Creep of Polycrystalline MgO-FeO-Fe 203 Solid Solutions42 1 strength retained for a given A T . In part, these deviations can be attributed to differences between the crack geometry in the refractory samples and that in the mechanical model used to derive Eq.(1). This derivation also assumes equal crack size and neglects crack interaction effects. Also, the proper values for ylroF. 0 , and E , are those corresponding to the quenching temperature, rather than to room temperature, as in the present calculations. A very likely explanation can also be based on an increase in crack density with increasing AT as the result of an expected nonuniform initial crack-size distribution. This increase will automatically give rise to experimental curves which are steeper than the theoretical curves for constant N . Crack densities which increased with increasing A T were observed by Roberts and Wronalj and Butsch et d . I 6 in the quenching of high-strength technical ceramics. Nevertheless, the crack-density values for the theoretical curves in Fig. 7 can be shown indirectly to be approximately correct for the corresponding experimental data on the following basis. Since the typical strength-vs-AT curve (Fig. 4) exhibits the gradual loss in strength typical for stable crack propagation, the crack length in the refractory specimens prior to quenching should correspond approximately to the minimum in the pIotsofAT(.rrcu~E,,/Zy,,,,.)"~ vsl. As indicated by Eq. (3). this minimum is a function of crack density. The experimental curves in Fig. 7 suggest that the minimum occurs for crack lengths near 0.1 cm. The crack lengths in the unquenched specimens, as calculated from K,, and MOR for all compositions, range from 0.078 to 0.254 cm, with corresponding crack densities of -10 to 0.5 cm-*, respectively, in good agreement with the values obtained by comparing the experimental and theoretical curves in Fig. 7. Because ofthe coarse microstructure, however, the crack densities could not be determined experimentally. It appears then that Eq. ( I ) may be used with a degree of reliability, especially when more information on crack length and crack density becomes available.In terms of development of materials with increased thermalshock resistance, the results of the present program suggest that, in addition to decreasing the coefficient of thermal expansion and Young's modulus, efforts devoted to increasing fracture energies, in particular yltor., should be successful. In addition, increasing crack densities through microstructural control also is expected to lead to improved spalling behavior. The latter approach has already been taken in the development of highly thermal-shock-resistant ZrO, partially stabilized with CaO,I7 foundry molds made by the Shaw process, and In summary, the present research has demonstrated the importance of fracture energies in establishing the spalling resistance of high-A120, refractories.
