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Copyright 2006, Offshore Technology Conference
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AbstractThe extensive use of chain as an element in multi-component
moorings by the offshore industry has led to a requirement to
be able to predict the torsional response of chain under a
variety of service applications. Chain exhibits some interesting
behaviour in that when straight and subject to an axial load, it
does not twist or generate any torque. However, if chain istwisted while carrying axial load, or subjected to axial load
when in a pre-twisted condition, it behaves in a highly non-
linear manner, with the magnitude of the torque dependent
upon the level of twist and the axial load. Consequences of
this behaviour can include handling difficulties or even a loss
of integrity in the mooring system, and care must be taken toavoid problems for both the chain and any components to
which it is connected.
Clearly an understanding of the way in which chains may
behave and interact with other mooring components (such as
wire rope, which also exhibits coupling between axial load and
generated torque) when they are in service is essential. Evenwith knowledge of the potential problems, there will always be
occasions where, despite the utmost care, twist occurs. Thus it
is important to be able to determine the effects, but the sizes of
chain which are in use in offshore moorings (typical bar
diameters are 75 mm and greater) are too large to allow easy
testing at meaningful loads and there is virtually no predictiveinformation on the torsional response of chain available in the
literature.
This paper addresses the issues and considerations relevant
to torque in large mooring chains. The authors introduce a
frictionless theory which predicts the torques and end-shortening in the chain as non-dimensionalised functions of
the angle of twist. The theoretical model is compared with
finite element studies that include friction.
Experimental data is also presented in both constant twist
and constant load forms for stud-less and stud-link chains of
41 and 56 mm bar diameter.
Non-dimensionalised design curves are then given for typical
stud-less and stud-link chain geometries, curves which will
allow a designer to estimate the torque and end-shortening for
any bar diameter, axial load and twist angle combination.
1 IntroductionChain is widely used in mooring applications for offshore oil
platforms, both drilling and production, as well as general
marine purposes. It may be used as the sole component in a
mooring line, but is more usually employed as part of a system
combining chain and rope, be it fibre or wire. There are a
number of reasons why chain is a popular choice in a system:
It is rugged and less damage prone than wire or fibre ropewhen operating on deck hardware or seabed.
It is less prone to corrosion than wire rope.
Chain weight per unit length is higher than for wire ropefor a given strength. Hence the chain may be used mid-line
as a clump weight to alter the catenary shape, or as a
ground line so that a smaller anchor may be employed.
Chain is intrinsically torque balanced, in that an axialload does not generate twist or torsional moments in a
straight chain.
It is easier to handle and requires smaller deck tensionequipment than a wire rope.
So why is torsional stiffness, or induced torque, relevant inmooring chain? There are two reasons:
Firstly, because (as just stated) typical moorings includewire or fibre rope in series with chain, and while chain is
intrinsically torque balanced, the other elements may not
be, and will try to turn the chain when the combination issubject to axial load.
Secondly, it is easy to get a mooring twisted duringdeployment, or during service, often in ways that were not
foreseen at the design stage. A means of transferring large
amounts of twist into a chain during installation when
under nominally zero tension has previously been reported
by Chaplin1, 2
.
OTC 17789
Predicting the Torsional Response of Large Mooring ChainsI.M.L. Ridge, CASAR Drahtseilwerk Saar GmbH; R.E. Hobbs, Imperial College/Tension Technology Intl.; andJ. Fernandez, Labein Technological Centre
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It is noted that industry is becoming increasingly aware of
the problems which may be caused by allowing components to
twist during installation, or by connecting torsionally mis-
matched components, but even so, twist may be unavoidable,
and the engineer may need to understand the response of the
system to such effects.
1.1 Previous researchMany previous investigations into the behaviour of chain
have considered various aspects of the strength and fatigue
performance, but all in cases where the chain is not twisted3-14
.
Casey15
provides a very useful summary of the available
laboratory strength and fatigue test data. Other authors have
considered the effects of stresses and proof loading in chainwith the use of FEA packages
12, 16, 17.
By comparison, very little work has been reported which
considers the torsional response of chain. It has been
traditionally assumed that up to 3 turn per link (or
equivalently 3 turn per link to link interface) there is very
little resistance to the twisting of a chain, while after that it
rises rapidly. It is not clear what the source of this folk-information is, or indeed how accurate it is.
Hiroshima and Sawa18
have considered the effect on
strength of twist in a chain which is subject to an impact load.
Making use of both finite element (FE) and experimental data
their paper considers the loss of strength caused in small
chains (approx 14 mm) such as those used in chain hoists and
lifting tackle, although it does not discuss the torque in the
chain itself.
Turning to some prior work specifically on the torque-twist
relationship, Economides19
suggests that the level of 3 turnper link is associated with the rather modest initial frictional
torque between any two contacting links. At greater levels of
twist the contact area starts to increase significantly beforesplitting into two separate patches and geometric interaction of
the links then causes the torque to rise very much more
rapidly.Chaplin et al.
20present a series of constant twist tests - in
which the twist in the chain is held constant - and the torque
measured as a function of load. This work is for a 20.5 mm
stud-link chain. It not only shows how the induced torque is
highly non-linear for a range of applied levels of twist up to
26.7 turn per link, but it also highlights how different theresponse is from that of six strand wire and parallel laid fibre
ropes.
Economides19
also presents some experimental data
measuring the torque in a 13 mm stud-less chain for a series of
four constant load tests. However, limitations in his equipment
meant that he could not investigate very high levels of twist,
with his tests typically running up to 10 per contact although
at lower loads he did get up to 16 twist per contact.
1.2 Types of chain
There are two main types of chain: stud-less and studdedor stud-link, which are illustrated in Figure 1. The selection of
the type of chain will be influenced by the application. Stud-
link chain is commonly used for moorings which have to be
re-set often during their service life, e.g. those for a semi-
submersible drilling platform, as it is less prone to knotting
during handling; whilst stud-less chain is more commonly
used for permanent moorings, (e.g. those for FPSO, FPS,
Spars or buoys). Stud-link chain tends to be stronger for a
given size and grade of steel, but it weighs more (about 9%)
and is more expensive to produce. There are also issues
concerned with the stud working loose, initiating corrosion or
promoting poor fatigue performance. However, it should be
noted that manufacturers are constantly working to address the
strength issues and industry seems to be moving towards usinglarge stud-less chain.
Figure 1 - Typical nominal link geometries for stud-less (left) andstud-link chain (right)
21
Referring to Figure 1, can be seen that it is usual to define the
main dimensions of the link in terms of its bar stock diameter,
D. Stud-less links are essentially two hemi-toroids of diametertypically 3.35 D, with a parallel section in between, whilst the
studded link geometry is more complicated resulting in a
slightly wider link of typically 3.6 D, although the outer radius
at the link-to-link interface is smaller than 1.8 D, (see below).
The size of chain in use varies greatly, and is of course
dependent upon the application. Stud-less chain may start as
small as 4 mm with stud-link available from 16 mm becauseof the manufacturing complication of positioning the stud. At
the other end of the spectrum, a stud-link chain fabricated
using 182 mm bar has been employed by Petrobras22
, whilst
stud-less links formed from 178 mm (7 inch) bar have been
used offshore in the Terranova project23
. Such links are 641
mm wide, 1068 mm long and weigh approximately 650 kg
each21
.
In addition to the range of sizes, chain is also produced in a
number of strength grades, again depending upon the
applications requirements. However, for all sizes of chain, the
basic geometric similarities hold for the two types, and are
used below to define the chain in the analysis.
1.3 Current work
The review of previous work shows that very little
information is available about the behaviour of chain whensubject to twist. In addressing this problem, there are two
related issues which need to be considered:
the torsional moment needed to cause a given twist in anaxially preloaded chain (assuming the load stays constant);and,
the response (in the form of generated torque) of applyingan axial load to a pre-twisted chain (assuming the twist
stays constant).
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This paper presents experimental work and results for tests
undertaken on realistically sized stud-less and stud-link chain.
The tests have been performed in both constant load and
constant twist modes. In addition to the experimental work,
two analyses have been made, the first a purely geometric,
frictionless analysis of the twist of one link upon another,
where a link is modelled as two rigid half toroids joined by
straight bars. This model works by following the movement ofthe contact patches as the link turns, and using their positions
to calculate the torque generated by an axial load. In addition,
the development of the lift between the links is treated, and
non-dimensionlised results obtained which may be used to
predict the torsional response for chains of varying diameters.
The geometric frictionless analysis has the advantage thatit can be used fairly quickly at the development stage to
provide a good indication of the torques which will be
produced up to realistic levels of twist. An additional
advantage is that it does not require expensive computing or
test equipment. (The computer code is presented in an
appendix to this paper.)
The second analysis is an FE model, which includes theeffect of friction. In addition to the torque and lift, it also
considers the stress levels in the links.
2 Experimental Study2.1 Test equipment
The equipment used for the experimental measurements
reported here was the 3 MN/14 kNm tension-torsion machine
at the University of Reading. This machine (Figs. 2 and 3) has
a hydraulic actuator with stroke of 1000 mm and load capacityof 3 MN. A hydraulic motor is mounted at the rear of the
linear actuator which is capable of providing torques up to 14
kNm. The tensile actuator may be controlled in either load orstroke, and the rotary motor in either rotation or torque control
mode. Thus tests may be run in either load or stroke control in
combination with either rotation or torque control, whilstmonitoring all four parameters.
Figure 2 - 41 mm chain in the 3 MN/14 kNm tension-torsion testmachine.
Figure 3 - Schematic of the 3 MN/14 kNm tension-torsion machine at the University of Reading. The bed length is approx. 5 m. (Note that mainpower pack, accumulators, controller, hydraulic hoses, etc. are not shown.)
Hydraulic motorMain actuator Load cylinderTension-torsion load
cell
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2.2 Test samples
Two chain samples were used in the series of tests reported
here: one stud-less, and one stud-link. The main parameters of
the samples are listed in Table 1. It should be noted that
considerable difficulty was experienced in obtaining suitably
sized samples of appropriate length for this study. Thus the
samples tested were a compromise based on availability and
cost.
Parameter
Nominal chain size (mm) 41 56
Chain type Stud-less Stud-link
Chain finish natural natural
Average bar diameter, D* (mm) 43.1 56.97
Average link length* (mm) 254.7 330.9
Average link width, W* (mm) 141.0 203.17
Nominal W/D (-) 3.35 3.6
Average measured, W/D (-) 3.27 3.57
Effective W/D at end of link (-) 3.22 3.37Chain breaking load B (kN) 973 ca. 2000
Number of links in test sample (-) 19 23
* Average of 5 links
Table 1 - Test chain parameters.
2.3 Experimental procedure
As mentioned earlier, two types of test were of interest in
this study:
Constant load tests, in which the chain is tensioned to agiven load which is then maintained as the chain is twisted
by the hydraulic motor and the applied torque measured.
Constant twist tests, in which the chain is twisted underlow load to a series of levels of twist in turn (defined in per contact of two adjacent links). For each level of twist,
with the twist held constant, the axial load is then varied,
measuring generated torque as a function of load. For the
tests described here, the levels of twist used were 0, 1, 2, 3,
6, 9 up to a maximum of 24 per contact. In each case
the chain was loaded to a maximum of 40% of the nominalchain breaking load.
A full description of the test procedure may be found in
Ridge and Hobbs24
.
3 Modelling3.1 Geometrical frictionless theory
The analysis presented here in summary (fuller details are
given by Hobbs and Ridge25
) models the interaction between
two chain links in a very simple manner, neglecting friction
and any elastic or plastic response of the links at the contact
between the links or elsewhere. As noted earlier, it is purely
geometric in nature, following the changes seen at the contact
point between two adjacent links as one of the links rotates
about the axis of the preloaded chain, before using statics to
find the relationship between torque, turn, and axial load in a
non-dimensional form. Additionally, the theory predicts theend-shortening of the chain as it is twisted.
Figure 4 defines some dimensional parameters for the
hemi-toroidal (half donut) end of each studless link. The
radius and diameter of the parent bar stock used in making the
chain are taken as randD, respectively. The torus centre-line
radius is taken asR, and the link width Wis then simply 2(r+
R). Wis typically 3.35 D over a wide range ofD for studless
chain, encouraging the development of the non-
dimensionalised results presented later.
r
R r
W
D
Figure 4 - Model of the interaction between the two stud-lesschain links: definition of variables.
Initially, the links are at 90 to each other (Fig. 5(a)), and
the contact patch is nominally circular, although it is probably
significantly bigger than Hertzian contact stress theory would
predict for the given axial load because of proof loading
during manufacture. As the links turn relative to each other
(Fig. 5(b)), the patch initially becomes oval, and then separates
into two distinct patches. These patches move up the
shoulders of the links as turn continues to grow, and a gap
appears between the links at the initial contact point. This gap
is the source of the end-shortening in a twisted chain. As the
turn is further increased, the patches move further and further
around the links, and in principle a lock-up situation occurs
(with perhaps 30 turn between a pair of links), Fig. 5(c), with
contact on the straight parts of the links.
It is recognised that this discussion is not fully applicable
to studded links whose ovoid shape means that less than a fullsemi-circle is available at the ends of a link, and the stud will
also impede large twists. Additionally, for studless links with
an overall length of 6D as shown in Figure 1, contact will
occur between a given link and the back of the next link but
one shortly before the situation envisaged in Figure 5(c) canbe achieved.
As indicated above, Figure 5 shows a sequence of views
along the axis of the chain as the two half-links are twisted
relative to each other. In each case, the acute angle to a mid-
plane between the links is identified. The symmetries revealed
on this plane are central to the analysis. Figures 6 and 7
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OTC 17789 5
indicate the coordinate systems used, where Figure 6 shows a
Cartesian system X, Y, Z defined so that X and Z lie in the
plane of the link. The angles and define a (contact) point Pon the surface of the torus. Using standard procedures
25it is
easy to define the X, Y, Z coordinates of P in terms ofand ,
and then transform these coordinates into a second set x, y, z
defined with respect to the mid-plane between the links,
Figure 7.
(a) Initial position = 45
(b) Intermediate < 45
(c) Final lock up = L
Figure 5 - Sequence of views along the axis of the chain as thetwo half links are twisted relative to each other.
R
r
A
A
Z
XO
P
Section A-A
Figure 6 - Definition of the X, Y, Z co-ordinate system (Y intopage).
Figure 7 - Definition of x, y, z co-ordinate system and (y intopage).
The cross-hatched area in Figure 7 represents the plane y =
0, a plane that by symmetry must contain the contact point or
points between the links. For close to 45 (small twists), thearea is roughly elliptical, while as twist increases the shaded
area becomes kidney shaped as shown in Figure 7. The contact
points C are to be found at the lowest point or points of the
boundary of the shaded area. This fact allows and to be
found25
in terms of:
=
r
R
21 sincos (1)
and
=
sin
cossinsin 1
t
r(2)
where
cosrRt = (3)
Since cos cannot exceed 1, Equation (1) gives an upper
limit on at which the initial single central contact separates
into two contacts. Denoting this value as u, and rearranging
Equation (1) with cos= 1 gives:
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R
ru
1sin= (4)
There is also a lower limit on , the value L at lock-up
shown in Figure 5(c). From that figure
= Rr
L
1sin (5)
For any value of between these limits, the torque T is
then given in terms of the axial loadPby:
tantanPRT= (6)
while the end-shortening per link on one interface (Figure 7)is:
cos)( trR = (7)
Working between the limits on given by Equations (4)
and (5), Equations (6) and (7) have been used to generate the
theoretical results presented in comparison with experimental
and FE data below, and the non-dimensionalised design curves
that follow later. The simple Fortran program used for these
calculations is presented in the Appendix.
3.2 Finite element model
All finite element analyses were performed at the LABEIN
Technological Centre, Spain, with the nonlinear codeABAQUS 6.5 of Hibbitt, Karlsson and Sorensen
26.
Two finite element models have been developed, one for
41 mm stud-less and the other for 56 mm stud-link chains,based on the actual measured geometry of the links as defined
in Table 1. The FE models consider inter-link contacts, large
displacements and material non-linearities.Figure 8 shows the finite element meshes used in the
computations. In each case, the interaction between three links
has been modelled, the complete middle link being solid and
the adjoining (half) links rigid. The solid link is built up
from eight node linear brick elements with reduced
integration, while the adjoining links are meshed with rigid
shell elements. The mechanical contact between the links has
been defined with a friction coefficient of 0.3.
The rigid half-link 1 is fully restrained, while rigid half-
link 2 can displace along its longitudinal axis and rotatearound it.
The simulations consider a material with an elastic-plastic
behaviour, with the material properties slightly higher than the
minimum properties dictated for grade 3 material by DNV CN
2.627
. This specifies a yield stress of 410 MPa, tensile strength
of 690 MPa and a corresponding tensile strength strain of
10%. The minimum elongation required by the CertificationNotes is 17%.
A bilinear hardening material curve was used considering
the true values corresponding to the engineering values above.
However, for the low axial loads, the behaviour depends
predominantly on the geometry, with the material having little
influence, the whole stress field being under the yield stress.
Thus, the same results may be expected for grades 4 and grade
5 now emerging in the market.
The axial loadPand the torque Tare applied to rigid half
link 2 consecutively, that is the assembly is loaded and then
twisted incrementally.
Figure 8 - Studless and studlink chain model meshes.
4. ResultsThe results from the tests on the different chain samples are
presented in three different types of graphs:
Firstly, the constant load tests are plotted as a graph of the
non-dimensionalised torque (T/PD; where T is the measured
torque,Pthe axial load andD the chains parent bar diameter)
as a function of the link rotation parameter expressed in
degrees. As is the angle from the plane of the link to the mid
plane between two links, note that starts at 45 and tends
towards L (angle at lock) as the chain is twisted (See Fig. 5).
Thus = 45 /2, where is the twist per link. The value ofL
will vary depending upon the ratio W/D.Secondly, the lift or gap, 2, between links as a function
of twist is also of interest. Here, the non-dimensionalised lift
/D is plotted as a function of.
Thirdly, the constant twist data are presented as a series of
lines for different levels of twist (expressed in terms of
degrees per contact) either as the non-dimensionalised torque(T/BD) plotted as a function of load (now expressed as a
percentage of the chain breaking load, B), or as torque as a
function of load.
4.1 Stud-less chain
Constant load tests
The chain was loaded to 10 kN in these tests, (which it is
recognised is a very low load in terms of the chain MBL)
which was just enough to remove the sag from the sample.
Testing was undertaken in three stages, to 300 overall twist
and then to 500, and 526 twist. The constant load results are
presented in Figs. 9 and 10. Figure 9 shows the torsional
response of the stud-less chain as it is twisted under constant
load. The upper part of the curves are the twisting-up part of
loading and the lower the un-twisting. The three sets of
experimental results presented show that at relatively low
levels of twist, the behaviour is very consistent, whilst at
higher levels, such as in the second and third twistings, there ismore variation. The local spikes on the graph are attributable
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OTC 17789 7
to a stick-slip behaviour between the links. It can be seen that
upon reversal of the twist, i.e. un-twisting, the torque
immediately falls very sharply, and the un-twisting
relationship for all three curves is very similar. The dashed
line shows the non-dimensionalised torque as predicted by the
FE model, which is in good agreement with the experimental
data in both the loading and unloading processes. It was found
that variation in the friction parameter in the FE model hadsome effect on the results. As previously mentioned, in themodel a coefficient of friction of 0.3 was used, which gave a
good agreement with the experimental results. This value
might seem unrealistically high in real terms, but is a result
of the resolution of the mesh used to model the links at their
points of contact.Also presented in Fig. 9 is the theoretical non-
dimensionalised torque for W/D = 3.22 (derived from the
geometrical analysis). Previous work has shown that it is more
accurate to use the local geometry of the chain link rather than
that defined by the manufacturers catalogue24
. The theory
shows some agreement with the experimental data,
particularly for the unloading curves. However, the point atwhich there is a sharp increase in torque is found in practice to
be at a lower level of twist (higher value of of 30.4) than
predicted by the geometry-based frictionless theory, which
gives a value ofL = 26.7 forW/D = 3.22.
With reference to the un-twisting part of the curves
presented in Fig. 9, a comparison with the theoretical values
shows that all three are in very good agreement following the
initial sharp drop in torque found as the direction of the twist
is reversed. It is suggested that friction and the need to shorten
the chain to generate the lift between the links increases thetorque above the geometrical theoretical value during the
loading process. On unloading, the release of stored elastic
energy, and the reduction of the lift (perhaps momentarilyunloading individual contacts) are available to drive the
unloading curve closer to the theoretical line.
The non-dimensionalised lift per link has been plotted inFigure 10. The experimental data here are averages for each
link, derived from the actuator stroke at a given twist. It is
assumed that the links remain axial to the centre-line of the
machine as they separate. At low levels of twist this
assumption is acceptable, but as the higher levels, it is clearly
not. Owing to the geometrical imperfections in the links, and
influenced by friction, at higher levels of twist the links start to
tilt. The horizontal sections of the second and third loading
lines in Figure 10 are associated with the sharp increase in the
torsional response (c.f. Fig. 9). This would suggest that the
links are in the process of locking at this level of twist. The
lift predicted by the FE model and the geometrical theory have
also been plotted on this graph. They are in very good
agreement with each other and in good agreement with the
experimental data, although they consistently underestimate
the experimental level of lift. This offset may be associated
with the mutual indentation of the links from previous loadingconditions.
Constant twist tests
Figure 11 presents the results of the constant twist test.
Each line on the graph is for one of the set levels of twist
(defined in per link-link contact). In this graph the loading
and un-loading sections have been indicated by means of solid
and dashed lines respectively. Note that the twist values are in
unequal increments of: 0, 1, 2, 3, then 6, 9 and 12/contact, in
this way attention has been focussed on the low levels of twist.
The low level twist tests are of interest to compare with the
traditionally quoted accommodation of 3/link. Twelve
degrees per contact is equivalent to = 39 which is quite a
low level of twist in terms of this study, but the associatedtorques at approx. 45% chain MBL approached the capacity ofthe machine so it was not possible to go any further with this
size chain. Figure 11 has been plotted using the chain breaking
strength B to normalise the torque (T/BD). The results
presented in this figure show that the torsional response for a
given state of twist is broadly linear as might be expected.Doubling the axial load doubles the torque until the load gets
too big and the contacts dig in and/or elastic effects take over.
As with the constant load tests, there is considerable
hysteresis at the higher twist levels and the torque falls sharply
on reversal of the loading. The graph also shows that the chain
tested is not perfectly torque balanced in its untwisted state.
This is thought to be due to geometrical imperfections in thechain links.
4.2 Stud-link chain
Constant load tests
Constant load tests on the 56 mm stud-link chain were
undertaken for a range of loads between 10 kN and 500 kN
(approximately 0.5% - 25% of chain breaking load). Owing to
the magnitude of the torques required, the chain could only be
taken to high twist levels at the lower loads. Figure 12 shows
the results for this series of tests. The upper part of the curvesare the twisting up part of loading and the lower the un-
twisting. For the range of loads investigated, the non-
dimensional torque response is very similar for a given levelof twist. (Note that the constant load tests were performed at a
single load of 10 kN for the stud-less chain.)
During this series of tests the opportunity was also taken tocompare the effects of twisting the chain in different
directions. The two curves for the constant load of 10 kN show
a broadly similar behaviour, any differences being attributable
to geometrical inconsistencies and friction between the links.
Note that all tests were undertaken on the same length of chain
and thus after the first loading some damage/wear would have
been caused at the inter-link contact points which would have
had an effect on subsequent loading/twisting.
As with the stud-less chain (Fig. 9) there is a series of
stick-slip spikes on the loading part of the curves. In this case
the spikes are more numerous and pronounced in size and
were accompanied by considerable noise from the test sample.
Here it may be seen that as with the stud-less chain, the
geometrical model gives a good prediction of the torque
during untwisting where the friction effects do not dominate.
The finite element model for the 10 kN load predicts that the
chain locks up somewhat earlier than was found in practice.Two other lines are presented in Figure 12, both simulating
twist with an axial load of 50 kN. In one instance the FE
model was set so that no plasticity was allowed in the material,
and in the second, plasticity was allowed. It can be seen that
both models fit well with the experimental data obtained for
the 50 kN load during testing. The no plasticity model is
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also in good agreement with the non-dimensionalised torque
found for the 10 kN data at higher levels of twist. This is
reasonable, since as stated earlier, the FE model determined
that the stresses in the 10 kN test would not reach the elastic
limit. The second 50 kN line on the graph shows what happens
at higher twist levels where the combination of axial load and
torsion cause the chain material to exceed its elastic limit.
Figure 13 plots the implied lift of each link as a function ofthe twist in the chain for the range of constant loads. Theseresults are very consistent, and in good agreement with the
theoretical results. As observed, with the stud-less chain, at the
higher twist levels the links tended to rotate rather than just
lift, so there is some source of error present. A further
limitation with stud-link chain is that the links will hit the studwhich will prevent further lift. Typical stud width is usually
just under D, which effectively limits the lift to a value of
approximately 0.25D.
Constant twist tests
Figure 14 below presents the constant twist results for the
56 mm stud-link chain. In an effort to be able to investigate
the higher twist range, the maximum load has been kept to 250
kN some 12.5% of the chains breaking load. As with the
stud-less chain the torsional response is broadly linear even at
higher levels of twist. The noise on the curves at higher twist
levels is due to the stick-slip behaviour of the chain.Hysteresis is quite marked at levels above 9 /link twist.
This data has not been non-dimensionalised note the
magnitude of the torque (approx. 12 kNm) at fairly low loads
but high levels of twist.
0
5
10
15
20
25
2527293133353739414345
(degrees)
Non-dimensio
nalisedtorque(T/PD)
1st loading 2nd loading 3rd loading FE model geometrical model W/D = 3.22
Figure 9 - Non-dimensionalised torque T/PD (-) vs. (degrees) for a constant load of 10 kN for 41 mm stud-less chain, twisting-up and un-twisting. Also presented are the results from the FE model (dashed line) and the geometrical model response forW/D = 3.22.
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OTC 17789 9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
2527293133353739414345
(degrees)
Non-dimensionalisedlinklift
(/D)
3rd loading 2nd loading 1st loading FE model geometrical model W/D = 3.22
Figure 10 - Non-dimensionalised lift /D (-) vs. (degrees) for constant load test (10 kN) for 41 mm stud-less chain. Also presented are theresults from the FE model (dashed line) and the geometrical model response forW/D = 3.22.
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0 10 20 30 40 50
Load (%B)
Non-dimensionalisedtorque(T/BD)
Twist (degrees per contact)
9
12
6
3
2
1
0
Figure 11 - Non-dimensionalised torque T/BD as a function of load (%B) for a series of constant twists (degrees per contact), loading (solidline) and un-loading (dashed line) for a nominal 41 mm stud-less chain.
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10 OTC 17789
0
5
10
15
20
202530354045
(degrees)
Non-dimensionalisedtorqu
e
(T/PD)
load = 10 kN load = 10 kN opposite load = 50 kN
load = 250 kN load = 500 kN geometrical model W/D = 3.37
FE model 50 kN no plasticity FE model 10 kN elasto-plastic FE model 50 kN elasto-plastic
Figure 12 - Non-dimensionalised torque T/PD as a function of for a 56 mm stud-link chain for a series of constant loads twisting up (upperpart of curves) and un-twisting. Also included is the geometrical theoretical data forW/D = 3.37 and three predictions comparing the elasto-plastic and no plastic behaviour of the FE model.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
202530354045
(degrees)
No
n-dimensionalisedlift(
/D)
load = 10 kN load = 10 kN opposite load = 20 kN
load = 20 kN repeat load = 50 kN load = 100 kN
load = 250 kN load = 500 kN repeat geometrical model W/D = 3.37
FE model 10 kN elasto-plastic
Figure 13 - Implied lift /D as a function of in the constant load tests for a 56 mm stud-link chain. Also included is the geometrical theoretical
prediction and FE model for a chain under 10 kN load.
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OTC 17789 11
-2000
0
2000
4000
6000
8000
10000
12000
0 50 100 150 200 250 300
Load (kN)
Torque(Nm)
Twist (degrees per contact)
24
9
6
3
0
12
15
18
21
Figure 14 - Torque as a function of load for a series of constant twists (degrees per contact) loading (solid line) and un-loading (dotted line)for a 56 mm stud-link chain.
4.3 Stress in the chain links
The finite element model allows an inspection of the
stresses to which the chain links are subject under differing
loading combinations of twist and axial load. It was noted atthe end of section 4.2 that the magnitude of torque in a twisted
chain was very large at fairly modest axial loads. Figure 15
shows the stress contour plot for a stud-less chain with very
low load (about 1% of its breaking load), but an extreme level
of twist (note the lift between the links). Similar levels of
maximum stress will be obtained for the same links underlower levels of twist but at higher axial load (Figure 16).
Figure 15 - Max principal stress. P = 10 kN and extreme twist = 28.8/link for studless chain
Figure 16 - Max principal stress. P = 200 kN and twist = 17/link for studless chain
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12 OTC 17789
Figures 17 and 18 show the same effect for a stud-link
chain.
Figure 17: Max principal stress. P = 10 kN; and extreme twist
= 28 for stud chainFigure 18: Max principal stress. P = 250 kN; and extreme twist
= 13 for stud chain
The same FE model was used to predict the response for
the chains under higher (service) loads (Figure 19). Here it can
be seen that permanent plastic deformation occurs at fairly
modest levels of twist. As a result of this analysis it may be
seen that for values greater than 38 (i.e. inter link angle
lower than 14), that the T/PD curves obtained are
approximately coincident under all axial loads considered (as
would be expected). For this angle and load range the stress
field of the link remains under yield, after which plasticity
begins and sooner for the higher axial load cases.
0
5
10
15
20
25
202530354045
(degrees)
T/PD
load = 10 kN load = 50 kN load = 250 kN load = 500 kN load = 600 kN
Figure 19 - Showing FE model prediction of plastic deformation of 56 mm stud-link chain links under high load at low angles of twist.
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OTC 17789 13
Using all the results obtained in the finite element simulations,
the following upper bound regression formulae have been
derived for the torque generated as twist increases under
constant axial load in studded and studless chains:
Studless chain:
04.00194.000196.00003.0 23 ++=
DP
T (8)
Studded chain:
04.00117.000054.000023.023 ++=
DP
T(9)
with
140
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14 OTC 17789
6. Stiff, J.J., Smith D.W., and Casey, N.F.: Fatigue of mooringchain in air and water - Results and analysis , paper no. OTC8147 presented at the Offshore Technology Conference,
Houston, Texas, May 1996 pp.291-297.7. Van Helviort, L.C.: Static and fatigue tests on chain links and
chain connecting links, paper no. OTC 4179 presented at the
Offshore Technology Conference, Houston, Texas, May 1982,
pp165-171.8. Abolfathi, E., Modlen, G.F., Webster, P.J. and Mills, G.: The
effect of the manufacturing test load on the fatigue of hoistchains, Proc. IMechE Part B - Journal of Engineering
Manufacture 1995, 209, 2 133-139.
9. Tipton S.M. and Shoup, G.J.: The effect of proof loading on thefatigue behaviour of open link chain, Journal of EngineeringMaterials and Technology - Trans. ASME1992 114 1 27-33.
10. Berg, A. and Taraldsen, A.: Long-term mooring and anchoringof large structure and drilling units (Reliability and safety of
anchor chain systems), paper no. OTC 3813 presented at theOffshore Technology Conference, Houston, Texas, May 1980.
11. Dowdy, M.J. and Graham, D.J.: A method for evaluating andextending the useful life of in-service anchor chain, papernumber OTC 5719 presented at the 20 th Annual Offshore
Technology Conference, Houston, Texas, May 1988.12. Pacheco, P.M.C.L., Kenedi, P.P. and Jorge. J.C.F.:
Elastoplastic analysis of the residual stress in chain links,Proc. OMAE02 21st International Conference on OffshoreMechanics and Arctic Engineering, Oslo, Norway, June 2002,pp39 46.
13. Brown, M.G., Hall, T.D., Marr, D.G., English, M. and Snell,R.O.: Floating production mooring integrity JIP keyfindings, paper OTC 17499 presented at the 2005 OffshoreTechnology Conference, Houston Texas, May 2005.
14. Jean, P., Goessens, K. and LHostis, D.: Failure of chains bybending on deepwater mooring systems, paper OTC 17238presented at the 2005 Offshore Technology Conference,
Houston Texas, May 2005.
15. Casey, N.F.: A review of available laboratory test data onmooring chain applications, OTO 96 033 Health & SafetyExecutive, February 1998.
16. Nicol, D.: Case Study: Use of studless mooring chain forFPSO mooring at Texacos Captain field, Vicinay Cadenas,S.A., Bilbao, Spain 1996.
17. Canada, L, Vicinay, J, Sanz, A, and Lopez, E.: New mooringchain designs, paper OTC 8148 presented at the OffshoreTechnology Conference, Houston, Texas, May 1996 pp.299-
314.
18. Hiroshima, T. and Sawa, T.: Three-dimensional elastoplasticfinite-element analysis of link chains in chain hoist subjected tocombined loads of torsion and impact tension, Transactions ofthe Japan Society of Mechanical Engineers, Part A (November
1995) 61, 591, 2442-2449.
19. Economides, C.: Torsion in offshore mooring, and thetorsional response of mooring chain, Final year MEng report,Imperial College of Science, Technology and Medicine,
University of London, Department of Civil Engineering, 2002.20. Chaplin, C.R., Rebel, G. and Ridge, I.M.L.: Tension-torsion
interactions in multicomponent mooring lines, paper OTC12173 presented at the Offshore Technology Conference,
Houston, Texas, May 2000.21. Vicinay Cadenas SA: Supremacy by innovation, (Chain
manufactures sales brochure) Bilbao, Spain, 2002.
22. Anon: World record, Newslink No. 8, 2002, Vicinay CadenasSA, Bilbao, Spain.
23. Anon: Bringing to the present our desires for the future,Newslink No. 3, 1999, Vicinay Cadenas SA, Bilbao, Spain.
24. Ridge, I.M.L. and Hobbs, R.E.: Torque in Mooring Chain Part II Experimental investigation J. Strain Analysis 2005 40,
7, 715-728.
25. Hobbs, R.E. and Ridge, I.M.L.: Torque in Mooring Chain Part I Background and Theory, J. Strain Analysis 2005 40,7,703-713.
26. ABAQUS: ABAQUS version 6.5 suite of manuals, Hibbit,Karlsson & Sorensen, Inc. www.abaqus .com
27. DNV Certification: Notes No. 2.6. Certification of offshoremooring chain, August 1995.
Appendix
Computer program to evaluate torque and lift as functions of
PROGRAM CHAIN
OPEN(UNIT=6,FILE=Resultname)
DEG = 180.0/(4.0*ATAN(1.0))
READ*,D,DRATIO
WIDTH = D*DRATIO
! D is the chainmakers serial size, DRATIO is, e.g., 3.35 to give the overall link WIDTH
WRITE(6,200) D,DRATIO, WIDTH
200 FORMAT(10F10.2)
! R=D/2, RA is the toroid radius
R = 0.5*D
RA = 0.5*WIDTH R
RRATIO = RA/R
WRITE(6,200)R,RA,RRATIO
! G is used as a header for the various gamma values
GLOCK = ASIN(1.0/RRATIO)
GLODEG = GLOCK*DEG
GLIFT = ASIN(SQRT(1.0/RRATIO))GLIDEG = GLIFT*DEG
WRITE(6,200)GLIFT,GLIDEG,GLOCK,GLODEG
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OTC 17789 15
DELG = (GLOCK-GLIFT)/100.0
G = GLIFT
GDEG = G*DEG
! Loop over the range of gamma between lift and lock
DO 100 I = 1,101
PHI = ACOS(RRATIO*SIN(G)*SIN(G))
PHIDEG = PHI*DEG
T = RA-R*COS(PHI)THETA = ASIN(R*SIN(PHI)*COS(G)/(T*SIN(G)))THDEG = THETA*DEG
DELTA = (RA-R)-T*COS(THETA)
DELTD = DELTA/D
TOVERP = RA*TAN(THETA)*TAN(PHI)
TOVERPD = TOVERP/DWRITE(6,200)GDEG,PHIDEG,THDEG,TOVERP,TOVERPD,DELTA,DELTD
G = GLIFT+DELG*FLOAT(I)
GDEG = G*DEG
100 CONTINUE
STOP
END