## The Thermal Stress Resistance

The thermal stress resistance (TSR) is the most important characteristic of the effiВӯciency of HRA construction elements [6, 14, 27, 28].

A thermal elastic stress can be easily determined at known temperature patterns from combined equations of stress and strains with consideration of thermal deforВӯmation. Dependences between shear stresses and strains, and also the static and geometrical equations are accepted without modifications on theory of elasticity [24, 29].

The thermal stresses a can be defined by following relationship:

a = E ■ a — ATm ■ Kf/(1 — ^),

where ATm = (Tm — T) is a calculated mean integrated temperature difference ATm = (Tm -1) at the moment of fracture (where Tm is a mean integrated temperaВӯture of a body cross-section and T is surface or center point temperature, assuming that properties of a material do not vary and material is elastic), a is a coefficient of thermal expansion, E is a modulus elasticity, ^вҖ”is PoissonвҖҷs ratio, Kf is form factor. Derived from the relationship at value Kf = 1 complex a(1 — ^)/E — a = ATm is accepted to

Fig. 4.21 TSR for ZrC disk (30 mm in diameter with thickness 2-3 mm) as function of temperature and heating rate. (1) 10K/s, (2) 50K/s,

(3) 100 K/s, (4) 200K/s

name the first criteria of thermal stress resistance R = at (1 — \,)/at E measured in degrees. The complex R’ = XR is a second criteria, which reflect ability of materials to maintain a thermal flow at stationary or nonstationary thermal influences.

The higher the heat conductivity X of a material is the greater the thermal flux that can be withstood by the body without its collapse. It should be noted that the choice of materials for heat insulators in constructions based on the value of R’ is meaningless. In this case, it is necessary to use the value of R for estimates because, given two materials with identical heat-insulating properties, the better material is the one capable of withstanding a greater temperature drop.

The TSR of most refractory ceramics lie in the range ofR = 30 вҖ”100 K (Table 4.6). The criterion R’ can change in more wide limits 100-1500 W/m. The thermal stress ath (causing appearance of first cracks) is slightly exceeds the tensile strength and ath/ab, lies in the range of 0.45-0.57 of bending strength value.

The knowledge of TSR versus temperature is necessary for the appraisals stability of ceramic articles under working conditions. The temperature dependence of TSR has three characteristic intervals . The TSR of ceramics is invariable in the elastic — brittle temperature range. A relaxation of thermal stresses increases the TSR with temperature rise in the second interval. The tests performed on ZrC disks by induction heating method  show this possibility (Fig. 4.21).

The R value of ZrC remains constant with temperature increase up to 1,700 K regardless of heating rate. The TSR criteria R and R’ of a porous ZrC considerably change when the materials porosity varies (Fig. 4.22). Pores reducing the crossВӯsection area of a body cause a drop in strength a and elasticity modulus E. The a and E dependencies on porosity P may be described by empirical relations of this sort:

a = a0exp(вҖ”BP), E = E0 ■ exp(вҖ”BP).

The invariability of TSR in the range from 500 to 1,700 K is conditioned excluВӯsively due to the constancy of strength in this range, since the E decay and a rise

with temperature compensate for each other and the product aE is kept practically constant. The lower is the velocity of thermal loading above 1,700 K the greater is the reduction of the local stresses and the greater is the up growth of TSR. The thermal fracture in the third temperature range cannot be observed when the thermal stresses relax more rapidly than their formation. The ZrC samples do not fracture even at 1,900 K at low heating velocities <10K/s and much less at the onset of the macroductility at 2,000-2,200 K.

Distribution of R values for ZrC, NbC measured on a representative number of samples (70-90) is characterized by exponential Weibull relation. The coefficient of variation W = S/Rm (S is deviation of TSR, Rm is average value) agrees closely with appropriate significance of the W value obtained under mechanical test of strength. The cyclic thermal loading does not decrease the carrying capacity of samples in elastic-brittle temperature range. TSR of the ceramic bodies can be seriously changed under combined influence of the thermal and mechanical loads .

TSR of the ceramic materials can be essentially raised by introduction of hard inclusions in a matrix. The introduction of second phases as carbon inclusions with the sizes varying from 0.5 up to 50 |x into ZrC and NbC matrixes inevitably reduces the strength but is capable to increase the fracture toughness by a factor 1.5-2 with an optimum choice of concentration and kind of carbon inclusions. With growth of the carbon content, the TSR either increased in case of use of carbon black or decreased for graphite . TSR of compositions with carbon black can be raised 2.5-3 times (Fig.4.23) due to an increase of relation a /E .

The volume content of the inclusions, their geometry and dimensions have also a notable effect on the TSR as shown by ZrC-compositions with diamond particles .

Use of synthetic diamond powders with a narrow spectrum of grains get to obtain the compositions (after sintering) with guaranteed dimensions of the carbon. The inclusions are distributed in the matrix uniformly due to a good mixing of the ZrC and diamond powders. In addition, the diamond volume change during the structural transformation has an active effect on the process of the composition compaction when sintering. With introducing small carbon particles (0.6-6 |x) up to 5 mass % of the strength and the fracture toughness are not practically changed but the modulus of elasticity is decreased considerably. Introduction of 50 |x particles results in simulВӯtaneous drop of a/E and Kic. Inadequate change of the strength and the modulus of

elasticity when increasing the volume content of the diamond particles, results in the a /E-value growth. Therefore, the TSR of the compositions with the diamond partiВӯcles 0.6-6 СҶ in size is increased to a greater extent. Apparently, some increase of the fracture toughness does not influence the TSR considerably. The TSR of composiВӯtions with carbon inclusions is left invariable in temperature range 400-1,900 K and the advent of the first evidence of macroductility happens at more higher temperature up to 2,400 K.