Degradation of 5 mol% yttria–zirconia by intergranular cracking in water at 300 °C

Abstract

Zirconia–5 mol% yttria has been used successfully for pH sensing in high temperature water (≥300 °C). However, this material, which consists of the cubic phase with 2–8 vol.% intergranular tetragonal precipitates, is not always stable in this environment and some batches were found to be fragmented by cracking within a few days. To study this effect, different samples of the material were structurally characterised and exposed to 300 °C water. It was found that the susceptibility to cracking increased with the volume content of the intergranular precipitates. The cracking mechanism was explained by the stress-induced grain boundary cracking of the cubic phase, the stress being due to the water-induced martensitic transformation of the tetragonal precipitates. A model has been proposed which allows to interpret the dependence of crack formation propensity on the size of the tetragonal precipitates.

Appendix

In this section, the stress intensity factor K _I is calculated for a crack ahead of a row of transformed precipitates as shown in Fig. 9. The distance between the transformation fronts approaching each other from both sides of the sample is 2b and the distance between the crack fronts is 2a. Therefore, the crack ahead of the last transformed particle has a length (b − a). This crack has to grow to a length d to reach the next particle. It follows that (b − a) values up to the interparticle distance, i.e. about 50 μm, have to be considered.

The lower part of Fig. 9 schematises the geometry by replacing the effect of the transformed particles by wedges of thickness 2 h inserted from both surfaces up to the innermost transformed particle. For this configuration, consisting of two wedges in a finite thickness plate no analytical expression for K _I was found. However, a solution for two wedges in an infinite specimen has been given by Tada [35]. This has been used since it is thought to be a good approximation, provided the wedge insertion depth is sufficient for surface proximity to be negligible.

The stress intensity factor given by Tada for the configuration shown in the lower part of Fig. 9, is as follows:

$$ K_{\text{I}} = {\frac{{Eh\left( {{\frac{\pi }{a}}} \right)^{0.5} }}{2kK (k )}} $$

(3)

where E is Young’s modulus (200 GPa), h is the half wedge thickness, a is defined above and K is a function of k tabulated in Appendix J.1 of [35] and

$$ k = \left[ {1 - \left( {\frac{a}{b}} \right)^{2} } \right]^{0.5} . $$

(4)

Cracks growing from a transformed to an untransformed particle have a length (b − a) which is always shorter than the interparticle spacing d. This means that, except for very small ligament sizes, a/b is close to 1 and k is close to zero. This allows to approximate (4) as

$$ k = \left[ {2\left( {1 - \frac{a}{b}} \right)} \right]^{0.5} . $$

(5)

For small k, K(k) is nearly constant and equal to 1.6. After modification, (3) can then be written as

$$ K_{I} = 0.392{\frac{Eh}{{\left( {b - a} \right)^{0.5} }}}. $$

(6)

There is no obvious way to express h as a function of precipitate size and distribution. To avoid this problem h was calculated supposing the average equivalent particle diameter 2R (Table 1) to determine the wedge height 2 h. Supposing that the particles show an isotropic linear expansion of 1.0% [29, 30], the expression for h is

$$ h = 0.0 1R. $$

(7)

Introducing (7) in equation (6) gives K _I as a function of crack size (b − a) and average precipitate diameter 2R

$$ K_{I} = 0.00196{\frac{E(2R)}{{(b - a)^{0.5} }}}. $$

(8)

Equation (8) was used to calculate the curves in Fig. 10.

It is acknowledged that considerable simplifications were necessary to arrive at expression (8). For example, only cracks perpendicular to the sample surface are considered, whereas in reality cracks occur in all directions. Furthermore, the precipitate density does not appear in the final expression. The absolute values for the stress intensity factor therefore should be considered with caution. However, the simplifying assumptions should affect the ranking of the three material types to a much lesser degree. The conclusion that the cracking propensity is dependent on the size of the intergranular tetragonal precipitates is therefore likely to be acceptable.