An Investigation into the use of FEA methods for the prediction of
Thermal Stress Ratcheting
by
Stephen Charles Huse
A Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Engineering Project Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
October, 2014
(For Graduation May, 2015)
i
CONTENTS
An Investigation into the use of FEA methods for the prediction of Thermal Stress
Ratcheting ..................................................................................................................... i
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
LIST OF SYMBOLS ........................................................................................................ vi
ACKNOWLEDGMENT ................................................................................................. vii
ABSTRACT ................................................................................................................... viii
1. Introduction.................................................................................................................. 1
2. Historical Review ........................................................................................................ 2
2.1
Bree Diagram ..................................................................................................... 2
2.2
Linear Thermal Discontinuity ............................................................................ 4
3. Theory .......................................................................................................................... 6
3.1
Discussion .......................................................................................................... 6
3.2
Conduction in a Hollow Cylinder ...................................................................... 7
3.3
Forced Convection Inside a Hollow Cylinder .................................................... 8
3.4
Numerical FEA Methods ................................................................................... 8
4. Method of Procedure ................................................................................................. 10
4.1
Discussion ........................................................................................................ 10
4.2
Thermal Analysis ABAQUS File..................................................................... 10
4.3
4.2.1
Node Section ........................................................................................ 10
4.2.2
Elements Section .................................................................................. 11
4.2.3
Analysis Information Section............................................................... 11
Stress analysis ABAQUS file........................................................................... 14
4.3.1
4.4
Analysis Information Section............................................................... 14
ABAQUS analysis inputs................................................................................. 16
5. Results........................................................................................................................ 22
ii
5.1
Calculation of Convective Heat Transfer Coefficient ...................................... 22
5.2
Thermal Analysis Results ................................................................................ 24
5.3
Stress Analysis Results .................................................................................... 25
6. Discussion and Conclusions ...................................................................................... 28
7. References.................................................................................................................. 29
Appendix A...................................................................................................................... 30
Appendix B ...................................................................................................................... 41
Appendix C ...................................................................................................................... 45
iii
LIST OF TABLES
Table 1: Pipe Size Dimensions from Table A-6 of [7] .................................................... 16
Table 2: Material Properties for Alloy N06600 from [1] ................................................ 19
Table 3: Water Properties from Table A-3 of [7] ............................................................ 20
Table 4: Thermal Transient Temperature vs Time .......................................................... 21
Table 5: Tabular Calculation of h, Hot Flow ................................................................... 22
Table 6: Tabular Calculation of h, Cold Flow ................................................................. 23
iv
LIST OF FIGURES
Figure 1: Bree’s Shakedown Diagram, figure 3 of [3], for non-work hardening material
with yield stress Sy unchanged by changes in temperature ............................................... 3
Figure 2: Illustration of temperature gradients from Figure NB-3653.2(b)-1 of [1] ......... 4
Figure 3: Stress versus time from page 2 of [5]................................................................. 9
Figure 4: Valve Nozzle Geometry ................................................................................... 17
Figure 5: Thermal Transient T vs time ............................................................................ 21
Figure 6: h vs T for 500 gpm Hot Flow ........................................................................... 23
Figure 7: h vs T for 500 gpm Cold Flow ......................................................................... 24
v
LIST OF SYMBOLS
Symbol
Description
Units
A
Surface area
in2
α
Mean coefficient of thermal
expansion
in/in/°F
cp
Specific heat
BTU/lb
Distance from flow entry region in
diameter lengths
diameters
di
Inner diameter
in
Do
Outer diameter
in
∆T1
Linear through-wall temperature
gradient
°F
∆T2
Surface temperature gradient
°F
E
Young’s Modulus
psi
h
Convective heat transfer coefficient
BTU/in2/s/°F
k
Thermal conductivity
BTU/in/s/°F
Nusselt number
none
P
Pressure
psi
Pr
Prandtl number
none
Radius
in
Reynold’s number
none
ρ
Density
lb/in3
T
Temperature
°F
t
Time
s
tw
Wall thickness
in
σp
Primary stress
psi
σt
Thermal secondary stress
psi
σy
Yield strength
psi

Kinematic viscosity
ft2/s
Poisson’s ratio
none
D/L
Nu
r
Re

vi
ACKNOWLEDGMENT
I would like to thank my wife, Sarah Huse, for being supportive and helpful during the
long hours spent on this project. Thanks also to my fellow workers at Electric Boat for
guidance and thanks to Ernesto for being a great advisor.
vii
ABSTRACT
The prediction of the onset of thermal ratcheting is a necessary requirement in the design
of piping and pressure vessels. Thermal ratcheting occurs due to severe pressure and
thermal stresses and is a low-cycle fatigue failure mode. This report documents a
numerical FEA method for predicting the onset of ratcheting and compares the results to
the current analytical methods used in the ASME commercial code [1]. The goal is to
more accurately predict the onset of thermal ratcheting for complex geometry.
This project focused on applying the FEA calculation method in the computer program
ABAQUS [2] for 3” schedule 80 piping connected to typical valve nozzle geometry in
order to predict the onset of thermal ratcheting. Thermal ratcheting requires two models,
one for heat transfer analysis and the other for elastic-plastic analysis using input from
the heat transfer analysis. The model inputs include geometry, thermal properties,
mechanical properties, and load conditions.
The results are …
viii
1. Introduction
Nuclear power plants, in particular, are susceptible to high thermal ratcheting strains due to rapid
increases and decreases in the temperature of the water flowing through the piping and pressure
vessels. When cold water from outside of the plant quickly flows through hot piping, the inside
of the pipe thermally contracts while the outside circumference remains hot, causing a through
wall temperature gradient resulting in tensile stress on the inside of the pipe. After the piping
cools down, hot water from inside the plant can quickly flow back through the same piping
resulting in the inside of the pipe thermally expanding while the outside remains cold creating a
compressive thermal stress on the inside of the pipe.
Related to the local through-wall temperature gradients is the gross thermal expansion and
contraction of the piping system due to changes in the mean temperature of the piping.
Constrained expansion results in secondary moments which bend the piping and create stress.
The arrangement of the pipes and support structure greatly influences this expansion moment.
For this report, however, the effects of mean thermal expansion of the piping system are not
included in the secondary stress. The secondary stress from through-wall temperature gradients
will be focused on as the linear temperature gradient is the largest factor in thermal ratcheting.
The previously discussed loads combined with large primary stresses due to high pressures result
in plastic strain and thermal ratcheting. This report documents a method for predicting the onset
of thermal ratcheting by the use of the FEA software, ABAQUS [2].
1
2. Historical Review
Thermal ratcheting failure was popularized by the work of Bree [3]. In his article, he proposed
what is now known as the Bree diagram or shakedown diagram, as shown in Figure 1. The Bree
diagram was created from analyses of thin walled tubing in nuclear fuel applications where
thermal gradient stresses can be very high. The diagram predicted the stress combinations
necessary for plastic strains to accumulate in piping and pressure vessels.
2.1 Bree Diagram
Bree analyzed a condition in which pressure builds up in nuclear fuel cans due to off gassing of
fission materials. Combined with the pressure was a thermal gradient that was present when the
reactor was operating, but not present when the reactor was cold. This cyclic thermal load
causes yielding of the material, maintaining stress at the yield strength [3]. When the plant cools
down, the residual stress may cause further plastic strains. Therefore, both cooldown and heatup
can result in plastic deformation that accumulates until fatigue failure occurs. The prevention of
this fatigue failure is the basis for thermal ratcheting requirements in commercial code.
2
Figure 1: Bree’s Shakedown Diagram, figure 3 of [3], for non-work hardening material
with yield stress Sy unchanged by changes in temperature
The different regions of Figure 1 are as follows: E is the pure elastic region where no plastic
strain occurs, S1 and S2 are the plastic shakedown regions where initially, plastic strain
accumulates but then tapers off as the pipe settles into a purely elastic response, P is the plastic
stability region where plastic strain will cycle between the maximum and minimum stresses, but
3
will not continue to failure, and lastly, R1 and R2 are the ratcheting regions where the
combination of primary and secondary stresses result in eventual failure of the structure.
The X axis of Figure 1 is equal to the primary stress over the yield strength. For primary stress
due to internal pressure in a cylinder, the stress can be calculated with a thin-walled
approximation resulting in  p 
PDo
PDo
which leads to X _ axis 
where the material
2t w y
2t w
yield strength is taken at the average bulk fluid temperature of the thermal transient.
The Y axis of Figure 1 is equal to the maximum secondary stress range due to a linear thermal
gradient over the yield strength. The stress resulting from a linear through wall temperature
gradient is
t 
ET1
21  v 
which leads to
Y _ axis 
ET1
.
21  v  y
2.2 Linear Thermal Discontinuity
The thermal discontinuity that Bree considered was a linearized temperature gradient through the
wall of the piping. Temperature gradients, as illustrated in Figure 2, are the sum of the mean
temperature, T, the linearized temperature gradient, V (also written as ∆T1), and the surface
temperature gradient, ∆T2.
Figure 2: Illustration of temperature gradients from Figure NB-3653.2(b)-1 of [1]
4
The mean temperature causes no local stresses to occur, but does cause thermal expansion
moments in a constrained run of piping. The linearized or average temperature difference
creates thermal stresses that lead to ratcheting failure. The surface temperature gradient creates
surface stresses which results in crack initiation and fatigue crack failure.
5
3. Theory
3.1 Discussion
Thermal ratcheting is a low cycle fatigue mechanism that accumulates plastic strain with each
stress cycle [4]. Structures such as nuclear piping systems are subjected to the type of low cycle,
high stress conditions that result in plastic strain and thermal ratcheting. Current ASME analysis
requirements in Section III NB-3653.7 are designed to prevent ratcheting from starting [1].
Primary and secondary stresses are limited such that the structure does not enter the ratcheting
regime. Primary stresses are loads such as deadweight and pressure that do not reduce when
strain occurs, but will continue until ductile failure occurs. Secondary stresses are loads such as
thermal expansion moments and thermal gradient stress that will reduce when strain occurs. In
the design of piping systems, it is important to give special attention to locations prone to stress
concentrations such as welds or geometry discontinuities [4].
Accurate modeling of accumulated plastic strain due to ratcheting is hindered by many complex
and hard to model factors. Material hardening and cyclic stress history are two of the major
factors that are difficult to accurately model. Kinematic hardening, the increase in strength after
yielding, occurs in many materials and continues as loading increases until the ultimate tensile
strength is reached at which point the material experiences ductile failure. A linear kinematic
hardening model will tend to under predict thermal ratcheting accumulated strains while a
nonlinear kinematic hardening model will tend to either over predict ratcheting strains or predict
elastic shakedown [5]. For this report, an elastic perfectly plastic assumption is used.
The stress history is not always well known and can affect the analysis. The earlier that larger
stress cycles are applied the earlier that failure of the material will occur. However, because
cyclic history is usually unknown, the worst case loading history is assumed for design analyses.
Thermal ratcheting strain will be calculated using the current requirements of the ASME Boiler
and pressure vessel code [1] Section III, Division 1 – NB-3653.7. As input, this requires that the
linear through-wall gradient of temperature, ∆T1, be known.
describe how ∆T1 can be calculated.
6
The following sections will
3.2 Conduction in a Hollow Cylinder
The general heat transfer partial differential equation for a hollow cylinder is
Equation 1
1   T 
T
 kr
  c p
r r  r 
t
where T is time and location dependent and material properties are for the cylinder.
For steady-state conditions, the right hand side goes to zero and the equation simplifies to
1   T 
 kr
  0 . Multiplying by r, dividing by k (independent of r for isotropic materials) and
r r  r 
integrating gives r
T
 A , where A is the first integration constant. Dividing by r gives
r
T A
 , which integrates to T r   A ln r   B . Boundary conditions are then used to solve for
r r
A and B.
For non steady state conditions, such as when the temperature of the fluid flow varies with time,
the easiest way to solve Equation 1 for ∆T1 is by numerical methods. Also, a common and
conservative analysis assumption is that the outside of the pipe is perfectly insulated, having
convective heat loss of zero resulting in a slightly higher ∆T1. This simplifying assumption is
reasonable based on the heat transfer rate for free convection between metal and air versus the
rate for forced convection between water and metal, and the rate of thermal conduction in metals.
The result of this comparison is that heat transfer for metal conduction and forced convection is
much faster than metal to air heat transfer in free convection. Additionally, much of the hot
piping in proximity to manned areas is insulated for safety, further reducing heat loss to the
environment.
The initial temperature of the pipe and the boundary conditions at the inside radius are needed
for solving Equation 1. The temperature of the inside of the cylinder depends on the energy
transferred from the fluid flowing inside of the cylinder due to forced convection.
7
3.3 Forced Convection Inside a Hollow Cylinder
The convective heat transfer coefficient, h, for turbulent flow inside a cylinder is calculated with
the Dittus-Boelter equation which is given in Equation (3.2.99) of [6].
Equation 2
Nu  0.023 Re 0.8 Pr n
where Nu 
vdi
hd i
, Re 
, n is 0.4 for the fluid cooling the pipe and 0.3 for the fluid heating
k

the pipe, k is for the fluid, and v in the numerator of the equation for the Reynold’s number is
velocity. All properties are at bulk fluid temperature. The qualifications for Equation 2 is that
0.7 ≤ Pr ≤ 160, Re > 10000, and D/L>10. By inspection, the water properties from Table 3
satisfy the requirement for Pr. Re is satisfied based on the problem parameters. D/L is the
measure of lengths in diameters from the entry region. It is assumed that the location of analysis
is more than 10 diameters from the entry region.
Knowing the fluid temperature versus time and fluid flow rate versus time, the convective heat
transfer coefficient, h, can be calculated. The convective heat transfer coefficient is then used to
calculate the heat transferred through convection to the piping,
Q  hAT where A is the area
of heat transfer and ∆T is the temperature difference between the bulk fluid temperature and the
inside surface of the cylinder. The heat transferred by convection is based on the surface area,
instantaneous difference in temperature between the bulk fluid and inside surface of the pipe, and
the convective heat transfer coefficient, h.
3.4 Numerical FEA Methods
ABAQUS accepts the convective heat transfer coefficient and bulk fluid temperature as input to
calculate the heat transferred between the fluid and the piping. ABAQUS also calculates ∆T1
through the numerical analysis of Equation 1. To model cyclic thermal cycles, the analysis
temperatures are increased and decreased repeatedly. The stress analysis ABAQUS file then
8
imports the varying temperatures at each node and applies a constant pressure. The constant
pressure and varying thermal cycles result in a stress load set similar to Figure 3 where the first
curve is primary stress versus time and the second curve is secondary stress versus time.
Figure 3: Stress versus time from page 2 of [5]
The geometry, material properties, and pressure films for the analysis files were created in the
ABAQUS pre-processor software, HYPERMESH. Load conditions are added by direct editing
of the .inp file as described in Section 4. The ABAQUS stress analysis uses nonlinear FEA
methods for calculating large plastic strains.
9
4. Method of Procedure
4.1 Discussion
This section describes the analysis files and the inputs to the thermal and stress analyses which
are provided in full in Appendix A. The student version of ABAQUS limits the user to 1000
nodes per model. In order to conserve the number of nodes, modeling is done axisymmetrically.
ABAQUS axisymmetric analysis, by default, defines the Y axis as the axis of symmetry equating
R,Z,θ with X,Y,Z respectively. Bending moments are not calculated as a three-dimensional halfsymmetry model would be needed, which requires the full version of ABAQUS. The slight
disadvantage to three-dimensional modeling is the increased computational times whereas an
axisymmetric model may take seconds, a complex three-dimensional model could take minutes
or hours to complete.
Section 4.2 details the thermal analysis model. Section 4.3 details the changes from the thermal
model for the stress analysis. Section 4.4 details the inputs to ABAQUS.
4.2 Thermal Analysis ABAQUS File
The ABAQUS file is broken into three main sections which are node, elements, and analysis
information. The majority of manual editing required is done in the analysis information section
of the ABAQUS input file. ** is a delimiter in the files that tells ABAQUS to ignore the line,
which is useful for commenting or having blank space.
4.2.1 Node Section
The first section defines node locations. *NODE, NSET=ALL denotes the start of the node
section. *NODE tells ABAQUS that the following lines will have a node number then node
coordinates based on analysis type. Since the analysis is 2D axisymmetric, two coordinates are
given: radial (X) and longitudinal (Y). NSET=ALL creates a set of node numbers. Appending
the *NODE card with NSET=ALL places all nodes into the set ALL which is then used for
assigning the initial temperature of all the nodes.
10
4.2.2 Elements Section
The second section is initiated with the card *ELEMENT, TYPE=DCAX8, ELSET=Pipe.
*ELEMENT tells ABAQUS the following lines will have an element number followed by nodes
defining the shape and normal. These are automatically created by HYPERMESH in the correct
order.
TYPE=DCAX8 defines the element type as D for diffusive heat transfer, C for
non-twisting, AX for axisymmetric, and 8 for 8-noded quadratic which is a second order
element. ELSET=Pipe creates a set of element numbers. Appending the *ELEMENT card with
ELSET places all elements defined in the card into the set which is then used for assigning the
material properties of the elements.
4.2.3 Analysis Information Section
The third section is where most editing of ABAQUS input files occurs. While it is laborious to
manually enter nodes and elements, the analysis section is often much faster to enter manually
than trying to navigate through a user interface. The following is one of the many ways to order
and build the analysis section.
4.2.3.1 Material Definitions
*MATERIAL, NAME=N06600 tells ABAQUS that the following material property cards apply
to the material N06600.
*CONDUCTIVITY, TYPE=ISO tells ABAQUS the following lines will have a thermal
conductivity in BTU/s/in/°F and the temperature in °F that each applies at. ISO denotes similar
properties in all directions.
*SPECIFIC HEAT tells ABAQUS that the following lines will have specific heat in BTU/lb and
the temperature in °F that each applies at.
*DENSITY tells ABAQUS the following line will have density in lb/in3 at 70 °F. For material
properties with one line, the property is applied at all temperatures.
11
*ELASTIC, TYPE = ISOTROPIC tells ABAQUS that the following lines contain Young’s
modulus in psi, Poisson’s ratio, and a temperature in °F that each applies at. ISOTROPIC
denotes similar properties in all directions.
*EXPANSION, ZERO = 70.0, TYPE = ISO tells ABAQUS the following lines contain the mean
coefficient of thermal expansion in in/in/°F and a temperature in °F that it applies at. ZERO
defines the ambient temperature at which no thermal expansion occurs. ISO denotes similar
properties in all directions.
*PLASTIC is the last material card and it tells ABAQUS that the following lines will have stress
in psi, plastic strain, and a temperature in °F that it applies at. Stress with a plastic strain of 0.0
denotes the yield strength. Entering no plastic strains creates an elastic perfectly plastic material
definition.
*SOLID SECTION, ELSET=Pipe, MATERIAL=N06600 places the material properties onto the
named set of elements. The line following this card is the attribute line, for which 1.0 is default.
4.2.3.2 Transient Information
*ELSET, ELSET=P2 creates a set of element numbers from the following lines and labels the set
as P2. This is used to define a set of elements that border the inside edge and have element edge
#2 at the inside of the piping. An easy way to find this set of elements is by defining a pressure
on the inside of the model in HYPERMESH.
*INITIAL CONDITIONS, TYPE=TEMPERATURE tells ABAQUS what the initial temperature
of the nodes in the following lines is, by listing the node set ALL and the initial temperature 70.
*AMPLITUDE, NAME=TEMPAMP, VALUE=ABSOLUTE tells ABAQUS that the following
lines have time in seconds then temperature in °F, repeating up to 4 times per line. This defines
the curve of bulk fluid temperature versus time for use in the numerical heat transfer analysis.
12
*AMPLITUDE, NAME=FILMAMP, VALUE=ABSOLUTE is the same card type as for the
temperature curves but is instead defining the convective heat transfer coefficient versus time.
*INCLUDE,INPUT=5cycles.th.inp tells ABAQUS to insert the lines found in the 5cycle.th file.
This card is used to reduce the repetition of lines in the main file by running 5 thermal cycles
with one line of code.
4.2.3.3 Step Definition in 5cycles.th
In order to reduce the repetition of multiple lines in the main ABAQUS stress analysis file, lines
were added in a separate file that is called from the main stress file. After properties and thermal
inputs are defined in the main file, the analysis steps are called.
*STEP, INC=5000 initiates a step with 5000 discrete analysis increments. The cards between
this and the following *END STEP card will define a step of the analysis. Multiple steps can be
entered to help with convergence for complicated loadings and geometry.
*HEAT TRANSFER, DELTMX=15.0 tells ABAQUS the following line defines the initial time
increment, the length of time to run the step for, the minimum time step size, the maximum time
step size, and steady state option where 0.0 denotes no steady state analysis. DELTMX defines
the maximum difference in temperature allowed between adjacent nodes.
The ABAQUS
program will use the DELTMX control to automatically increase or decrease the time for each
increment.
*FILM, AMPLITUDE=TEMPAMP, FILM AMPLITUDE=FILMAMP tells ABAQUS that the
following lines apply the time versus temperature and time versus heat transfer coefficient curves
to the elements by element set, edge of element, temperature (dummy value since
AMPLITUDE=TEMPAMP is appending the card), and film coefficient (dummy value since
FILM AMPLITUDE=FILMAMP is appending the card).
13
The lines *NODE FILE, FREQUENCY=1 | NT | *EL FILE | COORD, TEMP | *EL
FILE,POSITION=NODES, FREQUENCY=1 | TEMP create a binary data file of temperatures at
each time step which will be used later to import temperatures for the stress analysis.
*END STEP defines the completion of the analysis step. The lines from *STEP to *END STEP
are then repeated for the multiple thermal cycles.
4.3 Stress analysis ABAQUS file
The stress analysis file has the same geometry and material properties as the thermal file, but the
analysis information and element type are different. The element type is CAX8 instead of
DCAX8.
4.3.1 Analysis Information Section
Other than the material property cards, the analysis information section for the stress analysis is
completely different from the thermal analysis section as detailed below.
*BOUNDARY tells ABAQUS that the following lines will have a node, degree of freedom (2 is
Y), and prescribed displacement where 0.0 is for no deflection, essentially anchoring the node in
the selected degree of freedom.
*EQUATION tells ABAQUS that the following lines will have the number of variables for an
equation for node displacements multiplied by a factor and equal to zero, alternating with the
next line which inputs the variable information. The variable information is given as the first
node, degree of freedom, multiplication factor, second node, degree of freedom, and
multiplication factor. This card is used to tell ABAQUS that the nodes on the free end of the
pipe can move in the Y direction but must all have the same Y displacements.
14
*AMPLITUDE, NAME=PRESS,VALUE=ABSOLUTE defines the time versus pressure curve
in the following lines. This value controls the pressure on the model and is iterated to induce
ratcheting.
*STEP, INC=5000, AMPLITUDE=RAMP applies a ramp in pressure up to the input pressure.
*STATIC, DIRECT tells ABAQUS to discretize the stress analysis by the input in the following
line which gives the time of each increment and the total time.
*TEMPERATURE, FILE=valve.th, BSTEP=1, BINC=1,ESTEP=20,EINC=185 tells ABAQUS
to import temperatures from the thermal file from step 1, increment 1 to step 20, increment 185.
Modifying the thermal file usually requires modifying these values as well.
*DLOAD, AMPLITUDE=PRESS, OP=NEW tells ABAQUS that the following lines have the
following information: element, edge of element, and dummy value for load as the amplitude
card for PRESS overwrites these values. OP=NEW resets previous distributed load cards.
15
4.4 ABAQUS analysis inputs
This section provides the information entered into the ABAQUS input files. Table 1 details the
geometry of the piping which is connected to the valve nozzle. The geometry for the valve
nozzle is detailed in Figure 4.
Table 1: Pipe Size Dimensions from Table A-6 of [7]
Description
Value
Geometry
3 NPS, Schedule 80
Outer Diameter, Do
3.5
inches
Thickness, tw
0.3
inches
Inner Diameter, di
2.9
inches
Length
10.0
inches
16
Units
Pipe Length = 10.0”
Tangent Length = 0.5”
Length = 2.0”
Length = 4.0”
Figure 4: Valve Nozzle Geometry
17
Table 2 details the material properties entered into ABAQUS for the piping and the valve nozzle.
The material properties are for Alloy N06600 seamless pipe and tube, Spec SB-167 for sizes ≤ 5
inches from Reference [1], Section II, Part D, Material Properties, Tables Y-1, TE-4, TCD, TM4, and PRD. Conductivity was converted from units of BTU/hr/ft/°F by dividing by (3600*12).
Also, specific heat was calculated from the equation cp=k/TD/ρ where TD is thermal diffusivity
from Table TCD, and ρ is converted to units of lb/ft3 = 0.3*123=518.4
18
Table 2: Material Properties for Alloy N06600 from [1]
70
Conductivity
k
(10-3 BTU/s/in/°F)
0.199
0.108
100
0.201
150
Young’s
Modulus
E (106 psi)
31.0
Mean Coefficient of
Thermal Expansion
α (10-6 in./in./°F)
6.8
Yield
Stress
σy (ksi)
30.0
0.109
6.9
30.0
0.206
0.111
7.0
29.2
200
0.211
0.113
7.1
28.6
250
0.215
0.114
7.2
28.0
300
0.222
0.116
7.3
27.4
350
0.227
0.116
7.4
26.8
400
0.234
0.118
7.5
26.2
450
0.238
0.118
7.6
25.7
500
0.245
0.120
7.6
25.2
550
0.250
0.121
7.7
24.7
600
0.257
0.122
7.8
24.3
650
0.262
0.123
7.9
23.9
700
0.269
0.125
7.9
23.5
750
0.273
0.126
8.0
23.2
800
0.280
0.128
8.0
22.9
850
0.287
0.130
8.1
22.6
900
0.292
0.131
8.2
22.3
Temperature
T (°F)
Specific Heat
cp (BTU/lb)
Density
ρ (lb/in.3)
Poisson’s Ratio
v
30.3
29.9
29.4
0.30
29.0
28.6
28.1
27.6
27.1
19
0.31
Table 3 details the water properties used to calculate the convective heat transfer
coefficient for input into ABAQUS. The results of this calculation are provided in
Section 5.
Table 3: Water Properties from Table A-3 of [7]
Temperature
T (°F)
Conductivity
Kinetic Viscosity
Density
Prandtl
K (BTU/hr/ft/°F)
-5
ρ (lb/ft )
Number
2
3
v x 10 (ft /s)
32
0.319
1.93
62.4
13.7
40
0.325
1.67
62.4
11.6
50
0.332
1.4
62.4
9.55
60
0.34
1.22
62.3
8.03
70
0.347
1.06
62.3
6.82
80
0.353
0.93
62.2
5.89
90
0.359
0.825
62.1
5.13
100
0.364
0.74
62
4.52
150
0.384
0.477
61.2
2.74
200
0.394
0.341
60.1
1.88
250
0.396
0.269
58.8
1.45
300
0.395
0.22
57.3
1.18
350
0.391
0.189
55.6
1.02
400
0.381
0.17
53.6
0.927
450
0.367
0.155
51.6
0.876
500
0.349
0.145
49
0.87
550
0.325
0.139
45.9
0.93
600
0.292
0.137
42.4
1.09
20
Table 4 provides the assumed temperature versus time data used for the thermal
transient. This transient is then repeated multiple times in order to show ratcheting.
Figure 5 graphs the information from Table 4.
Table 4: Thermal Transient Temperature vs Time
t
(s)
T
(°F)
0
5
50
55
100
70
600
600
70
70
T vs time
700
600
500
400
300
T (°F)
200
100
0
-10
0
10
20
30
40
time
Figure 5: Thermal Transient T vs time
21
50
60
5. Results
Section 5 details the results of the thermal and stress analysis as well as the calculation
of the convective heat transfer coefficient.
5.1 Calculation of Convective Heat Transfer Coefficient
Table 5 and Table 6 provide the calculated values for the convective heat transfer
coefficient with an assumed flow rate of 500 gallons per minute, gpm. Flow rate was
converted from gpm to in/s using the conversions 231 in3 = 1 gallon, 60 sec = 1 min, and
by dividing by the cross-sectional area, πdi2/4=6.605 in2. This data is graphed in Figure
6 and Figure 7.
Table 5: Tabular Calculation of h, Hot Flow
T
(°F)
70
100
150
200
250
300
350
400
450
500
550
600
Flow
(gpm)
500
Flow
(in/s)
Re
291.44
553700
793137.8
1230444
1721179
2181866
2667827
3105407
3452482
3786593
4047738
4222460
4284102
Pr
6.82
4.52
2.74
1.88
1.45
1.18
1.02
0.927
0.876
0.87
0.93
1.09
22
Nu
1608.728464
1895.606899
2317.942143
2707.920921
3028.312594
3343.632851
3614.12138
3822.582869
4046.485601
4259.449759
4494.953159
4769.178986
h
(BTU/in2/s/°F)
0.00446
0.00551
0.0071
0.00852
0.00957
0.01054
0.01128
0.01163
0.01185
0.01187
0.01166
0.01112
Table 6: Tabular Calculation of h, Cold Flow
T
(°F)
600
550
500
450
400
350
300
250
200
150
100
70
Flow
(gpm)
500
Flow
(in/s)
Re
291.44
4284102
4222460
4047738
3786593
3452482
3105407
2667827
2181866
1721179
1230444
793137.8
553700
Pr
1.09
0.93
0.87
0.876
0.927
1.02
1.18
1.45
1.88
2.74
4.52
6.82
Nu
h
(BTU/in2/s/°F)
4810.456
4462.451
4200.543
3993.268
3793.717
3621.285
3399.435
3142.95
2884.375
2563.762
2204.256
1949.221
0.011212
0.011576
0.011702
0.011698
0.011537
0.011302
0.010718
0.009935
0.009071
0.007858
0.006404
0.005399
It is seen in Figure 6 and Figure 7 that the coefficient is not well represented by only the
start and end points; therefore, each data point is entered into ABAQUS for the
amplitude card containing the curve of film coefficient versus time.
h vs T for 500 gpm Hot Flow
0.012
0.011
0.01
0.009
0.008
0.007
0.006
h (BTU/in2/s/°F)
0.005
0.004
0
100
200
300
T (°F)
400
Figure 6: h vs T for 500 gpm Hot Flow
23
500
600
h vs T for 500 gpm Cold Flow
0.012
0.011
0.01
0.009
0.008
0.007
0.006
0.005
h (BTU/in2/s/°F)
0.004
600
500
400
300
200
100
T (°F)
Figure 7: h vs T for 500 gpm Cold Flow
5.2 Thermal Analysis Results
24
0
5.3 Stress Analysis Results
1000, 2000, and 3000 pressure, S2 vs E max principal at node 17
25
1000, 2000, and 3000 pressure, S2 vs U magnitude at node 17
26
1000, 2000, and 3000 pressure, S2 vs U magnitude at node 17
27
6. Discussion and Conclusions
The pressure at which ratcheting starts is between 1 and 2 ksi.
28
7. References
[1] 2010 ASME boiler & pressure vessel code an international code. (2010).
New York, NY: American Society of Mechanical Engineers.
[2] ABAQUS (Version 6.13) [Software]. (2013). Providence, RI: Dassault
Systèmes Simulia Corp.
[3] Bree, J. (1967). Elastic-plastic behaviour of thin tubes subject to internal
pressure and intermittent high-heat fluxes with application to fast nuclear
reactor fuel elements. Journal of Strain Analysis, (2), 226-38.
[4] Bari, S. (2001). Constitutive Modeling for Cyclic Plasticity and Ratcheting.
[5] Cailletaud, G. (2003). UTMIS Course 2003 – Stress Calculations for Fatigue
- 6. Ratcheting. Ecole des Mines de Paris: Centre des Materiaux.
[6] Kreith, F. (2000). The CRC handbook of thermal engineering. Boca Raton,
Fla.: CRC Press.
[7] Kreith, F. (1965). Principles of heat transfer. Second edition. Scranton, Pa.:
International Textbook.
29
Appendix A
Appendix A provides the full ABAQUS thermal input file, valve.th. Node and element
sections are minimized to reduce space.
**
** ABAQUS Input Deck Generated by HyperMesh Version :
12.0.110.40
** Generated using HyperMesh-Abaqus Template Version :
hwdesktop12.0.110
**
** Template: ABAQUS/STANDARD 2D
57, 1.5812500052154, 0.3043478168547
58, 1.5625000044704, 0.3043478168547
59, 1.5437500037253, 0.3043478168547
60, 1.5250000029802, 0.3043478168547
61, 1.5062500022352, 0.3043478168547
62, 1.4875000014901, 0.3043478168547
63, 1.4687500007451, 0.3043478168547
64, 1.7312500111759, 0.1521739084274
65, 1.7125000104308, 0.1521739084274
66, 1.6937500096858, 0.1521739084274
67, 1.6750000089407, 0.1521739084274
68, 1.6562500081956, 0.1521739084274
69, 1.6375000074506, 0.1521739084274
70, 1.6187500067055, 0.1521739084274
71, 1.6000000059605, 0.1521739084274
72, 1.5812500052154, 0.1521739084274
73, 1.5625000044704, 0.1521739084274
74, 1.5437500037253, 0.1521739084274
75, 1.5250000029802, 0.1521739084274
76, 1.5062500022352, 0.1521739084274
77, 1.4875000014901, 0.1521739084274
78, 1.4687500007451, 0.1521739084274
79, 1.6000000059605, 0.0760869542137
80, 1.6750000089407, 0.0760869542137
81, 1.7125000104308, 0.0760869542137
82, 1.6375000074506, 0.0760869542137
83, 1.5250000029802, 0.0760869542137
84, 1.5625000044704, 0.0760869542137
85, 1.4875000014901, 0.0760869542137
86, 1.6000000059605, 0.228260862641
87, 1.6750000089407, 0.228260862641
88, 1.7125000104308, 0.228260862641
89, 1.6375000074506, 0.228260862641
90, 1.5250000029802, 0.228260862641
91, 1.5625000044704, 0.228260862641
92, 1.4875000014901, 0.228260862641
93, 1.7312500111759, 0.4565217252821
94, 1.7125000104308, 0.4565217252821
95, 1.6937500096858, 0.4565217252821
96, 1.6750000089407, 0.4565217252821
97, 1.6562500081956, 0.4565217252821
98, 1.6375000074506, 0.4565217252821
99, 1.6187500067055, 0.4565217252821
100, 1.6000000059605, 0.4565217252821
101, 1.5812500052154, 0.4565217252821
102, 1.5625000044704, 0.4565217252821
103, 1.5437500037253, 0.4565217252821
104, 1.5250000029802, 0.4565217252821
105, 1.5062500022352, 0.4565217252821
106, 1.4875000014901, 0.4565217252821
107, 1.4687500007451, 0.4565217252821
108, 1.6000000059605, 0.3804347710684
109, 1.6750000089407, 0.3804347710684
110, 1.7125000104308, 0.3804347710684
111, 1.6375000074506, 0.3804347710684
112, 1.5250000029802, 0.3804347710684
113, 1.5625000044704, 0.3804347710684
114, 1.4875000014901, 0.3804347710684
115, 1.6000000059605, 0.5326086794958
116, 1.6750000089407, 0.5326086794958
117, 1.7125000104308, 0.5326086794958
118, 1.6375000074506, 0.5326086794958
119, 1.5250000029802, 0.5326086794958
120, 1.5625000044704, 0.5326086794958
121, 1.4875000014901, 0.5326086794958
122, 1.45
, -0.054124707193
**
*NODE, NSET=ALL
1, 1.45
, 0.0
2, 1.46875
, 0.0
3, 1.4875
, 0.0
4, 1.50625
, 0.0
5, 1.525
, 0.0
6, 1.54375
, 0.0
7, 1.5625
, 0.0
8, 1.58125
, 0.0
9, 1.6
, 0.0
10, 1.61875
, 0.0
11, 1.6375
, 0.0
12, 1.65625
, 0.0
13, 1.675
, 0.0
14, 1.69375
, 0.0
15, 1.7125
, 0.0
16, 1.73125
, 0.0
17, 1.75
, 0.0
18, 1.75
, 0.0760869565217
19, 1.75
, 0.1521739130435
20, 1.75
, 0.2282608695652
21, 1.75
, 0.304347826087
22, 1.75
, 0.3804347826087
23, 1.75
, 0.4565217391304
24, 1.75
, 0.5326086956522
25, 1.75
, 0.6086956521739
26, 1.73125
, 0.6086956521739
27, 1.7125
, 0.6086956521739
28, 1.69375
, 0.6086956521739
29, 1.675
, 0.6086956521739
30, 1.65625
, 0.6086956521739
31, 1.6375
, 0.6086956521739
32, 1.61875
, 0.6086956521739
33, 1.6
, 0.6086956521739
34, 1.58125
, 0.6086956521739
35, 1.5625
, 0.6086956521739
36, 1.54375
, 0.6086956521739
37, 1.525
, 0.6086956521739
38, 1.50625
, 0.6086956521739
39, 1.4875
, 0.6086956521739
40, 1.46875
, 0.6086956521739
41, 1.45
, 0.6086956521739
42, 1.45
, 0.5326086956522
43, 1.45
, 0.4565217391304
44, 1.45
, 0.3804347826087
45, 1.45
, 0.304347826087
46, 1.45
, 0.2282608695652
47, 1.45
, 0.1521739130435
48, 1.45
, 0.0760869565217
49, 1.7312500111759, 0.3043478168547
50, 1.7125000104308, 0.3043478168547
51, 1.6937500096858, 0.3043478168547
52, 1.6750000089407, 0.3043478168547
53, 1.6562500081956, 0.3043478168547
54, 1.6375000074506, 0.3043478168547
55, 1.6187500067055, 0.3043478168547
56, 1.6000000059605, 0.3043478168547
30
123,
124,
125,
126,
127,
128,
129,
130,
131,
132,
133,
134,
135,
136,
137,
138,
139,
140,
141,
142,
143,
144,
145,
146,
147,
148,
149,
150,
151,
152,
153,
154,
155,
156,
157,
158,
159,
160,
161,
162,
163,
164,
165,
166,
167,
168,
169,
170,
171,
172,
173,
174,
175,
176,
177,
178,
179,
180,
181,
182,
183,
184,
185,
186,
187,
188,
189,
190,
191,
192,
193,
194,
195,
196,
197,
198,
199,
200,
1.45
1.45
1.45
1.45
1.45
1.45
1.45
1.46875
1.4875
1.50625
1.525
1.54375
1.5625
1.58125
1.6
1.61875
1.6375
1.65625
1.675
1.69375
1.7125
1.73125
1.75
1.75
1.75
1.75
1.75
1.75
1.75
1.75
1.46875
1.4875
1.50625
1.525
1.54375
1.5625
1.58125
1.6
1.61875
1.6375
1.65625
1.675
1.69375
1.7125
1.73125
1.6
1.6
1.6
1.58125
1.5625
1.54375
1.525
1.50625
1.4875
1.46875
1.525
1.5625
1.4875
1.525
1.5625
1.4875
1.73125
1.7125
1.69375
1.675
1.65625
1.6375
1.61875
1.675
1.7125
1.6375
1.675
1.7125
1.6375
1.6
1.6
1.6
1.58125
,
,
,
,
,
,
,
-0.108249414387
-0.16237412158
-0.216498828774
-0.270623535967
-0.324748243161
-0.378872950354
-0.432997657548
, -0.432997657548
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, -0.432997657548
, -0.432997657548
, -0.432997657548
, -0.432997657548
, -0.432997657548
, -0.432997657548
, -0.432997657548
, -0.432997657548
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, -0.216498828774
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, -0.108249414387
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, -0.108249414387
, -0.108249414387
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, -0.054124707193
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, -0.108249414387
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, -0.16237412158
, -0.16237412158
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, -0.054124707193
, -0.054124707193
, -0.378872950354
, -0.324748243161
, -0.270623535967
, -0.324748243161
201,
202,
203,
204,
205,
206,
207,
208,
209,
210,
211,
212,
213,
214,
215,
216,
217,
218,
219,
220,
221,
222,
223,
224,
225,
226,
227,
228,
229,
230,
231,
232,
233,
234,
235,
236,
237,
238,
239,
240,
241,
242,
243,
244,
245,
246,
247,
248,
249,
250,
251,
252,
253,
254,
255,
256,
257,
258,
259,
260,
261,
262,
263,
264,
265,
266,
267,
268,
269,
270,
271,
272,
273,
274,
275,
276,
277,
278,
31
1.5625
, -0.324748243161
1.54375
, -0.324748243161
1.525
, -0.324748243161
1.50625
, -0.324748243161
1.4875
, -0.324748243161
1.46875
, -0.324748243161
1.525
, -0.378872950354
1.5625
, -0.378872950354
1.4875
, -0.378872950354
1.525
, -0.270623535967
1.5625
, -0.270623535967
1.4875
, -0.270623535967
1.73125
, -0.324748243161
1.7125
, -0.324748243161
1.69375
, -0.324748243161
1.675
, -0.324748243161
1.65625
, -0.324748243161
1.6375
, -0.324748243161
1.61875
, -0.324748243161
1.675
, -0.378872950354
1.7125
, -0.378872950354
1.6375
, -0.378872950354
1.675
, -0.270623535967
1.7125
, -0.270623535967
1.6375
, -0.270623535967
1.45
, -0.453835042696
1.45
, -0.474672427844
1.45
, -0.495509812992
1.45
, -0.51634719814
1.45
, -0.537184583288
1.45
, -0.558021968437
1.4708442304233, -0.558021968437
1.4916884608465, -0.558021968437
1.5125326912698, -0.558021968437
1.533376921693 , -0.558021968437
1.5542211521163, -0.558021968437
1.5750653825396, -0.558021968437
1.5959096129628, -0.558021968437
1.6167538433861, -0.558021968437
1.6375980738094, -0.558021968437
1.6584423042326, -0.558021968437
1.6792865346559, -0.558021968437
1.7001307650792, -0.558021968437
1.7209749955024, -0.558021968437
1.7418192259257, -0.558021968437
1.762663456349 , -0.558021968437
1.7835076867722, -0.558021968437
1.7734329409316, -0.538673424614
1.7650832464159, -0.518520279616
1.7585221766839, -0.497715976798
1.7537996868442, -0.47641891734
1.7509517333036, -0.454791254211
1.6117164704658, -0.537929003951
1.607541623208 , -0.517433738878
1.604261088342 , -0.496612894895
1.6018998434221, -0.475545672592
1.6004758666518, -0.454313148453
1.5308582352329, -0.53755679362
1.528770811604 , -0.516890468509
1.527130544171 , -0.496061353944
1.525949921711 , -0.475109050218
1.5252379333259, -0.454074095575
1.509078108703 , -0.516754650917
1.489385405802 , -0.516618833325
1.469692702901 , -0.516483015733
1.4904291176164, -0.537370688454
1.5069624412833, -0.474999894625
1.4879749608555, -0.474890739031
1.4689874804278, -0.474781583438
1.4885652720855, -0.495785583468
1.487618966663 , -0.453954569135
1.587848920307 , -0.517297921286
1.568156217406 , -0.517162103694
1.548463514505 , -0.517026286102
1.5712873528494, -0.537742898786
1.5829123629943, -0.475436516999
1.5639248825666, -0.475327361405
1.5449374021388, -0.475218205812
279,
280,
281,
282,
283,
284,
285,
286,
287,
288,
289,
290,
291,
292,
293,
294,
295,
296,
297,
298,
299,
300,
301,
302,
303,
304,
305,
306,
307,
308,
309,
310,
311,
312,
313,
314,
315,
316,
317,
318,
319,
320,
321,
322,
323,
324,
325,
326,
327,
328,
329,
330,
331,
332,
333,
334,
335,
336,
337,
338,
339,
340,
341,
342,
343,
344,
345,
346,
347,
348,
349,
350,
351,
352,
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523,
521,
624,
622,
522,
639,
623,
525,
523,
622,
620,
524,
640,
621,
527,
525,
620,
618,
526,
635,
619,
529,
527,
618,
616,
528,
638,
617,
531,
529,
616,
614,
530,
636,
615,
533,
531,
614,
608,
532,
637,
613,
626,
611,
590,
592,
627,
612,
591,
624,
626,
592,
594,
625,
634,
593,
622,
624,
594,
596,
623,
632,
595,
620,
622,
596,
598,
621,
633,
597,
618,
620,
598,
600,
619,
628,
599,
616,
618,
600,
602,
617,
631,
601,
614,
616,
602,
604,
615,
629,
603,
608,
614,
604,
606,
613,
630,
605,
548,
546,
562,
582,
547,
563,
583,
550,
548,
582,
580,
549,
589,
581,
552,
550,
580,
578,
551,
587,
579,
537,
552,
578,
535,
553,
588,
577,
582,
562,
525,
527,
583,
561,
526,
580,
582,
527,
529,
581,
586,
528,
578,
580,
529,
531,
579,
584,
530,
535,
578,
531,
533,
577,
585,
532,
540,
513,
515,
569,
539,
514,
570,
542,
540,
569,
567,
541,
576,
568,
544,
542,
567,
565,
543,
574,
566,
546,
544,
565,
562,
545,
575,
564,
569,
515,
517,
519,
570,
516,
518,
567,
569,
519,
521,
568,
573,
520,
565,
567,
521,
523,
566,
571,
522,
562,
565,
523,
525,
564,
572,
524,
552,
537,
335,
333,
553,
538,
334,
550,
552,
333,
331,
551,
560,
332,
548,
550,
331,
329,
549,
558,
330,
546,
548,
329,
327,
547,
559,
328,
544,
546,
327,
325,
545,
554,
326,
557
155,
555
154,
556
153,
512
152,
511
151,
509
150,
510
149,
338
148,
508
147,
506
146,
507
145,
336
144,
498
143,
496
142,
497
141,
485
140,
495
139,
493
138,
494
137,
483
136,
482
135,
480
134,
481
133,
342
132,
479
131,
477
130,
478
129,
340
128,
469
127,
467
126,
468
125,
456
124,
466
123,
464
122,
465
121,
454
120,
438
119,
436
118,
437
117,
37
542,
544,
325,
323,
543,
557,
324,
540,
542,
323,
321,
541,
555,
322,
513,
540,
321,
319,
539,
556,
320,
448,
446,
484,
504,
447,
485,
505,
450,
448,
504,
502,
449,
511,
503,
452,
450,
502,
500,
451,
509,
501,
339,
452,
500,
337,
453,
510,
499,
504,
484,
327,
329,
505,
483,
328,
502,
504,
329,
331,
503,
508,
330,
500,
502,
331,
333,
501,
506,
332,
337,
500,
333,
335,
499,
507,
334,
440,
315,
317,
491,
439,
316,
492,
442,
440,
491,
489,
441,
498,
490,
444,
442,
489,
487,
443,
496,
488,
446,
444,
487,
484,
445,
497,
486,
491,
317,
319,
321,
492,
318,
320,
489,
491,
321,
323,
490,
495,
322,
487,
489,
323,
325,
488,
493,
324,
484,
487,
325,
327,
486,
494,
326,
360,
358,
455,
475,
359,
456,
476,
362,
360,
475,
473,
361,
482,
474,
364,
362,
473,
471,
363,
480,
472,
343,
364,
471,
341,
365,
481,
470,
475,
455,
446,
448,
476,
454,
447,
473,
475,
448,
450,
474,
479,
449,
471,
473,
450,
452,
472,
477,
451,
341,
471,
452,
339,
470,
478,
453,
352,
311,
313,
462,
351,
312,
463,
354,
352,
462,
460,
353,
469,
461,
356,
354,
460,
458,
355,
467,
459,
358,
356,
458,
455,
357,
468,
457,
462,
313,
315,
440,
463,
314,
439,
460,
462,
440,
442,
461,
466,
441,
458,
460,
442,
444,
459,
464,
443,
455,
458,
444,
446,
457,
465,
445,
375,
373,
411,
431,
374,
412,
432,
377,
375,
431,
429,
376,
438,
430,
379,
377,
429,
427,
378,
436,
428,
347,
379,
427,
345,
380,
437,
426,
346
116,
435
115,
433
114,
434
113,
344
112,
425
111,
423
110,
424
109,
412
108,
422
107,
420
106,
421
105,
410
104,
409
103,
407
102,
408
101,
350
100,
406
99,
404
98,
405
97,
348
96,
396
95,
394
94,
395
93,
383
92,
393
91,
391
90,
392
89,
381
88,
303
87,
252
86,
302
85,
250
84,
298
83,
248
82,
294
81,
285
80,
293
79,
283
78,
431,
411,
358,
360,
432,
410,
359,
429,
431,
360,
362,
430,
435,
361,
427,
429,
362,
364,
428,
433,
363,
345,
427,
364,
343,
426,
434,
365,
367,
307,
309,
418,
366,
308,
419,
369,
367,
418,
416,
368,
425,
417,
371,
369,
416,
414,
370,
423,
415,
373,
371,
414,
411,
372,
424,
413,
418,
309,
311,
352,
419,
310,
351,
416,
418,
352,
354,
417,
422,
353,
414,
416,
354,
356,
415,
420,
355,
411,
414,
356,
358,
413,
421,
357,
241,
239,
382,
402,
240,
383,
403,
243,
241,
402,
400,
242,
409,
401,
245,
243,
400,
398,
244,
407,
399,
247,
245,
398,
349,
246,
408,
397,
402,
382,
373,
375,
403,
381,
374,
400,
402,
375,
377,
401,
406,
376,
398,
400,
377,
379,
399,
404,
378,
349,
398,
379,
347,
397,
405,
380,
233,
231,
305,
389,
232,
304,
390,
235,
233,
389,
387,
234,
396,
388,
237,
235,
387,
385,
236,
394,
386,
239,
237,
385,
382,
238,
395,
384,
389,
305,
307,
367,
390,
306,
366,
387,
389,
367,
369,
388,
393,
368,
385,
387,
369,
371,
386,
391,
370,
382,
385,
371,
373,
384,
392,
372,
143,
141,
284,
300,
142,
285,
301,
145,
143,
300,
251,
144,
303,
299,
300,
284,
282,
296,
301,
283,
297,
251,
300,
296,
249,
299,
302,
295,
296,
282,
243,
245,
297,
281,
244,
249,
296,
245,
247,
295,
298,
246,
139,
137,
256,
291,
138,
257,
292,
141,
139,
291,
284,
140,
294,
290,
291,
256,
254,
287,
292,
255,
288,
284,
291,
287,
282,
290,
293,
286,
287,
254,
239,
241,
288,
253,
240,
289
77,
281
76,
280
75,
257
74,
279
73,
255
72,
275
71,
253
70,
271
69,
262
68,
270
67,
260
66,
266
65,
258
64,
225
63,
223
62,
224
61,
148
60,
222
59,
220
58,
221
57,
146
56,
212
55,
210
54,
211
53,
199
52,
209
51,
207
50,
208
49,
197
48,
196
47,
194
46,
195
45,
152
44,
193
43,
191
42,
192
41,
150
40,
183
39,
38
282,
287,
241,
243,
286,
289,
242,
135,
133,
261,
277,
134,
262,
278,
137,
135,
277,
256,
136,
280,
276,
277,
261,
259,
273,
278,
260,
274,
256,
277,
273,
254,
276,
279,
272,
273,
259,
235,
237,
274,
258,
236,
254,
273,
237,
239,
272,
275,
238,
131,
129,
227,
268,
130,
226,
269,
133,
131,
268,
261,
132,
271,
267,
268,
227,
229,
264,
269,
228,
265,
261,
268,
264,
259,
267,
270,
263,
264,
229,
231,
233,
265,
230,
232,
259,
264,
233,
235,
263,
266,
234,
162,
160,
198,
218,
161,
199,
219,
164,
162,
218,
216,
163,
225,
217,
166,
164,
216,
214,
165,
223,
215,
149,
166,
214,
147,
167,
224,
213,
218,
198,
137,
139,
219,
197,
138,
216,
218,
139,
141,
217,
222,
140,
214,
216,
141,
143,
215,
220,
142,
147,
214,
143,
145,
213,
221,
144,
154,
125,
127,
205,
153,
126,
206,
156,
154,
205,
203,
155,
212,
204,
158,
156,
203,
201,
157,
210,
202,
160,
158,
201,
198,
159,
211,
200,
205,
127,
129,
131,
206,
128,
130,
203,
205,
131,
133,
204,
209,
132,
201,
203,
133,
135,
202,
207,
134,
198,
201,
135,
137,
200,
208,
136,
11,
9,
169,
189,
10,
170,
190,
13,
11,
189,
187,
12,
196,
188,
15,
13,
187,
185,
14,
194,
186,
17,
15,
185,
151,
16,
195,
184,
189,
169,
160,
162,
190,
168,
161,
187,
189,
162,
164,
188,
193,
163,
185,
187,
164,
166,
186,
191,
165,
151,
185,
166,
149,
184,
192,
167,
3,
1,
123,
176,
2,
122,
177,
5,
3,
176,
174,
4,
183,
175,
181
38,
182
37,
170
36,
180
35,
178
34,
179
33,
168
32,
121
31,
119
30,
120
29,
115
28,
118
27,
116
26,
117
25,
24
24,
114
23,
112
22,
113
21,
108
20,
111
19,
109
18,
110
17,
22
16,
92
15,
90
14,
91
13,
86
12,
89
11,
87
10,
88
9,
20
8,
85
7,
83
6,
84
5,
79
4,
82
3,
80
2,
81
1,
18
7,
5,
174,
172,
6,
181,
173,
9,
7,
172,
169,
8,
182,
171,
176,
123,
125,
154,
177,
124,
153,
174,
176,
154,
156,
175,
180,
155,
172,
174,
156,
158,
173,
178,
157,
169,
172,
158,
160,
171,
179,
159,
39,
41,
43,
106,
40,
42,
37,
39,
106,
104,
38,
121,
105,
35,
37,
104,
102,
36,
119,
103,
33,
35,
102,
100,
34,
120,
101,
31,
33,
100,
98,
32,
115,
99,
29,
31,
98,
96,
30,
118,
97,
27,
29,
96,
94,
28,
116,
95,
25,
27,
94,
23,
26,
117,
93,
106,
43,
45,
62,
107,
44,
63,
104,
106,
62,
60,
105,
114,
61,
102,
104,
60,
58,
103,
112,
59,
100,
102,
58,
56,
101,
113,
57,
98,
100,
56,
54,
99,
108,
55,
96,
98,
54,
52,
97,
111,
53,
94,
96,
52,
50,
95,
109,
51,
23,
94,
50,
21,
93,
110,
49,
62,
45,
47,
77,
63,
46,
78,
60,
62,
77,
75,
61,
92,
76,
58,
60,
75,
73,
59,
90,
74,
56,
58,
73,
71,
57,
91,
72,
54,
56,
71,
69,
55,
86,
70,
52,
54,
69,
67,
53,
89,
68,
50,
52,
67,
65,
51,
87,
66,
21,
50,
65,
19,
49,
88,
64,
77,
47,
1,
3,
78,
48,
2,
75,
77,
3,
5,
76,
85,
4,
73,
75,
5,
7,
74,
83,
6,
71,
73,
7,
9,
72,
84,
8,
69,
71,
9,
11,
70,
79,
10,
67,
69,
11,
13,
68,
82,
12,
65,
67,
13,
15,
66,
80,
14,
19,
65,
15,
17,
64,
81,
16,
*CONDUCTIVITY,TYPE=ISO
1.9900E-04,70.0
2.0100E-04,100.0
2.0600E-04,150.0
2.1100E-04,200.0
2.1500E-04,250.0
2.2200E-04,300.0
2.2700E-04,350.0
2.3400E-04,400.0
2.3800E-04,450.0
2.4500E-04,500.0
2.5000E-04,550.0
2.5700E-04,600.0
2.6200E-04,650.0
2.6900E-04,700.0
2.7300E-04,750.0
2.8000E-04,800.0
2.8700E-04,850.0
2.9200E-04,900.0
2.9900E-04,950.0
3.0600E-04,1000.0
*SPECIFIC HEAT
0.108 ,70.0
0.109 ,100.0
0.111 ,150.0
0.113 ,200.0
0.114 ,250.0
0.116 ,300.0
0.116 ,350.0
0.118 ,400.0
0.118 ,450.0
0.12
,500.0
0.121 ,550.0
0.122 ,600.0
0.123 ,650.0
0.125 ,700.0
0.126 ,750.0
0.128 ,800.0
0.13
,850.0
0.131 ,900.0
0.132 ,950.0
0.135 ,1000.0
*DENSITY
0.3
,70.0
*ELASTIC, TYPE = ISOTROPIC
31000000.0,0.31 ,70.0
30300000.0,0.31 ,200.0
29900000.0,0.31 ,300.0
29400000.0,0.31 ,400.0
29000000.0,0.31 ,500.0
28600000.0,0.31 ,600.0
28100000.0,0.31 ,700.0
27600000.0,0.31 ,800.0
27100000.0,0.31 ,900.0
26500000.0,0.31 ,1000.0
107,
*MATERIAL, NAME=N06600
39
*EXPANSION, ZERO = 70.0
, TYPE = ISO
6.8000E-06, 70.0
6.9000E-06, 100.0
7.0000E-06, 150.0
7.1000E-06, 200.0
7.2000E-06, 250.0
7.3000E-06, 300.0
7.4000E-06, 350.0
7.5000E-06, 400.0
7.6000E-06, 450.0
7.6000E-06, 500.0
7.7000E-06, 550.0
7.8000E-06, 600.0
7.9000E-06, 650.0
7.9000E-06, 700.0
8.0000E-06, 750.0
8.0000E-06, 800.0
8.1000E-06, 850.0
8.2000E-06, 900.0
8.2000E-06, 950.0
8.3000E-06, 1000.0
*PLASTIC
30000.0 ,0.0
,70.0
30000.0 ,0.0
,100.0
29200.0 ,0.0
,150.0
28600.0 ,0.0
,200.0
28000.0 ,0.0
,250.0
27400.0 ,0.0
,300.0
26800.0 ,0.0
,350.0
26200.0 ,0.0
,400.0
25700.0 ,0.0
,450.0
25200.0 ,0.0
,500.0
24700.0 ,0.0
,550.0
24300.0 ,0.0
,600.0
23900.0 ,0.0
,650.0
23500.0 ,0.0
,700.0
23200.0 ,0.0
,750.0
22900.0 ,0.0
,800.0
22600.0 ,0.0
,850.0
22300.0 ,0.0
,900.0
*SOLID SECTION, ELSET=Pipe,
MATERIAL=N06600
1.,
**
*ELSET, ELSET=P2
8,16,24,32,36,40,52,56
66,68,70,92,96,108,112,124
128,140,144,164,168,184,192,200
208,216,224,232,240,248,256,264
272
*ELSET, ELSET=P4
153
**
*INITIAL CONDITIONS,
TYPE=TEMPERATURE
ALL, 70.0
**
*AMPLITUDE,NAME=TEMPAMP,VALUE=
ABSOLUTE
0,70,5,600,50,600,55,70,
100,70
**
*AMPLITUDE,NAME=FILMAMP,VALUE=A
BSOLUTE
0,0.00446,0.28,0.00551,0.75,0.0071,1.23,0.0085
2
1.7,0.00957,2.17,0.01054,2.64,0.01128,3.11,0.0
1163
3.58,0.01185,4.06,0.01187,4.53,0.01166,5,0.011
12
50,0.01121,50.47,0.01158,50.94,0.0117,51.42,0.
0117
51.89,0.01154,52.36,0.0113,52.83,0.01072,53.3,
0.00993
53.77,0.00907,54.25,0.00786,54.72,0.0064,55,0.
0054
100,0.0054
**
*INCLUDE,INPUT=5cycles.th.inp
*INCLUDE,INPUT=5cycles.th.inp
*INCLUDE,INPUT=5cycles.th.inp
*INCLUDE,INPUT=5cycles.th.inp
40
Appendix B
This appendix details the analysis information section of the ABAQUS stress file,
valve.st, along with the portions changed from the thermal file.
**
** ABAQUS Input Deck Generated by HyperMesh Version : 12.0.110.40
** Generated using HyperMesh-Abaqus Template Version : hwdesktop12.0.110
**
** Template: ABAQUS/STANDARD 2D
**
*NODE, NSET=ALL
1, 1.45
, 0.0
2, 1.46875
, 0.0
3, 1.4875
, 0.0
…
SAME AS THERMAL FILE
…
899, 1.5250000029802, 9.1425330795996
900, 1.5625000044704, 9.1425330795996
901, 1.4875000014901, 9.1425330795996
**HWCOLOR COMP
1 55
*ELEMENT,TYPE=CAX8,ELSET=Pipe
272,
675,
677,
679,
886,
676,
901
271,
673,
675,
886,
884,
674,
899
270,
671,
673,
884,
882,
672,
900
…
SAME AS THERMAL FILE
…
3,
67,
69,
11,
80
2,
65,
67,
13,
81
1,
19,
65,
15,
18
*MATERIAL, NAME=N06600
*CONDUCTIVITY,TYPE=ISO
1.9900E-04,70.0
2.0100E-04,100.0
2.0600E-04,150.0
2.1100E-04,200.0
2.1500E-04,250.0
2.2200E-04,300.0
2.2700E-04,350.0
2.3400E-04,400.0
2.3800E-04,450.0
678,
887,
901,
885,
899,
883,
13,
68,
82,
12,
15,
66,
80,
14,
17,
64,
81,
16,
41
2.4500E-04,500.0
2.5000E-04,550.0
2.5700E-04,600.0
2.6200E-04,650.0
2.6900E-04,700.0
2.7300E-04,750.0
2.8000E-04,800.0
2.8700E-04,850.0
2.9200E-04,900.0
2.9900E-04,950.0
3.0600E-04,1000.0
*SPECIFIC HEAT
0.108 ,70.0
0.109 ,100.0
0.111 ,150.0
0.113 ,200.0
0.114 ,250.0
0.116 ,300.0
0.116 ,350.0
0.118 ,400.0
0.118 ,450.0
0.12
,500.0
0.121 ,550.0
0.122 ,600.0
0.123 ,650.0
0.125 ,700.0
0.126 ,750.0
0.128 ,800.0
0.13
,850.0
0.131 ,900.0
0.132 ,950.0
0.135 ,1000.0
*DENSITY
0.3
,70.0
*ELASTIC, TYPE = ISOTROPIC
31000000.0,0.31 ,70.0
30300000.0,0.31 ,200.0
29900000.0,0.31 ,300.0
29400000.0,0.31 ,400.0
29000000.0,0.31 ,500.0
28600000.0,0.31 ,600.0
28100000.0,0.31 ,700.0
27600000.0,0.31 ,800.0
27100000.0,0.31 ,900.0
26500000.0,0.31 ,1000.0
*EXPANSION, ZERO = 70.0
, TYPE = ISO
6.8000E-06, 70.0
6.9000E-06, 100.0
7.0000E-06, 150.0
7.1000E-06, 200.0
7.2000E-06, 250.0
7.3000E-06, 300.0
7.4000E-06, 350.0
7.5000E-06, 400.0
7.6000E-06, 450.0
42
7.6000E-06, 500.0
7.7000E-06, 550.0
7.8000E-06, 600.0
7.9000E-06, 650.0
7.9000E-06, 700.0
8.0000E-06, 750.0
8.0000E-06, 800.0
8.1000E-06, 850.0
8.2000E-06, 900.0
8.2000E-06, 950.0
8.3000E-06, 1000.0
*PLASTIC
30000.0 ,0.0
,70.0
30000.0 ,0.0
,100.0
29200.0 ,0.0
,150.0
28600.0 ,0.0
,200.0
28000.0 ,0.0
,250.0
27400.0 ,0.0
,300.0
26800.0 ,0.0
,350.0
26200.0 ,0.0
,400.0
25700.0 ,0.0
,450.0
25200.0 ,0.0
,500.0
24700.0 ,0.0
,550.0
24300.0 ,0.0
,600.0
23900.0 ,0.0
,650.0
23500.0 ,0.0
,700.0
23200.0 ,0.0
,750.0
22900.0 ,0.0
,800.0
22600.0 ,0.0
,850.0
22300.0 ,0.0
,900.0
*SOLID SECTION, ELSET=Pipe, MATERIAL=N06600
1.,
**
*INITIAL CONDITIONS, TYPE=TEMPERATURE
ALL, 70.0
**
*EQUATION
2
666,2,1.0,665,2,-1.0
2
667,2,1.0,666,2,-1.0
2
668,2,1.0,667,2,-1.0
2
669,2,1.0,668,2,-1.0
2
670,2,1.0,669,2,-1.0
2
671,2,1.0,670,2,-1.0
2
672,2,1.0,671,2,-1.0
2
673,2,1.0,672,2,-1.0
2
674,2,1.0,673,2,-1.0
43
2
675,2,1.0,674,2,-1.0
2
676,2,1.0,675,2,-1.0
2
677,2,1.0,676,2,-1.0
2
665,2,1.0,664,2,-1.0
2
664,2,1.0,663,2,-1.0
2
663,2,1.0,662,2,-1.0
2
662,2,1.0,661,2,-1.0
*BOUNDARY
594,2, ,0.0
595,2, ,0.0
596,2, ,0.0
597,2, ,0.0
598,2, ,0.0
599,2, ,0.0
600,2, ,0.0
601,2, ,0.0
602,2, ,0.0
603,2, ,0.0
604,2, ,0.0
605,2, ,0.0
606,2, ,0.0
590,2, ,0.0
591,2, ,0.0
592,2, ,0.0
593,2, ,0.0
*ELSET, ELSET=P2
8,16,24,32,36,40,52,56
66,68,70,92,96,108,112,124
128,140,144,164,168,184,192,200
208,216,224,232,240,248,256,264
272
*ELSET, ELSET=P4
153
*AMPLITUDE,NAME=PRESS,VALUE=ABSOLUTE
0,1000,200000,1000
**
**
********************************************************
*STEP, INC=5000, AMPLITUDE=RAMP
**, NLGEOM=YES
**
*STATIC, DIRECT
.5,2000
*TEMPERATURE, FILE=valve.th, BSTEP=1, BINC=1,ESTEP=20,EINC=185
*DLOAD, AMPLITUDE=PRESS, OP=NEW
P2, P2,1.0
P4, P4,1.0
*END STEP
44
Appendix C
Appendix C details the sub-input file, 5cycles.th, which is used in the thermal file to
minimize repeating lines.
*******************************************
*STEP, INC=5000
**
** {EST OF TIME STEP,MAX TIME,MIN TIME INCR, MAX TIME INC,SS RATE
*HEAT TRANSFER,DELTMX=15.0
0.05,100,0.001,10.0,0.0
**
*FILM,AMPLITUDE=TEMPAMP, FILM AMPLITUDE=FILMAMP
P2, F2,1.0,1.0
P4, F4,1.0,1.0
*NODE FILE, FREQUENCY=1
NT
*EL FILE
COORD,TEMP
*EL FILE,POSITION=NODES, FREQUENCY=1
TEMP
*END STEP
…
Repeats 4 more times for 5 total thermal cycles
…
45