String Fatigue

7/27/2019 String Fatigue

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ORAL REFERENCE: FT588

FATIGUE ON DRILL STRING CONICAL THREADED CONNECTIONS,

TEST RESULTS AND SIMULATIONS

L. Bertini1, M. Beghini1, C. Santus1, and A. Baryshnikov2

1DIMNP - Dipartimento di Ingegneria Meccanica Nucleare e della Produzione - Universit a di Pisa.

Via Diotisalvi n.2, Pisa. 56100 - Italy.2ENI S.p.A. - San Donato Milanese (MI) - Italy.

ABSTRACT

The paper is concerned with fatigue life of drill string threaded connections used in Oil drilling technology.

Full scale tests, finite element simulations and discussion of fatigue models are reported.

Full scale fatigue tests were performed at the University of Pisa. Two kinds of not standard fatigue test rigs

are proposed for different geometry and connection constructions, both exploiting near resonance conditions

induced in the specimens to get the overall structure not loaded and test time reduced.

Finite element analyses were performed to get an interpretation of tests and particular care was devoted to

model the connection presetting and the following fatigue loading.

Prediction of the specimen fatigue life was performed to reproduce test results and different approaches are

proposed. Basic material resistance properties were previously produced to apply fatigue models.Some limitations in prediction were observed, in particular due to high mean stress generated at notched

nucleation sites and also not clear demarcation between nucleation and propagation in full scale tests.

KEYWORDS:

full scale tests, fatigue life prediction, drill string threaded connections, finite element simulations.

1 INTRODUCTION

Oil drilling typically employs long hollow drill string to reach the production area [1]. Fatigue damage in drill

string is a well known issue in oil drilling technology, recording more than 50% failures [2]. Since failures

entails the lost of the drilling site, drill string failures are time consuming and very costly.

Failure usually results from material fatigue aggravated by the corrosive environment, improper equipment

handling, excessive rotational speeds or loading. Coupling of various damage conditions reduces dramatically

the fatigue life of the string. In particular, corrosion effect is a key factor [3, 4] primarily related to hydrogen

sulfide (H2S) which can drastically reduce or eliminate the endurance limit.

Full Scale fatigue tests (i.e. tests on real components) are therefore strategic for oil drilling companies. Indeed

devices for drilling elements fatigue tests have been recently proposed based on four points bending scheme

[5].

Connections between elements working for long periods in deviated wells or experiencing buckling tilting plus

bending lateral vibration [6] are the drill string typical locations of fatigue damage.

To connect drill string elements in situ conical shouldered threaded connections are used (briefly named as

Copyright (c) 2006 Elsevier Ltd. All Rights Reserved.


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rotary shouldered connections). Pin and Box components and their usual locations for fatigue damage, are

showed in Fig.1(a) [7]. In the typical construction, schematically depicted in Fig.1(a), the connection end (tool

joint) is fixed to the pipe through stir welding. The whole component is made by low alloy steels for heat

treatment [7].

The paper mainly considers these components. However, the construction of Fig.1(b) is considered as well,

referred to ISO standard [8]. The aluminum pipe element is connected to the steel connection through a steel-

aluminum threaded connection which is not broken out during the operation.

(a)

Box fatigue

locationPin fatigue

location

(b)

steel

Fatigue location Fatigue location

Boxside

alluminum steel alluminum

Pin side

Figure 1: (a) Fatigue locations in steel construction. The root of the Last Engaged Thread is the weakest

point in fatigue, both for Pin and Box. (b) Fatigue locations in aluminum construction. The end of the steel-

aluminum connection is the typical fatigue nucleation site.

Full scale fatigue tests were carried out through a cooperation between University of Pisa andENIoil company.

Results are divided in the two experimental activities regarding:

steel heavy construction [9, 10], Fig.1(a);

aluminum light construction, Fig.1(b).

A brief description of the test equipments and interpretation of results is proposed by means of numerical sim-

ulations, through Finite Element (FE), to find a good approximation of the stress state at the fatigue nucleation

site, and fatigue model to predict fatigue life.

In the scope of Oil Drilling applications, fatigue life mainly concerns with High Cycle Fatigue (HCF). WhenStress Life and Strain Life produce similar results, as widely stated in the literature [11, 12]. Stress life ap-

proach (and related nomenclature) is followed in the present paper. Basic material fatigue strength was eval-

uated through small scale tests, therefore fatigue models applied. Indeed a well calibrated fatigue analytical

model is a powerful tool if accurate fatigue life prediction is required on components of similar construction,

to reduce the number of expensive and time consuming full scale tests. Furthermore, if the material and tech-

nological process are the same, only numerical calculations need to be re-run.

A deeper investigation on the local effective stress state, and the analysis of factors influencing material fatigue

strength, leads to a very useful understanding of possible improvements to enhance fatigue strength.

2 FULL SCALE FATIGUE TESTS

2.1 Steel heavy construction

In this section tests related to the construction introduced in Fig.1(a) are reported, in which fatigue crack nu-

cleates at the thread roots.

The material used is a Chromium Molybdenum tempering steel as defined by API standard [7], which has

basically the same composition and heat treatment of AISI 4145H steel.

Main specimen dimensions are Outside Diameter OD = 88.9[mm], Inside Diameter ID = 38.1[mm] and Spec-imen Length SL = 1.5[m].By means of a bending test rig, designed and manufactured at the Mechanical Department of Pisa University,

full scale tests were carried out on specimens obtained from a pipe segment including a connection. The testmachine induces alternating (not rotating) bending load, as shown schematically in Fig.2. The nominal stress

distribution, with maximum 0, is referred as the load applied remotely from connection zone.

In Fig.3(a) the test rig is showed and in Fig.3(b) it shows how alternating bending is applied to the specimen.



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Alternating Bending

0 0

Figure 2: Sketch of the specimen and the load applied remotely in alternating bending condition, and the

nominal bending stress with max value 0

(a)

Bending arms SpecimenRotating masses Strain gauge

1 m

(b)

F

t

F

t

-

Specimen

Rotating eccentric masses

--

Bending armBending arm

F2

Zt

de

H

Figure 3: (a) Pictures of the Test Rig and specimen location. (b) Test rig operation working.

Rotating eccentric masses, at the top of two bending arms, can be shifted in phase and alternating bending

amplitude can be tuned.

The test rig operates at a frequency which is near, a little bit lower, to the first resonance of the specimen dy-

namic system in which the specimen is the spring and the arms the inertial masses. At this condition eccentric

masses excitation is strongly amplified, therefore high alternative bending moment is induced in the specimen

by means of little masses.

Closed-loop control is applied through strain gauges that measure longitudinal strain far from the thread zone.

Further information about the test rig are reported in [9].

It is well known that fatigue life is due to Crack Nucleation plus Crack Propagation. In full scale tests, propa-

gation time can not be neglected as compared to nucleation time, in particular for tough materials [11]. Thus,

nucleation and total fatigue life need to be distinguished. In the performed tests, specimens were not inspectedduring the test, but their dynamic behavior was monitored. In the first part of the test, while the specimen

is flawless (or the crack is small), dynamic response is steady, on the contrary when a big enough crack is

present, dynamic behavior changes.

The Fast Fourier Transform (FFT) was applied to analyze the strain signals. Unless the specimen was signif-

icantly damaged, the amplitude of the first harmonic is uppermost than the second. Therefore as symptom of

fatigue crack presence, second harmonic is compared to the first until it starts to get predominant. Therefore

it is possible to understand that the dimension of the crack, to be detected through dynamic global response,

is quite large (around half the thickness of the pipe wall) then a remarkable portion of the fatigue propagation

is included in the life which is experimentally detected as nucleation. In the following, to highlight this issue,

the term experimental nucleation will be used.

In Tab.1 a summary of the experimental results about the full scale fatigue tests is reported.Test results are also reported in Fig.4 as S-N curve for alternating bending load, showing the typical linear

correlation between nominal bending stress 0 and number of cycles to failure (or to experimental nucleation)

in log-log scales, but here reported in semi-log scales.



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Table 1: Steel connection full scale fatigue test results.

Alt. Stress Exp. nucleation Fatigue life Failure mode

0[MPa] [cycles] [cycles]

50 > 10 106 > 10 106 Run out

55 2.95 106 5.915 106 Pin side

60 1.75 106 5.034 106 Pin side

70 1.77 106 3.39 106 Pin side

70 1.54 106 4.085 106 Pin side80 0.829 106 1.32 106 Pin side

90 0.390 106 0.860 106 Pin side

100 0.180 106 0.550 106 Pin side

(a)

105

106

107

108

0

20

40

60

80

100

120

cycles

0

[MPa]

Exp. nucleationFatigue lifeExp. nucleation fit lineFatigue life fit line

(b)

Figure 4: (a) Fatigue test results for the steel connection, (b) Pin fatigue failure surface.

2.2 Aluminum light construction

The aluminum light construction is briefly introduced in Fig.1(b).

The alloy used for pipe is defined in ISO standard [8] and is basically an artificially aged Al-Zn alloy similarto AA7014-T6.

Specimen dimensions are Outside Diameter OD = 147[mm], Inside Diameter OD = 107[mm] and SpecimenLength SL = 3.7[m]. where OD and ID dimensions are related to the aluminum section.Test rig designed and manufactured at Mechanical Department of Pisa University is shown in Fig.5.

(a)

Aluminum

pipe

Steel

connection

Fatigue

section

Fatigue

sectionAluminum

pipe

0.5 m

Steel

connection

Strain

gauge

(b)

X

Y

Z

Deformed shape

Undeformed shape

Fix

point 2

Fix

point 1

Eccentric rotating

mass

Specimen prop

at fix points

Figure 5: (a) Picture of the connection to test. (b) Vibration induced in the specimen.

It is worth noting that displacements in Fig.5(b) are strongly amplified for graphical reason, and that the

specimen is not rotating, but rotating bending is induced.

Fatigue crack nucleates at the end section interface between steel and aluminum pipe. Fatigue test results are



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reported in Fig.6 along with crack surface at the fracture section.

(a)10

5

106

107

108

0

20

40

60

80

100

120

140

cycles

0

[MPa]

TestsFit line

(b)

Figure 6: (a) Fatigue test results for aluminum light construction. (b) Fatigue crack surface at the fracture

section.

Propagation was a significant portion of fatigue life for steel connection tests, on the contrary, aluminumconnection test propagation life can be neglected compared to whole fatigue life, basically for two reasons:

1. specimen wall thickness is smaller,

2. aluminum alloy has lower toughness.

Therefore the dynamic behavior of the specimen remains steady up to the end of the test, and no macroscopical

evidence of the crack can be obtained. For this reason, fatigue life experimentally detected is mainly nucleation

life.

3 FINITE ELEMENT ANALYSES

3.1 Threaded steel connection

Finite Element (FE) simulations have been developed in order to evaluate the stress-strain at the connection

critical points where fatigue failures were detected.

Taking into consideration a cylindrical frame with z axis along the axis, some insight on stress state are given

in the following. If thread helix angle and thread conical shape are neglected, cylindrical frame axis are stress

principal directions at the thread root location, then r, , and z are principal stresses under both axial or

bending load. At the thread root location, stress state features:

r = 0z > > 0

r = rz = z = 0(1)

Moreover under prevailing elastic strain, since the the fillet radius is small as compared to the distance to the

axis, almost plane strain conditions locally arise:

z (2)

As a consequence, threaded connections was modeled by a plane (bi-dimensional) Axi-Symmetric geometry

[13], under the following assumptions:

thread helical angle neglected, threads modeled as multiple rings;

torsional and tangential loads neglected;

after the plasticity induced by the first loading ramp, elastic shakedown is assumed.



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With this model only axial and bending loads can be considered on the connection. It is remarkable that

pure bending in a circular geometry can be correctly modeled in elastic conditions by means of 2D Harmonic

elements. As harmonic analysis is based on the linearity of the problem any non-linearity (such as local

yielding) could not be modeled. However this limit can be overcome by a proper sequence of FE analyses, as

hereafter shown, and bending FE fatigue assessment can be accurately performed also with a bi-dimensional

model.

The bi-dimensional model is shown in Fig.7. The material was modeled as linear elastic far from stress

concentration since yield could not be reached, while it is modeled as Elastic-Plastic where material was

supposed to reach yield point, see Fig.7(b).For the elastic-plastic material, bilinear stress-strain curve was assumed with kinematic hardening rule.

Constraint equation have been used, Fig.7(c), since the contact is not supposed to be lost due to make up

presetting. Then contact non linearity is avoided.

(a)

X

Y

Z

Axial

simmetry

Box

Pin

(b)

Elasto-

Plastic

material

model

Perfect

elastic

material

model

(c)

Element

discretization

at thread root

Bonded

contact

condition

Figure 7: Bi-dimensional model featuring: (a) Axial symmetry. (b) Elastic-plastic material model (only elastic

in Harmonic model). (c) Bonded contact at thread edges, and fine discretization at thread roots.

Due to the high make up presetting, during rotating (or alternating) bending the material at the thread root

experiences stress fluctuations at high tensile mean stress. In this conditions mean stress relaxation occurs,

so this feature should be included in the constitutive material model. As a complete knowledge of these

properties were not achieved, monotonic curve was considered. Presently, the authors are investigating the

cyclic properties of the material to propose a more accurate model on stress-strain state at fatigue locations.

Load cases (or load steps) needed to be considered in the analysis are:

1. Make up presetting: make up produces quite high stress, so plastic strain arises at the roots of the

last engaged threads of the pin elements. Axi-Symmetric model along with Elastic-Plastic hardening

material was used at this stage. Interference at the shouldered face (or stop face) was imposed to induce

an axial load equivalent to that produced by make up torque presetting.

2. Application of external axial stress, simulating bending load after presetting: far field axial stress

was applied after load case 1. Stress imposed equals the value of the far field bending stress at the last

engaged root radial position. At thread root an increment of plastic strain can be observed during this

phase. The highest tensile condition is reached;

3. Alternating stress with elastic model: after experiencing previous load cases, the material is cyclicallyloaded remaining in elastic conditions (elastic shakedown). Therefore, alternate stress state, to be super-

imposed, can be calculated independently through Harmonic linear analysis, performed with 2D Fourier

elements.

Stress state, at the last engaged thread root after load cases 2 and 3 is reported in Fig.8.

It is worth noting that for the elastic-plastic solution, maximum stress can be found at a point located under

the thread surface due to the plastic strain [14]. However the maximum stress range under variable bending is

located at the thread root surface, due to elastic stress concentration.

3.2 Conical shoulder aluminum connection

In this case thread roots are not nucleation site basically because the outer steel connection, much stiffer than

the aluminum pipe, produce a strong shielding for bending stress at inner threads. The issue is described in

Fig.9(a), while in Fig.9(b) the stress field is reported.

As the stress at the shoulder is singular if no fillet is modeled, the elastic model point does not give sound



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(a)

Stress

path

(b)

0 1 2 3 40

300

600

900

1200

1500

0 1 2 3 40

0.002

0.004

0.006

0.008

0.01

Stress path coordinate [mm]

Stresses[MPa] pl

z

r

Equ

ivalentplasticstrainpl

Figure 8: (a) Axial stress component (z) at the Pin last engaged thread root after load cases 1 and 2. (b)

Principal stress components and equivalent elastic strain along the thread root path. It is worth noting how

stress gradients are smoothened by yielding.

(a)

Undeformed

Exagerated bending

deformation

Strong stiffness drop

(b)

Stress raiser

point

Aluminum-steel interface,

fretting nucleation induced

Figure 9: (a) Deformation (exaggerated) of the aluminum-steel interface, the strong drop of stiffness produces

stress intensification. (b) Stress state at the fatigue nucleation site.

information. The Theory of Critical Distance (TCD) was then applied to bypass this problem [15], in particular

for fretting conditions, as in the present case, the crack analogy [16] should be used in order to identify a

parameter able to describe fretting damage. The results of this analysis is in an early stage and no definitiveconclusions can be stated.

4 FATIGUE LIFE MODELS

Steel connection results, reported in Tab.1, are discussed in the following. Fatigue models are applied in order

to give an interpretation of full scale tests, indeed it is very useful to understand the limitations that can arise

from fatigue life calculation.

From numerical results obtained through FE, stress state is known at the root of last engaged thread both Pin

and Box for each full scale test in Tab.1. Reported tests only account for Pin failures, however for different

geometry Box failures can be found as well.In order to reproduce experimental conditions, the fatigue model needs to consider the following issues:

finite life prediction is needed, instead of fatigue limit only;

thread root stress state is biaxial, as reported in Eq.1;

notch effect is clearly playing a significant role, since stress gradient at the thread root is quite strong, as

shown in Fig.8;

thread root machined surface is important in the nucleation process;

mean stress effect needs to be considered. The make up presetting at the connection coupling induceshigh tensile stress in particular at the Pin last engaged thread root, as shown in Fig.8.

Regarding the last issue, two different models were considered:



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1. Gerbermodel, in which mean stress effect is accounted for by a parabolic relation between alternate and

mean stress [11];

2. Smith Watson and Topper(SWT) model, in which an equivalent fully reversed stress is considered [12].

Details of the fatigue models can be found in [17]. To determine basic material fatigue data, small scale tests

were performed on specimens extracted from real components, to let them be representative of metallurgical

conditions Fig.10(a) and surface state effect Fig.10(b).

-

Figure 10: Small scale specimen extracted from real components (left) for obtaining basic fatigue properties

and small scale specimen used for evaluating the surface state effect (right).

4.1 Fatigue prediction results

In Fig.11 Pin and Box sites stress condition, for each tested connection, are reported along with material fatigue

Gerber model.

(a)

0 200 400 600 800 10000

100

200

300

400

500

Eq. mean stress

Eq.a

lternatestress

Failures

No failures

Run out

FatigueLimit

105 cycles

104 cycles

0

Pin stress stateBox stress state

(b)

103

104

105

106

107

103

104

105

106

107

Gerber model prediction [cycles]

Exp.nucle

ation

[cycles]

Tests

Figure 11: (a) Equivalent stress state at Pin and Box locations. (b) Comparison between predicted nucleation

(Gerber model) and experimental nucleation.

The following conclusions can be stated:

the mean stress at the Pin location is larger than at the Box, this is due to the connection make up;

for the Pin the higher alternate bending nominal load (0) the higher is the alternate stress but the lower

the mean stress, this is due to the local yielding of the material at the thread root;

for the Box the higher alternate external load 0, the higher are both alternate and mean stresses, since

no local yielding of the material is obtained at the thread root;

for each test, Pin site is in a worse condition as compared to the Box one.

The prediction of the SWT model is reported in Fig.12(a). In Fig.12(b) Gerber and SWT models are compareddemonstrating that they produce similar predictions, which almost coincide near the fatigue limit conditions.

A wide mismatch seems to be obtained against experimental results, however it is important to remember

that nucleation vs. propagation is strongly related to fatigue crack dimension resolution which is available.



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(a)

104

105

106

107

104

105

106

107

SWT model prediction [cycles]

Exp.n

ucleation[cycles]

Tests

(b)

103

104

105

106

107

103

104

105

106

107

Gerber model prediction [cycles]

SWTmodelprediction[cycles]

Tests

Figure 12: (a) Comparison between predicted nucleation (SWT model) and experimental nucleation. (b)

Comparison between the two analytical models.

In the tests here reported, nucleation was considered as the condition on whole structure dynamic behavior,

as previously discussed. It is obvious that the minimum detectable crack is quite large, estimated about fewcentimeters. For this reason experimental nucleation (as considered in the paper) includes a quite remarkable

portion of propagation. Thus, it is conceivable that experimental cycles are much higher then predicted.

Even this is a conservative condition the mismatch is too wide and then a propagation calculation should be

performed.

5 DISCUSSION AND CONCLUSIONS

In the paper two kinds of resonant fatigue rigs for testing drilling elements were presented, along with real

component (full scale) test results. FE analysis were proposed to evauate stress state at the nucleation sites. Fi-

nally fatigue models were applied to match experimental results with calculation starting from FE simulations

and material fatigue strength.

For the steel connection the following indications were obtained:

high tensile mean stress induced by the connection make up presetting leads to Pin failures instead of

Box failure and this is correctly predicted by the model;

the high crack toughness of the Chromium Molybdenum alloy steel, used for these connections, offers

an extended service life before a large fatigue crack is produced in the connection;

this damage tolerance is indeed strongly appreciated from an engineering point of view, but it produces

a wide mismatch from nucleation predicted life and test results.

To better understanding the limits of the calculation it is also useful to introduce the following issues in future

analyses:

the presetting stress state, applied to the connection, is known with not enough accuracy since friction

play a significant role during make up operation. Since mean stress effect is very important, prediction

accuracy is affected;

the material experiences relaxation at high mean stress, then monotonic curve is not the best way to

model the stress strain behavior. A complete cyclic-properties characterization of the material is neces-

sary.

According to these intrinsic losses of accuracy the bi-dimensional model can be considered adequate to the

precision expected.

The following steps to better predict connections fatigue life are going to undertaken:



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experimental nucleation life needs to be better resolved, otherwise fatigue life data to be matched is

known with little accuracy itself;

relaxation can be investigated through small specimens and properly modeled in the FE analysis.

Therefore full scale fatigue tests are required since these issues can strongly reduce calculation a priori relia-

bility. However after running a sequence of full scale tests the analytical fatigue model can be calibrated and

applied with more confidence to similar components.

ACKNOLEDGEMENTS

The authors are grateful to ENI S.p.A., for founding the research, and technically supporting each phase of the

study.

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