Residual Stress Characterization In Zirconium Oxides Using
Synchrotron XRD
Manchester Materials Science Centre, The University of Manchester, Grosvenor Street , Manchester M1 7HS, United Kingdom
Efthymios Polatidis, Philipp Frankel, Jianfei Wei, Michael Preuss
Uses and corrosion of Zr-Alloys
Zr-alloys used as cladding materials of the fuel rods.
In service environments oxidation occurs limiting their service life.
OXIDE
METAL
Uses and corrosion of Zr-Alloys
Zr-alloys used as cladding materials of the fuel rods.
In service environments oxidation occurs limiting their service life.
Better understanding of the corrosion mechanisms could lead to improvement of the burn up efficiency.
Residual stresses in the oxide are believed to play key role on the corrosion properties of the material.
Origin of stressesTransformation strain. Transformation of Zr-ZrO2 is accompanied by volume dilatation. (volume of ZrO2 is 1.56 times greater than Zr)
How do stresses affect oxidation?• The tetragonal phase can be stress stabilised
• As oxidation proceeds stresses might be reduced in the oxide away from the interface, which could lead to t m phase transformation
• This phase transformation is associated with a further volume increase ─ cracks─ acceleration of corrosion kinetics
Stresses in Zr-alloys oxides
Synchrotron X-Ray diffraction experiment at BESSY EDDI, Berlin
Residual strain (along the oxide thickness) can be extracted by altering the incident angle theta. Sin2psi method.
Fixed angle
detector
Sample
Diffracted beam Incoming white beampsi
θ
m(-
111)
t(10
1)
Zr(
100)
m(0
02)
Zr(
002)
Zr(
101)
m(-
211)
m(2
11)
Zr(
102)
m(-
122)
m(2
21)
Zr(
103)
Synchrotron X-Ray diffraction experiment at BESSY EDDI, Berlin
Increasing penetration
Higher energy - greater penetration - depth profile
Diffraction spectrum for each measurement angle ψ
Lowest angle= highest energy
Max. Pen. greater than oxide thickness
Highest angle= lowest energy
Max. Pen. Only samples part of oxide thickness
≈
θ θθ
metal metal metal
Penetration depth with 2θ
Results
ZIRLO™ SR/80 days at 360°C ZIRLO™ SR/160 days at 360°C
Maximum stress - close to the O/M interface
Oxide Metal Oxide Metal
Distance from outer surface (um) Distance from outer surface (um)
Res
idua
l Str
ess
(MPa
)
Res
idua
l Str
ess
(MPa
)
Synchrotron XRD experiment at ESRF ID11, France
Using XRD diffraction in transmission geometry and monochromatic beam, the setup allows strain characterization along the oxide thickness:
DetectorSample
Diffracted cones
Incoming beam
Residual strain (along the oxide thickness) can be extracted by comparing “strain free” samples with strained lattice spacing values.
(dstrained-dstrain free )/dstrained = strain
y
z
oxide 85º95º
5º
-5º
For each measurement point
Diffraction Pattern
Synchrotron XRD experiment at ESRF ID11, France
For each measurement point
Diffraction pattern85º95º
5º
-5º
Diffraction spectrum
Synchrotron XRD experiment at ESRF ID11, France
Stress calculation
• Strain= (dhkl-d0)/d0
• Extract stress tensor using Hooke’s Law, knowing in plane (εxx) and out of plane
(εyy) strain.
x
y
oxide
Metal
z
FE analysis suggests that the out of plane stress (σyy) is equal to zero, thus out of plane strain (εyy) occurs due to Poisson’s contraction.
Results
Compressive stresses - Oxide
Balancing tensile stresses-Metal- High temperature/time-Creep
FEM simulating the stress due to oxide volume expansion and relaxation due to
creep
High TTensionHigh T
compression
Relaxed TensionHigh T
Relaxed compression
TensionHigh T
compression
Relaxed TensionHigh T
Relaxed compressionRelaxed compression
compression
Creep of the substrate
Measured Elongation by creep (M. Blat‐Yrieix et. al)FEM creep strain
Evolution of strain versus oxide thickness
Creep of the substrate
Blat-Yrieix M. et. al, Toward a Better Understanding of Dimensional Changes in Zircaloy-4: What is the Impact Induced by Hydrides and Oxide Layer?, Journal of ASTM International, Vol. 5, No. 9, 2008.
Distance from O/M interface (μm)
Creep of the substrate
Conclusions
• A stress profile exists through oxide thickness - maximum compressive
stresses near the O/M interface stress decay away from interface may enable
tetragonal to monoclinic phase transformation.
• Stress reduces with oxidation time.
• A stress profile may be produced by creep of substrate – however
the shape of the measured profile does not match the profiles predicted by
substrate creep alone.
• Stress profile affected by other factors such as cracks between the oxide
layers.
Thank you!