ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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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, K
Ic
, 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 K
Ic
values for several ceramics and a few CMCs are
shown in Table 1. Where possible, the values of K
Ic
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
Material
K
Ic
(MPa )
Method
Reference
2.7 CSF
72
2.5 DCB
72
2.9 ISB
73
2.4 CMDCB
50
Glass ceramic pyroceram (Corning)
2.2 MDBT
70
2.6 CSF
72
3.9 DCB
72
Al
2
O
3
AD999 (Coors)
3.1 ISB
73
4 CSF
50
2.1 CSF
72
2.9 DCB
72
Al
2
O
3
AD90 (Coors)
2.8 ISB
73
1.6 CSF
72
2.1 DCB
72
Al
2
O
3
sapphire (Coors)
3 ISB
73
4 CSF
72
4 DCB
72
5 ISB
73
Si
3
N
4
NC132 (Norton)
4.6 CSF
50
2.1 CSF
72
2 DCB
72
Si
3
N
4
NC350 (Norton)
2.1 ISB
75
Si
3
N
4
NBD200 (Norton) 5.4 CSF
50
Si
3
N
4
NT154 (Norton) 5.8 CSF
50
Si
3
N
4
5 MDBT
70
3.5 CSF
72
4 DCB
72
SiC NC203 (Norton)
4.5 ISB
73
3 CN, CSF
50
3.3 SENB
68
α-SiC (Carborundum)
2.7 CN
68
NiAl polycrystalline 1.75 MDBT
75
Y-PSZ 3.6 SENB
59
6.8 SENB
68
SiC/TiB
2
composite
4.1 CN 68
CMDCB, constant moment double cantilever beam; CN, chevron notch; CSF, controlled surface flaw; DCB,
double cantilever beam; ISB, indentation strength in bending; MDBT, miniature disk bend test; SENB, single
edge notch bend
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 (Si
3
N
4
) materials, A, B, and C. The R-
curves were measured using short bar chevron notch methods. Material A is a hot pressed commercial Si
3
N
4
(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 Si
3
N
4
(AS700 by Allied
Signal Inc.) prepared by gas pressure sintering green billets, which were formed by cold isostatic pressing.
These two Si
3
N
4
materials exhibit rising R-curve behavior (Ref 67).
Fig. 12 R-curves of three Si
3
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, J
c
, for short Nicalon fiber-reinforced
foam glass matrix composites (Ref 63). Values for J
c
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 J
c
(Ref 64). Table 3 shows a
wide range of J
c
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 J
c
to vary over a wide range from 11800 to 28520 N/m. Also notice that the
values of J
c
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 J
c
values for short Nicalon fiber reinforced foam glass matrix composites
Fiber length, mm
Fiber volume fraction, %
J
c
, N/m
3 1.0
61.6
6 1.0
147.5
13 0.1
3.5
13 0.2
14.8
13 0.8
210.0
13 1.0 241.8
Source: Ref 63
Table 3 J
c
values for continuous Nicalon fiber fabric reinforced SiC composites
Interface condition
J
c
, N/m
1
11,800
2
19,200
3
19,400
4
24,700
5
10,700
6
18,900
7
15,650
8
19,340
9
14,400
10 28,520
Source: Ref 64
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 elastic-
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.
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 Lockheed-
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.
Fracture Toughness of Ceramics and Ceramic Matrix Composites
J.H. Miller, Oak Ridge National Laboratory P.K. Liaw, The University of Tennessee, Knoxville
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