SPECIAL REPORT: REFRACTORIES: Predicting Refractory Failure
It is common practice to assess damage resistance by measuring the material properties of the refractories that are contained in thermal stress damage resistance parameters such as Rst.1 However, thermal stress damage resistance is also dependent on the number of cracks that propagate during thermal shock, which is not taken into account in Rst. A better measure of damage resistance has been proposed2 and is given by:
Of course, C0 is difficult to measure directly. However, Co and ΔTc, and thus R"st, can be determined from resonant frequency measurements by measuring the dynamic Young's modulus retained after a series of simple water quenching experiments and by comparing these results to a theoretical model.
Resonant FrequencyA material will tend to vibrate at its natural resonant frequencies following a mechanical excitation. There are two methods to excite these frequencies:
- Sonic resonance,3 in which a driver attached to a frequency generator is used to vibrate the sample (forced vibration). The maximum amplitude is then measured on the sample as the applied frequency sweeps through the resonant frequency.
- Impulse excitation,4 in which a small hammer or impulse tool is used to strike the solid at specific locations.
In both cases, a well-defined standing wave is developed in the solid, and both methods yield the same results. For a bar with a uniform cross section, the fundamental flexural frequency of this wave is related to the size, shape, bulk density and elastic properties of the solid.5,6,7 All things being equal, the Young's modulus is proportional to the square of the frequency. Although the sonic resonance method was used for the purposes of this article (since it was based on some earlier work), the impulse excitation technique is now generally preferred because of its simplicity, speed and repeatability.8
Composite ModelA method to determine R"st is presented here in which the observed Young's modulus after water quenching is used as a measure of damage resistance. A theoretical model is then fit to the observed values and R"st is determined. The theoretical model is described next.
The only unknowns in Equation 4 are C0 and ΔTc; Eu* and W can be measured directly. C0 and ΔTc are determined simply from resonant frequency measurements. R"st can then be determined and the thermal stress damage resistance quantified.
*A minor correction was made for the lowering of Eu2 with soak temperature.
Refractory AnalysesTo demonstrate how thermal stress damage resistance can be quantified using resonant frequency measurements, some results obtained from the earlier study2 were reanalyzed. Two types of magnesia refractories were studied: one type was bonded with gels derived from ethyl silicate or with a gel derived from tetra-isopropyl titanate;9 the other type was a commercial, pressed refractory. The gel bonding systems were used because they had been shown to enhance thermal stress damage resistance.10
Four different grain size distributions, based on Andreasen11 size gradings, were used for the ethyl silicate bonded refractories. From fine to coarse size gradings, the refractories were labeled EA1, EA2, EA3 and EA4. The same size grading for EA2 was used in the titanate gel-bonded refractory (T-T). The pressed refractory (PB) was used for comparison purposes, as this material is low density and is known to have good thermal stress damage resistance.
The refractories were thermally shocked by quenching them in water. Bars of 25 x 25 x 128 mm were suspended with platinum wire into the hot zone of an electrically heated vertical furnace. After the samples reached thermal equilibrium, they were dropped into a bath of water flowing at 2 l.min-1. The bars were quenched from soak temperatures of 100-1300°C at 100°C intervals.
The temperature difference, ΔT, was taken to be the soak temperature. Five samples were quenched at each temperature. The extent of the damage caused by the thermal shock was evaluated by measuring the Young's modulus before and after quenching. Although the resonant frequencies were measured using the sonic resonance technique,12,13 similar results could have been obtained using impulse excitation.
C0 and ΔTc were estimated simply by measuring the Young's modulus after quenching and fitting Equation 4 to the results. A best fit was obtained with Mathematica* 5.1 by using an iterative least squares method. Once C0 and ΔTc were determined in this way, then the damage resistance of the refractories could be quantified through the parameter R"st (ΔTc/C03/2). In addition, the failure temperature difference of the refractories, ΔTf, could be predicted from Equation 3 (putting Cf = W/2).
The results of the quenching experiments are shown in Figure 2. As can be seen, the fit from Equation 4 is very good. R"st and ΔTf were determined for each refractory as shown and appear to give a reasonable measure of thermal stress damage resistance, as can be seen by comparing the left columns of the graphs in Figure 2. Generally, the damage resistance increased with the fines content and decreased with increasing mean pore size2 (see Figure 3), which is a similar result to that obtained by Carswell.14 As might be expected, the theoretical curves deviate most from the measured values when ΔT > ΔTf.
*Wolfram Research, http://www.wolfram.com .
In this work, the damage resistance of the refractories could have been increased by increasing the fines content and by using the titanate gel binder in place of ethyl silicate.
Improved PerformanceRefractory manufacturers can use the resonant frequency techniques shown here to more easily and accurately measure the damage resistance of their refractories than by measuring traditional parameters such as Rst. Armed with this knowledge, manufacturers will be able to reduce development times and improve the quality of their products.
For additional information regarding predicting refractory failure, contact BuzzMac International LLC at 620 North Sidney Place #104, Glendale, WI 53209; (414) 352-5419; fax (253) 540-9798; e-mail firstname.lastname@example.org ; or visit http://www.buzzmac.com .