ASTM_C_1239_-_13.pdf

Designation:C123913Standard Practice forReporting Uniaxial Strength Data and Estimating WeibullDistribution Parameters for Advanced Ceramics1This standard is issued under the fixed designation C1239;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 practice covers the evaluation and reporting ofuniaxial strength data and the estimation of Weibull probabilitydistribution parameters for advanced ceramics that fail in abrittle fashion(see Fig.1).The estimated Weibull distributionparameters are used for statistical comparison of the relativequality of two or more test data sets and for the prediction ofthe probability of failure(or,alternatively,the fracturestrength)for a structure of interest.In addition,this practiceencourages the integration of mechanical property data andfractographic analysis.1.2 The failure strength of advanced ceramics is treated as acontinuous random variable determined by the flaw population.Typically,a number of test specimens with well-definedgeometry are failed under isothermal,well-defined displace-ment and/or force-application conditions.The force at whicheach test specimen fails is recorded.The resulting failure stressdata are used to obtain Weibull parameter estimates associatedwith the underlying flaw population distribution.1.3 This practice is restricted to the assumption that thedistribution underlying the failure strengths is the two-parameter Weibull distribution with size scaling.Furthermore,this practice is restricted to test specimens(tensile,flexural,pressurized ring,etc.)that are primarily subjected to uniaxialstress states.The practice also assumes that the flaw populationis stable with time and that no slow crack growth is occurring.1.4 The practice outlines methods to correct for bias errorsin the estimated Weibull parameters and to calculate confi-dence bounds on those estimates from data sets where allfailures originate from a single flaw population(that is,a singlefailure mode).In samples where failures originate from mul-tiple independent flaw populations(for example,competingfailure modes),the methods outlined in Section 9 for biascorrection and confidence bounds are not applicable.1.5 This practice includes the following:SectionScope1Referenced Documents2Terminology3Summary of Practice4Significance and Use5Interferences6Outlying Observations7Maximum Likelihood Parameter Estimators forCompeting Flaw Distributions8Unbiasing Factors and Confidence Bounds9Fractography10Examples11Keywords12Computer Algorithm MAXLAppendixX1Test Specimens with Unidentified FractureOriginsAppendixX21.6 The values stated in SI units are to be regarded as thestandard per IEEE/ASTM SI 10.2.Referenced Documents2.1 ASTM Standards:2C1145 Terminology of Advanced CeramicsC1322 Practice for Fractography and Characterization ofFracture Origins in Advanced CeramicsE6 Terminology Relating to Methods of Mechanical TestingE178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality and StatisticsIEEE/ASTM SI 10 American National Standard for Use ofthe International System of Units(SI):The Modern MetricSystem3.Terminology3.1 Proper use of the following terms and equations willalleviate misunderstanding in the presentation of data and inthe calculation of strength distribution parameters.3.1.1 censored strength datastrength measurements(thatis,a sample)containing suspended observations such as thatproduced by multiple competing or concurrent flaw popula-tions.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 Aug.1,2013.Published September 2013.Originallyapproved in 1993.Last previous edition approved in 2007 as C1239 07.DOI:10.1520/C1239-13.2For 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.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 3.1.1.1 Consider a sample where fractography clearly estab-lished the existence of three concurrent flaw distributions(although this discussion is applicable to a sample with anynumber of concurrent flaw distributions).The three concurrentflaw distributions are referred to here as distributions A,B,andC.Based on fractographic analyses,each test specimenstrength is assigned to a flaw distribution that initiated failure.In estimating parameters that characterize the strength distri-bution associated with flaw distribution A,all test specimens(and not just those that failed from Type A flaws)must