MODELING THE EFFECT OF HYDROGEN ON CREEP
BEHAVIOR OF ZIRCALOY CLADDING
VenkatRao Mallipudi, Stéphane Valance and Johannes Bertsch
Laboratory for Nuclear Materials, Paul Scherrer Institut, 5232 Villigen, Switzerland
Keywords: Dry storage, Zircaloy, Creep, Hydrogen, Hydride.
Abstract: During dry storage of used nuclear fuel, creep is the most likely degradation mechanism for the zirconium
alloy fuel cladding. The cladding integrity during dry storage depends on the internal fuel rod pressure, the
temperature, the amount of oxidation, irradiation hardening and the content of hydrogen which has been
taken up during in-reactor operation. In this paper, the effect of hydrogen on the creep behavior of zirco-
nium alloy cladding material was investigated at the temperature of 400°C. Depending on temperature, hy-
drogen can be found in the material under the form of solid solution and/or precipitated hydride. To capture
this phenomenon, a numerical mesoscale model of the hydrogenated material has been built using the Finite
Element (FE) method. The numerical setup explicitly describes the hydrides as an inclusion in a hydroge-
nated matrix. The matrix creep behavior follows combined Norton-Bailey creep rules whereas the hydrides
are considered to be elastic material. The creep law was defined in FE Code ABAQUS using the user sub-
routine CREEP. The comparison of predicted creep behavior obtained from FE showed good agreement
with the results reported in literature. Particularly, our model is able to seize the competition between the
creep strain rate enhancement induced by hydrogen in solid solution and its reduction due to precipitated
hydrogen.
1 INTRODUCTION
Zirconium alloys are used as cladding material for
nuclear fuel in Light Water Reactors (LWRs) be-
cause of the low thermal neutron capture cross sec-
tion of zirconium, the good mechanical properties
and limited corrosion. The fuel cladding is the first
barrier against release of radionuclides and its inte-
grity is therefore essential. In order to maintain the
integrity, assessment of all relevant degradation and
failure mechanisms need to be considered (Rosen
and O'Connell, 1994). Dry storage is the solution
used by many facilities worldwide in order to in-
crease their storage capacity while awaiting a peren-
nial storing solution. During dry storage creep is one
of the degradation mechanisms for used fuel clad-
ding, as an excessive creep strain may lead to an
eventual ductile fracture (Blackbum et al., 1978).
The creep strain is limiting the possible life time,
during dry storage as well as dictating the maximum
allowable temperature in order to maintain the inte-
grity of the cladding. Therefore the integrity of used
fuel cladding during dry storage has been evaluated
by predicting its creep behavior. Mayuzumi and
Onchi (Mayuzumi and Onchi, 1990) proposed an
empirical creep model, which covers a wide temper-
ature range to be used under long-term storage con-
ditions. In the reactor environment, hydrogen is
generated in coolant water due to oxidation of Zry-4
or radiolysis, and diffuses into the cladding material.
Depending upon the temperature i.e. Terminal Solid
Solubility for Dissolution (TSSD), hydrogen can be
found in the material under the form of solid solu-
tion or/and precipitated hydrides. For example the
solubility limit of hydrogen in Zry-4 is about
170 ppm at 400°C (Rui and Xiaoxue, 2009) and
excess hydrogen forms zirconium hydrides. In the
framework of continuum mechanics, hydrides preci-
pitates in the α-Zr can be viewed as a metal-matrix
composite.
Among the different variations of zirconium al-
loys, the so-called Zircaloy-4 (Zry-4) is used as
cladding material for fuel in Pressurized Water Re-
actors (PWRs). The creep strain rates of Zry-4 under
annealed condition (annealed at 650°C for 4 hours)
show an increase when hydrogen is in solid solution
and a decrease when part of the hydrogen precipi-
tates as hydrides (Rupa et al., 2002). Setoyama and
293
Mallipudi V., Valance S. and Bertsch J..
MODELING THE EFFECT OF HYDROGEN ON CREEP BEHAVIOR OF ZIRCALOY CLADDING.
DOI: 10.5220/0003615402930299
In Proceedings of 1st International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2011), pages
293-299
ISBN: 978-989-8425-78-2
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
Yamanaka (Setoyama and Yamanaka, 2004) studied
the effect of hydrogen on creep behavior of zirco-
nium and Zry-4 using the indentation technique.
They observed an increase in the creep rate with the
addition of hydrogen when hydrogen is in the form
of solid solution. In addition, they stated that the
creep exponent is independent of hydrogen content
and the increase in creep rate is due to the change in
the Young’s modulus with hydrogen Yamanaka et
al., 2002).
Since the Zry-4 cladding material is subjected to
stress for long periods of time at elevated tempera-
tures, a thorough knowledge of creep behavior is
required for their engineering applications. How-
ever, costly and time consuming creep experiments
make it difficult to experimentally assess the creep
behavior of the cladding. Therefore, the develop-
ment of analytical and/or numerical approaches for
predicting the creep behavior is indispensable. How-
ever, the analytical models cannot directly represent
the actual creep behaviors of the heterogeneous
materials, because the local state of stress and strain
in the matrix is highly heterogeneous in nature.
On the other hand, numerical methods such as
the FE Method enable to evaluate the micro-
mechanical/meso-mechanical behaviors during the
creep of the heterogeneous materials, since they can
successfully model the time-dependent problems and
local stress field. Numerous reports can be found in
the literature explaining the numerical studies re-
lated to the creep behavior of heterogeneous materi-
als (Dragone and Nix, 1992, Sørensen et al., 1993
and Sabbah and Essam, 2007). Dragone and Nix,
Sørensen et al. developed numerical frameworks for
stress analysis and prediction of creep behavior of
metal matrix composites by using unit cell model-
ing. The creep behavior of magnesium alloys rein-
forced with short fibers was numerically determined
by Sabbah and Essam, using simple idealization of
the composite material. In their work, modeling was
carried out using three relationships describing sepa-
rately the three stages (i.e. primary, secondary and
tertiary) of the creep behavior of magnesium alloys.
The present paper focuses on the influence of
hydrogen in solid solution and hydrides precipitates
at 400°C on the creep behavior of Zry-4 using a
numerical modeling approach. The Zry-4 is consid-
ered as annealed and in sheet form. Thus, the result-
ing behavior may differ from that of typical Zry-4
tubes being used as cladding material and exhibiting
high deformation and thus residual stresses.
2 NUMERICAL MODELING
2.1 Creep Constitutive Law
The creep constitutive law for describing the creep
behavior of the Zry-4 matrix is similar to the one
used for magnesium alloys (Sabbah and Essam,
2007). An empirical relationship is applied for each
creep stage of the creep curve (primary, secondary).
A mathematical relationship for the description of
the creep behavior up to the secondary stage could
be achieved by combining these two relations as
follows:
sp
n
vs
m
n
vpeffc
AtmA
σσε
+=
1
,
(1)
where
effc,
ε
is the effective creep strain rate, σ
v
is
the von Mises stress, t is the time, and m, A
p
, A
s
, n
p
and n
s
are material constants. The first term (Norton-
Bailey) on the right-hand side of equation (1)
represents the primary creep and the second term
(Norton) describes the secondary state creep strain.
According to Setoyama and Yamahaka, the
change in creep strain with presence of hydrogen in
the form of solid solution is due to change of
Young’s modulus. The change in Young’s modulus
of Zry-4 as function of hydrogen content up to the
TSSD is given by the equation (2) by Yamanaka et
al. (Yamanaka et al., 2002) as follows:
,)..10518.21(
4
ECE
HH
×=
(2)
where E
H
is Young‘s modulus of Zry-4 with hydro-
gen in the form of solid solution at the content C
H
(ppm), and E
is Young‘s modulus of the material
without hydrogen.
Thus, the creep coefficients as a function of hydro-
gen content A
pH
and A
sH
can be written as follows:
.)].10518.21[(.
,)].10518.21[(.
1
4
1
4
×=
×=
s
p
n
HssH
n
HppH
CAA
CAA
and
(3)
To predict the creep behavior of Zry-4 with the
presence of hydrogen in the form of solid solution,
in the present work, equation (1) with the modified
creep coefficients according to the equation (3) is
used. While for further increase of hydrogen content
(hydrogen is precipitated in form of hydrides), a
numerical mesoscale model of the hydrogenated
material has been built using the FE method. The
numerical setup explicitly describes the hydrides as
an inclusion in a hydrogenated Zry-4 matrix. The
creep behavior the hydrogenated Zry-4 matrix fol-
lows a combined Norton-Bailey and Norton creep
rule equation (1) and its creep strain coefficients are
SIMULTECH 2011 - 1st International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
294
defined according to the equation (3), whereas the
hydrides are considered to be elastic material. The
creep law was implemented in FE code ABAQUS
using the user subroutine CREEP.
2.2 Details of Hydrided
Zircaloy- 4 a - Finite Element
Modeling.
Hydrided Zry-4 consists of the idealized, untextured
hydrogenated matrix (i.e. hydrogen up to TSSD limit
dissolved in Zry-4 matrix) and precipitated hydrides.
The size of the hydrided Zry-4 considered in the
present work is 600 μm x 600 μm as the thickness of
the cladding material is approximately 600 μm. The
distribution of hydrides is assumed to follow the
symmetries about the radial and transverse axes,
hence in the present work, one quarter of the hy-
drided Zry-4 was modeled (300 μm x 300 μm). It
was also assumed that all the hydrides are δ type
(Daum et al., 2009) and that the bonding between
hydrides and Zry-4 matrix is perfect. The orientation
and length distribution of hydrides have been taken
from scaling the measured real hydride distribution
in a cladding tube (
Valance et al., 2010). The thickness
of the hydrides considered is 0.5 μm. The FE simu-
lation code ABAQUS was used to carry out the
finite element modeling and analysis. The hydrided
Zry-4 was discretized, using four-noded plane stress
solid elements with reduced integration (CPS4R).
After checking for convergence, approximately
45000 elements and 65000 nodes were used in the
FE mesh. The hydrogenated Zry-4 matrix was con-
sidered as elasto-plastic with creep, while hydrides
were considered as elastic bodies. The material
properties of non-hydrogenated Zry-4 matrix were
taken from the literature (Puls et al, 2005). The elas-
tic properties of the hydrides were assumed to be the
same as for Zry-4 matrix, as reported in the literature
(Nho et al., 1989), at room temperature the mechani-
cal properties of solid hydrides remain about the
same as the original zirconium alloy and decrease
with temperature at about the same rate as the zirco-
nium alloy. The Young’s modulus and Poisson’s
ratio at 400°C are 74.78 GPa and 0.346, respective-
ly. The creep parameters used here for non-
hydrogenated Zry-4 are A
p
=
4.06x10
-14
MPa
-n
hr
-1
,
A
s
= 9.16x10
-19
MPa
-n
hr
-1
, n
p
= 5.2
,
n
s
= 6.97 and m =
0.34
obtained experimentally in this study (not re-
ported here). The Young’ modulus E
H
and creep
coefficients (A
pH
and A
sH
) for the hydrogenated Zry-
4 matrix were estimated according to the equations 2
and 3.
In order to predict the creep behavior, finite ele-
Figure 1: Hydrided Zry-4 (hydrogen content = 500ppm)
with boundary conditions.
ment calculations were performed in two steps: first,
the stress field in the hydrogenated Zry-4 matrix and
hydrides is calculated for a given initial tensile stress
in terms pressure (equal to the stress) using a nonlin-
ear elastic-plastic calculation at time t = 1x10
-10
hour. The stress is then kept constant and subsequent
time-dependent creep analyses were performed. The
large strain FE model is employed by invoking the
NLGEOM option within ABAQUS. Figure 1 illus-
trates the boundary condition for the FE analysis.
The average creep strain versus time curve was
computed by taking the ratio of average elongation
at the load application region (see Figure 1) to the
original length of microstructure.
3 RESULTS AND DISCUSSION
Figure 2 depicts the von Mises stress distribution of
hydrogenated Zry-4 matrix for a hydrogen content of
500 ppm initially and after 250 hours at 400°C under
a stress of 120 MPa. From this figure it can be ob-
served that the von Mises stresses are reduced in the
matrix as a consequence of the compressive stresses
induced in the matrix during creep. Though there is
a slight increase in local stresses (131 MPa to
147 MPa) the reduction in stress around the hydrides
is much higher. The von Mises stress in the matrix
around the hydrides was initially about 115 MPa for
an applied stress of 120 MPa, and is reduced to
58 MPa after 250 hours. The reduction in stress is
about 50%. As the equivalent stress level is de-
creased, the creep strain rate decreases. The magn-
tude of stress depends on the distribution and quanti-
ty of hydrides in the hydrogenated matrix.
MODELING THE EFFECT OF HYDROGEN ON CREEP BEHAVIOR OF ZIRCALOY CLADDING
295
Figure 2: von Mises stress distribution of sample with a 500 ppm loaded under 120MPa at 400°C; (a) initially and (b)
250 hours von Mises stress filed (stress direction according to figure 1).
Figure 3: von Mises stress distribution at 250 hours, creep duration for different hydrogen contents, (a) 300 ppm, (b)
400 ppm, (c) 450 ppm and (d) 500 ppm (stress direction according to figure 1).
and the creep strain dropped to 4.05% when the
hydrogen content was 500 ppm. The comparison of
creep strain without hydrogen and with 170 ppm
hydrogen content shows a relative increase of creep
strain by 28%, whereas the creep strain without
hydrogen and with 500 ppm hydrogen content shows
a relative decrease of 51%. At a hydrogen content of
240 ppm, the same creep strain as for a Zry-4 with
out hydrogen was predicted.
Figure 3 shows the von Mises stress after
250 hours at 400°C and under a stress of 120 MPa
for different hydrogen contents. From this figure it
can be seen that the von Mises stress in the matrix
decreases with increase of hydrogen content, which
leads to a reduction in creep strain.
The overall creep strain as a function of time for
SIMULTECH 2011 - 1st International Conference on Simulation and Modeling Methodologies, Technologies and
Applications
296
Figure 4: Creep strain versus time for different hydrogen contents.
different hydrogen content and creep strain after
250 hours is shown in figure 4. The creep strains
increases with the increase of hydrogen content up
to the TSSD, thereafter decreases for further in-
crease of hydrogen content. Similar behavior was
reported in the literature by Rupa et al., 2002. After
250 hour the maximum creep strain was found to be
10.23% when the hydrogen content was170 ppm
(corresponding to TSSD for temperature 400°C),
A similar trend in creep behavior is observed for
the other stress levels studied in this work. The creep
strains (on log scale) at 250 hours at a temperature
of 400°C and under different applied stresses
(80 MPa, 100 MPa, 120 MPa and 130 MPa) are
shown in figure 5. The creep strain increases with
stress magnitude, however, the hydrogen content at
which the creep strain equals the one for Zry-4 with-
out hydrogen decreases with an increase of the ap-
plied stress (indicated by the small circles in fig-
ure 5). The hydrogen content at which this is the
case is 442 ppm at 80 MPa, 302 ppm at 100 MPa,
262 ppm at 120 MPa and 251 ppm at 130 MPa.
Figure 6 shows the variation of the steady state
creep rates as a function of hydrogen content for
different applied stress values. The curves show that,
as expected for all the hydrogen contents below the
solubility limit, the steady state creep strains are
higher for higher applied stresses.
Figure 5: Creep strain (on log scale) at 250 hours as a
function of hydrogen content for different applied stresses;
the circles indicate the hydrogen contents for the same
creep strain as without hydrogen.
It can also be observed that the drop in steady
state creep rate is higher for higher applied stress
when the hydrogen content increases from 250 ppm
to 500 ppm. For a stress of 130 MPa, the drop in
steady state creep rate is about 68%, whereas the
drop is about 33% for a stress of 80 MPa. From
MODELING THE EFFECT OF HYDROGEN ON CREEP BEHAVIOR OF ZIRCALOY CLADDING
297
these steady state creep rates, the equivalent steady
state creep parameters are estimated. The equivalent
steady state creep parameters as a function of hydro-
gen content are depicted in figure 7. The stress ex-
ponents decrease linearly with the increase of the
hydrogen content, while the creep coefficients show
an exponential increase with hydrogen content.
Figure 6: Steady state creep strain rate as a function of
hydrogen content.
Figure 7: Steady state creep stress exponent (ns) and creep
strain coefficient (As) as a function of hydrogen content.
4 COMPARISON OF PRESENT
RESULTS AND LITERATURE
In order to validate the present model, it is attempted
to compare the calculated creep curves for Zry-4
with hydrogen contents of 180 ppm and 500 ppm
with those published by Rupa et al., 2002. Figure 8
reveals a good agreement of the creep curves ob-
tained in this present work and from literature.
Figure 8: Comparison of creep strain versus time curves
obtained by present work and literature Rupa et al., 2002
for two hydrogen contents.
5 CONCLUSIONS
In this paper a numerical model was proposed to
investigate the effect of hydrogen on the creep beha-
vior of Zry-4. This zirconium alloy being used as
tube cladding for nuclear fuel, the material has been
considered here as texture-free and in sheet form.
The creep behavior of hydrided Zry-4 is analyzed by
the Finite Element Method.
For all applied stresses, the creep strain increases
with increase of the hydrogen content up to TSSD,
and decreases for a further increase of the hydrogen
content. As the level of applied stress increases, the
hydrogen content for the same creep strain without
hydrogen decreases.
The stress exponent decreases linearly with in-
crease of hydrogen content, while the creep coeffi-
cient value shows an increase exponentially with
increase of hydrogen content. A comparison of pre-
dicted creep curves obtained from the present work
with the creep curves reported in literature showed
good agreement.
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