ASTM_D_7846_-_21.pdf

Designation:D784621Standard Practice forReporting Uniaxial Strength Data and Estimating WeibullDistribution Parameters for Advanced Graphites1This standard is issued under the fixed designation D7846;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.Scope*1.1 This practice covers the reporting of uniaxial strengthdata for graphite and the estimation of probability distributionparameters for both censored and uncensored data.The failurestrength of graphite materials is treated as a continuous randomvariable.Typically,a number of test specimens are failed inaccordance with the following standards:Test Methods C565,C651,C695,C749,Practice C781 or Guide D7775.The load atwhich each specimen fails is recorded.The resulting failurestresses are used to obtain parameter estimates associated withthe underlying population distribution.This practice is limitedto failure strengths that can be characterized by the two-parameter Weibull distribution.Furthermore,this practice isrestricted to test specimens(primarily tensile and flexural)thatare primarily subjected to uniaxial stress states.1.2 Measurements of the strength at failure are taken forvarious reasons:a comparison of the relative quality of twomaterials,the prediction of the probability of failure for astructure of interest,or to establish limit loads in an applica-tion.This practice provides a procedure for estimating thedistribution parameters that are needed for estimating loadlimits for a particular level of probability of failure.1.3 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade(TBT)Committee.2.Referenced Documents2.1 ASTM Standards:2C565 Test Methods for Tension Testing of Carbon andGraphite Mechanical MaterialsC651 Test Method for Flexural Strength of ManufacturedCarbon and GraphiteArticles Using Four-Point Loading atRoom TemperatureC695 Test Method for Compressive Strength of Carbon andGraphiteC749 Test Method for Tensile Stress-Strain of Carbon andGraphiteC781 Practice for Testing Graphite Materials for Gas-CooledNuclear Reactor ComponentsD4175 Terminology Relating to Petroleum Products,LiquidFuels,and LubricantsD7775 Guide for Measurements on Small Graphite Speci-mensE6 Terminology Relating to Methods of Mechanical TestingE178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality and Statistics3.Terminology3.1 Proper use of the following terms and equations willalleviate misunderstanding in the presentation of data and inthe calculation of strength distribution parameters.3.2 Definitions:3.2.1 estimator,na well-defined function that is dependenton the observations in a sample.The resulting value for a givensample may be an estimate of a distribution parameter(a pointestimate)associated with the underlying population.The arith-metic average of a sample is,for example,an estimator of thedistribution mean.3.2.2 population,nthe totality of valid observations(per-formed in a manner that is compliant with the appropriate teststandards)about which inferences are made.3.2.3 population mean,nthe average of all potentialmeasurements in a given population weighted by their relativefrequencies in the population.3.2.4 probability density function,nthe function f(x)is aprobability density function for the continuous random variableX if:fx!$0(1)and1This practice is under the jurisdiction of ASTM Committee D02 on PetroleumProducts,Liquid Fuels,and Lubricants and is the direct responsibility of Subcom-mittee D02.F0 on Manufactured Carbon and Graphite Products.Current edition approved Dec.1,2021.Published February 2022.Originallyapproved in 2012.Last previous edition approved in 2016 as D7846 16.DOI:10.1520/D7846-21.2For 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.*A Summary of Changes section appears at the end of this standardCopyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade(TBT)Committee.1*2fx!dx 5 1(2)The probability that the random variable X assumes avalue between a and b is given by:Pra,X,b!5*abfx!dx(3)3.2.5 sa