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**Significance and Use**

This test method may be used for material development, material comparison, quality assurance, and characterization. Extreme care should be exercised when generating design data.

For a C-ring under diametral compression, the maximum tensile stress occurs at the outer surface. Hence, the C-ring specimen loaded in compression will predominately evaluate the strength distribution and flaw population(s) on the external surface of a tubular component. Accordingly, the condition of the inner surface may be of lesser consequence in specimen preparation and testing.

Note 1—A C-ring in tension or an O-ring in compression may be used to evaluate the internal surface.

The flexure stress is computed based on simple curved-beam theory (1, 2, 3, 4, 5). It is assumed that the material is isotropic and homogeneous, the moduli of elasticity are identical in compression or tension, and the material is linearly elastic. These homogeneity and isotropy assumptions preclude the use of this standard for continuous fiber reinforced composites. Average grain size(s) should be no greater than one fiftieth (^{1}/_{50}) of the C-ring thickness. The simple curved-beam theory stress solution is in good agreement (typically better than 1%) with a theory of elasticity solution as discussed in (3) for the geometries chosen for this standard. The simple beam theory stress equations are relatively simple. They are relatively easy to integrate for Weibull effective volume or effective area computations as shown in Appendix X1.

The simple curved beam and theory of elasticity stress solutions both are two-dimensional plane stress solutions. They do not account for stresses in the axial (parallel to b) direction, or variations in the circumferential (hoop, σ_{θ}) stresses through the width (b) of the test piece. The variations in the circumferential stresses increase with increases in width (b) and ring thickness (t). The variations can be substantial (> 10 %) for test specimens with large b. The circumferential stresses peak at the outer edges. Therefore, the width (b) and thickness (t) of the specimens permitted in this test method are limited so that axial stresses are negligible (see Ref. 5) and the variations of the circumferential stresses from the nominal simple curved beam theory stress calculations are typically less than 4 %. See Ref. (3) and (4) for more information on the variation of the circumferential stresses as a function of ring thickness (t) and ring width (b).

The test piece outer rim corners are vulnerable to edge damage, another reason to minimize the differences in the circumferential stresses across the ring outer surface.

Other geometry C–ring test specimens may be tested, but comprehensive finite element analyses shall be performed to obtain accurate stress distributions. If strengths are to be scaled (converted) to strengths of other sizes or geometries, then Weibull effective volumes or areas shall be computed using the results of the finite element analyses.

Because advanced ceramics exhibiting brittle behavior generally fracture catastrophically from a single dominant flaw for a particular tensile stress field, the surface area and volume of material subjected to tensile stresses is a significant factor in determining the ultimate strength. Moreover, because of the statistical distribution of the flaw population(s) in advanced ceramics exhibiting brittle behavior, a sufficient number of specimens at each testing condition is required for statistical analysis and design. This test method provides guidelines for the number of specimens that should be tested for these purposes (see 8.4).

Because of a multitude of factors related to materials processing and component fabrication, the results of C-ring tests from a particular material or selected portions of a part, or both, may not necessarily represent the strength and deformation properties of the full-size end product or its in-service behavior.

The ultimate strength of a ceramic material may be influenced by slow crack growth or stress corrosion, or both, and is therefore, sensitive to the testing mode, testing rate, or environmental influences, or a combination thereof. Testing at sufficiently rapid rates as outlined in this test method may minimize the consequences of subcritical (slow) crack growth or stress corrosion.

The flexural behavior and strength of an advanced monolithic ceramic are dependent on the material's inherent resistance to fracture, the presence of flaws, or damage accumulation processes, or a combination thereof. Analysis of fracture surfaces and fractography, though beyond the scope of this test method, is highly recommended (further guidance may be obtained from Practice C1322 and Ref (6)).

**1. Scope**

1.1 This test method covers the determination of ultimate strength under monotonic loading of advanced ceramics in tubular form at ambient temperatures. The ultimate strength as used in this test method refers to the strength obtained under monotonic compressive loading of C-ring specimens such as shown in Fig. 1 where monotonic refers to a continuous nonstop test rate with no reversals from test initiation to final fracture. This method permits a range of sizes and shapes since test specimens may be prepared from a variety of tubular structures. The method may be used with microminiature test specimens.

1.2 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.

1.2.1 Values expressed in this test method are in accordance with the International System of Units (SI) and .

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

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

C1368 Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by Constant Stress-Rate Strength Testing at Ambient Temperature

C1683 Practice for Size Scaling of Tensile Strengths Using Weibull Statistics for Advanced Ceramics

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)

**ICS Code**

ICS Number Code 19.060 (Mechanical testing); 81.060.99 (Other standards related to ceramics)

**UNSPSC Code**

UNSPSC Code

**DOI:** 10.1520/C1323-10

ASTM International is a member of CrossRef.