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**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 experimental data to a mathematical relationship between strength and applied stress rate, log σ_{f } = 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[K_{I}/K_{IC}]^{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. 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.*

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**ASTM Standards**

C1145 Terminology of Advanced Ceramics

C1161 Test Method for Flexural Strength of Advanced Ceramics at Ambient Temperature

C1239 Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics

C1273 Test Method for Tensile Strength of Monolithic Advanced Ceramics at Ambient Temperatures

C1322 Practice for Fractography and Characterization of Fracture Origins in Advanced Ceramics

C1499 Test Method for Monotonic Equibiaxial Flexural Strength of Advanced Ceramics at Ambient Temperature

E4 Practices for Force Verification of Testing Machines

E6 Terminology Relating to Methods of Mechanical Testing

E337 Test Method for Measuring Humidity with a Psychrometer (the Measurement of Wet- and Dry-Bulb Temperatures)

E1823 Terminology Relating to Fatigue and Fracture Testing

**ICS Code**

ICS Number Code 81.060.30 (Advanced ceramics)

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**DOI:** 10.1520/C1368-10R17

**Citation Format**

ASTM C1368-10(2017), Standard Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by Constant Stress-Rate Strength Testing at Ambient Temperature, ASTM International, West Conshohocken, PA, 2017, www.astm.org

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