FATIGUE LIFE PREDICTION OF UMBILICALS CONSIDERING NON-LINEAR STRESS

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1 POLISH MARITIME RESEARCH Specal Issue 2017 S2 (94) 2017 Vol. 24; pp /pomr FATIGUE LIFE PREDICTION OF UMBILICALS CONSIDERING NON-LINEAR STRESS Lu Qngzhen 1, Lecturer Yn Yuanchao 2, Ph. D. Yang Zhxun 2, Ph. D. Chen Jnlong 2, Ph. D. Yan Jun 2, Prof. Yue Qanjn 1,2, Prof. 1 School of Ocean Scence and Technology, Dalan Unversty of Tech Dalan, Laonng, Chna 2 Department of Engneerng Mechancs, Dalan Unversty of Tech Dalan, Laonng, Chna ABSTRACT The fatgue problem nduced by wave loads and floater movements of dynamc umblcals n deepwater s studed. The predcton method of the fatgue lfe s nvestgated by consderng no-lnear local stress due to contact and frcton between components of the umblcal. A case study of a dynamc umblcal for 1500 meters depth n South Chna Sea was presented. The results showed that the more accurate result of the fatgue lfe was calculated by consderng non-lnear local stress. The fatgue lfe by consderng local stress wth the no-slp assumpton was conservatve. An obvously longer fatgue lfe was obtaned by consderng local stress wth the full-slp assumpton. Keywords: steel tube umblcal; fatgue lfe; contact and frcton; non-lnear local stress INTRODUCTION Steel tube umblcal s one of the key equpment n subsea producton system, whch supples a communcaton and control lnk between the subsea system and surface vessels. A typcal umblcal conssts of varous functonal components for electrcal power, sgnal transmsson and hydraulc such as electrc cables, optcal fber cables and steel tubes. The functonal components are surrounded by amour wres and polymerc sheaths. All the components are unbonded together and can slde freely. The umblcal near the vessel s usually subjected to large tenson load and alternatve bendng load due to self-weght, currents, waves and motons of the vessel. The accumulated damage of the component s nduced by the alternatve load whch can lead the fatgue falure of the umblcal. The Method of the fatgue lfe analyss based on Mner accumulated damage theory s usually recommended by many specfcatons for marne engneerng. However, there are stll lots of uncertan factors durng the analyss of the fatgue lfe because of the complexty of umblcal structures. Hoffman et al.[1] and Jose et al.[2] presented a procedure of the fatgue lfe analyss of flexble rses and umblcals based on Mner accumulated damage method. Song et al. [3] studed the dynamc response and the fatgue lfe analyss of flexble rses. The calculaton method of dynamc analyss of global load had been a relatvely perfect method durng the fatgue lfe analyss of umblcals. However, compared wth 154 POLISH MARITIME RESEARCH, No S2/2017 Unauthentcated

2 the stress analyss of metal ppes of rgd rses whch can be calculated by smple formulas, the local stress analyss was stll dffcult due to the nonlnear factor nduced by the frcton of adjacent components. Regardng the complexty and mportance of the local stress of umblcal, numerous studes have been conducted n ths feld over last decades. Skee et al. [4] analyzed the stress nduced by tenson, bendng and frcton, respectvely. The local stress n the fatgue analyss was calculated by addng the tenson stress, bendng stress and frcton stress. Knapp [5] establshed a two-dmensonal fnte element model of umblcal to analyss the deformaton and stress. All the components n the model were modeled by macro-elements. Sævk [6,7] presented a fnte element model for predctng the stress of umblcals by curved-beam knematcs and thn-shell theory. The contact and frcton between components are set by sprng elements. Wang and Ekeberg [8] studed the nfluence of frcton on the fatgue lfe. The results shown the fatgue lfe wthout consderng frcton was nearly ten tme the lfe wth consderng frcton. Parsnejad et al. [9] analyzed the fatgue stress and lfe of two dfferent types of umblcals by consderng frcton. Probyn et al. [10] establshed a threedmenson fnte element model of a steel tube umblcal by ABAQUS. Contact and Coulomb frcton was defned between the adjacent components. The functonal components and polymerc sheaths were modeled by sold elements and beam elements, respectvely. Corre and Probyn [11] used beam elements nstead of sold elements to save the calculaton resources. L and Yang [12] establshed a three-dmenson fnte element model of an umblcal wth sx steel tubes. The stress under dfferent load case and the nfluence of frcton coeffcents were nvestgated. Non-lnear local stress due to contact and frcton between components of the steel tube umblcal s presented. A numercal model s establshed by usng Orcaflex to predct the fatgue lfe by consderng non-lnear local stress as the nput parameters. A case study of a dynamc umblcal for 1500 meters depth n South Chna Sea was presented. The results showed that the fatgue lfe by consderng local stress wth the no-slp assumpton was conservatve. An obvously longer fatgue lfe was obtaned by consderng local stress wth the full-slp assumpton. The more accurate result of the fatgue lfe was calculated by consderng non-lnear local stress. The method presented n ths paper provde a techncal support for the desgn and applcaton of umblcals. ANALYSIS METHOD OF FATIGUE LIFE The method of the fatgue lfe analyss based on Mner accumulated damage theory s shown n ths secton. Frstly, the tme-doman respond of the global load under short sea states should be calculated. Then, the tme-doman respond of local stress could be analyzed under the global load. The long-term of the accumulated fatgue damage and the fatgue lfe are obtaned by probablstc statstcs and S-N curve of the materal. The method s recommended by DNV and API standards [13, 14] to predct the fatgue lfe of marne structures. The standards also state that the predcted fatgue lfe of umblcal should be 10 tmes the servce lfe [15]. The procedure of the fatgue analyss based on Mner accumulated damage theory s shown as below. 1. Global Analyss Tme doman analyss based on the lumped-mass method s used n the global analyss of umblcals. The umblcal s dvded to a seres of segments wthout mass and nodes wth mass. The propertes of the tenson, torson and bendng stffness of the umblcal are gven by the segments. The propertes of the mass, gravty and buoyancy are shown on the nodes [16]. Accordng to Longuet-Hggns equaton [17], the gven scatter dagrams of the rregular wave s dspersed nto a serous of scatter dagrams of the regular wave. The tme doman of tenson and bendng under each sea state s calculated, respectvely. The frequency probablty of the sea state n one year s p. The correspondng perod of the sea state s T z. The number of the sea state n one year n, whch can be expressed as: n 365* 24*3600* p * T = z (1) 2. Local Stress Analyss The tenson and bendng load calculated n the global analyss are actng on the local structure. The local stress of the crtcal component can be calculated based on the Eq.(2). σ ( C snθ C cosθ ) = KtT + K (2) c x y Where K t represents the coeffcent of the tenson stress, K c represents the coeffcent of bendng stress, θ s the stress of the calculated pont along the crcumference, C x represents curvature n the x drecton of the component, C y represents curvature n the y drecton of the component. 3. S-N Curve of Materal The fatgue property of the materal s usually expressed by a S-N curve, whch s a graph of the alternatng stress aganst the logarthmc scale of cycle tmes to falure (N ) (3) a and m are materal constants. 4. Fatgue Lfe of Umblcal The fatgue accumulated damage of the umblcal can be calculated based on formulas above, whch can be wrtten as: D = N = 1 n N (4) ( ) (5) Where N represents the number of the alternatng stress, D represents the fatgue accumulated damage. Fatgue falure POLISH MARITIME RESEARCH, No S2/ Unauthentcated

3 occurs when D=1. No damage accumulates are generated when D=0. The fatgue lfe s the recprocal of D, whch can be expressed as: Lfe 1 D = (6) The flow of the fatgue lfe analyss s shown n Fg Tenson Stress Tenson stress of each steel tube s determned by the total tenson stffness of the umblcal and the tenson stffness of the steel tube, whch can be calculated by: Where σ T (t) represents the tme-doman of the tenson stress, T (t) represents the tme-doman of the tenson load, K T represents the tenson stffness of umblcal, E, A denotes the elastc modulus and the cross-secton area of the steel tube, respectvely. (7) Fg.2 Compostons of a steel tube umblcal Fg. 1 Fatgue analyss flow of dynamc umblcal The fatgue lfe analyss of dynamc umblcal s more dffcult than steel rses. The materal of steel tubes s more homogeneous compared wth the materal of umblcals. The stress analyss s relatvely smple because of the rng structure of the cross-secton. The stress state of umblca s complex and the calculaton of the local stress s more dffcult. Non-lnear local stress due to contact and frcton between components of the steel tube umblcal s mportant for the fatgue analyss of umblcal. A more accurate fatgue lfe could be got based on the non-lnear local stress. ANALYSIS METHOD OF LOCAL STRESS The structure of a typcal steel tube umblcal s shown n Fg.2. The functonal components and armor wres are helcal wound by a specal angle. The helcal angle of the functonal components s usually less than 10 degree. The armor wres are wound at an angle above 20 degree. The steel tube s the most crtcal components durng the fatgue falure. The stress of the steel tube can be calculated by tenson stress, bendng stress and frcton stress. 2. Bendng Stress The nsde condtons of umblcals can be dvded nto a no-slp stage and a full-slp state durng bendng. The perod of the no-slp stage can be ncreased as the ncrease of the tenson load. The bendng stress can be expressed by dfferent stages. Bendng Stress of No-slp Stage The steel tube s bent wth the center axs of the umblcal before the component sldes. The bendng stress s equal to the statc frcton stress, whch can be expressed as: Where s the tme-doman of the bendng stress before slppng, κ (t) s the tme-doman of the curve, R L s the dstance between the center of the steel tube and the umblcal. Bendng Stress of Full-Slp Stage The bendng stress caused by bendng s determned by the dameter of each steel tube after the sldng of the component. The bendng stress can be calculated by the formula below: s the tme-doman of the bendng stress after slppng, R s the dameter of the steel tube. (8) (9) 156 POLISH MARITIME RESEARCH, No S2/2017 Unauthentcated

4 Frcton Stress When the steel tube s under the full-slp stage, the statc frcton force turns to the dynamc frcton force. The followng assumptons have been made for the dervatons and analyss n ths paper: 1) The sldng s only occurred along the helx axs of the steel tube; 2) The end effects can be neglected; 3) The dynamc and statc frcton coeffcents are equal. Only one steel tube s analyzed as shown n Fg. 3. The model of the frcton stress analyss can be establshed by the equlbrum between the axal force caused by bendng and the statc frcton force whch prevent the axal movement of the steel tube. The sldng crteron can be establshed based on the equlbrum equaton along the axal drecton of the steel tube. The steel tube begn sldng when the axal force gradent(dn/ds) reaches the statc frcton force f of per unte length.: (13) The tenson gradent reaches the max value when ϕ =0, the steel tube begns sldng at the neutral axs. The crtcal curvature can be establshed as: (14) The frcton force F equals the statc frcton force N When the full sldng occurs at the neutral axs. (15) (10) Where N s the axal force, f s the frcton load per unt length. (16) N fds ds N + dn The full-slp state s assumed to be started when the max crtcal curvature can be expressed as: π ϕ =, 2 Fg.3 Force on nfntesmal helx element ds (17) The steel tube s assumed to be fully fxed on the cylnder. The axal load caused by bendng can be expressed as: N = EAR cos 2 L α sn( ϕ) κ (11) Where α s the helcal angle of the steel tube, ϕ s the angle of the helcal pont, as shown n Fg.4. S s the length of the steel tube along the helcal drecton. The relaton between ϕ and S can be wrtten as: S ϕ snα = (12) R L The sldng frcton stress can be obtaned by: (18) The frcton force of the steel tube s affected by the frcton coeffcent and the length of the contact. (19) The key problem to calculate the frcton force s to accurately determne the frcton coeffcent µ between components, the contact stress q c and the contact length L c. The contact stress s analyzed by fnte element model whch s establshed by ANSYS software. The radal contact pressure nduced by tenson s acted on the fnte element model to calculate the contact stress q c and the contact length L c of the crtcal steel tube. The 2-D FE model of the umblcal s shown as Fg.5. Fg.4 Helx postons for steel tube POLISH MARITIME RESEARCH, No S2/ Unauthentcated

5 EXPRERIMENT METHODS TO APPROACH FATIGUE LIFE Fg.5 2-D model of the umblcal core The transfer stage between no-slp to full slp s very short. The stress calculaton of the stage s also qute dffcult. So, the frcton stress s assumed to be dvded nto two stages: no-slp stage and full-slp stage. As shown n Fg.6, the value of the no-slp stage s that of the bendng stress. When the crtcal curvature reach to, the full-slp occurs. The value of the frcton stress s that of the slp frcton stress. Two straght lnes s used to smulate the varaton trend of the fatgue stress n ths study. σ F σ FB max κ cr σ FC Fg.6 Defnton of frcton stress 3. Local Stress The local stress at the no-slp stage s the sum of the tenson stress and the bendng stress. It can be expressed as: (20) The local stress at the full-slp stage s the sum of the tenson stress, the bendng stress and the frcton stress, whch can be wrtten as: (21) As the structure of umblcal s complcated, accurate fatgue lfe s hard to approach by theoretcal calculaton or fnte element method. An mportant way to access the fatgue lfe of an umblcal s to conduct a fatgue test, especally for a new desgned cross secton. The length n actual applcaton of a typcal dynamc umblcal s usually over a thousand meters. The sea state s also complcated. So t s mpossble and useless to smulate the whole length of umblcal under the floater and wave condton n a laboratory. A feasble soluton s to cut out the crtcal umblcal locaton and exert the load-tme hstory calculated by global analyss to the test specmen by an actuator. In order to approach the fatgue lfe accurately, the real load case should be conducted to the test umblcal specmen by the test machne and test method, a more precse deformaton of each elements should be measured. A typcal set up for a dynamc fatgue test s to smulate the real n-place condton of an umblcal whle the force s tenson combned wth bendng. The specmen was cut off at the crtcal locaton whch s at the top of the umblcal. The test sample comprses the assembly of the umblcal body, end fttngs, fasteners, and all devces and components smulate the umblcal top connecton, and a bend stffener/bellmouth [18]. The tenson and curvature dstrbuton at the crtcal area can be calculated through the global analyss of the dynamc umblcal. The tenson and curvature can be appled by the force or dsplacement actuators at ether end of the umblcal sample. Nondestructve measurement should be conducted durng and after the fatgue test, whch ncludes: 1) Tenson stffness. When the tenson stffness s declned over 20% or the rupture percent of the armor wre s over 5%, the tensle armor layer s regarded as falure. 2) Inner pressure of the steel tube. The decompresson should be montored durng and after the fatgue test. 3) The DC power and nsulaton resstance of the electrc cable. 4) The sgnal attenuaton of the optcal fber cable. The dynamc fatgue test whch smulates real workng condton usually requres a large-szed test devce. The length of test sample s greater than 8 meters, real end fttng and bend stffener are also requred. The whole test usually takes a long tme over 3 months. The cost of the test s also very expensve. Wth the study of umblcal cable, a pure bendng fatgue test can be conducted to test the fatgue lfe of umblcal for cost savng. The load response at crtcal area can be obtaned through global analyss. Then the local stress can be obtaned by accurate analyss, whch contans tenson stress, bendng stress and stress caused by frcton. Ths test method can save the tme and cost of a typcal dynamc fatgue test. The local stress should be estmated accurately and the nfluence of end fttngs and bend stffness cannot be s neglected. The fatgue damage at crtcal area can be calculated to pure bendng stress damage, whch s more easy to exert by the test devce. 158 POLISH MARITIME RESEARCH, No S2/2017 Unauthentcated

6 The fatgue property of umblcal can be tested faster by ths method. Tab. 1 Parameters of umblcal system Parameters Value Parameters Value Length of umblcal Angle of top pont Dameter of the stff cabn Heght of the stff cabn 1850m m Sze of the soft cabn Heght of the soft cabn Length of man truss 37.2 m 37.2 m 6.1 m 94.5 m m Centre of gravty Tab.2 Parameters of the umblcal Fg.7 Testng rg of bendng fatgue The testng rg of bendng fatgue s shown n Fg.7. The test specmen s placed on the holder, there were four constraned pont of the test rg. The test rg should be axal symmetry durng and after the fatgue test. The rght constraned pont on the holder s clamped to the umblcal specmen, whle the specmen s free to slde at the other three ponts. The bendng movement s exerted by a hydraulc actuator A CASE STUDY 1. Case Descrpton A dynamc umblcal wth a catenary curve of an applcaton of 1500m meters s shown n Fg.8. The seabed s plan and the sold can be consders as sandy slt. The structure of the umblcal s shown n Fg.1. The system parameters of the umblcal and the Spar platform are lsted n Tab.1. The structural parameters whch contans the dameter, weght, tenson, torson and bendng stffness are lsted n Tab.2. Fg.8 A dynamc umblcal n depth of 1500m Parameters Value Outer dameter(m) 0.1 Dry weght(kg/m) 25.3 Wet weght(kg/m) 15.9 Tenson stffness(kn) 3.5e5 Torson stffness(knm 2 ) 35.9 Bendng stffness(knm 2 ) 6.6 The wave scatter dagram s the probablty dstrbuton of the wave heght and the perod, as shown n Tab.3. The gven scatter dagram of the rregular wave s dspersed nto a serous of scatter dagram of the regular wave accordng to Longuet-Hggns equaton. The coverage rate of ths method can be reached 99%. The cases of the regular wave used n ths paper are shown n Tab. 4. The condtons of near, far and lateral poston of the vessel are consdered durng the analyss. Each condton s set at a 33.33% probablty. The proporton of a 0 angle of the heat sea wave s 60%, whle the proporton of a 30 angle s 40%. The probablty dstrbuton of the wave s dvde to 42 blocks of the scatter dagram of the regular wave. 252 load cases are consdered n the calculaton example. A numercal model of the dynamc umblcal s establshed by usng Orcaflex software. The jont between the umblcal and the bottom of the Spar platform s fxed wth a draft of 164.6m. The termnal end of the umblcal s anchored to the seabed. The axal frcton coeffcent between the umblcal and the seabed s set as The overall length of the model s 1850m. The response ampltude operator of the movement s set at the gravty center of the platform. Dfferent meshng s adopted n order to get the real respond of the umblcal. There s a hgh mesh densty at the senstve areas of the model. The whole model of the umblcal s dvded nto four parts. The upper area connected to the floater and the bottom area near the touchdown pont are senstve areas wth a hgh mesh densty. The length of each element of these areas s 1 meter. The statc part on the seabed and the mddle part of the model are dvded nto elements wth 5 meters n length. POLISH MARITIME RESEARCH, No S2/ Unauthentcated

7 Tab.3 Wave scatter dagram (Jont probablty dstrbuton of rregular wave) Probablty (%) Wave heght (m) Perods (s) <=3 3~4 4~5 5~6 6~7 7~8 8~9 9~10 >10 0~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ > Tab.4 Regular wave cases for fatgue calculaton of umblcal Wave heght Probablty Perod Analyss of Local Stress The steel tube of the nnermost layer s squeezed by the armor wres and adjacent components. The contact pressure s analyzed by fnte element method of the model whch s shown n Fg. 5. The results of the contact stress s shown n Fg.9. The bggest contact stress s occurred at the ponts where the outer steel tubes couple wth the nner steel tube. The value of the contact stress are extracted from the crossover elements. The result shows that the maxmum contact stress s at the connecton area between the outer tube and the center tube. The value of the contact stress of all steel tube elements along the crcle s shown n Fg. 10. Fg. 9 Result of contact stress 160 POLISH MARITIME RESEARCH, No S2/2017 Unauthentcated

8 processng of umblcal fatgue lfe analyss. Each square of the rectangle represents the occurrence tmes probablty of a range of alternatng stress as shown n Fg. 7. The total tmes n Fg 7 s 91%. The relatonshp between alternatng stress σ and pure bendng curvature κ can be establshed as: σ = E R κ 2 (22) Fg.10 Contact stress values of the nodes along the tube The crtcal curvature where the components begn to slde can be calculated by Eq. (17). The value of the sldng frcton stress of each unt length can be obtaned by Eqs. (18), (19). The total stress as the change of curvature can be got by Eqs. (20), (21). In addton, the other two assumptons of the stress condton are also consdered. In the no-slp assumpton, the stress s equal to the statc frctonal stress whch can be calculated by Eq. (20). In the full- slp assumpton, the stress s obtaned based on Eq. (21). The results of the total stress under three condtons are shown n Fg. 11. The alternatng stress n Fg. 12 can be equvalent to pure bendng curvature. The fatgue ampltude should be accelerated for determne the loadng of fatgue test. The curvature of 0.03, 0.04, 0.05 and 0.06 were chosen to conduct the fatgue test. The probablty of occurrence tmes of each curvature s 36%, 24%, 16% and 15%. The curvature and damage tmes of alternatng stress based on S-N curve s shown n Tab. 5. Tab.5 Curvature and damage tmes of alternatng stress type curvature (rad/m) damage tmes of alternatng stress Fg. 11 Results of the total stress 3. Predcton of Fatgue Lfe The load case of fatgue at the upper dangerous pont are consdered. When the stress consderng the no-slp assumpton are nputted, the calculated fatgue lfe s 1850 years. The servce lfe s 185 years by consderng a safety factor of 10 tmes. The fatgue lfe s 250 years by consderng the non-lnear stress as nput. It s 35% larger than the lfe calculated under the no-slp assumpton. When the stress consderng the full-slp are nputted, the calculated lfe s 3116 years, whch s far larger than the other condtons. TEST VERIFICATION Dynamc fatgue test can be conducted by a pure bendng fatgue devce to qualfy an umblcal for ts servce lfe. The fatgue test stated n ths paper s to qualfy the 250 years servce lfe of a dynamc umblcal. The loadng procedure of the fatgue test should be gven by the global analyss. The relatonshp of alternatng stress and the probablty of the actual number can be accessed by post Fg. 12 Alternatng stress-tmes probablty Where f s the loadng frequency (whch s 0.5 Hz n ths test) and h s the loadng tme(hours). The relatonshp between accumulated damage D and loadng tmes n and total number N can be accessed by Mner accumulated damage theory, whch can be establshed as: n D = (24) N The fatgue lfe of the umblcal s 1850 years. In order to guarantee the servce lfe of 250 years, the load case tmes POLISH MARITIME RESEARCH, No S2/ Unauthentcated

9 should get the fatgue damage to D =250/1850= The load case of fatgue test s shown n Table 6. Chna Sea was presented. The fatgue lfe of an umblcal s verfed by a pure bendng fatgue test. The results show that: 1) The fatgue lfe of the umblcal by consderng local stress wth the no-slp assumpton was conservatve. The dfference s 35%, whch may cause unnecessary waste for engneer. 2) An obvously longer fatgue lfe was obtaned by consderng local stress wth the full-slp assumpton, whch has a certan rsk. The more accurate result of the fatgue lfe was calculated by consderng the non-lnear local stress as the nputs. The concluson of ths paper provdes a techncal support for desgn of and applcaton dynamc umblcal. ACKNOWLEDGMENTS Fnancal support for ths research was provded by the program of NSFC and the Natonal Hgh Technology Research and Development Program of Chna 2014AA09A224. Ther supports are gratefully apprecated. BIBLIOGRAPHY Fg. 13 Broken-out secton vew of umblcal after test In order to check the fatgue damage of the body and each element of the umblcal, a dssecton was conducted to the umblcal after the test whch s shown n Fg. 13. There was wear between the armor wres and no damage happens. A hydrostatc pressure test was conducted to the steel tube wth a 2 Mpa nner pressure. No decompresson or leakage occurs durng the test, whch ndcates there was no damage of the steel tubes. CONCLUSION The fatgue lfe of umblcals s nvestgated n ths paper. A predcton model of the fatgue lfe s presented. Non-lnear stress due to contact and frcton between components of umblcals s consdered durng the local analyss n ths method. A numercal model was establshed by Orcaflex software based on Mner accumulated damage theory. A case study of a dynamc umblcal for 1500 meters depth n South 1. Hoffman J: Dupont W, Reynolds B. A fatgue-lfe predcton model for metallc tube umblcals. Proceedng of Offshore Technology Conference, Houston, de Sousa J R M, de Sousa F J M, de Squera M Q, et al: A theoretcal approach to predct the fatgue lfe of flexble ppes. Journal of Appled Mathematcs, (2012), 2012, p Song L J, Fu S X, Chen X Q: Deepwater umblcal overall response characterstc comparson research. Journal of Vbraton and Shock (Chna), 33(1), 2014, p Skee G, Sodahl N, Stenkjer O: Effcent fatgue analyss of helx elements n umblcals and flexble rsers: Theory and applcatons. Journal of Appled Mathematcs, (2012), 2012, p Knapp R H: Structural analyss of composte umblcal cables. Internatonal Socety of Offshore and Polar Engneers, Lsbon, 2007, p Tab. 6 Load case of fatgue test 162 type curvature (rad/m) frequency (Hz) tme (hours) test tmes damage tmes of alternatng stress fatgue damage POLISH MARITIME RESEARCH, No S2/2017 Unauthentcated

10 6. Sævk S: Theoretcal and expermental studes of stresses n flexble ppes. Computers & Structures, 89(23), 2011, p Sævk S: Comparson between theoretcal and experment flexble ppe bendng stresses. Internatonal Conference on Ocean, Offshore Mechancs and Artc Engneerng, Shangha, June 6 to11, Wang H H, Ekeberg K I: Internal frcton effects on fatgue lfe of steel tube umblcal. The 24th Internatonal Ocean and Polar Engneerng Conference. Busan, June 15 to 20, CONTACT WITH THE AUTHOR Lu Qngzhen e-mal: luqngzhen@dlut.edu.cn School of Ocean Scence and Technology Dalan Unversty of Tech Dalan, Laonng CHINA 9. Parsnejad F, Kassner C, Kurtz M, et al: Frcton, contact pressure, and nonlnear behavor of steel tubes n subsea umblcals. Journal of energy resources technology, 137(3), 2015, p Probye I, Dobsom A: Mchael Martnez. Advances n 3D FEA technques for metallc tube umblcals. Internatonal Socety of Offshore and Polar Engneers, Lsbon, 2007, p Le Corre V, Probyn I: Valdaton of a 3-Dmensonalfnte element analyss model of deep water steel tube umblcal n combned tenson and cyclc bendng. The 28th Internatonal Conference on Ocean, Offshore and Arctc Engneerng. Hawa, May 31 to June 11, 2009, p L Q Q, Yang H Z: Statc Analyss of the Tubes Interacton n Deep-sea Umblcals. Journal of Chna Offshore Platform (Chna), (6), 2011 p API RP 2A: Recommended practce for plannng, desgn, and constructng fxed offshore structures DNV. Rules for the desgn, constructon, and nspecton of fxed offshore structures. 15. ISO : Petroleum and natural gas ndustres-desgn and operaton of subsea producton systems-part 5: Subsea Umblcals Orcna Ltd: Orcaflex Manual,Verson 9.4a, Longuet-Hggns M S: On the jont dstrbuton of wave perods and ampltudes n a random wave feld. Proceedngs Royal Socety London, Mathematcal and Physcal Scences.389, 1983, p Ap, R. P. (2008). 17B. Recommended practce for flexble ppe, 4. POLISH MARITIME RESEARCH, No S2/ Unauthentcated