1、Designation: C 1421 09Standard Test Methods forDetermination of Fracture Toughness of Advanced Ceramicsat Ambient Temperature1This standard is issued under the fixed designation C 1421; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revisio
2、n, 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. Scope*1.1 These test methods cover the fracture toughness, KIc,determination of advanced ceramics at ambient tem
3、perature.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 flex
4、ure (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
5、 rising 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 toughnes
6、s values 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 which are macroscopically h
7、omogeneous.Certain whisker- or particle-reinforced ceramics may also meetthe macroscopic behavior assumptions. Single crystals mayalso be tested.1.5 This standard begins with a main body that providesinformation on fracture toughness testing in general. It isfollowed by annexes and appendices with s
8、pecific 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 and Preparations 8General P
9、rocedures 9Report (including reporting tables) 10Precision and Bias 11Keywords 12Summary of ChangesAnnexesTest Fixture Geometries A1Procedures and Special Requirements for Precracked BeamMethodA2Procedures and Special Requirements for Surface Crack in Flex-ure MethodA3Procedures and Special Requirem
10、ents for Chevron Notch FlexureMethodA4AppendicesPrecrack Characterization, Surface Crack in Flexure Method X1Complications in Interpreting Surface Crack in Flexure Precracks X2Alternative Precracking Procedure, Surface Crack in FlexureMethodX3Chamfer Correction Factors, Surface Crack in Flexure Meth
11、od Only X4Crack Orientation X51.6 Values expressed in these test methods are in accordancewith the International System of Units (SI) and Practice E 380.1.7 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.8 This standard does
12、not purport to address all of thesafety concerns, if any, associated with its use. 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 Standa
13、rds:2C 1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient TemperatureC 1322 Practice for Fractography and Characterization ofFracture Origins in Advanced CeramicsE4 Practices for Force Verification of Testing MachinesE112 Test Methods for Determining Average Grain SizeE 177 Practi
14、ce for Use of the Terms Precision and Bias inASTM Test Methods1This test method is under the jurisdiction of ASTM Committee C28 onAdvanced Ceramics and is the direct responsibility of Subcommittee C28.01 .Current edition approved May 1, 2009. Published August 2009. Originallyapproved in 1999. Last p
15、revious edition approved in 2007 as C 1421 - 01b (2007).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1*A S
16、ummary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.E 337 Test Method for Measuring Humidity with a Psy-chrometer (the Measurement of Wet- and Dry-Bulb Tem-peratures)E 691 Prac
17、tice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE 740 Practice for Fracture Testing with Surface-CrackTension SpecimensE 1823 Terminology Relating to Fatigue and Fracture Test-ingIEEE/ASTM SI 10 Standard for Use of the InternationalSystem of Units (SI) (The Mod
18、ern Metric System)2.2 Reference Material:NIST SRM 2100 Fracture Toughness of Ceramics33. Terminology3.1 Definitions:3.1.1 The terms described in Terminology E 1823 are ap-plicable to these test methods. Appropriate sources for eachdefinition are provided after each definition in parentheses.3.1.2 fr
19、acture toughnessa generic term for measures ofresistance of extension of a crack. (E 1823)3.1.3 R-curvea plot of crack-extension resistance as afunction of stable crack extension.3.1.4 slow crack growth (SCG)sub critical crack growth(extension) which may result from, but is not restricted to, suchme
20、chanisms 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 aparticular mode in a homogeneous, linear-elastic body.(E 1823)3.2 Definitions of Terms Specific to Th
21、is 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 surface of the test specimen as tested)3.2.2 crack depth, a Lin surface-cracked test speci-mens, t
22、he normal distance from the cracked beam surface tothe point of maximum penetration of crack front in thematerial.3.2.3 critical crack size LThe crack size at whichmaximum force and catastrophic fracture occur in the pre-cracked beam and the surface crack in flexure configurations.In the chevron-not
23、ched 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, flat R-curve material.3.2.4 four-point -14 point flexureflexure configurationwhere a beam test sp
24、ecimen is symmetrically loaded at twolocations that are situated one quarter of the overall span, awayfrom the outer two support bearings (see Fig. A1.1) (C 1161)3.2.5 fracture toughness KIcFL-3/2the critical stress in-tensity factor, Mode I, for fracture. It is a measure of theresistance to crack e
25、xtension 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 sawnnotch or Vickers or Knoop indentation(s). The measurement isperformed according to the operatio
26、nal 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 the extension resistance of a semi-elliptical crackformed via Knoop indentation, for which the
27、 residual stressfield due to indentation has been removed. The measurement isperformed according to the operational procedure herein andsatisfies all the validity requirements. (See Annex A3).3.2.8 fracture toughness KIvbFL-3/2the measured stressintensity factor corresponding to the extension resist
28、ance 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 Annex A4).3.2.9 minimum stress-intensity factor coeffcient, Y*mintheminimum value of Y* determined from Y* as
29、a function ofdimensionless crack length, a = 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 applied force-displacementcurve. Pop-in may be accompanied by an audible sound orother acoustic energy emissi
30、on.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 specimen cross sections and crack types. Four-point loading may be used with all three methods.Three-point
31、may be used with the pb and vb specimens.FIG. 1 The Three Test MethodsC14210923.2.11 precracka crack that is intentionally introducedinto the test specimen prior to testing the test specimen tofracture.3.2.12 stable crack extensioncontrollable, time-independent, noncritical crack propagation.3.2.12.
32、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-point flexureflexure configuration
33、where abeam test specimen is loaded at a location midway betweentwo support bearings (see Fig. A1.2) (C 1161)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 aochevron tip dimension, vb method,
34、Fig. A4.1.3.3.3 a1chevron dimension, vb method, (a1=(a11+ a12)/2), Fig. A4.13.3.4 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 measured at 0.5B, pb method, Fig.A4.2.3
35、.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 method, Fig. A3.7.3.3.12 dlength o
36、f 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 method3.3.17 g(a/W)function of the rat
37、io 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, sc method, Eq A3.7.3.3.20 H2(a/c
38、, 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 intensity fac-tor, Mode I.3.3.23 KIpbfracture toughness, pb method, Eq A2.1 andEq A2.3.3
39、.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 intensityfactor coefficient, sc method
40、, 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 test fixture. Figs.A1.1 and A1.
41、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 inA2.4,A3.7, andA4.1.3.3.37 Ystress intensity factor coefficient.3.3.38 Y*
42、stress intensity factor coefficient for vb method.3.3.39 Ymaxmaximum stress intensity factor coefficientoccurring around the periphery of an assumed semi-ellipticalprecrack, sc method3.3.40 Y*minminimum stress intensity factor coefficient,vb method, Eq A4.2-A4.53.3.41 Ydstress intensity factor coeff
43、icient at the deepestpart of a surface crack, sc method, Eq A3.23.3.42 Ysstress intensity factor coefficient at the intersec-tion of the surface crack with the test specimen surface, scmethod, Eq A3.64. Summary of Test Methods4.1 These methods involve application of force to a beamtest specimen in t
44、hree- 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 toughness have been established on thebasis of el
45、astic 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-AnnexA4 have more specific information and requirements for eachmethod.4.2 Each method has advantages and disadvantages that arelist
46、ed 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 successful outcomes. Some trial and error may benecessary wi
47、th 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).4.3 Precracked Beam MethodAstraight-through precrackis created in a beam test specimen via t
48、he 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 displacement orC1421093alternative (for example, time, back-fac
49、e 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 welldesigned and well crafted bridge precracking fixture is nee
