Thermal Stress Formula for Estimation of Spalling Strength of Rectangular Refractories

For the purpose of designing a long life furnaces, much efforts toward preventing thermal spalling attack of inner lining refractories have been made. The present study has been undertaken to investigate the quantitative effect of the size, heating conditions, and external constrains on the thermal stresses in duced in a rectangular refractory heated from one end. The main results obtained are as follows : 1) According to the result of F.E.M. calculations, a large tensile stress (σz) perpendicular to the hot face which may cause thermal spalling cracking is induced along the center axis of a refractory heated from one end. 2) σz can be well approximated by the sum of two 2-dim. solutions, each corresponding to the analysis on the x-z plane and y-z plane. 3) The maximum thermal stress (σMZ) perpendicular to the hot face is approximately obtained using nondimensional functions Hstress, Hstrain, which are monotonously increasing functions. σMZ≅α ·E · T{ζx·Hstress (a /√ kt) + ζy · Hstrain (b/:√ kt) } Here, α : Thermal expansion coefficient, E : Young's Modulus, T: Temperature of hot face, a, b : widths of hot face, k : thermal diffusivity, t : elapsed time, ζx, ζz : parameters representing external constrains. Through this Eq. effects of sizes, heating condition, external constraints on the thermal spalling can be obtained quantitatively. It also explains the experimental results fairly well.