## ASTM C1674 – **Standard Test Method for Flexural Strength of Advanced Ceramics with Engineered Porosity (Honeycomb Cellular Channels) at Ambient Temperatures**

**Description**:

Significance and Use

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 *S _{NB}* 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, *S _{NB}*, to be within a 10 % overestimate of the wall fracture strength

*S*.

_{WF}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, S* _{WF}*, 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, S* _{HS}*, is calculated from the wall fracture strength

*S*. 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.

_{WF}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 *S _{NB}* calculation and the honeycomb structure strength

*S*are roughly equivalent in value (within 10 %). The nominal beam strength

_{HS}*S*calculation can be used considering this variability.

_{NB}5.7.4.2 For flexure test specimens *where the linear cell count is between 5 and 15*, the nominal beam strength *S _{NB}* calculation may produce a 10 % to 20 % overvalue. The

*S*value should be used with caution.

_{NB}5.7.4.3 For flexure test specimens *where the linear cell count is less than 5*, the nominal beam strength *S _{NB}* calculation may produce a 20 % to 100 % overvalue. It is recommended that the honeycomb structure strength

*S*be calculated and used as a more accurate flexure strength number.

_{HS}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 *S _{NB}* 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.

Scope

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 Structures**

1.3 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 Configurations**

*L* = 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, and

1.3.2 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.