Mechanical Properties of Fuel and Structural Materials
4.3.1 Strength of Materials at Different Loading Mode
The change of loading mode from tension to bending and compression for ZrC, NbC, ZrC+NbC at the deformation rate 103 s1 decreases brittleductile transition temperature Tbd and rises the level of ductile deformation. The strength level of ceramics in brittle condition in most cases depends on the stress state considerably so while passing from tension to bending and compression the strength increases in relation 1:(1.52.0):(810) (Table4.4) [14]. This phenomenon is associated with kinetic peculiarities of crack propagation. Start of a crack in tension begins under attainment of critical coefficient of stress intensity Kic, which gives rise to further avalanche crack propagation till full body fragmentation. The crack initiated under compression at Kic is capable to grow uniformly under increase of continuous load only on a curved trajectory and tends to take its orientation toward the compression axis (Fig.4.10).
Eventually, the transition of equilibrium crack propagation into avalanche crack stage, leading to full fragmentation is made possible after interaction of equilibrium growth of cracks at loads many times higher than the initial load for crack start. Experiments and theoretical analysis [6, 14] show that the total body fragmentation arises under the combined development of the interacting cracks after some equilibrium growth, as the growth of single crack cannot cause fracture even at infinite load. The steady creep rate of carbides does depend on kind of loading (compression, bending, tension) at temperatures T > (0.650.70) Tm [22].
Kind of sample, material 
Stress conditiona base (mm) 
Test number 
om/(omin omax) (MPa) 
Ao (MPa) 
W (%) 
m 
Cylinder, ZrC, 
I, 80 
703 
195/(105 — 135) 
43 
22.0 
4.0 
d = 3 — 4 mm, P = 7 % 
II, 15 
603 
217/45 — 345 
47 
21.7 
4.2 
dg = 9 — 20 ^m 
III, 50 
60 
80/57 — 129 
18 
22.2 
4.3 
IV, 4 
40 
97/36 — 158 
28 
29.3 
2.6 

V, 6 
36 
920/230 — 1240 
24 
26.0 
2.5 

Cylinder, d = 3 mm 
I, 80 
256 
215/45 — 345 
56 
26.0 
3.8 
NbC, P = 8%, 
II, 15 
340 
210/145 — 375 
50 
21.1 
5.0 
dg=15 ^m ZrC+5wt%C, P = 
I, 80 
120 
85/28 — 220 
43 
51 
2.3 
20%, dg = 15 ^m ZrC, P = 75 % 
VI 
35 
6.5/2.8 — 8.1 
1.3 
20.2 

ZrC+50%NbC, P = 65 
VI 
48 
9.1/2.3 — 13 
2.2 
24 
Table 4.4 Strength variation of refractory compounds at various loading modes (T = 280 K) 
The variation of loading conditions radically altering the strength level has no influence on the variation coefficient = S/o and Weibull coefficient m (Table4.4), where S is a root mean square strength deviation and am is a mean arithmetic strength value. The W and m are in the range 20 % and 35, respectively, for monophase dense and porous ceramic. The W value increases by two times for heterophase carbides with carbon inclusions owing to damage of carbide matrix. It is significant that the strength variation parameters of various ceramics in the brittle state are not affected markedly by electron band structure and atomic bonding but are governed primarily by the variation of surface and volume flaws.
Transition from axial compression to multiaxial compressive loading by intrusion of indenter initiates the ductile deformation in carbides of transition metals even at 80 K. Temperature dependence of microhardness reveals deformation peculiarities (Fig.4.11), undetectable under other kinds of loading.
The variation of loading conditions radically altering the strength level has no influence on the variation coefficient W = Aa/a, and Weibull coefficient m (Table4.4), where A a is a root mean square strength deviation and am is a mean arithmetic strength value. Between distribution parameters m and W there is a correlation. Comparative tests of large and small sets of samples have shown that reliable enough estimation am can be obtained from a test of 57 samples, and distribution parameters an, W and m on 2530 samples. The W and m are in the range of 20 % and 35, respectively, for monophase dense and porous ceramics. The W value increases by double for heterophase carbides with carbon inclusions, owing to damage of carbide matrix.
Transition from axial compression to multiaxial compressive loading by intrusion of indenter initiates the ductile deformation in carbides of transition metals even at 80 K. Temperature dependence of microhardness reveals deformation peculiarities, undetectable under other kinds of loading.
The first bend on the curve of microhardness takes into account the transition of gliding system {110} <110> to the system {111} <100> (Fig.4.11). This is typical for transition metal carbides [20, 21]. The second bend associated with further development of ductile deformation and disappearance of cracks near indentations. The variation of load on indenter from 200 to 1,000g changes the temperature of crack (c) disappearance from 800 to 1,400K. The dislocation configuration around indentation (d) and elastic distortion zone (A), measured by BergBarret method, changing with orientation (Fig. 4.12), give valuable information about evolution of the deformation mechanism. The ratio of elastic zone (A) to the length of dislocation scatters (L) decreases by two times with temperature rise from 300 to 1,080K through dislocation motion and relaxation of elastic stresses. Observation for changes
300K 
1080K 

P, g 
A/d 
L/d 
A/L 
A/C 
P, g 
A/d 
L/d 
A/L 
200 
6.7 
2.1 
3.2 
1.5 
200 
5.0 
2.9 
1.7 
100 
7.6 
2.3 
3.3 
1.8 

50 
8.5 
2.0 
4.3 
2.3 
of elastic distortion and dislocation motion after annealing of carbide samples with indentations at various temperatures permits to determine the starting stress as, for dislocation motion and yield stress ay [20]. The as for ZrC and other refractory carbides is high in the low temperature range of 0.150.3 Tm as in covalent crystals (Ge, Si) with high Peierls stress (intrinsic lattice resistance to dislocation motion). ay is three orders of magnitude higher than as. This suggests the controlling rate of dislocation generation and dislocation pinning. The value of as for metals is three orders lower than in ZrC and Ge. At temperatures above 0.4Tm, the deformation mechanism changes and diffusion rate of metal and carbon atoms increases markedly. An active nonconservative motion of dislocations causes the relaxation of local stresses and subsequent decrease of yield stress. Elongated dipoles and dislocation loops disappear and generation of dislocation networks begins. The further temperature increase up to 0.6 Tm brings into existence the cell appearance. The formation of
dislocation in carbides and metals during deformation are very similar. However, the temperature levels for initiation of dislocation motion and formation of cell structure are higher for carbides.
The fuel and structural NRE materials prepared predominantly by the methods of powder metallurgy have many structural defects, since the level of their strength is quite uncertain; varying within 1525 % nears the mean value. The strength level depends on the loading method; but the variation coefficient W is in fact independent of the loading method. Changes in the strength of singlephase and heterophase carbide materials in passing from tension to bending calculated by the Weibull method are in good agreement with experimental data. This circumstance is taken into account in determining the reliability of mechanically loaded NRE constructions.
Dispersion of strength in an engineering practice most often is appreciated by Weibull distribution function:
where a > an and an is a stress below which the probability of fracture is equal to zero, irrespective of the dimensions of a body; a0 is the normalizing parameter; m is the parameter describing uniformity of a material, i. e., degree of distribution uniformity of defects on the body’s volume. The distribution of stress estimated on the basis of a bendandtorsion test of hundreds of samples of ZrC and NbC submits to the normal law and is described conveniently by the Weibull function.