Creep Analysis of a Bolted Joint- A Sensitivity Study of Bolt Relaxation
Due To Different Assembly Preloads
by
Zachariah K. John
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Sudhangshu Bose, Thesis Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December, 2012
(For Graduation May, 2013)
i
© Copyright 2012
by
Zachariah K. John
All Rights Reserved
ii
CONTENTS
Creep Analysis of a Bolted Joint- A Sensitivity Study of Bolt Relaxation Due To
Different Assembly Preloads ........................................................................................ i
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
LIST OF SYMBOLS ........................................................................................................ vi
ACKNOWLEDGMENT ................................................................................................. vii
ABSTRACT ................................................................................................................... viii
1. Introduction.................................................................................................................. 1
2. Methodology ................................................................................................................ 3
2.1
Validation of ANSYS Model for Creep ............................................................. 3
2.1.1
Curve Fitting .......................................................................................... 3
2.1.2
Hand Calculation for Stress Relaxation in a Solid Cylinder .................. 6
2.1.3
FE Model of Solid Cylinder for Stress Relaxation Calculations ........... 8
3. FE Analysis and Results of Bolted Flange ................................................................ 12
3.1
Bolted Flange Model ........................................................................................ 12
3.2
Results & Discussion ....................................................................................... 15
4. Conclusions................................................................................................................ 19
5. References.................................................................................................................. 20
6. Appendix.................................................................................................................... 21
iii
LIST OF TABLES
Table 1: Regressed Coefficients for Modified Time Hardening Creep Law at the
Specified Temperatures (Accounts for 0.1% & 0.2% Strains) .................................. 5
Table 2: Bolt Stress Relaxation for Different Preload Conditions .................................. 16
Table A 1: Data from Analysis Results used for generating Figure 12 and Figure 14.... 24
Table A 2: Data from Analysis Results used for generating Figure 13 ........................... 25
Table A 3: Experimental data for curve fitting using modified time hardening rule ...... 27
Table A 4: Ansys executable macro for generating regression coefficients for modified
time hardening creep model..................................................................................... 28
Table A 5: Database and macros used for generating results documented in this report. 29
iv
LIST OF FIGURES
Figure 1: Schematic of Creep Curve ([1], Chapter 8.2) .................................................... 2
Figure 2: Average isothermal 0.2% Creep Curves for Inco 718 Forgings [3] ................. 3
Figure 3: Curve Fit Comparison for different Creep Models against Experimental Data
@ 1000 F .................................................................................................................. 4
Figure 4: Curve Fit Comparison for Different Creep Models against Experimental Data
@ 1100 F .................................................................................................................. 4
Figure 5: FE Validation Model of Solid Shaft for Creep Analysis with Applied Boundary
Conditions .................................................................................................................. 8
Figure 6: Stress Relaxation for FE Results show good correlation with the exact solution
when limits on creep ratio and time increments are enforced ................................. 10
Figure 7: Creep Strain for FE Results show good correlation with the exact solution
when limits on creep ratio and time increments are enforced ................................. 11
Figure 8: Finite Element 3D Model of Bolted Flange ..................................................... 12
Figure 9: Contact definition at bolted flange interfaces .................................................. 13
Figure 10: Boundary conditions employed for the creep analysis .................................. 14
Figure 11: Flange models with creep properties applied on components. ...................... 14
Figure 12: Preload Loss in Bolt: “Flange + Bolt” vs. “Bolt alone” subject to creep....... 15
Figure 13: Stress Relaxation at Bolt Shank as a Function of Time ................................. 17
Figure 14: Preload Relaxation is not significant for the given Scenario ......................... 18
Figure A 1: A square cycle that describes a simplified flight cycle. ............................... 21
Figure A 2: Flange Contact Pressure and Contact Status for Max. Preload Condition ... 22
Figure A 3: Stress relaxation at Flange 1......................................................................... 23
Figure A 4: Maple work sheet to obtain the solution stated in Eqn. 7 ............................ 26
v
LIST OF SYMBOLS
SYMBOL
DESCRIPTION
UNITS
 cr
Equivalent creep strain rate
1/Hour

Equivalent stress
T
Absolute temperature

C1, C 2, C 3, C 4
Regression coefficients
based on experimental data
 cr
t
Equivalent creep strain
time
Psi
Rankine (  R)
Not applicable
Inch/inch
Hour
T
Total equivalent strain
Inch/Inch
E
Equivalent elastic strain
Inch/Inch


E
Eo
 (t )
Equivalent elastic strain
rate
Modulus of elasticity
Time dependent equivalent
stress
1/Hour
Psi
Psi
o
Initial equivalent stress
Psi
Cons tan t
Constant of integration
Not applicable
vi
ACKNOWLEDGMENT
I would like to thank my colleagues at Pratt & Whitney, for their advice and support
through out the project.
I am also thankful for the valuable guidance of Prof.
Sudhangshu Bose. Moreover, I would like to thank my wife and daughter for their
support and patience in completing this paper.
vii
ABSTRACT
Bolted joints in high temperature environments are subject to creep relaxation which
results in a loss of preload of the bolt. The assessment of the bolt preload relaxation due
to creep is difficult to perform in a multi-axial loading environment. A finite element
approach is employed to capture the interaction of these multiple loading environments.
Instances of this approach are observed in the work of many researchers. A range
(min/max) for the assembly preload (assembly torque for bolts) needs to be determined
for a given bolted joint. This paper explores the different creep models that the finite
element software (ANSYS) provides so that an acceptable curve fit is obtained for the
given material’s experimental creep data. It focuses on the effect of the minimum and
maximum assembly preloads on bolt relaxation due to creep using finite element
analysis. Analysis shows that the pre-load relaxation can be underestimated by up to
50% if the flange material is not considered for creep assessment (i.e. if only bolt shank
is used for creep assessment). The range of relaxed stress constricts as the initial
equivalent stress state approaches the yield strength of the material. Moreover, 50% of
stress relaxation in bolt and flange components occurs in the 1st 100 hours of creep and
the remainder of the stress relaxation occurs in the next 2900hrs of analyzed creep.
viii
1. Introduction
Bolted joints are very common in flange connections and are often subject to high
temperature environments especially in gas turbine engines. Due to the high temperature
environments, commercial and military applications of the bolted flanges also warrant
appropriate creep resistant materials. Creep is a time dependent plastic deformation of
materials when subject to high temperatures under stress [1]. Since bolted joints are
known for their reduction in assembly preloads due to long exposures to high
temperatures, it is necessary to account for the bolts’ stress relaxation and subsequent
reduction in flange stiffness. Creep stress relaxation is a phenomenon that occurs over
time when the load bearing capability of a component drops due to creep or other
mechanisms under a strain/deflection controlled environment such as the case of the
bolted joint [2]. This is a concern for bolted flanges because the stress relaxation can
lead to leakage through the flange interface and bending in the bolt. This problem is
very common in steam turbine industry. The addition of bending stress to the bolt
preload stress can lead to a low cycle fatigue (LCF) failure. A corollary to the creep
stress relaxation is creep rupture (not studied in this paper). Both phenomena are
associated with the inelastic behavior at high temperatures. Creep rupture is concerned
with the growth under a constant load where as creep stress relaxation is concerned with
the loss of load under a constant strain. Creep is categorized into three stages namely 1)
primary stage /stage 1 (region b of Figure 1), 2) steady state / secondary stage (region c
of Figure 1), and 3) tertiary stage (region c of Figure 1).
1
Figure 1: Schematic of Creep Curve ([1], Chapter 8.2)
The effect of secondary stage creep on bolted joints is the main focus of this paper
where a considerable amount of creep strain is accumulated. Inconel 718 (also known as
Inco718) is a common material found in gas turbine engine applications where creep
resistance is desirable. The material has high resistance to creep up to 1300  F [3].
Elastic and creep properties of this material are used for assessing the sensitivity of bolt
relaxation due to varying assembly preloads. A finite element model approach using
ANSYS is used to facilitate this investigation. Similar investigations haven been
adopted by other researchers and an instance of this approach is seen in the work of
Boudiz, A. and Nechache, A. [4].
2
2. Methodology
2.1 Validation of ANSYS Model for Creep
2.1.1
Curve Fitting
One needs to verify that the creep behavior that the finite element model predicts is
in line with the experimental results. Data for 0.1% and 0.2% creep strain for Inco 718
[3] are used for this analysis, and the exact solution (closed form solution) for a simple
problem is compared against the Finite Element (FE) results for verification. The creep
data is regressed with one or more of the 13 available creep models in ANSYS [5]. The
model that yields the best curve fit is chosen for the creep analysis. The experimental
data available in the public domain [3] for the 0.2% creep strain is shown in Figure 2.
Figure 2: Average isothermal 0.2% Creep Curves for Inco 718 Forgings [3]
Since the data is available in terms of hours for a given creep strain, applied stress
and temperature, two ANSYS creep models are chosen for curve fitting. One is the
3
Norton creep model and the other is the Modified Time Hardening Creep Model. The
available experimental data is for the secondary and tertiary stages of creep. In an effort
to obtain a good regression for the creep data, only the 0.1% and 0.2% creep regime is
sought after for a temperature and stress range of 1000  F - 1100  F and 100 ksi – 140
ksi respectively. Since Norton creep law requires creep strain rate as well, one can
assume a linear slope between the 0.1% and 0.2% creep strains. This assumption will
introduce some error in the regression data. The Modified Time Hardening creep model
only requires stress, strain and time for the given temperature.
Since all of these
quantities are available from the experimental data, one can obtain a better regression for
this model. A comparison of the non linear regression results between the two models
against the experimental data is shown in Figure 3 and Figure 4.
Stress Vs Strain @ 1000degF
Creep Strain [in/in]
0.0025
0.002
Actual_Data
0.0015
ModifiedTimeHardening
0.001
Norton
0.0005
0
100000
110000
120000
130000
140000
Stress [psi]
Figure 3: Curve Fit Comparison for different Creep Models against Experimental
Data @ 1000 F
Stress Vs Strain @ 1100degF
Creep Strain [in/in]
0.0025
0.002
Actual_Data
0.0015
ModifiedTimeHardening
0.001
Norton
0.0005
0
100000
110000
120000
130000
140000
Stress [psi]
Figure 4: Curve Fit Comparison for Different Creep Models against Experimental
Data @ 1100 F
4
The ANSYS creep models depicted by the Norton and the Modified Time hardening
rules are given by the following equations [5]:

  C1 *  c 2 * e C 3 / T
Norton Creep Law: cr
Eqn. 1

Here,  cr = equivalent creep strain rate [1/hrs]
 = equivalent stress [psi]
T = absolute temperature [R- Rankine], and
C1, C2, C3 etc. = regression coefficients based on experimental data.
Modified Time Hardening Rule:  cr 
C1 *  C 2 * t C 31 * e C 4 / T
C3  1
Eqn. 2
Here,  cr = equivalent creep strain [in/in]
t = time in hours [hrs.], and
All other variables are as described in the above Eqn. 1.
The regressed curves in Figure 3 and Figure 4 clearly show a good fit for the Modified
Time Hardening Creep Law for the given temperatures. Coefficients obtained for the
Modified Time Hardening Creep Equation is thus used for the validation model as well
as for the bolted flange model. The regressed coefficients for the above mentioned
modified time hardening rule at 1000  F and 1100  F are shown in Table 1 below.
Table 1: Regressed Coefficients for Modified Time Hardening Creep Law at the
Specified Temperatures (Accounts for 0.1% & 0.2% Strains)
Regression based Coefficients
Coefficients
Values
1000F
1100F
C1
4.915E-55 4.3381E-54
C2
9.71011441 9.71011441
C3
-0.468065 -0.468065
C4
0
0
5
2.1.2
Hand Calculation for Stress Relaxation in a Solid Cylinder
In order to validate the creep model set up in ANSYS, a uni-axial creep model is
used. A solid cylinder with the dimensions of a ¼” bolt is used for the analysis. The
model is held at 1000  F isothermally and at a fixed uni-axial displacement to produce
an equivalent stress (von-mises stress) of 130ksi.
This problem of fixed strain is
formulated mainly to simulate the strain driven environment of the bolted flange model.
For a fixed strain condition and ignoring strains due to plasticity and thermals, the total
strain (fixed strain) can be expressed as follows [6].
 T   E   cr
Eqn. 3
Here,  T = total equivalent strain [in/in],  E = equivalent elastic strain [in/in], and
 cr = equivalent creep strain [in/in] as stated in Eqn. 2 above.
To calculate the relaxed stress for a given time, one needs to express stress as a
function of time. At a fixed displacement, the strain rate will satisfy the following
equation [6, 7]:


 E   cr  0
Eqn. 4


Here,  E = equivalent elastic strain rate, and  cr = equivalent creep strain rate as
described in Eqn. 1 above.
The elastic strain rate can be expressed as
1 d  (t )
, and the creep strain rate for the
Eo dt
above mentioned modified time hardening rule is C1 *  (t ) C 2 * t C 3 since C4=0 (if
temperature is held constant, the coefficient C4 can be assumed zero). Thus Eqn. 4
becomes
1 d (t )
 C1 *  (t ) C 2 * t C 3  0
Eo dt
Eqn. 5
6
Here, Eo = modulus of elasticity [psi],  (t ) = time dependant equivalent stress [psi],
and other variables are as described in Eqn. 1 and Eqn. 2.
This is a non-linear differential equation with a closed form solution [8] and is of the
form
1
 (t ) 
1
 t C 31 * Eo * C1 * C 2  t C 31 * Eo * C1  Cons tan t * C 3  Cons tan t  C 21


C3  1


Eqn. 6
Here, ‘Constant’ is the constant of integration.
Solving for the constant by utilizing the initial condition  (0)   0 , and through back
substitution, one can arrive at the following particular solution
1
 (t ) 
 t C 31 * Eo * C1 * C 2  t C 31 * Eo * C1   0 * e C 2*ln( 0 ) * C 3   o * e C 2*ln( o )


C3  1

1
 C 21



Eqn. 7
Here,  o = initial equivalent stress [psi] at time t = 0 hrs.
Thus, plugging in the creep regression coefficients at 1000F from Table 1, Elastic
Modulus- E0 of 0.25416 *10 8 psi, and initial stress-  0 of 130,000 psi into Eqn. 7 one
can evaluate the relaxed stress after 1475 hrs to be 109.487 ksi. Similarly, one can find
the creep strain after 1475 hrs in the following manner. Rearranging Eqn. 3, we get
 cr   T   E
Eqn. 8
From Hook’s Law, we have   Eo , and substituting
0
Eo
for  T and
 (1475)
Eo
for
 E one can solve for creep strain. Thus, the creep strain in Eqn. 8 can be written as
 cr 
0
Eo

 (1475)
Eo
Eqn. 9
7
Therefore the equivalent creep strain after 1475 hrs for the validation model that
represents a bolt in uni-axial fixed displacement is
 cr 
2.1.3
130000
109487

 8.0708 * 10  4 .
8
8
0.25416 * 10
0.25416 *10
FE Model of Solid Cylinder for Stress Relaxation Calculations
A solid cylinder representing the bolt shank of the bolted flange is modeled in ANSYS
with the same assumptions as mentioned in section 2.1.2. The cylinder is meshed with
8-node brick elements that support creep and other physical phenomenon including
plasticity. Figure 5 shows the model with the applied boundary conditions.
Figure 5: FE Validation Model of Solid Shaft for Creep Analysis with Applied
Boundary Conditions
Curve fitted creep data shown in Table 1 and the relevant elastic material properties
for Inco718 are entered into ANSYS and are solved for the initial stress state. Once the
initial stress state is solved, the creep effects are turned on and the creep analysis is
conducted for 1475 hours. A sensitivity study has been conducted on the FE model for
the following parameters: maximum equivalent creep ratio (‘cutcontrol’ option for creep
strain) for each iteration/sub step, and maximum time increment allowed for the
analysis. The creep strain and the relaxed stress match to within 0.025% of the exact
8
solution when the creep ratio is kept to a very small number (0.001) between iterations,
and the maximum time step is not allowed to exceed 1hr. These stringent constraints on
the iteration parameters however require the most amount of solution time. When the
analysis model gets large in conjunction with the introduction of non-linear effects due
to contact elements at component interfaces, large strains (as opposed to small strain
theory), and plasticity, more iterations are necessary to obtain convergence. Thus, it is
imperative to have a balance between solution time and solution accuracy. Removing
the restraint on the creep ratio between iterations and setting the not-to-exceed maximum
time step to 100 hrs, the model attains a converged solution to within 1.72% of the exact
solution. Comparisons of these sensitivity studies are plotted against the theoretical
values and are shown in Figure 6 and Figure 7 below.
9
Stress Relaxation Comparison
130000
Stress (psi)
125000
Exact Soln
120000
creep ratio <=0.001, MaxTime
Increment <=1hrs
115000
creep ratio =none, MaxTime
Increment <=100 hrs
110000
105000
0
500
1000
Time (hrs.)
Stress (psi)
Stress Relaxation Comparison
115500
115400
115300
115200
115100
115000
114900
114800
114700
114600
475
Exact Soln
creep ratio <=0.001, MaxTime
Increment <=1hrs
creep ratio =none, MaxTime
Increment <=100 hrs
500
525
Time (hrs.)
Close View of Stress Relaxation at 500 hrs
Figure 6: Stress Relaxation for FE Results show good correlation with the exact
solution when limits on creep ratio and time increments are enforced
10
Creep Strain (in/in)
Creep Strain Comparison
9.00E-04
8.00E-04
7.00E-04
6.00E-04
5.00E-04
4.00E-04
3.00E-04
2.00E-04
1.00E-04
0.00E+00
Exact Soln
creep ratio <=0.001, MaxTime
Increment <=1hrs
creep ratio =none, MaxTime
Increment <=100 hrs
0
500
1000
Time (hrs.)
Creep Strain Comparison
Creep Strain (in/in)
6.05E-04
6.00E-04
Exact Soln
5.95E-04
creep ratio <=0.001, MaxTime
Increment <=1hrs
5.90E-04
5.85E-04
creep ratio =none, MaxTime
Increment <=100 hrs
5.80E-04
5.75E-04
5.70E-04
475
500
525
Time (hrs.)
Close View of Creep Strain at 500hrs
Figure 7: Creep Strain for FE Results show good correlation with the exact solution
when limits on creep ratio and time increments are enforced
11
3. FE Analysis and Results of Bolted Flange
3.1 Bolted Flange Model
A 1/80th sector of the bolted flange has been built with 8-noded brick elements.
Figure 8 shows the bolted flange modeled in ANSYS.
Figure 8: Finite Element 3D Model of Bolted Flange
Surface-to-surface contact-elements are employed at all interfaces to simulate inter
component interaction. See Figure 9 for details. The bolt is modeled without the threads
and represents a 0.375-24 bolt. The nut is coupled to the bolt to simulate the threaded
joint. Weak springs are employed between the bolt shank and the flange holes in the
radial direction (with respect to the bolt hole) to facilitate convergence. Initial assemblypreloads are attained using appropriate interference fit between bolt under-head and
flange 1 contact elements. After solving for the assembly condition at room temperature
(70  F), an axial load representing a limiting engine condition (a representative axial
blow off load of 56,000 lbf is applied. Since only one sector is modeled, an equivalent
blow-off load of 700 lbf is applied at the end of the 2nd flange. The entire flange is held
12
isothermally at 1000  F. The effect of creep on different preload values is then assessed
by initializing the creep properties. A Separate creep analysis is performed for each
preload condition. Three preload scenarios are evaluated and are labeled as max (9000
lbf), mid (7500 lbf) and min (6000 lbf) preloads. Detailed boundary conditions for the
analysis are also shown in Figure 10.
Figure 9: Contact definition at bolted flange interfaces
13
Figure 10: Boundary conditions employed for the creep analysis
Two scenarios- one model with creep properties only at the bolt shank, and the other
with creep properties at the bolt shank and the flanges –are evaluated to gage the error in
neglecting flange components for creep evaluation. The models with the two scenarios
are shown in Figure 11.
Figure 11: Flange models with creep properties applied on components.
14
3.2 Results & Discussion
The thermal strains at 1000 F are very large compared to the creep strains at the
constrained ends. In order to assess only the effect of creep induced stress-relaxation,
the effect of thermal strains is not captured.
To simulate this condition, thermal
expansion coefficients are set to zero (this is consistent with the validation model of
solid cylinder described in section 2.1.3). Analysis has been performed at isothermal
conditions of 1000 F and the limiting stress condition is held to 3000 hours for creep
effects to develop.
A comparison of preload loss in the bolt due to creep relaxation is made between the
two models shown in Figure 11. The analysis shows that the bolt loses twice as much
preload when creep effects in the flange materials are considered in addition to the bolt
shank. Though the percent reduction in preload compared to the initial preload is very
small (1.066 %-reduction when bolt & flange materials are subject to creep, and 0.498
%-reduction when only bolt material is subject to creep), the preload reduction varies
greatly between the two models. This comparison is made at maximum preload
condition with a constant blow-off load. The load reduction for both the models at the
flange interface is shown in Figure 12. Thus, it is important to include flange materials
in addition to the bolt shank when creep effects are assessed on bolted joints.
Bolt Preload Relaxation
Bolt Preload [lbf]
7050
7030
7010
w/creep prop on bolt and flange
6990
w/ creep prop only on bolt
6970
6950
0
500
1000
1500
2000
2500
3000
Time[hrs]
Figure 12: Preload Loss in Bolt: “Flange + Bolt” vs. “Bolt alone” subject to creep
15
Sensitivity to creep of the bolt flange due to different preloads is assessed with the
‘bolt and flange materials’ subject to creep. The bolt relaxed stresses for each preload
scenario- max, mid and min preloads are 85.4%, 82.1%, and 72.8% of yield strength
(  ys ) respectively. The bolt stress relaxation (reduction) compared to their respective
initial stress states is the highest for the max preload condition and reduces as the initial
preload decreases. See Table 2 for details.
Table 2: Bolt Stress Relaxation for Different Preload Conditions
Bolt Stress Relaxation
Preload Values
Max Preload
(100%)
Mid Preload
(83.33%)
Min Preload
(66.67%)
Relaxed Stress Stress Reduction
as a percentage as a percentage
of Yield Strength of initial stress
[%]
[%]
85.4
27.6
82.1
16.2
72.8
6.64
The Table 2 suggests that the bolt equivalent stress (von-mises) relaxes more with
increasing preloads. It is also observed that the max and mid relaxed stress states only
vary within 3.3% of each other. This observation shows that as the initial stress state
approaches the material’s yield strength, the range of relaxed stresses constricts
(narrows). Creep stress reduction for each of the preload conditions is plotted as a
function of time in Figure 13.
16
Normalized Equivalent
Stress to Yield Strength
Stress Relaxation at Bolt Shank
1.2
1.1
max_preload
1
mid_preload
0.9
min_preload
0.8
0.7
0
500
1000
1500
2000
2500
3000
Time [hrs]
Figure 13: Stress Relaxation at Bolt Shank as a Function of Time
The plot suggests that more than 50% of the stress relaxation occurs during the first
100 hrs of creep. This can be very significant in-terms of assessing the life of the bolt
due to creep. For instance, let us assume that most of the creep damage on a given
bolted flange takes place during the take off and climb regime of a flight cycle (see
Figure A 1 in Appendix), and that the duration for this scenario is 50sec per mission.
Also assume that the life expectancy of the bolt is 30,000 flight cycles. This would
mean that the creep life of the part should be around 416 hrs. If the blow-off load is to
exceed the flange separation load such that the bolt is undergoing bending, the stress
relaxation characteristics shown in Figure 13 become very significant. Thus, the first 100
hrs of creep where more than 50% of stress relaxation occurs would constitute almost
25% of the bolt’s life. Therefore, it is important to ensure that the given stress relaxation
is acceptable and that the bolt preload loss is not significant enough to induce a design
shortfall in meeting the bolt’s life requirement.
For the given analysis, the author could not ascertain a significant preload loss due
to creep and this is attributed to insufficient blow-off load to effect a change in
overcoming the flange’s separation load. As shown in Figure 14, the preload loss for the
maximum preload condition is only 1% of initial preload value and reduces to 0.09% of
initial preload value for the minimum preload condition. Details on flange contact
behavior and pertinent deflections are shown in the Appendix.
17
Bolt Preload Relaxation
Flange Load [lbf]
6900
6400
max_preload
5900
mid_preload
5400
min_preload
4900
4400
0
500
1000
1500
2000
2500
3000
Time [hrs]
Figure 14: Preload Relaxation is not significant for the given Scenario
18
4. Conclusions
The creep analysis of the bolted flange provides an insight on the different
mechanisms involved in assessing its structural integrity. The analysis shows that one
needs to assess the creep effects of the flange material in conjunction with the bolt
shank. Otherwise, one might risk under predicting the bolt preload reduction by as much
as 50%. Bolts with higher assembly pre-loads relax more in their equivalent stresses
than the bolts with lower pre-loads. However, the range of the relaxed stresses constricts
as the initial stress state approaches the material’s yield strength. This range widens as
the initial stress state falls below 80% of the material’s yield strength. For the given
material (Inconel 718) and for the analyzed conditions (1000F Isothermal + initial
preload + representative blow-off load), it is seen that more than 50% of the bolt’s stress
relaxation occurs within the 1st 100 hrs of creep assessment.
It is observed that the equivalent stress states analyzed for some of the preload
conditions exceed the modeled creep data.
Subsequent extrapolations beyond the
modeled stress and strain ranges for creep will not yield accurate results that are
consistent with the field/experimental data. Thus, for a more accurate creep assessment
that correlates with the field data one needs to utilize a creep model that spans the design
space for temperature, creep strains and stress ranges of the component’s operating
environment.
19
5. References
1. Raman, Aravamudhan, Materials Selection and Applications in Mechanical
Engineering; Industrial Press Inc., New York, 2007.
2. Garofalo, Frank, Fundamentals of Creep and Creep-Rupture in Metals; The
MacMillan Company, New York, 1965.
3. United States. Federal Aviation Administration et-al., Metallic Materials
Properties Development and Standardization (MMPDS) [electronic resource]:
MMPDS-05; Federal Aviation Administration, Washington D.C, 2010.
4. Bouzid, Abdel- Hakim and Nechache, Akil, The Effect of Cylinder and Hub
Creep on the Load Relaxation in Bolted Flanged Joints; Journal of Pressure
Vessel Technology, August 2008, Vol. 130, pp: 031211-1 – 031211-9.
5. Release 10.0 Documentation for ANSYS.
6. Kraus, Harry, Creep Analysis; John Wiley & Sons, New York, 1980, pg. 57
7. Timoshenko, Stephen, Strength of Materials, Part II, Advanced Theory And
Problems, 3rd Edition, D. Van Nostrand Company Inc., New Jersey, 1956, article
93, pg. 532.
8. Maple 13.0 Software.
20
6. Appendix
Figure A 1: A square cycle that describes a simplified flight cycle.
Figure A 1 describes a simplified flight cycle that consists of idle, taxi, take-off,
climb, cruise, descent, landing, idle, and shut down.
21
Figure A 2: Flange Contact Pressure and Contact Status for Max. Preload
Condition
Figure A 2 shows the contact pressure and the contact status of interface # 3 labeled in
Figure 9. As expected, the contact pressure at the flange interface decreases from a peak
of 128.7 ksi to 113.6 ksi as creep stress relaxation occurs.
22
Normalized Equivalent
Stress to Yield Strength
Stress Relaxation at Flange 1
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
max_preload
mid_preload
min_preload
0
500
1000
1500
2000
2500
3000
Time [hrs]
Figure A 3: Stress relaxation at Flange 1
Figure A 3 shows the stress relaxation at flange 1. Here, the stress reduction as a
percentage of initial stress is almost the same for each of the three preload scenarios
(max, mid and min preloads) and are 22.5%, 20.6% and 20.7% respectively. This is not
the case for the bolt shank as indicated in Table 2.
23
Table A 1: Data from Analysis Results used for generating Figure 12 and Figure 14
9000lb Preload
Time
[hrs]
assembly
0.00001
initial stress state 0.00002
103.4132
206.5271
313.2101
416.3728
520.9777
615.0147
722.4011
803.7073
925.6665
1006.973
1128.932
1210.238
1332.197
1413.504
1535.463
1657.422
1747.661
1837.9
1928.139
2028.139
2128.139
2228.139
2328.139
2428.139
2528.139
2628.139
2728.139
2828.139
2928.139
3000
Load
[lbf]
9013.397
7045.934
7023.985
7017.22
7012.325
7008.571
7005.391
7002.871
7000.334
6998.46
6995.993
6994.478
6992.356
6991.027
6989.143
6987.954
6986.253
6984.658
6983.54
6982.466
6981.427
6980.32
6979.254
6978.215
6977.197
6976.196
6975.216
6974.253
6973.308
6972.388
6971.484
6970.84
Normalize
d to Initial
Preload
1.279234
1
0.996885
0.995925
0.99523
0.994697
0.994246
0.993888
0.993528
0.993262
0.992912
0.992697
0.992396
0.992207
0.99194
0.991771
0.99153
0.991303
0.991145
0.990992
0.990845
0.990688
0.990536
0.990389
0.990244
0.990102
0.989963
0.989827
0.989693
0.989562
0.989434
0.989342
7500lb Preload
Time
[hrs]
0.00001
0.00002
109.0912
216.7638
309.5309
433.3878
509.5027
643.1222
749.1339
809.4327
938.1724
1006.613
1161.653
1249.285
1336.917
1435.802
1534.686
1634.686
1734.686
1834.686
1934.686
2034.686
2134.686
2234.686
2334.686
2434.686
2534.686
2634.686
2734.686
2834.686
2934.686
3000
24
Load
[lbf]
7505.679
5761.586
5756.424
5754.52
5753.306
5751.995
5751.302
5750.227
5749.47
5749.07
5748.275
5747.879
5747.044
5746.604
5746.182
5745.728
5745.293
5744.871
5744.465
5744.074
5743.697
5743.332
5742.978
5742.635
5742.302
5741.978
5741.663
5741.194
5740.908
5740.689
5740.403
5740.221
6000lb Preload
Time
[hrs]
0.00001
0.00002
101.8785
210.7394
316.4384
455.1172
538.8377
633.3476
733.3476
833.3476
933.3476
1033.348
1133.348
1233.348
1333.348
1433.348
1533.348
1633.348
1733.348
1833.348
1933.348
2033.348
2133.348
2233.348
2333.348
2433.348
2533.348
2633.348
2733.348
2833.348
2933.348
3000
Load
[lbf]
5999.467
4487.982
4487.237
4486.896
4486.647
4486.382
4486.243
4486.1
4485.96
4485.831
4485.71
4485.595
4485.487
4485.384
4485.286
4485.191
4485.101
4485.013
4484.929
4484.847
4484.768
4484.691
4484.617
4484.544
4484.473
4484.404
4484.337
4484.271
4484.206
4484.143
4484.081
4484.04
9000lb Preload (bolt shank alone
for creep)
Time
[hrs]
0.00001
0.00002
107.3742
208.2189
323.2642
413.74
528.5123
618.677
722.1536
840.8186
904.2293
1049.286
1131.801
1214.315
1308.068
1401.822
1501.822
1601.822
1701.822
1801.822
1901.822
2001.822
2101.822
2201.822
2301.822
2401.822
2501.822
2601.822
2701.822
2801.822
2901.822
3000
Load
[lbf]
9013.397
7045.934
7037.739
7034.847
7032.272
7030.874
7029.169
7027.974
7026.724
7025.423
7024.772
7023.376
7022.635
7021.925
7021.154
7020.416
7019.66
7018.935
7018.236
7017.563
7016.911
7016.28
7015.667
7015.072
7014.493
7013.93
7013.38
7012.844
7012.32
7011.808
7011.306
7010.825
Normalize
d to Initial
Preload
1.279234
1
0.998837
0.998426
0.998061
0.997863
0.997621
0.997451
0.997274
0.997089
0.996997
0.996798
0.996693
0.996592
0.996483
0.996378
0.996271
0.996168
0.996069
0.995973
0.995881
0.995791
0.995704
0.99562
0.995538
0.995458
0.99538
0.995304
0.995229
0.995157
0.995085
0.995017
Table A 2: Data from Analysis Results used for generating Figure 13
Ys [psi] = 135000
9000lb Preload (bolt shank alone
9000lb Preload
7500lb Preload
6000lb Preload
for creep)
Normalize
Normalize
Normalize
Normalize
Time
EQV
d to Ys Time
EQV
d to Ys Time
EQV
d to Ys Time
EQV
d to Ys
[hrs]
[psi]
[hrs]
[psi]
[hrs]
[psi]
[hrs]
[psi]
0.00001 183914.31 1.3623282 0.00001 153035.28 1.133595 0.00001 122250.08 0.905556 0.00001 183914.31 1.362328
assembly
initial stress state 0.00002 159179.42 1.1791068 0.00002 132197.70 0.979242 0.00002 105251.96 0.779644 0.00002 159179.42 1.179107
103.41300 135235.08 1.0017413 109.09100 122546.39 0.907751 101.87800 101346.07 0.750712 107.37400 135607.41 1.004499
206.52700 131441.71 0.9736423 216.76400 120752.05 0.89446 210.73900 101005.30 0.748187 208.21900 132009.06 0.977845
313.21000 129055.71 0.9559682 309.53100 119681.38 0.886529 316.43800 100757.83 0.746354 323.26400 129491.50 0.959196
416.37300 127377.48 0.9435369 433.38800 118583.16 0.878394 455.11700 100494.63 0.744405 413.74000 128068.20 0.948653
520.97800 126095.47 0.9340405 509.50300 118025.87 0.874266 538.83800 100357.30 0.743387 528.51200 126612.80 0.937873
615.01500 125091.24 0.9266018 643.12200 117190.73 0.868079 633.34800 100216.04 0.742341 618.67700 125674.90 0.930925
722.40100 124164.42 0.9197364 749.13400 116623.54 0.863878 733.34800 100079.27 0.741328 722.15400 124750.99 0.924081
803.70700 123416.88 0.9141991 809.43300 116330.17 0.861705 833.34800 99952.77 0.740391 840.81900 123830.56 0.917263
925.66700 122536.24 0.9076759 938.17200 115759.12 0.857475 933.34800 99834.86 0.739517 904.22900 123388.09 0.913986
1006.97000 122019.79 0.9038503 1006.61000 115481.36 0.855417 1033.35000 99724.10 0.738697 1049.29000 122487.46 0.907315
1128.93000 121314.31 0.8986245 1161.65000 114907.39 0.851166 1133.35000 99619.59 0.737923 1131.80000 122026.84 0.903903
1210.24000 120882.52 0.8954261 1249.28000 114611.52 0.848974 1233.35000 99520.44 0.737188 1214.32000 121597.86 0.900725
1332.20000 120286.96 0.8910145 1336.92000 114332.11 0.846905 1333.35000 99426.09 0.73649 1308.07000 121143.60 0.89736
1413.50000 119918.71 0.8882867 1435.80000 114035.84 0.84471 1433.35000 99335.94 0.735822 1401.82000 120718.97 0.894215
1535.46000 119401.10 0.8844526 1534.69000 113755.91 0.842636 1533.35000 99249.60 0.735182 1501.82000 120297.85 0.891095
1657.42000 118932.67 0.8809827 1634.69000 113488.46 0.840655 1633.35000 99166.64 0.734568 1601.82000 119899.85 0.888147
1747.66000 118617.00 0.8786444 1734.69000 113234.31 0.838773 1733.35000 99086.81 0.733976 1701.82000 119528.55 0.885397
1837.90000 118320.64 0.8764492 1834.69000 112992.65 0.836983 1833.35000 99009.79 0.733406 1801.82000 119175.14 0.882779
1928.14000 118035.43 0.8743365 1934.69000 112761.96 0.835274 1933.35000 98935.39 0.732855 1901.82000 118842.42 0.880314
2028.14000 117738.90 0.87214 2034.69000 112541.53 0.833641 2033.35000 98863.36 0.732321 2001.82000 118525.33 0.877965
2128.14000 117458.38 0.8700621 2134.69000 112330.25 0.832076 2133.35000 98793.56 0.731804 2101.82000 118224.37 0.875736
2228.14000 117185.15 0.8680381 2234.69000 112127.57 0.830575 2233.35000 98725.81 0.731302 2201.82000 117936.61 0.873605
2328.14000 116915.76 0.8660427 2334.69000 111932.62 0.829131 2333.35000 98659.98 0.730815 2301.82000 117662.29 0.871573
2428.14000 116648.87 0.8640657 2434.69000 111744.97 0.827741 2433.35000 98595.93 0.73034 2401.82000 117398.76 0.86962
2528.14000 116387.66 0.8621308 2534.69000 111563.94 0.8264 2533.35000 98533.58 0.729878 2501.82000 117146.82 0.867754
2628.14000 116130.01 0.8602223 2634.69000 111388.39 0.825099 2633.35000 98472.79 0.729428 2601.82000 116903.91 0.865955
2728.14000 115877.95 0.8583552 2734.69000 111215.61 0.823819 2733.35000 98413.49 0.728989 2701.82000 116670.92 0.864229
2828.14000 115635.26 0.8565575 2834.69000 111052.12 0.822608 2833.35000 98355.59 0.72856 2801.82000 116445.75 0.862561
2928.14000 115396.33 0.8547876 2934.69000 110895.45 0.821448 2933.35000 98299.02 0.728141 2901.82000 116229.08 0.860956
3000.00000 115224.89 0.8535177 3000.00000 110796.42 0.820714 3000.00000 98261.96 0.727866 3000.00000 116022.94 0.859429
25
Figure A 4: Maple work sheet to obtain the solution stated in Eqn. 7
26
Table A 3: Experimental data for curve fitting using modified time hardening rule
/temp,1000
/1,seqv
/3,time
/2,creq
140000
0.001
88.95386144
140000
0.002
287.8490532
130000
0.001
455.9942943
130000
0.002
1475.568612
120000
0.001
2204.719233
120000
0.002
7134.331591
110000
0.001
9969.465819
110000
0.002
32260.55902
100000
0.001
41802.2829
100000
0.002
135269.5359
/temp,1100
/1,seqv
/3,time
/2,creq
140000
0.001
1.483080775
140000
0.002
4.799155316
130000
0.001
7.602552161
130000
0.002
24.60137656
120000
0.001
36.75811996
120000
0.002
118.9469446
110000
0.001
166.215641
110000
0.002
537.863271
100000
0.001
696.9473964
100000
0.002
2255.277567
Here, the 1st set of data is for a constant temperature of 1000 F and the 2nd set is for
a constant temperature of 1100 F. 1st column is stress in psi, 2nd column is creep strain,
and the 3rd column is time to reach the given creep strain in hours.
The data in the 1st set needs to be saved as an ASCII file with name
InpCrvFit_ModTimeHardn_1000degF.inp
The data in the 2nd set needs to be saved as an ASCII file with name
InpCrvFit_ModTimeHardn_1100degF.inp
Once these two files are created, one can run the ansys script provided in Table A 4 to
generate the regression coefficients for the creep model shown in Table 1.
27
Table A 4: Ansys executable macro for generating regression coefficients for
modified time hardening creep model.
!/input,curve_fitting,mac
fini
/clear,start
/filname,file1,1
/prep7
toffset,0
/com,BEGIN: CURVE FITTING USING MODIFIED TIME HARDENING LAW FOR 1100degF
tbft,eadd,2,creep,InpCrvFit_ModTimeHardn_1100degF,inp
tbft,list,2,
tbft,fadd,2,creep,mtha,
tbft,set,2,creep,mtha,,1,1
tbft,set,2,creep,mtha,,2,1
tbft,set,2,creep,mtha,,3,1
tbft,set,2,creep,mtha,,4,0
tbft,fix,2,creep,mtha,,4,1
tbft,set,2,creep,mtha,,tdep,1
tbft,set,2,creep,mtha,,tref,all
tbft,solve,2,creep,mtha,,0,1e5,1e-8,1e-8
!using modified time hardening creep law- model # 6
!tbft,plot,2,creep,hyper,mtha
tbft,fset,2,creep,mtha,
/com,END: CURVE FITTING USING MODIFIED TIME HARDENING LAW FOR 1100degF
/com,BEGIN: CURVE FITTING USING MODIFIED TIME HARDENING LAW FOR 1000degF
tbft,eadd,1,creep,InpCrvFit_ModTimeHardn_1000degF,inp
tbft,list,1,
tbft,fadd,1,creep,mtha,
tbft,set,1,creep,mtha,,1,1
tbft,set,1,creep,mtha,,2,1
tbft,set,1,creep,mtha,,3,1
tbft,set,1,creep,mtha,,4,0
tbft,fix,1,creep,mtha,,4,1
tbft,set,1,creep,mtha,,tdep,1
tbft,set,1,creep,mtha,,tref,all
tbft,solve,1,creep,mtha,,0,1e5,1e-8,1e-8
!using modified time hardening creep law- model # 6
!tbft,plot,1,creep,hyper,mtha
tbft,fset,1,creep,mtha,
/com,END: CURVE FITTING USING MODIFIED TIME HARDENING LAW FOR 1000degF
Save this script as an ASCII file with name curve_fitting.mac and execute the file in
ansys command line for generating the regression coefficients shown in Table 1.
28
Table A 5: Database and macros used for generating results documented in this
report.
Item #
Filename
Description
1
verify1.db
Ansys Version 10.0
database with the
verification model shown in
Figure 5
2
FLANGE4.db
Ansys Version 10.0
database with the Bolted
Flange Model shown in
Figure 8
3
run_verify1.mac
Macro for solving the
verification model (used
with verify1.db database)
4
run_flange4.mac
Macro for solving the
Bolted flange model (used
with FLANGE4.db
database)
Parameters in the “User Inputs” section of run_flange4.mac macro are modified to
analyze the different preload scenarios. Since the ansys log files to generate the database
and the control files for running the analysis are rather lengthy, they are not explicitly
documented in the appendix section. However, they are submitted in their entirety to the
university in compressed format.
Zipped file comprising of ansys databases is called AnsysDatabases_Version10.0.zip
Zipped file comprising of the executable macros is called Macros.zip.
29