Effect of Hydrogen Isotopes on Delayed Hydride Cracking Behavior of Zr-2.5Nb Pressure Tube Material

Abstract

To study the effect of hydrogen isotopes on the delayed hydride cracking (DHC) behavior, Zr-2.5Nb pressure tube (PT) material was charged with about 100wppm hydrogen or deuterium and DHC tests were carried out between 202 and 283 °C. At 202 °C, DHC velocity ratio of hydrogen- and deuterium-charged Zr-2.5Nb PT material was less than the ideal value of √2. The lower velocity ratio was explained on the basis of terminal solid solubility for dissolution (TSSD) and residual hydrogen (H_R) present in deuterium-charged PT material. Using TSSD and H_R, a mixture rule was developed to predict the DHC velocity of deuterium-charged material (${V}_{DHC}^{D}$) as well as DHC velocity ratio of hydrogen- and deuterium-charged material. The mixture rule was evaluated using present data and data reported in literature.

Appendix

1.1 Rule of Mixture for Prediction of ${\varvec{V}}_{{{\varvec{DHC}}}}^{{\varvec{D}}}$ and ${\varvec{V}}_{{{\varvec{DHC}}}}^{{\varvec{H}}} /{\varvec{V}}_{{{\varvec{DHC}}}}^{{\varvec{D}}}$.

As mentioned in subsection 4.2, when H_R is equal to TSSD, all the H_R would be in solution and there would be no deuterium in solution. When TSSD is more than the H_R, both hydrogen and deuterium would be in solution. In this case, hydrogen and deuterium present in the solution would be H_R and TSSD-H_R, respectively. As per the rule of mixture, the ${V}_{DHC}^{D}$ would be governed by hydrogen and deuterium present in solution as a fraction of TSSD.

Let us assume a temperature such that TSSD ≥ H_R.

Hydrogen in solution as a fraction of TSSD = H_R/TSSD

Deuterium in solution as a fraction of TSSD = (TSSD-H_R)/TSSD

So, the predicted ${V}_{DHC}^{D}$ in terms of ${V}_{DHC}^{H}$ would be given by:

$$\left( {V_{DHC}^{D} } \right)_{P} = \frac{{H_{R} }}{TSSD} \times V_{DHC}^{H} + \frac{{TSSD - H_{R} }}{TSSD} \times \frac{{V_{DHC}^{H} }}{\surd 2}$$

(A1)

And predicted ${V}_{DHC}^{H}/{V}_{DHC}^{D}$ would be given by:

$$\left( {\frac{{V_{DHC}^{H} { }}}{{V_{DHC}^{D} { }}}} \right)_{P} = \frac{{V_{DHC}^{H} { }}}{{\frac{{H_{R} }}{TSSD} \times V_{DHC}^{H} { } + \frac{{TSSD - H_{R} }}{TSSD} \times \frac{{V_{DHC}^{H} { }}}{\surd 2}}}$$

$$\left( {\frac{{V_{DHC}^{H} { }}}{{V_{DHC}^{D} { }}}} \right)_{P} = \frac{1}{{\frac{{H_{R} }}{TSSD} + \frac{{TSSD - H_{R} }}{TSSD} \times \frac{1}{\surd 2}}}$$

(A2)

Equation (A2) can also be written as follows:

$$\left( {\frac{{V_{DHC}^{H} { }}}{{V_{DHC}^{D} { }}}} \right)_{P} = \frac{1}{{\frac{{H_{R} }}{TSSD}\left( {1 - \frac{1}{\sqrt 2 }} \right) + \frac{1}{\sqrt 2 }}}$$

(A3)

The values of TSSD were obtained from Eq. A4 [23]. The TSSD at 202, 250 and 283 °C is 14, 28 and 50 Wppm, respectively.

$${\text{C}}^{{{\text{TSSD}}}}_{{\text{H}}} = { 8}.0{8}0{\text{ x 1}}0^{{4}} {\text{x exp}}[ - {3452}0/{\text{RT}}]{\text{TSSD}}$$

(A4)

It must be noted that Equations (A1) to (A3) are applicable only when TSSD ≥ H_R. When TSSD < H_R, only hydrogen would be in solution, and hence, the ${V}_{DHC}^{D}$ would be fully controlled by residual hydrogen present in the form of solution and ${V}_{DHC}^{D}$ is going to be same as ${V}_{DHC}^{H}$ and ${V}_{DHC}^{H}/{V}_{DHC}^{D}$ would be one.