ASTM C1421-01b(2007)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation: C 1421 – 01b (Reapproved 2007)
Standard Test Methods for
Determination of Fracture Toughness of Advanced Ceramics
at Ambient Temperature
This standard is issued under the fixed designation C1421; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 1.4 Thesetestmethodsgivefracturetoughnessvalues,K ,
Ipb
K , and K , for specific conditions of environment, test rate
1.1 These test methods cover the fracture toughness deter- Isc Ivb
andtemperature.Thefracturetoughnessvalues,K ,K ,and
Ipb Isc
mination of K (precracked beam test specimen), K (surface
Ipb Isc
K for a material can be functions of environment, test rate
crack in flexure), and K (chevron-notched beam test speci- Ivb
Ivb
and temperature.
men) of advanced ceramics at ambient temperature. The
1.5 These test methods are intended primarily for use with
fracture toughness values are determined using beam test
advanced ceramics which are macroscopically homogeneous.
specimens with a sharp crack. The crack is either a straight-
Certainwhisker-orparticle-reinforcedceramicsmayalsomeet
through crack (pb), or a semi-elliptical surface crack (sc), or it
the macroscopic behavior assumptions.
is propagated in a chevron notch (vb).
1.6 These test methods are divided into three major parts
NOTE 1—Thetermsbend(ing)andflexurearesynonymousinthesetest
andrelatedsubpartsasshownbelow.Thefirstmajorpartisthe
methods.
main body and provides general information on the test
1.2 These test methods determine fracture toughness values
methods described, the applicability to materials comparison
based on a force and crack length measurement (pb, sc), or a
and qualification, and requirements and recommendations for
force measurement and an inferred crack length (vb). In
fracture toughness testing. The second major part is composed
general, the fracture toughness is determined from maximum
of annexes that provide procedures, test specimen design,
force. Applied force and displacement or an alternative (for
precracking, testing, and data analysis for each method.Annex
example, time) are recorded for the pb test specimen and vb
A1 describes suggested test fixtures, Annex A2 describes the
test specimen.
pb method,AnnexA3 describes the sc method, andAnnexA4
1.3 These test methods are applicable to materials with
describes the vb method.The third major part consists of three
either flat or with rising R-curves. The fracture toughness
appendices detailing issues related to the fractography and
measured from stable crack extension may be different than
precracking used for the sc method.
that measured from unstable crack extension. This difference
Main Body Section
may be more pronounced for materials exhibiting a rising Scope 1
Referenced Documents 2
R-curve.
Terminology (including definitions, orientation and symbols) 3
Summary of Test Methods 4
NOTE 2—One difference between the procedures in these test methods
Significance and Use 5
and test methods such as Test Method E399, which measure fracture
Interferences 6
toughness, K , by one set of specific operational procedures, is that Test
Ic
Apparatus 7
Method E399 focuses on the start of crack extension from a fatigue
Test Specimen Configurations, Dimensions and Preparations 8
precrack for metallic materials. In these test methods the test methods for General Procedures 9
Report (including reporting tables) 10
advanced ceramics make use of either a sharp precrack formed via bridge
Precision and Bias 11
flexure (pb) or via Knoop indent (sc) prior to the test, or a crack formed
Annexes
during the test (vb). Differences in test procedure and analysis may cause
Test Fixture Geometries A1
the values from each test method to be different. Therefore, fracture
Special Requirements for Precracked Beam Method A2
toughness values determined with these methods cannot be interchanged
Special Requirements for Surface Crack in Flexure Method A3
with K as defined inTest Method E399 and may not be interchangeable Special Requirements for Chevron Notch Flexure Method A4
Ic
Appendices
with each other.
Precrack Characterization, Surface Crack in Flexure Method X1
Complications in Interpreting Surface Crack in Flexure Precracks X2
Alternative Precracking Procedure, Surface Crack in Flexure X3
This test method is under the jurisdiction of ASTM Committee C28 on Method
Advanced Ceramics and is the direct responsibility of Subcommittee C28.01 .
1.7 Valuesexpressedinthesetestmethodsareinaccordance
Current edition approved Feb. 1, 2007. Published March 2007. Originally
approved in 1999. Last previous edition approved in 2001 as C1421-01b. withtheInternationalSystemofUnits(SI)andPracticeE380.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
C 1421 – 01b (2007)
1.8 This standard does not purport to address all of the particular mode in a homogeneous, linear-elastic body.
safety concerns, if any, associated with its use. It is the (E 1823)
responsibility of the user of this standard to establish appro-
3.2 Definitions of Terms Specific to This Standard:
priate safety and health practices and determine the applica-
3.2.1 back-face strain—the strain as measured with a strain
bility of regulatory limitations prior to use.
gagemountedlongitudinallyonthecompressivesurfaceofthe
test specimen, opposite the crack or notch mouth (often this is
2. Referenced Documents
the top surface of the test specimen as tested)
2.1 ASTM Standards:
3.2.2 crack depth, a [L]—in surface-cracked test speci-
C1161 Test Method for Flexural Strength of Advanced
mens, the normal distance from the cracked beam surface to
Ceramics at Ambient Temperature
the point of maximum penetration of crack front in the
C1322 Practice for Fractography and Characterization of
material.
Fracture Origins in Advanced Ceramics
3.2.3 crack orientation—a description of the plane and
E4 Practices for Force Verification of Testing Machines
directionofafractureinrelationtoacharacteristicdirectionof
E112 Test Methods for Determining Average Grain Size
the product. This identification is designated by a letter or
E177 Practice for Use of the Terms Precision and Bias in
letters indicating the plane and direction of crack extension.
ASTM Test Methods
The letter or letters represent the direction normal to the crack
E337 Test Method for Measuring Humidity with a Psy-
plane and the direction of crack propagation.
chrometer (the Measurement of Wet- and Dry-Bulb Tem-
3.2.3.1 Discussion—The characteristic direction may be
peratures)
associated with the product geometry or with the microstruc-
E399 Test Method for Linear-Elastic Plane-Strain Fracture
tural texture of the product.
Toughness K of Metallic Materials
Ic
3.2.3.2 Discussion—The fracture toughness of a material
E691 Practice for Conducting an Interlaboratory Study to
may depend on the orientation and direction of the crack in
Determine the Precision of a Test Method
relation to the material anisotropy, if such exists. Anisotropy
E740 Practice for Fracture Testing with Surface-Crack
maydependontheprincipalpressingdirections,ifany,applied
Tension Specimens
during green body forming (for example, uniaxial or isopress-
E1823 Terminology Relating to Fatigue and Fracture Test-
ing, extrusion, pressure casting) or sintering (for example,
ing
uniaxial hot-pressing, hot isostatic pressing). Thermal gradi-
IEEE/ASTM SI10 Standard for Use of the International
ents during firing can also lead to microstructural anisotropy.
System of Units (SI) (The Modern Metric System)
3.2.3.3 Discussion—The crack plane is defined by letter(s)
2.2 Reference Material:
representing the direction normal to the crack plane as shown
NIST SRM 2100 Fracture Toughness of Ceramics
in Fig. 1, Fig. 2, and Fig. 3.The direction of crack extension is
defined also by the letter(s) representing the direction parallel
3. Terminology
tothecharacteristicdirection(axis)oftheproductasillustrated
3.1 Definitions:
in Fig. 1b, Fig. 2b and Fig. 3b.
3.1.1 The terms described in Terminology E1823 are ap-
HP = hot-pressing direction (See Fig. 1)
plicable to these test methods. Appropriate sources for each
EX = extrusion direction (See Fig. 2)
AXL = axial, or longitudinal axis (if HP or EX are not applicable)
definition are provided after each definition in parentheses.
-3/2 -1 R = radial direction (See Fig. 1, Fig. 2 and Fig. 3)
3.1.2 crack extension resistance, K [FL ], G [FL ], or
R R
C = circumferential direction (See Fig. 1, Fig. 2 and Fig. 3)
-1
J [FL ],—a measure of the resistance of a material to crack
R/C = mixed radial and circumferential directions (See Fig. 3b)
R
extension expressed in terms of the stress-intensity factor, K,
3.2.3.4 Discussion—For a rectangular product, R and C
strain energy release rate, G, or values of J derived using the
may be replaced by rectilinear axes x and y, corresponding to
J-integral concept. (E 1823)
two sides of the plate.
3.1.3 fracture toughness—a generic term for measures of
3.2.3.5 Discussion—Depending on how test specimens are
resistance of extension of a crack. (E 399, E 1823)
sliced out of a ceramic product, the crack plane may be
3.1.4 R-curve—a plot of crack-extension resistance as a
circumferential,radial,oramixtureofbothasshowninFig.3.
function of stable crack extension.
3.2.3.6 Identification of the plane and direction of crack
3.1.5 slow crack growth (SCG)—sub critical crack growth
extension is recommended. The plane and direction of crack
(extension)whichmayresultfrom,butisnotrestrictedto,such
extension are denoted by a hyphenated code with the first
mechanisms as environmentally-assisted stress corrosion or
letter(s) representing the direction normal to the crack plane,
diffusive crack growth.
-3/2
and the second letter(s) designating the expected direction of
3.1.6 stress-intensity factor, K [FL ]—the magnitude of
crack extension. See Fig. 1, Fig. 2 and Fig. 3.
the ideal-crack-tip stress field (stress field singularity) for a
3.2.3.7 Discussion—In many ceramics, specification of the
crack plane is sufficient.
3.2.3.8 Isopressed products, amorphous ceramics, glasses
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
and glass ceramics are often isotropic, and crack plane orien-
Standards volume information, refer to the standard’s Document Summary page on
tation has little effect on fracture toughness. Nevertheless, the
the ASTM website.
designation of crack plane relative to product geometry is
Available from National Institute of Standards and Technology (NIST), 100
Bureau Dr., Stop 1070, Gaithersburg, MD 20899-1070, http://www.nist.gov. recommended.Forexample,iftheproductisisopressed(either
C 1421 – 01b (2007)
NOTE 1—Precracked beam test specimens are shown as examples. The small arrows denote the direction of crack growth.
FIG. 1 Crack Plane Orientation Code for Hot-Pressed Products
NOTE 1—Precracked beam test specimens are shown as examples. The small arrows denote the direction of crack growth.
FIG. 2 Crack Plane Orientation Code for Extruded Products
coldorhot)denotethecrackplaneanddirectionrelativetothe equivalently,thecracksizeatwhichthemaximumforcewould
axial direction of the product. Use the same designation occur in a linear elastic, flat R-curve material.
scheme as shown in Figs. 1 and 2, but with the letters “AXL”
3.2.5 four-point - ⁄4 point flexure—flexure configuration
to denote the axial axis of the product.
where a beam test specimen is symmetrically loaded at two
3.2.3.9 If there is no primary product direction, reference locationsthataresituatedonequarteroftheoverallspan,away
axes may be arbitrarily assigned but must be clearly identified. from the outer two support bearings (see Fig. A1.1) (C 1161)
-3/2
3.2.4 critical crack size [L]—in these test methods, the 3.2.6 fracture toughness K [FL ]—the measured stress
Ipb
crack size at which maximum force and catastrophic fracture intensity factor corresponding to the extension resistance of a
occurintheprecrackedbeam(seeFig.4)andthesurfacecrack straight-through crack formed via bridge flexure of a sawn
in flexure (see Fig. 5) configurations. In the chevron-notched notch or Vickers or Knoop indentation(s). The measurement is
test specimen (see Fig. 6) this is the crack size at which the performed according to the operational procedure herein and
stress intensity factor coefficient, Y*, is at a minimum or satisfies all the validity requirements. (See Annex A2).
C 1421 – 01b (2007)
NOTE 1—The R/C mix shown in b) is a consequence of the parallel slicing of the test specimens from the product.
NOTE 2—Precracked beam test specimens are shown as examples. The small arrows denote the direction of crack growth.
FIG. 3 Code for Crack Plane and Direction of Crack Extension in Test Specimens with Axial Primary Product Direction
FIG. 4 Cross Section of a pb Test Specimen Showing the
Precrack Configuration (a ,a ,a are the Points for Crack
0.25 0.50 0.75
Length Measurements)
FIG.5aandbCross Section of sc Test Specimens Showing the
Precrack Configurations for Two Orientations
-3/2
3.2.7 fracture toughness K or K *[FL ]—the mea-
Isc Isc
sured (K ) or apparent (K *) stress intensity factor corre-
Isc Isc
The measurement is performed according to the operational
sponding to the extension resistance of a semi-elliptical crack
procedure herein and satisfies all the validity requirements.
formed via Knoop indentation, for which the residual stress
(See Annex A4).
fieldduetoindentationhasbeenremoved.Themeasurementis
3.2.9 minimum stress-intensity factor coeffıcient, Y* —the
performed according to the operational procedure herein and
min
minimum value of Y* determined from Y* as a function of
satisfies all the validity requirements. (See Annex A3).
-3/2
dimensionless crack length, a = a/W.
3.2.8 fracture toughness K [FL ]—the measured stress
Ivb
intensity factor corresponding to the extension resistance of a 3.2.10 pop-in—in these test methods, the sudden formation
stably-extending crack in a chevron-notched test specimen. or extension of a crack without catastrophic fracture of the test
C 1421 – 01b (2007)
3.3.11 c—asusedinthesetestmethods,crackhalfwidth,sc
method, see Fig. 5 and Fig. A3.2.
3.3.12 d—as used in these test methods, length of long
diagonalforaKnoopindent,lengthofadiagonalforaVickers
indent, sc method.
3.3.13 E—elastic modulus.
...