Abstract
High-resolution neutron radiography has been used to image bulk circumferential hydride lens particles in unirradiated Zircaloy 4 tubing cross section specimens. Zircaloy 4 is a common light water nuclear reactor (LWR) fuel cladding; hydrogen pickup, hydride formation, and the concomitant effect on the mechanical response are important for LWR applications. Ring cross section specimens with three hydrogen concentrations (460, 950, and 2830 parts per million by weight) and an as-received reference specimen were imaged. Azimuthally anisotropic hydride lens particles were observed at 950 and 2830 wppm. The BISON finite element analysis nuclear fuel performance code was used to model the system elastic response induced by hydride volumetric dilatation. The compressive hoop stress within the lens structure becomes azimuthally anisotropic at high hydrogen concentrations or high hydride phase fraction. This compressive stress anisotropy matches the observed lens anisotropy, implicating the effect of stress on hydride formation as the cause of the observed lens azimuthal asymmetry. The cause and effect relation between compressive stress and hydride lens anisotropy represents an indirect validation of a key BISON output, the evolved hoop stress associated with hydride formation.
| Original language | English |
|---|---|
| Pages (from-to) | 129-139 |
| Number of pages | 11 |
| Journal | Journal of Nuclear Materials |
| Volume | 496 |
| DOIs | |
| State | Published - Dec 1 2017 |
Funding
This work was supported by the US Department of Energy Nuclear Energy Fuel Aging in Storage and Transportation IRP under Grant Number IRP-2011-05352 and by the US Department of Energy Accident Tolerant Fuel IRP under Contract Number IRP-12-4728 . In addition, this work was supported by the University of Illinois Campus Research Board under Award Number RB17006 . The use of the CG-1D Cold Neutron Imaging Facility at the High Flux Isotope Reactor, Oak Ridge National Laboratory, is supported by the Scientific User Facilities Division, the Office of Basic Energy Sciences, U.S. Department of Energy. The Zircaloy 4 tube cladding was supplied by Westinghouse Electric Corporation by P. Xu and this is gratefully acknowledged. Appendix Derivation of Eqns. (3) and (4 ) in Section 3 is as follows. The total hydrogen concentration in [wppm] units is given by, [A1] C H = m H δ m H δ + m Z r δ + m Z r α 10 6 where the mass m superscripts denotes the phase and the subscripts the element. For 1 g basis of a mixed δ−ZrH 1.7 plus α−Zr phase specimen, [A2] m δ + m α = 1 g r a m m H δ = m δ 1.7 g / m o l 92.924 g / m o l ; m Z r δ = m δ 91.224 g / m o l 92.924 g / m o l ; m Z r α = m α Defining κ and β as, [A3] κ ≡ m α m δ a n d β ≡ 1.7 [ g / m o l ] 92.924 [ g / m o l ] Substituting Eqn. (A2) into Eqn. (A1) and using Eqn. (A3) we have, [A4] C H = β 1 − κ ⇒ κ ( C H ) = β C H − 1 The atomic number densities are defined as, [A5] N H ≡ n H δ V δ + V α a n d N Z r ≡ n Z r δ + n Z r α V δ + V α with volume elements given by, [A6] V δ = m δ ρ δ a n d V α = m α ρ α The number of atoms in the basis are, [A7] n T o t a l δ = m δ 92.924 N A n H δ = 1.7 2.7 n T o t a l δ n Z r δ = 1 2.7 n T o t a l δ n Z r α = m α 91.224 N A Substituting Eqns. A6 and A7 into Eqn. (A5) and using Eqn. (A4) we have the final result, [A8] N H ( C H ) = β · N A 2.7 · 1 [ g / m o l ] [ 1 ρ δ + κ ( C H ) ρ α ] − 1 [A9] N Z r ( C H ) = N A · [ 1 2.7 · 92.924 [ g / m o l ] + κ ( C H ) 91.224 ] [ 1 ρ δ + κ ( C H ) ρ α ] − 1 These are Eqns. (3) and (4 ) in Section 3 . Equation (A8) for N H ( C H ) is simplified assuming 1atom = 1.000 [gram/mol] for hydrogen for the substitution of β , but requires a unit correction as shown. The derivation of Eqns. (9)–(11 ) in Section 5 is as follows. First the volume fraction is given by, [A10] V f δ , i = V δ , i V δ , i + V α , i Using Eqns. A1 and A2 , we can write, [A11] C H = 10 6 1.7 R i ρ δ 92.924 ρ α + 91.224 R i ρ δ + 1.7 R i ρ δ Where, R i = V δ , i V α , i Solving Eqn. (A11) for R i yields Eqn. (10) in Section 5 , [A12] R i = C H i · 10 − 6 ρ α · 92.924 1.7 ρ δ − C H i · 10 − 6 ρ δ · 92.924 Finally, writing Eqn. (A10) in terms of R i yields Eqn. (9) in Section 5 , [A13] V f δ , i = 1 1 R i + 1 = R i R i + 1
| Funders | Funder number |
|---|---|
| CG-1D Cold Neutron Imaging Facility | |
| Scientific User Facilities Division | |
| US Department of Energy Accident Tolerant Fuel IRP | IRP-12-4728 |
| US Department of Energy Nuclear Energy Fuel Aging in Storage and Transportation IRP | IRP-2011-05352 |
| University of Illinois campus research board | RB17006 |
| U.S. Department of Energy | |
| Basic Energy Sciences | |
| Oak Ridge National Laboratory |
Keywords
- BISON
- Finite element analysis
- Hydride
- Neutron radiography
- Zircaloy