFM concepts and methods that have been developed or adapted for
the evaluation of the fracture behavior of monolithic ceramics and CMCs. The general concepts of LEFM and
EPFM are briefly reviewed, and test methods are described for fracture toughness testing of monolithic
ceramics and CMCs. More detailed information on the fracture resistance testing of monolithic ceramics is also
contained in the article “Fracture Resistance Testing of Brittle Solids” in this Volume, while this article places
emphasis on the fracture toughness testing of cmcs. Measuring the fracture toughness of CMCs is not as
developed as toughness testing of monolithic ceramics. The toughening mechanisms of microcracking, crack
bridging, and crack branching cause CMCs to behave in an elastic-plastic-like manner, which makes EPFM
methods attractive. LEFM and EPFM methods have both been used to evaluate the toughness of CMCs, but
because the level of understanding of the complex fracture mechanisms present in CMCs is not well developed,
no connection has been made between the macroscopic toughness, either elastic or elastic-plastic, and the
fracture mechanisms. As a result, evaluation of the fracture toughness of CMCs has been limited. However, as
the cracking mechanisms become better understood, LEFM and EPFM methods will become better adapted for
use in the evaluation of CMC fracture toughness behavior.
References cited in this section
1. T.M. Besmann, B.W. Sheldon, R.A. Lowden, and D.P. Stinton, Vapor Phase Fabrication and Properties
of Continuous-Filament Ceramic Composites, Science, Vol 253, 1991, p 1104
2. M. Bouquet, J.M. Bribis, and J.M. Quenisset, Toughness Assessment of Ceramic Matrix Composites,
Compos. Sci. Technol., Vol 37, 1990, p 223–248
3. C.H. Hsueh, P.F. Becher, and P. Angelini, Effects of Interfacial Films on Thermal Stresses in Whisker-
Reinforced Ceramics, J. Am. Ceram. Soc., Vol 71 (No. 11), 1988, p 929–933
4. D.P. Stinton, A.J. Caputo, and R.A. Lowden, Synthesis of Fiber-Reinforced SiC Composites by
Chemical Vapor Infiltration, Am. Ceram. Soc. Bull., Vol 65 (No. 2), 1986, p 347–350
5. D.P. Stinton, W.J. Lackey, R.J. Lauf, and T.M. Besmann, Fabrication of Ceramic-Ceramic Composites
by Chemical Vapor Deposition, Ceram. Eng. Sci. Proc., Vol 5, 1984, p 668–676
6. J.H. Miller, R.A. Lowden, and P.K. Liaw, Fiber Coatings and the Fracture Behavior of a Continuous
Fiber Ceramic Composite, Symposium on Ceramic Matrix Composites—Advanced High-Temperature
Structural Materials, R.A. Lowden, M.K. Ferber, J.R. Hellmann, K.K. Chawla, and S.G. DiPietro, Ed.,
Vol 365, Materials Research Society, 1995, p 403–410
7. M.A. Borst, W.Y. Lee, Y. Zhang, and P.K. Liaw, Preparation and Characterization of Chemically Vapor
Deposited ZrO
2
Coating on Nickel and Ceramic Fiber Substrates, J. Am. Ceram. Soc., Vol 80 (No. 6),
1997, p 1591–1594
8. N. Miriyala, P.K. Liaw, C.J. McHargue, L.L. Snead, and J.A. Morrison, The Monotonic and Fatigue
Behavior of a Nicalon/Alumina Composite at Ambient and Elevated Temperatures, American Ceramic
Society Meeting, Ceram. Eng. Sci. Proc., Vol 18 (No. 3), 1997, p 747–756
9. W. Zhao, P.K. Liaw, and N. Yu, Effects of Lamina Stacking Sequence on the In-Plane Elastic Stress
Distribution of a Plain-Weave Nicalon Fiber-Reinforced SiC Laminated Composite with a Lay-Up of
[0/30/60], American Ceramic Society Meeting, Ceram. Eng. Sci. Proc., Vol 18 (No. 3), 1997, p 401–
408
10. W. Zhao, P.K. Liaw, and D.C. Joy, Microstructural Characterization of a 2-D Woven Nicalon/SiC
Ceramic Composite by Scanning Electron Microscopy Line-Scan Technique, American Ceramic
Society Meeting, Ceram. Eng. Sci. Proc., Vol 18 (No. 3), 1997, p 295–302
11. J.G. Kim, P.K. Liaw, D.K. Hsu, and D.J. McGuire, Nondestructive Evaluation of Continuous Nicalon
Fiber Reinforced SiC Composites, American Ceramic Society Meeting, Ceram. Eng. Sci. Proc., Vol 18
(No. 4), 1997, p 287–296
12. N. Miriyala, P.K. Liaw, C.J. McHargue, and L.L. Snead, The Monotonic and Fatigue Behavior of a
Nicalon/Alumina Composite at Ambient and Elevated Temperatures, Ceram. Eng. Sci. Proc., Vol 18
(No. 3), 1997, p 747–756
13. W. Zhao, P.K. Liaw, N. Yu, E.R. Kupp, D.P. Stinton, and T.M. Besmann, Computation of the Lamina
Stacking Sequence Effect on the Elastic Moduli of a Plain-Weave Nicalon Fiber Reinforced SiC
Laminated Composite with a Lay-Up of [0/30/60], J. Nucl. Mater., Vol 253, 1998, p 10–19
14. N. Miriyala, P.K. Liaw, C.J. McHargue, and L.L. Snead, “The Mechanical Behavior of A Nicalon/SiC
Composite at Ambient Temperature and 1000 °C”, J. Nucl. Mater., Vol 253, 1998, p 1–9
15. W.Y. Lee, Y. Zhang, I.G. Wright, B.A. Pint, and P.K. Liaw, Effects of Sulfur Impurity on the Scale
Adhesion Behavior of a Desulfurized Ni-Based Superalloy Aluminized by Chemical Vapor Deposition,
Metall. Mater. Trans. A, Vol 29, 1998, p 833
16. P.K. Liaw, Understanding Fatigue Failure in Structural Materials, JOM, Vol 49 (No. 7), 1997, p 42
17. N. Miriyala and P.K. Liaw, CFCC (Continuous-Fiber-Reinforced Ceramic Matrix Composites) Fatigue:
A Literature Review, JOM, Vol 49 (No. 7), 1997, p 59–66, 82
18. N. Miriyala and P.K. Liaw, Specimen Size Effects on the Flexural Strength of CFCCs, American
Ceramic Society Meeting, Ceram. Eng. Sci. Proc., Vol 19, 1998
19. W. Zhao, P.K. Liaw, and N. Yu, Computer-Aided Prediction of the First Matrix Cracking Stress for a
Plain-Weave Nicalon/SiC Composite with Lay-Ups of [0/20/60] and [0/40/60], Ceram. Eng. Sci. Proc.,
Vol 19, 1998, p 3
20. W. Zhao, P.K. Liaw, and N. Yu, Computer-Aided Prediction of the Effective Moduli for a Plain-Weave
Nicalon/SiC Composite with Lay-Ups of [0/20/60] and [0/40/60], Ceram. Eng. Sci. Proc., Vol 19, 1998
21. N. Miriyala, P.K. Liaw, C.J. McHargue, A. Selvarathinam, and L.L. Snead, The Effect of Fabric
Orientation on the Flexural Behavior of CFCCs: Experiment and Theory, The 100th Annual American
Ceramic Society Meeting, 3–6 May 1998 (Cincinnati), in press
22. N. Miriyala, P.K. Liaw, C.J. McHargue, and L.L. Snead, Fatigue Behavior of Continuous Fiber-
Reinforced Ceramic-Matrix Composites (CFCCs) at Ambient and Elevated Temperatures, invited paper
presented at symposium proceedings in honor of Professor Paul C. Paris, High Cycle Fatigue of
Structural Materials, W.O. Soboyejo and T.S. Srivatsan, Ed., The Minerals, Metals, and Materials
Society, 1997, p 533–552
23. W. Zhao, P.K. Liaw, and N. Yu, The Reliability of Evaluating the Mechanical Performance of
Continuous Fiber-Reinforced Ceramic Composites by Flexural Testing, Int. Conf. on Maintenance and
Reliability, 1997, p 6-1 to 6-15
24. P.K. Liaw, J. Kim, N. Miriyala, D.K. Hsu, N. Yu, D.J. McGuire, and W.A. Simpson, Jr., Nondestructive
Evaluation of Woven Fabric Reinforced Ceramic Composites, Symposium on Nondestructive
Evaluation of Ceramics, C. Schilling, J.N. Gray, R. Gerhardt, and T. Watkins, Ed., Vol 89, 1998, p 121–
135
25. M.E. Fine and P.K. Liaw, Commentary on the Paris Equation, invited paper presented at symposium
proceedings in honor of Professor Paul C. Paris, High Cycle Fatigue of Structural Materials, High Cycle
Fatigue of Structural Materials, W.O. Soboyejo and T.S. Srivatsan, Ed., The Minerals, Metals, and
Materials Society, 1997, p 25–40
26. W. Zhao, P.K. Liaw, D.C. Joy, and C.R. Brooks, Effects of Oxidation, Porosity and Fabric Stacking
Sequence on Flexural Strength of a SiC/SiC Ceramic Composite, Processing and Properties of
Advanced Materials: Modeling, Design and Properties, B.Q. Li, Ed., The Minerals, Metals, and
Materials Society, 1998, p 283–294
27. W. Zhao, P.K. Liaw, and N. Yu, Computer Modeling of the Fabric Stacking Sequence Effects on
Mechanical Properties of a Plain-Weave SiC/SiC Ceramic Composite, Proc. on Processing and
Properties of Advanced Materials: Modeling, Design and Properties, B.Q. Li, Ed., The Minerals,
Metals, and Materials Society, 1998, p 149–160
28. J. Kim and P.K. Liaw, The Nondestructive Evaluation of Advanced Ceramics and Ceramic-Matrix
Composites, JOM, Vol 50 (No. 11), 1998
29. N. Yu and P.K. Liaw, Ceramic-Matrix Composites: An Integrated Interdisciplinary Curriculum, J. Eng.
Ed., supplement, 1998, p 539–544
30. P.K. Liaw, Continuous Fiber Reinforced Ceramic Composites, J. Chin. Inst. Eng., Vol 21 (No. 6), 1998,
p 701–718
31. N. Yu and P.K. Liaw, “Ceramic-Matrix Composites: Web-Based Courseware and More,” paper
presented at the 1998 ASEE annual conference and exposition, June 28–July 1, 1998 (Seattle)
32. N. Yu and P.K. Liaw, “Ceramic-Matrix Composites,” http://www.engr.utk.edu/~cmc
33. P.K. Liaw. O. Buck, R.J. Arsenault, and R.E. Green, Jr., Ed., Nondestructive Evaluation and Materials
Properties III, The Minerals, Metals, and Materials Society, 1997
34. W.M. Matlin, T.M. Besmann, and P.K. Liaw, Optimization of Bundle Infiltration in the Forced
Chemical Vapor Infiltration (FCVI) Process, Symposium on Ceramic Matrix Composites—Advanced
High-Temperature Structural Materials, R.A. Lowden, M.K. Ferber, J.R. Hellmann, K.K. Chawla, and
S.G. DiPietro, Ed., Vol 365, Materials Research Society, 1995, p 309–315
35. P.K. Liaw, D.K. Hsu, N. Yu, N. Miriyala, V. Saini, and H. Jeong, Measurement and Prediction of
Composite Stiffness Moduli, Symposium on High Performance Composites: Commonalty of
Phenomena, K.K. Chawla, P.K. Liaw, and S.G. Fishman, Ed., The Minerals, Metals, and Materials
Society, 1994, p 377–395
36. N. Chawla, P.K. Liaw, E. Lara-Curzio, R.A. Lowden, and M.K. Ferber, Effect of Fiber Fabric
Orientation on the Monotonic and Fatigue Behavior of a Continuous Fiber Ceramic Composite,
Symposium on High Performance Composites, K.K. Chawla, P.K. Liaw, and S.G. Fishman, Ed., The
Minerals, Metals and Materials Society, 1994, p 291–304
37. P.K. Liaw, D.K. Hsu, N. Yu, N. Miriyala, V. Saini, and H. Jeong, Modulus Investigation of Metal and
Ceramic Matrix Composites: Experiment and Theory, Acta Metall. Mater., Vol 44 (No. 5), 1996, p
2101–2113
38. P.K. Liaw, N. Yu, D.K. Hsu, N. Miriyala, V. Saini, L.L. Snead, C.J. McHargue, and R.A. Lowden,
Moduli Determination of Continuous Fiber Ceramic Composites (CFCCs), J. Nucl. Mater., Vol 219,
1995, p 93–100
39. P.K. Liaw, book review on Ceramic Matrix Composites by K.K. Chawla, MRS Bull., Vol 19, 1994, p 78
40. D.K. Hsu, P.K. Liaw, N. Yu, V. Saini, N. Miriyala, L.L. Snead, R.A. Lowden, and C.J. McHargue,
Nondestructive Characterization of Woven Fabric Ceramic Composites, Symposium on Ceramic Matrix
Composites—Advanced High-Temperature Structural Materials, R.A. Lowden, M.K. Ferber, J.R.
Hellmann, K.K. Chawla, and S.G. DiPietro, Ed., Vol 365, Materials Research Society, 1995, 203–208
41. S. Shanmugham, D.P. Stinton, F. Rebillat, A. Bleier, E. Lara-Curzio, T.M. Besmann, and P.K. Liaw,
Oxidation-Resistant Interfacial Coatings for Continuous Fiber Ceramic Composites, S. Shanmugham,
D.P. Stinton, F. Rebillat, A. Bleier, T.M. Besmann, E. Lara-Curzio, and P.K. Liaw, Ceram. Eng. Sci.
Proc., Vol 16 (No. 4), 1995, p 389–399
42. C.B. Thomas, “Processing, Mechanical Behavior, and Microstructural Characterization of Liquid Phase
Sintered Intermetallic-Bonded Ceramic Composites,” M.S. Thesis, The University of Tennessee,
Knoxville, 1996
43. J.H. Miller, “Fiber Coatings and The Fracture Behavior of a Woven Continuous Fiber Fabric-
Reinforced Ceramic Composite,” M.S. Thesis, The University of Tennessee, Knoxville, 1995
44. I.E. Reimonds, A Review of Issues in the Fracture of Interfacial Ceramics and Ceramic Composites,
Materials Science and Engineering A, Vol 237 (No. 2), 1997, p 159–167
45. D.L. Davidson, Ceramic Matrix Composites Fatigue and Fracture, JOM, Vol 47 (No. 10), 1995, p 46–
50, 81, 82
46. J.C. McNulty and F.W. Zok, Application of Weakest-Link Fracture Statistics to Fiber-Reinforced
Ceramic-Matrix Composites, J. Am. Ceram. Soc., Vol 80 (No. 6), 1997, p 1535–1543
47. Z.G. Li, M. Taya, M.L. Dunn, and R. Watanbe, Experimental-Study of the Fracture-Toughness of a
Ceramic/Ceramic-Matrix Composite Sandwich Structure, J. Am. Ceram. Soc., Vol 78 (No. 6), 1995, p
1633–1639
48. A. Ishida, M. Miyayama, and H. Yanagida, Prediction of Fracture and Detection of Fatigue in Ceramic
Composites from Electrical-Resistivity Measurements, J. Am. Ceram. Soc., Vol 77 (No. 4), 1994, p
1057–1061
49. M. Sakai and H. Ichikawa, Work of Fracture of Brittle Materials with Microcracking and Crack
Bridging, Int. J. Fract., Vol 55 (No. 1), 1992, p 65–79
50. J.B. Quinn and G.D. Quinn, “Indentation Brittleness of Ceramics: A Fresh Approach,” J. Mater. Sci.,
Vol 32 (No. 16), 1997, p 4331–4346
Fracture Toughness of Ceramics and Ceramic Matrix Composites
J.H. Miller, Oak Ridge National Laboratory P.K. Liaw, The University of Tennessee, Knoxville
An Overview of Fracture Mechanics
Fracture mechanics involves the stress analysis of cracking in structures or bodies with cracks or flaws. Most of
the work in this field has concentrated on the cracking behavior of metals, so this brief overview introduces the
concepts and ideas of LEFM and EPFM for metals (Ref 51, 52, and 53). This is followed by a description of the
use of LEFM and EPFM methods in the evaluation of monolithic ceramic and CMCs, respectively.
Linear-Elastic Fracture Mechanics
The use of LEFM is applicable under two conditions:
• The applied load deforms a cracked body in a linear-elastic manner.
• The flaw or crack is assumed to be a sharp crack with a tip radius near zero.
The stresses required for cracking under these two conditions can be analyzed according to LEFM by two
parameters: the energy release rate and the stress intensity factor.
The energy release rate, G, is the amount of stored energy that is available for an increment of crack extension:
(Eq 1)
where Π is the stored potential energy and A is the crack surface area that is created as the crack grows. In other
words, G is the amount of store elastic energy that is converted to surface energy as the crack grows. Because
the body behaves in an elastic manner, all of the energy available is used to create the crack surfaces (Ref 51,
52, and 53).
Expressions for the energy release rate can be derived based on the geometry of the crack and the loading
conditions. Two basic types of configurations are shown in Fig. 1 and 2 for an edge crack and a central through-
thickness crack, respectively, for Mode I (tensile opening) loads. In this case, crack length is defined by typical
convention as a for an edge crack (Fig. 1) and as a 2a for a central through-thickness crack (Fig. 2). With this
convention, then the value of G for a wide plate (plate width >> a) in plane stress is as follows (Ref 51, 52, and
53):
(Eq 2)
where σ is the applied stress, E is Young's modulus, and a is either the total length of an edge crack (Fig. 1) or
half the length of center crack (2a in Fig. 2). Equation 2 thus applies to both of these basic configurations in
Fig. 1 and 2 with the appropriate definition for a as shown.
Fig. 1 Schematic illustration of an edge-notched specimen. (a) Crack length, a, and general coordinate
system for crack tip stresses in Mode I loading.
Fig. 2 Schematic illustration stress distributions near the tip of a through-thickness crack an infinitely
wide plate (plate width >> than the crack length, 2a)
The stress intensity factor, K, is a measure of stress intensity in the entire elastic stress field around the crack
tip. It is derived based on the analysis of the stress field near the tip of a sharp crack, rather than an energy
consideration, as in the case of the energy release rate. The stress intensity factor can be related to the local
stress at the crack tip as:
(Eq 3)
where σ
YY
is the local stress near the tip of the crack, K
I
is the stress intensity factor with a Mode I (tensile
opening) load, and r is the distance in front of the crack tip (with θ = 0) (Fig. 1). The stress intensity factor in
Mode I loading can also be related to the applied or nominal stress as (Ref 51, 52, 53):
K
I
= σ
nom
Y
(Eq 4)
where σ
nom
is the nominal or applied stress and Y is a geometrical factor that is specific to a particular loading
condition and crack configuration. As in the case of Eq 2, the crack length, a, in Eq 4 is defined either as the
length of an edge crack (a in Fig. 1) or as one-half the length of a through-thickness crack (2a in Fig. 2). With
these definitions for a, Eq 4 applies for both an edge crack and a center crack configuration.
Figure 3 shows a schematic plot of the stress normal to the crack plane as a function of the distance, r, from the
crack tip for both σ
YY
and σ
nom
(Ref 51, 52, and 53). According to Eq 3 and Fig. 3, there is a singularity in the
stress field at the tip of the crack. This fact is the reason why elastic action is an important assumption in
LEFM. If significant plasticity occurred, the crack would be blunted by the plastic flow, and the stress intensity
solution would no longer be valid.