4.1 This test method may be used for material development, material comparison, quality assurance, characterization, reliability assessment, and design data generation.4.2 Continuous fiber-reinforced ceramic matrix composites generally characterized by crystalline matrices and ceramic fiber reinforcements are candidate materials for structural applications requiring high degrees of wear and corrosion resistance, and elevated-temperature inherent damage tolerance (that is, toughness). In addition, continuous fiber-reinforced glass (amorphous) matrix composites are candidate materials for similar but possibly less demanding applications. Although flexural test methods are commonly used to evaluate strengths of monolithic advanced ceramics, the nonuniform stress distribution of the flexure test specimen, in addition to dissimilar mechanical behavior in tension and compression for CFCCs, leads to ambiguity of interpretation of strength results obtained from flexure tests for CFCCs. Uniaxially loaded tensile strength tests provide information on mechanical behavior and strength for a uniformly stressed material.4.3 Unlike monolithic advanced ceramics that fracture catastrophically from a single dominant flaw, CFCCs generally experience “graceful” (that is, non-catastrophic, ductile-like stress-strain behavior) fracture from a cumulative damage process. Therefore, the volume of material subjected to a uniform tensile stress for a single uniaxially loaded tensile test may not be as significant a factor in determining the ultimate strengths of CFCCs. However, the need to test a statistically significant number of tensile test specimens is not obviated. Therefore, because of the probabilistic nature of the strengths of the brittle fibers and matrices of CFCCs, a sufficient number of test specimens at each testing condition is required for statistical analysis and design. Studies to determine the influence of test specimen volume or surface area on strength distributions for CFCCs have not been completed. It should be noted that tensile strengths obtained using different recommended tensile test specimen geometries with different volumes of material in the gage sections may be different due to these volume differences.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 that may develop as the result of cumulative damage processes (for example, matrix cracking, matrix/fiber debonding, fiber fracture, delamination, and so forth) that may be influenced by testing mode, testing rate, effects of processing or combinations of constituent materials, environmental influences, or elevated temperatures. Some of these effects may be consequences of stress corrosion or subcritical (slow) crack growth that can be minimized by testing at sufficiently 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 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 or various elevated temperatures.4.6 For quality control purposes, results derived from standardized tensile test specimens may be considered indicative of the response of the material from which they were taken for the particular primary processing conditions and post-processing heat treatments.4.7 The tensile behavior and strength of a CFCC are dependent on its inherent resistance to fracture, the presence of flaws, or damage accumulation processes, or both. Analysis of fracture surfaces and fractography, though beyond the scope of this test method, is recommended.1.1 This test method covers the determination of tensile strength, including stress-strain behavior, under monotonic uniaxial loading of continuous fiber-reinforced advanced ceramics at elevated 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, temperature control, temperature gradients, and data collection and reporting procedures are addressed. Tensile strength as used in this test method refers to the tensile strength obtained under monotonic uniaxial loading, where monotonic refers to a continuous nonstop test rate with no reversals from test initiation to final fracture.1.2 This test method applies primarily to advanced ceramic matrix composites with continuous fiber reinforcement: unidirectional (1D), bidirectional (2D), and tridirectional (3D) or other multi-directional reinforcements. In addition, this test method may also be used with glass (amorphous) matrix composites with 1D, 2D, 3D, and other multi-directional continuous fiber reinforcements. This test method does not directly address discontinuous fiber-reinforced, whisker-reinforced, or particulate-reinforced ceramics, although the test methods detailed here may be equally applicable to these composites.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 by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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1.1 This specification covers the requirements for fabricated alumina parts suitable for electronic and electrical applications and ceramic-to-metal seals as used in electron devices. This specification specifies limits and methods of test for electrical, mechanical, thermal, and general properties of the bodies used for these fabricated parts, regardless of part geometry.1.2 The values stated in SI units are to be regarded as standard. The values given in parentheses after SI units are provided for information only and are not considered standard.1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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4.1 This practice may be used for material development, material comparison, quality assurance, characterization, reliability assessment, and design data generation.4.2 Continuous fiber-reinforced ceramic matrix composites are generally characterized by crystalline matrices and ceramic fiber reinforcements. These materials are candidate materials for structural applications requiring high degrees of wear and corrosion resistance, and high-temperature inherent damage tolerance (that is, toughness). In addition, continuous fiber-reinforced glass matrix composites are candidate materials for similar but possibly less demanding applications. Although flexural test methods are commonly used to evaluate the mechanical behavior of monolithic advanced ceramics, the nonuniform stress distribution in a flexural test specimen in addition to dissimilar mechanical behavior in tension and compression for CFCCs leads to ambiguity of interpretation of test results obtained in flexure for CFCCs. Uniaxially loaded tensile tests provide information on mechanical behavior for a uniformly stressed material.4.3 The cyclic fatigue behavior of CFCCs can have appreciable nonlinear effects (for example, sliding of fibers within the matrix) which may be related to the heat transfer of the specimen to the surroundings. Changes in test temperature, frequency, and heat removal can affect test results. It may be desirable to measure the effects of these variables to more closely simulate end-use conditions for some specific application.4.4 Cyclic fatigue by its nature is a probabilistic phenomenon as discussed in STP 91A (1) and STP 588 (2).4 In addition, the strengths of the brittle matrices and fibers of CFCCs 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. Studies to determine the influence of test specimen volume or surface area on cyclic fatigue strength distributions for CFCCs have not been completed. The many different tensile test 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 of material in the gage section of the test specimens.4.5 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, matrix microcracking, fiber/matrix debonding, delamination, cyclic fatigue crack growth, etc.)4.6 Cumulative damage 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, environmental influences (including test environment and pre-test conditioning), or combinations thereof. Some of these effects may be consequences of stress corrosion or subcritical (slow) crack growth which can be difficult to quantify. Other factors which may influence cyclic fatigue behavior are: matrix or fiber material, void or porosity content, methods of test specimen preparation or fabrication, volume percent of the reinforcement, orientation and stacking of the reinforcement, test specimen conditioning, test environment, force or strain limits during cycling, wave shapes (that is, sinusoidal, trapezoidal, etc.), and failure mode of the CFCC.4.7 The results of cyclic fatigue 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 cyclic fatigue behavior of the entire, full-size end product or its in-service behavior in different environments.4.8 However, for quality control purposes, results derived from standardized tensile test specimens may be considered indicative of the response of the material from which they were taken for given primary processing conditions and post-processing heat treatments.4.9 The cyclic fatigue behavior of a CFCC is dependent on its inherent resistance to fracture, the presence of flaws, or damage accumulation processes, or both. There can be significant damage in the CFCC test specimen without any visual evidence such as the occurrence of a macroscopic crack. This can result in a loss of stiffness and retained strength. Depending on the purpose for which the test is being conducted, rather than final fracture, a specific loss in stiffness or retained strength may constitute failure. In cases where fracture occurs, analysis of fracture surfaces and fractography, though beyond the scope of this practice, is recommended.1.1 This practice covers the determination of constant-amplitude, axial tension-tension cyclic fatigue behavior and performance of continuous fiber-reinforced advanced ceramic composites (CFCCs) at ambient temperatures. This practice builds on experience and existing standards in tensile testing CFCCs at ambient temperatures and addresses various suggested test specimen geometries, 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 ceramic matrix composites with continuous fiber reinforcement: uni-directional (1-D), bi-directional (2-D), and tri-directional (3-D) or other multi-directional reinforcements. In addition, this practice may also be used with glass (amorphous) matrix composites with 1-D, 2-D, 3-D, and other multi-directional continuous fiber reinforcements. This practice does not directly address discontinuous fiber-reinforced, whisker-reinforced or particulate-reinforced ceramics, although the methods detailed here may be equally applicable to these composites.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.

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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 (<50 μm) and bulk densities near the theoretical density. These materials are candidates for load-bearing structural applications requiring high degrees of wear and corrosion resistance, and high-temperature strength. Although flexural test methods are commonly used to evaluate strength of advanced ceramics, the nonuniform stress distribution in a flexure specimen limits the volume of material subjected to the maximum applied stress at fracture. Uniaxially loaded tensile strength tests may provide information on strength-limiting flaws from a greater volume of uniformly stressed material.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 be difficult to quantify. In addition, surface or near-surface flaws introduced by the test specimen fabrication process (machining) may or may not be quantifiable by conventional measurements of surface texture. Therefore, surface effects (for example, as reflected in cyclic fatigue reduction factors as classified by Marin (3)) must be inferred from the results of numerous cyclic fatigue tests performed with test specimens having identical fabrication histories.4.6 The results of cyclic fatigue tests of specimens fabricated to standardized dimensions from a particular material or selected portions of a part, or both, may not totally represent the cyclic fatigue behavior of the entire full-size end product or its in-service behavior in different environments.4.7 However, for quality control purposes, results derived from standardized tensile test specimens may be considered indicative of the response of the material from which they were taken for given primary processing conditions and post-processing heat treatments.4.8 The cyclic fatigue behavior of an advanced ceramic is dependent on its inherent resistance to fracture, the presence of flaws, or damage accumulation processes, or both. There can be significant damage in the test specimen without any visual evidence such as the occurrence of a macroscopic crack. This can result in a specific loss of stiffness and retained strength. Depending on the purpose for which the test is being conducted, rather than final fracture, a specific loss in stiffness or retained strength may constitute failure. In cases where fracture occurs, analysis of fracture surfaces and fractography, though beyond the scope of this practice, are recommended.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 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.

定价： 590元 / 折扣价： 502 元 加购物车

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 (<50 μm) and bulk densities near the theoretical density. These materials are candidates for load-bearing structural applications requiring high degrees of wear and corrosion resistance and elevated-temperature strength. Although flexural test methods are commonly used to evaluate strength of advanced ceramics, the nonuniform stress distribution of the flexure specimen limits the volume of material subjected to the maximum applied stress at fracture. Uniaxially loaded tensile strength tests provide information on strength-limiting flaws from a greater volume of uniformly stressed material.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 of the response of the material from which they were taken for particular primary processing conditions and post-processing heat treatments.4.7 The tensile strength of a ceramic material is dependent on both its inherent resistance to fracture and the presence of flaws. Analysis of fracture surfaces and fractography as described in Practice C1322 and MIL-HDBK-790, though beyond the scope of this test method, are recommended for all purposes, especially for design data.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 by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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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 experimental data to a mathematical relationship between strength and applied stress rate, log σf = 1/(n+1) log σ˙ + log D. The basic underlying assumption on the derivation of this relationship is that SCG is governed by an empirical power-law crack velocity, v = A[KI/KIC]n (see Appendix X1).NOTE 3: There are various other forms of crack velocity laws which are usually more complex or less convenient mathematically, or both, but may be physically more realistic (6). It is generally accepted that actual data cannot reliably distinguish between the various formulations. Therefore, the mathematical analysis in this test method does not cover such alternative crack velocity formulations.4.5 The mathematical relationship between strength and stress rate was derived based on the assumption that the slow crack growth parameter is at least n ≥ 5 (1, 7, 8). Therefore, if a material exhibits a very high susceptibility to SCG, that is, n < 5, special care should be taken when interpreting the results.4.6 The mathematical analysis of test results in accordance with the method in 4.4 assumes that the material displays no rising R-curve behavior. It should be noted that the existence of such behavior cannot be determined from this test method.4.7 Slow crack growth behavior of ceramic materials exposed to stress-corrosive gases or liquid environments can vary as a function of mechanical, material, and electrochemical variables. Therefore, it is essential that test results accurately reflect the effects of specific variables under study. Only then can data be compared from one investigation to another on a valid basis or serve as a valid basis for characterizing materials and assessing structural behavior.4.8 The strength of advanced ceramics is probabilistic in nature. Therefore, SCG that is determined from the strengths of a ceramic material is also a probabilistic phenomenon. Hence, a proper range and number of applied stress rates in conjunction with an appropriate number of specimens at each applied stress rate are required for statistical reproducibility and design (2). Guidelines are provided in this test method.NOTE 4: For a given ceramic material/environment system, the SCG parameter n is constant regardless of specimen size although its reproducibility is dependent on the variables mentioned in 4.8. By contrast, the SCG parameter D depends significantly on strength and thus on specimen size (see Eq X1.6 in Appendix X1).4.9 The strength of a ceramic material for a given specimen and test fixture configuration is dependent on its inherent resistance to fracture, the presence of flaws, and environmental effects. Analysis of a fracture surface, fractography, though beyond the scope of this test method, is highly recommended for all purposes, especially to verify the mechanism(s) associated with failure (refer to Practice C1322).4.10 The conventional analysis of constant stress rate testing is based on a critical assumption that stress is uniform throughout the test piece. This is most easily achieved in direct tension test specimens. Only test specimens that fracture in the inner gauge section in four-point testing should be used. Three-point flexure shall not be used. Breakages between the outer and inner fixture contact points should be discounted. The same requirement applies to biaxial disk strength testing. Only fractures which occur in the inner loading circle should be used. Furthermore, it is assumed that the fracture origins are near to the tensile surface and do not grow very large relative to the thickness of rectangular beam flexure or disk strength test specimens.4.11 The conventional analysis of constant stress rate testing is also based on a critical assumption that the same type flaw controls strength in all specimens at all loading rates. If the flaw distribution is multimodal, then the conventional analysis in this standard may produce erroneous slow crack growth parameter estimates.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.

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5.1 Interlaminar delamination growth can be a critical failure mode in laminated CMC structures. Knowledge of the resistance to interlaminar delamination growth of a laminated CMC is essential for material development and selection, and for CMC component design. (See (1-8)3 which give GIc values of 20 J/m2 to 800 J/m2 for different CMC and carbon-carbon composite systems at ambient temperatures.)5.2 Conducting this test produces multiple values of GIc which are traditionally plotted against the delamination length at which that value was measured (see Fig. 2). The specific data of value to the test requestor will depend on the end use that motivated testing.5.2.1 The first increment of growth, initiated from a pre-implanted insert or machined notch, is sometimes described as the non-precracked (NPC) toughness. NPC toughness may be of interest, as it can represent manufacturing or processing defects, such as foreign object debris in a laminate or an error during machining.5.2.2 The next increment of growth, initiated from the sharp crack tip assumed to be present after the first increment, is sometimes defined as the precracked (PC) toughness. PC toughness may be of interest, as it is more representative of the resistance to delamination growth from a naturally occurring or damage-induced delamination.5.2.3 The remaining increments of growth, collectively forming an R-curve, provide information on how GIc evolves as the delamination advances. In unidirectional tape laminates, the R-curve is often increasing due to bridging of nested fibers across the delamination plane, artificially increasing GIc. For 2-D woven laminates for which there is little interply nesting, the R-curve may be flat.5.2.4 The increments of growth in which the R-curve is flat, and GIc has reached a steady state value defined as GIR, may be of interest and may also useful in design and analysis.5.3 This test method for measurement of GIc of CMC materials can serve the following purposes:5.3.1 To establish quantitatively the effect of CMC material variables (fiber interface coatings, matrix structure and porosity, fiber architecture, processing and environmental variables, conditioning/exposure treatments, etc.) on GIc and the interlaminar crack growth and damage mechanisms of a particular CMC material;5.3.2 To determine if a CMC material shows R-curve behavior where GIc changes with crack extension or reaches a stable value at a given amount of delamination growth. Fig. 2 shows R-curve behavior for a SiC-SiC composite (1);5.3.3 To develop delamination failure criteria and design allowables for CMC damage tolerance, durability or reliability analyses, and life prediction;NOTE 3: Test data can only reliably be used for this purpose if there is confidence that the test is yielding a material property and not a structural, geometry-dependent, property.5.3.4 To compare quantitatively the relative values of GIc for different CMC materials with different constituents and material properties, reinforcement architectures, processing parameters, or environmental exposure conditions; and5.3.5 To compare quantitatively the values of GIc obtained from different batches of a specific CMC material, to perform lot acceptance quality control, to use as a material screening criterion, or to assess batch variability.1.1 This test method describes the experimental methods and procedures for the determination of the critical mode I interlaminar strain energy release rate of continuous fiber- reinforced ceramic matrix composite (CMC) materials in terms of GIc. This property is also sometimes described as the mode I fracture toughness or the mode I fracture resistance.1.2 This test method applies primarily to ceramic matrix composite materials with a 2-D laminate structure, consisting of lay-ups of continuous ceramic fibers, in unidirectional tape or 2-D woven fabric architectures, within a brittle ceramic matrix.1.3 This test method determines the elastic strain energy released per unit of new surface area created as a delamination grows at the interlaminar interface between two lamina or plies. The term delamination is used in this test method to specifically refer to this type of growth, while the term crack is a more general term that can also refer to matrix cracking, intralaminar delamination growth, or fiber fracture.1.4 This test method uses a double cantilever beam (DCB) specimen to determine the critical mode I interlaminar strain energy release rate (GIc). A DCB test method has been standardized for polymer matrix composites (PMCs) under Test Method D5528. This test method addresses a similar procedure, but with modifications to account for the different physical properties, reinforcement architectures, stress-strain response, and failure mechanisms of CMCs compared to PMCs.1.5 This test is written for ambient temperature and atmospheric test conditions, but the test method can also be used for elevated temperature or environmental exposure testing with the use of an appropriate environmental test chamber, measurement equipment for controlling and measuring the chamber temperature, humidity, and atmosphere, high temperature gripping fixtures, and modified equipment for measuring delamination growth.1.6 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.1.6.1 Values expressed in this test method are in accordance with the International System of Units (SI) and IEEE/ASTM SI 10.1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. Specific hazard statements are given in Section 8.1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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5.1 This test method is used to determine the mechanical properties in flexure of engineered ceramic components with multiple longitudinal hollow channels, commonly described as “honeycomb” channel architectures. The components generally have 30 % or more porosity and the cross-sectional dimensions of the honeycomb channels are on the order of 1 mm or greater.5.2 The experimental data and calculated strength values from this test method are used for material and structural development, product characterization, design data, quality control, and engineering/production specifications.NOTE 1: Flexure testing is the preferred method for determining the nominal “tensile fracture” strength of these components, as compared to a compression (crushing) test. A nominal tensile strength is required, because these materials commonly fail in tension under thermal gradient stresses. A true tensile test is difficult to perform on these honeycomb specimens because of gripping and alignment challenges.5.3 The mechanical properties determined by this test method are both material and architecture dependent, because the mechanical response and strength of the porous test specimens are determined by a combination of inherent material properties and microstructure and the architecture of the channel porosity [porosity fraction/relative density, channel geometry (shape, dimensions, cell wall thickness, etc.), anisotropy and uniformity, etc.] in the specimen. Comparison of test data must consider both differences in material/composition properties as well as differences in channel porosity architecture between individual specimens and differences between and within specimen lots.5.4 Test Method A is a user-defined specimen geometry with a choice of four-point or three-point flexure testing geometries. It is not possible to define a single fixed specimen geometry for flexure testing of honeycombs, because of the wide range of honeycomb architectures and cell sizes and considerations of specimen size, cell shapes, pitch, porosity size, crush strength, and shear strength. As a general rule, the experimenter will have to define a suitable test specimen geometry for the particular honeycomb structure of interest, considering composition, architecture, cell size, mechanical properties, and specimen limitations and using the following guidelines. Details on specimen geometry definition are given in 9.2.5.4.1 Four-point flexure (Test Method A1) is strongly preferred and recommended for testing and characterization purposes. (From Test Method C1161 section 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 simpler test fixtures, it is easier to adapt to high temperature and fracture toughness testing, and it is sometimes helpful in Weibull statistical studies. However, four-point flexure is preferred and recommended for most characterization purposes.”)5.4.2 The three-point flexure test configuration (Test Method A2) may be used for specimens which are not suitable for 4-point testing, with the clear understanding that 3-point loading exposes only a very small portion of the specimen to the maximum stress, as compared to the much larger maximum stress volume in a 4-point loading configuration. Therefore, 3-point flexural strengths are likely to be greater than 4-point flexural strengths, based on statistical flaw distribution factors.5.5 Test Method B (with a specified specimen size and a 4-point-1/4 point flexure loading geometry) is widely used in industry for cordierite and silicon carbide honeycomb structures with small cell size (cell pitch ~2 mm). Test Method B is provided as a standard test geometry that provides a baseline specimen size for honeycomb structures with appropriate properties and cell size with the benefit of experimental repeatability, reproducibility and comparability. (See 9.3 for details on Test Method B.)NOTE 2: Specific fixture and specimen configurations were chosen for Test Method B to provide a balance between practical configurations and linear cell count effect limits and to permit ready comparison of data without the need for Weibull-size scaling.5.6 The calculation of the flexure stress in these porous specimens is based on small deflection elastic beam theory with assumptions that (1) the material properties are isotropic and homogeneous, (2) the moduli of elasticity in tension and compression are identical, and (3) the material is linearly elastic. If the porous material in the walls of the honeycomb is not specifically anisotropic in microstructure, it is also assumed that the microstructure of the wall material is uniform and isotropic. To understand the effects of some of these assumptions, see Baratta et al. (6).NOTE 3: These assumptions may limit the application of the test to comparative type testing such as used for material development, quality control, and flexure specifications. Such comparative testing requires consistent and standardized test conditions both for specimen geometry and porosity architecture, as well as experimental conditions—loading geometries, strain rates, and atmospheric/test conditions.5.7 Three flexure strength values (defined in Section 3 and calculated in Section 11) may be calculated in this test method. They are the nominal beam strength, the wall fracture strength, and the honeycomb structure strength.5.7.1 Nominal Beam Strength—The first approach to calculating a flexure strength is to make the simplifying assumption that the specimen acts as a uniform homogeneous material that reacts as a continuum. Based on these assumptions, a nominal beam strength SNB can be calculated using the standard flexure strength equations with the specimen dimensions and the breaking force. (See Section 11.)5.7.1.1 A linear cell count effect (specimen size-cell count effect) has been noted in research on the flexure strength of ceramic honeycomb test specimens (7, 8). If the cell size is too large with respect to the specimen dimensions and if the linear cell count (the integer number of cells along the shortest cross-sectional dimension) is too low (<15), channel porosity has a geometric effect on the moment of inertia that produces an artificially high value for the nominal beam strength. (See Appendix X1.) With the standard elastic beam equations the strength value is overestimated, because the true moment of inertia of the open cell structure is not accounted for in the calculation.5.7.1.2 This overestimate becomes increasingly larger for specimens with lower linear cell counts. The linear cell count has to be 15 or greater for the calculated nominal beam strength, SNB, to be within a 10 % overestimate of the wall fracture strength SWF.NOTE 4: The study by Webb, Widjaja, and Helfinstine (7) showed that for cells with a square cross section a minimum linear cell count of 15 should be maintained to minimize linear cell count effects on the calculated nominal beam strength. (This study is summarized in Appendix X1.)5.7.1.3 For those smaller test specimens (where the linear cell count is between 2 and 15), equations for wall fracture strength and honeycomb structure strength are given in Section 11. These equations are used to calculate a more accurate value for the flexure strength of the honeycomb, as compared to the calculated nominal beam strength.5.7.2 Wall Fracture Strength, SWF, is calculated using the true moment of inertia of the honeycomb architecture, based on the geometry, dimensions, cell wall thickness, and linear count of the channels in the honeycomb structure. The wall fracture strength is a calculation of the true failure stress in the outer fiber surface of the specimen. (Appendix X1 describes the calculation as cited in the Webb, Widjaja, and Helfinstine (7) report). Section 11 on calculations gives the formula for calculating the moment of inertia for test specimens with square honeycomb channels and uniform cell wall thickness.NOTE 5: The moment of inertia formula given in Section 11 and Appendix X1 is only applicable to square cell geometries. It is not suitable for rectangular, circular, hexagonal, or triangular geometries. Formulas for those geometries have to be developed from geometric analysis and first principles.5.7.3 Honeycomb Structure Strength, SHS, is calculated from the wall fracture strength SWF. This calculation gives a flexure strength value which is independent of specimen-cell size geometry effects. The honeycomb structure strength value can be used for comparison of different specimen geometries with different channel sizes. It also gives a flexure strength value that can be used for stress models that assume continuum strength. (See Appendix X1.) Section 11 on calculations gives the formula for calculating the honeycomb structure strength for test specimens with square honeycomb channels and uniform cell wall thickness.5.7.4 The following recommendations are made for calculating a flexure strength for the ceramic honeycomb test specimens.5.7.4.1 For flexure test specimens where the linear cell count is 15 or greater, the nominal beam strength SNB calculation and the honeycomb structure strength SHS are roughly equivalent in value (within 10 %). The nominal beam strength SNB calculation can be used considering this variability.5.7.4.2 For flexure test specimens where the linear cell count is between 5 and 15, the nominal beam strength SNB calculation may produce a 10 % to 20 % overvalue. The SNB value should be used with caution.5.7.4.3 For flexure test specimens where the linear cell count is less than 5, the nominal beam strength SNB calculation may produce a 20 % to 100 % overvalue. It is recommended that the honeycomb structure strength SHS be calculated and used as a more accurate flexure strength number.5.7.4.4 If specimen availability and test configuration permit, test specimens with a linear cell count of 15 or greater are preferred to reduce the specimen linear cell count effect on nominal beam strength SNB to less than 10 %.5.8 Flexure test data for porous ceramics will have a statistical distribution, which may be analyzed and described by Weibull statistics, per Practice C1239.5.9 This flexure test can be used as a characterization tool to assess the effects of fabrication variables, geometry and microstructure variations, and environmental exposure on the mechanical properties of the honeycombs. The effect of these variables is assessed by flexure testing a specimen set in a baseline condition and then testing a second set of specimens with defined changes in geometry or fabrication methods or after controlled environmental exposure.5.9.1 Geometry and microstructure variations would include variations in cell geometry (shape dimensions, cell wall thickness, and count) and wall porosity (percent, size, shape, morphology, etc.).5.9.2 Fabrication process variations would include forming parameters, drying and binder burn-out conditions, sintering conditions, heat treatments, variations in coatings, etc.5.9.3 Environmental conditioning would include extended exposure at different temperatures and different corrosive atmospheres (including steam).5.10 This flexure test may be used to assess the thermal shock resistance of the honeycomb ceramics, as described in Test Method C1525.5.11 The flexure test is not the preferred method for determining the Young's modulus of these porous structures. (For this reason, the deflection of the flexure test bar is not commonly measured in this test.) Young's modulus measurements by sonic resonance (Test Method C1198) or by impulse excitation (Test Method C1259) give more reliable and repeatable data.5.12 It is beyond the scope of this standard to require fractographic analysis at the present time. Fractographic analysis for critical flaws in porous honeycomb ceramics is extremely difficult and of very uncertain value.1.1 This test method covers the determination of the flexural strength (modulus of rupture in bending) at ambient conditions of advanced ceramic structures with 2-dimensional honeycomb channel architectures.1.2 The test method is focused on engineered ceramic components with longitudinal hollow channels, commonly called “honeycomb” channels (see Fig. 1). The components generally have 30 % or more porosity and the cross-sectional dimensions of the honeycomb channels are on the order of 1 mm or greater. Ceramics with these honeycomb structures are used in a wide range of applications (catalytic conversion supports (1),2 high temperature filters (2, 3), combustion burner plates (4), energy absorption and damping (5), etc.). The honeycomb ceramics can be made in a range of ceramic compositions—alumina, cordierite, zirconia, spinel, mullite, silicon carbide, silicon nitride, graphite, and carbon. The components are produced in a variety of geometries (blocks, plates, cylinders, rods, rings).FIG. 1 General Schematics of Typical Honeycomb Ceramic Structures1.3 The test method describes two test specimen geometries for determining the flexural strength (modulus of rupture) for a porous honeycomb ceramic test specimen (see Fig. 2):FIG. 2 Flexure Loading ConfigurationsL = Outer Span Length (for Test Method A, L = User defined; for Test Method B, L = 90 mm)NOTE 1: 4-Point-1/4 Loading for Test Methods A1 and B.NOTE 2: 3-Point Loading for Test Method A2.1.3.1 Test Method A—A 4-point or 3-point bending test with user-defined specimen geometries, and1.3.2 Test Method B—A 4-point-1/4 point bending test with a defined rectangular specimen geometry (13 mm × 25 mm × > 116 mm) and a 90 mm outer support span geometry suitable for cordierite and silicon carbide honeycombs with small cell sizes.1.4 The test specimens are stressed to failure and the breaking force value, specimen and cell dimensions, and loading geometry data are used to calculate a nominal beam strength, a wall fracture strength, and a honeycomb structure strength.1.5 Test results are used for material and structural development, product characterization, design data, quality control, and engineering/production specifications.1.6 The test method is meant for ceramic materials that are linear-elastic to failure in tension. The test method is not applicable to polymer or metallic porous structures that fail in an elastomeric or an elastic-ductile manner.1.7 The test method is defined for ambient testing temperatures. No directions are provided for testing at elevated or cryogenic temperatures.1.8 The values stated in SI units are to be regarded as standard (IEEE/ASTM SI 10). English units are sparsely used in this standard for product definitions and tool descriptions, per the cited references and common practice in the US automotive industry.1.9 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.1.10 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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1.1 This terminology contains definitions and explanatory notes for the principal words, phrases, and terms used in advanced ceramics technology. The given definitions are technology specific and are directly applicable to the design, production, testing, analysis, characterization, and use of advanced ceramics for structural, electronic, coating, energy, chemical, nuclear, biomedical, and environmental applications.1.2 The purpose of the standard terminology is to provide a collected technical resource and reference that promotes a common understanding of the principal technical terms used within the advanced ceramics community and encourages the use of uniform terminology in specifications and reports.1.3 Definitions of terms appear in dictionary-definition form and include the term, part of speech (for example, n = noun; v = verb; adj = adjective), definition, and, when applicable, a delimiting phrase. Terms representing physical quantities have analytical dimensions stated immediately following the term (or letter symbol) in fundamental dimension form, using the following ASTM standard symbology for fundamental dimensions, shown within square brackets: [M] for mass, [L] for length, [T] for time, [θ] for thermodynamic temperature, and [nd] for non-dimensional quantities. Use of these symbols is restricted to analytical dimensions when used with square brackets, as the terms may have other definitions when used without the brackets.1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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5.1 Fracture mirror size analysis is a powerful tool for analyzing glass and ceramic fractures. Fracture mirrors are tell-tale fractographic markings in brittle materials that surround a fracture origin as discussed in Practices C1256 and C1322. Fig. 1 shows a schematic with key features identified. Fig. 2 shows an example in glass. The fracture mirror region is very smooth and highly reflective in glasses, hence the name “fracture mirror.” In fact, high magnification microscopy reveals that, even within the mirror region in glasses, there are very fine features and escalating roughness as the crack advances away from the origin. These are submicrometer in size and hence are not discernable with an optical microscope. Early investigators interpreted fracture mirrors as having discrete boundaries including a “mirror-mist” boundary and also a “mist-hackle” boundary in glasses. These were also termed “inner mirror” or “outer mirror” boundaries, respectively. It is now known that there are no discrete boundaries corresponding to specific changes in the fractographic features. Surface roughness increases gradually from well within the fracture mirror to beyond the apparent boundaries. The boundaries were a matter of interpretation, the resolving power of the microscope, and the mode of viewing. In very weak specimens, the mirror may be larger than the specimen or component and the boundaries will not be present.Eq 1 is hereafter referred to as the “empirical stress – fracture mirror size relationship,” or “stress-mirror size relationship” for short. A review of the history of Eq 1, and fracture mirror analysis in general, may be found in Refs (1)3 and (2).5.5 A, the “fracture mirror constant” (sometimes also known as the “mirror constant”) has units of stress intensity (MPa√m or ksi√in.) and is considered by many to be a material property. As shown in Figs. 1 and 2, it is possible to discern separate mist and hackle regions and the apparent boundaries between them in glasses. Each has a corresponding mirror constant, A. The most common notation is to refer to the mirror-mist boundary as the inner mirror boundary, and its mirror constant is designated Ai. The mist-hackle boundary is referred to as the outer mirror boundary, and its mirror constant is designated Ao. The mirror-mist boundary is usually not perceivable in polycrystalline ceramics. Usually, only the mirror-hackle boundary is measured and only an Ao for the mirror-hackle boundary is calculated. A more fundamental relationship than Eq 1 may be based on the stress intensity factors (KI) at the mirror-mist or mist-hackle boundaries, but Eq 1 is more practical and simpler to use.5.6 The size predictions based on Eq 1 and the A values, or alternatively stress intensity factors, match very closely for the limiting cases of small mirrors in tension specimens. This is also true for small semicircular mirrors centered on surface flaws in strong flexure specimens. So, at least for some special mirror cases, A should be directly related to a more fundamental parameter based on stress intensity factors.5.7 The size of the fracture mirrors in laboratory test specimen fractures may be used in conjunction with known fracture mirror constants to verify the stress at fracture was as expected. The fracture mirror sizes and known stresses from laboratory test specimens may also be used to compute fracture mirror constants, A.5.8 The size of the fracture mirrors in components may be used in conjunction with known fracture mirror constants to estimate the stress in the component at the origin. Practice C1322 has a comprehensive list of fracture mirror constants for a variety of ceramics and glasses.1.1 This practice pertains to the analysis and interpretation of fracture mirror sizes in brittle materials. Fracture mirrors (Fig. 1) are telltale fractographic markings that surround a fracture origin in brittle materials. The fracture mirror size may be used with known fracture mirror constants to estimate the stress in a fractured component. Alternatively, the fracture mirror size may be used in conjunction with known stresses in test specimens to calculate fracture mirror constants. The practice is applicable to glasses and polycrystalline ceramic laboratory test specimens as well as fractured components. The analysis and interpretation procedures for glasses and ceramics are similar, but they are not identical. Different optical microscopy examination techniques are listed and described, including observation angles, illumination methods, appropriate magnification, and measurement protocols. Guidance is given for calculating a fracture mirror constant and for interpreting the fracture mirror size and shape for both circular and noncircular mirrors including stress gradients, geometrical effects, residual stresses, or combinations thereof. The practice provides figures and micrographs illustrating the different types of features commonly observed in and measurement techniques used for the fracture mirrors of glasses and polycrystalline ceramics.FIG. 1 Schematic of a Fracture Mirror Centered on a Surface Flaw of Initial Size (a)NOTE 1: The initial flaw may grow stably to size ac prior to unstable fracture when the stress intensity reaches KIc. The mirror-mist radius is Ri, the mist-hackle radius is Ro, and the branching distance is Rb. These transitions correspond to the mirror constants, Ai, Ao, and Ab, respectively.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 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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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 same specific flaw type controls strength in the various specimen configurations. It is assumed that the material is uniform, homogeneous, and isotropic. If the material is a composite, it is assumed that the composite phases are sufficiently small that the structure behaves on an engineering scale as a homogeneous and isotropic body. The composite must contain a sufficient quantity of uniformly distributed, randomly oriented reinforcing elements such that the material is effectively homogeneous. Whisker-toughened ceramic composites may be representative of this type of material. This practice is also applicable to composite ceramics that do not exhibit any appreciable bilinear or nonlinear deformation behavior. This standard and the conventional Weibull strength scaling with size may not be suitable for continuous fiber-reinforced composite ceramics. The material is assumed to fracture in a brittle fashion, a consequence of stress causing catastrophic propagation of flaws. The material is assumed to be consistent (batch to batch, day to day, etc.). It is assumed that the strength distribution follows a Weibull two-parameter distribution. It is assumed that each test piece has a statistically significant number of flaws and that they are randomly distributed. It is assumed that the flaws are small relative to the specimen cross section size. If multiple flaw types are present and control strength, then strengths may scale differently for each flaw type. Consult Practice C1239 and the example in 9.1 for further guidance on how to apply censored statistics in such cases. It is also assumed that the specimen stress state and the maximum stress are accurately determined. It is assumed that the actual data from a set of fractured specimens are accurate and precise. (See Terminology E456 for definitions of the latter two terms.) For this reason, this standard frequently references other ASTM standard test methods and practices which are known to be reliable in this respect.5.6 Even if test data has been accurately and precisely measured, it should be recognized that the Weibull parameters determined from test data are in fact estimates. The estimates can vary from the actual (population) material strength parameters. Consult Practice C1239 for further guidance on the confidence bounds of Weibull parameter estimates based on test data for a finite sample size of test fractures.5.7 When correlating strength parameters from test data from one specimen geometry to a second, the accuracy of the correlation depends upon whether the assumptions listed in 5.5 are met. In addition, statistical sampling effects as discussed in 5.6 may also contribute to variations between computed and observed strength-size scaling trends.5.8 There are practical limits to Weibull strength scaling that should be considered. For example, it is implicitly assumed in the Weibull model that flaws are small relative to the specimen size. Pores that are 50 μm (0.050 mm) in diameter are volume-distributed flaws in tension or flexural strength specimens with 5 mm or greater cross section sizes. The same may not be true if the cross section size is only 100 μm.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.

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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-distributed with all flaws located on the outer specimen surface. Grinding cracks fit the latter category. Variations in the flaws cause a natural scatter in strengths for a set 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 Refs (3-5) 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 greater than four-point flexural strengths. Three-point flexure has some advantages. It uses simpler test fixtures, it is easier to adapt to high temperature and fracture toughness testing, and it is sometimes helpful in Weibull statistical studies. It also uses smaller force to break a specimen. It is also convenient for very short, stubby specimens which would be difficult to test in four-point loading. Nevertheless, four-point flexure is preferred and recommended for most characterization purposes.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 Configuration1.2 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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4.1 This test system has advantages in certain respects over the use of static loading systems in the measurement of glass and glass-ceramics:4.1.1 Only minute stresses are applied to the specimen, thus minimizing the possibility of fracture.4.1.2 The period of time during which stress is applied and removed is of the order of hundreds of microseconds, making it feasible to perform measurements at temperatures where delayed elastic and creep effects proceed on a much-shortened time scale, as in the transformation range of glass, for instance.4.2 The test is suitable for detecting whether a material meets specifications, if cognizance is given to one important fact: glass and glass-ceramic materials are sensitive to thermal history. Therefore the thermal history of a test specimen must be known before the moduli can be considered in terms of specified values. Material specifications should include a specific thermal treatment for all test specimens.1.1 This test method covers the determination of the elastic properties of glass and glass-ceramic materials. Specimens of these materials possess specific mechanical resonance frequencies which are defined by the elastic moduli, density, and geometry of the test specimen. Therefore the elastic properties of a material can be computed if the geometry, density, and mechanical resonance frequencies of a suitable test specimen of that material can be measured. Young's modulus is determined using the resonance frequency in the flexural mode of vibration. The shear modulus, or modulus of rigidity, is found using torsional resonance vibrations. Young's modulus and shear modulus are used to compute Poisson's ratio, the factor of lateral contraction.1.2 All glass and glass-ceramic materials that are elastic, homogeneous, and isotropic may be tested by this test method.2 The test method is not satisfactory for specimens that have cracks or voids that represent inhomogeneities in the material; neither is it satisfactory when these materials cannot be prepared in a suitable geometry. Non-glass and glass-ceramic materials should reference Test Method E1875  for non-material specific methodology to determine resonance frequencies and elastic properties by sonic resonance.NOTE 1: Elastic here means that an application of stress within the elastic limit of that material making up the body being stressed will cause an instantaneous and uniform deformation, which will cease upon removal of the stress, with the body returning instantly to its original size and shape without an energy loss. Glass and glass-ceramic materials conform to this definition well enough that this test is meaningful.NOTE 2: Isotropic means that the elastic properties are the same in all directions in the material. Glass is isotropic and glass-ceramics are usually so on a macroscopic scale, because of random distribution and orientation of crystallites.1.3 A cryogenic cabinet and high-temperature furnace are described for measuring the elastic moduli as a function of temperature from –195 to 1200 °C.1.4 Modification of the test for use in quality control is possible. A range of acceptable resonance frequencies is determined for a piece with a particular geometry and density. Any specimen with a frequency response falling outside this frequency range is rejected. The actual modulus of each piece need not be determined as long as the limits of the selected frequency range are known to include the resonance frequency that the piece must possess if its geometry and density are within specified tolerances.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 developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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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 parameter estimates be transformed and reported as material-specific parameters ( m^, ^σ0). In addition, different flaw distributions (for example, failures due to inclusions or machining damage) may be observed, and each will have its own strength distribution parameters. The procedure for transforming parameter estimates for typical test specimen geometries and flaw distributions is outlined in 8.6.5.4 Many factors affect the estimates of the distribution parameters. The total number of test specimens plays a significant role. Initially, the uncertainty associated with parameter estimates decreases significantly as the number of test specimens increases. However, a point of diminishing returns is reached when the cost of performing additional strength tests may not be justified. This suggests that a practical number of strength tests should be performed to obtain a desired level of confidence associated with a parameter estimate. The number of test specimens needed depends on the precision required in the resulting parameter estimate. Details relating to the computation of confidence bounds (directly related to the precision of the estimate) are presented in 9.3 and 9.4.1.1 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.

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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.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))21.2 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 developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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