ASTM_C_1683_-_10_2015.pdf

Designation:C168310(Reapproved 2015)Standard Practice forSize Scaling of Tensile Strengths Using Weibull Statisticsfor Advanced Ceramics1This standard is issued under the fixed designation C1683;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,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 This standard practice provides methodology to convertfracture strength parameters(primarily the mean strength 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 that 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 likely to be.1.2 As noted in Practice C1239,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 permits 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 Weibull 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 stable with time andthat no slow crack growth occurs.1.4 This practice includes the following topics:SectionScope1Referenced Documents2Terminology3Summary of Practice4Significance and Use5Probability of Failure Relationships6Test Specimens with Uniaxial Stress StatesEffectiveVolume and Area Relationships7Uniaxial Tensile Test Specimens7.1Rectangular Flexure Test Specimens7.2Round Flexure Test Specimens7.3C-Ring Test Specimens7.4Test Specimens with Multiaxial Stress StatesEffectiveVolume and Area Relationships8Pressure-on-Ring Test Specimens8.1Ring-on-Ring Test Specimens8.2Examples of Converting Characteristic Strengths9Report10Precision and Bias11Keywords12Combined Gamma Function for Round Rods Testedin FlexureAnnex A1Components or Test Specimens with MultiaxialStress DistributionsAnnex A2Components or Test Specimens with ComplexGeometries and Stress DistributionsAnnex A31.5 The values stated in SI units are to be regarded asstandard.No other units of measurement are included in thisstandard.1.5.1 The values stated in SI units are in accordance withIEEE/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 practices and determine the applica-bility of regulatory limitations prior to use.1This practice is under the jurisdiction of ASTM Committee C28 on AdvancedCeramics and is the direct responsibility of Subcommittee C28.01 on MechanicalProperties and Performance.Current edition approved Jan.1,2015.Published April 2015.Originallyapproved in 2008.Last previous edition approved in 2010 as C1683 10.DOI:10.1520/C1683-10R15.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 2.Referenced Documents2.1 ASTM Standards:2C1145 Terminology of Advanced CeramicsC1161 Test Method for Flexural Strength of AdvancedCeramics at Ambient TemperatureC1211 Test Method for Flexural Strength of AdvancedCeramics at Elevated TemperaturesC1239 Practice for Reporting Uniaxial Strength Data andEstimating Weibull Distribution Parameters for AdvancedCeramicsC1273 Test Method for Tensile Strength of MonolithicAdvanced Ceramics at Ambient TemperaturesC1322 Practice for Fractography and Characterization ofFracture Origins in Advanced CeramicsC1323 Test Method for Ultimate Strength of AdvancedCeramics with Diametrally Compressed C-Ring Speci-mens at Ambient TemperatureC1366 Test Method for Tensile Strength of MonolithicAdvanced Ceramics at Elevated TemperaturesC1499 Test Method for Monotonic Equibiaxial FlexuralStrength of Advanced Ceramics at Ambient TemperatureE6 Terminology Relating to Methods of Mechanical TestingE456 Terminology Relating to Quality and Statistics3.Terminology3.1 Unless otherwise noted,the Weibull parameter estima-tion terms and equations found in Practice C1239 sha