Volume 08 - Mechanical Testing and Evaluation Part 11 docx

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 t

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 JIc, 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 ZrO2 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 Reinforced Ceramic-Matrix Composites (CFCCs) at Ambient and Elevated Temperatures, invited paper

Fiber-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 Reinforced Ceramic Composite,” M.S Thesis, The University of Tennessee, Knoxville, 1995

Fabric-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:

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 σYY is the local stress near the tip of the crack, KI 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):

where σnom 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 σYY and σnom (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

Fig 3 Schematic plot of the stress field around a crack Source: Ref 52

With Eq 4, it is possible to relate the magnitude of the single parameter, K, to the applied stress and crack size

This is the basis for most common applications of LEFM Through the use of published expressions for the

geometry factor, Y, many common loading conditions and structures can be analyzed The published expressions for KI that include the proper Y for specific loading and cracking conditions are commonly called K-calibrations The calculated stress intensity factor from the K-calibration and the loading level can be

compared to a critical stress intensity value to determine the safety of the structure (Ref 51, 52, and 53)

The energy release rate is related to the stress intensity factor by the equation:

(Eq 5)

where E′ = E (Young's modulus) for plane stress conditions, or where:

(Eq 6) where ν is Poisson's ratio for plane strain conditions

Critical Crack Growth Crack extension can either be stable or unstable depending on material properties and specimen geometry Therefore, an important issue in LEFM is the definition of critical conditions that lead to unstable crack growth Critical conditions for unstable crack growth can be expressed as either a critical energy

release rate or a critical stress intensity factor The critical value is the value of G or K at the instant when

unstable crack extension occurs, that is, when the crack propagates through the specimen and thus causes the

specimen to break in two The critical energy release rate, Gc, or the critical stress intensity factor, Kc, are thus

defined as the values of G and K at the instant of unstable crack extension that leads to fracture Under these conditions, either parameter can be defined as the fracture toughness of the material Usually Kc is the chosen parameter to express the fracture toughness If the fracture toughness is not a function of specimen size or geometry then this fracture toughness value can be considered a material property Otherwise, the fracture toughness result is only valid under the conditions it was measured (Ref 51, 52, 53, and 54)

Crack Growth Resistance and R-Curves If stable crack growth occurs, a single value for fracture toughness is

difficult to define In the case of stable crack growth, a plot of the experimentally measured fracture parameter,

in terms of either G or K, versus crack length is developed This plot can be generated from the load and crack

length data taken from a material test The stress intensity or the energy release rate is calculated from the measured load and crack length data using expressions similar to those shown in Eq 2 and 4 (the correct expression must be used for the conditions of the test) Fracture parameters calculated in this way are defined as the resistance to crack growth parameters because they are calculated from a crack growing in a stable manner

The resistance to crack growth, expressed in terms of the energy release rate, is given the symbol R, and the resistance to crack growth, expressed in terms of the stress intensity factor, is given the symbol KR The plot of

resistance to crack growth, either R or KR, versus crack length is called a crack growth resistance curve, or

R-curve, and the entire curve becomes the measure of fracture toughness Schematic examples of R-curves plotted

in terms of G and K are shown in Fig 4 and 5, respectively (Ref 51, 52, andd 53)

Fig 4 Schematic crack growth resistance curves and crack driving force curves, in terms of the energy

release rate, G (a) Single-valued fracture toughness (b) Rising R-curve behavior Adapted from Ref 52

Fig 5 Schematic crack growth resistance curve and crack driving force curve in terms of the stress

intensity factor, K Adapted from Ref 52

Figure 5(a) shows a flat R-curve, which is the result of unstable crack growth The flat R-curve presents the ease of defining fracture toughness as a critical value for unstable crack growth, in this case Gc Figure 5(b) is

an example of an R-curve that demonstrates stable crack growth prior to instability Stable crack growth occurs because the crack growth resistance increases with increasing crack length This trend is called the rising R- curve behavior An R-curve plotted in terms of K rather than G is shown in Fig 5 (Ref 51, 52, and 53)

The R-curve can be used to predict the conditions that will cause crack extension To do this, it is necessary to

plot the crack driving force on the same axes as the crack growth resistance curve The curve for crack driving

force is calculated using the same expressions of K and G that relate the geometry and loading conditions to

fracture However, instead of using the data from a crack propagation test, the procedure is to calculate crack driving force curves by holding the stress, or load, constant and increasing the crack length incrementally The point where the crack driving force curve crosses the resistance curve represents the condition under which critical crack growth occurs (Ref 51, 52, and 53) The expected in-service stress levels of a cracked body can be evaluated from this

In summary, crack growth can either be stable or unstable If the driving force curve crosses the resistance curve at the tangency point, the crack growth will be unstable If it crosses below this point, the crack growth will be stable To determine the point where the unstable crack growth occurs it is necessary to establish an iterative scheme of generating driving force curves for different stress levels until tangency is achieved Schematic examples of driving force curves plotted with resistance to crack growth curves are also shown in

Fig 4 and 5 Also evident in the figures are definitions of the critical energy release rate, Gc Fig ( 4) and

critical stress intensity factor Kc (Fig 5) These critical values are defined at the point of instability (Ref 51, 52, and 53)

Elastic-Plastic Fracture Mechanics

EPFM does not have the requirement that the material behave in a linear-elastic manner Instead, nonlinear or plastic deformation is allowed in EPFM methods to a much greater extent than in LEFM methods The primary

fracture parameter for EPFM is the J-integral The J-integral, or more simply J, can be defined in two ways

(Ref 56, 57) The first is defined by a path-independent line integral around the crack tip The second is an

energy definition similar to G, except that linear behavior is not required

The energy definition of J states that J is a more general form of the energy release rate, G, where:

(Eq 7) When permanent deformation occurs (as in the case of plastic deformation of metals), some of the stored

potential energy, Π, is dissipated and is therefore unavailable for crack extension In this context, J can be thought of as the potential energy absorbed by a cracked body prior to crack growth In other words, J is a measure of the intensity of the entire elastic-plastic stress-strain field around the crack tip, and J reaches a

critical value just prior to crack extension

A special case of the energy definition of J is the value for G (when the energy is released as a crack grows in a

linear-elastic material) For the special case of linear-elastic behavior, there is little or no energy absorbed by permanent deformation, and the only energy dissipation is due to the crack surface creation Hence, under

linear-elastic conditions J = G:

(Eq 8)

where E′ is equal to E or is related to the elastic modulus per Eq 6

Under nonlinear conditions beyond the elastic regime, calculating J can be much more difficult Unlike the K solutions or K-calibrations (which exist for many different crack and load configurations with K values for many situations), expressions that relate J values to the applied load and crack configuration are very few For

the simple situation of an edge-cracked specimen under elastic-plastic loading conditions, the energy definition

of J is as follows:

(Eq 9)

where B is the specimen thickness, Δ is the load-line displacement, and U is the area under the P-Δ curve up to the initiation of crack growth (Ref 51, 52, and 53) where P is the applied load Because a certain amount of the deformation must always be elastic, the expression for J in Eq 9 can be separated into elastic and plastic

components and be rewritten as follows:

(Eq 10)

where ηPL is a dimensionless constant that depends on the specimen and loading configuration, UPL is the

plastic area under the P-Δ curve, and b is the remaining ligament (W-a, where W is the specimen width) Equation 11 is used in experimentally measuring J (Ref 51, 52, 53, and 57)

In the elastic-plastic regime, there is typically some amount of stable crack growth prior to an unstable crack extension The stable crack growth occurs because of energy dissipation and the crack blunting induced by

plastic deformation As a result, when J is experimentally measured, an R-curve based on the J parameter is generated This J-based R-curve is a plot of the resistance to crack growth, JR, as a function of crack length or

extension (Fig 4) The critical J, JIc in the opening mode, is then taken from the JR curve at a point near the initiation of crack growth (Ref 51, 52, 53, 54, 55, 56, and 57)

The basic procedure for experimentally measuring J involves testing a bend specimen or a compact tension specimen with a deep crack and using the load, displacement, and crack length data to calculate J with Eq 11 J

is calculated for several different crack lengths, and the JR curve is generated From the JR curve, the JIc is taken

at the point where initial crack extension occurred, as shown in Fig 6 The test can be done with one of two

goals If the point of the test is to determine JIc, J is calculated with less attention to the fact that some crack

extension occurred during the test Ignoring the crack extension does not present much error because the crack

growth initiation is the important feature in the test If the development of the full JR curve is the goal of the test, more care is taken in the data analysis to take into account the growing crack (Ref 51, 52, 53, 54, and 57)

Fig 6 Schematic crack growth resistance curve in terms of JR Adapted from Ref 52

References cited in this section

51 R.W Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley &

Sons, 1989

52 T.L Anderson, Fracture Mechanics, 2nd ed., CRC Press, 1995

53 J.M Barsom and S.T Rolfe, Fracture and Fatigue Control in Structures, Prentice-Hall, Inc., 1987

54 “Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials,” ASTM Standard E

399–90, ASTM Book of Standards, Vol 03.01, American Society for Testing and Materials, 1995

55 J.R Rice, Journal of Applied Mechanics, Vol 35, 1968, p 379–386

56 J.A Begley, G.A Clark, and J.D Landes, Results of an ASTM Cooperative Testing Procedure by

Round Robin Tests of HY130 Steel, JTEVA, Vol 10 (No 5), 1980

57 “Standard Test Method for JIC, A Measurement of Fracture,” ASTM Standard E 813-87, ASTM Book of Standards, Vol 03.01, American Society for Testing and Materials, 1995

Fracture Toughness of Ceramics and Ceramic Matrix Composites

J.H Miller, Oak Ridge National Laboratory P.K Liaw, The University of Tennessee, Knoxville

Fracture Mechanics of Ceramics and CMCs

The concepts of both LEFM and EPFM methods, as previously described in the context of metallic materials, provides a general basis for the fracture mechanics of monolithic ceramics and ceramic matrix composites Generally LEFM methods are applicable for monolithic ceramics while EPFM methods may be suitable for CMCs

Monolithic ceramics are inherently brittle due to their strong bonding and more complicated (less symmetric) crystal structures Compared to metallic materials, the mixed ionic and covalent atomic bonding and low-symmetry crystal structure of ceramics severely limit the opportunity for plastic deformation mechanisms from dislocation formation, movement, and slip Monolithic ceramics thus have high strength and stiffness with much less plastic deformation than metals As a result, their behavior is primarily linear-elastic, which is one of the required conditions for LEFM methods

The other condition for LEFM analysis is the presence of a sharp crack or flaw with a crack tip radius approaching zero Monolithic ceramics meet this condition as well, and LEFM has been used successfully to evaluate monolithic ceramic fracture behavior Some additional work was necessary to augment LEFM techniques to handle the difficulties of obtaining sharp starter cracks and maintaining stable crack growth that occur in brittle ceramics Nonetheless, the result of the application of LEFM to monolithic ceramics is a relatively mature state of the art Techniques exist to determine the single-valued critical fracture toughness and

to measure crack growth resistance behavior of monolithic ceramic materials Current research is centered on the further refinement of these techniques (see also the article“Fracture Resistance Testing of Brittle Solids” in this Volume)

Ceramic matrix composites are being developed in an attempt to increase the toughness and damage tolerance

of ceramic materials The toughness of CMCs is greater than the monolithic ceramics due to the toughening (energy-absorbing) mechanisms of microcracking, crack bridging, and crack branching These toughening mechanisms enable the CMC to behave in a manner that closely resembles the elastic-plastic behavior of metals Although this fact may suggest EPFM as appropriate for the study of CMCs, there are differences in the deformation mechanism of ductile metals and CMCs that can bring into question the appropriateness of metal-based EPFM methods for use with CMCs

Metals dissipate crack-tip energy by the plastic deformation mechanisms of slip, dislocation generation, and dislocation movement CMCs, on the other hand, dissipate crack tip energy through crack branching, fiber bridging, and microcracking In both cases, energy is dissipated by nonlinear deformation of the body prior to crack extension Fortunately, EPFM theory does not depend on the mechanism through which the energy is dissipated during nonlinear deformation, only on the fact that it does occur As a result, even though the deformation mechanisms are very different, EPFM theory is valid for both metals and CMCs Unfortunately, the complex nature of the processes that cause the nonlinear fracture behavior in CMCs complicates the

experimental application of EPFM methods to CMCs The following section describes toughness tests that are used on monolithic ceramics and CMCs

Fracture Toughness of Ceramics and Ceramic Matrix Composites

J.H Miller, Oak Ridge National Laboratory P.K Liaw, The University of Tennessee, Knoxville

Fracture Toughness Evaluation

This section describes some fracture toughness measurement techniques that are being used on ceramics and CMCs The descriptions are organized by specimen type, and they include advantages and disadvantages of each specimen type as well as experimental control schemes that have been employed on each specimen type More detailed information on the fracture toughness testing of monolithic ceramics is also provide in the article

“Fracture Resistance Testing of Brittle Solids” in this Volume

Single Edge Notch Bending (SENB) The SENB specimen, shown in Fig 7(a) has a rectangular cross section with a straight-through saw notch It is loaded in either three- or four-point bending The advantages of the SENB include ease of machining due to simple geometry and ease of use due to simple three- or four-point bend loading, which uses a fixture loaded in simple compression The SENB, while easy to machine and test, is not very stiff This leads to problems in starting a sharp crack at the end of the saw notch and in achieving stable crack extension (Ref 58)

Fig 7 Fracture toughness specimens (a) Single edge notch bending (SENB) (b) Compact tension (CT)

or wedge open loaded (WOL) (c) Double cantilever beam (DCB) tensile loading (d) DCB constant bending moment loading (e) DCB wedge loading (f) Tapered DCB (g) Chevron notch short rod (h) Chevron notch short bar (i) Chevron notch bending (j) Double torsion (DT) (k) Three-point bending

with controlled surface flaw (CSF) P, load Adapted from Ref 58

One method of producing a sharp starter crack in a SENB specimen involves using a hardness indenter to introduce a surface flaw and forcing the surface flaw to propagate to the outer edges and become a sharp edge crack This can be done by loading the indented specimen in compression between two rigid plates One of the plates has a single groove, and the indentation crack is positioned over the groove During the compressive loading, the surface flaw is subjected to tensile opening stresses due to the groove, while the bulk of the material is in compression This tension allows the crack to grow to become an edge crack, while the compression prevents the crack from propagating in an unstable manner through the specimen (Ref 59)

SENB specimens have been used to measure the fracture toughness of a yttria-partially stabilized zirconia PSZ) ceramic at ambient and elevated temperatures (Ref 59) The point of this work was to demonstrate the use

(Y-of a new technique (Y-of controlling the fracture test in such a way as to promote stable crack growth so that the

R-curve behavior of the ceramic could be measured Crack mouth opening displacement (CMOD) was monitored using a laser extensometer, and the CMOD signal was used in the control of the servohydraulic testing machine

in real time The results of this type of control were positive, and stable crack growth was achieved (Ref 59) The SENB method has also been improved by a scheme that employs both a method to provide for stable crack growth and better real-time computer-aided data acquisition (Ref 60) The crack growth stability was augmented by adjusting the stiffness of the test frame in such a way as to promote stable crack growth The test machine stiffness, or compliance, was adjusted by placing a “parallel elastic element” (PEL) supporting structure between the crosshead and the top of the three-point bend loading fixture (Fig 8) The optimum compliance for stable crack growth was determined by theoretical analysis and experimentation During testing, the compliance of the specimen and the test frame were continuously monitored in real time through the use of

a computer The real-time load and displacement data form various points in the test system, as presented in

Fig 8 After the optimum PEL compliance was determined, and stable crack growth was achieved, the R-curves

of the test materials were measured The real-time load and displacement (and, therefore, compliance) monitoring, along with compliance versus crack length calibrations and the stress intensity calibrations, allowed the crack length, crack velocity, and stress intensity level to be calculated in real time during the test (Ref 60)

Fig 8 Schematic of the compliance-controlled three-point bending test with a parallel elastic element (PEL) Adapted from Ref 60

Compact Tension (CT) The CT sample is a common specimen in fracture mechanics tests It is loaded in tension, but the primary stress is due to bending because the load line is offset from the crack front (Fig 7b) Relatively stable crack propagation is possible with the CT specimen if a stiff testing machine is used Also, a variant of the CT can be used in a wedge-opening mode to increase the stable crack growth capability (Ref 49)

The stable crack growth capability allows for the generation of R-curves using the CT specimen (Ref 61) The

CT specimen is complicated to machine in ceramic materials, and precracking the can be difficult (Ref 58)

In addition to R-curve measurements of monolithic ceramics (Ref 61), R-curves have been measured in CMCs using the CT specimen CT specimens have been employed to generate R-curves for CMCs in an attempt to

analyze the crack-face fiber-bridging stress field (the stress field in the wake of the crack that is due to fiber bridging) The crack-face fiber-bridging stress is evaluated by comparing the experimentally measured compliance versus crack length, which includes the contribution of the fiber bridging, to the compliance versus crack length data calculated from the elastic properties of the CMC, assuming no fiber bridges are present (Ref 62)

The J-parameter toughness has also been measured using a CT specimen (Ref 63) A J-based testing technique has been developed for CMCs using the CT specimen geometry The concept of the J-parameter is used to

determine the contribution of the process zone (the contribution of, for instance, fiber bridging and crack

branching, analogous to the plastic zone in metals) to the toughness of the CMC The J-parameter contribution

of the process zone is determined using Eq 12 (Ref 63):

where J∞ is the far field J, Jb is the process zone J (analogous to Jplastic), and Jtip is the crack tip J Also, it is assumed that elastic action takes place at the crack tip, so Jtip can be calculated from Ktip using Eq 9 The value

of J∞ was experimentally calculated from measurements using CT specimens with two different crack lengths,

a1 and a2 The value J∞ is the far-field J, as the crack grows from a1 to a2 Therefore, Jb was calculated from Eq

stable cracks The tapered DCB, shown in Fig 7(f), provides a constant KI level with crack growth Another

DCB variant that provides a constant KI level with crack growth is the moment-loaded DCB (Fig 7d) Unfortunately, the fixturing that applies the moment to the arms of the DCB can be difficult to deal with The final DCB variant is the wedge-loaded DCB (Fig 7e) The wedge loading allows the specimen to be tested in simple compression The wedge-loaded DCB specimen was first used in ASTM method E 561 All the DCB variants may need side grooves to keep the crack moving down the center of the specimen The grooves

complicate the K-calibration, and machining damage in the groove can affect the crack extension (Ref 58)

Specimens very similar to the constant bending moment DCB, called the Browne/Chandler test specimen, have

been employed in the determination of R-curves for monolithic ceramics (Ref 65) The Browne/Chandler

specimen geometry, shown in Fig 9, applies loads to the outside corners of a specimen, supported by a stiff solid base, that has a rectangular cross section and a vertical edge crack This loading induces a bending moment around the center of the specimen, which causes the crack to open and extend If the applied load were held constant, the stress intensity at the crack tip would decrease as the crack grew Therefore, the load must increase in order for crack growth to continue, which prevents unstable fracture Also, crack-guiding side grooves are not necessary because the compressive stress parallel to the crack keeps the crack growing down the center of the specimen Unfortunately, the Browne/Chandler test geometry does not lend itself to an

analytical solution of K-calibrations for all crack lengths As a result, stress intensities have to be estimated

using numerical methods at both very short and very long crack lengths (Ref 65)

Fig 9 Schematic sketch of the Browne/Chandler test geometry Adapted from Ref 65

Chevron Notch Methods (CHV) The chevron notch is used in three specimens (Ref 58, 66) There is a short rod CHV (Fig 7g), a short rectangular bar CHV (Fig 7h), and a bend bar with a rectangular cross section and a chevron notch (Fig 7i) The chevron notch geometry, due to the increase in the width of the crack surface

during crack extension, forces rising R-curve behavior in ideally brittle materials This means that after crack

initiation, the crack front is stable and is always ideally sharp Stable crack growth is not always found in practice due to the fact that excess stored energy in the specimen can overcome the geometrical tendency to

force rising R-curve behavior In these cases, the excess stored energy can cause catastrophic failure in the

specimen As a result, a stiff specimen geometry and test machine are important (Ref 58, 66)

One of the main advantages of the chevron notch geometry is the fact that it is possible to calculate the fracture toughness based on the maximum load and the specimen dimensions alone for ideally brittle materials Due to

the shape of the growing crack, the geometry factor, Y, goes through a minimum as crack growth occurs The

minimum in the geometry factor corresponds to the maximum load in the test This unique fact allows the fracture toughness to be calculated without knowledge of the crack length (Ref 58) However, calculation of fracture toughness from the maximum load and specimen dimensions does not work for materials that exhibit

natural rising R-curve behavior In these cases, the minimum in the geometry factor versus crack length does

not correspond with the maximum load, and the crack length must be known to calculate the fracture toughness (Ref 58)

The chevron notch specimen has become almost a standard for measuring fracture toughness in ceramic materials (Ref 58, 67, 68, and 69) In fact, the only ASTM standard test method for determining the fracture toughness of ceramics, B 771-87, uses the short rod and short bar chevron notch specimen (Ref 69) In addition, chevron notch samples are used in ASTM PS70, “Provisional Test Method For Determining The Fracture Toughness of Advanced Ceramics at Ambient Temperatures” (Ref 66) Also, researchers with new fracture tests use chevron notch results to benchmark the results of the new tests (Ref 61, 70, and 71)

Double Torsion (DT) The DT specimen, shown in Fig 7(j), is a flat plate with a longitudinal through crack that

is loaded in torsion The torsional loading applies a bending moment that opens the crack on the tensile surface

and closes the crack on the compressive surface The applied moment causes the KI level to be constant over a wide range of crack length It also causes the crack front to be significantly curved between the top and bottom surfaces This curvature of the crack front opposes the straight-through crack assumptions used in the stress intensity calculation, and causes errors in the toughness calculation (Ref 58)

Indentation Techniques Indentation fracture toughness techniques utilize a sharp crack introduced in the material by a Knoop or a Vickers indenter The Knoop indenter causes a single crack, which makes it attractive for use in fracture mechanics methods involving a surface flaw The Vickers indenter creates two cracks that

are mutually perpendicular to each other Both indentation methods can produce reproducible surface cracks, but the residual stress field from the indentation is complicated and must be removed or accounted for in the analysis (Ref 58, 72, 73, and 74)

Indentation creates subsurface cracks, due to tensile stress formation, just below the contact point of the indenter These subsurface cracks are called median cracks As the indenter is removed, the median cracks become unstable and grow to the indented surface The resulting crack is called a radial crack In some high-toughness brittle systems, small radial surface cracks can form prior to subsurface median crack formation These shallow surface cracks are called Palmqvist cracks Schematic drawings of median, radial, and Palmqvist cracks are shown in Fig 10 (Ref 58, 72, 73, 74)

Fig 10 Schematic diagram illustrating types of crack systems formed around an indentation Adapted from Ref 42, 71

There are three indentation-induced crack techniques for measuring fracture toughness in ceramics: the controlled surface flaw (CSF) technique, the indentation microfracture (IM) technique, and the indentation strength in bending (ISB) technique The CSF method can provide a quantitative measure of the fracture toughness because the stress intensity around the surface flaw is well known, but the IM and ISB provide only estimates based on empirical expressions (Ref 58, 72, 73,and 74)

The CSF method involves testing a bending specimen with an elliptical surface crack induced by a Knoop indenter (see Fig 7k) The Knoop indenter is used to create a subsurface median crack Then, the surface is carefully polished to remove the indent and the associated residual stresses The polishing also reveals the median crack to the surface, and an elliptical surface flaw with no residual stress is the result When the

specimen is tested, the surface flaw causes the initiation of fracture, and KIc can be calculated based on the applied loads and the crack size (Ref 58, 73)

The ISB is similar to the CSF technique (Ref 73) The ISB approach uses the Vickers indenter to induce

median-radial cracks on the tensile surface of a bending specimen Through manipulation of the K-calibrations

for the crack system, which account for both the applied and residual stresses, it is possible to develop an expression that relates the fracture stress in bending and the indentation load to the fracture toughness Therefore, the ISB method involves calculating the fracture toughness based on the indentation load and the experimental fracture stress from a bending test This method has the advantage of being relatively simple to conduct, and there is no need to measure crack size The disadvantage comes from the use of empirical factors

in the manipulation of the K-calibrations that are used to develop the expression relating the indentation load

and fracture stress to the fracture toughness This causes the fracture toughness measured by this method to be only an estimate (Ref 58, 73)

Another fracture toughness specimen that uses a Vickers hardness indenter to introduce sharp cracks into a ceramic material is the miniature disk bend test (MDBT) specimen (Ref 70, 75) These specimens are 3 mm (0.1 in.) in diameter and range in thickness from 200 to 700 μm Vickers indentation cracks are introduced into the center of the tensile side of the specimen The disk specimen is loaded in a ring-on-ring bending mode, schematically shown in Fig 11 The MDBT is similar to the ISB test In both experiments, the fracture stress

and indentation load are related to the fracture toughness Therefore, the fracture toughness is calculated from the indentation load and the fracture stress from the MDBT The advantages of the MDBT are the small amount

of material that is needed to conduct the test and the fact that the crack length need not be measured (Ref 70, 75)

Fig 11 Schematic sketch of the miniature disk bend test (MDBT) geometry Adapted from Ref 70

The indentation microfracture (IM) method introduces cracks into the surface of a sample with a Vickers indenter and uses the length of those cracks to estimate the fracture toughness (Ref 58, 72) This method is very attractive because it is so easy to conduct the test As a result, many good empirical toughness relations have been generated for specific crack geometries It is important in this method to ensure that median-radial cracks are analyzed rather than Palmqvist cracks The shallow Palmqvist cracks are hard to measure, and, consequently, significant error and scatter are introduced in the data (Ref 58, 71)

Typical Fracture Toughness Properties of Ceramics and CMCs The critical fracture toughness, KIc, of monolithic ceramics is low, on the order of 1 to 4 MPa (0.9 to 3.5 ksi ), while CMCs can have toughness values near 20 MPa (18 ksi ) The KIc values for several ceramics and a few CMCs are

shown in Table 1 Where possible, the values of KIc measured by different methods on the same material are included for comparison From the table, it is evident that the many methods agree well

Table 1 Typical ceramic and CMC properties

Ceramics can exhibit either flat or rising R-curve behavior, depending on processing-derived microstructure (Ref 67) Figure 12 shows R-curves for three different silicon nitride (Si3N4) materials, A, B, and C The R-

curves were measured using short bar chevron notch methods Material A is a hot pressed commercial Si3N4

(SN-84H by NGK Technical Ceramics) with low fracture toughness; it results in flat R-curve behavior

Materials B and C, which have relatively higher fracture toughness, are monolithic Si3N4 (AS700 by Allied Signal Inc.) prepared by gas pressure sintering green billets, which were formed by cold isostatic pressing These two Si3N4 materials exhibit rising R-curve behavior (Ref 67)

Fig 12 R-curves of three Si3 N 4 ceramic materials measured by the short rod chevron notch technique Adapted from Ref 67

An R-curve from short bar chevron notch tests on a SiC-whisker-reinforced alumina matrix composite is presented in Fig 13 (Ref 67) The whisker-reinforced alumina composite also exhibits rising R-curve behavior

Fig 13 Rising R-curve of a SiC whisker reinforced alumina ceramic matrix composite (CMC), measured

by the double cantilever beam technique Adapted from Ref 67

The rising R-curve behavior of an isostacally pressed and sintered ceria-partially stabilized zirconia (Ce-PSZ) ceramic is given in Fig 14 (Ref 61) This R-curve was measured using a crack line wedge-loaded (CLWL)

technique, which is a wedge-loaded variant of the compact tension specimen

Fig 14 Rising R-curve of a Ce-PSZ ceramic measured by the crack line wedge loaded technique a and w

refer to dimensions defined in Fig 7(c) Adapted from Ref 61

Table 2 presents critical toughness expressed in terms of the J-integral, Jc, for short Nicalon fiber-reinforced

foam glass matrix composites (Ref 63) Values for Jc range from 3.5 to 241.8 N/m, depending on fiber length

and fiber volume fraction The interface condition also strongly affects the value of Jc (Ref 64) Table 3 shows a

wide range of Jc values for continuous woven Nicalon fiber fabric-reinforced SiC matrix composites produced

by chemical vapor infiltration In Table 3, the interface condition is given an arbitrary designation of numbers from one to ten The interfaces of these composites were modified by applying various multilayered carbon and SiC fiber coatings, the details of which are can be found in Ref 64 Table 3 clearly shows that the interface

condition causes the value of Jc to vary over a wide range from 11800 to 28520 N/m Also notice that the

values of Jc for the materials of Tables 2 and 3 are quite different This fact indicates that composite constituent materials, volume fractions, and interfacial properties all have a very pronounced effect on the toughness of CMCs

Table 2 Jc values for short Nicalon fiber reinforced foam glass matrix composites

Fiber length, mm Fiber volume fraction, % Jc, N/m

References cited in this section

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

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

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

2), 1993, p 53–78

59 J.Y Pastor, J Llorca, J Planas, and M Elices, Stable Crack-Growth in Ceramics at Ambient and

Elevated-Temperatures, J Eng Mater Technol (Trans ASME), Vol 115 (No 3), 1993, 281–285

60 V.G Borovik, V.M Chushko, and S.P Kovalev, Computer-Aided, Single-Specimen Controlled

Bending Test for Fracture-Kinetics Measurements in Ceramics, J Am Ceram Soc., Vol 78 (No 5),

1995, p 1305–1312

61 J.C Descamps, A Poulet, P Descamps, and F Cambier, A Novel Method to Determine the R-Curve

Behavior of Ceramic Materials—Application to a Ceria-Partially Stabilized Zirconia, J Eur Ceram Soc., Vol 12 (No 1), 1993, p 71–77

62 V Kostopoulos and Y.P Markopoulos, On the Fracture Toughness of Ceramic Matrix Composites,

Mater Sci Eng A, Vol 250 (No 2), 1998, p 303–312

63 T Hashida, V.C Li, and H Takahashi, New Development of the J-Based Fracture Testing Technique

for Ceramic-Matrix Composites, J Am Ceram Soc., Vol 77 (No 6), 1994, p 1553–1561

64 C Droillard and J Lamon, Fracture Toughness of 2-D Woven SiC/SiC CVI-Composites with

Multilayered Interphases, J Am Ceram Soc., Vol 79 (No 4), 1996, p 849–858

65 H.W Chandler, R.J Henderson, M.N Al Zubaidy, M Saribiyik, and A Muhaidi, A Fracture Test for

Brittle Materials, J Eur Ceram Soc., Vol 17 (No 6), 1997, p 759–763

66 “Provisional Test Method For Determining The Fracture Toughness Of Advanced Ceramics At Ambient

Temperatures,” ASTM PS70, Annual Book of Standards, Vol 15.01, American Society for Testing and

Materials, 1996

67 D.J Lee, Simple Method to Measure the Crack Resistance of Ceramic Materials, J Mater Sci., Vol 30

(No 8), 1995, p 4617–4622

68 P.A Withey, R.L Brett, and P Bowen, Use of Chevron Notches for Fracture-Toughness Determination

in Brittle Solids, Mater Sci Technol., Vol 8 (No 9), 1992, p 805–809

69 “Standard Test Method for Short Rod Fracture Toughness of Cemented Carbides,” ASTM Standard B

771-87, ASTM Book of Standards, Vol 02.05, American Society for Testing and Materials, 1995

70 J.M Zhang and A.J Ardell, Measurement of the Fracture-Toughness of Ceramic Materials Using a

Miniaturized Disk-Bend Test, J Am Ceram Soc., Vol 76 (No 5), 1993, p 1340–1344

71 S Danchaivijt, D.K Shetty, and J Eldridge, Critical Stresses for Extension of Filament-Bridged Matrix Cracks in Ceramic-Matrix Composites—An Assessment with a Model Composite with Tailored

Interfaces, J Am Ceram Soc., Vol 78 (No 5), 1995, p 1139–1146

72 G.R Anstis, P Chantikul, B.R Lawn, and D.B 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

73 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., Vol 64 (No

9), 1981, p 539–543

74 B.R Lawn, A.G Evans, and D.B Marshall, Elastic/Plastic Indentation Damage in Ceramics: The

Median Radial Crack System, J Am Ceram Soc., Vol 63 (No 9/10), 1980, p 574–581

75 S.J Eck and A.J Ardell, Fracture Toughness of Polycrystalline NiAl from Finite-Element Analysis of

Miniaturized Disk-Bend Test Results, Metall Mater Trans A, Vol 28 (No 4), 1997, p 991–996

Fracture Toughness of Ceramics and Ceramic Matrix Composites

J.H Miller, Oak Ridge National Laboratory P.K Liaw, The University of Tennessee, Knoxville

Summary

As described in this article (and the article “Fracture Resistance Testing of Brittle Solids” in this Volume), several test methods are used for the determination of the fracture behavior of ceramics Many of these methods include several variations of their own, suggesting the need for more standardization of test methods

From the preceding discussions, fracture toughness determination of monolithic ceramics appears to be mature The fact that most monolithic ceramics behave in a linear-elastic manner has allowed the direct transition of theory from LEFM developed for metals to use on ceramics Current fracture toughness research on monolithic ceramics is centered on refining test methods, data acquisition techniques, and theoretical and numerical analyses (Ref 48, 60, 67, and 70) Methods have been developed to overcome the difficulties in initiating sharp starter cracks (Ref 58, 59), providing stable crack growth (Ref 61, 65, and 67), and minimizing the amount of expensive test materials required for fracture testing (Ref 59, 70)

Fracture toughness evaluation for CMCs is much less developed than for monolithic ceramics The plastic-like failure behavior of CMCs makes EPFM look like an attractive method for evaluating their fracture behavior Some, but not much, research based on EPFM methods has been used in attempts to quantify the contribution of plastic-like mechanisms in CMCs (Ref 63, 64) Unfortunately, the low level of understanding of the very complicated toughening mechanisms of microcracking, fiber bridging, and crack branching precludes a direct transition of the EPFM theory that exists for metals to CMCs

elastic-The permanent or plastic deformation that EPFM was developed to handle in metals is due to the dislocation creation, movement, and slip These metallic plasticity concepts were well understood prior to the development

of EPFM, and were, therefore, available to influence the development of EPFM In contrast, the plastic-like mechanisms in CMCs are microcracking, crack bridging, and crack branching A significant amount of work still needs to be done before these complicated mechanisms are well understood As a result, the development

of EPFM methods for CMCs is, and will continue to be, slow

The bulk of the current research on CMC behavior centers on increasing the understanding of the CMC toughening mechanisms Researchers continue to work on understanding the fracture mechanisms in CMCs at many levels (Ref 71, 76, 77, 78, and 79) Much research is still being done to evaluate the forces and stresses involved in the fiber bridging that occurs in the wake of cracks (Ref 71, 76, 77, 78, and 79) The ultimate goal

of the research is to develop theories that will connect the results of LEFM and EPFM tests to the complex mechanisms of microcracking, crack bridging, and crack branching As this goal is achieved, mature fracture mechanics technology will be realized for CMCs

References cited in this section

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

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

2), 1993, p 53–78

59 J.Y Pastor, J Llorca, J Planas, and M Elices, Stable Crack-Growth in Ceramics at Ambient and

Elevated-Temperatures, J Eng Mater Technol (Trans ASME), Vol 115 (No 3), 1993, 281–285

60 V.G Borovik, V.M Chushko, and S.P Kovalev, Computer-Aided, Single-Specimen Controlled

Bending Test for Fracture-Kinetics Measurements in Ceramics, J Am Ceram Soc., Vol 78 (No 5),

1995, p 1305–1312

61 J.C Descamps, A Poulet, P Descamps, and F Cambier, A Novel Method to Determine the R-Curve

Behavior of Ceramic Materials—Application to a Ceria-Partially Stabilized Zirconia, J Eur Ceram Soc., Vol 12 (No 1), 1993, p 71–77

63 T Hashida, V.C Li, and H Takahashi, New Development of the J-Based Fracture Testing Technique

for Ceramic-Matrix Composites, J Am Ceram Soc., Vol 77 (No 6), 1994, p 1553–1561

64 C Droillard and J Lamon, Fracture Toughness of 2-D Woven SiC/SiC CVI-Composites with

Multilayered Interphases, J Am Ceram Soc., Vol 79 (No 4), 1996, p 849–858

65 H.W Chandler, R.J Henderson, M.N Al Zubaidy, M Saribiyik, and A Muhaidi, A Fracture Test for

Brittle Materials, J Eur Ceram Soc., Vol 17 (No 6), 1997, p 759–763

67 D.J Lee, Simple Method to Measure the Crack Resistance of Ceramic Materials, J Mater Sci., Vol 30

(No 8), 1995, p 4617–4622

70 J.M Zhang and A.J Ardell, Measurement of the Fracture-Toughness of Ceramic Materials Using a

Miniaturized Disk-Bend Test, J Am Ceram Soc., Vol 76 (No 5), 1993, p 1340–1344

71 S Danchaivijt, D.K Shetty, and J Eldridge, Critical Stresses for Extension of Filament-Bridged Matrix Cracks in Ceramic-Matrix Composites—An Assessment with a Model Composite with Tailored

Interfaces, J Am Ceram Soc., Vol 78 (No 5), 1995, p 1139–1146

76 P Brenet, F Conchin, G Fantozzi, P Reynaud, D Rouby, and C Tallaron, Direct Measurement of Crack-Bridging Tractions: A New Approach to the Fracture Behavior of Ceramic/Ceramic Composites,

Compos Sci Technol., Vol 56 (No 7), 1996, p 817–823

77 C.H Hsueh, Crack-Wake Interfacial Debonding Criteria for Fiber-Reinforced Ceramic Composites,

Acta Metall., Vol 44 (No 6), 1996, p 2211–2216

78 D.R Mumm and K.T Faber, Interfacial Debonding and Sliding in Brittle-Matrix Composites Measured

Using an Improved Fiber Pullout Technique, Acta Metall., Vol 43 (No 3), 1995, p 1259–1270

79 A Domnanovich, H Peterlik, and K Kromp, Determination of Interface Parameters for Carbon/Carbon

Composites by the Fibre-Bundle Pull-Out Test, Compos Sci Technol, Vol 56, 1996, p 1017–1029

Fracture Toughness of Ceramics and Ceramic Matrix Composites

J.H Miller, Oak Ridge National Laboratory P.K Liaw, The University of Tennessee, Knoxville

Acknowledgments

Professor P.K Liaw is kindly and greatly supported by the NSF Division of Design, Manufacture, and Industrial Innovation, under Grant No DMI-9724476, and the Combined Research-Curriculum Development (CRCD) Program under EEC-9527527 to the University of Tennessee, Knoxville (UTK), with Dr Delcie R Durham and Ms Mary Poats as program managers, respectively We would like to acknowledge the financial support of the Office of Research and the Center for Materials Processing at UTK We would also like to express our appreciation to Dr John Landes, Dr Allen Yu, and Dr Ray Buchanan, all from UTK, for their comments and help during the preparation of this article

This research was performed in cooperation with the UTK under contract 11X-SN191V with the Martin Energy Research Corporation and is sponsored by the US Department of Energy, Assistant Secretary for Conservation and Renewable Energy, Office of Industrial Technology, Industrial Energy Division, under contract DE-AC05-84OR21400 with the Lockheed-Martin Energy Research Corporation

Lockheed-Fracture Toughness of Ceramics and Ceramic Matrix Composites

J.H Miller, Oak Ridge National Laboratory P.K Liaw, The University of Tennessee, Knoxville

References

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 ZrO2 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 Reinforced Ceramic-Matrix Composites (CFCCs) at Ambient and Elevated Temperatures, invited paper

Fiber-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,

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 Reinforced Ceramic Composite,” M.S Thesis, The University of Tennessee, Knoxville, 1995

Fabric-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

51 R.W Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd ed., John Wiley &

Sons, 1989

52 T.L Anderson, Fracture Mechanics, 2nd ed., CRC Press, 1995

53 J.M Barsom and S.T Rolfe, Fracture and Fatigue Control in Structures, Prentice-Hall, Inc., 1987

54 “Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials,” ASTM Standard E

399–90, ASTM Book of Standards, Vol 03.01, American Society for Testing and Materials, 1995

55 J.R Rice, Journal of Applied Mechanics, Vol 35, 1968, p 379–386

56 J.A Begley, G.A Clark, and J.D Landes, Results of an ASTM Cooperative Testing Procedure by

Round Robin Tests of HY130 Steel, JTEVA, Vol 10 (No 5), 1980

57 “Standard Test Method for JIC, A Measurement of Fracture,” ASTM Standard E 813-87, ASTM Book of Standards, Vol 03.01, American Society for Testing and Materials, 1995

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

2), 1993, p 53–78

59 J.Y Pastor, J Llorca, J Planas, and M Elices, Stable Crack-Growth in Ceramics at Ambient and

Elevated-Temperatures, J Eng Mater Technol (Trans ASME), Vol 115 (No 3), 1993, 281–285

60 V.G Borovik, V.M Chushko, and S.P Kovalev, Computer-Aided, Single-Specimen Controlled

Bending Test for Fracture-Kinetics Measurements in Ceramics, J Am Ceram Soc., Vol 78 (No 5),

1995, p 1305–1312

61 J.C Descamps, A Poulet, P Descamps, and F Cambier, A Novel Method to Determine the R-Curve

Behavior of Ceramic Materials—Application to a Ceria-Partially Stabilized Zirconia, J Eur Ceram Soc., Vol 12 (No 1), 1993, p 71–77

62 V Kostopoulos and Y.P Markopoulos, On the Fracture Toughness of Ceramic Matrix Composites,

Mater Sci Eng A, Vol 250 (No 2), 1998, p 303–312

63 T Hashida, V.C Li, and H Takahashi, New Development of the J-Based Fracture Testing Technique

for Ceramic-Matrix Composites, J Am Ceram Soc., Vol 77 (No 6), 1994, p 1553–1561

64 C Droillard and J Lamon, Fracture Toughness of 2-D Woven SiC/SiC CVI-Composites with

Multilayered Interphases, J Am Ceram Soc., Vol 79 (No 4), 1996, p 849–858

65 H.W Chandler, R.J Henderson, M.N Al Zubaidy, M Saribiyik, and A Muhaidi, A Fracture Test for

Brittle Materials, J Eur Ceram Soc., Vol 17 (No 6), 1997, p 759–763

66 “Provisional Test Method For Determining The Fracture Toughness Of Advanced Ceramics At Ambient

Temperatures,” ASTM PS70, Annual Book of Standards, Vol 15.01, American Society for Testing and

Materials, 1996

67 D.J Lee, Simple Method to Measure the Crack Resistance of Ceramic Materials, J Mater Sci., Vol 30

(No 8), 1995, p 4617–4622

68 P.A Withey, R.L Brett, and P Bowen, Use of Chevron Notches for Fracture-Toughness Determination

in Brittle Solids, Mater Sci Technol., Vol 8 (No 9), 1992, p 805–809

69 “Standard Test Method for Short Rod Fracture Toughness of Cemented Carbides,” ASTM Standard B

771-87, ASTM Book of Standards, Vol 02.05, American Society for Testing and Materials, 1995

70 J.M Zhang and A.J Ardell, Measurement of the Fracture-Toughness of Ceramic Materials Using a

Miniaturized Disk-Bend Test, J Am Ceram Soc., Vol 76 (No 5), 1993, p 1340–1344

71 S Danchaivijt, D.K Shetty, and J Eldridge, Critical Stresses for Extension of Filament-Bridged Matrix Cracks in Ceramic-Matrix Composites—An Assessment with a Model Composite with Tailored

Interfaces, J Am Ceram Soc., Vol 78 (No 5), 1995, p 1139–1146

72 G.R Anstis, P Chantikul, B.R Lawn, and D.B 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

73 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., Vol 64 (No

9), 1981, p 539–543

74 B.R Lawn, A.G Evans, and D.B Marshall, Elastic/Plastic Indentation Damage in Ceramics: The

Median Radial Crack System, J Am Ceram Soc., Vol 63 (No 9/10), 1980, p 574–581

75 S.J Eck and A.J Ardell, Fracture Toughness of Polycrystalline NiAl from Finite-Element Analysis of

Miniaturized Disk-Bend Test Results, Metall Mater Trans A, Vol 28 (No 4), 1997, p 991–996

76 P Brenet, F Conchin, G Fantozzi, P Reynaud, D Rouby, and C Tallaron, Direct Measurement of Crack-Bridging Tractions: A New Approach to the Fracture Behavior of Ceramic/Ceramic Composites,

Compos Sci Technol., Vol 56 (No 7), 1996, p 817–823

77 C.H Hsueh, Crack-Wake Interfacial Debonding Criteria for Fiber-Reinforced Ceramic Composites,

Acta Metall., Vol 44 (No 6), 1996, p 2211–2216

78 D.R Mumm and K.T Faber, Interfacial Debonding and Sliding in Brittle-Matrix Composites Measured

Using an Improved Fiber Pullout Technique, Acta Metall., Vol 43 (No 3), 1995, p 1259–1270

79 A Domnanovich, H Peterlik, and K Kromp, Determination of Interface Parameters for Carbon/Carbon

Composites by the Fibre-Bundle Pull-Out Test, Compos Sci Technol, Vol 56, 1996, p 1017–1029

Fracture Resistance Testing of Brittle Solids

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

Introduction

CATASTROPHIC FAILURE best typifies the characteristic behavior of brittle solids in the presence of cracks

or crack-like flaws under ambient conditions Examples of engineering materials that behave as brittle solids include glasses, ceramics, and hardened metal alloys, such as bearing or brake steels Figure 1 shows the linear-elastic stress-strain curves and abrupt failures of a glass and a ceramic This behavior is contrasted with the linear/nonlinear stress-strain curves and “graceful” failure of a ductile-like material, such as a metal, or in this case, a continuous fiber-reinforced composite

Fig 1 Comparison of stress-strain curves for ceramics and glasses (as examples of brittle solids) and fiber-reinforced composites (as examples of nonbrittle solids) Source: Ref 1

Sometimes under nonambient conditions, materials that normally fail in a ductile manner may fail in a brittle manner (e.g., carbon steel at temperatures less than their nil-ductility) and those materials that normally fail in a brittle manner may exhibit pseudo-plasticity and failure in a ductile manner (e.g., ceramics containing glassy secondary phases at temperatures greater than the glass-softening temperature)

Because catastrophic failure occurs without warning and can occur in any engineering material under the

“suitably wrong” conditions, it is important to characterize the fracture behavior of materials in order to produce engineering designs that can accommodate this phenomenon This article reviews the fracture behavior

of brittle solids and the various methods that have been developed to characterize this behavior

Reference cited in this section

1 G.D Quinn, Strength and Proof Testing, Ceramics and Glasses, Vol 4, Engineering Materials Handbook, ASM International, 1991, p 585–598

Fracture Resistance Testing of Brittle Solids

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

Concepts of Fracture Mechanics as Applied to Brittle Materials

Many assumptions accompany engineering analyses For example, in fundamental mechanics of materials it is often assumed that materials are linear elastic, homogeneous, uniform, and isotropic from a macroscopic view These assumptions are more or less appropriate for polycrystalline materials without any crystallographic ordering Microscopically, of course, these assumptions become tenuous at best, especially for dimensional scales on the order of grain sizes

In the study of crack and material interactions, fundamental engineering fracture mechanics also makes several assumptions These include the linear elastic, homogeneous, uniform, and isotropic assumptions of material response In addition, it is assumed that the change in stored elastic strain energy is used entirely by the fracture process in creating new fracture surfaces and that the crack itself exists in an infinite body and is not influenced

by any boundary conditions Using these assumptions, it is possible to write the original Griffith criterion for fracture in terms of an applied fracture stress (Ref 1, 2, and 3):

(Eq 1)

where σf is the applied stress at fracture, γf is the energy required to create a unit of fractured surface area (i.e.,

fracture surface energy), E is the elastic modulus, ν is Poisson's ratio, and c is the flaw (i.e., crack) dimension (in the case of an internal flaw, the radius) The observed fracture strengths, Sf, of brittle solids (i.e., the applied

stress at fracture given by Eq 1 where Sf = σf) are related to the size and distributions of the strength-limiting

flaws, c, in the material (assuming γf, E, and ν are deterministic material properties) Strength distributions are

therefore related to the distributions of these f laws: intrinsic flaws (e.g., those due to processing) are those that can be treated as microcracks (short cracks) and are on the order of the microstructure; extrinsic or induced flaws (e.g., those due to service) are those that can be treated as macrocracks (long cracks) and are on the order

of component dimensions Note that sometimes extrinsic flaws may be of the same dimensional order as intrinsic flaws

The microcrack-like flaws are randomly distributed in size, location, orientation, and shape (scattered) throughout brittle materials, causing a range of fracture strengths in otherwise identical components or parts This inherent scatter leads to fracture strengths that are related to the geometric size (i.e., surface area or volume) of the component In other words, the larger the component is, the greater the probability of a larger (or properly oriented, or properly shaped, etc.) flaw to occur and, hence, the lower the fracture strength is Therefore, fracture strength is not a deterministic property in brittle materials unless the flaws are extremely uniform and consistent Factors of safety in the conventional sense cannot be used Strength values vary significantly with size and shape of the component (or test specimen) and with processing conditions There may even be batch-to-batch differences as a consequence of material inconsistencies These factors, coupled with the “inherent” brittleness of the materials, mean that either extremely conservative stress/strength-based deterministic design philosophies or probabilistic reliability methods must be used for components fabricated from brittle materials

The concepts of engineering fracture mechanics can be applied when a flaw has a measurable crack size In this case, the stress field at the crack tip is described in terms of stress intensity factor, which can be written as (Ref

4, 5):

where K is the stress intensity factor, σ is an applied stress, Y is a geometry correction factor, and a is the

macrocrack dimension Three “modes” of fracture are related to the “mode” of loading (Fig 2) Mode I, the

“opening mode,” is considered to be the limiting case for the tendency to fracture because a tensile normal stress “opens” the crack with the resulting stresses in the material “carried” at the crack tip (as opposed to partially distribute through interaction of the crack faces as in modes II and III)

Fig 2 Modes of fracture Mode I (opening), mode II (sliding), and mode III (tearing) Source: Ref 4

The critical mode I condition for brittle fracture in a component with a crack-like flaw is reached at a

combination of the crack/component geometry correction factor, Y; a sufficiently high tensile, normal stress, σ; and a sufficiently long, sharp crack, a If the fracture resistance of the material is not a function of crack length

then catastrophic fracture will occur in the component when the stress intensity factor is equal to the critical stress intensity factor at fracture in the component:

where KI is the mode I stress intensity factor and KIc is the fracture toughness* of the material (i.e., resistance to fracture), which can be related to fundamental fracture behavior of the material through the Griffith approach (Ref 1, 4):

Note that Eq 3 is a necessary, but not sufficient, condition for fracture From the Griffith fracture criterion,

fracture does not occur at the extreme value of the energy balance as a function of crack length, U = f(c), but rather when the derivative of this energy with respect to the crack length, dU/dc, is equal to zero (Ref 3)

If the resistance of the material to fracture is denoted as R, then, according to Ref 3, the conditions for unstable

(brittle catastrophic) fracture can be written as:

(Eq 5a) Stable (noncatastrophic) fracture is represented as:

(Eq 5b)

where dK/dc and dR/dc are the derivatives of the stress intensity factor, K, and the fracture resistance of the material, R, with respect to the crack length, c, respectively Equations 5a(a) and 5b(b) can be illustrated as a fracture resistance or R-curve, as shown in Fig 3 Note that the R term can be further described in parts such

that (Ref 3):

where Ro can be considered the intrinsic fracture resistance, and R(c) is the R-curve component Note that at some finite length of crack extension, R becomes constant and R(c) is no longer a function of c This “steady- state” value of fracture resistance [R∞ ≠ f(c)] corresponds to fully developed “toughening mechanisms” (Ref 1, 3) R-curve behavior in brittle materials typically develops because of microstructural effects, as shown in Fig

4 R-curve effects often confuse and frustrate attempts to experimentally measure Ro (or KIc) because the effects

of crack growth history add to experimental scatter if R (or KIc) is measured and reported outside the context of the crack extension

Fig 3 Schematic representation of R-curve behavior

Fig 4 Microstructural features responsible for fracture resistance as a function of crack length (R-curve

effects) Source: Ref 1

Part of the debate surrounding the development of standardized test methods (Ref 7, 8, 9, and 10) for determining the fracture resistance of brittle ceramics has been whether the test method should measure the

intrinsic fracture resistance, Ro, or the fully developed fracture resistance, R∞ To address this question, the operational aspects of the test method must take into account intrinsic versus extrinsic flaws (or cracks), the degree of crack extension prior to measurement of the fracture resistance, the resulting linearity (or nonlinearity) of the loading curve, features on the fracture surfaces, and other “clues” indicating brittle or nonbrittle fracture

Typically, brittle materials exhibit low values of fracture toughness (KIc = Ro) (<1 MPa for many glasses,

<10 MPa for many monolithic ceramics, and <20 MPa for cast irons and hardened steel alloys) These low fracture toughnesses combined with moderate strengths mean that from a Griffith approach, intrinsic flaw sizes may only be on the order of 1 to 50 μm, which often lead to low, broad strength distributions From a fracture-mechanics approach, lower fracture toughness combined with detectable macrocrack sizes severely limit the design stresses allowable in components comprised of brittle materials

Thus, the real utility of measuring the fracture resistance of brittle materials may not be in its direct application

to crack- or flaw-based design (e.g., when does KI = KIc?) through either Griffith or fracture-mechanics

approaches Instead, measures of fracture resistance (e.g., KIc) may find their greatest utility when combined with other material properties in relative comparison indices, such as those that describe wear or brittleness One possible proposed abrasive wear model for ceramics is (Ref 11, 12):

(Eq 7)

where is the volume-loss rate of material, P is the applied load, Kc is the fracture resistance, and H is the

hardness Although the exponents in Eq 7 are specific to the application and material, it is apparent from the

model that to minimize abrasive wear at high loads, P, the material must possess high Kc, high H, and low E

A possible proposed erosive wear model for ceramics has the form (Ref 12, 13):

(Eq 8)

where εv is the volume of material removed, ν is the impact velocity of the particle with diameter d, and ρ is the

density of the particle Again, note that for high velocities of impacting particles, the erosive wear of the

material can be minimized by a high Kc, low E, and low ρ

Finally, the susceptibility of a material to cracking rather than deformation under the action of a concentrated stress can be defined in terms of its brittleness (Ref 14, 15):

of crack-tip sharpness, start of crack extension and crack-tip plane strain” (Ref 6)

References cited in this section

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

Fracture Resistance Testing of Brittle Solids

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

Fracture Toughness and R-Curve Testing at Ambient Temperature

In 1970, the fracture-mechanics and metals communities developed the premiere fracture—toughness testing standard for determining plane strain fracture toughness of metals: ASTM E 399, “Standard Test Method for Plane Strain Fracture Toughness of Metallic Materials” (Ref 6) ASTM Committee E-8 on “Fatigue and

Fracture” has defined the term fracture toughness and the symbol, KIc, based on the operational methods of ASTM E 399 This test method includes several necessary aspects for an acceptable fracture test method:

• All test specimens must have atomistically sharp precracks at the onset of fracture

• Precracks must be well characterized and measurable at the conclusion of the fracture measurement

• Crack geometry must have a valid stress intensity factor

• Plane strain conditions must exist at the crack tip for the measurement of plane strain fracture toughness

ASTM E 399 was developed and is appropriate for measuring plane strain fracture toughness in ductile metals but does not necessarily address the unique aspects of brittle solids (e.g., cyclic fatigue precracking is not easily accomplished in brittle materials) In addition, test specimens are rather large, as are the notches, cracks, and precracks, presumably for ease of implementation as well as to minimize the influence of dimensional variations on the repeatability and reproducibility of the fracture-resistance measurement In recent years, ASTM committees have developed numerous standard test methods for metals; recently, a “unified” standard test method for fracture testing was introduced (ASTM E 1820, “Standard Test Method for Measurement of Fracture Toughness”) (Ref 16) Although a variety of precracking, crack length, fracture parameter (e.g.,

fracture toughness, R-curve, etc.), gripping, and test-specimen preparation techniques are detailed in these

standards, many aspects may not be directly applicable to brittle materials

Since the introduction of ASTM E 399, standards-writing bodies worldwide have labored to develop similar robust and well-accepted test methods for brittle solids, particularly advanced ceramics (Ref 7, 8, 9, and 10) The following sections, where applicable, discuss general aspects of these test methods for extrinsic flaws (macrocracks) and intrinsic flaws (microcracks) in test specimens The reader is referred to the standards themselves for specific details when such standards exist and to appropriate references when a useful technique

is described

Standard Test Methods for Fracture Toughness at Ambient Temperature

ASTM Standard for Fracture Toughness of Ceramics After nearly eight years of focused effort, which included downselecting from five to three operational procedures and the introduction of an interim limited-life (two years) provisional standard (Ref 17), ASTM C 1421 “Standard Test Methods for the Determination of Fracture Toughness of Advanced Ceramics at Ambient Temperature” (Ref 18) was approved as a full consensus standard in early 1999 A technical and historical overview of the evolution of these test methods has been published (Ref 9) Only a summary of the test methods is discussed here

Generally, the test methods involve the flexural testing of extrinsically flawed bend bars, as shown in Fig 5 Regardless of test method, a minimum of four valid tests is required to complete a test series