ASTM C1683-2008 Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics.pdf
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1、Designation: C 1683 08Standard Practice forSize Scaling of Tensile Strengths Using Weibull Statisticsfor Advanced Ceramics1This standard is issued under the fixed designation C 1683; 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 (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This standard practice provides methodology to convertfracture strength parameters (primarily the mean st
3、rength andthe Weibull characteristic strength) estimated from data ob-tained with one test geometry to strength parameters represent-ing other test geometries. This practice addresses uniaxialstrength data as well as some biaxial strength data. It may alsobe used for more complex geometries proved t
4、hat the effectiveareas and effective volumes can be estimated. It is for theevaluation of Weibull probability distribution parameters foradvanced ceramics that fail in a brittle fashion. Fig. 1 shows thetypical variation of strength with size. The larger the specimenor component, the weaker it is li
5、kely to be.1.2 As noted in Practice C 1239, the failure strength ofadvanced ceramics is treated as a continuous random variable.Anumber of functions may be used to characterize the strengthdistribution of brittle ceramics, but the Weibull distribution isthe most appropriate especially since it permi
6、ts strength scalingfor the size of specimens or component. Typically, a number oftest specimens with well-defined geometry are broken underwell-defined loading conditions. The force at which each testspecimen fails is recorded and fracture strength calculated. Thestrength values are used to obtain W
7、eibull parameter estimatesassociated with the underlying population distribution.1.3 This standard is restricted to the assumption that thedistribution underlying the failure strengths is the two-parameter Weibull distribution with size scaling. The practicealso assumes that the flaw population is s
8、table with time andthat no slow crack growth occurs.1.4 This practice includes the following topics:SectionScope 1Referenced Documents 2Terminology 3Summary of Practice 4Significance and Use 5Probability of Failure Relationships 6Test Specimens with Uniaxial Stress StatesEffectiveVolume and Area Rel
9、ationships7Uniaxial Tensile Test Specimens 7.1SectionRectangular Flexure Test Specimens 7.2Round Flexure Test Specimens 7.3C-Ring Test Specimens 7.4Test Specimens with Multiaxial Stress StatesEffectiveVolume and Area Relationships8Pressure-on-Ring Test Specimens 8.1Ring-on-Ring Test Specimens 8.2Exa
10、mples of Converting Characteristic Strengths 9Report 10Precision and Bias 11Keywords 12Combined Gamma Function for Round Rods Testedin FlexureAnnex A1Components or Test Specimens with MultiaxialStress DistributionsAnnex A2Components or Test Specimens with ComplexGeometries and Stress DistributionsAn
11、nex A31.5 The values stated in SI units are to be regarded as thestandard per IEEE/ASTM SI 10.1.6 This standard does 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 pra
12、ctices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C 1145 Terminology of Advanced CeramicsC 1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient TemperatureC 1211 Test Method for Flexural Strength of AdvancedCera
13、mics at Elevated TemperaturesC 1239 Practice for Reporting Uniaxial Strength Data andEstimating Weibull Distribution Parameters for AdvancedCeramicsC 1273 Test Method for Tensile Strength of MonolithicAdvanced Ceramics at Ambient TemperaturesC 1322 Practice for Fractography and Characterization ofFr
14、acture Origins in Advanced CeramicsC 1323 Test Method for Ultimate Strength of AdvancedCeramics with Diametrally Compressed C-Ring Speci-mens at Ambient Temperature1This practice is under the jurisdiction of ASTM Committee C28 on AdvancedCeramics and is the direct responsibility of Subcommittee C28.
15、01 on MechanicalProperties and Performance.Current edition approved Jan. 1, 2008. Published January 2008.2For 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 standar
16、ds Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.C 1366 Test Method for Tensile Strength of MonolithicAdvanced Ceramics at Elevated TemperaturesC 1499 Test Method for Monotonic Equibiaxial F
17、lexuralStrength of Advanced Ceramics at Ambient TemperatureE6 Terminology Relating to Methods of Mechanical Test-ingE 456 Terminology Relating to Quality and Statistics3. Terminology3.1 Unless otherwise noted, the Weibull parameter estima-tion terms and equations found in Practice C 1239 shall beuse
18、d.3.2 For definitions of other statistical terms, terms related tomechanical testing, and terms related to advanced ceramicsused in this guide, refer to Terminologies E6, E 456, andC 1145, or to appropriate textbooks on statistics (1-4).33.3 Nomenclature:AT= gage area of a uniaxial tensile test spec
19、imenAB4= gage area of a four-point flexure test specimenAB3= gage area of a three-point flexure test specimenAPOR= gage area of a pressure-on-ring test specimenAROR= gage area of a ring-on-ring test specimenACR= gage area of a C-ring test specimenb = thickness of a C-ringb = width of a flexure test
20、specimend = thickness of a flexure test specimenD = diameter of a round flexure test specimenD = overall diameter of a ring-on-ring disk test specimenDL= loading (inner) ring diameter, ring-on-ring disk speci-menDS= support ring diameter, ring-on-ring or pressure-on-ringdisk specimenh = thickness of
21、 pressure-on-ring or ring-on-ring disk testspecimenk = load factorLgs= length of the gage section in a uniaxial tensile testspecimenLi4= length of the inner span for a four-point flexure testspecimenLo4= length of the outer span for a four-point flexure testspecimenLo3= length of the outer span for
22、a three-point flexure testspecimenm = Weibull modulusPf= probability of failureri= inner radius of a C-ringro= outer radius of a C-ringt = thickness of a C-ringRs= radius of the support ring for pressure-on-ringRd= radius of the pressure-on-ring disk specimenSE= effective surface area of a test spec
23、imenVE= effective volume of a test specimenVPOR= gage volume of a pressure-on-ring test specimenVROR= gage volume of a ring-on-ring disk test specimenVT= gage volume of tensile test specimenVB4= gage volume of a four-point flexure test specimenVB3= gage volume of a three-point flexure test specimenV
24、CR= gage volume of a C-ring test specimens = uniaxial tensile stresssmax= maximum tensile stress in a test specimen at fractures1, s2, s3= principal stresses (tensile) at the integrationpoints in any finite elements0= Weibull material scale parameter (strength relative tounit size)su= Weibull charac
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