Heat Engineering

The heat resistance of refractory and ceramic materials is considered from the standpoint of processes of wave formation in solids. A model and a computational formula are suggested for determining the destructive temperature gradient δTd. The quantity characterizing the dissipation of energy under a thermal load is equal to the ratio of the heat wave to the longitudinal acoustic wave in the solid body. The analytical formula for the disruptive temperature gradient contains only fundamental characteristics of the solid body, namely, the coefficient of thermal expansion and the speeds of the heat wave and the longitudinal acoustic wave, which distinguishes it from the employed criteria of heat resistance that include a strength parameter. The calculated values of δTd of various refractory and ceramic materials agree well with the experimental data. The concept of a depth of penetration of the thermal field that is proportional to the mean free path of thermic phonons under the condition of a thermal shock and determines the value of δTd is suggested. For polycrystalline materials with a density close to the theoretical value the value of δTd is limited by the Debye temperature. In the case of single crystals the value of δTd depends on the mutual orientation of the heat flow and the crystallographic directions in the crystal. The disruptive temperature gradient in porous materials is determined by the ratio of the rate of fall of the thermal conductivity to that of fall of the elasticity modulus, depending on the porosity. A formula for calculating the ultimate (critical) heating (cooling) rates in a one-dimensional formulation is derived. The calculated critical heating rates for parts and specimens agree well with experimental data. The notion of a characteristic size of a body is introduced and the disruptive temperature gradient is determined as a quantity numerically equal to the rate of variation of the temperature field in the body (or on its surface) the characteristic size of which in the direction of the heat flow is numerically equal to the square root of the thermal diffusivity. A new physical interpretation of δTd is suggested as the critical rate of variation of the temperature field in the body (or on its surface) that corresponds to the maximum gradient of the internal energy upon attainment of which the interatomic bonds in the body break in planes parallel to the front of the heat wave. The interatomic bonds break under the condition that the stress in front of the wave attains an acoustic range that corresponds to the ultimate tensile strength of the material. The developed theory can be useful in designing and improving refractory and ceramic materials resistant to thermal shock.