ANL-ART-138
Evaluation of methods to determine
strain ranges for use in SMT design
curves
Applied Materials Division
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ANL-ART-138
Evaluation of methods to determine
strain ranges for use in SMT design
curves
Applied Materials Division
Argonne National Laboratory
July 2018
Prepared by
M. C. Messner, Argonne National Laboratory
T.-L. Sham, Argonne National Laboratory
Yanli Wang, Oak Ridge National Laboratory
R. I. Jetter, R. I. Jetter Consulting
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
Abstract
This report describes progress on developing a new method for creep-fatigue design that re-
duces over conservatism, improves the treatment of elastic follow up effects, and simplifies the
design procedure, when compared to the existing ASME Boiler and Pressure Vessels Code,
Section III, Division 5 method for creep-fatigue design. Specifically, this report describes
the development of one of the three components of the new creep-fatigue design method:
a design analysis method to represent the steady cyclic strain range in a component in el-
evated temperature service. The method developed here uses an elastic perfectly plastic
(EPP) analysis with a pseudoyield stress selected to bound the width of the steady state
stress-strain hysteresis loop. The report also provides a description of the in-development
creep-fatigue design method, including a plan to complete the method by developing design
curves and a method to account for stress multiaxiality.
ANL-ART-138 i
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
Table of Contents
Abstract i
Table of Contents iii
List of Figures v
List of Tables vii
1 Introduction 1
1.1 Motivation and objectives for a new creep-fatigue design method . . . . . . . 1
1.2 Description of tentative design method . . . . . . . . . . . . . . . . . . . . . 2
2 Simplified method for analyzing design strain ranges 5
2.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Comparison to SMT experiments . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Comparison to full inelastic two bar models . . . . . . . . . . . . . . 8
2.2.3 Comparison to full inelastic nozzle problem . . . . . . . . . . . . . . . 9
3 Progress on SMT design curves 13
4 Conclusions 15
4.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Acknowledgments 17
Bibliography 19
Distribution List 21
ANL-ART-138 iii
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
List of Figures
1.1 Damage diagram and creep-fatigue data from the in-progress ASME Alloy
617 Code Case. The inverse design problem — determine the best-estimate
design life for a particular experiment — would provide extremely conservative
predicted creep-fatigue lives for the experiments colored in red. . . . . . . . 2
1.2 Defining the follow up factor q. . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Graphical explanation of the EPP methods for bounding steady strain ranges
based on material isochronous stress-strain curves. . . . . . . . . . . . . . . 6
2.2 Model of the SMT tests as two bar problems. . . . . . . . . . . . . . . . . . 8
2.3 Strain range comparison between experimental SMT tests and EPP simulations. 9
2.4 Problem setup for the two bar comparison. . . . . . . . . . . . . . . . . . . . 10
2.5 Graphical summary of the data in Table 2.1. . . . . . . . . . . . . . . . . . . 11
2.6 Axisymmetric simulation of a nozzle subject to a cyclic pressure and piping
load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.7 Fringe plot comparing a full inelastic simulation to a consistent EPP simula-
tion of the nozzle problem defined in Fig. 2.6. . . . . . . . . . . . . . . . . . 12
3.1 Available experimental data for Alloy 617 at 950
◦
C. . . . . . . . . . . . . . . 14
ANL-ART-138 v
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
List of Tables
2.1 Comparison between full inelastic analysis and simplified EPP analysis for the
two bar problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
ANL-ART-138 vii
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
1 Introduction
1.1 Motivation and objectives for a new creep-fatigue design method
Section III, Division 5 of the ASME Boiler and Pressure Vessel Code [3] includes two creep-
fatigue design methods, one based on elastic analysis and one based on inelastic analysis. A
nuclear Code Case allows a third method, based on elastic perfectly plastic (EPP) analysis
[2]. All three of these design approaches rely on the same fundamental method for calculating
creep-fatigue damage. The method requires computing separate creep and fatigue damages
and then uses a damage interaction diagram (D-diagram) to assess the interaction of creep
and fatigue.
This approach is very empirical, relying on correlating structural loading conditions to
creep, fatigue, and creep-fatigue experiments. The step-by-step procedure is:
1. Calculate a representative strain range in the structure using one of the three types of
analysis. Use this strain range and a design fatigue curve, developed from experimental
data modified by safety factors, to compute fatigue damage as N/N
f
where N is the
number of design cycles and N
f
is the number of allowable cycles from the design
fatigue curve. For multiple cycles sum damage using a linear damage summation rule
(i.e. Miner’s Rule).
2. Calculate creep damage by constructing a representative stress relaxation history using
results from one of the three types of analysis. The Code defines creep damage as
D
c
=
R
dt/t
r
where t
r
is the time to rupture at a given stress, calculated using a design
rupture life correlation generated by lower-bounding experimental data. For multiple
cycles sum damage using a linear damage summation rule.
3. Given the separate values of creep damage D
c
and fatigue damage D
f
consult the
design D-diagram to determine whether the point (D
f
, D
c
) falls inside or outside a
design envelope.
There are several aspects of this procedure that may lead to non-optimal creep-fatigue
designs:
1. The factors applied to experimental data to generate the design fatigue curve — a
factor of 2 on the strain range and 20 on the number of cycles to failure — may be
significantly over conservative.
2. The method for computing creep damage is highly empirical and there is limited avail-
able experimental data to support it.
3. The three existing analysis methods only approximately account for the effect of elastic
follow up on creep-fatigue life. Elastic follow up is described in greater detail below.
It tends to reduce the creep-fatigue life of test specimens, all other conditions being
equal, and so has a significant effect on the creep-fatigue design of actual components.
4. The D-diagram approach for representing creep-fatigue interaction is over conservative
even when compared to the creep-fatigue experimental data used to construct the
design envelope.
ANL-ART-138 1
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
0.00 0.25 0.50 0.75 1.00
Fatigue damage
0.0
0.2
0.4
0.6
0.8
1.0
Creep damage
Figure 1.1: Damage diagram and creep-fatigue data from the in-progress ASME Alloy 617
Code Case. The inverse design problem — determine the best-estimate design life for a
particular experiment — would provide extremely conservative predicted creep-fatigue lives
for the experiments colored in red.
5. The overall procedure has been perceived as complicated and difficult to execute. In
general, calculating creep damage with the Code procedure can be challenging, partic-
ularly for the elastic analysis methods where the relaxation profile must be constructed
through a complicated series of rules designed to account for plasticity and creep in an
otherwise linear elastic solution.
Figure 1.1 shows an example of the fourth issue in this list. This figure shows the
Alloy 617 D-diagram proposed by an in-progress Code Case and the underlying creep-fatigue
experimental data used to justify it. The proposed D-diagram adequately envelopes the
available experimental data. However, when compared to the points highlighted in red, it
is extremely conservative compared to the data. An improved procedure might reduce this
over conservatism.
Most of these issues tends to bias the Division 5 creep-fatigue design procedure towards
being over conservative. The Code procedures are viewed by the design community as very
conservative, possibly to the point of forcing uneconomical designs.
While all the listed issues are significant this report only addresses the final three. This
report describes progress towards an improved creep-fatigue design method that reduces over
conservatism, accounts for elastic follow up more accurately, and is easier to execute.
1.2 Description of tentative design method
The design method outlined here is based on experimental data from Simplified Model Test
(SMT) specimens. These specimens can be called “key-feature” tests as they represent many
of the important aspects of creep-fatigue in actual structural components. Test variables that
can be controlled in the SMT framework include the standard creep-fatigue variables of strain
range and hold time, but also the elastic follow up factor and the stress concentration factor.
Previous publications describe the development of these test specimens [10–12].
ANL-ART-138 2
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
Strain
Stress
Prior loading
During stress
relaxation
Actual, with follow up
Elastic
Pure strain
control
Subsequent
loading
(a) Definition of the follow up factor q.
0 25 50 75 100
Time (hrs)
180
190
200
Stress (MPa)
q = 1
q = 2
q = 3
q = 4
q = 5
(b) Effect of follow up on simulated stress relax-
ation curves.
Figure 1.2: Defining the follow up factor q.
Elastic follow up is resistance to stress relaxation in a test article or component caused
by a connection to another structure with a large amount of stored elastic energy. In the
uniaxial sense, it is a reduction in the relaxation rate caused by the gauge section being
mechanically linked to an elastic spring.
Figure 1.2a shows the definition of the elastic follow up factor, used here to quantify
the amount of follow up for a given combination of structural geometry and loading. Note
q = 1 means follow up has no effect — the loading is purely strain controlled. Figure 1.2b
shows simulation results quantifying the effect of follow up on stress relaxation. Increasing
amounts of follow up slow relaxation and therefore increase creep damage during the stress
relaxation part of a creep-fatigue cycle.
Accurately accounting for elastic follow up is therefore important in the creep-fatigue
design of components in elevated temperature service. The current Code rules deal with
follow up in an ad hoc manner.
An improved creep-fatigue design method could use data from SMT tests to better cap-
ture elastic follow up effects. At the same time the design process could be simplified and
the amount of over conservatism reduced to produce more economically efficient designs.
The conceptual design method explored in this report has only two steps:
1. Perform a structural analysis that represents or, at least, bounds the stable cyclic strain
range at all points in a component under elevated temperature, cyclic load. Calculate
a scalar effective strain from this analysis.
2. Compare the effective strain to a design chart that bounds elastic follow up and creep
hold time in high temperature nuclear structural components. The design chart will
be setup like a standard fatigue chart; given a strain range it provides a number of
cycles to failure. Compare the design allowable cycles to the actual number of design
cycles to complete the creep-fatigue design.
This report focuses on the first step in the process: determining a bounding strain range
ANL-ART-138 3
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
using a simple structural analysis for components under elevated temperature cyclic load.
Chapter 2 describes an elastic perfectly-plastic method of analysis for representing the sta-
ble cyclic strain range in such structures. This method is distinct from the previous EPP
methods for bounding long-term creep rupture, creep-fatigue damage, and ratcheting strain
accumulation. Chapter 3 briefly describes progress on developing design curves from SMT
data. Finally, Chapter 4 summarizes the conclusions developed here and discusses a path
towards completing the full design method.
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Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
2 Simplified method for analyzing design strain ranges
2.1 Method
Under cyclic load the stresses and strain rates at all points will eventually become periodic
in a structure made of a material with a constitutive response that can be represented with
a standard material model [9]. The specific requirement is that the material response follows
Drucker’s stability postulate. In this cyclic steady state the strain range — the width of the
stress/strain hysteresis loop — does not change cycle to cycle, though the center of the loop
may shift in the tensile or compressive directions [4]. The goal of this section is to develop
a simple analysis method that can represent or bound this stable strain range for a material
with a combined elastic, plastic, thermal, and creep constitutive response.
Elastic perfectly plastic (EPP) methods use an EPP analysis to bound the structural
response of a more complicated material. These methods typically retain the elastic and
thermal properties of the material but bound creep and plasticity using a pseudoyield stress,
which is not necessarily the actual material yield stress. The theory behind these types of
bounds has been developed over the past 30 years [5–8]. Two Code Cases allow the use
of EPP methods for ratcheting strain accumulation [1] and creep-fatigue damage [2] and
an in-progress Code Case will provide a method for bounding long-term creep rupture (i.e.
primary load design). These existing methods bound, respectively, ratcheting strain, creep-
fatigue damage, and creep rupture stress states. Each of the three existing methods uses
a different definition of the pseudoyield stress to bound the relevant quantity. This work
develops a similar method to bound the steady state strain range.
Consider the steady cyclic stress-strain hysteresis loop shown in Fig. 2.1 for strain-
controlled loading with holds on both the tensile and compressive sides of the cycle. The
goal of the EPP analysis is to represent the steady strain range ∆ε. Intuitively, an EPP
analysis using a pseudoyield stress equal to the lowest stress reached during the stress relax-
ation part of the cycle would bound the width of the full hysteresis loop, as shown on the
figure. Approximately, ignoring the effect of prior plasticity and creep on subsequent stress
relaxation, this relaxed stress is equal to the value of the material’s isochronous stress-strain
curve at a time equal to the cycle hold time and at the actual accumulated strain.
The actual accumulated strain cannot be determined directly from a simple bounding
analysis and a cycle may have multiple, unequal holds. Using the isochronous curve for the
longest hold during the cycle produces a conservative strain range, as the figure illustrates.
Similarly, using a lower value of the pseudoyield stress than the actual relaxed flow stress
will produce a conservative bound. Therefore, it is conservative to use a lower value of strain
when determining the pseudoyield stress from the isochronous curve. A reasonable value to
use is the apparent yield stress of the isochronous curve for a hold time equal to the cycle
period. Using the 0.2% offset provides a flow stress representative of inelastic flow, while
conservatively not accounting for any material hardening.
Fundamentally, this is the EPP method adopted here to bound the steady strain range.
Because of how the ASME Code defines the material yield stress S
y
and the Code isochronous
curves it is possible that the isochronous curve apparent yield stress may exceed the Code
S
y
for short hold times. Therefore, the recommended procedure sets the pseudoyield stress
to whichever of the two values is smaller.
The analysis procedure is then:
ANL-ART-138 5
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
Actual
Best bound
Lower bound
Isochronous curve
Actual
Conservative bound
Figure 2.1: Graphical explanation of the EPP methods for bounding steady strain ranges
based on material isochronous stress-strain curves.
1. Determine the maximum hold time during the cycle, t
max
.
2. Determine the pseudoyield stress S
p
as the lesser of the material yield stress S
y
and
the 0.2% offset stress for the material isochronous stress-strain curve for a time equal
to t
max
.
3. Run an analysis of the structure using a EPP material with the actual material elastic
and thermal properties and the pseudoyield stress S
p
. The analysis can neglect all
holds during the loading cycle, as the material model is rate independent.
4. Repeat the load cycle until the structure reaches the cyclic steady state. The analysis
does not need to model the full number of design cycles.
5. At each material point determine the steady cyclic strain range ∆ε by computing
the scalar effective strain from the steady periodic strain components and finding the
maximum effective strain range over the steady cycle.
The present report derives the EPP method intuitively, without a formal proof. Future
work ought to formalize the method by finding a mathematical bounding theorem. Fur-
thermore, a procedure will need to be created to handle load histories with multiple design
cycles, perhaps through a composite cycle approach like the one adopted for the existing
EPP Code Cases. Additionally, a scalar effective strain will need to be defined for multiaxial
loading. Currently, we use the von Mises strain as a first approximation.
2.2 Validation
The remainder of this chapter validates the EPP method for representing steady cyclic
strain ranges. The chapter describes two types of comparisons. The first type is a direct
ANL-ART-138 6
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
validation of the model compared to experimental data. The available test data is, at least
approximately, uniaxial and includes follow up effects. This means the sample stress state
is relatively simple.
The second type of comparison is a consistent comparison to a full inelastic finite element
simulation. The idea is to first run a finite element analysis of a potentially complex, realistic
component using a reference inelastic model. For this report this reference model is a non-
unified model representing 316H stainless steel superimposing an elastic strain, a thermal
expansion strain, a rate independent plastic strain, and a rate dependent creep strain. The
creep and plasticity models use a standard J
2
flow theory and the plasticity model uses
isotropic Voce hardening.
A second finite element simulation is then run to compare to the full inelastic results.
This second calculation is an EPP design analysis using consistent design data. In this
context, this means the EPP calculation uses the same elastic and thermal properties as
the reference model and sets the EPP pseudoyield stress using values of S
y
and isochronous
curve determined by simulated experiments using the reference model. This approach means
that the comparison is fair — the full inelastic calculation and the design data are consistent
— and means the reference inelastic model does not need to perfectly represent 316H steel,
as the design data is consistent with the inelastic model, not the Code design curves. This
approach allows the EPP method to be verified for more complicated structures and loading
histories than those available from experimental tests.
2.2.1 Comparison to SMT experiments
The first validation test compares the EPP method to SMT experiments conducted at Oak
Ridge National Laboratory. These tests were on samples of Alloy 617, and so the design
calculation uses the in progress Code Case values of the isochronous stress-strain curves and
the material yield stress.
The EPP calculations approximate the SMT geometry with a simple two bar problem.
Figure 2.2 shows the assumptions reducing the SMT specimen to two bars in series. The
SMT tests applies displacements at the top of the sample, but controls the displacements
to apply some cyclic displacement over the inner two stepped regions (δ in the figure). The
experimental result is a stress-strain hysteresis loop measured over the inner gauge region (ε
in the figure).
The corresponding two bar model assumes symmetry on the specimen centerline and
directly imposes the applied displacement to the outer bar 1, rather than control the dis-
placement at that point through feedback control between an extensometer and the machine
displacement. The two bar model neglects the triaxial stress state near the transition be-
tween the gauge and outer regions.
Oak Ridge National Laboratory has generated a large collection of experiments for Alloy
617 SMT specimens for a variety of imposed displacements δ, with a variety of specific
SMT geometries giving different follow up factors q, and at a variety of temperatures T .
Additionally, Idaho National Laboratory ran several standard, strain controlled creep-fatigue
specimens. Figure 2.3 compares the experimentally-measured steady, average, axial strain
range over the inner gauge to the two bar, EPP analysis predictions. In this figure the
abscissa plots the EPP strain range from the two bar analysis and the ordinate plots the
ANL-ART-138 7
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
1
2
Load frame
displacement
Applied
displacement
Figure 2.2: Model of the SMT tests as two bar problems.
experimentally-measured strain range. If the analysis method was perfect, that is there was
no difference between the experimental and EPP strain range, the data would all fall along
the black line plotted on the figure.
The creep-fatigue experiments fall along the line of perfect correlation. This is because
these tests are fully-strain controlled — the applied strain range by definition matches the
measured strain range — and of the corresponding EPP analysis is likewise fully strain con-
trolled. The more interesting data comes from the SMT tests. In these tests the displacement
applied to the outer gauge does not directly relate to the strains in the inner gauge due to
plasticity and creep and the geometric difference in cross section between the two sections.
For the SMT data the EPP analysis does not perfectly recover the measured strain
ranges. Some error is to be expected as the particular batch of Alloy 617 material will not
exactly match the Code description of the material due to heat-to-heat variation, there is
some prior history effect neglected by the EPP analysis, and due to general experimental
uncertainty. However, the EPP strain ranges strongly correlated with the measured strain
ranges, implying that the EPP method can be used to predict realistic design strain ranges
for a complete creep-fatigue design method. The squared Pearson correlation coefficient is
0.79, implying a strong correlation between the measured data and the EPP strain ranges.
The sample error is approximately uniformly distributed above and below the line of perfect
correlation, implying these discrepancies may be due to random error about an average
match between the experiments and the approximate design analysis.
2.2.2 Comparison to full inelastic two bar models
The second comparison is a consistent comparison to full inelastic analysis. As described
above, the reference inelastic material model approximates the elevated temperature response
of 316H stainless steel. Figure 2.4 shows the structural geometry and loading cycle used in
ANL-ART-138 8
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
0.00 0.25 0.50 0.75 1.00
EPP strain range (%)
0.00
0.25
0.50
0.75
1.00
Measured strain range (%)
R
2
= 0.79
Creep-fatigue
SMT
Figure 2.3: Strain range comparison between experimental SMT tests and EPP simulations.
the comparison. The two bars share a constant applied force. The figure shows the cyclic
temperature history of each bar. The delay in cooling bar 2 introduces differential thermal
expansion into the system, which causes non-uniform creep and plasticity in each of the two
bars. The EPP analysis was used to predict the steady cyclic strain range in each of the two
bars, compared to the full inelastic analysis, for a variety of loading conditions parameterized
by the applied load P and the delay time t
hold
. The common hold time for both bars at T
hot
is 1 hour. For these simulations T
cold
= 400
◦
C, T
hot
= 700
◦
C, and the heating and cooling
rates are both
˙
T = 30
◦
C/min. Both bars have equal 0.25 in diameters.
Two bar problems are often used to represent vessels under a combination of a primary
pressure load and secondary load from a cyclic thermal gradient. As such, this comparison
tests to see if the EPP method can accurately represent the steady strain range for a simple
realistic structure.
Table 2.1 lists the loading conditions used in the comparisons, the steady strain ranges
in each bar for the inelastic and EPP simulations, and the error for each bar between the
EPP and full inelastic simulations. In general, the discrepancy between the two calculations
is small.
Figure 2.5 is a graphical comparison between the inelastic and EPP simulations. The form
of the graph is identical to Fig. 2.3, described above. The graph shows that the EPP and full
inelastic strain ranges are nearly perfectly correlated, meaning in the absence of experimental
error and with no uncertainty in material properties the EPP method accurately captures
the steady strain range in a structural system. Two assumptions of the EPP method, the
lower-bounding decision to use the apparent isochronous yield stress and the absence of any
prior history effect on the flow stress, cause the small discrepancies between the EPP and
the inelastic strain ranges.
2.2.3 Comparison to full inelastic nozzle problem
Figure 2.6 describes the structural geometry and loading for the final validation example.
This is another consistent comparison between a full inelastic analysis and the EPP design
analysis method. The geometry is an axisymmetric representation of a flat vessel head with
ANL-ART-138 9
Evaluation of methods to determine strain ranges for use in SMT design curves
July 2018
1 2
time
temperature
Figure 2.4: Problem setup for the two bar comparison.
P t
delay
Inelastic range, EPP range, EPP error, Inelastic range, EPP range, EPP error,
(lbs) (min) bar 1 (%) bar 1 (%) bar 1 (%) bar 2 (%) bar 2 (%) bar 2 (%)
50 10 0.25 0.24 4.0 0.29 0.28 3.5
150 10 0.25 0.24 4.0 0.29 0.28 3.5
300 10 0.25 0.25 0.0 0.29 0.29 0.0
450 10 0.25 0.3 -20.0 0.29 0.27 6.9
-100 5 0.15 0.15 0.0 0.16 0.16 0.0
-100 10 0.25 0.26 4.0 0.31 0.31 0.0
-250 3 0.09 0.09 0.0 0.1 0.1 0.0
550 3 0.09 0.09 0.0 0.1 0.1 0.0
-550 3 0.09 0.09 0.0 0.1 0.1 0.0
-250 5 0.15 0.15 0.0 0.17 0.16 0.0
-100 8 0.23 0.25 -8.7 0.28 0.3 5.9
450 7 0.21 0.21 0.0 0.23 0.22 -7.1
-550 5 0.15 0.15 0.0 0.17 0.16 5.9
450 5 0.15 0.15 0.0 0.16 0.16 0.0
Table 2.1: Comparison between full inelastic analysis and simplified EPP analysis for the
two bar problem.
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July 2018
0.0 0.1 0.2 0.3
EPP strain range (%)
0.0
0.1
0.2
0.3
Inelastic strain range (%)
Bar 1
Bar 2
Figure 2.5: Graphical summary of the data in Table 2.1.
a nozzle leading to a pipe. The vessel head thickness is 1 inch, the vessel radius is 26.5
inches, the pipe thickness is 0.5 inches, and the pipe outer radius is 3 inches. The vessel,
nozzle, and pipe is subject to a cyclic pressure, shown in the figure, and a cyclic imposed
displacement on the pipe represents a load from a piping system. The whole structure is
held at T = 650
◦
C.
The results in Fig. 2.7 compare a full inelastic analysis to a consistent EPP design
analysis. Both simulations repeat the load cycle 20 times and compare the ASME Section
III, Division 5 equivalent strain range, plotted over the critical nozzle region. The EPP
strains well represent the full inelastic strain distribution, matching the location and relative
magnitude of the critical, highest strain range. Discrepancies between the EPP and the
full inelastic strains tend to be conservative, i.e. the EPP strain range exceeds the full
inelastic strain range. Overall this example shows that the EPP method can reliably bound
strain ranges in realistic high temperature components under realistic loads. Taken together,
these validation examples demonstrate the EPP method is a suitable analysis method for
determining design strain ranges for use with the improved creep-fatigue design method.
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Figure 2.6: Axisymmetric simulation of a nozzle subject to a cyclic pressure and piping load
Full inelastic EPP
ASME strain range
0.0% 0.1% 0.2% 0.3% 0.4% 0.5%
Figure 2.7: Fringe plot comparing a full inelastic simulation to a consistent EPP simulation
of the nozzle problem defined in Fig. 2.6.
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3 Progress on SMT design curves
The focus of this report is on developing the EPP method for representing design strain
ranges in components in high-temperature reactor operating conditions. This chapter pro-
vides a brief overview of the challenges in developing the second part of the complete design
method, the creep-fatigue design curves.
These curves will be developed from a database of experiments on SMT specimens.
In these tests the strain range, hold time, follow up factor, and temperature can all be
controlled independently. However, the design lives of actual reactor structural components
will far exceed the times examined directly in the experiments. Methods will be required to
extrapolate shorter hold times to longer hold times and to extrapolate larger strain ranges
to smaller strain ranges that cause failure in a longer amounts of time.
Previous work at Oak Ridge National Laboratory has collected data for several materials
using Type 1 and Type 2 SMT specimens, along with pressurized SMT tests [10–12]. This
data covers a wide range of temperatures, hold times, and elastic follow up factors. Of all
the test temperatures and test materials the most data is currently available for Alloy 617
at 950
◦
C. Figure 3.1 plots the available data for this material at this temperature in the
form that will be used for the design charts: a plot of strain range versus number of cycles
to failure.
Qualitatively, the data matches the expected trends. Creep-fatigue loading is more dam-
aging than pure fatigue loading and creep-fatigue loading with higher follow up is more
damaging than simple creep-fatigue loading with a follow up factor of q = 1. The green
circle on the plot is a Type 1 SMT specimen under pure fatigue loading, which is why it has
a higher than expected number of cycles to failure.
Given data of this type the steps towards creating a design curve would be:
1. Develop a model that explains and can extrapolate the data. This model should have
the form
N
f
= F (∆ε, t
h
, q, T )
where N
f
is the number of cycles to failure, ∆ε is the strain range, t
h
the hold time, q
the follow up factor, and T the temperature.
2. From engineering judgement and analysis of representative structural components de-
termine bounding values for the elastic follow up factor q and the hold time t
h
. This
reduces the model to a series of temperature dependent curves plotting the strain range
versus the number of cycles to failure. These would be the design curves for the new
creep-fatigue method.
3. Thus far the model would apply only to uniaxial load. The final step is to develop
a definition of the scalar equivalent strain range to capture observed multiaxial stress
state dependence in the failure data.
The previously collected data in Fig. 3.1 and similar data at other temperatures and for
other materials can be used to begin to work on a model. However, there is a significant
challenge in using the previous Type 1 and Type 2 SMT test data. These specimens did
not all fail in the straight gauge region of the specimens. Instead, many failed near the
transition radius stepping between the outer and inner diameters. The stress state near
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Fatigue
Creep-fatigue
Type 1 SMT
Type 2 SMT
Figure 3.1: Available experimental data for Alloy 617 at 950
◦
C.
this transition is not uniaxial, which complicates interpreting the failure data from these
experiments. Oak Ridge National Laboratory is developing test procedures which enforce
a uniaxial stress state at the failure location in SMT tests, still including follow up effects.
These tests are described in a companion report issued by ORNL [13]. Data from these
tests will be used, going forward, to develop the design curves following the process outlined
above.
The previous Type 1 and Type 2 sample data is still useful. It can be used to validate the
overall design procedure, including the equivalent strain range capturing multiaxial stress
state effects. A successful final design method should be able to predict the location of
failure (center gauge or near transition) in the previous SMT tests as well as bound the
measured number of cycles to failure. In addition, the specimens that failed in the straight
gauge portion of the test article can be included in the uniaxial database of result used to
determine the design curves.
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4 Conclusions
4.1 Summary
This report develops a design analysis method for the cyclic stable strain range in structural
components in high temperature service. The method is based on an elastic perfectly plastic
(EPP) analysis using a pseudoyield stress selected from values of the material isochronous
stress-strain curves. Several validation examples demonstrate the effectiveness of the method
in representing strain ranges in simple experimental tests and more complex, realistic struc-
tural components.
4.2 Future work
For the strain range analysis method future work should concentrate on providing a rigorous
proof of the proposed bounding method and on additional validation examples, likely focusing
on consistent comparisons to full inelastic simulations. Both efforts would support the use
of the EPP method in the design of high temperature nuclear structural components.
One additional issue to address will be the applicability of the proposed method of bound-
ing strain ranges to cyclic softening materials. These types of materials may not have the
stability required in the Frederick and Armstrong proof that the material response will be-
come steady. As such, modifications to the method may be needed to account for softening.
Chapter 3 provides an outline describing how to develop design curves from SMT data.
That chapter noted the challenges in using the existing Type 1 and Type 2 SMT test data
to formulate design curves but also noted that Oak Ridge National Laboratory has recently
developed improved test protocols that ensure future data will be collected for uniaxial
failures. Additionally, the improved test procedure provides finer control of the follow up
factor q, which could aid the development of a model to represent the test failure data by
providing finer granularity in the data for that particular test variable. With some caution,
inelastic modeling can also be used to develop methods for extrapolating creep-fatigue type
test data with follow up effects by directly simulating the new SMT test configurations.
These simulations would need to include a damage model to represent creep-fatigue failure.
This damage model would need to be selected carefully, in order to model realistic creep-
fatigue failure.
The final issue to be addressed is defining an effective strain measure to accurately rep-
resent multiaxial failure. Chapter 3 noted that the Type 1 and Type 2 SMT data could be
valuable for validating this strain measure. However, the stress state near the transition in
the SMT specimens is complicated. Creep-fatigue failure data, with follow up effects, for
simple test specimens with an easily-defined stress state would be more valuable for devel-
oping the procedure to account for multiaxiality. Future work, in collaboration with ORNL,
will develop tests of this type.
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Acknowledgments
The research was sponsored by the U.S. Department of Energy (DOE), under Contract
No. DE-AC02-06CH11357 with Argonne National Laboratory, managed and operated by
UChicago Argonne LLC. Programmatic direction was provided by the Office of Advanced
Reactor Technologies (ART) of the Office of Nuclear Energy (NE).
The authors gratefully acknowledge the support provided by Alice Caponiti, Director,
Office of Advanced Reactor Technologies (ART), Sue Lesica, Federal Manager, ART Ad-
vanced Materials Program, and Hans Gougar of INL, National Technical Director, ART
Gas-Cooled Reactors Campaign.
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Distribution List
Name Affiliation Email
Caponiti, A. DOE alice.caponiti@nuclear.energy.gov
Lesica, S. DOE sue.lesica@nuclear.energy.gov
Li, D. DOE diana.li@nuclear.energy.gov
ANL-ART-138 21
Applied Materials Division
Argonne National Laboratory
9700 South Cass Avenue, Bldg. 208
Argonne, IL 60439
www.anl.gov
Argonne National Laboratory is a U.S. Department of Energy
laboratory managed by UChicago Argonne, LLC
