ASTM_D_7846_-_12.pdf

Designation:D784612An American National StandardStandard 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.Scope1.1 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.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 andGraphiteC709 Terminology Relating to Manufactured Carbon andGraphiteC749 Test Method for Tensile Stress-Strain of Carbon andGraphiteC781 Practice for Testing Graphite and Boronated GraphiteMaterials for High-Temperature Gas-Cooled Nuclear Re-actor ComponentsD4175 Terminology Relating to Petroleum,PetroleumProducts,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)and*2fx!dx 5 1(2)The probability that the random variable X assumes avalue between a and b is given by:1This 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.1,2012.Published August 2013.DOI:10.1520/D7846-12.2For 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 Pra,X,b!5*abfx!dx(3)3.2.5 sample,na collection of measurements or observa-tions taken from a specified population.3.2.6 skewness,na term relating to the asymmetry of aprobability density function.The distribution of failurestrength for graphite is not symmetric with respect to themaximum value of the distribution function;one tail is longerthan the other.3.2.7 statistical bias,ninherent to most estimates,this is atype of consistent numerical offset in an estimate relative to thetrue underlying value.The magnitude of the bias error typicallydecreases as the sample size increases.3.2.8 unbiased estimator,nan estimator that has beencorrected for statistical bias error.3.2.9