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ASTM C1683-08e1

(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...
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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.
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.

General Information

Status
Historical
Publication Date
31-Dec-2007
ICS
81.060.30 - Advanced ceramics
Technical Committee
C28 - Advanced Ceramics
Drafting Committee
C28.01 - Mechanical Properties and Performance
Current Stage
Ref Project

Relations

Replaces
ASTM C1683-08 - Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics
Effective Date
01-Jan-2008
Replaced By
ASTM C1683-10 - Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics
Effective Date
01-Dec-2010
Referred By
ASTM C1783-15 - Standard Guide for Development of Specifications for Fiber Reinforced Carbon-Carbon Composite Structures for Nuclear Applications
Effective Date
01-Jan-2008
Referred By
ASTM C1793-15 - Standard Guide for Development of Specifications for Fiber Reinforced Silicon Carbide-Silicon Carbide Composite Structures for Nuclear Applications
Effective Date
01-Jan-2008
Referred By
ASTM C1323-22 - Standard Test Method for Ultimate Strength of Advanced Ceramics with Diametrally Compressed C-Ring Specimens at Ambient Temperature
Effective Date
01-Jan-2008
Referred By
ASTM C1899-21 - Standard Test Method for Flexural Strength of Continuous Fiber-Reinforced Advanced Ceramic Tubular Test Specimens at Ambient Temperature
Effective Date
01-Jan-2008

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ASTM C1683-08e1 - Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced CeramicsASTM C1683-08e1 - Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics
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ASTM C1683-08e1 - Standard Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´1
Designation: C1683 – 08
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
Section
Test Specimens with Uniaxial Stress States—Effective 7
1.1 This standard practice provides methodology to convert
Volume and Area Relationships
fracture strength parameters (primarily the mean strength and Uniaxial Tensile Test Specimens 7.1
Rectangular Flexure Test Specimens 7.2
the Weibull characteristic strength) estimated from data ob-
Round Flexure Test Specimens 7.3
tained with one test geometry to strength parameters represent-
C-Ring Test Specimens 7.4
ing other test geometries. This practice addresses uniaxial
Test Specimens with Multiaxial Stress States—Effective 8
Volume and Area Relationships
strength data as well as some biaxial strength data. It may also
Pressure-on-Ring Test Specimens 8.1
be used for more complex geometries proved that the effective
Ring-on-Ring Test Specimens 8.2
areas and effective volumes can be estimated. It is for the Examples of Converting Characteristic Strengths 9
Report 10
evaluation of Weibull probability distribution parameters for
Precision and Bias 11
advancedceramicsthatfailinabrittlefashion.Fig.1showsthe
Keywords 12
typical variation of strength with size. The larger the specimen Combined Gamma Function for Round Rods Tested Annex A1
in Flexure
or component, the weaker it is likely to be.
Components or Test Specimens with Multiaxial Annex A2
1.2 As noted in Practice C1239, the failure strength of
Stress Distributions
Components or Test Specimens with Complex Annex A3
advanced ceramics is treated as a continuous random variable.
Geometries and Stress Distributions
Anumberoffunctionsmaybeusedtocharacterizethestrength
distribution of brittle ceramics, but the Weibull distribution is 1.5 The values stated in SI units are to be regarded as
standard. No other units of measurement are included in this
themostappropriateespeciallysinceitpermitsstrengthscaling
for the size of specimens or component.Typically, a number of standard.
1.5.1 The values stated in SI units are in accordance with
test specimens with well-defined geometry are broken under
well-defined loading conditions. The force at which each test IEEE/ASTM SI 10.
1.6 This standard does not purport to address all of the
specimen fails is recorded and fracture strength calculated.The
strength values are used to obtain Weibull parameter estimates safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
associated with the underlying population distribution.
1.3 This standard is restricted to the assumption that the priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
distribution underlying the failure strengths is the two-
parameter Weibull distribution with size scaling. The practice
2. Referenced Documents
also assumes that the flaw population is stable with time and
2
2.1 ASTM Standards:
that no slow crack growth occurs.
C1145 Terminology of Advanced Ceramics
1.4 This practice includes the following topics:
C1161 Test Method for Flexural Strength of Advanced
Section
Scope 1
Ceramics at Ambient Temperature
Referenced Documents 2
C1211 Test Method for Flexural Strength of Advanced
Terminology 3
Ceramics at Elevated Temperatures
Summary of Practice 4
Significance and Use 5
C1239 Practice for Reporting Uniaxial Strength Data and
Probability of Failure Relationships 6
Estimating Weibull Distribution Parameters for Advanced
Ceramics
1
This practice is under the jurisdiction of ASTM Committee C28 on Advanced
Ceramics and is the direct responsibility of Subcommittee C28.01 on Mechanical
2
Properties and Performance.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Jan. 1, 2008. Published January 2008. DOI: 10.1520/
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
C1683-08.
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
1

---------------------- Page: 1 ----------------------
´1
C1683 – 08
FIG. 1 Strength Scales with Size
C1273 Test Method for Tensile Strength of Monolithic D = loading (inner) ring diameter, ring-on-ring disk speci-
L
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1.3 Units—When Knoop and Vickers hardness tests were developed, the force levels were specified in units of grams-force (gf) and kilograms-force (kgf). This standard specifies the units of force and length in the International System of Units (SI); that is, force in newtons (N) and length in mm or μm. However, because of the historical precedent and continued common usage, force values in gf and kgf units are occasionally provided for information. This test method specifies that Knoop hardness be reported either in units of GPa or as a dimensionless Knoop hardness number.  
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Standard Test Method for Effect of Surface Grinding on Flexure Strength of Advanced Ceramics

SIGNIFICANCE AND USE
5.1 Surface grinding can cause a significant decrease4 in the flexure strength of advanced ceramic materials. The magnitude of the loss in strength is determined by the grinding conditions and the response of the material. This test method can be used to obtain a detailed characterization of the relationship between grinding conditions and flexure strength for an advanced ceramic material. The effect on flexure strength of varying a single grinding parameter or several grinding parameters can be measured. The method may also be used to compare and rank different materials according to their response to one or more different grinding conditions. Results obtained by this method can be used to develop an optimum grinding process with respect to maximizing material removal rate for a specified flexure strength requirement. The test method can assist in the development of improved grinding-damage-tolerant ceramic materials. It may also be used for quality control purposes to monitor and assure the consistency of a grinding process in the fabrication of parts from advanced ceramic materials. The test method is applicable to grinding methods that generate a planar surface and is not directly applicable to grinding methods that produce non-planar surfaces such as cylindrical and centerless grinding.
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1.1 This test method covers the determination of the effect of surface grinding on the flexure strength of advanced ceramics. Surface grinding of an advanced ceramic material can introduce microcracks and other changes in the near surface layer, generally referred to as damage (see Fig. 1 and Ref. (1)).2 Such damage can result in a change—most often a decrease—in flexure strength of the material. The degree of change in flexure strength is determined by both the grinding process and the response characteristics of the specific ceramic material. This method compares the flexure strength of an advanced ceramic material after application of a user-specified surface grinding process with the baseline flexure strength of the same material. The baseline flexure strength is obtained after application of a surface grinding process specified in this standard. The baseline flexure strength is expected to approximate closely the inherent strength of the material. The flexure strength is measured by means of ASTM flexure test methods.
FIG. 1 Microcracks Associated with Grinding (Ref. (1))2  
1.2 Flexure test methods used to determine the effect of surface grinding are C1161 Test Method for Flexure Strength of Advanced Ceramics at Ambient Temperatures and C1211 Test Method for Flexure Strength of Advanced Ceramics at Elevated Temperatures.  
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SIGNIFICANCE AND USE
4.1 This test method may be used for material development, quality control, characterization, and design data generation purposes. This test method is intended to be used with ceramics whose flexural strength is ∼50 MPa (∼7 ksi) or greater.  
4.2 The flexure stress is computed based on simple beam theory, with assumptions that the material is isotropic and homogeneous, the moduli of elasticity in tension and compression are identical, and the material is linearly elastic. The average grain size should be no greater than 1/50 of the beam thickness. The homogeneity and isotropy assumptions in the test method rule out the use of it for continuous fiber-reinforced composites for which Test Method C1341 is more appropriate.  
4.3 The flexural strength of a group of test specimens is influenced by several parameters associated with the test procedure. Such factors include the testing rate, test environment, specimen size, specimen preparation, and test fixtures. Specimen and fixture sizes were chosen to provide a balance between the practical configurations and resulting errors as discussed in Test Method C1161, and Refs (1-3).4 Specific fixture and specimen configurations were designated in order to permit the ready comparison of data without the need for Weibull size scaling.  
4.4 The flexural strength of a ceramic material is dependent on both its inherent resistance to fracture and the size and severity of flaws. Variations in these cause a natural scatter in test results for a sample of test specimens. Fractographic analysis of fracture surfaces, although beyond the scope of this test method, is highly recommended for all purposes, especially if the data will be used for design as discussed in Ref (4) and Practices C1322 and C1239.  
4.5 This method determines the flexural strength at elevated temperature and ambient environmental conditions at a nominal, moderately fast testing rate. The flexural strength under these conditions may or may not necessarily be the...
SCOPE
1.1 This test method covers determination of the flexural strength of advanced ceramics at elevated temperatures.2 Four-point-1/4-point and three-point loadings with prescribed spans are the standard as shown in Fig. 1. Rectangular specimens of prescribed cross-section are used with specified features in prescribed specimen-fixture combinations. Test specimens may be 3 by 4 by 45 to 50 mm in size that are tested on 40-mm outer span four-point or three-point fixtures. Alternatively, test specimens and fixture spans half or twice these sizes may be used. The test method permits testing of machined or as-fired test specimens. Several options for machining preparation are included: application matched machining, customary procedures, or a specified standard procedure. This test method describes the apparatus, specimen requirements, test procedure, calculations, and reporting requirements. The test method is applicable to monolithic or particulate- or whisker-reinforced ceramics. It may also be used for glasses. It is not applicable to continuous fiber-reinforced ceramic composites.  
1.2 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.  
1.3 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM
ASTM C1323-22(Test Method)
Standard Test Method for Ultimate Strength of Advanced Ceramics with Diametrally Compressed C-Ring Specimens at Ambient Temperature

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, and characterization. Extreme care should be exercised when generating design data.  
4.2 For a C-ring under diametral compression, the maximum tensile stress occurs at the outer surface. Hence, the C-ring specimen loaded in compression will predominately evaluate the strength distribution and flaw population(s) on the external surface of a tubular component in the hoop direction. Accordingly, the condition of the inner surface may be of lesser consequence in specimen preparation and testing.
Note 1: A C-ring in tension or an O-ring in compression may be used to evaluate the internal surface.  
4.2.1 The flexure stress is computed based on simple curved beam theory (1-5).3 It is assumed that the material is isotropic and homogeneous, the moduli of elasticity are identical in compression or tension, and the material is linearly elastic. These homogeneity and isotropy assumptions preclude the use of this standard for continuous fiber reinforced composites. Average grain size(s) should be no greater than one fiftieth (1/50 ) of the C-ring thickness. The curved beam stress solution from engineering mechanics is in good agreement (within 2 %) with an elasticity solution as discussed in (6) for the test specimen geometries recommended for this standard. The curved beam stress equations are simple and straightforward, and therefore it is relatively easy to integrate the equations for calculations for effective area or effective volume for Weibull analyses as discussed in Appendix X1.  
4.2.2 The simple curved beam and theory of elasticity stress solutions both are two-dimensional plane stress solutions. They do not account for stresses in the axial (parallel to b) direction, or variations in the circumferential (hoop, σθ) stresses through the width (b) of the test piece. The variations in the circumferential stresses increase with increases in width (b) and ring thicknes...
SCOPE
1.1 This test method covers the determination of ultimate strength under monotonic loading of advanced ceramics in tubular form at ambient temperatures. The ultimate strength as used in this test method refers to the strength obtained under monotonic compressive loading of C-ring specimens such as shown in Fig. 1, where monotonic refers to a continuous nonstop test rate with no reversals from test initiation to final fracture. This method permits a range of sizes and shapes since test specimens may be prepared from a variety of tubular structures. The method may be used with microminiature test specimens.
FIG. 1 C-Ring Test Geometry with Defining Geometry and Reference Angle (θ) for the Point of Fracture Initiation on the Circumference  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.2.1 Values expressed in this test method are in accordance with the International System of Units (SI) and IEEE/ASTM SI 10.  
1.3 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM
ASTM C1292-22(Test Method)
Standard Test Method for Shear Strength of Continuous Fiber-Reinforced Advanced Ceramics at Ambient Temperatures

SIGNIFICANCE AND USE
5.1 Continuous fiber-reinforced ceramic composites can be candidate materials for structural applications requiring high degrees of wear and corrosion resistance, and damage tolerance at high temperatures.  
5.2 Shear tests provide information on the strength and deformation of materials under shear stresses.  
5.3 This test method may be used for material development, material comparison, quality assurance, characterization, and design data generation.  
5.4 For quality control purposes, results derived from standardized shear test specimens may be considered indicative of the response of the material from which they were taken for given primary processing conditions and post-processing heat treatments.
SCOPE
1.1 This test method covers the determination of shear strength of continuous fiber-reinforced ceramic composites (CFCCs) at ambient temperature. The test methods addressed are (1) the compression of a double-notched test specimen to determine interlaminar shear strength, and (2) the Iosipescu test method to determine the shear strength in any one of the material planes of laminated composites. Test specimen fabrication methods, testing modes (load or displacement control), testing rates (load rate or displacement rate), data collection, and reporting procedures are addressed.  
1.2 This test method is used for testing advanced ceramic or glass matrix composites with continuous fiber reinforcement having unidirectional (1D) or bidirectional (2D) fiber architecture. This test method does not address composites with 3D fiber architecture or discontinuous fiber-reinforced, whisker-reinforced, or particulate-reinforced ceramics.  
1.3 The values stated in SI units are to be regarded as the standard and are in accordance with IEEE/ASTM SI 10.  
1.4 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use. Specific hazard statements are given in 8.1 and 8.2.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM
ASTM C1469-22(Test Method)
Standard Test Method for Shear Strength of Joints of Advanced Ceramics at Ambient Temperature

SIGNIFICANCE AND USE
5.1 Advanced ceramics can be candidate materials for structural applications requiring high degrees of wear and corrosion resistance, often at elevated temperatures.  
5.2 Joints are produced to enhance the performance and applicability of materials. While the joints between similar materials are generally made for manufacturing complex parts and repairing components, those involving dissimilar materials usually are produced to exploit the unique properties of each constituent in the new component. Depending on the joining process, the joint region may be the weakest part of the component. Since under mixed-mode and shear loading the load transfer across the joint requires reasonable shear strength, it is important that the quality and integrity of joint under in-plane shear forces be quantified. Shear strength data are also needed to monitor the development of new and improved joining techniques.  
5.3 Shear tests provide information on the strength and deformation of materials under shear stresses.  
5.4 This test method may be used for material development, material comparison, quality assurance, characterization, and design data generation.  
5.5 For quality control purposes, results derived from standardized shear test specimens may be considered indicative of the response of the material from which they were taken for given primary processing conditions and post-processing heat treatments.
SCOPE
1.1 This test method covers the determination of shear strength of joints in advanced ceramics at ambient temperature using asymmetrical four-point flexure. Test specimen geometries, test specimen fabrication methods, testing modes (that is, force or displacement control), testing rates (that is, force or displacement rate), data collection, and reporting procedures are addressed.  
1.2 This test method is used to measure shear strength of ceramic joints in test specimens extracted from larger joined pieces by machining. Test specimens fabricated in this way are not expected to warp due to the relaxation of residual stresses but are expected to be much straighter and more uniform dimensionally than butt-jointed test specimens prepared by joining two halves, which is not recommended. In addition, this test method is intended for joints, which have either low or intermediate strengths with respect to the substrate material to be joined. Joints with high strengths should not be tested by this test method because of the high probability of invalid tests resulting from fractures initiating at the reaction points rather than in the joint. Determination of the shear strength of joints using this test method is appropriate particularly for advanced ceramic matrix composite materials but also may be useful for monolithic advanced ceramic materials.  
1.3 Values expressed in this test method are in accordance with the International System of Units (SI) and IEEE/ASTM SI 10.  
1.4 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use. Specific precautionary statements are noted in 8.1.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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