C28.01 - Mechanical Properties and Performance

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 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 one-fiftieth of the beam thickness. The homogeneity and isotropy assumption in the standard rule out the use of this test for continuous fiber-reinforced ceramics.  
4.3 Flexural strength of a group of test specimens is influenced by several parameters associated with the test procedure. Such factors include the loading rate, test environment, specimen size, specimen preparation, and test fixtures. Specimen sizes and fixtures were chosen to provide a balance between practical configurations and resulting errors, as discussed in MIL-STD-1942(MR) and Refs (1, 2).4 Specific fixture and specimen configurations were designated in order to permit 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 standard, is highly recommended for all purposes, especially if the data will be used for design as discussed in MIL-STD-1942(MR) and Refs (2-5) and Practices C1322 and C1239.  
4.5 The three-point test configuration exposes only a very small portion of the specimen to the maximum stress. Therefore, three-point flexural strengths are likely to be much greater than four-point flexural strengths. Three-point flexure has some advantages. It uses sim...
SCOPE
1.1 This test method covers the determination of flexural strength of advanced ceramic materials at ambient temperature. 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 sizes 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 method permits testing of machined or as-fired test specimens. Several options for machining preparation are included: application matched machining, customary procedure, or a specified standard procedure. This 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.

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 strength is 50 MPa (~7 ksi) or greater. The test method may also be used with glass test specimens, although Test Methods C158 is specifically designed to be used for glasses. This test method may be used with machined, drawn, extruded, and as-fired round specimens. This test method may be used with specimens that have elliptical cross section geometries.  
4.2 The flexure strength 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 one-fiftieth of the rod diameter. The homogeneity and isotropy assumptions in the standard rule out the use of this test for continuous fiber-reinforced ceramics.  
4.3 Flexural strength of a group of test specimens is influenced by several parameters associated with the test procedure. Such factors include the loading rate, test environment, specimen size, specimen preparation, and test fixtures (1-3).3 This method includes specific specimen-fixture size combinations, but permits alternative configurations within specified limits. These combinations were chosen to be practical, to minimize experimental error, and permit easy comparison of cylindrical rod strengths with data for other configurations. Equations for the Weibull effective volume and Weibull effective surface are included.  
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 in the material. Flaws in rods may be intrinsically volume-distributed throughout the bulk. Some of these flaws by chance may be located at or near the outer surface. Flaws may alternatively be intrinsically surface-distrib...
SCOPE
1.1 This test method is for the determination of flexural strength of rod-shaped specimens of advanced ceramic materials at ambient temperature. In many instances it is preferable to test round specimens rather than rectangular bend specimens, especially if the material is fabricated in rod form. This method permits testing of machined, drawn, or as-fired rod-shaped specimens. It allows some latitude in the rod sizes and cross section shape uniformity. Rod diameters between 1.5 and 8 mm and lengths from 25 to 85 mm are recommended, but other sizes are permitted. Four-point-1/4-point as shown in Fig. 1 is the preferred testing configuration. Three-point loading is permitted. This method describes the apparatus, specimen requirements, test procedure, calculations, and reporting requirements. The 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.
FIG. 1 Four-Point-1/4-Point Flexure Loading Configuration  
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.

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.
SCOPE
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.  
1.3 Materials covered in this standard are those advanced ceramics that meet criteria specified in flexure testing standards C1161 and C1211.  
1.4 The flexure test methods supporting this standard (C1161 and C1211) require test specimens that have a rectangular cross section, flat surfaces, and that are fabricated with specific dimensions and tolerances. Only grinding processes that are capable of generating the specified flat surfaces, that is, planar grinding modes, are suitable for evaluation by this method. Among the applicable machine types are horizontal and vertical spindle reciprocating surface grinders, horizontal and vertical spindle rotary surface grinders, double disk grinders, and tool-and-cutter grinders. Incremental cross-feed, plunge, and creep-feed grinding methods may be used.  
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.6 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.7 This international standard was develop...

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.

SIGNIFICANCE AND USE
5.1 For advanced ceramics, Knoop indenters are used to create indentations. The surface projection of the long diagonal is measured with optical microscopes.  
5.2 The Knoop indentation hardness is one of many properties that is used to characterize advanced ceramics. Attempts have been made to relate Knoop indentation hardness to other hardness scales, but no generally accepted methods are available. Such conversions are limited in scope and should be used with caution, except for special cases where a reliable basis for the conversion has been obtained by comparison tests.  
5.3 For advanced ceramics, the Knoop indentation is often preferred to the Vickers indentation since the Knoop long diagonal length is 2.8 times longer than the Vickers diagonal for the same force, and cracking is much less of a problem (1).5 On the other hand, the long slender tip of the Knoop indentation is more difficult to precisely discern, especially in materials with low contrast. The indentation forces chosen in this test method are designed to produce indentations as large as may be possible with conventional microhardness equipment, yet not so large as to cause cracking.  
5.4 The Knoop indentation is shallower than Vickers indentations made at the same force. Knoop indents may be useful in evaluating coating hardnesses.  
5.5 Knoop hardness is calculated from the ratio of the applied force divided by the projected indentation area on the specimen surface. It is assumed that the elastic springback of the narrow diagonal is negligible. (Vickers indenters are also used to measure hardness, but Vickers hardness is calculated from the ratio of applied force to the area of contact of the four faces of the undeformed indenter.)  
5.6 A full hardness characterization includes measurements over a broad range of indentation forces. Knoop hardness of ceramics usually decreases with increasing indentation size or indentation force such as that shown in Fig. 1.6 The trend is known as the in...
SCOPE
1.1 This test method covers the determination of the Knoop indentation hardness of advanced ceramics. In this test, a pointed, rhombic-based, pyramidal diamond indenter of prescribed shape is pressed into the surface of a ceramic with a predetermined force to produce a relatively small, permanent indentation. The surface projection of the long diagonal of the permanent indentation is measured using a light microscope. The length of the long diagonal and the applied force are used to calculate the Knoop hardness which represents the material’s resistance to penetration by the Knoop indenter.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 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.  
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.  
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.

SIGNIFICANCE AND USE
5.1 This test method may be used for material development, characterization, design data generation, and quality control purposes.  
5.2 This test method is specifically appropriate for determining the modulus of advanced ceramics that are elastic, homogeneous, and isotropic (1).4  
5.3 This test method addresses the room temperature determination of dynamic moduli of elasticity of slender bars (rectangular cross section) and rods (cylindrical). Flat plates and discs may also be measured similarly, but the required equations for determining the moduli are not addressed herein.  
5.4 This dynamic test method has several advantages and differences from static loading techniques and from resonant techniques requiring continuous excitation.  
5.4.1 The test method is nondestructive in nature and can be used for specimens prepared for other tests. The specimens are subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve, with the minimum possibility of fracture.  
5.4.2 The impulse excitation test uses an impact tool and simple supports for the test specimen. There is no requirement for complex support systems that require elaborate setup or alignment.  
5.5 This technique can be used to measure resonant frequencies alone for the purposes of quality control and acceptance of test specimens of both regular and complex shapes. A range of acceptable resonant frequencies is determined for a specimen with a particular geometry and mass. Deviations in specimen dimensions or mass and internal flaws (cracks, delaminations, inhomogeneities, porosity, etc.) will change the resonant frequency for that specimen. Any specimen with a resonant frequency falling outside the prescribed frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits of the selected frequency range are known to include the resonant frequency that the specimen must possess if its geometry and mass and in...
SCOPE
1.1 This test method covers determination of the dynamic elastic properties of advanced ceramics at ambient temperatures. Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the test specimen. The dynamic elastic properties of a material can therefore be computed if the geometry, mass, and mechanical resonant frequencies of a suitable (rectangular, cylindrical, or disc geometry) test specimen of that material can be measured. The resonant frequencies in flexure and torsion are measured by excitation of vibrations of the test specimen in a supported mode by a singular elastic strike with an impulse tool (Section 4 and Fig. 1, Fig. 3, and Fig. 4). Dynamic Young’s modulus is determined using the resonant frequency in the flexural mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young’s modulus and dynamic shear modulus are used to compute Poisson’s ratio.
FIG. 1 Block Diagram of Typical Test Apparatus  
1.2 Although not specifically described herein, this test method can also be performed at cryogenic and high temperatures with suitable equipment modifications and appropriate modifications to the calculations to compensate for thermal expansion, in accordance with Subsections 9.2, 9.3, and 10.4 of Test Method C1198.  
1.3 There are material-specific ASTM standards that cover the determination of resonance frequencies and elastic properties of specific materials by sonic resonance or by impulse excitation of vibration. Test Methods C215, C623, C747, C848, C1198, E1875, and E1876 may differ from this test method in several areas (for example, sample size, dimensional tolerances, sample preparation, calculation details, etc.). The testing of those materials should be done in compliance with the appropriate material-specific standards. Where possible, the pro...

SIGNIFICANCE AND USE
5.1 This test method may be used for material development, characterization, design data generation, and quality control purposes. It is specifically appropriate for determining the modulus of advanced ceramics that are elastic, homogeneous, and isotropic.  
5.1.1 This test method is nondestructive in nature. Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.  
5.1.2 The period of time during which measurement stress is applied and removed is of the order of hundreds of microseconds. With this test method it is feasible to perform measurements at high temperatures, where delayed elastic and creep effects would invalidate modulus measurements calculated from static loading.  
5.2 This test method has advantages in certain respects over the use of static loading systems for measuring moduli in advanced ceramics. It is nondestructive in nature and can be used for specimens prepared for other tests. Specimens are subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve with the minimum possibility of fracture. The period of time during which measurement stress is applied and removed is of the order of hundreds of microseconds. With this test method it is feasible to perform measurements at high temperatures, where delayed elastic and creep effects would invalidate modulus measurements calculated from static loading.  
5.3 The sonic resonant frequency technique can also be used as a nondestructive evaluation tool for detecting and screening defects (cracks, voids, porosity, density variations) in ceramic parts. These defects may change the elastic response and the observed resonant frequency of the test specimen. Guide E2001 describes a procedure for detecting such defects in metallic and nonmetallic parts using the resonant frequency method.  
5.4 Modification of this test method for use in quality control is possible. A range of acceptable resonant frequencies is determ...
SCOPE
1.1 This test method covers the determination of the dynamic elastic properties of advanced ceramics. Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the test specimen. Therefore, the dynamic elastic properties of a material can be computed if the geometry, mass, and mechanical resonant frequencies of a suitable rectangular or cylindrical test specimen of that material can be measured. The resonant frequencies in flexure and torsion are measured by mechanical excitation of vibrations of the test specimen in a suspended mode (Section 4 and Figs. 1 and 4). Dynamic Young’s modulus is determined using the resonant frequency in the flexural mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young’s modulus and dynamic shear modulus are used to compute Poisson’s ratio.  
1.2 This test method is specifically appropriate for advanced ceramics that are elastic, homogeneous, and isotropic  (1).2 Advanced ceramics of a composite character (particulate, whisker, or fiber reinforced) may be tested by this test method with the understanding that the character (volume fraction, size, morphology, distribution, orientation, elastic properties, and interfacial bonding) of the reinforcement in the test specimen will have a direct effect on the elastic properties. These reinforcement effects must be considered in interpreting the test results for composites. This test method is not satisfactory for specimens that have cracks or voids that are major discontinuities in the specimen. Neither is the test method satisfactory when these materials cannot be fabricated in a uniform rectangular or circular cross-section.  
1.3 A high-temperature furnace and cryogenic cabinet are described for measuring the dynamic elastic moduli as a function of temperature from −195 to 1200 °C.  
...

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization, reliability assessment, and design data generation.  
4.2 High-strength, monolithic advanced ceramic materials are generally characterized by small grain sizes (  
4.3 Because of the probabilistic strength distributions of brittle materials such as advanced ceramics, a sufficient number of test specimens at each testing condition is required for statistical analysis and eventual design with guidelines for sufficient numbers provided in this test method. Size-scaling effects as discussed in Practice C1239 will affect the strength values. Therefore, strengths obtained using different recommended tensile test specimen geometries with different volumes or surface areas of material in the gage sections will be different due to these size differences. Resulting strength values can, in principle, be scaled to an effective volume or effective surface area of unity as discussed in Practice C1239.  
4.4 Tensile tests provide information on the strength and deformation of materials under uniaxial stresses. Uniform stress states are required to effectively evaluate any nonlinear stress-strain behavior which may develop as the result of testing mode, testing rate, processing or alloying effects, environmental influences, or elevated temperatures. These effects may be consequences of stress corrosion or sub-critical (slow) crack growth which can be minimized by testing at appropriately rapid rates as outlined in this test method.  
4.5 The results of tensile tests of specimens fabricated to standardized dimensions from a particular material or selected portions of a part, or both, may not totally represent the strength and deformation properties of the entire full-size end product or its in-service behavior in different environments.  
4.6 For quality control purposes, results derived from standardized tensile test specimens can be considered to be indicative ...
SCOPE
1.1 This test method covers the determination of tensile strength under uniaxial loading of monolithic advanced ceramics at elevated temperatures. This test method addresses, but is not restricted to, various suggested test specimen geometries as listed in the appendix. In addition, test specimen fabrication methods, testing modes (force, displacement, or strain control), testing rates (force rate, stress rate, displacement rate, or strain rate), allowable bending, and data collection and reporting procedures are addressed. Tensile strength as used in this test method refers to the tensile strength obtained under uniaxial loading.  
1.2 This test method applies primarily to advanced ceramics which macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method applies primarily to monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behavior and application of this test method to these materials is not recommended.  
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. Refer to Section 7 for specific precautions.  
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 b...

SIGNIFICANCE AND USE
5.1 For advanced ceramics, Vickers indenters are used to create indentations whose surface-projected diagonals are measured with optical microscopes. The Vickers indenter creates a square impression from which two surface-projected diagonal lengths are measured. Vickers hardness is calculated from the ratio of the applied force to the area of contact of the four faces of the undeformed indenter. (In contrast, Knoop indenters are also used to measure hardness, but Knoop hardness is calculated from the ratio of the applied force to the projected area on the specimen surface.)  
5.2 Vickers indentation hardness is one of many properties that is used to characterize advanced ceramics. Attempts have been made to relate Vickers indentation hardness to other hardness scales, but no generally accepted methods are available. Such conversions are limited in scope and should be used with caution, except for special cases where a reliable basis for the conversion has been obtained by comparison tests.  
5.3 Vickers indentation diagonal lengths are approximately 2.8 times shorter than the long diagonal of Knoop indentations, and the indentation depth is approximately 1.5 times deeper than Knoop indentations made at the same force.  
5.4 Vickers indentations are influenced less by specimen surface flatness, parallelism, and surface finish than Knoop indentations, but these parameters must be considered nonetheless.  
5.5 Vickers indentations are much more likely to cause cracks in advanced ceramics than Knoop indentations. The cracks may influence the measured hardness by fundamentally altering the deformation processes that contribute to the formation of an impression, and they may impair or preclude measurement of the diagonal lengths due to excessive damage at the indentation tips or sides.  
5.6 A full hardness characterization includes measurements over a broad range of indentation forces. Vickers hardness of ceramics usually decreases with increasing indentation size o...
SCOPE
1.1 This test method covers the determination of the Vickers indentation hardness of advanced ceramics. In this test, a pointed, square-based, pyramidal diamond indenter of prescribed shape is pressed into the surface of a ceramic with a predetermined force to produce a relatively small, permanent indentation. The surface projection of the two diagonals of the permanent indentation is measured using a light microscope. The average diagonal size and the applied force are used to calculate the Vickers hardness, which represents the material’s resistance to penetration by the Vickers indenter. Hardness is computed as the ratio of the force to the contact surface area.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 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 Vickers hardness be reported either in units of GPa, or a dimensionless Vickers hardness number that has implied units of kgf/mm2.  
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.  
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 R...

SIGNIFICANCE AND USE
5.1 This practice is suitable for monolithic and some composite ceramics, for example, particulate- and whisker-reinforced and continuous-grain-boundary phase ceramics. (Long- or continuous-fiber reinforced ceramics are excluded.) For some materials, the location and identification of fracture origins may not be possible due to the specific microstructure.  
5.2 This practice is principally oriented towards characterization of fracture origins in specimens loaded in so-called fast fracture testing, but the approach can be extended to include other modes of loading as well.  
5.3 The procedures described within are primarily applicable to mechanical test specimens, although the same procedures may be relevant to component fracture analyses as well. It is customary practice to test a number of specimens (constituting a sample) to permit statistical analysis of the variability of the material’s strength. It is usually not difficult to test the specimens in a manner that will facilitate subsequent fractographic analysis. This may not be the case with component fracture analyses. Component fracture analysis is sometimes aided by cutting test pieces from the component and fracturing the test pieces. Fracture markings and fracture origins from the latter may aid component interpretation.  
5.4 Optimum fractographic analysis requires examination of as many similar specimens or components as possible. This will enhance the chances of successful interpretations. Examination of only one or a few specimens can be misleading. Of course, in some instances the fractographer may have access to only one or a few fractured specimens or components.  
5.5 Successful and complete fractography also requires careful consideration of all ancillary information that may be available, such as microstructural characteristics, material fabrication, properties and service histories, component or specimen machining, or preparation techniques.  
5.6 Fractographic inspection and analysis can b...
SCOPE
1.1 The objective of this practice is to provide an efficient and consistent methodology to locate and characterize fracture origins in advanced ceramics. It is applicable to advanced ceramics that are brittle; that is, fracture that takes place with little or no preceding plastic deformation. In such materials, fracture commences from a single location which is termed the fracture origin. The fracture origin in brittle ceramics normally consists of some irregularity or singularity in the material which acts as a stress concentrator. In the parlance of the engineer or scientist, these irregularities are termed flaws or defects. The latter word should not be construed to mean that the material has been prepared improperly or is somehow faulty.  
1.2 Although this practice is primarily intended for laboratory test piece analysis, the general concepts and procedures may be applied to component fracture analyses as well. In many cases, component fracture analysis may be aided by cutting laboratory test pieces out of the component. Information gleaned from testing the laboratory pieces (for example, flaw types, general fracture features, fracture mirror constants) may then aid interpretation of component fractures. For more information on component fracture analysis, see Refs (1, 2).2  
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.

SIGNIFICANCE AND USE
4.1 This practice may be used for material development, material comparison, quality assurance, characterization, reliability assessment, and design data generation.  
4.2 High-strength, monolithic advanced ceramic materials are generally characterized by small grain sizes (  
4.3 Cyclic fatigue by its nature is a probabilistic phenomenon as discussed in STP 91A and STP 588 (1, 2).4 In addition, the strengths of advanced ceramics are probabilistic in nature. Therefore, a sufficient number of test specimens at each testing condition is required for statistical analysis and design, with guidelines for sufficient numbers provided in STP 91A (1), STP 588 (2), and Practice E739. The many different tensile specimen geometries available for cyclic fatigue testing may result in variations in the measured cyclic fatigue behavior of a particular material due to differences in the volume or surface area of material in the gage section of the test specimens.  
4.4 Tensile cyclic fatigue tests provide information on the material response under fluctuating uniaxial tensile stresses. Uniform stress states are required to effectively evaluate any nonlinear stress-strain behavior which may develop as the result of cumulative damage processes (for example, microcracking, cyclic fatigue crack growth, etc.).  
4.5 Cumulative damage processes due to cyclic fatigue may be influenced by testing mode, testing rate (related to frequency), differences between maximum and minimum force (R or Α), effects of processing or combinations of constituent materials, or environmental influences, or both. Other factors that influence cyclic fatigue behavior are: void or porosity content, methods of test specimen preparation or fabrication,test specimen conditioning, test environment, force or strain limits during cycling, wave shapes (that is, sinusoidal, trapezoidal, etc.), and failure mode. Some of these effects may be consequences of stress corrosion or sub-critical (slow) crack growth which can...
SCOPE
1.1 This practice covers the determination of constant-amplitude, axial, tension-tension cyclic fatigue behavior and performance of advanced ceramics at ambient temperatures to establish “baseline” cyclic fatigue performance. This practice builds on experience and existing standards in tensile testing advanced ceramics at ambient temperatures and addresses various suggested test specimen geometries, test specimen fabrication methods, testing modes (force, displacement, or strain control), testing rates and frequencies, allowable bending, and procedures for data collection and reporting. This practice does not apply to axial cyclic fatigue tests of components or parts (that is, machine elements with nonuniform or multiaxial stress states).  
1.2 This practice applies primarily to advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this practice applies primarily to monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics, as well as certain discontinuous fibre-reinforced composite ceramics, may also meet these macroscopic behavior assumptions. Generally, continuous fibre-reinforced ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behavior and application of this practice to these materials is not recommended.  
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. Refer to Section 7 for specific precautions.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established ...

SIGNIFICANCE AND USE
5.1 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.  
5.2 Two- and three-parameter formulations exist for the Weibull distribution. This standard is restricted to the two-parameter formulation.  
5.3 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.  
5.4 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.  
5.5 The scaling of strength with size in accordance with the Weibull model is based on several key assumptions (5). It is assumed that th...
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.  
1.5 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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.7 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.

SIGNIFICANCE AND USE
4.1 For many structural ceramic components in service, their use is often limited by lifetimes that are controlled by a process of slow crack growth. This test method provides the empirical parameters for appraising the relative slow crack growth susceptibility of ceramic materials under specified environments at elevated temperatures. This test method is similar to Test Method C1368 with the exception that provisions for testing at elevated temperatures are given. Furthermore, this test method may establish the influences of processing variables and composition on slow crack growth as well as on strength behavior of newly developed or existing materials, thus allowing tailoring and optimizing material processing for further modification. In summary, this test method may be used for material development, quality control, characterization, and limited design data generation purposes.
Note 3: Data generated by this test method do not necessarily correspond to crack velocities that may be encountered in service conditions. The use of data generated by this test method for design purposes may entail considerable extrapolation and loss of accuracy.  
4.2 In this test method, the flexural stress computation is based on simple beam theory, with the 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 one fiftieth (1/50) of the beam thickness.  
4.3 In this test method, the test specimen sizes and test fixtures were chosen in accordance with Test Method C1211, which provides a balance between practical configurations and resulting errors, as discussed in Refs (5, 6). Only the four-point test configuration is used in this test method.  
4.4 In this test method, the slow crack growth parameters (n and D) are determined based on the mathematical relationship between flexural strength and applied stress rate, log σ...
SCOPE
1.1 This test method covers the determination of slow crack growth (SCG) parameters of advanced ceramics by using constant stress-rate flexural testing in which flexural strength is determined as a function of applied stress rate in a given environment at elevated temperatures. The strength degradation exhibited with decreasing applied stress rate in a specified environment is the basis of this test method which enables the evaluation of slow crack growth parameters of a material.
Note 1: This test method is frequently referred to as “dynamic fatigue” testing (1-3)2 in which the term “fatigue” is used interchangeably with the term “slow crack growth.” To avoid possible confusion with the “fatigue” phenomenon of a material which occurs exclusively under cyclic loading, as defined in Terminology E1823, this test method uses the term “constant stress-rate testing” rather than “dynamic fatigue” testing.
Note 2: In glass and ceramics technology, static tests of considerable duration are called “static fatigue” tests, a type of test designated as stress-rupture (Terminology E1823).  
1.2 This test method is intended primarily to be used for negligible creep of test specimens, with specific limits on creep imposed in this test method.  
1.3 This test method applies primarily to advanced ceramics that are macroscopically homogeneous and isotropic. This test method may also be applied to certain whisker- or particle-reinforced ceramics that exhibit macroscopically homogeneous behavior.  
1.4 This test method is intended for use with various test environments such as air, vacuum, inert, and any other gaseous environments.  
1.5 Values expressed in this standard test are in accordance with the International System of Units (SI) and 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 a...

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization, and design code or model verification.  
4.2 Engineering applications of ceramics frequently involve biaxial tensile stresses. Generally, the resistance to equibiaxial flexure is the measure of the least flexural strength of a monolithic advanced ceramic. The equibiaxial flexural strength distributions of ceramics are probabilistic and can be described by a weakest-link failure theory (1, 2).4 Therefore, a sufficient number of test specimens at each testing condition is required for statistical estimation or the equibiaxial strength.  
4.3 Equibiaxial strength tests provide information on the strength and deformation of materials under multiple tensile stresses. Multiaxial stress states are required to effectively evaluate failure theories applicable to component design, and to efficiently sample surfaces that may exhibit anisotropic flaw distributions. Equibiaxial tests also minimize the effects of test specimen edge preparation as compared to uniaxial tests because the generated stresses are lowest at the test specimen edges.  
4.4 The test results of equibiaxial test specimens fabricated to standardized dimensions from a particular material or selected portions of a component, or both, may not totally represent the strength properties in the entire full-size component or its in-service behavior in different environments.  
4.5 For quality control purposes, results derived from standardized equibiaxial test specimens may be considered indicative of the response of the bulk material from which they were taken for any given primary processing conditions and post-processing heat treatments or exposures.
SCOPE
1.1 This test method covers the determination of the equibiaxial strength of advanced ceramics at ambient temperature via concentric ring configurations under monotonic uniaxial loading. In addition, test specimen fabrication methods, testing modes, testing rates, allowable deflection, and data collection and reporting procedures are addressed. Two types of test specimens are considered: machined test specimens and as-fired test specimens exhibiting a limited degree of warpage. Strength as used in this test method refers to the maximum strength obtained under monotonic application of load. Monotonic loading refers to a test conducted at a constant rate in a continuous fashion, with no reversals from test initiation to final fracture.  
1.2 This test method is intended primarily for use with advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method is intended for use on monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics, as well as certain discontinuous fiber-reinforced composite ceramics, may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites do not macroscopically exhibit isotropic, homogeneous, continuous behavior, and the application of this test method to these materials is not recommended.  
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
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.  
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.

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization, and design data generation.  
4.2 Generally, resistance to compression is the measure of the greatest strength of a monolithic advanced ceramic. Ideally, ceramics should be compressively stressed in use, although engineering applications may frequently introduce tensile stresses in the component. Nonetheless, compressive behavior is an important aspect of mechanical properties and performance. Although tensile strength distributions of ceramics are probabilistic and can be described by a weakest-link failure theory, such descriptions have been shown to be inapplicable to compressive strength distributions in at least one study (1).3 However, the need to test a statistically significant number of compressive test specimens is not obviated. Therefore, a sufficient number of test specimens at each testing condition is required for statistical analysis and design.  
4.3 Compression tests provide information on the strength and deformation of materials under uniaxial compressive stresses. Uniform stress states are required to effectively evaluate any nonlinear stress-strain behavior which may develop as the result of cumulative damage processes (for example, microcracking) which may be influenced by testing mode, testing rate, processing or compositional effects, microstructure, or environmental influences.  
4.4 The results of compression tests of test specimens fabricated to standardized dimensions from a particular material or selected portions of a part, or both, may not totally represent the strength and deformation properties in the entire full-size product or its in-service behavior in different environments.  
4.5 For quality control purposes, results derived from standardized compressive test specimens may be considered indicative of the response of the material from which they were taken for given primary processing conditions and post-proces...
SCOPE
1.1 This test method covers the determination of compressive strength including stress-strain behavior, under monotonic uniaxial loading of advanced ceramics at ambient temperature. This test method is restricted to specific test specimen geometries. In addition, test specimen fabrication methods, testing modes (force or displacement), testing rates (force rate, stress rate, displacement rate, or strain rate), allowable bending, and data collection and reporting procedures are addressed. Compressive strength as used in this test method refers to the compressive strength obtained under monotonic uniaxial loading. Monotonic loading refers to a test conducted at a constant rate in a continuous fashion, with no reversals from test initiation to final fracture.  
1.2 This test method is intended primarily for use with advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method is intended for use on monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics, as well as certain discontinuous fiber-reinforced composite ceramics, may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behavior and, application of this test method to these materials is not recommended.  
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.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established i...

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization, and design data generation.  
4.2 High-strength, monolithic advanced ceramic materials generally characterized by small grain sizes (  
4.3 Although the volume or surface area of material subjected to a uniform tensile stress for a single uniaxially loaded tensile test may be several times that of a single flexure test specimen, the need to test a statistically significant number of tensile test specimens is not obviated. Therefore, because of the probabilistic strength distributions of brittle materials such as advanced ceramics, a sufficient number of test specimens at each testing condition is required for statistical analysis and eventual design, with guidelines for sufficient numbers provided in this test method. Note that size-scaling effects as discussed in Practice C1239 will affect the strength values. Therefore, strengths obtained using different recommended tensile test specimens with different volumes or surface areas of material in the gage sections will be different due to these size differences. Resulting strength values can be scaled to an effective volume or surface area of unity as discussed in Practice C1239.  
4.4 Tensile tests provide information on the strength and deformation of materials under uniaxial tensile stresses. Uniform stress states are required to effectively evaluate any nonlinear stress-strain behavior which may develop as the result of testing mode, testing rate, processing or alloying effects, or environmental influences. These effects may be consequences of stress corrosion or subcritical (slow) crack growth, which can be minimized by testing at appropriately rapid rates as outlined in this test method.  
4.5 The results of tensile tests of test specimens fabricated to standardized dimensions from a particular material or selected portions, or both, of a part may not totally represent the strength and deforma...
SCOPE
1.1 This test method covers the determination of tensile strength under uniaxial loading of monolithic advanced ceramics at ambient temperatures. This test method addresses, but is not restricted to, various suggested test specimen geometries as listed in the appendixes. In addition, test specimen fabrication methods, testing modes (force, displacement, or strain control), testing rates (force rate, stress rate, displacement rate, or strain rate), allowable bending, and data collection and reporting procedures are addressed. Note that tensile strength as used in this test method refers to the tensile strength obtained under uniaxial loading.  
1.2 This test method applies primarily to advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method applies primarily to monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behavior and application of this practice to these materials is not recommended.  
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 given in Section 7.  
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, Guid...

SIGNIFICANCE AND USE
5.1 Advanced ceramics usually display a linear stress-strain behavior to failure. Lack of ductility combined with flaws that have various sizes and orientations leads to scatter in failure strength. Strength is not a deterministic property, but instead reflects an intrinsic fracture toughness and a distribution (size and orientation) of flaws present in the material. This practice is applicable to brittle monolithic ceramics that fail as a result of catastrophic propagation of flaws present in the material. This practice is also applicable to composite ceramics that do not exhibit any appreciable bilinear or nonlinear deformation behavior. In addition, the composite must contain a sufficient quantity of uniformly distributed reinforcements such that the material is effectively homogeneous. Whisker-toughened ceramic composites may be representative of this type of material.  
5.2 Two- and three-parameter formulations exist for the Weibull distribution. This practice is restricted to the two-parameter formulation. An objective of this practice is to obtain point estimates of the unknown parameters by using well-defined functions that incorporate the failure data. These functions are referred to as “estimators.” It is desirable that an estimator be consistent and efficient. In addition, the estimator should produce unique, unbiased estimates of the distribution parameters (6). Different types of estimators exist, including moment estimators, least-squares estimators, and maximum likelihood estimators. This practice details the use of maximum likelihood estimators due to the efficiency and the ease of application when censored failure populations are encountered.  
5.3 Tensile and flexural test specimens are the most commonly used test configurations for advanced ceramics. The observed strength values are dependent on test specimen size and geometry. Parameter estimates can be computed for a given test specimen geometry ( m^, ^σθ), but it is suggested that the paramet...
SCOPE
1.1 This practice covers the evaluation and reporting of uniaxial strength data and the estimation of Weibull probability distribution parameters for advanced ceramics that fail in a brittle fashion (see Fig. 1). The estimated Weibull distribution parameters are used for statistical comparison of the relative quality of two or more test data sets and for the prediction of the probability of failure (or, alternatively, the fracture strength) for a structure of interest. In addition, this practice encourages the integration of mechanical property data and fractographic analysis.  
1.6 The values stated in SI units are to be regarded as the standard per IEEE/ASTM SI 10.  
1.7 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.

SIGNIFICANCE AND USE
5.1 The high temperature capabilities of advanced ceramics are a key performance benefit for many demanding engineering applications. In many of those applications, advanced ceramics will have to perform across a broad temperature range with exposure to sudden changes in temperature and heat flux. Thermal shock resistance of the ceramic material is a critical factor in determining the durability of the component under transient thermal conditions.  
5.2 This test method is useful for material development, quality assurance, characterization, and assessment of durability. It has limited value for design data generation, because of the limitations of the flexural test geometry in determining fundamental tensile properties.  
5.3 Appendix X1 (following EN 820-3) provides an introduction to thermal stresses, thermal shock, and critical material/geometry factors. The appendix also contains a mathematical analysis of the stresses developed by thermal expansion under steady-state and transient conditions, as determined by mechanical properties, thermal characteristics, and heat transfer effects.
SCOPE
1.1 This test method describes the determination of the resistance of advanced ceramics to thermal shock by water quenching. The method builds on the experimental principle of rapid quenching of a test specimen at an elevated temperature in a water bath at room temperature. The effect of the thermal shock is assessed by measuring the reduction in flexural strength produced by rapid quenching of test specimens heated across a range of temperatures. For a quantitative measurement of thermal shock resistance, a critical temperature interval is determined by a reduction in the mean flexural strength of at least 30 %. The test method does not determine thermal stresses developed as a result of a steady-state temperature difference within a ceramic body or of thermal expansion mismatch between joined bodies. The test method is not intended to determine the resistance of a ceramic material to repeated shocks. Since the determination of the thermal shock resistance is performed by evaluating retained strength, the method is not suitable for ceramic components; however, test specimens cut from components may be used.  
1.2 The test method is intended primarily for dense monolithic ceramics, but may also be applicable to certain composites such as whisker- or particulate-reinforced ceramic matrix composites that are macroscopically homogeneous.  
1.3 Values expressed in this standard 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.  
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.

SIGNIFICANCE AND USE
4.1 For many structural ceramic components in service, their use is often limited by lifetimes that are controlled by a process of SCG. This test method provides the empirical parameters for appraising the relative SCG susceptibility of ceramic materials under specified environments. Furthermore, this test method may establish the influences of processing variables and composition on SCG as well as on strength behavior of newly developed or existing materials, thus allowing tailoring and optimizing material processing for further modification. In summary, this test method may be used for material development, quality control, characterization, and limited design data generation purposes. The conventional analysis of constant stress rate testing is based on a number of critical assumptions, the most important of which are listed in the next paragraphs.  
4.2 The flexural stress computation for the rectangular beam test specimens or the equibiaxial disk flexure test specimens is based on simple beam theory, with the 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 one-fiftieth of the beam thickness.  
4.3 The test specimen sizes and fixtures for rectangular beam test specimens should be in accordance with Test Method C1161, which provides a balance between practical configurations and resulting errors, as discussed in Refs  (4, 5). Only four-point test configuration is allowed in this test method for rectangular beam specimens. Three-point test configurations are not permitted. The test specimen sizes and fixtures for disk test specimens tested in ring-on-ring flexure should be chosen in accordance with Test Method C1499. The test specimens for direct tension strength testing should be chosen in accordance with Test Method C1273.  
4.4 The SCG parameters (n and D) are determined by fitting the measured ...
SCOPE
1.1 This test method covers the determination of slow crack growth (SCG) parameters of advanced ceramics by using constant stress rate rectangular beam flexural testing, ring-on-ring biaxial disk flexural testing, or direct tensile strength, in which strength is determined as a function of applied stress rate in a given environment at ambient temperature. The strength degradation exhibited with decreasing applied stress rate in a specified environment is the basis of this test method which enables the evaluation of slow crack growth parameters of a material.
Note 1: This test method is frequently referred to as “dynamic fatigue” testing (1-3)2 in which the term “fatigue” is used interchangeably with the term “slow crack growth.” To avoid possible confusion with the “fatigue” phenomenon of a material which occurs exclusively under cyclic loading, as defined in Terminology E1823, this test method uses the term “constant stress rate testing” rather than “dynamic fatigue” testing.
Note 2: In glass and ceramics technology, static tests of considerable duration are called “static fatigue” tests, a type of test designated as stress rupture (See Terminology E1823).  
1.2 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.

SIGNIFICANCE AND USE
5.1 Fracture toughness, KIc, is a measure of the resistance to crack extension in a brittle material. These test methods may be used for material development, material comparison, quality assessment, and characterization.  
5.2 The pb and the vb fracture toughness values provide information on the fracture resistance of advanced ceramics containing large sharp cracks, while the sc fracture toughness value provides this information for small cracks comparable in size to natural fracture sources. Cracks of different sizes may be used for the sc method. If the fracture toughness values vary as a function of the crack size it can be expected that KIsc will differ from KIpb and KIvb. Table 1 tabulates advantages, disadvantages, and applicability of each method.
SCOPE
1.1 These test methods cover the fracture toughness, KIc, determination of advanced ceramics at ambient temperature. The methods determine KIpb (precracked beam test specimen), KIsc (surface crack in flexure), and KIvb (chevron-notched beam test specimen). The fracture toughness values are determined using beam test specimens with a sharp crack. The crack is either a straight-through crack formed via bridge flexure (pb), or a semi-elliptical surface crack formed via Knoop indentation (sc), or it is formed and propagated in a chevron notch (vb), as shown in Fig. 1.  
1.6 Values expressed in these test methods are in accordance with the International System of Units (SI) and IEEE/ASTM SI 10.  
1.7 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.8 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.  
1.9 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.

SIGNIFICANCE AND USE
4.1 Creep tests measure the time-dependent deformation under force at a given temperature, and, by implication, the force-carrying capability of the material for limited deformations. Creep rupture tests, properly interpreted, provide a measure of the force-carrying capability of the material as a function of time and temperature. The two tests complement each other in defining the force-carrying capability of a material for a given period of time. In selecting materials and designing parts for service at elevated temperatures, the type of test data used will depend on the criteria for force-carrying capability that best defines the service usefulness of the material.  
4.2 This test method may be used for material development, quality assurance, characterization, and design data generation.  
4.3 High-strength, monolithic ceramic materials, generally characterized by small grain sizes (  
4.4 Data obtained for design and predictive purposes shall be obtained using any appropriate combination of test methods that provide the most relevant information for the applications being considered. It is noted here that ceramic materials tend to creep more rapidly in tension than in compression (1-3).4 This difference results in time-dependent changes in the stress distribution and the position of the neutral axis when tests are conducted in flexure. As a consequence, deconvolution of flexural creep data to obtain the constitutive equations needed for design cannot be achieved without some degree of uncertainty concerning the form of the creep equations, and the magnitude of the creep rate in tension vis-a-vis the creep rate in compression. Therefore, creep data for design and life prediction shall be obtained in both tension and compression, as well as the expected service stress state.
SCOPE
1.1 This test method covers the determination of tensile creep strain, creep strain rate, and creep time to failure for advanced monolithic ceramics at elevated temperatures, typically between 1073 and 2073 K. A variety of test specimen geometries are included. The creep strain at a fixed temperature is evaluated from direct measurements of the gage length extension over the time of the test. The minimum creep strain rate, which may be invariant with time, is evaluated as a function of temperature and applied stress. Creep time to failure is also included in this test method.  
1.2 This test method is for use with advanced ceramics that behave as macroscopically isotropic, homogeneous, continuous materials. While this test method is intended for use on monolithic ceramics, whisker- or particle-reinforced composite ceramics as well as low-volume-fraction discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Continuous fiber-reinforced ceramic composites (CFCCs) do not behave as macroscopically isotropic, homogeneous, continuous materials, and application of this test method to these materials is not recommended.  
1.3 The values in SI units are to be regarded as the standard (see IEEE/ASTM SI 10). The values given in parentheses are mathematical conversions to inch-pound units that are provided for information only and are not considered standard.  
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.  
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.

SIGNIFICANCE AND USE
5.1 Advanced ceramics are candidate materials for high-temperature structural applications requiring high strength along with wear and corrosion resistance. In particular, ceramic tubes are being considered and evaluated as hermetically tight fuel containment tubes for nuclear reactors. These ceramic tubes require end-plugs for containment and structural integrity. The end-plugs are commonly bonded with high-temperature adhesives into the tubes. The strength and durability of the test specimen joint are critical engineering factors, and the joint strength has to be determined across the full range of operating temperatures and conditions. The test method has to determine the breaking force, the nominal joint strength, the nominal burst pressure, and the failure mode for a given tube/plug/adhesive configuration.  
5.2 The EPPO test provides information on the strength and the deformation of test specimen joints under applied shear, tensile, and mixed-mode stresses (with different plug geometries) at various temperatures and after environmental conditioning.  
5.3 The end-plug test specimen geometry is a direct analog of the functional plug-tube application and is the most direct way of testing the tubular joint for the purposes of development, evaluation, and comparative studies involving adhesives and bonded products, including manufacturing quality control. This test method is a more realistic test for the intended geometry than the current shear test of ceramic joints (Test Method C1469), which uses an asymmetric four-point shear test on a flat adhesive face joint.  
5.4 The EPPO test method may be used for joining method development and selection, adhesive comparison and screening, and quality assurance. This test method is not recommended for adhesive property determination, design data generation, material model verification/validation, or combinations thereof.
SCOPE
1.1 This test method covers the determination of the push-out force, nominal joint strength, and nominal burst pressure of bonded ceramic end-plugs in advanced ceramic cylindrical tubes (monolithic and composite) at ambient and elevated temperatures (see 4.2). The test method is broad in scope and end-plugs may have a variety of different configurations, joint types, and geometries. It is expected that the most common type of joints tested are adhesively bonded end-plugs that use organic adhesives, metals, glass sealants, and ceramic adhesives (sintered powders, sol-gel, polymer-derived ceramics) as the bonding material between the end-plug and the tube. This test method describes the test capabilities and limitations, the test apparatus, test specimen geometries and preparation methods, test procedures (modes, rates, mounting, alignment, testing methods, data collection, and fracture analysis), calculation methods, and reporting procedures.  
1.2 In this end-plug push-out (EPPO) test method, test specimens are prepared by bonding a fitted ceramic plug into one end of a ceramic tube. The test specimen tube is secured into a gripping fixture and test apparatus, and an axial compressive force is applied to the interior face of the plug to push it out of the tube. (See 4.2.) The axial force required to fracture (or permanently deform) the joined test specimen is measured and used to calculate a nominal joint strength and a nominal burst pressure. Tests are performed at ambient or elevated temperatures, or both, based on the temperature capabilities of the test furnace and the test apparatus.  
1.3 This test method is applicable to end-plug test specimens with a wide range of configurations and sizes. The test method does not define a standardized test specimen geometry, because the purpose of the test is to determine the nominal joint strength and nominal burst pressure of an application-specific plug-tube design. The test specimen should be similar in size and configuration with the intended application and product desig...

SIGNIFICANCE AND USE
4.1 The service life of many structural ceramic components is often limited by the subcritical growth of cracks. This test method provides an approach for appraising the relative slow crack growth susceptibility of ceramic materials under specified environments at ambient temperature. Furthermore, this test method may establish the influences of processing variables and composition on slow crack growth as well as on strength behavior of newly developed or existing materials, thus allowing tailoring and optimizing material processing for further modification. In summary, this test method may be used for material development, quality control, characterization, design code or model verification, and limited design data generation purposes.
Note 4: Data generated by this test method do not necessarily correspond to crack velocities that may be encountered in service conditions. The use of data generated by this test method for design purposes, depending on the range and magnitude of applied stresses used, may entail extrapolation and uncertainty.  
4.2 This test method is related to Test Method C1368 (“constant stress-rate flexural testing”), however, C1368 uses constant stress rates to determine corresponding flexural strengths whereas this test method employs constant stress to determine corresponding times to failure. In general, the data generated by this test method may be more representative of actual service conditions as compared with those by constant stress-rate testing. However, in terms of test time, constant stress testing is inherently and significantly more time consuming than constant stress rate testing.  
4.3 The flexural stress computation in this test method is based on simple elastic beam theory, with the 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 grain size should be no greater than one-fiftieth (1/50 ) of the beam depth...
SCOPE
1.1 This standard test method covers the determination of slow crack growth (SCG) parameters of advanced ceramics by using constant stress flexural testing in which time to failure of flexure test specimens is determined in four-point flexure as a function of constant applied stress in a given environment at ambient temperature. In addition, test specimen fabrication methods, test stress levels, data collection and analysis, and reporting procedures are addressed. The decrease in time to failure with increasing applied stress in a specified environment is the basis of this test method that enables the evaluation of slow crack growth parameters of a material. The preferred analysis in the present method is based on a power law relationship between crack velocity and applied stress intensity; alternative analysis approaches are also discussed for situations where the power law relationship is not applicable.
Note 1: The test method in this standard is frequently referred to as “static fatigue” or stress-rupture testing (1-3)2 in which the term “fatigue” is used interchangeably with the term “slow crack growth.” To avoid possible confusion with the “fatigue” phenomenon of a material that occurs exclusively under cyclic loading, as defined in Terminology E1823, this test method uses the term “constant stress testing” rather than “static fatigue” testing.  
1.2 This test method applies primarily to monolithic advanced ceramics that are macroscopically homogeneous and isotropic. This test method may also be applied to certain whisker- or particle-reinforced ceramics as well as certain discontinuous fiber-reinforced composite ceramics that exhibit macroscopically homogeneous behavior. Generally, continuous fiber ceramic composites do not exhibit macroscopically isotropic, homogeneous, continuous behavior, and the application of this test method to these materials is not recommended.  
1.3 This test method is intended for us...

SIGNIFICANCE AND USE
4.1 The service life of many structural ceramic components is often limited by the subcritical growth of cracks over time, under stress at a defined temperature, and in a defined chemical environment (Refs 1-3). When one or more cracks grow to a critical size, brittle catastrophic failure may occur in the component. Slow crack growth in ceramics is commonly accelerated at elevated temperatures. This test method provides a procedure for measuring the long term load-carrying ability and appraising the relative slow crack growth susceptibility of ceramic materials at elevated temperatures as a function of time, temperature, and environment. This test method is based on Test Method C1576 with the addition of provisions for elevated temperature testing.  
4.2 This test method is also used to determine the influences of processing variables and composition on slow crack growth at elevated temperatures, as well as on strength behavior of newly developed or existing materials, thus allowing tailoring and optimizing material processing for further modification.  
4.3 This test method may be used for material development, quality control, characterization, design code or model verification, time-to-failure, and limited design data generation purposes.
Note 2: Data generated by this test method do not necessarily correspond to crack velocities that may be encountered in service conditions. The use of data generated by this test method for design purposes, depending on the range and magnitude of applied stresses used, may entail extrapolation and uncertainty.  
4.4 This test method and Test Method C1576 are similar and related to Test Methods C1368 and C1465; however, C1368 and C1465 use constant stress-rates (linearly increasing stress over time) to determine corresponding flexural strengths, whereas this test method and C1576 employ a constant stress (fixed stress levels over time) to determine corresponding times-to-failure. In general, the data generated by this test m...
SCOPE
1.1 This test method covers the determination of the slow crack growth (SCG) parameters of advanced ceramics in a given test environment at elevated temperatures in which the time-to-failure of four-point-1/4 point flexural test specimens (see Fig. 1) is determined as a function of different levels of constant applied stress. This SCG constant stress test procedure is also called a slow crack growth (SCG) stress rupture test. The test method addresses the test equipment, test specimen fabrication, test stress levels and experimental procedures, data collection and analysis, and reporting requirements.  
1.2 In this test method the decrease in time-to-failure with increasing levels of applied stress in specified test conditions and temperatures is measured and used to analyze the slow crack growth parameters of the ceramic. The preferred analysis method is based on a power law relationship between crack velocity and applied stress intensity; alternative analysis approaches are also discussed for situations where the power law relationship is not applicable.
Note 1: This test method is historically referred to in earlier technical literature as static fatigue testing (Refs 1-3)2 in which the term fatigue is used interchangeably with the term slow crack growth. To avoid possible confusion with the fatigue phenomenon of a material that occurs exclusively under cyclic stress loading, as defined in E1823, this test method uses the term constant stress testing rather than static fatigue testing.  
1.3 This test method uses a 4-point-1/4 point flexural test mode and applies primarily to monolithic advanced ceramics that are macroscopically homogeneous and isotropic. This test method may also be applied to certain whisker- or particle-reinforced ceramics as well as certain discontinuous fiber-reinforced composite ceramics that exhibit macroscopically homogeneous behavior. Generally, continuous fiber ceramic composites do not ...

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.

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 strength is 50 MPa (~7 ksi) or greater. The test method may also be used with glass test specimens, although Test Methods C158 is specifically designed to be used for glasses. This test method may be used with machined, drawn, extruded, and as-fired round specimens. This test method may be used with specimens that have elliptical cross section geometries.  
4.2 The flexure strength 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 one-fiftieth of the rod diameter. The homogeneity and isotropy assumptions in the standard rule out the use of this test for continuous fiber-reinforced ceramics.  
4.3 Flexural strength of a group of test specimens is influenced by several parameters associated with the test procedure. Such factors include the loading rate, test environment, specimen size, specimen preparation, and test fixtures (1-3).3 This method includes specific specimen-fixture size combinations, but permits alternative configurations within specified limits. These combinations were chosen to be practical, to minimize experimental error, and permit easy comparison of cylindrical rod strengths with data for other configurations. Equations for the Weibull effective volume and Weibull effective surface are included.  
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 in the material. Flaws in rods may be intrinsically volume-distributed throughout the bulk. Some of these flaws by chance may be located at or near the outer surface. Flaws may alternatively be intrinsically surface-distrib...
SCOPE
1.1 This test method is for the determination of flexural strength of rod-shaped specimens of advanced ceramic materials at ambient temperature. In many instances it is preferable to test round specimens rather than rectangular bend specimens, especially if the material is fabricated in rod form. This method permits testing of machined, drawn, or as-fired rod-shaped specimens. It allows some latitude in the rod sizes and cross section shape uniformity. Rod diameters between 1.5 and 8 mm and lengths from 25 to 85 mm are recommended, but other sizes are permitted. Four-point-1/4-point as shown in Fig. 1 is the preferred testing configuration. Three-point loading is permitted. This method describes the apparatus, specimen requirements, test procedure, calculations, and reporting requirements. The 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.
FIG. 1 Four-Point-1/4-Point Flexure Loading Configuration  
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.

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 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 one-fiftieth of the beam thickness. The homogeneity and isotropy assumption in the standard rule out the use of this test for continuous fiber-reinforced ceramics.  
4.3 Flexural strength of a group of test specimens is influenced by several parameters associated with the test procedure. Such factors include the loading rate, test environment, specimen size, specimen preparation, and test fixtures. Specimen sizes and fixtures were chosen to provide a balance between practical configurations and resulting errors, as discussed in MIL-STD-1942(MR) and Refs (1, 2).4 Specific fixture and specimen configurations were designated in order to permit 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 standard, is highly recommended for all purposes, especially if the data will be used for design as discussed in MIL-STD-1942(MR) and Refs (2-5) and Practices C1322 and C1239.  
4.5 The three-point test configuration exposes only a very small portion of the specimen to the maximum stress. Therefore, three-point flexural strengths are likely to be much greater than four-point flexural strengths. Three-point flexure has some advantages. It uses sim...
SCOPE
1.1 This test method covers the determination of flexural strength of advanced ceramic materials at ambient temperature. 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 sizes 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 method permits testing of machined or as-fired test specimens. Several options for machining preparation are included: application matched machining, customary procedure, or a specified standard procedure. This 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.

SIGNIFICANCE AND USE
5.1 For advanced ceramics, Knoop indenters are used to create indentations. The surface projection of the long diagonal is measured with optical microscopes.  
5.2 The Knoop indentation hardness is one of many properties that is used to characterize advanced ceramics. Attempts have been made to relate Knoop indentation hardness to other hardness scales, but no generally accepted methods are available. Such conversions are limited in scope and should be used with caution, except for special cases where a reliable basis for the conversion has been obtained by comparison tests.  
5.3 For advanced ceramics, the Knoop indentation is often preferred to the Vickers indentation since the Knoop long diagonal length is 2.8 times longer than the Vickers diagonal for the same force, and cracking is much less of a problem (1).5 On the other hand, the long slender tip of the Knoop indentation is more difficult to precisely discern, especially in materials with low contrast. The indentation forces chosen in this test method are designed to produce indentations as large as may be possible with conventional microhardness equipment, yet not so large as to cause cracking.  
5.4 The Knoop indentation is shallower than Vickers indentations made at the same force. Knoop indents may be useful in evaluating coating hardnesses.  
5.5 Knoop hardness is calculated from the ratio of the applied force divided by the projected indentation area on the specimen surface. It is assumed that the elastic springback of the narrow diagonal is negligible. (Vickers indenters are also used to measure hardness, but Vickers hardness is calculated from the ratio of applied force to the area of contact of the four faces of the undeformed indenter.)  
5.6 A full hardness characterization includes measurements over a broad range of indentation forces. Knoop hardness of ceramics usually decreases with increasing indentation size or indentation force such as that shown in Fig. 1.6 The trend is known as the in...
SCOPE
1.1 This test method covers the determination of the Knoop indentation hardness of advanced ceramics. In this test, a pointed, rhombic-based, pyramidal diamond indenter of prescribed shape is pressed into the surface of a ceramic with a predetermined force to produce a relatively small, permanent indentation. The surface projection of the long diagonal of the permanent indentation is measured using a light microscope. The length of the long diagonal and the applied force are used to calculate the Knoop hardness which represents the material’s resistance to penetration by the Knoop indenter.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 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.  
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.  
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.

SIGNIFICANCE AND USE
4.1 For many structural ceramic components in service, their use is often limited by lifetimes that are controlled by a process of SCG. This test method provides the empirical parameters for appraising the relative SCG susceptibility of ceramic materials under specified environments. Furthermore, this test method may establish the influences of processing variables and composition on SCG as well as on strength behavior of newly developed or existing materials, thus allowing tailoring and optimizing material processing for further modification. In summary, this test method may be used for material development, quality control, characterization, and limited design data generation purposes. The conventional analysis of constant stress-rate testing is based on a number of critical assumptions, the most important of which are listed in the next paragraphs.  
4.2 The flexural stress computation for the rectangular beam test specimens or the equibiaxial disk flexure test specimens is based on simple beam theory, with the 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 one-fiftieth of the beam thickness.  
4.3 The test specimen sizes and fixtures for rectangular beam test specimens should be in accordance with Test Method C1161, which provides a balance between practical configurations and resulting errors, as discussed in Refs  (4, 5). Only four-point test configuration is allowed in this test method for rectangular beam specimens. Three-point test configurations are not permitted. The test specimen sizes and fixtures for disk test specimens tested in ring-on-ring flexure should be chosen in accordance with Test Method C1499. The test specimens for direct tension strength testing should be chosen in accordance with Test Method C1273.  
4.4 The SCG parameters (n and D) are determined by fitting the measured ...
SCOPE
1.1 This test method covers the determination of slow crack growth (SCG) parameters of advanced ceramics by using constant stress-rate rectangular beam flexural testing, or ring-on-ring biaxial disk flexural testing, or direct tensile strength, in which strength is determined as a function of applied stress rate in a given environment at ambient temperature. The strength degradation exhibited with decreasing applied stress rate in a specified environment is the basis of this test method which enables the evaluation of slow crack growth parameters of a material.
Note 1: This test method is frequently referred to as “dynamic fatigue” testing (1-3)2 in which the term “fatigue” is used interchangeably with the term “slow crack growth.” To avoid possible confusion with the “fatigue” phenomenon of a material which occurs exclusively under cyclic loading, as defined in Terminology E1823, this test method uses the term “constant stress-rate testing” rather than “dynamic fatigue” testing.
Note 2: In glass and ceramics technology, static tests of considerable duration are called “static fatigue” tests, a type of test designated as stress-rupture (See Terminology E1823).  
1.2 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 and health practices and determine the applicability of regulatory limitations prior to use.

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.
SCOPE
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.  
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.  
1.3 Materials covered in this standard are those advanced ceramics that meet criteria specified in flexure testing standards C1161 and C1211.  
1.4 The flexure test methods supporting this standard (C1161 and C1211) require test specimens that have a rectangular cross section, flat surfaces, and that are fabricated with specific dimensions and tolerances. Only grinding processes that are capable of generating the specified flat surfaces, that is, planar grinding modes, are suitable for evaluation by this method. Among the applicable machine types are horizontal and vertical spindle reciprocating surface grinders, horizontal and vertical spindle rotary surface grinders, double disk grinders, and tool-and-cutter grinders. Incremental cross-feed, plunge, and creep-feed grinding methods may be used.  
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.6 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.

SIGNIFICANCE AND USE
4.1 Creep tests measure the time-dependent deformation under force at a given temperature, and, by implication, the force-carrying capability of the material for limited deformations. Creep-rupture tests, properly interpreted, provide a measure of the force-carrying capability of the material as a function of time and temperature. The two tests complement each other in defining the force-carrying capability of a material for a given period of time. In selecting materials and designing parts for service at elevated temperatures, the type of test data used will depend on the criteria for force-carrying capability that best defines the service usefulness of the material.  
4.2 This test method may be used for material development, quality assurance, characterization, and design data generation.  
4.3 High-strength, monolithic ceramic materials, generally characterized by small grain sizes (  
4.4 Data obtained for design and predictive purposes shall be obtained using any appropriate combination of test methods that provide the most relevant information for the applications being considered. It is noted here that ceramic materials tend to creep more rapidly in tension than in compression (1, 2, 3).4 This difference results in time-dependent changes in the stress distribution and the position of the neutral axis when tests are conducted in flexure. As a consequence, deconvolution of flexural creep data to obtain the constitutive equations needed for design cannot be achieved without some degree of uncertainty concerning the form of the creep equations, and the magnitude of the creep rate in tension vis-a-vis the creep rate in compression. Therefore, creep data for design and life prediction shall be obtained in both tension and compression, as well as the expected service stress state.
SCOPE
1.1 This test method covers the determination of tensile creep strain, creep strain rate, and creep time-to-failure for advanced monolithic ceramics at elevated temperatures, typically between 1073 and 2073 K. A variety of test specimen geometries are included. The creep strain at a fixed temperature is evaluated from direct measurements of the gage length extension over the time of the test. The minimum creep strain rate, which may be invariant with time, is evaluated as a function of temperature and applied stress. Creep time-to-failure is also included in this test method.  
1.2 This test method is for use with advanced ceramics that behave as macroscopically isotropic, homogeneous, continuous materials. While this test method is intended for use on monolithic ceramics, whisker- or particle-reinforced composite ceramics as well as low-volume-fraction discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Continuous fiber-reinforced ceramic composites (CFCCs) do not behave as macroscopically isotropic, homogeneous, continuous materials, and application of this test method to these materials is not recommended.  
1.3 The values in SI units are to be regarded as the standard (see IEEE/ASTM SI 10). The values given in parentheses are mathematical conversions to inch-pound units that are provided for information only and are not considered standard.  
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
5.1 Fracture toughness, KIc, is a measure of the resistance to crack extension in a brittle material. These test methods may be used for material development, material comparison, quality assessment, and characterization.  
5.2 The pb and the vb fracture toughness values provide information on the fracture resistance of advanced ceramics containing large sharp cracks, while the sc fracture toughness value provides this information for small cracks comparable in size to natural fracture sources. Cracks of different sizes may be used for the sc method. If the fracture toughness values vary as a function of the crack size it can be expected that KIsc will differ from KIpb and KIvb. Table 1 tabulates advantages, disadvantages, and applicability of each method.
SCOPE
1.1 These test methods cover the fracture toughness, KIc, determination of advanced ceramics at ambient temperature. The methods determine KIpb (precracked beam test specimen), KIsc (surface crack in flexure), and KIvb (chevron-notched beam test specimen). The fracture toughness values are determined using beam test specimens with a sharp crack. The crack is either a straight-through crack formed via bridge flexure (pb), or a semi-elliptical surface crack formed via Knoop indentation (sc), or it is formed and propagated in a chevron notch (vb), as shown in Fig. 1.  
Note 1: The figures on the right show the test specimen cross sections and crack types. Four-point loading may be used with all three methods. Three-point may be used with the pb and vb specimens.
Note 1: The terms bend(ing) and flexure are synonymous in these test methods.  
1.2 These test methods are applicable to materials with either flat or with rising R-curves. Differences in test procedure and analysis may cause the values from each test method to be different. For many materials, such as the silicon nitride Standard Reference Material 2100, the three methods give identical results at room temperature in ambient air.  
1.3 The fracture toughness values for a material can be functions of environment, test rate and temperature. These test methods give fracture toughness values for specific conditions of environment, test rate and temperature.  
1.4 These test methods are intended primarily for use with advanced ceramics that are macroscopically homogeneous and microstructurally dense. Certain whisker- or particle-reinforced ceramics may also meet the macroscopic behavior assumptions. Single crystals may also be tested.  
1.5 This standard begins with a main body that provides information on fracture toughness testing in general. It is followed by annexes and appendices with specific information for the particular test methods.
Main Body  
Section  
Scope  
1  
Referenced Documents  
2  
Terminology (including definitions, orientation and symbols)  
3  
Summary of Test Methods  
4  
Significance and Use  
5  
Interferences  
6  
Apparatus  
7  
Test Specimen Configurations, Dimensions and Preparations  
8  
General Procedures  
9  
Report (including reporting tables)  
10  
Precision and Bias  
11  
Keywords  
12  
Summary of Changes  
Annexes  
Test Fixture Geometries  
Annex A1  
Procedures and Special Requirements for Precracked Beam Method  
Annex A2  
Procedures and Special Requirements for Surface Crack in Flexure Method  
Annex A3  
Procedures and Special Requirements for Chevron Notch Flexure Method  
Annex A4  
Appendices  
Precrack Characterization, Surface Crack in Flexure Method  
Appendix X1  
Complications in Interpreting Surface Crack in Flexure Precracks  
Appendix X2  
Alternative Precracking Procedure, Surface Crack in Flexure Method  
Appendix X3  
Chamfer Correction Factors, Surface Crack in Flexure Method Only  
Appendix X4  
Crack Orientation  
Appendix X5  
1.6 Values expressed in these test methods are in accordance with the...

SIGNIFICANCE AND USE
5.1 This practice is suitable for monolithic and some composite ceramics, for example, particulate- and whisker-reinforced and continuous-grain-boundary phase ceramics. (Long- or continuous-fiber reinforced ceramics are excluded.) For some materials, the location and identification of fracture origins may not be possible due to the specific microstructure.  
5.2 This practice is principally oriented towards characterization of fracture origins in specimens loaded in so-called fast fracture testing, but the approach can be extended to include other modes of loading as well.  
5.3 The procedures described within are primarily applicable to mechanical test specimens, although the same procedures may be relevant to component fracture analyses as well. It is customary practice to test a number of specimens (constituting a sample) to permit statistical analysis of the variability of the material’s strength. It is usually not difficult to test the specimens in a manner that will facilitate subsequent fractographic analysis. This may not be the case with component fracture analyses. Component fracture analysis is sometimes aided by cutting test pieces from the component and fracturing the test pieces. Fracture markings and fracture origins from the latter may aid component interpretation.  
5.4 Optimum fractographic analysis requires examination of as many similar specimens or components as possible. This will enhance the chances of successful interpretations. Examination of only one or a few specimens can be misleading. Of course, in some instances the fractographer may have access to only one or a few fractured specimens or components.  
5.5 Successful and complete fractography also requires careful consideration of all ancillary information that may be available, such as microstructural characteristics, material fabrication, properties and service histories, component or specimen machining, or preparation techniques.  
5.6 Fractographic inspection and analysis can b...
SCOPE
1.1 The objective of this practice is to provide an efficient and consistent methodology to locate and characterize fracture origins in advanced ceramics. It is applicable to advanced ceramics that are brittle; that is, fracture that takes place with little or no preceding plastic deformation. In such materials, fracture commences from a single location which is termed the fracture origin. The fracture origin in brittle ceramics normally consists of some irregularity or singularity in the material which acts as a stress concentrator. In the parlance of the engineer or scientist, these irregularities are termed flaws or defects. The latter word should not be construed to mean that the material has been prepared improperly or is somehow faulty.  
1.2 Although this practice is primarily intended for laboratory test piece analysis, the general concepts and procedures may be applied to component fracture analyses as well. In many cases, component fracture analysis may be aided by cutting laboratory test pieces out of the component. Information gleaned from testing the laboratory pieces (for example, flaw types, general fracture features, fracture mirror constants) may then aid interpretation of component fractures. For more information on component fracture analysis, see Ref (1 and 2).2  
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization, and design data generation.  
4.2 Generally, resistance to compression is the measure of the greatest strength of a monolithic advanced ceramic. Ideally, ceramics should be compressively stressed in use, although engineering applications may frequently introduce tensile stresses in the component. Nonetheless, compressive behavior is an important aspect of mechanical properties and performance. Although tensile strength distributions of ceramics are probabilistic and can be described by a weakest link failure theory, such descriptions have been shown to be inapplicable to compressive strength distributions in at least one study (1).3 However, the need to test a statistically significant number of compressive test specimens is not obviated. Therefore, a sufficient number of test specimens at each testing condition is required for statistical analysis and design.  
4.3 Compression tests provide information on the strength and deformation of materials under uniaxial compressive stresses. Uniform stress states are required to effectively evaluate any nonlinear stress-strain behavior which may develop as the result of cumulative damage processes (for example, microcracking) which may be influenced by testing mode, testing rate, processing or compositional effects, microstructure, or environmental influences.  
4.4 The results of compression tests of test specimens fabricated to standardized dimensions from a particular material or selected portions of a part, or both, may not totally represent the strength and deformation properties in the entire, full-size product or its in-service behavior in different environments.  
4.5 For quality control purposes, results derived from standardized compressive test specimens may be considered indicative of the response of the material from which they were taken for given primary processing conditions and post-proce...
SCOPE
1.1 This test method covers the determination of compressive strength including stress-strain behavior, under monotonic uniaxial loading of advanced ceramics at ambient temperature. This test method is restricted to specific test specimen geometries. In addition, test specimen fabrication methods, testing modes (force or displacement), testing rates (force rate, stress rate, displacement rate, or strain rate), allowable bending, and data collection and reporting procedures are addressed. Compressive strength as used in this test method refers to the compressive strength obtained under monotonic uniaxial loading. Monotonic loading refers to a test conducted at a constant rate in a continuous fashion, with no reversals from test initiation to final fracture.  
1.2 This test method is intended primarily for use with advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method is intended for use on monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behavior and, application of this test method to these materials is not recommended.  
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization, and design data generation.  
4.2 High strength, monolithic advanced ceramic materials generally characterized by small grain sizes (  
4.3 Although the volume or surface area of material subjected to a uniform tensile stress for a single uniaxially-loaded tensile test may be several times that of a single flexure test specimen, the need to test a statistically significant number of tensile test specimens is not obviated. Therefore, because of the probabilistic strength distributions of brittle materials such as advanced ceramics, a sufficient number of test specimens at each testing condition is required for statistical analysis and eventual design, with guidelines for sufficient numbers provided in this test method. Note that size-scaling effects as discussed in Practice C1239 will affect the strength values. Therefore, strengths obtained using different recommended tensile test specimens with different volumes or surface areas of material in the gage sections will be different due to these size differences. Resulting strength values can be scaled to an effective volume or surface area of unity as discussed in Practice C1239.  
4.4 Tensile tests provide information on the strength and deformation of materials under uniaxial tensile stresses. Uniform stress states are required to effectively evaluate any non-linear stress-strain behavior which may develop as the result of testing mode, testing rate, processing or alloying effects, or environmental influences. These effects may be consequences of stress corrosion or subcritical (slow) crack growth which can be minimized by testing at appropriately rapid rates as outlined in this test method.  
4.5 The results of tensile tests of test specimens fabricated to standardized dimensions from a particular material or selected portions, or both, of a part may not totally represent the strength and deforma...
SCOPE
1.1 This test method covers the determination of tensile strength under uniaxial loading of monolithic advanced ceramics at ambient temperatures. This test method addresses, but is not restricted to, various suggested test specimen geometries as listed in the appendix. In addition, test specimen fabrication methods, testing modes (force, displacement, or strain control), testing rates (force rate, stress rate, displacement rate, or strain rate), allowable bending, and data collection and reporting procedures are addressed. Note that tensile strength as used in this test method refers to the tensile strength obtained under uniaxial loading.  
1.2 This test method applies primarily to advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method applies primarily to monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behavior and application of this practice to these materials is not recommended.  
1.3 Values expressed in this test method are in accordance with the International System of Units (SI) and SI10-02 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 and health practices and determine the applicability of regulatory limitations prior to use. Specific precautionary statements are given in Section 7.

SIGNIFICANCE AND USE
4.1 This practice may be used for material development, material comparison, quality assurance, characterization, reliability assessment, and design data generation.  
4.2 High-strength, monolithic advanced ceramic materials are generally characterized by small grain sizes (  
4.3 Cyclic fatigue by its nature is a probabilistic phenomenon as discussed in STP 91A and STP 588.(1,2)4 In addition, the strengths of advanced ceramics are probabilistic in nature. Therefore, a sufficient number of test specimens at each testing condition is required for statistical analysis and design, with guidelines for sufficient numbers provided in STP 91A, (1) STP 588, (2) and Practice E739. The many different tensile specimen geometries available for cyclic fatigue testing may result in variations in the measured cyclic fatigue behavior of a particular material due to differences in the volume or surface area of material in the gage section of the test specimens.  
4.4 Tensile cyclic fatigue tests provide information on the material response under fluctuating uniaxial tensile stresses. Uniform stress states are required to effectively evaluate any non-linear stress-strain behavior which may develop as the result of cumulative damage processes (for example, microcracking, cyclic fatigue crack growth, etc.).  
4.5 Cumulative damage processes due to cyclic fatigue may be influenced by testing mode, testing rate (related to frequency), differences between maximum and minimum force (R or Α), effects of processing or combinations of constituent materials, or environmental influences, or both. Other factors that influence cyclic fatigue behaviour are: void or porosity content, methods of test specimen preparation or fabrication,test specimen conditioning, test environment, force or strain limits during cycling, wave shapes (that is, sinusoidal, trapezoidal, etc.), and failure mode. Some of these effects may be consequences of stress corrosion or sub critical (slow) crack growth which can...
SCOPE
1.1 This practice covers the determination of constant-amplitude, axial tension-tension cyclic fatigue behavior and performance of advanced ceramics at ambient temperatures to establish “baseline” cyclic fatigue performance. This practice builds on experience and existing standards in tensile testing advanced ceramics at ambient temperatures and addresses various suggested test specimen geometries, test specimen fabrication methods, testing modes (force, displacement, or strain control), testing rates and frequencies, allowable bending, and procedures for data collection and reporting. This practice does not apply to axial cyclic fatigue tests of components or parts (that is, machine elements with non uniform or multiaxial stress states).  
1.2 This practice applies primarily to advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behaviour. While this practice applies primarily to monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fibre-reinforced composite ceramics may also meet these macroscopic behaviour assumptions. Generally, continuous fibre-reinforced ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behaviour and application of this practice to these materials is not recommended.  
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 and health practices and determine the applicability of regulatory limitations prior to use. Refer to Section 7 for specific precautions.

SIGNIFICANCE AND USE
5.1 Fracture toughness, KIc, is a measure of the resistance to crack extension in a brittle material. These test methods may be used for material development, material comparison, quality assessment, and characterization.  
5.2 The pb and the vb fracture toughness values provide information on the fracture resistance of advanced ceramics containing large sharp cracks, while the sc fracture toughness value provides this information for small cracks comparable in size to natural fracture sources. Cracks of different sizes may be used for the sc method. If the fracture toughness values vary as a function of the crack size it can be expected that KIsc will differ from KIpb and KIvb. Table 1 tabulates advantages, disadvantages, and applicability of each method.
SCOPE
1.1 These test methods cover the fracture toughness, KIc, determination of advanced ceramics at ambient temperature. The methods determine KIpb (precracked beam test specimen), KIsc (surface crack in flexure), and KIvb (chevron-notched beam test specimen). The fracture toughness values are determined using beam test specimens with a sharp crack. The crack is either a straight-through crack formed via bridge flexure (pb), or a semi-elliptical surface crack formed via Knoop indentation (sc), or it is formed and propagated in a chevron notch (vb), as shown in Fig. 1.  
Note 1: The figures on the right show the test specimen cross sections and crack types. Four-point loading may be used with all three methods. Three-point may be used with the pb and vb specimens.
Note 1: The terms bend(ing) and flexure are synonymous in these test methods.  
1.2 These test methods are applicable to materials with either flat or with rising R-curves. Differences in test procedure and analysis may cause the values from each test method to be different. For many materials, such as the silicon nitride Standard Reference Material 2100, the three methods give identical results at room temperature in ambient air.  
1.3 The fracture toughness values for a material can be functions of environment, test rate and temperature. These test methods give fracture toughness values for specific conditions of environment, test rate and temperature.  
1.4 These test methods are intended primarily for use with advanced ceramics that are macroscopically homogeneous and microstructurally dense. Certain whisker- or particle-reinforced ceramics may also meet the macroscopic behavior assumptions. Single crystals may also be tested.  
1.5 This standard begins with a main body that provides information on fracture toughness testing in general. It is followed by annexes and appendices with specific information for the particular test methods.
Main Body  
Section  
Scope  
1  
Referenced Documents  
2  
Terminology (including definitions, orientation and symbols)  
3  
Summary of Test Methods  
4  
Significance and Use  
5  
Interferences  
6  
Apparatus  
7  
Test Specimen Configurations, Dimensions and Preparations  
8  
General Procedures  
9  
Report (including reporting tables)  
10  
Precision and Bias  
11  
Keywords  
12  
Summary of Changes  
Annexes  
Test Fixture Geometries  
Annex A1  
Procedures and Special Requirements for Precracked Beam Method  
Annex A2  
Procedures and Special Requirements for Surface Crack in Flexure Method  
Annex A3  
Procedures and Special Requirements for Chevron Notch Flexure Method  
Annex A4  
Appendices  
Precrack Characterization, Surface Crack in Flexure Method  
Appendix X1  
Complications in Interpreting Surface Crack in Flexure Precracks  
Appendix X2  
Alternative Precracking Procedure, Surface Crack in Flexure Method  
Appendix X3  
Chamfer Correction Factors, Surface Crack in Flexure Method Only  
Appendix X4  
Crack Orientation  
Appendix X5  
1.6 Values expressed in these test methods are in accordance with the...

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization and design code or model verification.  
4.2 Engineering applications of ceramics frequently involve biaxial tensile stresses. Generally, the resistance to equibiaxial flexure is the measure of the least flexural strength of a monolithic advanced ceramic. The equibiaxial flexural strength distributions of ceramics are probabilistic and can be described by a weakest link failure theory, (1, 2)4. Therefore, a sufficient number of test specimens at each testing condition is required for statistical estimation or' the equibiaxial strength.  
4.3 Equibiaxial strength tests provide information on the strength and deformation of materials under multiple tensile stresses. Multiaxial stress states are required to effectively evaluate failure theories applicable to component design, and to efficiently sample surfaces that may exhibit anisotropic flaw distributions. Equibiaxial tests also minimize the effects of test specimen edge preparation as compared to uniaxial tests because the generated stresses are lowest at the test specimen edges.  
4.4 The test results of equibiaxial test specimens fabricated to standardized dimensions from a particular material and/or selected portions of a component may not totally represent the strength properties in the entire, full-size component or its in-service behavior in different environments.  
4.5 For quality control purposes, results derived from standardized equibiaxial test specimens may be considered indicative of the response of the bulk material from which they were taken for any given primary processing conditions and post-processing heat treatments or exposures.
SCOPE
1.1 This test method covers the determination of the equibiaxial strength of advanced ceramics at ambient temperature via concentric ring configurations under monotonic uniaxial loading. In addition, test specimen fabrication methods, testing modes, testing rates, allowable deflection, and data collection and reporting procedures are addressed. Two types of test specimens are considered: machined test specimens and as-fired test specimens exhibiting a limited degree of warpage. Strength as used in this test method refers to the maximum strength obtained under monotonic application of load. Monotonic loading refers to a test conducted at a constant rate in a continuous fashion, with no reversals from test initiation to final fracture.  
1.2 This test method is intended primarily for use with advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method is intended for use on monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites do not macroscopically exhibit isotropic, homogeneous, continuous behavior, and the application of this test method to these materials is not recommended.  
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
5.1 This test method may be used for material development, characterization, design data generation, and quality control purposes.  
5.2 This test method is specifically appropriate for determining the modulus of advanced ceramics that are elastic, homogeneous, and isotropic (1).3  
5.3 This test method addresses the room temperature determination of dynamic moduli of elasticity of slender bars (rectangular cross-section) and rods (cylindrical). Flat plates and disks may also be measured similarly, but the required equations for determining the moduli are not addressed herein.  
5.4 This dynamic test method has several advantages and differences from static loading techniques and from resonant techniques requiring continuous excitation.  
5.4.1 The test method is nondestructive in nature and can be used for specimens prepared for other tests. The specimens are subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve, with the minimum possibility of fracture.  
5.4.2 The impulse excitation test uses an impact tool and simple supports for the test specimen. There is no requirement for complex support systems that require elaborate setup or alignment.  
5.5 This technique can be used to measure resonant frequencies alone for the purposes of quality control and acceptance of test specimens of both regular and complex shapes. A range of acceptable resonant frequencies is determined for a specimen with a particular geometry and mass. Deviations in specimen dimensions or mass and internal flaws (cracks, delaminations, inhomogeneities, porosity, etc) will change the resonant frequency for that specimen. Any specimen with a resonant frequency falling outside the prescribed frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits of the selected frequency range are known to include the resonant frequency that the specimen must possess if its geometry and mass and int...
SCOPE
1.1 This test method covers determination of the dynamic elastic properties of advanced ceramics at ambient temperatures. Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the test specimen. The dynamic elastic properties of a material can therefore be computed if the geometry, mass, and mechanical resonant frequencies of a suitable (rectangular, cylindrical, or disc geometry) test specimen of that material can be measured. Dynamic Young’s modulus is determined using the resonant frequency in the flexural mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young’s modulus and dynamic shear modulus are used to compute Poisson’s ratio.  
1.2 This test method measures the fundamental resonant frequency of test specimens of suitable geometry by exciting them mechanically by a singular elastic strike with an impulse tool. Specimen supports, impulse locations, and signal pick-up points are selected to induce and measure specific modes of the transient vibrations. A transducer (for example, contact accelerometer or non-contacting microphone) senses the resulting mechanical vibrations of the specimen and transforms them into electric signals. (See Fig. 1.) The transient signals are analyzed, and the fundamental resonant frequency is isolated and measured by the signal analyzer, which provides a numerical reading that is (or is proportional to) either the frequency or the period of the specimen vibration. The appropriate fundamental resonant frequencies, dimensions, and mass of the specimen are used to calculate dynamic Young’s modulus, dynamic shear modulus, and Poisson’s ratio.  
1.3 Although not specifically described herein, this test method can also be performed at cryogenic and high temperatures with suitable equipment modifications and appropriate modificat...

SIGNIFICANCE AND USE
5.1 For advanced ceramics, Vickers indenters are used to create indentations whose surface-projected diagonals are measured with optical microscopes. The Vickers indenter creates a square impression from which two surface-projected diagonal lengths are measured. Vickers hardness is calculated from the ratio of the applied force to the area of contact of the four faces of the undeformed indenter. (In contrast, Knoop indenters are also used to measure hardness, but Knoop hardness is calculated from the ratio of the applied force to the projected area on the specimen surface.)  
5.2 Vickers indentation hardness is one of many properties that is used to characterize advanced ceramics. Attempts have been made to relate Vickers indentation hardness to other hardness scales, but no generally accepted methods are available. Such conversions are limited in scope and should be used with caution, except for special cases where a reliable basis for the conversion has been obtained by comparison tests.  
5.3 Vickers indentation diagonal lengths are approximately 2.8 times shorter than the long diagonal of Knoop indentations, and the indentation depth is approximately 1.5 times deeper than Knoop indentations made at the same force.  
5.4 Vickers indentations are influenced less by specimen surface flatness, parallelism, and surface finish than Knoop indentations, but these parameters must be considered nonetheless.  
5.5 Vickers indentations are much more likely to cause cracks in advanced ceramics than Knoop indentations. The cracks may influence the measured hardness by fundamentally altering the deformation processes that contribute to the formation of an impression, and they may impair or preclude measurement of the diagonal lengths due to excessive damage at the indentation tips or sides.  
5.6 A full hardness characterization includes measurements over a broad range of indentation forces. Vickers hardness of ceramics usually decreases with increasing indentation size o...
SCOPE
1.1 This test method covers the determination of the Vickers indentation hardness of advanced ceramics. In this test, a pointed, square base, pyramidal diamond indenter of prescribed shape is pressed into the surface of a ceramic with a predetermined force to produce a relatively small, permanent indentation. The surface projection of the two diagonals of the permanent indentation is measured using a light microscope. The average diagonal size and the applied force are used to calculate the Vickers hardness, which represents the material’s resistance to penetration by the Vickers indenter. Hardness is computed as the ratio of the force to the contact surface area.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 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 Vickers hardness be reported either in units of GPa, or a dimensionless Vickers hardness number that has implied units of kgf/mm2.  
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
5.1 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.  
5.2 Two- and three-parameter formulations exist for the Weibull distribution. This standard is restricted to the two-parameter formulation.  
5.3 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.  
5.4 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.  
5.5 The scaling of strength with size in accordance with the Weibull model is based on several key assumptions (5). It is assumed that the...
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.Geometries and Stress Distributions  
Annex A3  
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.

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization, and design data generation.  
4.2 Generally, resistance to compression is the measure of the greatest strength of a monolithic advanced ceramic. Ideally, ceramics should be compressively stressed in use, although engineering applications may frequently introduce tensile stresses in the component. Nonetheless, compressive behavior is an important aspect of mechanical properties and performance. Although tensile strength distributions of ceramics are probabilistic and can be described by a weakest link failure theory, such descriptions have been shown to be inapplicable to compressive strength distributions in at least one study (1).3 However, the need to test a statistically significant number of compressive test specimens is not obviated. Therefore, a sufficient number of test specimens at each testing condition is required for statistical analysis and design.  
4.3 Compression tests provide information on the strength and deformation of materials under uniaxial compressive stresses. Uniform stress states are required to effectively evaluate any nonlinear stress-strain behavior which may develop as the result of cumulative damage processes (for example, microcracking) which may be influenced by testing mode, testing rate, processing or compositional effects, microstructure, or environmental influences.  
4.4 The results of compression tests of test specimens fabricated to standardized dimensions from a particular material or selected portions of a part, or both, may not totally represent the strength and deformation properties in the entire, full-size product or its in-service behavior in different environments.  
4.5 For quality control purposes, results derived from standardized compressive test specimens may be considered indicative of the response of the material from which they were taken for given primary processing conditions and post-proce...
SCOPE
1.1 This test method covers the determination of compressive strength including stress-strain behavior, under monotonic uniaxial loading of advanced ceramics at ambient temperature. This test method is restricted to specific test specimen geometries. In addition, test specimen fabrication methods, testing modes (load or displacement), testing rates (load rate, stress rate, displacement rate, or strain rate), allowable bending, and data collection and reporting procedures are addressed. Compressive strength as used in this test method refers to the compressive strength obtained under monotonic uniaxial loading. Monotonic loading refers to a test conducted at a constant rate in a continuous fashion, with no reversals from test initiation to final fracture.  
1.2 This test method is intended primarily for use with advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method is intended for use on monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites (CFCCs) do not macroscopically exhibit isotropic, homogeneous, continuous behavior and, application of this test method to these materials is not recommended.  
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
5.1 This test method may be used for material development, characterization, design data generation, and quality control purposes.  
5.2 This test method is specifically appropriate for determining the modulus of advanced ceramics that are elastic, homogeneous, and isotropic (1).3  
5.3 This test method addresses the room temperature determination of dynamic moduli of elasticity of slender bars (rectangular cross-section) and rods (cylindrical). Flat plates and disks may also be measured similarly, but the required equations for determining the moduli are not addressed herein.  
5.4 This dynamic test method has several advantages and differences from static loading techniques and from resonant techniques requiring continuous excitation.  
5.4.1 The test method is nondestructive in nature and can be used for specimens prepared for other tests. The specimens are subjected to minute strains; hence, the moduli are measured at or near the origin of the stress-strain curve, with the minimum possibility of fracture.  
5.4.2 The impulse excitation test uses an impact tool and simple supports for the test specimen. There is no requirement for complex support systems that require elaborate setup or alignment.  
5.5 This technique can be used to measure resonant frequencies alone for the purposes of quality control and acceptance of test specimens of both regular and complex shapes. A range of acceptable resonant frequencies is determined for a specimen with a particular geometry and mass. Deviations in specimen dimensions or mass and internal flaws (cracks, delaminations, inhomogeneities, porosity, etc) will change the resonant frequency for that specimen. Any specimen with a resonant frequency falling outside the prescribed frequency range is rejected. The actual modulus of each specimen need not be determined as long as the limits of the selected frequency range are known to include the resonant frequency that the specimen must possess if its geometry and mass and int...
SCOPE
1.1 This test method covers determination of the dynamic elastic properties of advanced ceramics at ambient temperatures. Specimens of these materials possess specific mechanical resonant frequencies that are determined by the elastic modulus, mass, and geometry of the test specimen. The dynamic elastic properties of a material can therefore be computed if the geometry, mass, and mechanical resonant frequencies of a suitable (rectangular, cylindrical, or disc geometry) test specimen of that material can be measured. Dynamic Young's modulus is determined using the resonant frequency in the flexural mode of vibration. The dynamic shear modulus, or modulus of rigidity, is found using torsional resonant vibrations. Dynamic Young's modulus and dynamic shear modulus are used to compute Poisson's ratio.  
1.2 This test method measures the fundamental resonant frequency of test specimens of suitable geometry by exciting them mechanically by a singular elastic strike with an impulse tool. Specimen supports, impulse locations, and signal pick-up points are selected to induce and measure specific modes of the transient vibrations. A transducer (for example, contact accelerometer or non-contacting microphone) senses the resulting mechanical vibrations of the specimen and transforms them into electric signals. (See Fig. 1.) The transient signals are analyzed, and the fundamental resonant frequency is isolated and measured by the signal analyzer, which provides a numerical reading that is (or is proportional to) either the frequency or the period of the specimen vibration. The appropriate fundamental resonant frequencies, dimensions, and mass of the specimen are used to calculate dynamic Young's modulus, dynamic shear modulus, and Poisson's ratio.
1.3 Although not specifically described herein, this test method can also be performed at cryogenic and high temperatures with suitable equipment modifications and appropriate modificatio...

SIGNIFICANCE AND USE
5.1 Advanced ceramics usually display a linear stress-strain behavior to failure. Lack of ductility combined with flaws that have various sizes and orientations leads to scatter in failure strength. Strength is not a deterministic property but instead reflects an intrinsic fracture toughness and a distribution (size and orientation) of flaws present in the material. This practice is applicable to brittle monolithic ceramics that fail as a result of catastrophic propagation of flaws present in the material. This practice is also applicable to composite ceramics that do not exhibit any appreciable bilinear or nonlinear deformation behavior. In addition, the composite must contain a sufficient quantity of uniformly distributed reinforcements such that the material is effectively homogeneous. Whisker-toughened ceramic composites may be representative of this type of material.  
5.2 Two- and three-parameter formulations exist for the Weibull distribution. This practice is restricted to the two-parameter formulation. An objective of this practice is to obtain point estimates of the unknown parameters by using well-defined functions that incorporate the failure data. These functions are referred to as estimators. It is desirable that an estimator be consistent and efficient. In addition, the estimator should produce unique, unbiased estimates of the distribution parameters (6). Different types of estimators exist, including moment estimators, least-squares estimators, and maximum likelihood estimators. This practice details the use of maximum likelihood estimators due to the efficiency and the ease of application when censored failure populations are encountered.  
5.3 Tensile and flexural test specimens are the most commonly used test configurations for advanced ceramics. The observed strength values are dependent on test specimen size and geometry. Parameter estimates can be computed for a given test specimen geometry ( m^, σ^θ), but it is suggested that the parameter...
SCOPE
1.1 This practice covers the evaluation and reporting of uniaxial strength data and the estimation of Weibull probability distribution parameters for advanced ceramics that fail in a brittle fashion (see Fig. 1). The estimated Weibull distribution parameters are used for statistical comparison of the relative quality of two or more test data sets and for the prediction of the probability of failure (or, alternatively, the fracture strength) for a structure of interest. In addition, this practice encourages the integration of mechanical property data and fractographic analysis.
1.2 The failure strength of advanced ceramics is treated as a continuous random variable determined by the flaw population. Typically, a number of test specimens with well-defined geometry are failed under isothermal, well-defined displacement and/or force-application conditions. The force at which each test specimen fails is recorded. The resulting failure stress data are used to obtain Weibull parameter estimates associated with the underlying flaw population distribution.  
1.3 This practice is restricted to the assumption that the distribution underlying the failure strengths is the two-parameter Weibull distribution with size scaling. Furthermore, this practice is restricted to test specimens (tensile, flexural, pressurized ring, etc.) that are primarily subjected to uniaxial stress states. The practice also assumes that the flaw population is stable with time and that no slow crack growth is occurring.  
1.4 The practice outlines methods to correct for bias errors in the estimated Weibull parameters and to calculate confidence bounds on those estimates from data sets where all failures originate from a single flaw population (that is, a single failure mode). In samples where failures originate from multiple independent flaw populations (for example, competing failure modes), the methods outlined in Section 9 for bias correction and confid...

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 strength is 50 MPa (~7 ksi) or greater. The test method may also be used with glass test specimens, although Test Methods C158 is specifically designed to be used for glasses. This test method may be used with machined, drawn, extruded, and as-fired round specimens. This test method may be used with specimens that have elliptical cross section geometries.  
4.2 The flexure strength 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 one fiftieth of the rod diameter. The homogeneity and isotropy assumptions in the standard rule out the use of this test for continuous fiber-reinforced ceramics.  
4.3 Flexural strength of a group of test specimens is influenced by several parameters associated with the test procedure. Such factors include the loading rate, test environment, specimen size, specimen preparation, and test fixtures (1-3).3 This method includes specific specimen-fixture size combinations, but permits alternative configurations within specified limits. These combinations were chosen to be practical, to minimize experimental error, and permit easy comparison of cylindrical rod strengths with data for other configurations. Equations for the Weibull effective volume and Weibull effective surface are included.  
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 in the material. Flaws in rods may be intrinsically volume-distributed throughout the bulk. Some of these flaws by chance may be located at or near the outer surface. Flaws may alternatively be intrinsically surface-distrib...
SCOPE
1.1 This test method is for the determination of flexural strength of rod shape specimens of advanced ceramic materials at ambient temperature. In many instances it is preferable to test round specimens rather than rectangular bend specimens, especially if the material is fabricated in rod form. This method permits testing of machined, drawn, or as-fired rod shaped specimens. It allows some latitude in the rod sizes and cross section shape uniformity. Rod diameters between 1.5 and 8 mm and lengths from 25 to 85 mm are recommended, but other sizes are permitted. Four-point-1/4 point as shown in Fig. 1 is the preferred testing configuration. Three-point loading is permitted. This method describes the apparatus, specimen requirements, test procedure, calculations, and reporting requirements. The 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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
4.1 For many structural ceramic components in service, their use is often limited by lifetimes that are controlled by a process of slow crack growth. This test method provides the empirical parameters for appraising the relative slow crack growth susceptibility of ceramic materials under specified environments at elevated temperatures. This test method is similar to Test Method C1368 with the exception that provisions for testing at elevated temperatures are given. Furthermore, this test method may establish the influences of processing variables and composition on slow crack growth as well as on strength behavior of newly developed or existing materials, thus allowing tailoring and optimizing material processing for further modification. In summary, this test method may be used for material development, quality control, characterization, and limited design data generation purposes.Note 3—Data generated by this test method do not necessarily correspond to crack velocities that may be encountered in service conditions. The use of data generated by this test method for design purposes may entail considerable extrapolation and loss of accuracy.  
4.2 In this test method, the flexural stress computation is based on simple beam theory, with the 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 one fiftieth (1/50) of the beam thickness.  
4.3 In this test method, the test specimen sizes and test fixtures were chosen in accordance with Test Method C1211, which provides a balance between practical configurations and resulting errors, as discussed in Refs (5, 6). Only the four-point test configuration is used in this test method.  
4.4 In this test method, the slow crack growth parameters (n and D) are determined based on the mathematical relationship between flexural strength and applied stress rate, log σf  =...
SCOPE
1.1 This test method covers the determination of slow crack growth (SCG) parameters of advanced ceramics by using constant stress-rate flexural testing in which flexural strength is determined as a function of applied stress rate in a given environment at elevated temperatures. The strength degradation exhibited with decreasing applied stress rate in a specified environment is the basis of this test method which enables the evaluation of slow crack growth parameters of a material.Note 1—This test method is frequently referred to as “dynamic fatigue” testing (Refs (1-3))2 in which the term “fatigue” is used interchangeably with the term “slow crack growth.” To avoid possible confusion with the “fatigue” phenomenon of a material which occurs exclusively under cyclic loading, as defined in Terminology E1823, this test method uses the term “constant stress-rate testing” rather than “dynamic fatigue” testing.Note 2—In glass and ceramics technology, static tests of considerable duration are called “static fatigue” tests, a type of test designated as stress-rupture (Terminology E1823).  
1.2 This test method is intended primarily to be used for negligible creep of test specimens, with specific limits on creep imposed in this test method.  
1.3 This test method applies primarily to advanced ceramics that are macroscopically homogeneous and isotropic. This test method may also be applied to certain whisker- or particle-reinforced ceramics that exhibit macroscopically homogeneous behavior.  
1.4 This test method is intended for use with various test environments such as air, vacuum, inert, and any other gaseous environments.  
1.5 Values expressed in this standard test are in accordance with the International System of Units (SI) and 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 ap...

SIGNIFICANCE AND USE
4.1 This test method may be used for material development, material comparison, quality assurance, characterization and design code or model verification.  
4.2 Engineering applications of ceramics frequently involve biaxial tensile stresses. Generally, the resistance to equibiaxial flexure is the measure of the least flexural strength of a monolithic advanced ceramic. The equibiaxial flexural strength distributions of ceramics are probabilistic and can be described by a weakest link failure theory, (1, 2)4. Therefore, a sufficient number of test specimens at each testing condition is required for statistical estimation or' the equibiaxial strength.  
4.3 Equibiaxial strength tests provide information on the strength and deformation of materials under multiple tensile stresses. Multiaxial stress states are required to effectively evaluate failure theories applicable to component design, and to efficiently sample surfaces that may exhibit anisotropic flaw distributions. Equibiaxial tests also minimize the effects of test specimen edge preparation as compared to uniaxial tests because the generated stresses are lowest at the test specimen edges.  
4.4 The test results of equibiaxial test specimens fabricated to standardized dimensions from a particular material and/or selected portions of a component may not totally represent the strength properties in the entire, full-size component or its in-service behavior in different environments.  
4.5 For quality control purposes, results derived from standardized equibiaxial test specimens may be considered indicative of the response of the bulk material from which they were taken for any given primary processing conditions and post-processing heat treatments or exposures.
SCOPE
1.1 This test method covers the determination of the equibiaxial strength of advanced ceramics at ambient temperature via concentric ring configurations under monotonic uniaxial loading. In addition, test specimen fabrication methods, testing modes, testing rates, allowable deflection, and data collection and reporting procedures are addressed. Two types of test specimens are considered: machined test specimens and as-fired test specimens exhibiting a limited degree of warpage. Strength as used in this test method refers to the maximum strength obtained under monotonic application of load. Monotonic loading refers to a test conducted at a constant rate in a continuous fashion, with no reversals from test initiation to final fracture.  
1.2 This test method is intended primarily for use with advanced ceramics that macroscopically exhibit isotropic, homogeneous, continuous behavior. While this test method is intended for use on monolithic advanced ceramics, certain whisker- or particle-reinforced composite ceramics as well as certain discontinuous fiber-reinforced composite ceramics may also meet these macroscopic behavior assumptions. Generally, continuous fiber ceramic composites do not macroscopically exhibit isotropic, homogeneous, continuous behavior, and the application of this test method to these materials is not recommended.  
1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
4.1 For many structural ceramic components in service, their use is often limited by lifetimes that are controlled by a process of slow crack growth. This test method provides the empirical parameters for appraising the relative slow crack growth susceptibility of ceramic materials under specified environments at elevated temperatures. This test method is similar to Test Method C1368 with the exception that provisions for testing at elevated temperatures are given. Furthermore, this test method may establish the influences of processing variables and composition on slow crack growth as well as on strength behavior of newly developed or existing materials, thus allowing tailoring and optimizing material processing for further modification. In summary, this test method may be used for material development, quality control, characterization, and limited design data generation purposes.Note 3—Data generated by this test method do not necessarily correspond to crack velocities that may be encountered in service conditions. The use of data generated by this test method for design purposes may entail considerable extrapolation and loss of accuracy.  
4.2 In this test method, the flexural stress computation is based on simple beam theory, with the 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 one fiftieth (1/50) of the beam thickness.  
4.3 In this test method, the test specimen sizes and test fixtures were chosen in accordance with Test Method C1211, which provides a balance between practical configurations and resulting errors, as discussed in Refs (7, 8). Only the four-point test configuration is used in this test method.  
4.4 In this test method, the slow crack growth parameters (n and D) are determined based on the mathematical relationship between flexural strength and applied stress rate, log σf  =...
SCOPE
1.1 This test method covers the determination of slow crack growth (SCG) parameters of advanced ceramics by using constant stress-rate flexural testing in which flexural strength is determined as a function of applied stress rate in a given environment at elevated temperatures. The strength degradation exhibited with decreasing applied stress rate in a specified environment is the basis of this test method which enables the evaluation of slow crack growth parameters of a material.Note 1—This test method is frequently referred to as “dynamic fatigue” testing (Refs (3-5))2 in which the term “fatigue” is used interchangeably with the term “slow crack growth.” To avoid possible confusion with the “fatigue” phenomenon of a material which occurs exclusively under cyclic loading, as defined in Terminology E1823, this test method uses the term “constant stress-rate testing” rather than “dynamic fatigue” testing.Note 2—In glass and ceramics technology, static tests of considerable duration are called “static fatigue” tests, a type of test designated as stress-rupture (Terminology E1823).  
1.2 This test method is intended primarily to be used for negligible creep of test specimens, with specific limits on creep imposed in this test method.  
1.3 This test method applies primarily to advanced ceramics that are macroscopically homogeneous and isotropic. This test method may also be applied to certain whisker- or particle-reinforced ceramics that exhibit macroscopically homogeneous behavior.  
1.4 This test method is intended for use with various test environments such as air, vacuum, inert, and any other gaseous environments.  
1.5 Values expressed in this standard test are in accordance with the International System of Units (SI) and 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 ap...

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 ...
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 and health practices and determine the applicability of regulatory limitations prior to use.

SIGNIFICANCE AND USE
5.1 For advanced ceramics, Knoop indenters are used to create indentations. The surface projection of the long diagonal is measured with optical microscopes.  
5.2 The Knoop indentation hardness is one of many properties that is used to characterize advanced ceramics. Attempts have been made to relate Knoop indentation hardness to other hardness scales, but no generally accepted methods are available. Such conversions are limited in scope and should be used with caution, except for special cases where a reliable basis for the conversion has been obtained by comparison tests.  
5.3 For advanced ceramics, the Knoop indentation is often preferred to the Vickers indentation since the Knoop long diagonal length is 2.8 times longer than the Vickers diagonal for the same force, and cracking is much less of a problem  (1).5 On the other hand, the long slender tip of the Knoop indentation is more difficult to precisely discern, especially in materials with low contrast. The indentation forces chosen in this test method are designed to produce indentations as large as may be possible with conventional microhardness equipment, yet not so large as to cause cracking.  
5.4 The Knoop indentation is shallower than Vickers indentations made at the same force. Knoop indents may be useful in evaluating coating hardnesses.  
5.5 Knoop hardness is calculated from the ratio of the applied force divided by the projected indentation area on the specimen surface. It is assumed that the elastic springback of the narrow diagonal is negligible. (Vickers indenters are also used to measure hardness, but Vickers hardness is calculated from the ratio of applied force to the area of contact of the four faces of the undeformed indenter.)  
5.6 A full hardness characterization includes measurements over a broad range of indentation forces. Knoop hardness of ceramics usually decreases with increasing indentation size or indentation force such as that shown in Fig. 1.
SCOPE
1.1 This test method covers the determination of the Knoop indentation hardness of advanced ceramics. In this test, a pointed, rhombic base, pyramidal diamond indenter of prescribed shape is pressed into the surface of a ceramic with a predetermined force to produce a relatively small, permanent indentation. The surface projection of the long diagonal of the permanent indentation is measured using a light microscope. The length of the long diagonal and the applied force are used to calculate the Knoop hardness which represents the material’s resistance to penetration by the Knoop indenter.  
1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.  
1.3 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.  
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 and health practices and determine the applicability of regulatory limitations prior to use.