Stress Corrosion Cracking in a Dissimilar Metal Butt Weld in a 2 inch
Nozzle
by
Thomas E. Demers
An Engineering Project Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute
in Fulfillment of the Requirements for the Degree of
Master of Engineering in Mechanical Engineering
Approved:
____________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
April, 2012
Table of Contents
1.0
Introduction/Background and Purpose....................................................................................... 3
2.0
Input and Methodology .............................................................................................................. 3
3.0
2.1
Stress Intensity Factor (K) Solution ................................................................................... 3
2.2
Stress Input ...................................................................................................................... 7
2.3
Crack Growth Methodology and Growth Laws ................................................................ 11
2.4
Limiting Flaw Depth Methodology ................................................................................... 12
Results and Discussion ........................................................................................................... 13
3.1
Calculation of Stress Intensity Factor KI .......................................................................... 13
3.2
Calculation of Stress Corrosion Cracking Growth ........................................................... 15
4.0
Summary and Conclusion ....................................................................................................... 19
5.0
References .............................................................................................................................. 19
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Table of Contents
List of Tables
List of Figures
List of Symbols
Acronyms
Keywords
Acknowledgements
I would like to thank Professor Ernesto Guiterrez-Miravete and my Current and Former Westinghouse
colleagues David Ayres, Warren Bamford, and Reddy Ganta for their advice on this project and subject
matter.
I would like to thank Ya T. Wu for his work developing the residual stresses used as input to this report,
and his assistance in providing additional information and clarification when necessary.
I would also like to thank Westinghouse Electric Company for their financial support of my engineering
masters degree.
Abstract
Residual stress distributions in a dissimilar metal butt weld in a 2-inch nozzle due to an inside diameter
(ID) weld repair as well as a weld overlay (WOL) are available in a report submitted to Rensselaer
Polytechnic Institute (RPI) by Ya Tao Wu [1]. This information can be used as input to a stress
corrosion cracking evaluation for this component. Residual stresses are available for both before and
after the weld overlay, which provides the opportunity for comparison between how a flaw would
behave for each condition. It is expected that the weld overlay will significantly impact the behavior of a
flaw in the dissimilar metal butt weld.
In addition to weld residual stresses, stresses induced by mechanical loadings and pressure stresses
are also included. Representative stresses are used for this study based on experience in the nuclear
industry. Circumferential flaws are evaluated herein, where the flaw is oriented along the length of the
weld. Semi‐elliptical flaws of varying geometry on the inside diameter (ID) are considered. Aspect
ratios of 2, 4, and 8 are considered as reasonable flaw geometries based on experience. Flaw growth
calculations are performed, and the acceptability of flaws of different sizes are determined.
1.0
Introduction/Background and Purpose
2.0
Input and Methodology
2.1
Stress Intensity Factor (K) Solution
This project will study the growth of semi-elliptical, circumferentially oriented flaws in the butt
weld of a 2-inch pipe. The growth laws used herein (discussed in Section 2.3) require a stress
intensity factor as an input. Stress intensity factors for semi-elliptical surface flaws can be found
in API-579 [2]. Specifically, for evaluating stress corrosion cracking (SCC), flaws are postulated
on the inside diameter (ID) of the component. This is because flaws on the ID will grow due to
SCC, while flaws on the outside diameter and embedded flaws would not grow due to SCC
because they would not be exposed to the coolant in the pipe.
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Section C.5.14 of [2] provides the solution for a “Cylinder – Surface Crack, Circumferential
Direction – Semi-Elliptical Shape, Through-Wall Fourth Order Polynomial Stress Distribution
with a Net Section Bending Stress.” This is applicable to the scenario evaluated herein.
Equation 2-1: Mode I Stress Intensity Factor Solution
In Equation 2-1:

a = the flaw depth

t = the wall thickness

σ0 through σ4 are the coefficients of the fourth order polynomial of stress distribution
through the wall thickness.

σ5 and σ6 are the net section bending stresses about the x-axis and y-axis. For the
depth point, only σ5 is necessary for the calculation. Additionally, only one bending
stress is used herein, so the σ6 term is discarded.

The influence coefficients G0, G1, G5 and G6 for inside and outside surface cracks can be
determined using the following equations:
where the parameters Aij are provided in Table C.14 of [2] for an inside diameter crack
and β = 2φ/π
φ is the angle between the surface and the point being evaluated. In this case, φ = π/2
to obtain the stress intensity factor solution at the deepest point.
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
G2, G3, and G4 are calculated using the following equations for the deepest point (φ=
π/2):
where M1 through M3 are calculated as:
and Q is calculated as:
The ratio a/c is always less than zero for the aspect ratios evaluated herein.

pc = crack face pressure (2500 psi in this calculation)
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Figure 2-1: Component and Crack Geometry
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2.2
Stress Input
Stress input is available in [1] that contains the weld residual stresses. Two sets of stresses are
available; one that is applicable for an ID repair weld, and one that is applicable for a weld
overlay. Stress distributions are provided at 70°F and 650°F. Because this calculation will be a
stress corrosion cracking calculation, the stress distribution experienced during normal
operation is most applicable for studying the growth of a flaw. This corresponds to the stresses
at 650°F. These stress distributions can be seen in Figure 2-2 and Figure 2-3.
Figure 2-2: Axial and Hoop Residual Stresses at 650°F after ID Repair
Figure 2-3: Axial and Hoop Residual Stresses at 650°F after Weld Overlay (WOL) Repair
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The stresses that will drive a circumferentially oriented weld are the tensile axial stresses,
because they act normal to the surface of the flaw and will cause crack opening. As explained
in [1], the stresses already contain the axial stress due to the 2250 psi internal pressure
experienced by the pipe at normal operation. Steady-state thermal stresses would also be
included, because only the ID of the pipe sees the 650°F normal operating temperature.
In addition to the pressure, residual, and thermal stresses contained in the stress distributions
from [1], representative mechanical stresses must be considered. For this analysis, the
mechanical loads are summarized in Table 2-1. The loads provided are applicable to normal
operating conditions.
Table 2-1: Mechanical Loading
Normal Operation
Axial (lb)
0
Bend (in-lb)
10,000
To determine the stresses, the geometry of the butt weld is needed.
summarized in Table 2-2.
This geometry is
Table 2-2: Butt Weld Geometry
Dimensions - Butt Weld
Inside Radius (Ri)
0.8435
Outside Radius (Ro)
1.1875
Thickness (t)
0.344
Area (A)
2.194918
Moment of Inertia (I)
1.164211
in
in
in
In2
In4
The axial stress is calculated using Equation 2-2.
F/A + M∙c/I
Equation 2-2: Combined Mechanical Stress Equation
Where:
F = axial force for a given loading condition
A = cross sectional area
M = moment for a given loading condition
c = radius where the stress result is desired
I = moment of ineria
The mechanical stresses calculated for normal operating conditions are provided in Table 2-3.
Table 2-3: Normal Operating Condition Mechanical Stresses
Axial
Bend (OD)
Bend (ID)
Stress
0
10200.04
7245.25
Units
psi
psi
psi
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The stress distributions from [1] used to make Figure 2-2 and Figure 2-3 are provided in Table
2-4, along with the mechanical stress distribution for normal operation.
Table 2-4: Stress Distributions from [1] and Mechanical Stress Distributions (psi)
%
0%
4%
9%
13%
17%
22%
26%
30%
35%
39%
43%
48%
52%
56%
61%
65%
69%
74%
78%
82%
87%
91%
95%
100%
x-coordinate
(in)
0
0.01488
0.02976
0.04465
0.05953
0.07441
0.08929
0.10417
0.11906
0.13394
0.14882
0.1637
0.17859
0.19347
0.20835
0.22323
0.23811
0.253
0.26788
0.28276
0.29764
0.31252
0.32741
0.344
Radius
(in)
0.8435
0.85838
0.87326
0.88815
0.90303
0.91791
0.93279
0.94767
0.96256
0.97744
0.99232
1.0072
1.02209
1.03697
1.05185
1.06673
1.08161
1.0965
1.11138
1.12626
1.14114
1.15602
1.17091
1.1875
Residual Before WOL
43337
45784
48527
55110
61119
63763
65833
65923
64165
57895
47605
31467
14597
-3774
-21971
-37342
-40697
-43954
-47117
-51564
-56263
-56303
-45974
-35565
Residual After WOL
-56700
-55621
-54670
-55151
-55334
-53780
-52015
-49514
-47602
-47067
-46808
-46942
-46712
-45673
-44640
-44001
-44233
-44418
-44558
-41246
-37431
-33752
-30746
-27841
Mechanical
7245
7373
7501
7629
7757
7884
8012
8140
8268
8396
8524
8651
8779
8907
9035
9163
9290
9418
9546
9674
9802
9930
10058
10200
As indicated in Section 2.1, the input should be applied separately as a fourth order polynomial
of the stress distribution from [1], and the net section bending should be provided individually.
The stress distribution including the axial stress due to pressure, steady-state thermal, and
residual stress due to the inside surface weld repair (prior to the weld overlay (WOL)) is
provided in Figure 2-4. The stress distribution after the WOL is provided in Figure 2-5.
The stress distribution though the thickness of the butt weld is what will be used to evaluate
flaws. It can be observed in Figure 2-5 that after the WOL is applied, the entire butt weld is put
into compression.
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Figure 2-4: Stress Distribution for Normal Operating Conditions (650°F) (Before WOL)
Figure 2-5: Stress Distribution for Normal Operating Conditions (650°F) (After WOL)
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2.3
Crack Growth Methodology and Growth Laws
Crack growth in Alloy 82/182 welds is described in MRP-115 [3], which is a public document
available through EPRI. The Alloy 82/182 growth rates from [3] also match those available for
Alloy 82/182 in Section C-8511 of Section XI of the ASME Code [4]. Specifically, it provides the
following equations:
Equation 2-3: Alloy 182 Growth Rate at 617°F
More generically:
Equation 2-4: Generic Alloy 182 Growth Rate
where:
adot = crack growth rate at temperature T in in/h
Qg = thermal activation energy for crack growth (31.0 kcal/mole)
R = universal gas constant (1.103x10-3 kcal/mole-°R)
T = absolute operating temperature at location of crack (°R)
Tref = absolute reference temperature used to normalize data (1076.67°R)
α = power-law constant (2.47x10-7)
falloy = 1.0 for Alloy 182 and 1/2.6 for Alloy 82
forient = 1.0
K = crack tip stress intensity factor (ksi√in)
β = exponent = 1.6
Additionally, for the purpose of comparison, the growth rate for stainless steel available in
Section C-8520 of [4] was also used to predict growth. This allows observation of the increased
predicted crack growth in Alloy 82/182 welds versus typical stainless steel components.
The crack growth is performed in 1 month intervals or __ month intervals, depending on the set
of calculations. 1 month intervals were adequate for the calculations using the stainless steel
growth rate, however the allowable operating period is significantly reduced when using the
Alloy 82/182 growth rate, and a shorter interval was used to provide more data points over the
shortened operating period.
All crack calculations start with a flaw that is 10% through the wall of the component.
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2.4
Limiting Flaw Depth Methodology
The flaw depth can be limited by two things:
1. The stress intensity factor when compared to fracture toughness.
2. A limit load evaluation, which ensures that the remaining cross section of the component
does not experience plastic collapse.
Therefore, in this set of calculations, the stress intensity factor is compared to a fracture
toughness. The fracture toughness of Alloy 82/182 is not readily available, but based on
literature [] it is expected to be high compared to other materials. In order to come up with a
conservative value for use in these calculations, a fracture toughness of 150 ksi√in is obtained
from [5]. This corresponds to stainless steel. For these calculations, a safety factor of 3 will be
applied to this fracture toughness and a value of 50 ksi√in will be used going forward.
Additionally, allowable flaw depths are established based on limit load per Article C-5000 of [4].
MORE DETAIL
The most limiting allowable flaw depth, as determined by stress intensity factor or limit load
calculation per Article C-5000 of [4], is used to establish the final allowable flaw depth for a
given flaw and loading.
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3.0
Results and Discussion
3.1
Calculation of Stress Intensity Factor KI
Figure 3-1 and Figure 3-2 provide the stress intensity factors as a function of the flaw depth.
Figure 3-1: Stress Intensity Factor vs. Flaw Depth for Mechanical Loads Only
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Figure 3-2: Stress Intensity Factor vs. Flaw Depth for Combined Mechanical, Thermal, and Residual Loads
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3.2
Calculation of Stress Corrosion Cracking Growth
Figure 3-3: Stainless Steel Growth Rate Calculations - Mechanical Only
Figure 3-4: Stainless Steel Growth Rate Calculations (AR = 2) - Mechanical Only
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Figure 3-5: Stainless Steel Growth Rate Calculations (AR = 4) - Mechanical Only
Figure 3-6: Stainless Steel Growth Rate Calculations (AR = 8) - Mechanical Only
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Figure 3-7: Stainless Steel Growth Rate Calculations - Mechanical + Thermal + Residual
Figure 3-8: Stainless Steel Growth Rate Calculations (AR = 2) - Mechanical + Thermal + Residual
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Figure 3-9: Stainless Steel Growth Rate Calculations (AR = 4) - Mechanical + Thermal + Residual
Figure 3-10: Stainless Steel Growth Rate Calculations (AR = 8) - Mechanical + Thermal + Residual
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4.0
Summary and Conclusion
5.0
References
1. Wu, Ya T, “Residual Stress Study at the Dissimilar Metal Butt Weld due to the Weld Overlay
Repair on 2 inch Nozzle Using ANSYS,” Rensselear Polytechnic institute, Hartford, CT, April
2012.
2. API 579-1/ASME FFS-1, “Fitness-for-Service,” Annex C, “Compendium of Stress Intensity
Factor Solutions,” June 5, 2007.
3. Materials Reliability Program Crack Growth Rates for Evaluating Primary Water Stress
Corrosion Cracking (PWSCC) of Alloy 82, 182, and 132 Welds (MRP-115), EPRI, Palo Alto, CA:
2004. 1006696.
4. ASME Boiler & Pressure Vessel Code, Section XI, 2010.
5. BWR-VIP-76NP, Revision 1: BWR Vessel and Internals Project, BWR Core Shroud Inspection
and Flaw Evaluation Guidelines. EPRI, Palo Alto, CA: 2011. 1022843NP.
6.
7.
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