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Resonant test rigs for fatigue full scale testing of oil drillstring connectionsL. Bertinia, M. Beghinia, C. Santusa,*, A. BaryshnikovbaDipartimento di Ingegneria Meccanica, Nucleare e della Produzione, Universita di Pisa, Via Diotisalvi n?2, 56126 Pisa, ItalybEni S.p.A. Exploration and Production Division, Via Emilia n. 1, San Donato Milanese (MI) 20097, ItalyReceived 26 February 2007; received in revised form 27 July 2007; accepted 21 August 2007Available online 1 September 2007AbstractThe paper presents two test rigs designed at the University of Pisa to perform bending fatigue tests on full scale drill pipe connectionsused for oil drilling. Two types of connection required different configurations of test rig. In both cases, specimen resonance wasexploited in order to reduce the loads on the structure and the test duration. This allowed a cost reduction in both the experimental appa-ratus and tests. Results of fatigue tests are reported and discussed.? 2007 Elsevier Ltd. All rights reserved.Keywords: Drill pipe connections; Full scale tests; Test rig design; Resonant testing machine; Fretting fatigue1. IntroductionIn oil exploration long hollow drill strings are employedto reach the production area 4. Fatigue damage in drillstring is a well known issue in oil drilling technology,recording more than 50% of failures 5, and failures atthe drilling sites can be very costly and time consumingfor the recovery procedures.The working conditions of the drill string is described inRef. 6. Drill strings rotating inside deviated wells experi-ence rotating bending and then fatigue damage, particularlyattheconnectionswhicharedrillstringweakestpoints.Fati-gue failures usually are aggravated by corrosive environ-ment, improper equipment handling, excessive rotationalspeeds or loading. Coupling of various damage conditionsreduces dramatically the fatigue life of the string.Full scale fatigue tests are therefore strategic for drillingcontractors. Recently devices to test drill string connectionshave been proposed. Miscow et al. 7 proposed a test rigbased on four points bending scheme. The specimen isrotated at a frequency in the range 515 Hz and a constanttensile axial load can also be superimposed. To produce therequired high axial load the test structure is heavily loadedand a massive frame is necessary to this purpose. A similarfour point bending test equipment has been employed byGrondin et al. 8 at a test frequency of around 7 Hz. Theyalso developed an interesting solution for producing axialloading employing a compressed rod inserted inside thehollow string under testing. With this solution the requiredaxial load can be produced without any external frame.Moreover, tests in corrosive environment (NaCl solution)could be performed at low frequency (around 15 Hz, nearto the actual frequency during drilling). These tests can beconsidered very representative of the operative conditionswhere fatigue acts in combination with mean stress andcorrosive environment which is particularly effective atlow rotating speed. However, this kind of test is very timeconsuming, indeed to produce a 10 106cycles test, on asingle specimen, four full months are necessary. Then thiskind of test is not suitable for a systematic assessment ofthe fatigue resistance, in particular when statistical evalua-tions are required.Smith et al. 9 employed a four point bending rig and arotating cantilever beam rig to test innovative titanium drillpipe design.0142-1123/$ - see front matter ? 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijfatigue.2007.08.013*Corresponding author. Tel.: +39 050 836607; fax: +39 050 836665.E-mail address: ciro.santusing.unipi.it (C. Santus)./locate/ijfatigueAvailable online at International Journal of Fatigue 30 (2008) 978988InternationalJournalofFatigueVeidt et al. 10 adopted a four point bending test facilitysimilar to that employed by Miscow et al. 7, consisting ina very strong external frame able to produce tensile axialload in the specimen.In the present paper different schemes of test rigs forbending fatigue tests on drill string connections are pro-posed. The dynamic behavior near the resonance frequencyis exploited to induce high bending moment in the connec-tion. The resonant condition is reached by means of rotat-ing eccentric masses. Through this technique the test framejust hold the specimen and no hydraulic actuator isemployed, since the load is provided by inertia forces. Asa consequence, both the complexity and the structuralstrength of the testing apparatus is much lower as com-pared to the four point test rig. Moreover, the resonancecan be set by a proper choices of the masses and full scaletests can be run at a frequency up to 2530 Hz, thus reach-ing 10 106fatigue cycles in about four full days test. Adrawback of proposed test rigs is that mean axial loadcan not be applied (only alternating or rotating bending,i.e. cyclic stress at load ratio R = ?1). On the contraryheavy test rig frame is able to exert high tensile axial load(as proposed in Refs. 10,7). Moreover, the choice of highfrequency tests (faster than the working condition) reducesthe possibility to test the effect of environment on fatigue.However, interesting comparisons between the basic fati-gue strength of different design solutions can be obtainedin a relatively short time at a reasonable cost.2. Connection types to testTwo types of connections were considered:? high-strength steel connection (hereafter named as steelconnection), related to standards Refs. 1,2;? aluminum light-weight pipe connection with steel tooljoint (hereafter named as aluminum to steel connection),related to standard Ref. 3.NomenclatureNC 26type of connection according to API stan-dard 1,2NC 50type of connection according to API stan-dard 1,2ADP-STJ147 13type of connection according to ISO stan-dard 3F1eccentric rotating mass inertial force onbending arm 1F2eccentric rotating mass inertial force onbending arm 2meeccentric rotating massReeccentricity of the rotating massesddisplacement of the bending arm pointwhere rotating masses are placedderelative displacement of the rotating massesfrotational frequency of eccentric rotatingmassesxrotationalspeedofeccentricrotatingmassesfnnatural frequency of the specimen acting asa dynamic systemxnnatural frequency of the specimen expressedas rotating speednrotational frequency over natural frequencyratioDadynamic amplification factorcphase angle between the two couples ofrotational masseskbbending stiffness of the specimenmamass of the bending armLalength of the bending armIQmass moment of inertia of the bending armIDinner diameterODouter diameterJarea moment of inertia of the sectionWbsection bending modulusLspecimen lengthEYoung modulusAivibrating beam shape coefficients (i = 1,2,3,4)u(x,t)vibrating beam displacement as a functionof position x and time tmmass of the vibrating beammffix mass to be placed at vibrating beam endsm?erotating mass at one vibrating beam endR?erotating mass eccentricityd?erelative displacement of the rotating massqSpecimen material densityvlength frequency of the vibrating beamACross section area of the specimena1first harmonic amplitude of the strain gaugesignala2second harmonic amplitude of the straingauge signalRload ratiornnominal bending stress at the fatigue failuresectionMbbendingmomentatthefatiguefailuresectionBBasquin equation constantbBasquin equation exponentialrn,enominal bending fatigue endurance limitjnnucleation slope of SN curve, in loglogcoordinatejffatigue failure slope of SN curve, in loglog coordinateL. Bertini et al. / International Journal of Fatigue 30 (2008) 978988979The steel connection is much more common in oildrilling and extensive technical literature can be found(papers 6,11,12 report the state of art about steel drillstring connection fatigue). On the contrary, aluminum tosteel connections have been recently developed by Russiandrilling contractors and no systematic studies have beenconducted yet. Aluminum drill pipes are spreading world-wide due to potential advantages, discussed in Ref. 13,based on the elevated strength-over-weight ratio and lowstiffness of the material as compared to quenched and tem-pered steels.Steel connections are composed of two conical threadedsides: Pin and Box attached to the pipe body by means offriction welding, as shown in Fig. 1a. Typical fatigue cracks,leading to failure, usually nucleate at last engaged threadroot either of the pin or of the box, as shown in Fig. 1b.For aluminum to steel connection, tool joints at pin andbox sides feature conical thread and they are made of steelbecause they need to be engaged and disengaged very often,during the drilling operation. In this design, to connect thealuminum pipe body to the steel tool joints two otherthreaded connections are required; one for each side,Tool joint PinTool joint BoxFrictionweldingFrictionweldingBodypipeBodypipeStop face (shoulder)ConicalthreadedconnectionBox fatigue site (last engaged thread)Pinfatigue site (last engaged thread)timennnFig. 1. (a) Conical threaded connection between pin and box steel tool joints, attached to the body pipe by friction welding. (b) Fatigue nucleation siteseither at the pin or the box sides.Tool joint Pin(Steel)Conicalthread free portionAluminum -steel conical threadedconnectionBody pipe (Aluminum)ConicalthreadedconnectionTool joint Box(Steel)Body pipe (Aluminum)Aluminum -steel conical threadedconnectionConicalthread free surfaceSteelSteel edge, fretting on aluminumAluminumConicalthreadfreesurfacetimennFig. 2. (a) Aluminum to steel threaded connection is required (instead of friction welding) to connect the pipe body to the tool joint. (b) Fretting fatigue, atthe steel edge, is the failure mode of this type of connection.980L. Bertini et al. / International Journal of Fatigue 30 (2008) 978988Fig. 2a. These other connections are assembled at the com-ponent manufacturing stage and they do not have to be dis-engaged for the whole life of the drill pipe. As depicted inFig. 2a, the steel components feature a conical end withoutinternal threads to shield the last engaged thread of the alu-minum pipe against fatigue due to bending. Fretting fati-gue, at the contact between the rounded edge of the steelcomponent and the aluminum pipe body, generates fatiguecrack nucleation, as illustrated in Fig. 2b.The main dimensions of the tested specimens arereported in Table 1.It is worth noting that the overall length of the alumi-num to steel connection is higher than the steel connec-tions, since two extra connections are required. As aconsequence, two different test rigs were designed to pro-duce full scale fatigue testing on these two different connec-tion types.3. Test rig design3.1. Test rig for steel connectionsIn Fig. 3 the test rig for steel connection is shown. Twocouples of counter-rotating eccentric masses, at the top oftwo bending arms, induce inertial forces on the specimen.Force and displacements are in plane, then alternating(not rotating) bending is applied to the specimen, as sche-matically shown in Fig. 4.The system allows for shifting the phase between thetwo couples of rotating masses, then a phase angle c isintroduced.The eccentric counter-rotating masses generate two lon-gitudinal forces at the top of the two arms which, if thespecimen is assumed to be rigid, are given byF1t 2mex2RecosxtF2t 2mex2Recosxt c1while the transversal components of the two forces are bal-anced for each couple of masses.If the forces F1and F2are in-phase (c = 0), no bendingmoment is induced in the specimen, since the specimen issupported by springs which allow in plane free rigid dis-placements. On the contrary, in the out-phase condition(c = p), the bending moment induced in the specimen ismaximum. Moreover, the test rig operates at a frequencywhich is near (but lower) to the first resonance of thedynamic system in which the specimen is the spring andthe two bending arms are the inertial bodies. Near to theresonance frequency the bending moment experienced bythe specimen is much greater than that produced by forcesF1and F2.On the basis of the following reasonable assumptions, asimple dynamic model of the system can be obtained:1. out-phase condition, c = p;2. bending arms are rigid as compared to the specimen;3. specimen inertia is negligible in comparison to bendingarms inertia;4. bending deflection of the specimen is prevailing;5. no damping effect is considered.Table 1Main dimensions of the tested connection specimensConnectiontypeStandardnomenclatureOuterdiameter(mm)Innerdiameter(mm)Specimenlength (m)Steel connectionNC 2688.938.11.2Steel connectionNC 50168.871.41.2Aluminum tosteelconnectionADP-STJ147 131471073.7Fig. 3. (a) Picture of the test rig. (b) Steel connection specimen.Steel connection specimenBending arm 2Bending arm 1Re-meF1F2Fig. 4. Two couple of counter-rotating masses, each hinged at the top ofmassive arms, generate cyclic bending on the specimen.L. Bertini et al. / International Journal of Fatigue 30 (2008) 978988981For assumption 1, half structure can be considered dueto symmetry. As observed, by imposing different phaseangle c, the bending moment can be continuously variedby a factor sin(c/2) ranging from the maximum value(c = p), to zero in the in-phase condition (c = 0). Forassumptions 2 and 3 it follows that the dynamic systemhas one degree of freedom with the specimen as a springand the arms as inertia. Moreover, by neglecting the spec-imen mass, the bending moment can be considered to beuniform along the specimen length. The here suggestedmodel is depicted in Fig. 5.In order to estimate the natural frequency, fn= xn/(2p),model parameters can be evaluated as follows:? bending stiffness: kb= 2EJ/L, where E is the materialYoungmodulus,J p64OD4? ID4thesectionmoment of inertia about the bending neutral axis andL the free bending specimen length;? the mass moment of inertia about the axis through pointQ of the arm having mass mais IQ13maL2a, by assumingmass mauniformly distributed over its length La;? the natural frequency is xnffiffiffiffiffiffiffiffiffiffiffiffikb=IQp.Let us consider the system loaded by a periodic force with arotational speed of x as indicted in Fig. 5b. The displace-ment d can be obtained by solving the equation, neglectingany damping:kbdL2a IQdL2a 2x2Remecosxt2giving, the solution1:d 2x2Remekb? IQx2L2acosxt3The nominal bending stress amplitude rnis defined asbending moment divided by bending modulus of the pipesection. It can be related to the frequency ratio n = x/xnas follows:rn2RemeLaWbx211 ? n24where Wb= J/(OD/2) is the bending modulus. The form ofEq. 4 suggests the definition of a dynamic amplificationfactor:Da11 ? n25which is the amplification of the forces (F1,F2) due to theeccentric masses produced by the inertia forces at the arms.As the damping has been neglected, Eq. 4 indicates thatthe bending stress increases indefinitely when the frequencyof the rotating masses approaches the natural frequency(n ! 1). In practice, it was observed that for the proposedtest rig, Eq. 4 gives reasonable prediction up to n ? 0.95.For frequency near to the resonance the dynamic amplifi-cation depends strongly on damping, particularly whendamping is a small quantity as in the present condition.In order to obtain a controllable behavior, the test rigwas operated in sub-resonance (more details are givenlater) then Eq. 4 is accurate enough.It is worth noting that previous assumptions and modelapproximations were used for interpreting the phenome-non and defining the main quantities of the apparatus,however they produce no effect on the accuracy of the test.Indeed, the effective dynamic bending stress was continu-ously measured on the specimens by means of straingauges, during tests. Set point was keep constant within apredetermined range (5% of the nominal value) by a closedloop system controlling the phase shift between the twocouples of counter-rotating masses.3.2. Test rig for aluminum to steel connectionsThe rig for testing the aluminum to steel connectionswas designed for longer specimens as previously discussed.Its layout is shown in Fig. 6.The axial extension of the connections and the reducedbending stiffness did not allow the previous testing schemeto be adopted. In this case, it was decided to give to thespecimen both the elastic and inertia characteristics of thedynamic system. As previously, it was set to operate inthe region of sub-resonance. The external load was pro-duced by rotating an eccentric mass located at one end ofthe specimen. In order to keep the symmetry of the struc-ture and to produce the maximum bending load in the cen-ter (where the connection is located), two masses wereclamped at the ends of the specimen.This configuration can be modeled by assuming thespecimen as a massive beam (with total mass m uniformlydistributed on its length L) carrying two point-like massesmfat the ends, Fig. 7a. By spinning the eccentric mass m?e,rotating bending was induced in the specimen (with highamplification near the resonance) Fig. 7b.The dynamic behavior of the system can be predicted bysolving the 4th order partial differential equation 14:QbnIkamaLQIQIDODbk2/LbknQQIaLe2mdcos(eet)RdFig. 5. (a) Natural frequency of the dynamic system, fn= xn/(2p). (b)Excited vibration of the system, at an imposed frequency f = x/(2p).Resonance is the condition: n = x/xn= 1.1Initial condition transient is neglected, since it vanishes very quickly,due to actual damping.982L. Bertini et al. / International Journal of Fatigue 30 (2008) 978988?EJ4ux; tox4mLo2ux; tot26where u(x,t) indicates the lateral displacement of the spec-imen axis as function of the position x and time t. The solu-tion isux;t A1cosvx A2sinvx A3coshvx A4sinhvx?cosxt7where the time frequency x and the length frequency vare related by the relation:v2 xffiffiffiffiffiffiqAEJr8Natural frequencies xnare those values of x, solutions ofthe characteristic equation, that make null the determinantof the linear system (having the unknown coefficients Ai(i = 1,2,3,4) obtained by imposing boundary conditions.The vibration of a uniform beam (without masses mf) isa classic result 14, giving the following characteristicequation:cosvL coshvL ? 1 09For the considered condition (E = 73 GPa, m = 54.6 kg,OD = 147 mm, ID = 121 mm and L = 3.7 m) the first nat-ural frequency is 64.4 Hz.The characteristic equation for the vibrating beam withpoint-like masses at the two ends was obtained2:coshvL cosvL ? 2mfmvLsinvL? 2mfmLmfEJffiffiffiffiffiffiEJqAsxsinvL ? vLcosvL !? sinhvL ? 1 010The external masses introduce a parameter mf/m in thecharacteristic equation. The solution of transcendentalEqs. (9) and (10) cannot be obtained in analytic form. InFig. 8 the graphs of Eqs. (9) and (10) are plotted versusf, showing the graphical determination of the first two res-onant frequencies (the case of mf= 30 kg was considered).The reduction of the first natural frequency produced bythe masses mf(the other natural frequencies are reducedtoo) is particularly remarkable since masses mfare compa-rable to the mass of the specimen and they are placed theends. The value mfwas chosen to set the natural frequencyat the required value for the fatigue test with the availablespecimen length.Inorderto improve theaccuracyof the dynamic model, afinite element (FE) analysis was performed as shown inFig. 9. By introducing the actual properties for any crossFig. 6. (a) Picture of test rig for aluminum to steel connection specimens. (b) Details of the connection to test.fmx),(txuLm,fmIDODNull displacement pointsfm*efmmLm,),(txume*x)cos(*e*etRdFig. 7. (a) Dynamic model to find the natural frequency. (b) Eccentricrotating mass m?eto excite the dynamic system.2Symbolic software Mathematica? ver. 5.1 was used to manipulate thealgebra.0501001502000150300450beam, xxxxxxxxxxxxbeam,1stfn= 36.22 Hzf =/ (2 ) Hz Matrix det.mf= 30 kgwithout mffn, mf= 30 kgfn, without mfFig. 8. Natural frequencies fnare the zeros of the characteristic equation.To understand the effect of the masses mf, the model without masses at theends is also reported.L. Bertini et al. / International Journal of Fatigue 30 (2008) 978988983section of the specimen, in particular in the central regionwhere the connection is located, the first natural frequencywas found to be equal to 34.8 Hz, value which does not sig-nificantly differ form 36.2 Hz estimated by the analyticalmodel.In any considered model, the specimen was assumedto be free in the space, thus no external force (other thanthat generated by the motion of the rotating mass) isapplied. In order to reproduce this boundary condition,the specimen was simply supported by two couples ofrubber wheels. The supports were located in the twopoints where the deformed axis has null displacement(i.e. the modal nodes), Fig. 9. The rotating eccentric massm?ewas driven by an electric motor at constant speed.The rotating mass was connected to the end of the spec-imen by a couple of bearings thus a negligible torque wasapplied to the specimen, but the friction at the support-ing wheels was large enough to prevent the rotation ofthe specimen about its axis. The maximum displacementof the specimen axis can be strongly amplified when thetest is operated near the resonance frequency, as in theprevious solution.Vibrating displacement amplitude, along the pipe, ismaximum at the ends, where it ranges 1020 mm, depend-ing on the bending amplitude imposed to the specimen.Displacements in Fig. 9 are strongly amplified for graphicalreason. The proper choice of specimen length and massesallowed to obtain equal bending moment (difference below1%) at the two critical sections located at the ends of thesteel connection, Fig. 10.Bending moment distribution along the specimen wasevaluated by means of FE analysis. In Fig. 10 a typical test-ing conditions (f = 32.3 Hz, fn= 34.75 Hz, n = f/fn= 0.93)is shown. Same bending stress at the two critical sectionswas also verified through strain gauges measurements dur-ing tests. As explained later, three couples of strain gaugeswere applied along the specimen, to experimentally repro-duce bending moment distribution.Fig. 9. Vibration induced in the specimen. Null displacement points, at the modal nodes, are used to hold the specimen.159037001535-1.4754812962514439192522406628879SG1SG2SG3Mb= 26.65 kN mn= 118.8 MPaMb= 26.90 kN mn= 119.9 MPaBending moment Mb N m f30kgm =f30kgm =n34.8Hzf =*e3.3kgm=*e67mmR=32.3Hzf =Fig. 10. SamebendingmomentMb(andthenbendingstressrn)atthetwocriticalsectionsofthespecimen.PositionsofthethreestraingaugesSG1,SG2,SG3.984L. Bertini et al. / International Journal of Fatigue 30 (2008) 9789884. Test monitoring techniquesFig. 11 illustrates the possibilities to control bendingamplitude during the test. The test frequency is chosenwithin a working frequency region in sub-resonant condi-tion. The bending stress amplitude is controlled duringthe test in order to keep it constant.Strain gauges were attached to the specimen surface inorder to measure longitudinal strain and the effective bend-ing moment is deduced. The half-bridge strain gauges con-figuration was adopted since bending stress is measured,and the temperature effect is eliminated 15. For steel con-nection test rig, the bending moment can be measured by asingle couple of strain gauges (as the bending moment isuniform along the specimen). The bending moment is keptconstant by a closed loop system operating on the phaseshift between the counter-rotating masses. While the fati-gue crack is small the dynamic response is steady, thenDadoes not change during time. When the crack propa-gates through the specimen wall thickness, specimen natu-ral frequency reduces, then the bending moment increasessince the working condition approaches the resonanceand then Daincreases. To continue the test, the externalforces are reduced by modifying the phase angle c betweenthe two couples of counter-rotating masses, for the wholetest duration. Moreover the unilateral contact betweenthe crack surfaces introduces a nonlinearity in the dynamicsystem which can be detected when the crack has a suffi-cient extension. The fast Fourier transform (FFT) wasapplied to the strain gauge signal.3In the first part of thefatigue life, when the specimen was not significantly dam-aged, the amplitude of the first harmonic a1is prevailing.It was found that the ratio between the amplitudes of thesecond and the first harmonics a2/a1can be used as an indi-cator of the presence of a fatigue crack, as shown inFig. 12.This quantity can be used to distinguish a phase ofnucleation of a macroscopic crack to the following phaseof crack propagation. From Fig. 12 it can be observed thatalso the dynamic amplification could be used to detect thepresence of the crack, but the change in the curve is usuallytoo smooth to be considered as a valid indicator. Internalpressure is a very good indicator as well, detecting the fati-gue crack as soon as it reaches the pipe wall thickness, butthe set up was too demanding to be applied for each test.Obviously the minimum dimension of the crack that canbe detected through the dynamic global response (as theharmonic amplitude ratio) is quite large, even larger thanthe wall thickness (as detected by the internal pressuredrop), Fig. 12. Therefore a significant portion of crackgrowth (in terms of elapsed cycles) could be erroneouslyconsidered in the nucleation life. To solve this problema backward calculation of the propagation portion canbe performed in order to predict the cycles necessary tonucleate a small crack (for example 1.0 mm long, muchsmaller than the wall thickness).For aluminum to steel connections, bending momentdistribution is not uniform along the specimen, then toproperly measure the bending stress, strain gauges wereapplied along the pipe at three different locations: at themiddle of the steel connection (SG1) and at the two alumi-num pipe body sides (SG2 and SG3), Fig. 10. Strain gaugeswere applied far enough from critical sections (SG2), andcross section modifications (SG3) to avoid the local effectof stress concentration. To deduce the nominal bendingstress the FE solution was used (as the one of Fig. 10)obtained simulating the working frequency of the actualtest with full geometry details. Also in this case, a singlecouple of strain gauges could be used, however as the bend-ing moment varies along the specimen, a redundancy ofsignals was preferred.For this test rig, the bending moment is controlled bychanging the speed of the motor and consequently modify-ing the working frequency. The fatigue crack propagationwas negligible as compared to the nucleation and, in prac-tice, the test was conducted at a constant frequency, up toalmost the end of the specimen fatigue life. This is due toImposed frequency fBending nominal stress amplitudenResonance,f = fnNo dampingbehaviorTrue behaviorWorking frequency range, sub-resonance conditionDifferent masses or mass phaseFig. 11. Amplification induced by resonance condition. Bending stressamplitude can be controlled either by frequency or mass phase.3Visual programming software LabVIEW?ver. 7.1 was used to handlesignals and monitor tests.-52105410561058105106Control parametersCycles05101520Harmonic ratio 2/1Internal pressure MPa NucleationPropagationDynamic ampl. factor DaFig. 12. Variables used to check specimen integrity: ratio between thesecond harmonic wave amplitude a2over the first a1, internal pressure,amplification factor Da.L. Bertini et al. / International Journal of Fatigue 30 (2008) 978988985the fact that the wall thickness of the aluminum pipes is sig-nificantly smaller than that of the steel connections and thefracture toughness of aluminum is lower that that of thesteel. For these reasons, the maximum extension of the fati-gue crack tolerable in the aluminum pipe was not much lar-ger than that required to produce a detectable change inthe global dynamic behavior. As a consequence, no globalsignal gave indication of the presence of the crack, for thistype of tests, up to few hundreds cycles before the suddenfinal failure.Applying frequency control to the steel connectionwould have caused time delay due to the sizable fatiguepropagation portion.5. Test results5.1. Steel connection testsTest results are reported in Fig. 13 as SN curves. Nom-inal bending stress amplitude (half full range) rnis thebending moment amplitude Mbdivided by bending modu-lus Wbat the fatigue fracture section. The meaning of rnisas monolithic component, regardless internal notchedgeometry due to thread. As previously discussed, these testrigs do not allow for any mean stress applied to the speci-men during testing, then the test is performed at load ratioR = ?1. It is worth noting that little scatter was obtained ifcompared to the typical scatter of fatigue tests. Nucleationlife is reported according to the threshold produced by theratio a2/a1, as discussed in the previous section. Linear leastsquares fitting regression is calculated on the experimentaldata on loglog scale. Then SN curves can be expressedaccording to Basquin equation: rn BNbf, j = ?1/b isthe slope and B is a fit constant.Slopes are reported on Fig. 14a and b for both types ofspecimen, jn(nucleation), jf(final failure). Fatigue limitsrn, eare also reported (considering endurance limit at 107cycles).All types of fatigue fracture surfaces, experimentallyobtained with steel connections, are shown in Fig. 14.Crack fronts shown in Fig. 14 were not clearly visible onthe fracture surface which looked quite smooth. Therefore,white lines are qualitatively drawn to enhance the interpre-tation of the figure. However, it was possible to detectnucleation point and the final crack front. Steel fracturetoughness was so high that some tests were stopped beforethe final failure with a fatigue crack size as large as halfthe pipe diametrical periphery. After reaching the wall10510610710820406080100120NucleationFatgiue life, Pin failuresNucleation fitFatigue line fitn,e= 52 MPaf= 4.35n= 5.31Nfn MPa 10510610710820406080100120NucleationFatgiue life, Pin failuresFatgiue life, Box failuresNucleation fitFatigue line fitn,e= 55 MPaf= 4.74n= 5.70Nfn MPa Fig. 13. Steel connections SN curves. Nucleation and propagation are distinguished for each test. Run out are considered as fatigue life 107cycles.(a) NC 26 specimen. (b) NC 50 specimen.Fig. 14. (a) NC 26 pin fatigue fracture surface. (b) NC 50 pin fatigue fracture surface. (c) NC 50 box fatigue fracture surface.986L. Bertini et al. / International Journal of Fatigue 30 (2008) 978988thickness the fatigue crack splits in two fronts, with radialorientation, Fig. 14a and b. Some tests showed two nucle-ation sites at the two maximum bending stress locations,Fig. 14c.5.2. Aluminum to steel connectionAluminum to steel connection test results are reportedas SN curve in Fig. 15a, along with a typical fatigue frac-ture surface, Fig. 15b and c. Nominal bending stress ampli-tude rnhas the same meaning as previous, regardless stressconcentration at the critical sections and the load ratio isR = ?1.Fig. 15c shows a stable fatigue crack propagation sur-face. Beach marks were difficult to be detected, howeverthe final position of the crack front, before unstable prop-agation leading to sudden failure, can be easily detected.Moreover, it is evident how the fatigue crack experiencedmultiple nucleation. This is due to the loading mode whichis rotating fatigue. On the contrary, multiple fatigue cracknucleation was not observed for the other type of test,Fig. 14.Stable crack growth took a significant part of the fatiguelife for steel connections (high toughness and large wallthickness), while for aluminum to steel connection (lowtoughness and small wall thickness) the life spent in thisphase is short in comparison with to whole fatigue life.The size of the crack, before sudden failure was never lar-ger than pipe thickness. This issue influenced the way tocontrol tests, as discussed in previous section.6. ConclusionsTwo types of resonant full scale fatigue test rigs wereproposed. Their application was devoted to test drill stringconnections, however any kind of tubular structure couldbe tested by using these test rigs.The basic idea of working near the specimen resonancefrequency leads to a remarkable reduction of the structuralstrength demanded from the overall frame.Short connections (as the presented steel connectiontype) can be tested by means of a test rig with two bendingarms, and two couples of rotating masses on top of thebending arms. In this way alternating bending tests canbe performed, but not rotating bending tests.For long connections (as the presented aluminum tosteel connection type) the test rig with single rotating massat one end is to be preferred. In this way rotating bending isapplied to the tubular specimen.Test monitoring techniques were also shown. Sincethreaded connection is very difficult to be inspected (notdestructively, to continue the test) a symptom of the pres-ence of the fatigue crack, is the dynamic behavior modifica-tion. Test rig for steel connections was controlled throughthe phase angle between the two couples of rotatingmasses. During the (long) propagation life, when the1051061071082030405060708090100TestsFatigue life, fit linen,e= 50 MPaf= 13.
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