-
Pergamon Engineering Failure Analysis, Vol 2, No. 1 pp. 1-30,
1995
Copyright 1995 Elsevier Science Ltd Printed in Great Britain.
All rights reserved
1350-6307/95 $9.50 + 0.00
1350-6307(95)00007-0
STRESS ANALYSIS OF DRILLSTRING THREADED CONNECTIONS USING THE
FINITE ELEMENT METHOD
K. A. M A C D O N A L D and W. F. D E A N S
Department of Engineering, University of Aberdeen, Kings
College, Aberdeen AB9 2UE, U.K.
(Received 25 January 1995)
Abstract--Stress analysis of the threaded connections in
drillstrings and bottom hole assem- blies has contributed to the
successful resolution of some downhole failures. The preload
applied from joint make-up torque directly affects the static
stress distribution within the connection--it also affects the
local mean stress levels about which the stresses arising from
fatigue loading oscillate. Considering a generic trapezoidal
threadform, the relationship between the nominal applied load and
the resulting peak and local elastic stresses at the critical
thread roots are established using the finite element method. The
distribution of peak stress in the connection is determined based
on the axial preload arising from make-up, and how this
distribution is modified by tensile and compressive axial loads.
Starting with a procedure of mesh convergence and model validation,
a two-dimensional axisymmetric elastostatic modelling approach is
used. In all cases, the roots of the first loaded tooth in the pin
and the last loaded tooth in the box are the sites of maximum peak
stress as expected, the pin peak stress being the greater. However,
considering the effects of fatigue loading by relating the
individual preload and tensile load cases to local and peak stress
ranges and mean levels demonstrates that the box becomes the
critical component.
1. I N T R O D U C T I O N
Downhole failure of the threaded connections in drillstrings and
bot tom hole assembly components by fracture and fatigue, although
uncommon, nevertheless occurs with sufficient frequency [1] to
focus attention on the detail design aspects of the connections.
The pr imary factors influencing connection failure are the
stresses at critical locations, and the material 's fatigue and
mechanical properties. Knowledge of the applied loads during
drilling in many circumstances carries with it great uncer- tainty.
Material strength requirements, wellbore geometric constraints,
hydraulic flow area considerations, and economic limitations have
all led to the widespread, if not universal, selection of
high-strength low-alloy (HSLA) steels for the majority of
drillstring tubular applications [2]. Hence , as the loading regime
and material selection are essentially either predetermined or
uncertain, detail design aspects of threaded connections have a
predominant role in offering control of fatigue and fracture
performance.
The search for new hydrocarbon resources and the development of
existing reserves are taking place in an economic climate
characterised by a depressed oil price and a concerted
industry-wide initiative to reduce costs. Such pressures have
dictated modern industry trends towards deeper and deviated wells
which place more stringent demands on the design and operat ion of
the load-carrying components of the drillstring.
Conventional drillstring connections are geometrically complex
and, in their threads, exhibit inherently severe geometr ic stress
concentrations. The criticality with regard to fatigue that this
infers is further exacerbated by the widely acknowledged
differential distribution of the load in such joints. The body of
knowledge regarding load distributions in threads dates f rom
earlier this century [3] and has since been contributed to by many
workers, whose collective efforts have been reviewed elsewhere [4].
Consideration of the stress concentrations in threads and notches
has also been made [5, 6]. Estimating the fatigue behaviour of a
connect ion-- in terms of
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K. A. MACDONALD and W. F. DEANS
crack initiation life--is readily accomplished in two stages
[7], where the stress concentration factor (SCF) resulting from the
main body stresses and thread bending stresses is first evaluated,
followed by determination of the material's fatigue strength
reduction factor, itself based on the SCF and the notch sensitivity
of the material. Finite element (FE) analysis readily provides the
first part of this two-stage fatigue analysis process by
determining the connection's general stress state and critical
SCFs.
The objective of the present work is to provide stress analysis
data in support of a wider ongoing research programme concerned
with the development of predictive models of fatigue damage
accumulation and limit state failure in drillstring threaded
connections, particularly those in the bottom hole assembly, i.e.
drill collars and stabilisers. Threadforms under consideration
include standard API designs (V-0.038R) in addition to the
trapezoidal type reported here.
1.1. Downhole failures
Fatigue has been recognised for some time as an important cause
of failure in general drillstring connections [8, 9], but it is
only in recent years that the serious problems arising from such
failures have occurred with sufficient frequency to merit detailed
attention to their cause and prevention [2, 10-14]. Recent North
Sea data from a single operator puts costs associated with downhole
separation of the drillstring at ca 10 million per annum [1].
Investigations of recent failures of drillstring components [1]
have, in the case of the most common casualty connections, revealed
a clear distinction between failure modes and the corresponding
failure sites. Connections (Fig. 1) when failing primarily by
fatigue, break consistently in the box at the root of the last
engaged thread (LET) farthest from the seal face (Fig. 2). However,
when the same connection fails entirely by ductile overload shear
fracture, the site of failure is in the pin LET adjacent to the
shoulder (Fig. 2). These observations are based on some 25
connection failures, where, subject to the difficulties presented
by post-separation damage to fracture surfaces and equipment [1],
no material or manufacturing deficiencies were apparent. In
section, the morpho- logy of fatigue cracks (Fig. 1) is
characterised by an approximate 45 orientation to the thread flank
at positions at and adjacent to the thread root, becoming more
straight (transverse to the drillstring axis) once a distance of
more than a few thread root radii away (Fig. 2). This behaviour is
consistent with tooth bending stresses influencing the short crack,
with body stresses becoming dominant at greater crack depths
[15].
1.2. FE analysis o f large threaded connections
The severe SCFs in threaded connections give rise to stresses
with high peak values and rapidly increasing gradients approching
the thread roots. The accurate estimation of highly localised
stresses in these regions is consequently an exacting computational
task. The task is demanding to the extent that a sufficiently
enriched three-dimen- sional FE model targeted to capture the peak
stress and gradient would in practice be unsolvable with most
generally available maniframe computing installations. Novel
solution strategies have been formulated [16] whereby a coarse
layer of anisotropic elements substitutes the threads, replicating
the differential load distribution. The method does not directly
yield the peak stresses giving the load distribution only-- the
local stresses must be computed subsequently.
The oil and gas industry has widely adopted two-dimensional
axisymmetric elasto- static FE analysis in the stress analysis of
threaded connections in oilfield tubulars [17]. This arises
primarily from the ability of the method to generate and solve
meshes sufficiently refined to correctly compute the localised
thread root stress field, other benefits accruing from ease of
modelling and reduced solution time, although in some cases it is
the only route possible to produce a solution. Elastic analysis is
sufficient unless thread root plasticity is so extensive as to
influence the overall load
rfenyvesHighlight
-
Stress analysis of drillstring threaded connections 3
Box connection
vNi ~x~
\
\ \ \ \
!
Pin connection
Pin LET
Z
R
Box LET
Drill collar Rotary shouldered
connection
Fig. 1. Drill collar showing the connection and its failure
sites.
distribution by affecting the relative strains within the
connection [15], and in any case is a recommended initial
approximation. Axisymmetric models give a parallel thread
representation of the joint and can accommodate axial and radial
loading and boundary conditions, the latter seemingly representing
a limitation for simulating drillstring components in bending. Some
FE solver codes now offer axisymmetric elements capable of
asymmetric loading [18] which facilitate non-uniform distributed
loads and allow modelling of applied bending in two-dimensional
axisymmetric models. Inevitably, however, such two-dimensional
analyses fail to represent both the thread helix and the runout
regions--important features of threaded connections.
Three-dimensional FE studies of threaded connections have been
conducted [19, 20], investigating the effects of pitch, stress
relief features and thread geometry
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K. A. M A C D O N A L D and W. F. DEANS
modifications, with helpful results. However, the models are of
necessity generally coarse and in some cases only a few threads are
considered and with simplified thread profiles.
2. C O N N E C T I O N S T U D I E D
2.1. Geometry
The geometry of the connection studied is shown in Fig. 1. It is
a 9 in. outside diameter drill collar connection but with a generic
trapezoidal threadform dimen-
(a)
(b)
S c a l e c m
Fig. 2(a) and (b). Caption on p. 5.
-
Stress analysis of drillstring threaded connections 5
(c)
Fig. 2. Drillstring service failures: (a) fatigue failure of a
6.625 in. diameter stabiliser pin; (b) overload failure of a pin
from a crossover connection; (c) macrograph showing a fatigue crack
at a thread root.
sioned and pitched to approximately match a standard API NC-61
V-profile thread- form (V-0.038R) [21, 22]. An analysis of the
NC-61 connection in standard form is included in this study and may
be published at a later date.
2.2. Material
For the purposes of this numerical study, both the pin and box
materials were assumed linear elastic with the general mechanical
properties of steel, elastic modulus E = 207,000Nmm -2 and
Poisson's ratio v = 0.29, and for the analyses involving
plasticity, a yield point of 800Nmm -2 (116 ksi). In reality, the
majority of ferritic drillstring materials are specified according
to AISI 4145 H and AISI 4142 H, both HSLA steels in the quenched
and tempered condition. Typical mechanical properties are given in
Table 1.
3. NUMERICAL ANALYSIS METHOD
3.1. Computational facilities
Preparatory work and the FE analyses proper were performed using
ABAQUS/ Standard, a general-purpose FE program [18], across a
number of software releases:
Table 1. Typical specified mechanical properties for AISI 4145
H
Mechanical property Material specification
Charpy V-notch impact energy Hardness Minimum yield strength
Ultimate tensile strength Reduction of area Elongation
41 J (30 ft-lbs) at RT 285-341 BHN 758.6 Nmm -2 (110 ksi) 965.5
Nmm -2 (140 ksi) 45% min 13% min
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K. A. MACDONALD and W. F. DEANS
v. 4.9-v. 5.3, Presently, the software is mounted on the
Aberdeen University Com- puting Centre's Sun SparcServer 1000
computer (four 50 MHz CPUs) running the SOLARIS v. 2.3 operating
system, and accessed via SunSparc IPC workstations. The FE models
were prepared using ABAQUS' s own model data definitions for the
more simple models, but employed P3 /PATRAN [23], a graphics-based
mesh-generating and results post-processing program, for the more
refined and complex meshes. Results post-processing was carried out
using both P3 /PATRAN and ABAQUS/Pos t .
Particular features of ABAQUS exploited in these analyses
included geometric nonlinearity, frictional contact modelling using
interface elements, automatic resolu- tion of overclosed interfaces
(shrink fitting) and the nonlinear asymmetric deforma- tion
capability for axisymmetric solid elements.
3.2. Axisymmetric modelling
The single most important approximation made in constructing the
FE model is that of axisymmetry, where the geometry is considered a
body of revolution about the Z-axis modelled in the R - Z plane
(Fig. 1). This approximation significantly alleviates the
computational load which would otherwise be associated with a
three-dimensional analysis and has consequently been widely adopted
by the oil and gas industry [17]. The validity of this assumption
is inferred from corroboration between two-dimensional FE analyses
and three-dimensional photoelastic studies performed on standard
(ISO M30) nut and bolt connections [24]. The axisymmetric
representation of the three-dimensional component does not,
however, represent either the thread helix or the runout regions,
simply modelling the connection as a series of parallel threads
with a constant runout geometry. A further limitation exists in
that conventional axisymmetric models are limited to axial loads,
but bending loads are a major contributor to the stress state in a
drillstring [8]. This apparent restriction is rationalised by
arguments constructed around the remoteness of the connection wall
from the neutral axis (small ratio of wall thickness to diameter)
which leads to a limited stress gradient across the wall under
applied bending loads, which conse- quently can be adequately
approximated by a uniform membrane load (Fig. 3). This assumes no
coupling between the regions of maximum tensile and compressive
stress, disposed 180 apart, so that separate analyses of equivalent
tension and compression loads are considered to give reliable
results.
ABAQUS/Standard includes in its element library elements suited
for the nonlinear analysis of initially axisymmetric components
which undergo non-linear, asymmetric deformat ion--as occurs with
tooljoints subjected to bending loads. Whereas the conventional
axisymmetric continuum elements use standard isoparametric
interpola- tion with respect to R and Z, such
asymmetric-axisymmetric elements have ad- ditional Fourier
interpolation with respect to 0. The use of such elements allows
the recovery from a single model of stresses in a connection loaded
in pure bending, or bending combined with axial load, and removes
the simplification of replacing the actual non-uniform load with an
idealised uniform load. However, the effects of thread helix and
runout are still not considered.
4. MESH C O N V E R G E N C E
The extremes of mesh density can produce an incorrect solution
if too coarse, and analysis costs disproportionate to the results
if too fine. A fine mesh is needed in regions of high stress (and
strain) gradient which occur at geometric discontinuities, where a
coarser mesh will suffice in areas of constant stress or low stress
gradient. Furthermore, element formulation is important in that,
for a given problem, a linear displacement element enquires a finer
mesh than a parabolic one which, in turn, needs a finer mesh
density than a cubic element.
Because the effect of a stress concentration on the elastic
stress field is local and
-
Stress analysis of drillstring threaded connections
outer fibre stress
stress differen wall t ickness across wall --,
inside diameter
Fig. 3. Through-wall distribution of stress in a pipe under a
bending load.
outside diameter
. . . . longitudinal axis
dies away or diffuses with distance, a graduated mesh can be
used in such areas [25], accommodating the transition from a fine
mesh at the stress concentration to a coarse mesh in remote
regions. On occasions where the local stress at a particular dis-
continuity is not of primary interest, but the stress at another
site is, a coarse mesh can be used at the discontinuity and
accurate stresses still obtained at the site of interest (with
appropriate local mesh density) provided this site is sufficiently
remote from the discontinuity, in doing so recognising that
accurate stresses will not be obtained in the coarsely modelled
region. Such an approach is useful provided the coarsely modelled
region gives correct load paths, stiffness and boundary
conditions.
Elements are typically defined in terms of the basic shape of
the parent element, for example a square for a quadrilateral
element, an isosceles triangle for a triangular element and so on.
Complex geometries can pose difficulties in controlling element
shape, increasingly distorted elements generally producing less
accurate results. In general, more distortion can be accommodated
without loss of accuracy with both higher-order elements and
smaller stress gradients.
4.1. Mesh convergence study
With the aim of refining the mesh at the geometric discontinuity
represented by the thread root, a series of small submodels were
constructed covering a range of mesh densities local to the thread
root (Fig. 4). The boundary conditions and loads were identical for
each model: uniform axial pressure (stress) on one component;
removal of the axial (Z-direction) rigid body mode on the other.
Radial interference between the box and pin was also included by
setting extreme typical manufacturing tolerances to give a radial
interference of 0.0508 mm (0.002 in.). Due to their reliable
perform- ance [18, 24, 25] eight-noded, biquadratic interpolation,
reduced integration, axisym- metric quadrilateral elements were
used. Contact was modelled using interface elements between the
mating thread surfaces, these elements allowing for closing and
opening of contacting surfaces, small relative sliding and the
modelling of friction by means of the classical Coulomb model [18].
Although a coefficient of friction of 0.09 was selected, being
appropriate to drillstring connections [21], this coefficient was
extremed in this study to investigate the sensitivity of the
results to this assumption.
-
K. A. MACDONALD and W. F. DEANS
t J t l ~
~ - ~ H mesh
J-
) ~ mesh
Fig. 4. FE meshes used for mesh optimisation study.
A l t h o u g h ex t r ac t ed in i so la t ion f rom the full
connec t ion , and desp i te its s impl ic i ty , the conf igura t
ion o f the m o d e l is cons ide red a d e q u a t e l y r ep re
sen t a t i ve o f the real case, in that the effect of the t h r
ead notch , too th bend ing loads and body stresses are all inc
luded.
The ax i symmet r i c F E mode l s were so lved for s tat ic
load cond i t ions using gener ic elast ic ma te r i a l p rope r t
i e s for s teel ( E = 2 0 7 , 0 0 0 N m m -2, v = 0.29) by, f irst
ly, reso lv ing the rad ia l i n t e r fe rence b e t w e e n the
pin t h r ead and box, and , secondly , app ly ing a subsequen t un
i fo rm axial stress. The va r ia t ion of m a x i m u m pr inc ipa
l stress* a r o u n d the roo t rad ius of the p in ' s e nga ge d
t h r e a d is shown in Fig. 5 for a range of mesh densi t ies ,
where it is c lear that s ignif icant mesh r e f i ne me n t is n e
e d e d to accura te ly r ep re sen t the stress d i s t r ibu t
ion a r o u n d the t h r ead roo t radius. This peak stress occu r
red at abou t 40 f rom the t h r e a d f lank (Fig. 6). The rad ia
l ( th rough-wal l )
*From a rigorous theoretical standpoint, the maximum tensile
stress at the thread root is located at an unloaded (free-surface)
boundary and hence occurs at the site of the tangential in-plane
principal stress at that point. This theoretical uniaxial stress
state may not be recovered exactly by an FIE analysis where the
maximum principal stress is potentially matched with a
complementary but spurious non-zero minimum principal stress normal
to the free surface. Taking the maximum principal stress difference
in preference to the absolute maximum principal stress can
ameliorate this marginal inaccuracy. However, such errors amounted
to < 0.8% of peak values in the mesh optimisation study: hence,
the maximum principal stress alone was used for convenience.
-
(a)
cO
1600
1200
800
400
-400
Stress analysis of drillstring threaded connections
I I I I I | I
0 0.5 1 1.5 2 2.5 3
1 D
2
4 O
8 a
16
Distance, mm
(b) ~u
&
.,4
.M
@ n.
1500-
i000
500
A
< -500 , t w
0 1 2 3 4
box r'l
pin
Distance, mm
Fig. 5. Distribution of peak stress around the thread root: (a)
mesh optimisation study (pin); (b) pin and box (mesh 4).
gradients of maximum principal stress approaching the thread
roots (Fig. 7) are consistent for all mesh densities, only
diverging close to the thread root where the stress gradient
increases rapidly. Again, the more refined meshes capture the
stress gradient: however, the maximum peak stress is only obtained
with the most highly refined meshes. The accuracy and efficiency of
the five meshes studied are clearly represented in Fig. 8, where
the convergence of peak stress is evident, as is the associated
computational cost. The results from a similar series of analyses
using
-
1600
1200
.I
800
400
0
K. A. M A C D O N A L D and W. F. DEANS I0
Fig. 6. Contours of maximum principal stress showing the site of
max imum stress along the thread root radius.
0 . 7 0 . 7 5 0 . 8 0 . 8 5 0 . 9 0 . 9 5 1
Normalised wall thickness, mm
Fig. 7. Stress distributions resulting from the different
meshes.
16 []
8 :
4 O
2 & 1 -"
first-order quadrilateral elements are also given in Fig. 8,
where the consistent superiority of the second-order elements is
clear. Because the coefficient of friction used in the analyses ( f
= 0.09) is simply selected from standards appropriate to
drillstring connections [21], the effect of a higher value was also
studied ( f = 0.5), but the difference in peak stress proved
negligible (0.07%).
Mesh number 4 (Fig. 4), with eight elements defining the root
radius, was selected as the optimised mesh for use in subsequent
analyses based on its compromise between converged peak stress
output and reasonable computational cost.
-
Stress analysis of drillstring threaded connections 11
CAXSR stress 13 - - - 1 3 - - - CAXSR time
CAX4R stress & - ' - & - ' - CAX4R time
1600
1 4 o o
1200
~ lOOO
600
400
S I Q
$
800 ~ "//s/" --~
i I ,.o,A
200 ~.ii~ ~ ..41~. ~.
0 - - I I I 5 i0 15
8OO
700
600
5OO
4OO
'300
-200
-I00
0
2O
-r'l
O -r'l
r"4 O
r.t)
Number of elements
Fig. 8. Mesh optimisation results: dependence of peak stress and
solution time on mesh refinement.
5. AXISYMMETRIC MODEL VALIDATION
5.1. Thread runout geometry
Representation of a three-dimensional threaded connection by a
two-dimensional axisymmetric FE model inevitably fails to include
the effects of thread helix and runout geometries. These geometric
features combine in the critical regions of a connection--the pin
and box LETs--to produce a nonuniform thread load distribu- tion
around the runout thread progressing from the first contact when
partly formed to a fully developed inter-tooth load as the helix
progresses and the thread chamfer diminishes, typically occurring
in one complete revolution. The increased flexibility of the first
partly formed thread over its fully formed neighbours initially
encourages load shedding from the mating thread, until the thread
becomes completely formed, attaining the peak thread root stress
about one turn from the point of initial inter-tooth contact [26].
An attempt to model such behaviour in axisymmetry can be made by
considering the thread runout geometry at several meridional
sections, equi-spaced at angular sites. Although it is impossible
to argue that such an approach embodies the actual stress state,
the method has nevertheless been validated with experimental data
for standard nut-bolt connections [24, 26], and as such is
considered a viable approximation for use in the present study.
A typical FE mesh, from a series of three, representing
different meridional planes through the whole connection, is shown
in Fig. 9. The level of mesh refinement is identical at all
threads--as the peak stress distribution for all threads is of
interest-- and is based in the optimised mesh considered earlier.
The typical model size was approximately 13,600 elements and 40,000
modes. These models were solved for resolved radial interference
and axial tension loading, with the Z-direction rigid body
-
12 K. A. M A C D O N A L D and W. F. DEANS
/ _ . R[
Fig. 9. FE model of a full connection (perimeter plot) with pin
LET: details of uniform and differentially meshed models.
-
Stress analysis of drillstring threaded connections 13
mode restrained on the pin free end. Substructuring with
superelement generation was not employed because ultimately the
modes were intended to be solved for non-linear material behaviour
and non-linear asymmetric-axisymmetric deformation. The differences
in thread runout geometry gave rise to variations in peak stress
(Fig. 10). In contrast to results from studies of standard V-form
threads [24] the multi-meridional plane technique produces the
maximum stress in the thread at a point close to the first
attainment of full thread height on the contacting flank, i.e.
where the thread is still not yet fully formed (Fig. 9). The peak
stress occurs at this location due to the superposition of the
maximum connector body stress and the
(a) ~ 1250
I000
.~ 7 5 0
500
250
0
0 1 2 3 4 5 6 7
(b) 1250 -
d i000 -
750 -
500 -
25O
- A
Tooth pitches from shoulder
- _ . : $ . . . . . .
I I I I I I I
8 9 i0 Ii 12 13 14 15
Tooth pitches from seal-face
Fig. 10. Thread peak stress distribution from three separate
multi-meridional plane FE models with different thread runout
geometries: (a) pin; (b) box.
-
14 K. A. MACDONALD and W. F. DEANS
maximum possible tooth load bending stress. Furthermore, the
maximum pin and box stresses do not necessarily occur in the same
meridional plane because of non-ident- ical thread runout formation
in a given model. Based on these results, a single axisymmetric
geometry was chosen with similar states of runout evolution on both
the pin and box, maximising the thread peak stresses in both.
5.2. Preload from make-up
Established drilling practice is to further tighten connections
after assembly by applying a make-up torque. In addition to simply
removing slack in a joint and providing resistance to downhole
make-up arising from shock torsional loading and the reduced
coefficient of friction of pipe dope at elevated downhole
temperatures, this practice results in strong benefits from a live
load carrying perspective. Once preloaded, axial tension is
generated in the pin which is equilibrated by axial compression in
the box. Seemingly, an alternative load path is created through the
shoulder interface, bypassing the pin threads [15]: however, in
reality applied loads are still transferred through the pin,
causing it to stretch or shorten and the shoulder compression to
release or increase. The complexities of modelling the relationship
between applied torque and axial preload is sufficiently difficult
that, in this study, use was made of prescribed axial preloads from
drillstring standards. The re- commended make-up torques used for
connections are taken from drill collar guidance [21], where
specified torques are intended to generate a minimum axial stress
of 62,500 psi (431 N mm -2) in the weaker of the pin or box.
In FE modelling terms, overclosed interface elements were used
at the seal-face- shoulder region which, when resolved as an
interface fit, produce a compressive interfacial pressure which
reacts in the threads as an axial preload. Furthermore, interface
elements allow the shoulder interface pressure to vary in
accordance with applied loads, mimicking the make-up preload
mechanism in practice.
A series of identical FE models of the full connection with
increasing amounts of shoulder overclosure were solved by resolving
the overclosure. An overclosure of 0.3 mm produced-- f rom a
linearisation procedure -- a membrane stress component of 467 N m m
-2 located in the parallel section of the pin adjacent to the
shoulder (Fig. 11), and was thus considered to compare well with
the API guidance. This value of 0 . 3m m seal-face overclosure
compares favourably with a value of 0.008in. (0.203 mm) used
elsewhere for an analysis of a standard NC-46 connection [27]. The
resultant peak stress distribution (Fig. 12), demonstrates that the
pin LET and the other lower thread numbers* react with most of the
axial preload.
5.3. Differential mesh density at thread roots
Building on the earlier explanation that coarse modelling of
stress concentrations may not prevent a refined mesh elsewhere
returning accurate results at the stress concentration of interest,
a second mesh was prepared based on the same axisymetric geometry
as in Sections 5.1 and 5.2 but, unlike its predecessor, it was
targeted to give accurate results at the critical threads only
(Fig. 9), with a more coarse mesh at the intermediate threads. This
was done to provide an FE model of reduced size and attendant
reduced computational load for use in analyses where only the
critical threads will be of interest, as is the case with
comparative studies. The original model size was dramatically
reduced to about 4000 elements and 11,500 nodes. In solving the
model for combined preload and axial load, comparison with the
corresponding uniformly meshed model shows that the peak stress
results at the intermediate threads
*Thread numbers counted from the shoulder.
-
Stress analysis of drillstring threaded connections 15
1250
@
i000 o
o
750
500
,<
250
0
i
actual distribution
i
\
I I I I 0 0.2 0.4 0.6 0.8
linearisation
Normalised wall thickness
Fig. 11. Preload induced through-wall distribution of stress at
the pin parallel section (0.3 mm shoulder-seal-face
overclosure).
5000 -
d 4000 -
3ooo- -~I
i 2000 -.
m i000 -
box
D pin
O I , , , , , , , T7
0 2 4 6 8 I0 12 14 16
Tooth pitches from shoulder/seal-face
Fig. 12. Thread peak stress distribution solved for preload (0.3
mm seal face overclosure) from three runout geometries.
are significantly in e r ror (34 and 18% underpredic t ion for
pin and box, respectively), but , more impor tant ly , the results
at the critical threads are in g o o d ag reement (within 0 .41%).
These results validate the non-uni formly meshed model , demonst ra
t - ing that the coarsely model led region gives correct load
paths, stiffness and bounda ry condit ions.
-
16 K.A. MACDONALD and W. F. DEANS
5.4. Non-linear asymmetric-axisymmetric elements
The fundamental premise of the axisymmetric models dicussed
above is that drillstring loads can be adequately represented by
uniform axial loads at level equivalent to the average membrane
stress component across the pipe wall, or the extreme outer fibre
stress (Fig. 3). This approach requires separate analyses of equal
but opposite sign (tensile and compressive) axial loads to r~cover
the peak stress distributions disposed at the 0 and 180 positions.
Elements exist which allow the non-linear analysis of initially
axisymmetric components which undergo non-linear, asymmetric
deformation. In essence, such elements allow in-plane bending
loads, assumed to be symmetrical about 0 = 0 , to be applied to
axisymmetric models, overcoming the need for simplification of the
stress distribution and for separate solutions. Results can be
recovered at various angular positions depending on the number of
Fourier modes employed, the minimum being two nodal planes at 0 and
180 , and the maximum being five nodal planes at 0, 45, 90, 135 and
180 . Bending loads can be combined with uniform axial loads to
represent downhole loads comprised of a weight-on-bit or overpull
component , and a bending component from a dog-leg or deviated
wellbore. As the analysis is non-linear, a superelement solution
strategy cannot be adopted. The analysis is still in two dimensions
and the effects of thread helix and runout are still ignored.
To reduce the computational load, the differentially meshed
model was employed with asymmetric-axisymmetric elements and solved
for preload and an equivalent bending load (maximum outer fibre
stress = uniform membrane stress from the axisymmetric analysis).
Comparison with the corresponding results from the axisym- metric
solution revealed significant differences in peak stress,
particularly at the pin LET under preload and the box LET under
preload plus bending. Comparison of the through-wall stress
gradients at the straight section near to the pin shoulder showed
that the asymmetric-axisymmetric elements returned lower stresses
at near-surface positions than the plain asymmetric elements,
although the general distributions were similar (Fig. 13). The same
is true at the pin LET site, where the discrepancies at the
extremities are amplified in the region of high stress gradient
near to the thread root.
134
r~
~4
rO
1.4
c6
CAX8R
1
I I I I I
Normalised wall thlckness
Fig. 13. Differences in through-wall distribution of stress at
the pin parallel section returned by plain axisymmetric (CAX8R) and
asymmetric-axisymmetric (CAXA8R1) element types under preload
only.
-
Stress analysis of driUstring threaded connections 17
5.5. Elastic-perfectly plastic material behaviour
In order to test the contention that an elastic analysis is
sufficient unless thread root plasticity is so extensive as to
influence the overall load distribution within the connection (by
affecting the relative strains between threads), comparative
analyses were performed with both elastic material behaviour, and
with elastic-perfectly plastic behaviour using the Von-Mises yield
surface. The elastic-plastic material model used an identical
elastic modulus value of 207,000 N mm -2 and, beyond first yield at
800 N mm -2, assumed a constant value of yield stress (perfectly
plasticity). Analysing a case of preload and 200 N mm -2 applied
tension with the uniformly meshed model, the extent of plasticity
at the pin LET was found to be small [~0.261 mm (Fig. 14)] with the
through-wall stress gradients showing close agree- ment, only
diverging once yielding is promoted in the high-stress region local
to the thread root. The extent of plasticity at the next pin thread
was smaller still, 0.070 mm, with all other pin and box thread
roots remaining elastic. The non-uniform mesh was also analysed for
elastic and elastic-plastic material behaviour with the results
demonstrating excellent agreement with the uniform cases (Fig. 15).
In comparing the merits of the two material models, it is clear
that plasticity is sufficiently limited so as not to contribute
significantly to the relative strains within the joint, and as the
analysis costs of the elastic-plastic model are a factor of 5
greater than that of its elastic counterpart, it is concluded that
the assumption of elastic material behaviour is justified in this
case.
6. RESULTS AND DISCUSSION
The present interest lies in evaluating the stress distribution
and stress concentra- tion factors for a drillstring connection
with a trapezoidal threadform under preload and preload plus
uniform axial loads. Concerns over the discrepancies found between
the preload cases modelled with axisymmetric and
asymmetric-axisymmetric elements led to their suspension from this
study, and has prompted closer examination of this
l 1 z
Fig. 14. Extent of plasticity at the pin LET for preload plus
200 N mm -2 axial tension (0.261 mm).
-
18
m~ 1 rq(lO 134
d 120C)
m 0
E o o q(}O
O]
m ~J m c~ O 0
, - - I
.,--4 c< ~ 0{}
K. A. M A C D O N A L D and W. F. DEANS
-- Elast ic + $
Both meshes /~"
_ X Elas t i c -p las t i c . I l k . Differential mesh / '
~
A - - E las t i c -p las t i c ~
I I I I I
() . .~ {) . .1 / . (~ () . ,q ]
Hormalised wall thickness
Fig. 15. Differences in through-wall distribution ot stress at
the pin LET returned by plain axisymmetric (CAX8R) and
asymmetric-axisymmetric (CAXA8R1) element types in uniform and
differentially meshed models solved for preload plus 200 N mm 2
axial tension.
element type and its implementation. The results discussed here
for the plain axisymmetric FE analyses are in the most part
modelling make-up preload combined with uniform axial tension and
compression loads.
In assessing the effect of a logical modification to the
threadform, a comparative study considered the connection with
matched thread root radii on both pin and box threads, and a
modified thread with the root radii increased. These uniformly
meshed models were analysed for axial tension without preload and
the results clearly demonstrate the reduced thread root peak
stresses in all the box threads (Fig. 16).
The main body of analyses considered the uniformly meshed model
under preload (0.3 mm shoulder overclosure) combined with uniform
axial tension and compression at nominal stress levels ranging from
+ 100 to + 800 Nmm-: , representing a range approximately 12.5-100%
of assumed material yield strength. The primary results in terms of
the distribution of thread root peak stress demonstrate that the
preload effects dominate the overall distribution. The pin LET
consistently shows the highest peak stress and through-wall stress
gradient (Fig. 17). On first inspection the results for the box are
unusual in that the first engaged thread (FET) exhibits a higher
peak stress than the LET--a result apparently contradicting service
experience. However, examination of the stress gradients at the box
FET and LET positions (Fig. 18) reveals that, although the FET peak
stress is indeed high,* the through-wall gradient of stress is
largely compressive, only becoming slightly tensile once axial
loads reach levels which promote shoulder separation (Fig. 19). In
contrast, the box LET with a lower peak stress exhibits a
consistently tensile through-wall gradient, confirming it as the
known site of failure from service experience.
A vector representation of the thread root stress field
demonstrates the variation of maximum principal stress direction
(Fig. 20). The maximum principal stress direction is initially
tangential to the root radius at the point of peak stress, but
rotates to become axially aligned once more than a distance
equivalent to a few root radii away
*The existence of this highly localised SCF at the box FET has
been confirmed by metallographic examination, where loealised
damage to the thread root has been observed.
rfenyvesHighlight
rfenyvesHighlight
rfenyvesHighlight
-
8 0 0 -
~ 600
E ~ 200
Stress analysis of drillstring threaded connections
0 I I I I I I I 6 8 10 12 14 16 18
Tooth pi tches f rom seal-face
Fig. 16. Effect of enlarging the box thread root radius on the
thread peak stress distribution (axial tension Nmm-~; no
preload).
19
from the thread root. This gives rise to an initially curved
crack propagation path near to the thread root which produces a
characteristic lip feature on the failure surface. This fatigue
crack morphology potentially provides an important point of
reference for failure investigations as would be readily observed
even when post- failure mechanical damage has taken place [1].
These results exemplify the competing mechanisms of tooth bending
stress and the stress concentrating effect of the tooth notch on
the body stresses [5, 15].
Tooth separation occurs at the higher tooth numbers under
compressive loading, demonstrated by the tooth flank interface
element openings (Fig. 21), where the spread of tooth disengagement
from the box LET towards the pin LET at increasing compressive
loads is clear. Radial interface displacements between the pin and
box threads under preload and tension loading demonstrate the
extent of radial expansion and contraction of the connection* (Fig.
21), the greatest changes from the preload state taking place at
the connection extremities due to the high proportion of load
transfer and increased flexibility arising from the taper at these
sites.
6.1. SCFs
In preloaded connections, the representation of the stress state
local to the critical thread root using classical SCFs is
substantially dependent on how the SCF is defined. Evidenced by
Fig. 12, the preload has a pronounced effect upon the stresses at
low thread numbers while the preload remains in force. The notch
local stress, defined as the sum of linearised bending and membrane
through-wall stress components, displays non-proportional behaviour
in the case of the pin where the LET local stress is clearly a
nonlinear function of nominal pipe stress (Figs 22 and 23). The box
LET local stress remains largely unaffected by the preload and
consequently exhibits a proportional response to applied stress.
The change in gradient of the pin local stress response at
*This relative radial displacement is measured between the crest
of the box thread and the root of the pin thread, and is composed
of both increases and decreases in radial displacement of the box
and pin, respectively.
rfenyvesHighlight
-
20 K.A. MACDONALD and W. F. DEANS
7000 -
d 6000-
aa 5000 -
-,-I 4000 -
3000 -
< 2000 -
i000 -
600 MPa -- 400 MPa at 200 MPa
(a) 100 MPA [] preload
: i1200; MM~: -- -400 MPa i -600 MPa
. 4 ; 8 1 ~) ! 2 14 I
16
Tooth pitches from shoulder
~. 600 MPa -- 400 MPa at, 200 MPa - 100 MPa [] preload
~ 4000 1 m $ -100 MPa 1 at -200 MPa
- 4% ~ -400 MPa t~ ~ ~ 2 -600MPa / 3000]
2000
1i] II 2 4 6 8 i0 12 14 16
Tooth pitches from seal-face
Fig. 17. Effect of axial load oll the thread peak stress
distribution: (a) pin: (b) box.
-
n.
S o
o
U
4J m
r6 .,-I
I000
800
600
400
200
0
-200
-400
-600
Stress analysis of drillstring threaded connections
I I I I
0 0.2 0.4 0.6 0.8 1
[] FET
: LET
21
Normalised wall thickness
Fig. 18. Differences in through-wall distribution of stress at
the box FET and LET sites (preload plus 200 N mm -2 axial
tension).
1250
d i000
75O 0
500
I--4
250
tension []
compression
i l t I
200 400 600 800
Axial stress, MPa
Fig. 19. Effect of applied axial tension and compression on
shoulder-seal-face interface pressure.
nomina l app l i ed s t resses of a p p r o x i m a t e l y
___450 N m m -2 (Fig. 22) def ines wel l the po in t s w h e r e
the t o o t h p r e l o a d is o v e r c o m e in c o m p r e s s i
o n and the shou lde r p r e l o a d is r e l e a s e d in tens ion
. T h e va r i a t i on of no tch p e a k stress d e m o n s t r a
t e s s imi lar b e h a v i o u r in tha t the box L E T re sponse
is e f fec t ive ly l inear* bu t the pin L E T
-
22
\
{ {
3
K. A. M A C D O N A L D and W. F. D E A N S
I \ \ \ \ "" \ '
\
Fig. 20. Variation of maximum principal stress direction within
the complex thread root stress field (preload plus 200 N m m - :
axial tension).
response is evidently nonlinear (Fig. 22). Thus, the peak
stresses cannot be expressed as constant geometric SCFs. In order
to describe these peak stresses with respect to some reference
stress within the connection, three appropriate definitions of SCF
(Kt) can be used:
( i) K t relative to the nominal pipe membrane stress. Although
the most con- veniently derived SCF, this classical geometric
definition does not accommodate the potentially non-proportional
relationship between the peak and nominal pipe stresses (Fig. 22)
and fails to take account of the preload's profound effect upon the
SCF.
(ii) Kt relative to the local membrane component of stress.
Linearisation of the through-wall stress distribution at the
critical thread (Fig. 23) to give the membrane stress component
takes account of the body stresses and gives a better
representation of the SCF.
(iii) Kt relative to the local membrane and bending components
of stress. Although more onerous in terms of data reduction, a full
linearisation of the through-wall stress distribution at the
critical thread (Fig. 23) evaluates the thread root peak stress
relative to the most effective measure of the notch nominal local
stress.
Considering first the box LET, Fig. 24 gives the SCFs computed
on the basis of the three above definitions as functions of nominal
applied pipe stress. The SCF based on pipe stress is a weak
function of applied stress, but when expressed with reference to
the sum of local membrane and bending stress components it becomes
effectively constant at a value of approximately 3.5 in tension,
even when the preload mechan- ism is substantially overcome at pipe
stresses above about 450 N mm -2. In compres- sion, the box LET is
no longer loaded by a meshing pin tooth but is simply subjected to
compressive body stresses: consequently, the stress state alters
accordingly and a lower SCF of 2.0 is the result.
*Under compressive load, the box LET disengages and is no longer
loaded. In this condition, the stress state is characterised by the
box body in compression and the site of compressive peak stress
moves from the former site of the tensile peak stress to another
position on the thread root.
-
(a)
0
,,~
Q)
~Z
0.35 -
0 . 3 -
0 . 2 5 -
0.2-
0.15 -
0.i-
0.05 -
0
0
Stress analysis of drillstring threaded connect ions
[] 100 MPa / A 200 MPa -- 400 MPa
I 2 4 6 8 i0 12 14 16
23
(b) 0.14 -
~ o . 1 2 - o
0.i-
@
0 . 0 8 - J.a in @
0.06 - o
0 0 0.04 - b
~Z
0 0.02 - 0
0
0
Tooth pitches from shoulder/seal-face
m preload t : 100 MPa l
/
200 MPa [ I
I 400 MPa ] /
! !
2 4 6 8 i0 12 14
i
16
Tooth pitches from shoulder/seal-face
Fig. 21. Effect of load on the thread flank and crest interface
openings: (a) flank; (b) crest.
Identical but magnified effects are apparent for the pin LET in
tension (Fig. 24), which might be expected as the preload mechanism
has been shown to have most effect at this site. The SCF in tension
with reference to pipe stress is profoundly affected by applied
stress while the preload remains effective at applied stress levels
below about 450 N mm -2. Computed on the basis of the linearised
local bending plus membrane stresses, the pin SCF reduces to a
linear and very weakly dependent function of applied stress, almost
constant at a value of approximately 5.5. Similar behaviour
persists into the compressive loading regime but, unlike the box
LET, the pin LET remains initially engaged by the preload
mechanism, with the pin SCF reducing once the preload is fully
overcome at applied stresses below -450 N mm -2.
-
K. A . M A C D O N A L D a n d W . F. D E A N S
(a) 3.
r~
o~
c~
i g 08 n
~000
2 5 0 0
l
24
2 :. 0 0 I I I I 1 I
~':~: - 6 0 : ; 20: i 2 0 0 o~U-P'- 90@
,~ 2 0 0 0
1 5 0 0
i000
500 -
5 0 0 - O 0
-i000 -
(b)
Nominal applied stress, MPa
n pin
11. box
1 5 0 0 I i I I I I
- 9 0 0 . . . . . . . . -60,-: ~i,~ - 2 0 0 64r, : ,~, ,
N o m i n a l a p p l i e d s t r e s s , M P a
Fig. 22. Effect of appl ied load on LET: (a) peak: (b) l oca l
stresses.
Once the dominant effects of preload are adequately considered,
the SCFs for tension loading become effectively constant at 3.5 for
the box LET and 5.5 for the pin LET (Table 2), reflecting the
greater thread root radius of the box postulated in this study.
6 . 2 . Response of local stress to cyclic loading
Cyclic fluctuation of the applied pipe stress promotes an
oscillatory response in the local stresses at the critical threads.
These alternating through-wall stresses at the pin
-
Stress analysis of drillstring threaded connections
- - peak stress
- - . i - - - -
Pb
linearised stress distribution Pm
Pm+Pb A t
25
A
1
Stress distribution at AA
Fig. 23. Stress linearisation procedure to give stresses used in
the definition of SCFs.
and box L E T sites are the driving force for fatigue crack
initiation and propagation behaviour, and are the foundations on
which the notch peak stresses are based. Considering the axial
tension load FE analyses, and the preload case, stress ranges and
mean levels were computed for the local stresses at a stress ratio*
of R = 0. Of particular note are the pin L E T responses in range
and mean where clearly observable changes in slope take place at
approximately 450 N mm -2 nominal pipe stress (Fig. 25). As with
the peak stresses, this behaviour represents the point at which the
preload is overcome and the seal-face-shoulder interface begins to
open.
The box L E T has consistently higher local stress ranges than
the pin L E T across the full extent of the applied stress ranges
(Fig. 25). The difference between the two initially diverges but
then converges with increasing applied stress range. Such behaviour
occurs because the pin L E T receives most of the protection
afforded by the preload mechanism [15, 28] whereas the box L E T
receives virtually none and as such is exposed to the full effect
of the applied stress range. The benefit afforded the pin is lost
once the preload is overcome, accounting for the convergence of the
pin and box responses at higher stress ranges. Notably, the limited
stress range at the pin L E T is apparently obtained at the
considerable expense of a consistently elevated mean level (Fig.
25) much higher than the mean level experienced by the box LET.
6.3. Response of peak stress to cyclic loading
The peak stresses are in fact idealised elastic stresses and as
such these extremely high magnitudes do not occur in practice due
to localised yielding. The effect of the stress concentration is to
form a localised region of plastically deformed material which is
best characterised by a strain parameter and not stress. In any
case, it is alternating plastic strain that is acknowledged as the
mechanism promoting the fatigue crack initiation process [29].
These points combine to make a peak stress represen- tation of
cyclic loading response unsuitable. However , for the
straightforward case of pulsating tension at R = 0, it is
nonetheless both justifiable and helpful to consider the range and
mean levels of peak stress in order to examine the relative
severity of the pin and box L E T sites under fatigue loading (Fig.
26). As with the local stresses,
*Stress ratio definitions: R = -1 is fully reversed
tension-compression; R = 0 is pulsating tension from zero; R > 0
(positive R ratio) is tension-tension.
-
26 K.A. MACDONALD and W. F, DEANS
-
Stress analysis of drillstring threaded connections 27
Table 2. SCFs in tension for a preloaded connection in a 9 in.
diameter drill collar with a trapezoidal threadform
Nominal pipe stress Pin SCF Box SCF (Nmm -~)
Pipe Pm + Pb Pipe* Pm + Pb-t
100 50.7 6.5 7.0 3.7 200 27.1 6.1 6.3 3.5 300 18.9 5.8 6.0 3.5
400 14.6 5.5 5.9 3.4 500 12.2 5.5 5.8 3.4 600 11.1 5.1 5.8 3.4 700
11.1 4.9 5.7 3.4 800 11.0 4.9 5.8 3.4
*Constant value assumed = 5.5. ?Constant value assumed =
3.5.
results p resen ted here , the cor robora t ing service data
refers to whole fatigue life and, as such, a combined and
qualitative in terpreta t ion of the peak and local stress results
is justified. In this respect , of the two critical threads, the
box L E T displays the higher local and peak stress range but the
lower mean level. The relative impact on connec t ion fat igue is
then primari ly a funct ion o f the ferritic mater ia l ' s
response to mean stress effects. For similar structural steels the
stress range tends to be much m o r e significant than the m e a n
level [30, 31]. Fat igue loading then induces a critical failure
site at the box L E T under fatigue loading at R = 0, but, under
static tension loading, the pin L E T has the greatest local and
peak stress levels making it the ant icipated critical failure site
when the joint is statically loaded (summarised in Table 3).
7. C O N C L U S I O N S
The stress distributions and stress concent ra t ion factors in
a drillstring th readed connec t ion with a t rapezoidal t h read
fo rm have been evaluated using the F E me thod
(a) 1400
1200
d i000
800
600
4OO
2OO
0
0 200 400 600 800
[] pin
& box
Nominal applied stress range, MPa
Fig. 25(a). Caption on p. 28.
-
28
(b) nJ
d m
m
0) N
i400
1200
i000
800
600
400
2 O0 -
0
K. A. MACDONALD and W. F. DEANS
I I I I
. , I 4 ; % f!, (3
pin
,I. box
Nominal applied stress range, MPa
Fig. 25. Effect of cyclic loading R = () on the LET local
stress: (a) stress range; (b) mean level.
supported by a rigorous model validation exercise. The
non-uniform distribution of idealised elastic peak stress was in
agreement with existing analytical, experimental and numerical data
for generic threaded connections. The classical stress concentra-
tion factor was found to be inconstant and a decreasing function of
nominal applied load in tension. Allowing for the non-linear
relationship between applied stress and tooth notch peak stress,
and for the effects of make-up preload, constant stress
concentration factors of 3.5 and 5.5 were derived for the box and
pin L E T positions,
(a) 7000 ]
d 6000 ]
C
5000 1 m
4000
ooo 1 . / /
i001~- I I I I
0 200 400 600 800
[] pin
,L box
Nominal applied stress range, MPa
Fig. 26(a). Caption on p. 29.
-
(b) 7000
6000
5000
4000
3000
2000
i000
Stress analysis of drillstring threaded connections
I I I I
200 400 600 800
O pin
A box
29
Nominal applied stress range, MPa
Fig. 26. Effect of cyclic loading at R = 0 on the LET peak
stress: (a) stress range; (b) mean level.
Table 3. Stresses at critical threads under static and cyclic
loading
Cyclic pipe stress range (0-400 N mm -2)
Static pipe stress (400 N mm -2) Peak stress Local stress*
Location Peak stress Local stress Range Mean Range Mean
Pin LET I 5857 1073 I 1156 5279 388 879 Box LET 2350 686 ~ 1244
~ 351
*The sum of linearised membrane and bending stress
components.
respectively, reflecting in par t the greater thread root radius
of the box implemented in this study. The stress state at the
thread root is character ised by a varying max imum principal
stress direct ion which produces a characterist ic lip feature on
the failure surface, potent ial ly providing an impor tan t point o
f reference for failure
investigations. U n d e r cyclic loading in pulsating tension (R
= 0), the p re loaded joint analysed
p roduced local and peak stress ranges marked ly reduced at the
critical pin thread, but oscillating about high mean levels. In
contrast , the critical box thread exhibited larger local and peak
stress ranges but with lower mean levels. Overal l fatigue pe r fo
rmance of a p re loaded connect ion is thus a compromise be tween
decreased stress ranges and
increased mean levels. Pre load directly affects the static
stress distr ibution within the connect ion making
the pin L E T the critical failure site for static loading, but
it also affects the local and peak mean stress levels and stress
ranges arising f rom fatigue loading, making the box L E T the
expected critical site for fat igue loading at R = 0.
Acknowledgements--Particular thanks are due to D. M. R. Bell of
the Aberdeen University Computing Centre for his expertise and
assistance with the University's computing facilities, and to I.
Mackinnon of the Department of Engineering for reprographic
services.
-
30 K.A. MACDONALD and W. F. DEANS
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