ASTM C1239-06

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Designation: C 1239 – 06
Standard Practice for
Reporting Uniaxial Strength Data and Estimating Weibull
1
Distribution Parameters for Advanced Ceramics
This standard is issued under the fixed designation C1239; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope
Outlying Observations 6
Maximum Likelihood Parameter Estimators for Competing 7
1.1 This practice covers the evaluation and subsequent
Flaw Distributions
reporting of uniaxial strength data and the estimation of
Unbiasing Factors and Confidence Bounds 8
Fractography 9
probability distribution parameters for advanced ceramics that
Examples 10
fail in a brittle fashion. The failure strength of advanced
Keywords 11
ceramics is treated as a continuous random variable.Typically,
ComputerAlgorithm MAXL Appendix X1
Test Specimens with Unidentified Fracture Origins Appendix X2
a number of test specimens with well-defined geometry are
failed under well-defined isothermal forcing conditions. The
1.4 The values stated in SI units are to be regarded as the
force at which each test specimen fails is recorded. The
standard per IEEE/ASTMSI10.
resultingfailurestressesareusedtoobtainparameterestimates
2. Referenced Documents
associated with the underlying population distribution. This
2
practice is restricted to the assumption that the distribution
2.1 ASTM Standards:
underlying the failure strengths is the two-parameter Weibull
C1145 Terminology of Advanced Ceramics
distribution with size scaling. Furthermore, this practice is
C1322 Practice for Fractography and Characterization of
restricted to test specimens (tensile, flexural, pressurized ring,
Fracture Origins in Advanced Ceramics
etc.) that are primarily subjected to uniaxial stress states.
E6 Terminology Relating to Methods of Mechanical Test-
Section 8 outlines methods to correct for bias errors in the
ing
estimated Weibull parameters and to calculate confidence
E178 Practice for Dealing With Outlying Observations
bounds on those estimates from data sets where all failures
E456 Terminology Relating to Quality and Statistics
originate from a single flaw population (that is, a single failure
IEEE/ASTMSI10 American National Standard for Use of
mode). In samples where failures originate from multiple
the International System of Units (SI): The Modern Metric
independent flaw populations (for example, competing failure
System
modes), the methods outlined in Section 8 for bias correction
3. Terminology
and confidence bounds are not applicable.
1.2 Measurementsofthestrengthatfailurearetakenforone
3.1 Proper use of the following terms and equations will
of two reasons: either for a comparison of the relative quality
alleviate misunderstanding in the presentation of data and in
of two materials, or the prediction of the probability of failure
the calculation of strength distribution parameters.
(or, alternatively, the fracture strength) for a structure of
3.1.1 censored strength data—strength measurements (that
interest. This practice will permit estimates of the distribution
is, a sample) containing suspended observations such as that
parameters that are needed for either. In addition, this practice
produced by multiple competing or concurrent flaw popula-
encourages the integration of mechanical property data and
tions.
fractographic analysis.
3.1.1.1 Considerasamplewherefractographyclearlyestab-
1.3 This practice includes the following:
lished the existence of three concurrent flaw distributions
(although this discussion is applicable to a sample with any
Section
Scope 1
number of concurrent flaw distributions).The three concurrent
Referenced Documents 2
flaw distributions are referred to here as distributions A, B, and
Terminology 3
Summary of Practice 4 C. Based on fractographic analyses, each test specimen
Significance and Use 5
strength is assigned to a flaw distribution that initiated failure.
1 2
This practice is under the jurisdiction ofASTM Committee C28 onAdvanced For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Ceramics and is the direct responsibility of Subcommittee C28.02 on Reliability. contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Current edition approved Jan. 1, 2006. Published January 2006. Originally Standards volume information, refer to the standard’s Document Summary page on
approved in 1993. Last previous edition approved in 2005 as C1239–00 (2005). the ASTM website.
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