ASTM C1683-10
(Practice)Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics
Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics
SIGNIFICANCE AND USE
Advanced ceramics usually display a linear stress-strain behavior to failure. Lack of ductility combined with flaws that have various sizes and orientations typically leads to large scatter in failure strength. Strength is not a deterministic property but instead reflects the intrinsic fracture toughness and a distribution (size and orientation) of flaws present in the material. This standard is applicable to brittle monolithic ceramics which fail as a result of catastrophic propagation of flaws. Possible rising R-curve effects are also not considered, but are inherently incorporated into the strength measurements.
Two- and three-parameter formulations exist for the Weibull distribution. This standard is restricted to the two-parameter formulation.
Tensile and flexural test specimens are the most commonly used test configurations for advanced ceramics. Ring-on-ring and pressure-on-ring test specimens which have multi-axial states of stress are also included. Closed-form solutions for the effective volume and effective surfaces and the Weibull material scale factor are included for these configurations. This practice also incorporates size scaling methods for C-ring test specimens for which numerical approaches are necessary. A generic approach for arbitrary shaped test specimens or components that utilizes finite element analyses is presented in Annex A3.
The fracture origins of failed test specimens can be determined using fractographic analysis. The spatial distribution of these strength controlling flaws can be over a volume or an area (as in the case of surface flaws). This standard allows for the conversion of strength parameters associated with either type of spatial distribution. Length scaling for strength controlling flaws located along edges of a test specimen is not covered in this practice.
The scaling of strength with size in accordance with the Weibull model is based on several key assumptions (5). It is assumed that the same specific flaw type...
SCOPE
1.1 This standard practice provides methodology to convert fracture strength parameters (primarily the mean strength and the Weibull characteristic strength) estimated from data obtained with one test geometry to strength parameters representing other test geometries. This practice addresses uniaxial strength data as well as some biaxial strength data. It may also be used for more complex geometries proved that the effective areas and effective volumes can be estimated. It is for the evaluation of Weibull probability distribution parameters for advanced ceramics that fail in a brittle fashion. Fig. 1 shows the typical variation of strength with size. The larger the specimen or component, the weaker it is likely to be.
1.2 As noted in Practice C1239, the failure strength of advanced ceramics is treated as a continuous random variable. A number of functions may be used to characterize the strength distribution of brittle ceramics, but the Weibull distribution is the most appropriate especially since it permits strength scaling for the size of specimens or component. Typically, a number of test specimens with well-defined geometry are broken under well-defined loading conditions. The force at which each test specimen fails is recorded and fracture strength calculated. The strength values are used to obtain Weibull parameter estimates associated with the underlying population distribution.
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Designation: C1683 − 10
StandardPractice for
Size Scaling of Tensile Strengths Using Weibull Statistics
1
for Advanced Ceramics
This standard is issued under the fixed designation C1683; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope also assumes that the flaw population is stable with time and
that no slow crack growth occurs.
1.1 This standard practice provides methodology to convert
fracture strength parameters (primarily the mean strength and 1.4 This practice includes the following topics:
the Weibull characteristic strength) estimated from data ob-
Section
Scope 1
tained with one test geometry to strength parameters represent-
Referenced Documents 2
ing other test geometries. This practice addresses uniaxial
Terminology 3
strength data as well as some biaxial strength data. It may also
Summary of Practice 4
Significance and Use 5
be used for more complex geometries proved that the effective
Probability of Failure Relationships 6
areas and effective volumes can be estimated. It is for the
Test Specimens with Uniaxial Stress States—Effective 7
evaluation of Weibull probability distribution parameters for
Volume and Area Relationships
Uniaxial Tensile Test Specimens 7.1
advancedceramicsthatfailinabrittlefashion.Fig.1showsthe
Rectangular Flexure Test Specimens 7.2
typical variation of strength with size. The larger the specimen
Round Flexure Test Specimens 7.3
or component, the weaker it is likely to be.
C-Ring Test Specimens 7.4
Test Specimens with Multiaxial Stress States—Effective 8
1.2 As noted in Practice C1239, the failure strength of
Volume and Area Relationships
advanced ceramics is treated as a continuous random variable. Pressure-on-Ring Test Specimens 8.1
Ring-on-Ring Test Specimens 8.2
Anumberoffunctionsmaybeusedtocharacterizethestrength
Examples of Converting Characteristic Strengths 9
distribution of brittle ceramics, but the Weibull distribution is
Report 10
themostappropriateespeciallysinceitpermitsstrengthscaling Precision and Bias 11
Keywords 12
for the size of specimens or component.Typically, a number of
Combined Gamma Function for Round Rods Tested Annex A1
test specimens with well-defined geometry are broken under
in Flexure
well-defined loading conditions. The force at which each test Components or Test Specimens with Multiaxial Annex A2
Stress Distributions
specimen fails is recorded and fracture strength calculated.The
Components or Test Specimens with Complex Annex A3
strength values are used to obtain Weibull parameter estimates
Geometries and Stress Distributions
associated with the underlying population distribution.
1.5 The values stated in SI units are to be regarded as
1.3 This standard is restricted to the assumption that the
standard. No other units of measurement are included in this
distribution underlying the failure strengths is the two- standard.
parameter Weibull distribution with size scaling. The practice
1.5.1 The values stated in SI units are in accordance with
IEEE/ASTM SI 10.
1
1.6 This standard does not purport to address all of the
This practice is under the jurisdiction of ASTM Committee C28 on Advanced
Ceramics and is the direct responsibility of Subcommittee C28.01 on Mechanical
safety concerns, if any, associated with its use. It is the
Properties and Performance.
responsibility of the user of this standard to establish appro-
Current edition approved Dec. 1, 2010. Published January 2011. Originally
ε1 priate safety and health practices and determine the applica-
approved in 2008. Last previous edition approved in 2008 as C1683 – 08 . DOI:
10.1520/C1683-10. bility of regulatory limitations prior to use.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1
---------------------- Page: 1 ----------------------
C1683 − 10
3.3 Nomenclature:
A = gage area of a uniaxial tensile test specimen
T
A = gage area of a four-point flexure test specimen
B4
A = gage area of a three-point flexure test specimen
B3
A = gage area of a pressure-on-ring test specimen
POR
A = gage area of a ring-on-ring test specimen
ROR
A = gage area of a C-ring test specimen
CR
b = thickness of a C-ring
b = width of a flexure test specimen
d = thickness of a flexure test specimen
D = diameter of a round flexure test specimen
D = overall diameter of a ring-on-ring disk test specimen
D = loading (inner) ring diameter, ring-on-ring disk speci-
L
men
D = support ring diameter, ring-on-ring or pressure-on-ring
S
disk specimen
h = thickness of pressure-on-ring or ring-on-ring disk test
specimen
FIG. 1 Strength Scales wi
...
This document is not anASTM standard and is intended only to provide the user of anASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
´1
Designation:C1683–08 Designation: C1683 – 10
Standard Practice for
Size Scaling of Tensile Strengths Using Weibull Statistics
1
for Advanced Ceramics
This standard is issued under the fixed designation C1683; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1
´ NOTE—Editorial changes were made throughout in January 2010.
1. Scope
1.1 This standard practice provides methodology to convert fracture strength parameters (primarily the mean strength and the
Weibull characteristic strength) estimated from data obtained with one test geometry to strength parameters representing other test
geometries. This practice addresses uniaxial strength data as well as some biaxial strength data. It may also be used for more
complex geometries proved that the effective areas and effective volumes can be estimated. It is for the evaluation of Weibull
probabilitydistributionparametersforadvancedceramicsthatfailinabrittlefashion.Fig.1showsthetypicalvariationofstrength
with size. The larger the specimen or component, the weaker it is likely to be.
1.2 As noted in Practice C1239, the failure strength of advanced ceramics is treated as a continuous random variable.Anumber
of functions may be used to characterize the strength distribution of brittle ceramics, but the Weibull distribution is the most
appropriate especially since it permits strength scaling for the size of specimens or component. Typically, a number of test
specimens with well-defined geometry are broken under well-defined loading conditions. The force at which each test specimen
fails is recorded and fracture strength calculated. The strength values are used to obtain Weibull parameter estimates associated
with the underlying population distribution.
1.3 This standard is restricted to the assumption that the distribution underlying the failure strengths is the two-parameter
Weibull distribution with size scaling.The practice also assumes that the flaw population is stable with time and that no slow crack
growth occurs.
1.4 This practice includes the following topics:
Section
Scope 1
Referenced Documents 2
Terminology 3
Summary of Practice 4
Significance and Use 5
Probability of Failure Relationships 6
Test Specimens with Uniaxial Stress States—Effective 7
Volume and Area Relationships
Uniaxial Tensile Test Specimens 7.1
Rectangular Flexure Test Specimens 7.2
Round Flexure Test Specimens 7.3
C-Ring Test Specimens 7.4
Test Specimens with Multiaxial Stress States—Effective 8
Volume and Area Relationships
Pressure-on-Ring Test Specimens 8.1
Ring-on-Ring Test Specimens 8.2
Examples of Converting Characteristic Strengths 9
Report 10
Precision and Bias 11
Keywords 12
Combined Gamma Function for Round Rods Tested Annex A1
in Flexure
Components or Test Specimens with Multiaxial Annex A2
Stress Distributions
1
ThispracticeisunderthejurisdictionofASTMCommitteeC28onAdvancedCeramicsandisthedirectresponsibilityofSubcommitteeC28.01onMechanicalProperties
and Performance.
Current edition approved Jan. 1, 2008. Published January 2008. DOI: 10.1520/C1683-08.
´1
Current edition approved Dec. 1, 2010. Published January 2011. Originally approved in 2008. Last previous edition approved in 2008 as C1683 – 08 . DOI:
10.1520/C1683-10.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1
---------------------- Page: 1 ----------------------
C1683 – 10
Section
Components or Test Specimens with Complex Annex A3
Geometries and Stress Distributions
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.5.1 The values stated in SI units are in accordance with IEEE/ASTM SI 10.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory
limitations prior to use.
2. Referenced Documents
2
2.1 ASTM Standards:
C1145 Terminology of Advanced Ceramics
C1161 Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature
C1211 Test Method for Flexural Strength of Advanced Ceramics at Elevated Temperatures
C1239 Practice for Reporting Uniaxial Strength Data and Estimating Weibul
...
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