Furnace designers are demanding accurate representative data on the modulus of elasticity (MOE) of modern refractories, in conjunction with thermal expansion and failure strain or stress, to calculate lining and roof stress during initial dewatering and heat-up and during steady state use.[1-11] For years, MOE has been measured at room temperature because no instrument has been capable of accurately measuring it at elevated temperatures.[12-19] However, measuring MOE at room temperature provides only a partial analysis.

Recently, the impulse excitation technique (IET) has been proven to provide reliable data at elevated temperatures and virtually continuous measurement capability over a wide temperature range. This advancement makes it possible to locate the phase changes and determine the rate of change of MOE with respect to temperature.

Static MOE Measurement

MOE can be measured either statically or dynamically. The three most common ways of measuring MOE on refractories statically are tensile, compression and bending. Static MOE is not truly static; the load or displacement is applied slowly so the test approaches static conditions. Static MOE is rate sensitive, and the loading rate should be given. Increasing the loading rate increases the apparent MOE, as inelastic processes are generally time-dependent, while elastic processes are time-independent.[20]

Tensile MOE of refractory castables is measured using a specimen with a machined gage section that is gripped at the ends and stretched. The stress and strain, or load and displacement, in the gage section are monitored. The tensile MOE is important for determining failure as most refractories fail due to resolved tensile stress. However, it is very difficult to test refractories in tension. Grips that do not cause stress concentrations are difficult to develop and use, especially at elevated temperatures. Grip misalignment can also create high stress concentrations. These stress concentrations frequently cause failure to occur at the grips. It is difficult to machine the reduced gage section without inducing microcracks, and it can be difficult to measure the strain in the gage section due to the coarse microstructure.

Additionally, strain gages cannot be used above 450°C. Contacting extensometers may be used above this temperature, but they may react with the specimen or undergo creep. Optical or laser extensometers have also been used above 450°C with promising results, but they also have their deficiencies.[21] The MOE can only be determined prior to microcrack initiation and growth or any other inelastic deformations that cause reductions in the apparent MOE. Thus, only the very small linear portion of the stress-strain curve is valid for MOE determination.

Compressive MOE is most widely measured for refractories. Refractories are usually loaded in compression according to furnace geometry and self-loading due to gravity. Gripping is straightforward in testing; cylinders or cubes can be easily loaded in compression without the need for grips. It is relatively simple to load specimens at a constant stress or strain rate. Stress and strain are easily determined from load and displacement for pure compression; however, there are problems with measurements of MOE in compression. The stress field in compression is generally not pure compression due to the large thickness of the specimens. The Poisson effect leads to high tensile and shear stresses due to plane strain. This complicates the calculation of MOE and may lead to higher apparent MOE than expected in pure compression. Large aspect ratio specimens leading to plane stress are hard to test due to the large aggregate grains in many refractories and the need for structural averaging. In addition, beam buckling is a problem with large aspect ratio specimens. In cases where the deflection of the gage section of a compression specimen is not measured directly, it is important to use a very stiff machine. The machine stiffness must be much greater than that of the specimen. Machine stiffness can only be ignored if it is many orders of magnitude greater than that of the specimen; otherwise, a compliance correction must be applied.

MOE can be measured in 3 point, 4 point or cantilever[22] bending, but these methods are usually inaccurate due to several complications. The specimen is in tension changing symmetrically to compression. Since compressive and tensile MOE have different values, this results in an average MOE. It is also difficult to accurately measure the displacement or strain of the specimen with respect to the supports.

Dynamic MOE Measurement

The two most common methods of measuring MOE dynamically are the IET and resonant techniques. The IET uses a single sharp strike to induce a standing wave in a specimen, and the frequency of the decaying standing wave is measured.[23-25] The resonant technique continuously excites a specimen through vibration, and the frequency of the vibration is increased until a standing wave is produced.[26-28] Both methods are based on the MOE being a function of the harmonic frequency, mass and shape of the material.[29] Dynamic methods may be adapted to high temperature measurement.[30] Dynamic MOE is nondestructive and can be measured on every item produced on a production line for quality control purposes.

The dynamic methods measure MOE at almost zero stress and are highly accurate. Indeed, near zero stress, the MOE measurement is a truly elastic process. The dynamic MOE represents purely elastic behavior incorporating the effect of microcracks and porosity, while the intrinsic Young's modulus of a material is based on theoretical density with no microcracks. Intrinsic Young's modulus varies only with respect to composition and temperature. Intrinsic Young's modulus cannot be measured for castables, but may be estimated by the mixture rule and the intrinsic Young's modulus of each phase making up the material.[20]

Tensile, compressive, bending and dynamic MOE vary widely in some refractory systems. The static MOE builds upon the dynamic MOE by incorporating the effects of inelastic deformations, which are irreversible in addition to the effects of porosity and microcracks. In addition, Poisson's effect may further complicate compressive measurements as discussed earlier. The dynamic MOE falls between or is greater than the tensile MOE and the compressive MOE.[31] The dynamic MOE should always be higher than static MOE, because inelastic processes cannot come into effect at high loading rates. Thermal shock is related to the dynamic MOE since it is a fast process.[20] Most modelers request full stress strain curves to failure strain in both compression and tension.

It is important that MOE be measured below the stress level at which strain softening begins. Strain softening occurs in most refractories at low stress levels. Strain softening is microcrack growth and coalescence, or may be tied to microcrack nucleation along the aggregate-matrix interfacial zone. Strain softening is often imperceptible, as it occurs in some refractories at less than 10% of the ultimate strength. It has been proposed that strain softening is the cause of the differences in values between tensile, dynamic and compressive MOE.[32] If this is true, dynamic MOE is the correct MOE to use as a starting point in design. Fracture micromechanics or strain softening theory should then be used to account for strain softening above the softening limit.[33,34]

To illustrate this point, the MOE and bulk density of cured self-flow castable refractories were measured by IET from 25°C to approximately 1200°C based on either tabular alumina aggregate (T) or white fused alumina aggregate (W) at four cement levels: high, low, ultralow and no cement.

Experimental Procedures

Equation 1

Bulk density and room temperature sonic elastic properties were measured for eight compositions of self-flow refractory castables on 9-in. straights, 22.8 x 11.4 x 6.4 cm (9 x 4-1/2 x 2-1/2 in.), as cast and cured for four weeks. The compositions of the mixes were based on two types of aggregate: tabular alumina (supplied by Alcoa Aluminum Co. of America, Pittsburgh, Pa.) and white fused alumina (supplied by C-E Minerals, King of Prussia, Pa.). Each of the aggregate systems was produced with four binder systems: high cement (TH and WH), low cement (TL and WL), ultralow cement (TU and WU) and no cement (TN and WN).

The aggregate was combined based on a Furnas distribution with an R-value of 1.25 and a maximum Tyler sieve size of 3200. Five wt. % fumed silica (Elkem 971U) and 0.075 wt. % flow additive (Darvan 7S, R.T. Vanderbilt Co., Inc., Norwalk, Conn.) was added to the aggregate to aid in flow and packing prior to adding the binder mix.

The high cement compositions were formed by adding 15 wt. % high alumina cement (CA25R, Alcoa Aluminum Co. of America) to the aggregate mixture. The low cement compositions were formed by adding 5 wt. % high alumina cement (CA25R, Alcoa Aluminum Co. of America) and 5 wt. % ultrafine alumina (A-3000, Alcoa Aluminum Co. of America) to the aggregate mixture. The ultra-low cement compositions were formed by adding 2.5 wt. % high alumina cement (CA25R, Alcoa Aluminum Co. of America) and 5 wt. % ultrafine alumina (A-3000, Alcoa Aluminum Co. of America) to the aggregate mixture. The no-cement compositions were formed by adding

5 wt. % hydratable alumina cement (Alphabond 200, Alcoa Aluminum Co. of America) and 5 wt. % ultrafine alumina (A-3000, Alcoa Aluminum Co. of America) to the aggregate mixture. Casting water was added by dry weight: 6.5% for the high cement compositions, 6.25% for the low cement compositions, 4.5% for the ultra-low cement compositions and 6.25% for the no-cement compositions.

Room temperature elastic constants and bulk density were calculated using the GrindoSonic apparatus (based on the IET technique) and its included EMOD version 9.16 software (supplied by J.W. Lemmens, Inc., Leuven, Belgium). The software calculates the MOE in flexure and longitudinally, Poisson's ratio and shear modulus using formulas by Spinner and Tefft.[35] The elastic constants reported are the average of 20 specimens measured in two directions for each composition.

Elevated temperature elastic constants were measured on two rectangular prismatic bars of 6.4 x 2.5 x 1.3 cm (2.5 x 1 x 0.5 in.) cut from two randomly selected 9-in. straights. The elevated temperature natural frequency of vibration in flexure was measured by J.W. Lemmens, Inc. in Belgium. Equipment used included a GrindoSonic MK5i, a personal computer running GrindoSonic ETMTS software and a horizontal cylindrical furnace type 44C. The bar shape sample is suspended on nickel-chrome wires between parallel alumina rods. The rods are mounted on the front flange of the furnace and are exposed when the door is opened. When the door is closed, the specimen is positioned in the center of the furnace chamber between a pneumatic tapping device from below and a microphone and thermocouple assembly from above. The apparatus is controlled by the personal computer. Temperature rise is normally 2°C per minute with frequency measurements taken every 5°C, thus producing a curve of frequency versus temperature. The curves of the two samples of the same composition follow the same pattern. The frequency response used in calculations for elevated temperature MOE in flexure is the average frequency response for the two specimens. MOE in flexure was calculated by normalizing the change in frequency as a function of temperature using the equation shown in Equation 1, where ET is the elevated temperature MOE, ERT is the mean room temperature MOE prior to heating, fT is the elevated temperature frequency and f25°C is frequency measured at 25°C prior to heating on the elevated temperature specimen. This method does not take into account the coefficient of thermal expansion.

Equation 2

This method was used as imperfections in the dimensions and parallelism of the rectangular prismatic bars lead to large uncertainties in the calculation of MOE. By using the room temperature measurements in conjunction with the elevated temperature frequency response, uncertainty was reduced. This method is based on the equation given by ASTM E 1876-99 (see Equation 2), where E is the elastic modulus; C is a dimensional constant that depends upon the shape and size of the specimen, and Poisson's ratio; M is the mass of the specimen and f is the fundamental flexural mode of vibration.

Results

Figure 1. Sonic flexural MOE vs. composition and testing direction.

The measured densities varied from a low of 2.95 g/cc for the TH composition to a high of 3.17 g/cc for the WU composition. The data is shown in graphical form in Figure 1.

The error bars are +/-1 standard deviation. Table 1 gives the average bulk density for each composition along with its percent increase above the TH composition.

The measured MOE in flexure at room temperature varied from a low of 35 GPa for the WN to a high of 97 GPa for the WH composition. Tables 2-5 give the average and standard deviation of the flexural,

longitudinal,

and torsional MOE,

and Poisson's ratio for each composition along with its percent change from that of the TH composition. The overall average Poisson's ratio was 0.18, with a standard deviation of 0.07 for all compositions.

The calculated elevated temperature MOE in flexure varied from a low of 24 GPa for the WN composition at 850°C to a high of 97 GPa for the WH composition at 25°C. The maximum and minimum elevated temperature MOE and percent reduction in MOE from 25°C is given in Table 6. The MOE in general decreased from 25°C to approximately 750°C, at which point MOE increased.

Discussion of the Results

Figure 2. MOE as a function of temperature for self-flow castables with tabular alumina and white fused alumina aggregate.

Room Temperature

The bulk density was found to be higher in all cases for the castables with white fused as opposed to tabular alumina aggregate. Bulk density changed very little with respect to cement level; the ultra-low cement castables have the highest bulk density. Sonic elastic properties, including MOE, Poisson's ratio and shear modulus were approximately the same for castables with white fused or tabular alumina aggregate. The high cement level castables had the highest room temperature elastic properties.

The increases in bulk density for the ultra-low cement compositions are due to this composition being originally developed as an ultra-low or no-cement composition. The other cement levels were adjusted by varying the amount of cement in the mix and holding the aggregate and additive constituents constant. The bulk density of the no-cement composition was expected to have the same bulk density as that of the ultra-low cement composition. This was not observed, and may be due to the hydrous phases of alumina cement having a lower packing factor than that of calcium-aluminate cement. It was also expected that the bulk density would increase in the order of high, low to ultra-low cement compositions due to the particle size distribution being optimized for a Furnas distribution with 5% by weight cement. The additional 5 and 10% cement added to the low and high cement compositions, respectively, should have decreased the packing efficiency. A decrease from the ultra-low was observed, but the low and high cement compositions have approximately the same bulk density. This is probably due to the hydrous and gel phase rearrangement in the castable coating aggregate and filling pores better in the high cement compositions than in the low cement compositions.

It was expected and observed that the white fused alumina aggregate based castables would have a higher bulk density than those of the tabular alumina aggregate based castables. This is caused by two factors: 1) the white fused alumina aggregate is denser than the tabular aggregate; and 2) the white fused alumina has a shape factor closer to spherical than the tabular alumina, allowing it to pack more efficiently.

It was expected that the elastic constants would follow approximately the same trend as the bulk density, as the MOE is a function of the bulk density and the square of the fundamental resonant which is function of the mean bond strength in the material.[36] It was assumed that the bond strength would be highest for the high cement compositions, with the bond strength reducing in proportion to the amount of bonding cement phase. It was also assumed that the hydratable alumina cement would have lower bond strength than the calcium-aluminate cement. The anticipated trend was not followed. The high alumina cement compositions did have the highest MOE, approximately twice that of the remaining compositions as shown in Figure 1 and Table 2; however, the low, ultra-low and no-cement compositions had similar MOE. The ultra-low cement compositions had the second highest MOE in flexure. This could be due in part to their higher density. The no-cement compositions had the lowest MOE, affirming the assumption that the alumina cement has lower bond strength than the calcium-aluminate cement. The low cement compositions had a lower MOE than the ultra-low cement compositions. This could be due to the higher density of the ultra-low compositions overshadowing the expected increase in bond strength due to the additional 5% cement, but this is contrary to what would be expected based on the two-fold increase in MOE for the high cement compositions. There is no clear trend of MOE with respect to aggregate type.

The other moduli, longitudinal and shear follow the same trends as shown in Tables 3 and 4. Poisson's ratio shows no clear trends; the no-cement compositions had the lowest Poisson's ratio, as shown in Table 5, again leading to the conclusion that alumina cement has a lower bond strength than calcium-aluminate cement.

The flexural MOE is easy to determine and is considered to accurately represent the magnitude of the elastic modulus. On these refractories, the fundamental resonant frequencies needed to calculate the longitudinal MOE and shear (torsion) modulus are hard to accurately measure. Therefore, the calculated results are not believed to be strongly representatvie of the true values. Poisson's ratio is calculated from the flexural MOE and shear modulus. Due to inaccuracies in measuring the shear modulus, the Poisson's ratio is also suspect. Errors in Poisson's Ratio determinations may lead to an error of 0.3% in the calculation of flexural MOE and longitudinal MOE.[37] This small amount of error is negligible in terms of the overall standard deviation for the flexural MOE of 6.2% of the calculated value. The uncertainty of all values due to uncertainties in dimensional measurements is 6% of the value. The uncertainty due to mass measurements is only 0.02% and can be considered negligible in relation to the uncertainty in dimensional measurements. The uncertainty in fundamental vibrational frequency is 0.005% if a reading can be taken. The GrindoSonic rejects readings if damping or harmonics lead to large errors.

Figure 1 illustrates that there is no variation in sonic flexural MOE with respect to direction of testing. The transverse direction corresponds to bending across the 11.4 cm (4.5 in.) dimension of the 9-in. straight; the impact is applied to the 6.4 cm (2.5 in.) side. The normal mode of flexure corresponds to bending across the 6.4 cm (2.5 in.) dimension of the 9-in. straight, and the impact is applied to the 11.4 cm (4.5 in.) side.

Elevated Temperature

The elevated temperature MOE decreased rapidly for most of the samples from 25 to 250°C, as shown in Figure 2.

The slope decreased at 250°C, although MOE continued to slowly decrease to 750°C. Between 650 and 800°C, the slope of MOE changed sign, and the MOE rapidly increased to about 1000°C. At 1000°C the increase in MOE tended to level off. TH does not follow this trend after 850°C. At 850°C, MOE for TH rapidly decreased until 880°C, when no further measurements could be made. WH leveled off rapidly at 1000°C, and MOE began to slowly decrease. MOE for WN increased above 100°C to a value higher than that at 25°C. This could be due to water removal. At 220°C, the MOE for WN slowly decreased until 850°C. At 850°C, the MOE for WN slowly increased, until measurements stopped at 1030°C. The MOE as a function of temperature was very similar for materials containing white fused aggregate and tabular aggregate. The drop from room temperature MOE to the minimum MOE was between 30 and 50% with no clear trends in relation to cement content, as shown in Table 3. Water removal in the range of 100°C to 250°C caused a slight hump in the apparent MOE, as seen in Figure 2.

MOE reduction for the castables during initial heating was expected to be due to the conversion of high hydrates (AH3 gel, C2AH8) to low hydrates (AH3, C3AH(8-12) and C3AH6). Above ~800°C, the MOE increased due to the conversion of low hydrates to ceramic materials (A, CA and CA2), which begin formation at temperatures in excess of 600°C. In the case of the no-cement compositions, the change should be similar, excluding the calcia containing phases. The observed change in MOE is similar in shape to that expected for strength.[38] It has been reported that no-cement castables do not begin to attain good strength until 1000°C and should not be handled if heat treated between 400 and 1000°C.[39] No data on MOE as a function of temperature of cured refractory castables has been found in literature for comparison. References given earlier for MOE as a function of temperature were for prefired refractory castables. The changes in MOE could be estimated from the changes in intrinsic Young's Modulus of the constituent phases as a function of temperature and the rule of mixtures for spherical particles.[40,41] Sintering may occur at high temperatures, leading to shrinkage and the reduction in porosity. The change in MOE due to the reduction in porosity may be estimated as above, treating the pores as spherical inclusions or using empirical models developed for refractories.[20,42]

Water removal results in an apparent increase in MOE as the mass of the specimen is reduced by the water content. This results in a corresponding increase in apparent MOE, as the loss in mass is not taken into account during the calculation of MOE. The room temperature mass and dimensions were used for the calculations as explained in the experimental section of this article. The percentage increase in MOE will be equivalent to the percentage decrease in water content. Measured MOE will be higher by the amount of water lost: 6.5% for the high cement compositions, 6.25% for the low cement compositions, 4.5% for the ultra-low cement compositions and 6.25% for the no-cement compositions.

Thermal expansion of the specimen also causes a slight error in the MOE. The samples expand on average 0.8% during heating to 1000°C. The change in dimensions due to thermal expansion is on the same order of magnitude as the dimensional uncertainty and less than the measurement standard deviation. The total error in the calculated MOE is 2% due to thermal expansion to 1000°C.

Above 800°C, increased vibration damping due to increased internal friction made it more difficult to measure the resonant frequencies. Figure 2 shows that data points were lost for all of the materials above 850°C. The loss of data points may be due to damping, as the IET instrument used requires a clear signal of the harmonic frequency many cycles long prior to damping below the level of the background noise.[43] It was not possible to calculate elevated temperature MOE on the TN specimens as they are highly damped and require a geometry much larger than the elevated temperature apparatus can support in order to measure the fundamental resonant frequency of flexural vibration.

A Thorough Analysis

By using IET, a more thorough analysis was performed on the self-flow castable refractories.

The bulk density was found to be higher (~3%) in all cases for the castables with white fused as opposed to tabular alumina aggregate. Bulk density changed very little with respect to cement level, though the ultra-low cement castables have the highest bulk density (~3.1 g/cc). Sonic elastic properties, including MOE, Poisson's ratio and shear modulus, were approximately the same for castables with white fused and tabular alumina. The high cement level castables had the highest elastic properties (Flexural MOE ~90 GPa), with the remaining castables about half (~48 GPa). Poisson's Ratio was about 0.18 for all castables with large deviations in the measurements. Elevated temperature MOE decreased by 30-50% between 25 and 750°C, then increased above 800°C.

Through this technique, refractory suppliers and furnace designers can now obtain an accurate representative data on the modulus of elasticity (MOE) of modern refractories.

Editor's Note

The study described in this article was sponsored by The Refractory Collaborative Group of the American Iron and Steel Institute (AISI) under the Refractory Development Program at the University of Missouri-Rolla. This article is based in part on the dissertation submitted by W. L. Headrick, Jr. for the Ph.D. degree in ceramic engineering, University of Missouri-Rolla, Rolla, Mo.

For More Information

For more information about using the impulse excitation technique to measure the MOE of refractories, contact J.W. Lemmens Inc., Dynamic Materials Testing Instruments, 3466 Bridgeland Dr., Bridgeton, MO 63044-2606; (314) 770-2200; fax (314) 770-2262; or e-mail jwlinc@grindosonic.com.

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