IADC/SPE 112105
Connection Fatigue Index (CFI): An Engineered Solution for Connection
Selection and a Replacement for BSR
Sean Ellis, SPE, Thomas Wadsworth, SPE, Dr. Kang Lee, SPE, Michael Gerdes, and Shawn Altizer, SPE, T.H.
Hill Associates, Inc.
Copyright 2008, IADC/SPE Drilling Conference
This paper was prepared for presentation at the 2008 IADC/SPE Drilling Conference held in Orlando, Florida, U.S.A., 4–6 March 2008.
This paper was selected for presentation by an IADC/SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not
been reviewed by the International Association of Drilling Contractors or the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily
reflect any position of the International Association of Drilling Contractors or the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any
part of this paper without the written consent of the International Association of Drilling Contractors or the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is
restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of IADC/SPE copyright.
Abstract
For decades, the industry has used Bending Strength
Ratio (BSR) as a guideline for fatigue design
considerations in drill collars and other stiff body BHA
components. While the use of BSR as a design tool is
standard practice, it has limited value as a predictor of
connection fatigue. For example, two dissimilar
connections (type, size, or both) can have the same BSR
but display dramatically different fatigue performance.
Connection Fatigue Index (CFI) is a new design approach
that considers the dimensional, material, and operational
parameters that directly impact fatigue performance.
Using finite element analysis simulation, specific
connections are modeled under cyclic loading conditions
to produce CFI values. By accounting for variables that
impact fatigue, such as connection features, material
properties, stress relief features, applied make-up torque,
and loading conditions, CFI offers a more accurate and
robust tool for BHA design.
The CFI for each connection type is calculated for
common box ODs, pin IDs and dog leg severities and
presented in tabular format. The designer need only look
in the tables for the largest CFI value (of available
options) to know which connection type and size has the
best fatigue performance, and how the planned trajectory
impacts fatigue in the connection. Additionally, since the
values are quantitatively comparable, CFI allows the
designer to easily determine how much better one option
is relative to another (i.e. an option with a CFI value of 10
has twice the fatigue resistance of an option with a CFI
value of 5.) CFI tables exist for the most common
connection types and sizes, and separate tables will exist
for connections with stress relief features and those
operated in especially corrosive environments.
This paper describes the need for a technology like CFI,
the advantages CFI presents over currently available
technology, the basic methodology used to determine
CFI, and how and when to use CFI.
Introduction
Dramatic increases in rig spread costs and activity levels,
coupled with the technical challenges of today’s wells,
have magnified the risk of connection fatigue failure in
BHA components. Addressing fatigue concerns at the
design stage is a low-cost or no-cost method for
mitigating the risk of BHA connection failures while
operating and increasing the service life of the BHA
component.
An effective design tool should be accurate, technicallybased, and robust, offering the user the ability to compare
alternatives and select the best fit for a given project. To
create a design tool for a mechanism as complex as
fatigue requires computing power that was not available
at the time BSR was introduced. As such, BSR is a ratio
of box section modulus to the pin section modulus, a
relatively simple hand calculation.
Based on empirical data, a connection with a BSR of 2.5
should be "balanced", with equal fatigue loading between
the box and pin. Initially a BSR acceptance range of 2.252.75 was established. Subsequent acceptance ranges have
been adopted which index the BSR range to the
connection OD as shown below.
Connection OD
<6"
6" to 7-7/8"
≥ 8"
BSR Range
1.8 to 2.5
2.25 to 2.75
2.5 to 3.2
2
IADC/SPE 112105
As noted, BSR describes the simple geometric
relationship between pin and box section moduli, which is
a coarse and inaccurate predictor of connection fatigue
life. Thread profile, make up torque, stress relief features,
and bending moment can all have significant impact on
fatigue performance but are not part of BSR
methodology. This explains why two connections with the
same BSR may have dramatically different fatigue lives,
and connections outside the acceptable BSR range may
actually perform much better from a fatigue standpoint
than acceptable connections. CFI offers a much more
accurate method to compare and select connections and
considers the major drivers of fatigue not reflected in
BSR calculations.
back (BBB), dog leg severity/bending moment (DLS/BM). *CFI
methodology allows for the inclusion of corrosion as a
fatigue life input.
As Table 1 shows, BSR methodology considers only the
pin ID, box OD, and taper of the connection as inputs,
which, depending on other factors, may have negligible
impact on fatigue performance. Even in analyses where
DLS and connection type are held constant, and only
OD/ID and MUT are varied, BSR can yield inaccurate
results.
Pin ID
1.5
P
Contrasting CFI and BSR
Major Fatigue
Driver
Connection Factor
BSR
CFI
PIN
BOX
Thread Root Radius
X
X
X
MUT
X
P
1.314
4.5
B
P
6,315
6(3.33)
5
B
P
13,949
6(4.50)
B
P
P
17,564
6,315
6(3.13)
B
P
B
P
13,949
6(3.75)
P
P
2.712
P
14,653
CFI
1.638
BSR
6,315
MUT
6(2.66)
CFI
2.612
BSR
10,977
MUT
6(3.43)
CFI
3.166
BSR
10,977
MUT
6(4.06)
CFI
3.769
BSR
17,564
P
14,653
BSR High
BSR In Range
P
10,977
BSR Low
MUT
3.024
5.5
P
P
6(3.95)
P
6(1.75)
3.229
P
6(4.21)
P
2.237
2.54
5.25
6(2.29)
2.5
1.403
2.095
Box OD
CFI is based on application of the Morrow Strain-Life
Model, which considers both the crack initiation and
propagation phases in determining fatigue life.
Connection features and loading conditions are modeled
using a finite element analysis program, which provides
critical input parameters for the Morrow Strain-Life
Model. Connection fatigue life is then estimated using the
Morrow Strain-Life Model which is converted to CFI.
The numeric representation of CFI values is a simplified
representation of relative logarithmic fatigue life values
and is detailed in the Appendix. For example, 23(9.6)
represents 9.6 x 1023. Details of the process used to
calculate CFI can be found in the Appendix. All relevant
geometric factors, such as outer diameter, inner diameter,
thread form, and stress relief features are considered in
the model, as are make up torques and bending moments.
Table 1 compares the inputs used to calculate BSR and
CFI, and indicates whether they impact pin fatigue life,
box fatigue life, or both. See the Appendix for more detail
on these drivers of connection fatigue life.
6(2.65)
2
P
Table 2 – CFI and BSR value chart for NC 38 at 6°/100' for
different OD/ID combinations (P and B indicate the weak
member (pin or box) in fatigue based on CFI, and the limiting
member for MUT). Note for 4.5” box OD, BSR predicts box
failure while CFI more accurately predicts pin failure.
As Table 2 illustrates, only two connection sizes (5" x
1.5" and 5" x 2") are within the recommended BSR range
of 1.8 – 2.5 for this connection. CFI values, though,
indicate that fatigue performance across the various
OD/ID combinations actually falls into a narrow range
while BSR fluctuates significantly. Additionally, the two
connections deemed acceptable by BSR criteria have CFI
values in the lower half of the sample.
X
Thread Taper
X
X
X
Pin ID
X
X
X
Box OD
X
X
X
X
Pin SRG
X
X
Box Boreback
X
DLS/Bending
Moment
X
X
X
Material Properties
X
X
X
Mud Corrosion
*
X
X
Table 1 – Factors that impact connection fatigue life: make
up torque (MUT), pin stress relief groove (SRG), box bore
Also interesting to note in Table 2 is the impact of
increased pin ID on the fatigue life of the connection. The
5.5" x 2.5" connection has predicted fatigue life very
similar to the 5.5" x 1.5", with obviously a much larger
pin ID. While the BSR for both connections exceeds the
recommended maximum, each performs better than the
two connections that BSR would indicate as optimum. In
this particular example, large connection pin IDs typically
thought unreliable are in fact acceptable. Tool design
engineers may appreciate this facet in that larger bores
may be designed to facilitate more room for equipment
and electronics in specialty tools without sacrificing
connection fatigue performance.
IADC/SPE 112105
3
Using CFI
CFI allows the user to compare and select connections
based on type, size, and operational parameters that
impact fatigue life. Specifically, dog leg severity and
make up torque contribute to the loading conditions, and
thus fatigue, on the connection, but can change as defined
by the operational needs of the user. To address this and
offer a more robust design tool, CFI values for the same
connection type and size are listed in tabular form with
these parameters varied. Separate tables also exist for
those connections with and without stress relief features.
Table 3 shows an example of a CFI chart for two
connections with stress relief features. CFI values can
have dramatic range across connection type or other
dimension and the numbering convention was developed
to accommodate this.
DLS(degree/100feet)
Connection
OD
ID
1
2
6
NC 46
6 3/4
2 13/16
23(9.6)
18(5.1)
11(1.0)
NC 50
6 3/4
2 13/16
21(2.4)
16(3.6)
9(1.0)
Table 3 – Example CFI value chart for NC 46 and NC 50
connections with SRF
Connection Selection
CFI can be used to compare connections when BHA
materials are defined and only a connection selection
remains. A common example is the choice of NC 50 or
NC 46 connections with 6 3/4" drill collars.
The CFI values for each connection can be compared for
the same well bore conditions. Table 4 shows the CFI
and BSR for NC 46 and NC 50 connections with SRF
used on 6 3/4" OD and 2 13/16" ID drill collars at two
DLS.
CFI
Connection
BSR
1°/100'
6°/100'
NC 46
3.53
23(9.6)
11(1.0)
NC 50
2.37
21(2.4)
9(1.0)
Table 4 – CFI and BSR for NC 46 and NC 50 connections
used on 6 3/4" OD and 2 13/16" ID drill collars
The BSR comparison between these connections would
predict the NC 50 connection as the superior connection,
as it falls within the accepted range. However, at a near
vertical 1°/100' DLS, CFI comparison shows that the NC
46 connection will have a relative fatigue life
approximately 400 times that of the NC 50 connection.
At a deviated wellbore of 6°/100' DLS, CFI comparison
shows that the NC 46 connection CFI value of 11(1.0)
should have a relative fatigue life approximately 100
times that of the NC 50 connection CFI value of 9(1.0).
An Extreme Example: Drill Collar Size and Connection
Type
Determining drill collar sizes and connection types is a
common task in BHA design, but the designer often
makes selections based on heuristic and not technical
methods. To illustrate this point, consider an extreme
example in evaluating drill collar options for a slick BHA
design. The well parameters are shown in Table 5, and the
drill collar options are shown in Table 6. Given the hole
diameter and BSR, the 6 5/8 REG connection on the 8
1/4" collars seems the obvious choice for the well section.
Hole Diameter (in)
13.5
Hole Angle (deg)
45
Mud Weight (ppg)
10
Weight on Bit (kips)
15
Table 5 – Wellbore parameters
Connection
OD
ID
SRF
BSR
NC 46
6 1/2"
2 13/16"
YES
3.07
6 5/8 REG
8 1/4"
2 13/16"
NO
2.61
Table 6 – Available drill collars dimensions and connection
types
However, as Table 7 shows, the NC 46 connection on the
6 1/2" collar actually offers a far superior fatigue life. To
compare the options, the relative DLS for each drill collar
was determined and the resulting CFI values were
calculated.
Connection
OD
ID
DLS
CFI
NC 46
6 1/2"
2 13/16"
3.631
13(7.1)
6 5/8 REG
8 1/4"
2 13/16"
2.454
9(4.7)
Table 7 – Available drill collars effective DLS and CFI value
The NC 46 option actually offers a fatigue life
approximately 15,000 times longer than 6 5/8 REG
connection on the 8 1/4" collars despite the significantly
higher relative DLS. The superior thread root design,
thread taper, and the use of SRF on the NC 46 connection
far outweigh the impact of the smaller drill collar size.
While the smaller collars may not be a realistic option,
CFI can still be used to optimize fatigue performance for
the 6 5/8 REG connection. With larger connection sizes,
make up torque can often be reduced without affecting
drilling operations.
Table 8 displays the fatigue
performance gained by reducing MUT for 6 5/8 REG
connection.
API
-10% API
-20% API
MUT (ft-lbs)
53,346
48,011
42,676
CFI
9(4.7)
11(1.4)
11(7.9)
Table 8 – Increase in CFI by reducing MUT for a 6 5/8 REG
connection with 8 1/4" OD and 2 13/16" ID without SRF at a
2.454 DLS
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IADC/SPE 112105
A 20% reduction in MUT translates to a comparative
fatigue life approximately 170 times that at standard API
make up torque while still maintaining adequate seal
integrity (49.7 ksi seal stress with 7 23/32 bevel diameter
and 42,676 ft-lbf MUT).
sizes within a particular connection type or across
different connection types and sizes.
Summary
•
BSR is limited in effectiveness of predicting the
comparative fatigue life between connections.
Using BSR criteria to select connections can
produce inaccurate results.
•
CFI offers a more accurate and robust method
for predicting the comparative fatigue of
different connections, and accounts for multiple
factors that affect connection fatigue life.
•
CFI can also be used to:
1. Evaluate the impact of WOB on the fatigue
performance of rotary shouldered
connections
2. Understand how hole size vs. connection
OD (hole clearance) affects fatigue
performance
3. Choose the best connection type for fatigue
performance from available options
4. Select the optimal connection dimensions
(Box OD, Pin ID) for fatigue performance
5. Compare the fatigue performance of HWDP
and drill collars
6. Quantify the fatigue life benefit of stress
relief features on rotary shouldered
connections
7. Evaluate the fatigue impact of increasing or
decreasing MUT on rotary shouldered
connections
8. Determine how connection geometry
impacts tool design considerations from a
fatigue perspective
Analysis of HWDP vs. Drill Collars
When configuring a BHA, a designer must often choose
between heavy weight drill pipe (HWDP) and drill collars
for added bit weight. HWDP has a smaller moment of
inertia relative to drill collars and requires a lower
bending moment force to conform to a specific dog leg.
However, by calculating an equivalent DLS, the
connection fatigue performance for HWDP can be
compared quantitatively to drill collar connection
performance.
Consider a typical choice between 8" drill collars using
NC 56 connections with SRF, 8" OD and 2 13/16" ID,
and 6 5/8" HWDP with 6 5/8 FH connections with SRF,
8" OD and 4" ID, both deployed in a 5°/100' DLS. An
equivalent DLS of 2.56°/100' for the HWDP is calculated,
with the resulting CFI values displayed in Table 9.
Connection
CFI
6 5/8" HWDP w/ 6 5/8 FH
12(7.0)
8" Drill collar w/ NC56
9(9.6)
Table 9 – CFI of HWDP and Drill collar connections at 5°/100'
DLS
The comparison of CFI values shows that the HWDP
would have a fatigue life approximately 730 times that of
the drill collar. In this example the better performance of
the HWDP results not from connection design, but from
the lower equivalent DLS applied to the HWDP. With all
conditions equal, the NC 56 connection would offer better
fatigue performance than the 6 5/8 FH.
Impact of Stress Relief Features on Fatigue Life
Stress relief features have been shown to
fatigue performance of rotary shouldered
Using the CFI tables, the designer can
benefits of adding stress relief features to
An example is illustrated in Table 10.
improve the
connections.
quantify the
connections.
Connection
OD
ID
SRF
CFI @ 6°/100’
6 5/8 REG
8 1/4"
2 13/16"
NO
5(1.3)
6 5/8 REG
8 1/4"
2 13/16"
YES
7(1.3)
Appendix
For the analyses to be discussed herein (taking plastic
strain, stress, and fatigue into account), the Morrow
Strain-Life Model is used. The Morrow Strain-Life
Model was chosen as it accounts for the fatigue crack
initiation phase, not just the crack propagation phase.
This is important as the connection geometry (thread
design or stress relief groove width) heavily influences
fatigue performance. Using a fatigue model such as the
Forman model, which assumes an initial crack size, would
not capture the effects of connection geometry. Equation
1 is the Morrow Strain-Life Equation used to calculate
fatigue life.
Table 10 – 6 5/8 REG fatigue performance at 6°/100'
Comparing the CFI values, it is clear that having stress
relief features on the 6 5/8 REG improves the relative
performance of the connection by a factor of 100. This
approach may be taken and used to compare connection
εa =
σ ′f − σ m
Where:
E
(2 N ) + (ε ′
b
f
f
− ε mp )(2 N f
) ...... (1)
c
IADC/SPE 112105
εa
σ ′f
σm
5
= Strain amplitude
= Material fatigue constant determined
experimentally
= Mean stress (psi), when
σ m = σ mys
σ m > σ mys , set
E
= Young’s Modulus (psi)
Nf
= Number of cycles to failure
b
= Material fatigue constant determined
experimentally
ε ′f
ε mp
= Material fatigue constant determined
experimentally
= Mean plastic strain, when
ε mp
c
σ m ≤ σ mys , set
=0
= Material fatigue constant determined
experimentally
A quick study of this equation shows that if the mean
stress in the critical area is above the yield strength of the
material (100 KSI in the case of the drill collars used in
these studies), the variables that drive the fatigue life
calculation are strain amplitude and mean plastic strain.
Therefore, the model with the highest combination of
strain amplitude and mean plastic strain will have the
lowest fatigue life. If the mean stress in the critical area is
less than the yield strength of the material, the strain
amplitude and mean stress are the variables that drive the
fatigue life calculation. In these cases, the model with the
highest combination of strain amplitude and mean stress
will have the lowest fatigue life.
Mesh
An example of the type and size of mesh used is shown in
Figure A1. Each model that is evaluated is “broken up”
into discrete pieces or “elements.” The mesh is the lattice
that is the sum total of all of the elements. In order to
accurately describe the geometry and shape of a model,
the elements must be small enough to closely approximate
the contours present in the specific area(s) of interest. In
the case of a rotary shouldered connection, the threads
and the stress relief features are the prime areas of
interest. Therefore, it is important to have a dense mesh
in these regions. Regions of the connection away from
these critical areas may have a coarser mesh as the
stresses and strains here are generally not of much
interest.
Figure A1 – 6 5/8 REG axis symmetric connection model.
Smaller elements are necessary in the regions of interest,
while coarser mesh is allowable in non-critical areas.
Application of MUT
Applying torque to a computer generated model of a
rotary shouldered connection is much more difficult than
loading an actual connection into an iron roughneck and
pressing the “GO” button. Successfully modeling a threedimensional connection (getting a convergent solution)
can be a daunting task because of the amount of sliding
contact between the thread flanks, the helical nature of the
thread path, and the boundary conditions. As a result,
rotary shouldered connections are most easily modeled in
two dimensions.
Two dimensional axis-symmetric
models with asymmetric (bending) loads must be created.
MUT is approximated by either assuming a certain
amount of thread and shoulder overlap, or by applying a
thermal gradient (to expand the material thereby creating
thread flank and shoulder interference) to the pin and/or
box. The bulk stresses induced from applying MUT to an
actual connection are known or calculable in three key
areas (Figure A2). Using these known or calculable
values, correctly approximating the MUT on the two
dimensional connection model can be achieved by
adjusting the overlap or thermal layer temperature, and
comparing the resultant stresses to those defined to be
present in an actual connection of the same type and
dimensions.
6
IADC/SPE 112105
high stress and strain amplitude and propagate across the
drill collar resulting in a failure. To evaluate the
differences in connection fatigue life, the numerous
factors which affect the stress level at the last engaged
tooth need to be considered. Often these factors influence
or are dependant on one another and need to be evaluated
together in order to determine the fatigue life.
Bending Moment
Figure A2 – 6 5/8 REG 8" x 2-13/16" rotary shouldered
connection critical stress areas:
Seal area, 3/4" from
shoulder in pin, 3/8" from shoulder in box.
Bending Load
Axial loads and pressure are generally simple to apply.
Applying a bending load to a two dimensional axissymmetric asymmetric model generally requires the use
of a special element type. When modeling bending in a
rotary shouldered connection, it is important to bend the
connection multiple times in order to generate the best
approximation of the stress state at the thread roots.
During connection make up, the last few engaged pin
threads, any remaining unengaged pin threads, and some
areas of a stress relief groove (if present) are usually
plastically deformed. Since the stresses are plastic,
bending the connection once will not give accurate stress
and strain values. The connection must be bent multiple
times to allow for the effects of stress relieving and stress
redistribution. In an actual connection made up and run
down hole, this will occur once the connection is rotated
more than one revolution while bent or buckled.
CFI Calculation
CFI is expressed as a numeric representation of the
fatigue life. The fatigue life is determined by entering the
stress and strain values determined from FEA into the
Morrow Strain Life equation. These resulting values are
often expressed as a logarithmic value. CFI is represented
by a simplified expression of the logarithmic value. The
exponent of the base 10 multiplier is displayed as the first
number and the coefficient is displayed in parenthesis.
The exponent value affects the fatigue life far more than
the coefficient. By displaying the fatigue life in this
manner a quick comparison may be made.
25,600,000 = 2.56 x 107 = 7(2.56)
Connection Attributes
CFI is directly related to the calculated fatigue life of a
connection and in turn the attributes input into the
calculations. The fatigue life of a connection based on the
CFI method is driven by the Morrow strain-life model as
described previously. The point of lowest fatigue life
found through FEA is generally at the last engaged thread
of either the box or pin, depending on the size of the
connection. Fatigue cracks will initiate at this point of
Applied bending moment will directly affect the fatigue
life of a connection. Any applied bending force on a
connection will cause a compressive force and a tensile
force on opposing sides of the connection bending plane
(unless there is a net compressive or tensile axial force
applied in addition to the bending load). The increased
tensile force will cause increased strain in the pin and
box. As the connection is rotated this strain is oscillated
between maximum and minimum throughout every point
in the connection. These oscillating forces cause the
fatigue which leads to crack initiation, crack propagation,
and eventual failure. The amount of bending moment
applied to a connection will significantly change the
connection fatigue life. Figure A3 shows the increase in
stress levels in a connection with increased bending
moment.
Figure A3 – 6 5/8 REG connection at two different DLS
bending moments, DLS = 6°/100' (left) vs DLS = 2°/100'
(right), and corresponding critical stress of 119.69 ksi vs
95.29 ksi.
Thread Taper
The taper of a thread will directly affect the stress levels
in a connection during fatigue. For two given thread
tapers, the larger taper will result in a larger cross
sectional area at the back of the box and the neck of the
pin. Figure A4 illustrates the differences in cross section
area between a 6 5/8 REG connection with a 2" taper and
a NC 56 connection with a 3" taper. Most of the bending
in a connection will occur in the back of the box and the
pin neck and will directly influence the stress level at the
last engaged tooth. The taper with the larger cross section
area will have lower bending stresses for a given load
than the connection with a smaller cross section area.
These lower bending stresses in the connection will result
in a longer fatigue life.
IADC/SPE 112105
7
improved fatigue performance of the connection. Figure
A6 shows the strain distribution at the pin neck of two
connections, with the same connection type, subjected to
the same loading with one of the connections having a
SRF.
Figure A6 – Last engaged thread root in pin, 6 5/8 REG with
same OD and ID, without any SRF (left) vs. with both pin &
box SRF (right). Note the SRF reduced the pin critical stress
from 188.74 ksi to 159.07 ksi or by 12%.
Make Up Torque
Figure A4 – Dimensional differences between 6 5/8 REG and
NC 56 connections. Differences in thread taper and root
radius drive the difference in box fatigue life. (The difference
in thread root radius can be seen more clearly in figure A5.)
Root Radius
Thread root radius acts as a stress concentrator when a
connection is subjected to a bending moment. The stress
concentration level at the thread root is dependant on the
size of the root radius. Stresses at a root radius become
more evenly distributed with a larger root radius and will
result in a lower stress at the root radius. The lower stress
concentration of a larger root radius will typically result
in a longer fatigue life.
Figure A5 – Last engaged thread root in box, 6 5/8 REG (left)
vs. NC 56 (right) with same OD and ID. Note the thread root
radius difference and corresponding critical stress of 119.69
ksi for 6 5/8 REG vs. 103.83 ksi for NC 56 and 15% stress
reduction.
Stress Relief Features
Stress Relief Features (SRF) will reduce stress at the last
engaged thread. SRF remove unengaged threads that act
as stress concentrators and add flexibility in the
connection outside of the threaded area. This allows for
bending across the groove rather than across the
unengaged threads. The SRF will improve the stress
distribution in the connection, reduce stress concentration,
and improve flexibility in the connection when a bending
moment is applied. These attributes will result in
Make up torque (MUT) will directly affect the mean
stress level at the last engaged thread prior to fatigue. As
the MUT increases or decreases, the stress level at the last
engaged thread of both the pin and box will change. The
pin neck will be strained further due to the threaded
portion of the pin being pulled from the pin shoulder face
as the MUT increases. This causes more stress at the last
engaged pin thread. The box will be strained radially due
to the taper and flank angle of the thread as MUT is
increased, causing more stress at the last engaged box
thread. These increased stress levels caused by MUT will
reduce the fatigue life of a connection.
Figure A7 – Last engaged thread root in box. Same 6 5/8 REG
connections with both pin & box SRF. API MUT (left) vs. -20%
API MUT (right). Note: -20% API MUT reduced the box critical
stress from 109.18 ksi to 90.58 ksi or by 21%.
If the local stress levels at the last engaged thread result in
plastic yielding, MUT will not have a significant affect on
fatigue life. For most connections, stresses at the last
engaged pin thread which cause plastic strain will be
created at MUT much lower than API MUT. Therefore
the fatigue lives of most pin weak connections are not
significantly affected by MUT. Mean stress changes at
the box last engaged thread are far more significant than
at the pin, and for most connections remain in the elastic
region beyond API MUT. Typically only box weak
connections in which the strain level at the last engaged
box thread does reach plastic yielding will be significantly
affected by MUT.
8
IADC/SPE 112105
Box OD / Pin ID
Outer Diameter (OD) and Inner Diameter (ID) changes
may affect the stress level at the last engaged thread
because both dimensions directly affect MUT required
and the bending moment the connection the connection
experiences under a given load.
OD and ID will affect the bending moment required to
force a BHA body to conform to a specific size hole or
dog leg. When BHA components are placed down hole
and weight is applied, the BHA will generally conform to
the internal geometry of the wellbore. The bending
moment required to deflect a BHA into a hole is directly
related to the BHA moment of inertia. The moment of
inertia is directly dependant on the OD and ID of the
BHA. This relationship can be seen by examining a
simple equation for stresses in a beam subjected to a
bending moment.
σ = My/I........................................................................ (2)
where:
σ
= maximum compressive or tensile stresses in the
beam (psi)
M
= bending moment (in-lbs)
Y
= axis of symmetry (in)
I
= Moment of Inertia
where:
I
= π/64 (OD4 – ID4) (in4)................................ (3)
where:
OD = outer diameter (in)
ID = inner diameter (in)
OD and ID can change MUT by changing the pin and box
cross sectional areas by which MUT is generally
dependant. MUT is determined by calculating a torque
that will achieve a desired stress level in the weaker
member, pin or box. The cross sectional area which the
MUT stress is applied to the pin and box is directly
dependant on the ID for the pin area and the OD for the
box area. By changing the OD or ID the MUT may
change and possibly affect the fatigue life of the
connection.
References
1. T H Hill Associates, Inc.: DS-1®, Volume 2, Drill Stem
Design and Operation, third edition, T H Hill Associates,
Inc. (Jan. 2004).
2. API Recommended Practice 7G, Recommended Practice
for Drill Stem Design and Operating Limits, sixteenth
edition, American Petroleum Institute (August 1998).
3. Dowling, Norman E., Mechanical Behavior of Materials:
Engineering Methods for Deformation, Fracture, and
Fatigue. Prentice Hall, 1993, ch. 9 & 14.
4. Ellis, S., Reynolds, N., Lee, K.: “Use NC56 Connections
on 8˝ Drill Collars and Cut 1˝ or ¾˝ Pin Stress Relief
Grooves on Rotated BHA Connections NC38 and Larger”,
SPE 87191 (2004).
5. Hill, T., Ellis, S., Lee, K., Reynolds, N.: “An Innovative
Approach To Reduce Drill String Fatigue”, SPE/IADC
87188 (2004).
6. McCarthy, J. Everage, D., Lee, K.: “Application of
Increased MUT on API Rotary-Shouldered Connection:
Goodman Diagram vs. Strain-Life Model”, SPE 87190
(2004).
7. Gokhale, S., Ellis, S., Lee, K.,: “The Effects of Stress
Relief Features on HWDP and Drill Collars: Are Stress
Relief Features Necessary and When are They Most
Beneficial?”, SPE 98992 (2006).