ASTM C1239-2007 Standard Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics《高级陶瓷用报告单轴强度数据和评估维泊尔分布参数的标准实施规程》.pdf
《ASTM C1239-2007 Standard Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics《高级陶瓷用报告单轴强度数据和评估维泊尔分布参数的标准实施规程》.pdf》由会员分享,可在线阅读,更多相关《ASTM C1239-2007 Standard Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics《高级陶瓷用报告单轴强度数据和评估维泊尔分布参数的标准实施规程》.pdf(19页珍藏版)》请在麦多课文档分享上搜索。
1、Designation: C 1239 07Standard Practice forReporting Uniaxial Strength Data and Estimating WeibullDistribution Parameters for Advanced Ceramics1This standard is issued under the fixed designation C 1239; the number immediately following the designation indicates the year oforiginal adoption or, in t
2、he case of revision, 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 practice covers the evaluation and reporting ofuniaxial strength data and the e
3、stimation 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
4、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 pop
5、ulation.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
6、 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, flexura
7、l,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 cal
8、culate 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 Sectio
9、n 9 for biascorrection and confidence bounds are not applicable.1.5 This practice includes the following:SectionScope 1Referenced Documents 2Terminology 3Summary of Practice 4Significance and Use 5Interferences 6Outlying Observations 7Maximum Likelihood Parameter Estimators forCompeting Flaw Distrib
10、utions8Unbiasing Factors and Confidence Bounds 9Fractography 10Examples 11Keywords 12Computer Algorithm MAXL AppendixX1Test Specimens with Unidentified Fracture Ori-ginsAppendixX21.6 The values stated in SI units are to be regarded as thestandard per IEEE/ASTM SI 10.1This practice is under the juris
11、diction of ASTM Committee C28 on AdvancedCeramics and is the direct responsibility of Subcommittee C28.02 on Reliability.Current edition approved Feb. 1, 2007. Published February 2007. Originallyapproved in 1993. Last previous edition approved in 2006 as C 1239 06a.FIG. 1 Example of Weibull Plot of
12、Strength Data1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.2. Referenced Documents2.1 ASTM Standards:2C 1145 Terminology of Advanced CeramicsC 1322 Practice for Fractography and Characterization ofFracture Origins in Advanced Ceram
13、icsE6 Terminology Relating to Methods of Mechanical Test-ingE 178 Practice for Dealing With Outlying ObservationsE 456 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 P
14、roper 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
15、competing or concurrent flaw popula-tions.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
16、 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 n
17、ot just those that failed from Type A flaws) must beincorporated in the analysis to ensure efficiency and accuracyof the resulting parameter estimates. The strength of a testspecimen that failed by a Type B (or Type C) flaw is treated asa right censored observation relative to the A flaw distributio
18、n.Failure due to a Type B (or Type C) flaw restricts, or censors,the information concerning Type A flaws in a test specimen bysuspending the test before failure occurred by a Type A flaw(1).3The strength from the most severe Type A flaw in thosetest specimens that failed from Type B (or Type C) flaw
19、s ishigher than (and thus to the right of) the observed strength.However, no information is provided regarding the magnitudeof that difference. Censored data analysis techniques incorpo-rated in this practice utilize this incomplete information toprovide efficient and relatively unbiased estimates o
20、f thedistribution parameters.3.2 Definitions:3.2.1 competing failure modesdistinguishably differenttypes of fracture initiation events that result from concurrent(competing) flaw distributions.3.2.2 compound flaw distributionsany form of multipleflaw distribution that is neither pure concurrent nor
21、pureexclusive. A simple example is where every test specimencontains the flaw distribution A, while some fraction of the testspecimens also contains a second independent flaw distributionB.3.2.3 concurrent flaw distributionstype of multiple flawdistribution in a homogeneous material where every test
22、specimen of that material contains representative flaws fromeach independent flaw population. Within a given test speci-men, all flaw populations are then present concurrently and arecompeting with each other to cause failure. This term issynonymous with “competing flaw distributions.”3.2.4 effectiv
23、e gage sectionthat portion of the test speci-men geometry that has been included within the limits ofintegration (volume, area, or edge length) of the Weibulldistribution function. In tensile test specimens, the integrationmay be restricted to the uniformly stressed central gagesection, or it may be
24、 extended to include transition and shankregions.3.2.5 estimatorwell-defined function that is dependent onthe 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 av
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