Client Data: Thermal Shock Testing MgO

The model used to predict the degradation in Young's modulus with quenching temperature difference is an extension of the Hasselman 2D model3. In this extended model, the refractory bar is assumed to have a cracked outer layer, due to the water quenching, and an uncracked inner core. So, the quenched refractory can be considered a composite material (figure 1).

The flexural rigidity of a bar of uniform cross-section is given by the product of the Young’s modulus (E) of the material and the second moment of area of the cross section (I) about the neutral axis (i.e., the stiffness due to the material multiplied by the stiffness due to shape). For the damaged refractory shown in figure 1, the total rigidity of the bar is the sum of the flexural rigidities of each component, thus:

...........................................1

If a uniform distribution of pre-existing cracks propagates simultaneously under the action of stresses induced by the quenching, the damaged layer will extend into the core as follows1:

...........................................2

where Cf = final crack length, C0 = initial crack length, =temperature difference, c = critical temperature difference (minimum temperature difference to cause significant change in Young's modulus)

This leads to1:

...........................................3

A damage resistance parameter, Rst'', based on equation 2 was proposed as an alternative to the Rst parameter advanced by Hasselman3 and is given by1:

...........................................4

where N = number of cracks per unit area

The only unknowns in Equation 3 are C0 and c; Eu and W can be measured directly. However, C0 and c can be determined indirectly from quenching experiments by fitting equation 3 to the data. Then R''st can be determined and the thermal stress damage resistance quantified, as shown in figure 2.

NOTE: f = quenching temperature difference estimated to completely fracture the bar; i.e. when Cf=W/2

PB = MgO bar cut from a pressed brick. T-T = MgO bar bonded with an alternative TiO2-based gel binder4.

The results above were obtained on ethyl-silicate bonded MgO refractories made with various grain size distributions (samples EA1-EA4). The curves were fit to equation 3 by adjusting assumed values of Co and c until the best fit was obtained. This was achieved automatically by using Mathematica 5.15.

The mean pore-size of each refractory was measured, using the water expulsion method6, and compared to R''st and f (figure 3)

As expected6, the damage resistance measured by R''st and f increased as the mean pore-size was reduced for the ethyl silicate bonded materials. Also, the titanate gel-bonded refractory (T-T) had a lower thermal stress damage resistance than would be expected from its mean pore-size. So, although the T-T material had a finer pore-size than the similar ethyl silicate bonded material with the same grain size distribution (adjacent point to the right in each graph), the damage resistance did not improve. From a thermal stress damage resistance stand point, the ethyl silicate materials are superior. However, the ethyl silicate materials contained much more second phase resulting in agglomeration of the fines - hence the coarser pore structure compared to T-T.