Influence of Structural Parameters on Strength and Fracture

The strength of ceramics is dispersed in brittle condition in considerably greater degree than the strength of metals. This feature is defined, first of all, by variation of both superficial and volumetric deficiency and lack of stress relaxation on stress concentrator’s influence on structural strength parameters.

The strength of ceramics in brittle condition is defined predominantly by the surface and volume defects [3, 14] and an alloying with formation of solid solu­tion has practically no influence on the strength. Severe surface relief on sintered ceramic samples or microcracks appearing after electromachining or diamond cut­ting is responsible for the low strength level [14]. Elimination of these surface defects by mechanical grinding and polishing increases the strength by 50-70 % leaving the strength variance practically constant at the expense of volume flaws. The volume defects in the form of large rounded flaws with sizes of 100-400 ц are responsible for 40 % of all the cases of fracture in monophase ceramics. In some cases, the fracture occurs at lower stress at the cost of zone peculiarities appearing during inhomoge­neous forming and subsequent inhomogeneous shrinkage during sintering.

Severe surface relief on sintered ceramic samples or microcracks appearing after electromachining or diamond cutting is responsible for the low strength level [14].

Fig. 4.13 Influence of surface sample defects of ZrC0.97 after an electroerosive cutting — (2), grinding (3), polishing (4), and indentation (1) on the average level of strength and extent of data dispersion [14]

Fig. 4.14 Origination of residual stresses on both lobes of twisted fuel elements ZrC+UC owing to structural and chemical inhomogeneity in groups of grains

Elimination of these surface defects by mechanical grinding and polishing increases the strength by 50-70 % leaving the strength variance practically constant at the expense of volume flaws (Fig. 4.13).

Introduction of more dangerous stress concentrators on a surface, than in volume of the sample, by an indentation, reduces the average strength level but decreases dispersion sharply.

The dangerous defects in the form of cracks should be estimated by an X-ray method based on a measurement of a broadening of X-ray lines at the application of load to the sample, placed in a special prefix to a diffractometer [23] (Fig.4.14).

The volume defects in the form of large rounded flaws with sizes of 100-400 ^m are responsible for 40 % of all the cases of fracture in monophase ceramics. In some cases, the fracture occurs at lower stress at the cost of zone peculiarities appearing

Fig. 4.15 Strength and deformation of ZrC with zone peculiarities (П2, П6) and without them (П0, П5) under tension in vacuum with deformation rate 3 — 10—3s—1 (a). Microstructure of ZiC with zone peculiarities: (П2) (b) and without them (П3) (c). Batches of ZrC are manufactured by cold rolling (П2, П3) and pressing (П5, П6) with following sintering at 2,800K in argon atmosphere 1 h [12]

during inhomogeneous forming and subsequent inhomogeneous shrinkage during sintering (Fig. 4.15).

These zones in the form of friable porous layers lower the strength by 30-50 %. Maximum of strength and Tb—d is increased by 300-400K in comparison with ceramics having the same porosity level but without these zones [12, 14]. In most cases, sources of failure of ceramic materials are small cracks faintly visible at the magnification of 1,000 with a radius many orders of magnitude lower than for large pores; so, the former are able to cause more dangerous stress concentration.

The availability of pores decreasing the body’s cross-section clearly reduces the strength. The pore size increased from 3 to 90 ^ and emergence of elliptical pore form at a constant porosity level led to strength reduction of ZrC under bending from 300 to 170MPa with constant porosity level of 5-7 %. The exact influence of porosity on the strength is difficult to determine as in most cases, simultaneously with porosity, other structural parameters are varied: grain size, surface and volume defects, and impurity segregation [3].

Structural parameters depend to a great extent on the chosen technological para­meters. The presence of pores in a material naturally reduces the cross-section of a body and its strength, which can be described, for example, by an empirical relation like

a = a0exp(—BP),

Fig. 4.16 Temperature strength dependence of zirconium carbides at bending (a) and compression (b) with various porosity at deformation rate 3 • 10-3s-1

where o0 is the strength of a body without pores and B is a coefficient depending on the pore size and configuration [24]. The temperature of brittle-ductile transition of ceramics versus porosity increases. For example, Tb-d of ZrC, NbC at raise of porosity from 7 to 60 % increase Tb-d by 400 K at a bend test and by 600-700 K at compression (Fig.4.16). The maximum strength, owing to suppression of a plastic deformation is decreased and shifted toward to higher temperatures. Similar changes occur at carbide-graphite compositions.

The relationship between strength and grain size is rather complicated due to simultaneous variation with grain size of flaws, segregation additives on the grain boundaries and ratio of grain and boundary volumes in ceramics [2, 3, 14] (Fig.4.16).

The primary recrystallization (annealing of material after preliminary deforma­tion) makes it possible to vary the grain size of ZrC in the wide range from 5 up to 2,500 ^ without altering the boundary conditions. In this case, the variation of grain size retains carbide strength at 280 K constant while a decrease of strength of ZrC samples is observed after accumulative recrystallization (Fig. 4.17). The latter is more common for ceramics, as mentioned in references. The yield stress o0.2 of ceramics follows Hall-Petch law in the temperature range 0.6Tm <T> Tb-d [25].

00.2 = 00 + kydg-1/2

where o0 is the Peierls stress and ky is the coefficient of deformation resistance through grain boundaries. The relationship is altered radically at temperatures above 0.6 Tm. The yield stress o0.2 decreases owing to the grain boundary sliding and rotation of crystals.

Microstructural defects such as pores, grain boundaries, and microcracks located between grains or phase components influence the resistance to cracks for materials prepared by powder metallurgy methods. The value of K1c for carbide single-phase materials does not exceed 3MPam1/2. As a rule, K1c no monotonically changes with temperature. First, K1c decreases or remains unchanged with increasing the

Fig. 4.17 Compression strength oc for ZrC in vacuum after primary recrystallization and bending strength Ob for ZrC obtained by accumulative recrystallization against grain size

Table 4.5 Results of rejection of fuel elements from ZrC + NbC + UC

Loading

mode

Level of loading

Orj (MPa) Orj /Om

Amount of fuel elements

Amount of rejection (%)

Strength gain (%)

Bending with rotation

125

0.6

300

5

5

140

0.7

1,800

8

20

175

0.85

450

35

23

Rotation

10

0.6

23,000

3

1.5

temperature and begins to increase only when plasticity develops. The effective surface energy depends on the environment in a complicated way.

For exclusion of the most defective work pieces and the decrease of strength dispersion, it is expedient to carry out rejection by a preliminary mechanical loading [6]. For achievement of a positive effect of the rejection, it is necessary for each product to install the mode and level of a loading on the basis of the statistical data about strength distribution taking into account a possible damageability and economic feasibility (Table4.5).

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