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Engineering Failure Analysis 50 (2015) 51–61 Contents lists available at ScienceD i rect Engineering Failure Analysis journal h omepage: www.elsevier.com/l o cate/engfailana l Failure analysis of thermowell weldment cracking M.M. Megahed, M.S. Attia Faculty of Engineering, Cairo University, 12613 Giza, Egypt a r t i c l e i n f o Article history: Received 13 September 2014 Received in revised form 16 January 2015 Accepted 2 February 2015 Available online 10 February 2015 Keywords: Thermowells Natural gas plants Failure analysis Flow-induced vibrations Finite element analysis a b s t r a c t This study presents the root cause analysis of a weldment failure in a thermowell assembly operating in a natural gas processing plant. Laboratory investigations indicated inferior quality for the llet weld joining the thermowell ange to the pipe supporting the thermowell to the main pipe. The llet weld exhibited excessive concavity, lack of penetra- tion and lack of fusion. This led to minute weldment cracking, which was exacerbated by ow- induced vibrations exceeding safe operational limits. This promoted small magnitude, high frequency stress cycling coupled with high mean stress at the poorly welded joint, which led to accumulation of high cycle fatigue damage and nal fracture causing gas leakage. Mitigation plans included use of a shorter support pipe and revised safe opera- tional envelope of the pipeline under consideration. 2015 Elsevier Ltd. All rights reserved. 1. Introduction Thermowells are hollow cylindrical metallic structures used in process and petrochemical industries to shield tem- perature sensors from the process uid. The presence of a bluff body such as the thermowell in the uid ow causes the vor- tex-shedding phenomenon, in which the passing uid separates and creates wakes downstream of the bluff. These low- pressure wakes alternate around the bluff and interact with the bluff inertial, damping, and elastic stiffness to generate ow-induc ed vibrations (FIV). Analysis of FIV and its structural implications has received signi cant research efforts as out- lined in two comprehensive reviews [1,2]. In particular, FIV analysis behind cylindrical bluffs attracted substantial attention due to its close relevance to various industrial applications in power, oil and gas, and aerospace industries. The presence of FIV

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Failure analysis of thermowell weldment cracking

Engineering Failure Analysis 50 (2015) 5161Contents lists available at ScienceDirectEngineering Failure Analysisjournal h omepage: www.elsevier.com/lo cate/engfailanal Failure analysis of thermowell weldment crackingM.M. Megahed, M.S. Attia Faculty of Engineering, Cairo University, 12613 Giza, Egypta r t i c l e i n f o Article history:Received 13 September 2014Received in revised form 16 January 2015Accepted 2 February 2015Available online 10 February 2015Keywords: Thermowells Natural gas plants Failure analysisFlow-induced vibrationsFinite element analysis

a b s t r a c t This study presents the root cause analysis of a weldment failure in a thermowell assembly operating in a natural gas processing plant. Laboratory investigations indicated inferior quality for the llet weld joining the thermowell ange to the pipe supporting the thermowell to the main pipe. The llet weld exhibited excessive concavity, lack of penetra- tion and lack of fusion. This led to minute weldment cracking, which was exacerbated by ow-induced vibrations exceeding safe operational limits. This promoted small magnitude, high frequency stress cycling coupled with high mean stress at the poorly welded joint, which led to accumulation of high cycle fatigue damage and nal fracture causing gas leakage. Mitigation plans included use of a shorter support pipe and revised safe opera- tional envelope of the pipeline under consideration. 2015 Elsevier Ltd. All rights reserved.1. IntroductionThermowells are hollow cylindrical metallic structures used in process and petrochemical industries to shield tem- perature sensors from the process uid. The presence of a bluff body such as the thermowell in the uid ow causes the vor- tex-shedding phenomenon, in which the passing uid separates and creates wakes downstream of the bluff. These low- pressure wakes alternate around the bluff and interact with the bluff inertial, damping, and elastic stiffness to generate ow-induced vibrations (FIV). Analysis of FIV and its structural implications has received signicant research efforts as out- lined in two comprehensive reviews [1,2]. In particular, FIV analysis behind cylindrical bluffs attracted substantial attention due to its close relevance to various industrial applications in power, oil and gas, and aerospace industries. The presence of FIV becomes critical as the magnitude of the vortex shedding frequency; or Strouhal frequency, f s approaches the naturalfrequency of the bluff f N . This situation promotes resonance and the magnitude of lift and drag forces is severely amplied,which may lead to catastrophic failure [3]. Several authors identied FIV as the root cause of observed failure in in-servicethermowells [47], where the failure was characterized by crack propagation due to high-cycle fatigue damage in the ther- mowell structure.Design of thermowells against FIV has for long time aimed at preventing high-cycle fatigue damage as detailed in ASME PTC19.3-1974 [8] and Murdock [9] using the following formula:f s 6 0:8f N1where Strouhal frequency fs is dened as Corresponding author.E-mail addresses: [email protected] (M.M. Megahed), [email protected] (M.S. Attia).http://dx.doi.org/10.1016/j.engfailanal.2015.02.0021350-6307/ 2015 Elsevier Ltd. All rights reserved.f Ns v2where v is the undisturbed ow velocity far from the thermowell, D is the thermowell diameter and Ns is the non-dimen- sional Strouhal number, which is a function of Reynolds number of the ow RN. This design condition ensures that the lift force cyclic frequency is well below the thermowell natural frequency. The rationale for selecting a 0.8 ratio is attributed to the lock-in phenomenon observed as fs approaches fN. Due to the nonlinear uid-structural elastic coupling near resonance and numerous manufacturing tolerances, the thermowell may actually lock into resonance at a frequency lower than fN; hence it is necessary to maintain f s below 0:8f N . ASME PTC19.3 [8] adopts a simplied criterion of Ns 0:22 and ignores its variation with Reynolds number. Furthermore, it accounts only for the lift force Fl in evaluating thermowell fatigue limit.The design rule in Eq. (1) was broadly adopted for thermowell design against fatigue damage due to FIV. However, sub-sequent research [1012] shed light on the signicant variation of Strouhal number over a wide range of Reynolds number. In fact, the value of Ns 0:22 is valid for steam pipelines with NR in the range of 103105, while experimental measurements showed that Ns can be as high as 0.45 for NR in the range of 107 [10]. Furthermore, a severe failure in a pressurized water reactor in Monju, Japan [5,6] was driven by thermowell high-cycle fatigue damage due to in-line cyclic drag forces. These ndings have eventually led to the issuance of a completely revised ASME PTC19.3 standard in 2010 [13]. The fundamental changes in the revised standard are:(i) consideration of Strouhal number as variable with Reynolds number, and(ii) inclusion of a stress-based high-cycle fatigue design criterion again cyclic drag-induced fatigue damage such that:rd < Sa3where rd is cyclic bending stress due to in-line drag forces and Sa is the fatigue strength of the thermowell material for a fatigue life of 1011 cycles.2. Problem descriptionFig. 1 illustrates the assembly details of the failed thermowell, which was used in a 3200 diameter, 29.5 mm thick pipeline in a natural gas processing plant. The pipeline was 5 years old at the time of the incident. Table 1 presents the design and operational details of the pipeline. The thermowell diameter is 33.5 mm and is fastened to a 1.500 SW-RF Class 600- ASTM A350 LF2 XS B16 ange using four in. (12.7 mm) bolts. The ange is connected to the sockolet through an NPS 1.500 (38 mm) ASTM A333 Gr 6-XS support pipe using llet welds on both ange and sockolet sides. Gross gas leak was observed on the ange-support pipe welded joint, which was later identied due to a 62 mm long circumferential crack around the weld neck. The crack location spans approximately 90 angle between the uppermost point along weldment circumference (12 oclock position) and 3 oclock position. Fig. 2(a and b) illustrates the failed assembly and a zoomed view of the cracked weld neck, respectively. Visual examination of the failed components did not reveal any sign of internal corrosion or erosion. Furthermore, the cracked weldment passed routine visual inspection approximately 12 months prior to the incident. The analysis employed the guidelines in [8], upon which the thermowell was designed and operated. Furthermore, while theFig. 1. Schematic of thermowell assembly.

Table 1Design and operational conditions of the pipeline.Pressure (barg)Design pressure, Pd102

MAWP79

Operating pressure, Po68

Temperature ( C)Min. design temperature 46

Max. design temperature85

Operating temperature, To25

Gas ow rate (MMSCFD)Minimum1100

Average1121

Current1180

Fig. 2. Cracked thermowell assembly: (a) assembly view, (b) ange weldment crack view.updated standard [13] issued in 2010 is not retroactive, it is prudent to consider the implications of the more stringent acceptance criteria on the results based on 1974 version of the standard.3. Laboratory investigationsChemical analysis of support pipe material has shown compliance with relevant material standard [14]. Similarly, hard- ness measurement and microstructural analysis of base metal, weld material and HAZ are in agreement with applicable welding standards.Fig. 3 illustrates two macro-etched cross sections of the pipe-to-ange weldment. Fig. 3(a) indicates a one-pass llet weld with a weld leg length of 45 mm on both ange and pipe sides. Excessive concavity is visible with a weld throat ranging

Fig. 3. Visual examination of pipe-to-ange macroetched specimen.between 2.3 and 2.5 mm, which does not conform to applicable standards [15]. Fig. 3(b) depicts another cross section in the vicinity of the crack, where a visible lack of sidewall fusion at pipe side is shown in addition to excessive concavity. Further- more, two cracks are observed in this gure; a side wall crack at ange side (crack A) and a weld throat crack (crack B). The ange side crack (crack A) apparently emanates from lack of sidewall fusion and lack of penetration. The weld throat crack (crack B) emanated from inside due to poor penetration. Fig. 4(a and b) illustrates a macro-etched views of cracks A and B, shown in Fig. 3, respectively. Furthermore, the microstructure of the pipe, ange, and the weld is shown in Fig. 5. The microstructure of the pipe is a rened banded structure of ferrite and pearlite. The microstructure of the ange is a normal structure ferrite and pearlite, while the weldment microstructure is a normal dendritic structure. No particular microstruc- tural anomalies were observed in these components.4. Thermowell structural analysis4.1. Thermowell assembly loadsThe thermowell assembly is subjected to the following loads:(a) Steady internal gas pressure, which induces hoop membrane stresses in the wall of the support pipe.(b) Weight of the assembly components in Fig. 1, which induce bending stresses in the support pipe wall that are tensile at the observed cracking location.(c) FIV lift and drag forces; with the lift force, Fl , oscillating lateral to the ow at the vortex shedding frequency f s , with a zero mean value, and the drag force oscillating in-line with the ow at a mean value of F D with a superimposed alter- nating component Fd at 2f s . The magnitudes of these forces per unit projected area of the thermowell immersed length are given as:

Fig. 4. Weldment cracks: (a) weld-throat crack, (b) ange-side crack.Fig. 5. Microstructure of thermowell assembly components (200 ), (a) pipe, (b) ange, (c) weld metal.F1 C qv 22

4 1 2Fd 2 Cd qv sin4pf s t5 1 2Fl 2 Cl qv sin2pf s t6where q is the gas density, and Cl ; CD ; and Cd are the lift, stationary drag, and oscillatory drag coefcients, respectively. It should be noted that Fd and Fl oscillate at 2f s and f s , respectively, hence the maximum stress states are coincident every sec- ond cycle. Nevertheless, the resulting maximum stress location due to each of these forces is spaced by an angle 90 around the weldment circumference. Hence, the resultant peak stress is attained every two cycles and its position lies between drag and lift directions and depends on the relative magnitude of acting forces.4.2. Finite element analysisBoth modal analysis and forced excitation dynamic stress analysis of thermowell assembly were conducted using nite element analysis (FEA). The assembly was modeled using eight-node continuum solid elements in COSMOS/M package [17] with three translational degrees-of-freedom at each node. Fig. 6(a and b) depict the FE model of the thermowell assembly. The 3200 pipe segment at the sockolet intersection was assumed plane, i.e. its curvature was ignored, which is justied since the sockolet diameter (1.500 ) is very small compared to the 3200 main pipe. Furthermore, due to the vast difference in stiffness between the main pipe and the thermowell assembly, it was feasible to rigidly x the end of the support pipe to the wall of the 3200 main pipe. In order to account for the poor weldment quality, the observed concavity was digitized and mapped onto the FE mesh to accurately simulate the weld geometry.5. Results and discussionDesign calculations of the support pipe [16] indicate that the thickness required to resist pressure stresses is about4.5 mm, which is less than the support pipe thickness of 5.0 mm. Furthermore, bending stress induced in the support pipe wall by the dead weights was found to be much smaller than pressure stresses. Hence, the support pipe meets static strength requirements against steady forces and internal pressure. It thus remains to examine thermowell structural response against FIV using applicable guidelines.5.1. PTC19.3-1974-based assessment5.1.1. Thermowell modal analysisModal analyses of both the stand-alone thermowell and the thermowell assembly were performed using FEA to evaluate the natural frequency. Both the rst and second natural modes excite the thermowell in a cantilever-like pattern. The rst natural frequency of the installed thermowell was found to be 97.5 Hz, while the rst natural frequency of the thermowell- only was found to be 106.7 Hz. This reduction in natural frequency can be explained by considering the spring-mass analogy of a cantilever beam having length L, mass per unit length m, elastic modulus E, and second moment of area I. The following proportionality relation between natural frequency f N and these quantities can be written as:Fig. 6. FE Model of thermowell assembly: (a) full model, (b) cracked weldment.f N /

sEImL4

7Accordingly, the introduction of the support pipe, which increased the total unsupported assembly length outside the main pipe, would reduce the rst natural frequency. Due to the absence of detailed history of pipeline operational ow rate, pressure, and temperature data, a parametric study was conducted to evaluate Strouhal frequency under all pressure and ow rate conditions using the operational data.

Fig. 7. Strouhal frequency at various operating conditions.Fig. 7 illustrates the variation of Strouhal frequency at various operating conditions (maximum allowable working pres- sure (MAWP) and ow rate) as well as the safe operating frequency limits according to PTC 19.3-1974 [8]. When the safe operational limit is established on the basis of natural frequency of the installed thermowell (97.5 Hz), values of f s willexceed the 80% limit for operating pressure of 69 barg at all operational levels of ow rate. Evidently, exceeding the 80% safelimit increases the potential of resonance. Meanwhile, if the safe operational limit is established on the basis of the natural frequency for the stand-alone thermowell, the operation will be safe up to a ow rate of 1130 MMSCFD at the same operating pressure. In contrast, the pipeline operation is safe when it is operated at MAWP for the all ow rates under consideration. This can be explained by reduction in gas density with reduced pressure, which implies increased ow velocity to maintain constant mass ow rate.5.1.2. Weldment stress analysisModal analysis results indicate that the thermowell may have tripped the safe operating limit depending on gas ow pressure as shown in Fig. 7. Hence, it is anticipated that the proximity to the natural frequency would magnify cyclic stress magnitudes due to lift force. This, coupled with the evident poor weld quality, potentially indicates that fatigue crack growth could be the culprit in the observed failure. Therefore, dynamic stress analysis of the thermowell assembly was conducted using FEA. In this case, the thermowell is oscillating lateral to the ow and is acted upon by static and cyclic loads as detailed in Section 4.1. The steady drag CD and cyclic lift Cl coefcients in [8] are equal to 0.75 and 0.25, respectively.The observed cracking indicates that the axial stress perpendicular to the crack is the opening component. A worst casescenario comprising a ow rate of 1180 million standard cubic feet per day (MMSCUFD) at 69 barg was assumed. Figs. 7 and8 illustrate the axial stress contours due to static and cyclic forces, respectively, using drag and lift coefcients in [10]. It is evident that the most highly stressed section is the ange-to-support pipe weldment, which is consistent with the observed cracking.5.2. PTC19.3-2010-based assessmentThe new edition of PTC19.3 standard [13] provides a comprehensive assessment against both lift- and drag-induced FIV damage. Due to the complex relation between Strouhal number Ns and Reynolds numberRe , it was rst necessary to evaluate Re for all ow conditions using the relation:Re qv

Dtw

8lwhere Dtw is the tip diameter of the thermowell and l is the dynamic viscosity, equal to 2 10 5 Pa s for dried feed gas. Thevalues of Re for the current operational envelope were evaluated and found to vary between 8:6 10

and 9:3 105 . Thisrange of Re values results in a constant Ns equal to 0.22. This value indicates similar FIV frequencies to those shown in Fig. 7, indicating that the current design violates the new standard safe operating limit for all ow rate levels at an operating pressure of 69 barg.FE predictions using the lift and drag coefcients in [13] showed similar peak stress locations to those shown in Fig. 9. Noteworthy is that the corresponding values of CD and Cl in [13], given as 1.4 and 1, respectively, suggest an increased ana- lysis conservatism regarding the assessment of lift-induced stresses. Table 2 depicts a comparison between total axial stress- es at the weldment due to sustained loads such as weight in addition to the dynamic lift forces. Estimates are made according to the two standards assuming the worst case scenario comprising a ow rate of 1180 MMSCUFD at 69 barg. The change in lift coefcient in the most recent standard is reected in the increased cyclic stress amplitude Dr, while the mean stress component remained nearly constant since the static loads did not change. The observed high stress ratio in both cases keeps the circumferential crack open all the time and the large number of accumulated cycles aids in inducing minute increments of crack growth and associated fatigue damage. Table 3 compares the resulting total drag-induced stress- es according to both standards for the worst-case ow scenario of 1180 MMSCUFD at 69 barg. It is seen that 1974 editionignores the cyclic drag stress component; hence Drd 0. Furthermore, drag stresses predictions using 2010 edition arealmost two orders of magnitudes lower than the lift stresses shown in Table 2. Accordingly, drag forces are not expected to play a signicant role in the development of the crack.5.3. Thermowell fatigue life estimationLinear elastic fracture mechanics tools can be used to evaluate the total number of cycles required to drive the weldment crack to the nal length of 62 mm. The poor weldment quality observed in Fig. 3 suggests that the crack growth started from a relatively nite crack size that resulted in a stress intensity factor higher than the critical threshold value. Accordingly, crack life can be assumed to consist mainly of critical crack growth regime. In particular, the effect of observed high R-ratio on crack life can be accounted for using Walker equation [18]:dadN C

DK mc

91 R

Fig. 8. Static axial stress distribution in the weldment.where da is the crack growth rate, C and m are Paris formula crack growth parameters and c is a curve-tting material para- meter that ranges between 0 and 1 to adjust the effect of load ratio R on crack growth characteristics. For ferritic-pearlitesteels, the values of C and m are 6:89 10 9 mm ; MPapm

and 3, respectively [19]. In the absence of reliable test data,the effect of c was assessed by considering a number of limiting cases (c 0, c 0:5, and c 1). The problem can be ide- alized as a cantilever pipe welded to the ange and subjected to internal pressure P and net-section bending stress distribu- tion. The pipe weldment has an internal semi-elliptical crack as shown in Fig. 10. The mode-I stress intensity factor K I for this conguration under a fourth-order polynomial stress distribution can be evaluated using Eq. (10) below [20]#r" 4 a n paK I Go P XGi rii0

10

Fig. 9. Weldment oscillatory axial stresses: (a) upward lift, (b) downward lift.Table 2Characteristics of weldment lift-induced cyclic axial stress history.PTC 19.3-1974PTC 19.3-2010

Maximum stress rmax (MPa)89.894.5

Mean stress rmean (MPa)87.787.8

Minimum stress rmin (MPa)84.181.6

Stress range Dr (MPa)5.712.9

Stress ratio R = rmin/rmax0.940.86

Table 3Characteristics of weldment drag-induced cyclic axial stress history.PTC 19.3-1974PTC 19.3-2010

Maximum stress rmax (MPa)0.591.25

Mean stress rmean (MPa)0.591.096

Minimum stress rmin (MPa)0.590.94

Stress range Dr (MPa)00.31

Stress ratio R = rmin/rmax10.75

Fig. 10. Schematic support pipe showing crack location and geometry.where ri and Gi linearized stress components and inuence coefcients [19], and Q is geometry factor given as: a 1:65Q 1 1:464 c

11The thermowell fatigue life can be evaluated by combining Eqs. (9)(11) and performing necessary numerical integration. Fatigue life was evaluated for a range of initial crack lengths 2ci between 0.1 mm and 1 mm. Fig. 11 depicts a parametric evaluation for the thermowell weldment fatigue life for various values of 2ci and c values ranging between 0 and 1. Further-more, it shows the observed thermowell life assuming 300 operational days per year for 5 years at 80 Hz lift frequency,10which yields 1:04 10

cycles. Clearly, the fatigue life prediction is very sensitive to the value of c, where life is seen to varyby three orders of magnitude as c varies between 0 and 1. This indicates the critical role of the stress ratio R upon life pre-diction. Setting c 0 essentially reduces Eq. (9) to Paris formula and eliminates stress ratio contribution to da=dN, whereas setting c 1 corresponds to the maximum contribution of R-ratio implying higher levels of da=dN. Furthermore, the value of2ci has a pronounced effect on predicted life, which varies by almost 5 times as the initial crack length 2ci increases from0.1 mm to 0.4 mm. However, further increase of 2ci has a rather marginal effect on predicted crack growth life. Therefore, the close match between observed and predicted fatigue life for the case of c 0 should be assessed conservatively in the absence of accurate initial crack size and crack growth parameters.On the other hand, the stress-based design criterion against drag stresses in Eq. (3) is valid only for defect-free construc- tion design. In the current problem, however, a fracture mechanics-based approach similar to that used to evaluate crack life under lift-induced stresses should be used. Since drag-induced stresses are almost two orders of magnitudes lower than theFig. 11. Parametric evaluation of thermowell weldment fatigue life.lift-induced stresses, it is highly unlikely that the observed minute drag stresses could have driven the measured crack with- in the observed time period.6. Conclusions and recommendationsThis study presented detailed failure analysis of a thermowell assembly used for temperature measurements in a natural gas plant. The support pipe-to-ange weldment exhibited excessive weld llet concavity, lack of penetration at the weld root. Furthermore, lack of fusion at sidewalls of pipe and the ange were observed. These features represent a potential crack initiation site in the same region that witnessed the actual weld cracking. FIV analysis showed that Strouhal frequency exceeded the safe design threshold of 80% of the natural frequency of the installed thermowell whenever the pipeline oper- ated at the operational pressure of 69 barg, which implies operation close to resonance conditions. Finite element analysis showed that weldment is subjected to constant tensile mean stress component super-imposed on a small magnitude, high- frequency cyclic component due to lift-induced forces. On the other hand, drag-induced stresses at the weldment were found to be two orders of magnitude less that stresses due to lift force. The stress-based design against fatigue failure proposed in2010 standard is not applicable for the present failure case due presence of a defective weld, at which cracking started and propagated. A parametric study was conducted to evaluate crack life under the lift-induced stresses assuming a worst case ow scenario. It has been shown that both initial crack size and crack growth parameters have a signicant effect on crack life prediction delity.The repair and mitigation plan comprised a revised pipeline operational envelope to maintain Strouhal frequency within the acceptable safe limits in the standards. Furthermore, a shorter support pipe was used in place of the current one, effec- tively increasing the lowest natural frequency for the installed thermowell to 101.1 Hz instead of the original 97.5 Hz value.AcknowledgementThe authors would like to thank Professor M.R. El-Koussy and Mr. M. Naguib of the Faculty of Engineering, Cairo Univer- sity, for their help with metallurgical examinations and weldment inspection.References[1] Weaver DS, Ziada S, Au-Yang MK, Chen SS, Paidoussis MP, Pettigrew MJ. Flow-induced vibrations in power and process plant components progress and prospects. ASME J Press Vess Technol 2000;122:33948.[2] Sarpkaya T. A critical review of the intrinsic nature of vortex-induced vibrations. J Fluid Struct 2004;19(4):389447. [3] Shellard HC. Collapse of cooling towers in a Gale, Ferrybridge, 1 November 1965. Weather 1967;22(6):23240.[4] El-Batahgy A, Fathy G. Fatigue failure of thermowells in feed gas supply downstream pipeline at a natural gas production plant. Case Stud Eng Fail Anal2013;1:7984.[5] Morishita M, Dozaki K. History of ow-induced vibration incident occurred in Monju. ASME Trans PVP 1998;363:1038.[6] Odahara S, Murakami Y, Inoue M, Sueoka M. Fatigue failure by in-line ow-induced vibration and fatigue life evaluation. JSME Int J, Ser A 2005;48(2). [7] Haslinger KH. Flow-induced vibration testing of replacement thermowell designs. J Fluid Struct 2003;18:42540.[8] ASME PTC19.3: performance test codes, Part 3: temperature measurements, instruments and apparatus. American Society of Mechanical Engineers;1974.[9] Murdock JW. Power test code thermowells. J. Eng. Power (ASME Trans.) 1959:40316.[10] Brock JE. Stress analysis of thermowells. Monterey, California: Naval Postgraduate School; 1974.[11] Blevins RD, Tilden BW, Martens DH. Vortex induced vibration and damping of thermowells. J Fluid Struct 1998;12:42744. [12] Roshko A. Experiments on the ow past a circular cylinder at very high Reynolds number. J Fluid Mech 1961;10:34556. [13] ASME PTC19.3 TW-2010: performance test codes: thermowells. American Society of Mechanical Engineers; 2010.[14] Annual Book of ASTM Standards, Vol. 01.01 Steel piping, tubing, ttings. ASTM International; 2004. [15] AWS D1.1, 2004.[16] ASME B31.3.: Process piping. ASME Code for Pressure Piping; 2004.[17] COSMOSM Theory manual. Structural Research and Analysis Corp., 2004.[18] Walker K. The Effect of stress ratio during crack propagation and fatigue for 2024T3 and 7075T6 Aluminum. ASTM STP 462. American Society forTesting and Materials; 1970. p. 114.[19] API 5791/ASME FFS-1, Fitness-For-Service, 2007.[20] Anderson TL. Development of stress intensity factor solutions for surface and embedded cracks in API 579, WRC Bulletin 471. New York (NY): WeldingResearch Council, Inc.; May 2002.

s D

D D

5

dN

cycle

Q

t