1、Designation: C1421 15Standard Test Methods forDetermination of Fracture Toughness of Advanced Ceramicsat Ambient Temperature1This standard is issued under the fixed designation C1421; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision,
2、 the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 These test methods cover the fracture toughness, KIc,determination of advanced ceramics at ambient temper
3、ature.The methods determine KIpb(precracked beam test specimen),KIsc(surface crack in flexure), and KIvb(chevron-notched beamtest specimen). The fracture toughness values are determinedusing beam test specimens with a sharp crack. The crack iseither a straight-through crack formed via bridge flexure
4、 (pb),or a semi-elliptical surface crack formed via Knoop indentation(sc), or it is formed and propagated in a chevron notch (vb), asshown in Fig. 1.NOTE 1The terms bend(ing) and flexure are synonymous in these testmethods.1.2 These test methods are applicable to materials witheither flat or with ri
5、sing R-curves. Differences in test procedureand analysis may cause the values from each test method to bedifferent. For many materials, such as the silicon nitrideStandard Reference Material 2100, the three methods giveidentical results at room temperature in ambient air.1.3 The fracture toughness v
6、alues for a material can befunctions of environment, test rate and temperature. These testmethods give fracture toughness values for specific conditionsof environment, test rate and temperature.1.4 These test methods are intended primarily for use withadvanced ceramics that are macroscopically homog
7、eneous andmicrostructurally dense. Certain whisker- or particle-reinforced ceramics may also meet the macroscopic behaviorassumptions. Single crystals may also be tested.1.5 This standard begins with a main body that providesinformation on fracture toughness testing in general. It isfollowed by anne
8、xes and appendices with specific informationfor the particular test methods.Main Body SectionScope 1Referenced Documents 2Terminology (including definitions, orientation and symbols) 3Summary of Test Methods 4Significance and Use 5Interferences 6Apparatus 7Test Specimen Configurations, Dimensions an
9、d Preparations 8General Procedures 9Report (including reporting tables) 10Precision and Bias 11Keywords 12Summary of ChangesAnnexesTest Fixture Geometries Annex A1Procedures and Special Requirements for Precracked BeamMethodAnnex A2Procedures and Special Requirements for Surface Crack inFlexure Meth
10、odAnnex A3Procedures and Special Requirements for Chevron Notch FlexureMethodAnnex A4AppendicesPrecrack Characterization, Surface Crack in Flexure Method AppendixX1Complications in Interpreting Surface Crack in Flexure Precracks AppendixX2Alternative Precracking Procedure, Surface Crack in FlexureMe
11、thodAppendixX3Chamfer Correction Factors, Surface Crack in Flexure Method Only AppendixX4Crack Orientation AppendixX51.6 Values expressed in these test methods are in accordancewith the International System of Units (SI) and PracticeIEEE/ASTM SI 10.1.7 The values stated in SI units are to be regarde
12、d asstandard. No other units of measurement are included in thisstandard.1This test method is under the jurisdiction of ASTM Committee C28 onAdvanced Ceramics and is the direct responsibility of Subcommittee C28.01 .Current edition approved July 1, 2015. Published September 2015. Originallyapproved
13、in 1999. Last previous edition approved in 2010 as C1421 10. DOI:10.1520/C1421-15.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States11.8 This standard does not purport to address all of thesafety concerns, if any, associated with its use
14、. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient Tempe
15、ratureC1322 Practice for Fractography and Characterization ofFracture Origins in Advanced CeramicsE4 Practices for Force Verification of Testing MachinesE112 Test Methods for Determining Average Grain SizeE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE337 Test Method for M
16、easuring Humidity with a Psy-chrometer (the Measurement of Wet- and Dry-Bulb Tem-peratures)E691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE740 Practice for Fracture Testing with Surface-Crack Ten-sion SpecimensE1823 Terminology Relating to Fatigue and
17、 Fracture TestingIEEE/ASTM SI 10 Standard for Use of the InternationalSystem of Units (SI) (The Modern Metric System)2.2 Reference Material:NIST SRM 2100 Fracture Toughness of Ceramics33. Terminology3.1 Definitions:3.1.1 The terms described in Terminology E1823 are appli-cable to these test methods.
18、 Appropriate sources for eachdefinition are provided after each definition in parentheses.3.1.2 fracture toughnessa generic term for measures ofresistance of extension of a crack. (E1823)3.1.3 R-curvea plot of crack-extension resistance as afunction of stable crack extension.3.1.4 slow crack growth
19、(SCG)sub critical crack growth(extension) which may result from, but is not restricted to, suchmechanisms as environmentally-assisted stress corrosion ordiffusive crack growth.3.1.5 stress-intensity factor, K FL-3/2the magnitude ofthe ideal-crack-tip stress field (stress field singularity) for apart
20、icular mode in a homogeneous, linear-elastic body.(E1823)3.2 Definitions of Terms Specific to This Standard:3.2.1 back-face strainthe strain as measured with a straingage mounted longitudinally on the compressive surface of thetest specimen, opposite the crack or notch mouth (often this isthe top su
21、rface of the test specimen as tested).3.2.2 crack depth, a Lin surface-cracked test specimens,the normal distance from the cracked beam surface to the pointof maximum penetration of crack front in the material.3.2.3 critical crack size LThe crack size at whichmaximum force and catastrophic fracture
22、occur in the pre-cracked beam and the surface crack in flexure configurations.In the chevron-notched test specimen this is the crack size atwhich the stress intensity factor coefficient, Y*, is at a mini-mum or equivalently, the crack size at which the maximumforce would occur in a linear elastic, f
23、lat R-curve material.3.2.4 four-point -14 point flexureflexure configurationwhere a beam test specimen is symmetrically loaded at twolocations that are situated one quarter of the overall span, awayfrom the outer two support bearings (see Fig. A1.1). (C1161)3.2.5 fracture toughness KIcFL-3/2the crit
24、ical stressintensity factor, Mode I, for fracture. It is a measure of theresistance to crack extension in brittle materials.3.2.6 fracture toughness KIpbFL-3/2the measured stressintensity factor corresponding to the extension resistance of astraight-through crack formed via bridge flexure of a sawnn
25、otch or Vickers or Knoop indentation(s). The measurement isperformed according to the operational procedure herein andsatisfies all the validity requirements. (See Annex A2).3.2.7 fracture toughness KIscor KIsc* FL-3/2the mea-sured (KIsc) or apparent (KIsc*) stress intensity factor corre-sponding to
26、 the extension resistance of a semi-elliptical crackformed via Knoop indentation, for which the residual stressfield due to indentation has been removed. The measurement is2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For An
27、nual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from National Institute of Standards and Technology (NIST), 100Bureau Dr., Stop 1070, Gaithersburg, MD 20899-1070, http:/www.nist.gov.NOTE 1The figures on the right show the test
28、 specimen cross sections and crack types. Four-point loading may be used with all three methods.Three-point may be used with the pb and vb specimens.FIG. 1 The Three Test MethodsC1421 152performed according to the operational procedure herein andsatisfies all the validity requirements. (See Annex A3
29、).3.2.8 fracture toughness KIvbFL-3/2the measured stressintensity factor corresponding to the extension resistance of astably-extending crack in a chevron-notched test specimen.The measurement is performed according to the operationalprocedure herein and satisfies all the validity requirements.(See
30、Annex A4).3.2.9 minimum stress-intensity factor coeffcient, Y*mintheminimum value of Y* determined from Y* as a function ofdimensionless crack length, = a/W.3.2.10 pop-inThe sudden formation or extension of acrack without catastrophic fracture of the test specimen,apparent from a force drop in the a
31、pplied force-displacementcurve. Pop-in may be accompanied by an audible sound orother acoustic energy emission.3.2.11 precracka crack that is intentionally introducedinto the test specimen prior to testing the test specimen tofracture.3.2.12 stable crack extensioncontrollable, time-independent, nonc
32、ritical crack propagation.3.2.12.1 DiscussionThe mode of crack extension (stableor unstable) depends on the compliance of the test specimenand test fixture; the test specimen and crack geometries;R-curve behavior of the material; and susceptibility of thematerial to slow crack growth.3.2.13 three-po
33、int flexureflexure configuration where abeam test specimen is loaded at a location midway betweentwo support bearings (see Fig. A1.2). (C1161)3.2.14 unstable crack extensionuncontrollable, time-independent, critical crack propagation.3.3 Symbols:3.3.1 acrack depth, crack length, crack size.3.3.2 aoc
34、hevron tip dimension, vb method, Fig. A4.1.3.3.3 a1chevron dimension, vb method, (a1=(a11+a12)/2), Fig. A4.1.3.3.4 a11chevron dimension, vb method, Fig. A4.1.3.3.5 a12chevron dimension, vb method, Fig. A4.1.3.3.6 a0.25crack length measured at 0.25B, pb method,Fig. A4.2.3.3.7 a0.50crack length measur
35、ed at 0.5B, pb method, Fig.A4.2.3.3.8 a0.75crack length measured at 0.75B, pb method,Fig. A4.2.3.3.9 a/Wnormalized crack size.3.3.10 Bthe side to side dimension of the test specimenperpendicular to the crack length (depth) as shown in Fig.A2.4, Fig. A3.7, and Fig. A4.1.3.3.11 ccrack half width, sc m
36、ethod, Fig. A3.7.3.3.12 dlength of long diagonal for a Knoop indent,length of a diagonal for a Vickers indent, sc method.3.3.13 Eelastic modulus.3.3.14 f(a/W)function of the ratio a/W, pb method, four-point flexure, Eq A2.6.3.3.15 Findent force, sc method.3.3.16 FCchamfer correction factor, sc metho
37、d.3.3.17 g(a/W)function of the ratio a/W, pb method, three-point flexure, Eq A2.2 and Eq A2.4.3.3.18 hdepth of Knoop or Vickers indent, sc method, EqA3.1.3.3.19 H1(a/c, a/W)a polynomial in the stress intensityfactor coefficient, for the precrack periphery where it intersectsthe test specimen surface
38、, sc method, Eq A3.7.3.3.20 H2(a/c, a/W)a polynomial in the stress intensityfactor coefficient, for the deepest part of a surface crack, scmethod, see Eq A3.5.3.3.21 KIstress intensity factor, Mode I.3.3.22 KIcfracture toughness, critical stress intensityfactor, Mode I.3.3.23 KIpbfracture toughness,
39、 pb method, Eq A2.1 andEq A2.3.3.3.24 KIscfracture toughness, sc method, Eq A3.9.3.3.25 KIvbfracture toughness, vb method, Eq A4.1.3.3.26 Ltest specimen length, Fig. A2.1and Fig. A3.1.3.3.27 L1,L2precracking fixture dimensions, pb method,Fig. A2.2.3.3.28 M(a/c, a/W)a polynomial in the stress intensi
40、tyfactor coefficient, sc method, see Eq A3.4.3.3.29 Pforce.3.3.30 Pmaxforce maximum.3.3.31 Q(a/c)a polynomial function of the surface crackellipticity, sc method, Eq A3.3.3.3.32 S(a/c, a/W)factor in the stress intensity factorcoefficient, sc method, Eq A3.8.3.3.33 Soouter span, three- or four-point
41、test fixture. Figs.A1.1 and A1.2.3.3.34 Siinner span, four-point test fixture, Fig. A1.1.3.3.35 tnotch thickness, pb and vb method, Fig. A2.3 andFig. A4.1.3.3.36 Wthe top to bottom dimension of the test specimenparallel to the crack length (depth) as shown in A2.4, A3.7, andA4.1.3.3.37 Ystress inten
42、sity factor coefficient.3.3.38 Y*stress intensity factor coefficient for vb method.3.3.39 Ymaxmaximum stress intensity factor coefficientoccurring around the periphery of an assumed semi-ellipticalprecrack, sc method.3.3.40 Y*minminimum stress intensity factor coefficient,vb method, Eq A4.2-A4.5.3.3
43、.41 Ydstress intensity factor coefficient at the deepestpart of a surface crack, sc method, Eq A3.2.C1421 1533.3.42 Ysstress intensity factor coefficient at the intersec-tion of the surface crack with the test specimen surface, scmethod, Eq A3.6.4. Summary of Test Methods4.1 These methods involve ap
44、plication of force to a beamtest specimen in three- or four-point flexure. The test specimenis very similar to a common flexural strength test specimen.The test specimen either contains a sharp crack initially (pb, sc)or develops one during loading (vb). The equations forcalculating the fracture tou
45、ghness have been established on thebasis of elastic stress analyses of the test specimen configura-tions. Specific sizes are given for the test specimens and theflexure fixtures. Some are shown in Fig. 2. Annex A2, AnnexA3, and Annex A4 have more specific information andrequirements for each method.
46、4.2 Each method has advantages and disadvantages that arelisted in the following three paragraphs. These factors may beconsidered when choosing a test method. Nuances and impor-tant details for each method are covered in the specificannexes. Experience with a method increases the chances ofobtaining
47、 successful outcomes. Some trial and error may benecessary with a new material or the first time a method isused, so it is wise to prepare extra test specimens. Backgroundinformation concerning the basis for development of these testmethods may be found in Refs. (1-6).44.3 Precracked Beam MethodA st
48、raight-through precrackis created in a beam test specimen via the bridge-flexuretechnique. In this technique the precrack is extended frommedian cracks associated with one or more Vickers or Knoopindentations or a shallow saw notch. The fracture force of theprecracked test specimen as a function of
49、displacement oralternative (for example, time, back-face strain, or actuatordisplacement) in three- or four-point flexure is recorded foranalysis. The fracture toughness, KIpb, is calculated from thefracture force, the test specimen size and the measured pre-crack size. Advantages of this method are that it uses a classicfracture configuration and the precracks are large and not toodifficult to measure. A disadvantage is that a special bridgeprecracking fixture is required to pop in a precrack. A we
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