Stress concentration factor analysis for welded, notched tubular T-joints under combined axial, bending and dynamic loading

International Journal of Fatigue 31 (2009) 367–374

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Stress concentration factor analysis for welded, notched tubular T-joints under combined axial, bending and dynamic loading A. N’Diaye a,*, S. Hariri b,1, G. Pluvinage a, Z. Azari a a b

Laboratoire de Fiabilité Mécanique (L.F.M.) de l’Université de METZ-E.N.I.M., Ile du Saulcy, 57045 Metz Cedex, France Département Technologie des Polymères et Composites and Ingénierie Mécanique, Ecole des Mines de Douai 941, rue Charles Bourseul, B.P. 10838, 59508 Douai Cedex, France

a r t i c l e

i n f o

Article history: Received 20 March 2008 Received in revised form 21 June 2008 Accepted 29 July 2008 Available online 8 August 2008 Keywords: Tubular T-joints Stress concentration factors Notched weld Finite element method

a b s t r a c t The finite element analysis will be used in this study to predict the location of hot-spot stresses in a welded tubular T-joint. The fillet weld has been modeled all around the joint. Using symmetry, the tubular T-joint is submitted to axial, in-plane bending (IPB) and out-of-plane bending (OPB) loadings. The finite element method analysis shows that stresses are very high on the brace member in the vicinity of the fillet weld and gradually decrease, with a quasi-stable difference, in the direction of the brace extremity. Both on the brace member and along the fillet weld (from crown to saddle), stresses are high at the crown toe, decrease in the middle and increase once again at the saddle point. From a general perspective, this stress distribution analysis reveals that hot-spot stresses (HSS) are located at the crown and saddle points. Dynamic loading greatly increases the stress concentration factor at the hot-spot stress (HSS) located on the brace member where fatigue damage is capable of appearing quickly. In the U-notch, this stress concentration factor (SCF) increases as notch width decreases. In a general way therefore, stress concentration factors decrease on the brace and chord members (in the vicinity of the weld) and increase considerably in the notch, which underscores the deleterious nature of such a defect. Consequently, these zones (HSS) require reinforcement solutions in order to ensure a sufficiently long fatigue life for offshore structures. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Offshore structures are composed of tubular T-joints that contain geometric discontinuities. In order to avoid shape instability problems, a chord member D/T (diameter-to-thickness) ratio must be set between 50 and 100. Effective tube-cutting enables avoiding punching problems in the skin and improves their fatigue resistance. These tubular T-joints concentrate stresses in the vicinity of the fillet weld. These zones are also the location of fatigue crack initiation and propagation risks due to point loading and the combined action of instantaneous and cyclic loadings (swells, wind, operations, tide). From an experimental perspective, stress gauges were used to locate the stress concentrations due to fatigue. The point where such stress concentration is maximized is known as the hot-spot stress (HSS), and the finite element method is used to locate these stresses. During preparation of the fillet weld, some defects can appear (U, V or elliptical-notch) and cyclic loading (axial, IPB and OPB) will lead to fatigue cracks initiation at these defects [1–9]. The stress distribution analysis in the vicinity of the

tubular T-joints exhibiting such defects proves very important in locating hot-spot-stresses (HSS). This study consists of: – calculating the elastic stress concentration factor kt in the vicinity of the fillet weld and comparing results with existing values in the literature; – studying the influence of both static type loading ([axial, IPB (in-plane bending), OPB (out-of-plane bending)] and dynamic type) on the elastic stress concentration factor kt values; – simulating a notch with right angles in the middle of the fillet weld and all around the tubular T-joint; and – calculating the elastic stress concentration factors kt in the vicinity of the fillet weld (on the brace and chord members) and in the notch bottom. The parameter kt is calculated for a range of values of notch width e. As part of the validation process, these results have been compared with those found in the literature. 2. Literature survey

* Corresponding author. Tel.: +33 3 87 31 53 47; fax: +33 3 87 31 53 03. E-mail addresses: [email protected] (A. N’Diaye), [email protected] (S. Hariri), [email protected] (G. Pluvinage), [email protected] (Z. Azari). 1 Tel.: +33 3 27 71 23 12; fax: +33 3 27 71 23 18. 0142-1123/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2008.07.014

The literature introduces us to international organizations, such as API (American Petroleum Institute) and FEM (the UK

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Nomenclature A Q L D T d t

crown toe point (see Fig. 1) saddle point length of chord member external diameter of chord member wall thickness of chord member external diameter of brace member wall thickness of brace member a = 2L/D chord length to half-chord diameter ratio b = d/D brace to chord diameter ratio U=0 origin of angular position (A–A, crown to crown; Q–Q, saddle to saddle), see Fig. 1 Ui angle defining element position at the joint, see Figs. 7 and 8b c = D/2T radius to wall thickness ratio of chord member

angle defining the brace member inclination brace to chord wall thickness ratio thin-shell element thickness (on the weld extremities) e1 (see Fig. 8b) thin-shell element thickness (at the middle of the weld) e2 p = (e1–e2)/2 depth of the U-notch (mm) k U-notch width (mm) e = k/2 variable half U-notch width (mm) rV+ maximum Von Mises stress on the upper face, MPa rmax maximum stress extrapolated at the fillet weld foot (MPa), see [1–3,10,30] rN nominal stress (MPa), see [30] elastic stress concentration factor (kt = rmax/rN) kt h

s = t/T

Department of Energy Guidance) and the Polytechnic school (ARSEM [1], Radenkovic [2] and Recho [3]). These authors have studied several types of structures and published their results. Other authors, including Pang and Lee [10], Chang and Dover [11], applied the finite element program Abaqus, which contains thin-shell elements with five degrees of freedom per node in order to study the X-joint. Kuang and Potvin [12], Gibstein [13], Efthymiou and Durkin [14], and Hellier [15] studied a welded tubular T-joint by using the Marc finite element program. Romeijn [16] and Spyros [21] studied tubular T, Y and K-joints using the Marc program as well; they employed brick elements with five degrees of freedom, and their results were compared with those stemming from the API computation code. Research carried out by some authors on notched cylinders has been presented in [10]. Noda et al. [25] studied certain formulations of the Ichihiko et al. [26] conducted research on thick plates, welded with an X-joint and featuring a notched weld foot, in order to study joint behavior in fatigue loading. In our previous study a V-notch was simulated so as to analyze stress distribution in the weld from the notch bottom towards the load-bearing segment [30]. All of these authors have focused on static loading cases and, in general terms, results have been calculated on just the brace member. Furthermore, following a comparison of results for the static loading case, this paper will also report on chord results for the dynamic axial loading case, in order to analyze the impact of this type of loading on the stress concentration factor. Other authors have proposed analytical solutions that determine stress distribution in the notch bottom.

3. T-joint geometry and loading The elastic stress distribution has been calculated for a tubular T-joint whose geometry is shown in Fig. 1. The structure and corresponding dimensions (see Table 1), the properties of the ordinary steel composing the T-joint (see Table 2) and all notations are the same as those presented in [10]; the purpose herein is threefold: to draw comparisons between our results and those derived by the other authors, verify the validity of these results, and then carry out other studies (e.g. on crack mechanics in a subsequent paper

Table 1 Dimensions of the tubular T-joint [10] L = 4130 mm d = 406 mm t = 9.5 mm d/D = 0.8 t/T = 0.75

T = 12.7 mm D = 508 mm Base and height of the fillet weld = 5 mm R/T = 20 L/D = 16.25

Table 2 Properties of the ordinary steel used for the T-joint E = 207 GPa m = 0.3 q = 7.8  106 kg/mm3 re = 248 MPa

Young’s modulus Poisson’s ratio Specific mass Yield stress

Y d Brace member φ=45˚

Crown toe point t

θ° Chord member

A

5 mm Φ°

T

Q

A Z

Q

Fillet weld D

5 mm Saddle point

L Fig. 1. Dimensions of the welded tubular T-joint.

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published – IJF). The structure will be loaded with axial, IPB and OPB loadings, respectively; the intensity of each type of loading is generated by a 1 MPa-distributed load applied at the brace summit. Symmetry has been used herein as well (see Figs. 2–4). Stresses in the vicinity of the fillet weld, on the brace and chord member, have been calculated for static axial, IPB and OPB loadings (see Figs. 2–4) and dynamic axial loadings. These stress distributions are generally provided by means of stress concentration factors obtained from dividing the maximum geometric stress of each element by the appropriate nominal stress measured on the brace member. The associated definitions and notations have been listed in the nomenclature section.

Y

Z

X

Fig. 1 shows the dimensions of the tubular T-joint considered herein. Three load cases were considered: axial loading (Fig. 2), IPB (Fig. 3), and OPB (Fig. 4). Each displays an intensity due to the distributed load of 1 MPa applied at the brace summit [10]. Symmetries are used for this configuration. 3.1. Modeling and meshing process for the tubular T-joint In this study, quadrangular and triangular thin-shell elements have been used for modeling the structure with the Effel program. Each node possesses six degrees of freedom. The local axis z for the thin-shell elements is normal to the surface. The modeling rules have been applied at the joint, and meshing must be regular and refined in the vicinity of the filled weld in order to obtain the best results. Lastly, the weld was modeled in this manner, as clearly indicated in Fig. 5a, with a focus on hot-spot locations. In light of the modeling rules mentioned above, n = 60 elements were used over a full 360° along the fillet weld. This set-up resulted in a model with 2600 nodes, 3000 thin-shell elements and 15,900 degrees of freedom. Fig. 5a shows the meshing of the tubular T-joint using the Effel FEM package and angular position Ui along the fillet weld (see Fig. 1). 3.2. Definition of the stress concentration factor kt

Fig. 2. Axial loading (in the Y-direction).

The analysis conducted herein provides maximum stress values

rmax in the vicinity of the weld; these values are related to a nominal stress rN through the following stress concentration factor: kt ¼ rmax =rN

ð1Þ

where rmax and rN are the maximum Von Mises stress calculated respectively at the foot of the fillet weld and on the brace member, where two stress distribution zones can be observed and SCF extrapolated (see Fig. 5b) at the hot-spot stress (HSS) located at the saddle point. The finite element analysis allows obtaining the maximum Von Mises stresses on the surface of the tube: rV+ (on the surface), rV (under the surface) and r0 (along the Gauss line in the middle of the thickness) [10].

Fig. 3. IPB loading (rotation around the X-axis).

3.3. Comparison and evaluation of results Table 3 displays a comparison between our results and results published by Pang et al. The stress concentration factors derived are all located on the brace, at the same side of the weld: The calculation results of hot-spot stress concentration factors for the three loading cases considered herein are presented in Table 4. Fig. 4. OPB loading (rotation around the Z-axis).

a

b

σN

Brace

Brace A

Fillet weld

Extrapolated stress Real stress

B Chord

Neutral axis of thin-shell elements

Chord member

σmax

Fig. 5. (a) Meshing of the welded tubular T-joint using the Effel FEM package. (b) Schematic representation of the stress extrapolation method [10].

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Table 3 Calculated stress concentration factors kt, as compared with results from the literature Loading case

UEG [10]

Kuang et al. [12]

Gibstein [13]

Efthymiou and Dirkin [14]

Hellier et al. [15]

N’Diaye

Axial IPB OPB

8.6 3.2 9.1

9.6 3.3 8.6

11.2 3.4 11.3

12.8 3.6 14.0

11.7 4.6 13.5

9.62 3.11 10.45

Table 4 Maximum stress concentration factors kt Loading case

Axial IPB OPB

SCF (kt)

Angular position (U)

Brace member

Chord member

9.62 3.11 10.45

9.27 3.08 11.86

90° 45° 0°

brace. A comparison of stress concentration factors kt for both the dynamic and static analyses is provided in Fig. 6. Following this comparison of our results for the static case (Tables 3 and 4), chord member results were considered for the dynamic case as well (Table 5), so as to analyze the impact of this type of loading case, for axial loading, on the stress concentration factor. Fig. 6 displays the stress concentration factor kt for both the dynamic and static analyses. 3.6. Discussion

3.4. Influence of dynamic loading Offshore structures are submitted to several types of cyclic loadings. Except for operating loads, it is important to examine the other type of loads due to the environment (swells, wind, flows). A dynamic axial loading of the step type is applied for a duration of 0.6 s; it has been divided into six time intervals of 0.1 s each. The kt values resulting from the dynamic analysis are presented in Table 5. 3.5. Discussion Table 5 shows that for the static axial loading case, an SCF value of 9.62 was found on the brace member and 9.27 on the chord member (see Table 4). For the dynamic loading case, Table 5 indicates that an SCF value of 14.69 was measured on the brace and 11.96 on the chord member. These results serve to explain that the SCF is higher for the dynamic case than for the static one; moreover, the SCF is higher on the brace member than on the chord member and the hot-spot stress (HSS) is located on the

Fig. 6 shows the half-polynomial SCF curves, which can explain the minor difference with the line for brace statics. From a general standpoint and for the same weld angle (u = 45°), we observed a high stress concentration on the brace member and at the saddle for static loading (see Table 5 and Fig. 6). The SCF results for the chord member in the static case differ from those at the brace since the wall thickness of the brace is less than that of the chord and, consequently, the brace is capable of cracking. The stress concentration factor due to dynamic loading is higher than that due to static loading (Fig. 6). For both these loading cases, the hot-spot stress (HSS) is located on the brace member [16–30].

4. Detail of the T-joint structure with a U-notch The elastic stress concentration factors were calculated on the brace and chord members along the fillet weld using thin-shell elements. Structure geometry is shown in Fig. 7 and the associated definitions and notations have been listed in Table 1.

Table 5 Comparison of static and dynamic stress concentration factors kt Loading case

Angular position

Mode

Member

kt

Axial – 1 MPa

U = 90° (saddle)

Static

Brace member Chord member Brace member Chord member

9.62 9.27 14.69 11.96

Dynamic

16 14 12

(brace - dynamic)

kt

10

(chord - dynamic)

8 6

(brace - static)

4

(chord - static)

2 0

0

30

60

90

Φ i (degrees) Fig. 6. Variation curves of elastic stress concentration factors kt vs. angular position Ui, for an axial loading (weld angle u = 45°), in both the static and dynamic (t = 0.6 s) cases.

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Y

d

t

U- notch

φ=45˚ θ°

5 mm T

A Φ

5 mm

Q

A notch-free weld

Z

Q

D crown toe point

saddle point L

Fig. 7. Dimensions of the welded tubular T-joint with a U-notch.

a b Y

brace member

ε

nodes of thinshell elements

middle elements

Φi extremity elements center of gravity of thin-shell elements

e1=5mm P=(e1-e2)/2 e2=3mm neutral axis thin-shell elements

chord member

Fig. 8. (a) Meshing of the U-notched, welded tubular T-joint using the Effel FEM package. (b) Meshing diagram of the U-notched weld, modeled with thin-shell elements, and of the location angle Ui in the notch.

4.1. Modeling of the tubular T-joint with a U-notch

4.2. Results

In this part of the study, a U-notch with right sections in the fillet weld is simulated by reducing the thickness of the thin-shell element in the middle of the fillet weld. The lower part of the notch is considered as penetrated in the structure (Fig. 8a and b). Symmetry will be used to generate a small size model. Each half notch width e = k/2 will be varied from 0.005 to 1 mm and requires a specific fillet weld model in order to study its influence on stress distribution in the notch bottom as well as on the brace and chord members in the immediate vicinity of the weld. The meshing of both the brace and chord members remains unchanged. Three load cases were considered: axial (Fig. 2), IPB (Fig. 3) and OPB (Fig. 4), each with an intensity due to the distributed load of 1 MPa applied at the summit of the brace. Stresses were extrapolated at the hotspot stress (HSS) located at the saddle point (Fig. 5b) [30–31].

The results calculated for the stress concentration factor of the notch-free fillet weld are depicted in Fig. 9. This SCF is applied at the middle elements (see Fig. 8b). 6 5

kt

4 3 2 1 0

0

15

30

45 Φ i (degrees)

60

75

90

Fig. 9. Stress concentration factor kt for axial loading on the notch-free weld.

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Y

36,16

σN=36.16 MPa

element 1: extr. σV+=37.38 MPa element 15. Φ15=90˚ σv+=370,48 MPa (on the brace)

from Φ=0 to Φ=6˚

(element 2) Φ2=12˚

hot-spot stress zone at Φ=90° (element 14) Φ14=84˚ σV+=340.95 MPa

σV+=36.49 MPa σyy=65.82 MPa

σyy=373.16 MPa (in notch bottom)

Z

Fig. 10. Example of stresses calculated in a weld with a U-notch under axial loading.

It can be noted from Fig. 10 a peak hot-spot stress located at

4.3. Discussion

U = 90°, a stress ryy = 373.16 MPa in the notch bottom and a nominal stress rN = 36.16 MPa measured on the brace member. An analysis of stress distribution in the vicinity of the fillet weld reveals that stresses decrease on both the brace and chord members and then increase in the notch bottom (i.e. the notched weld). The Von Mises stresses rV+ in the notch bottom were used to derive the stress concentration factors presented in Figs. 11–14.

Fig. 10 shows that the values of stress concentration factors kt(rV+) in the case of the notch-free weld element tend to decrease slightly on the brace member and much more noticeably on the chord member; they then increase sharply in the notch bottom when the weld element is notched. The distribution of calculated stresses in the notch bottom indicates that stress concentration

12 10

kt

8

brace (notch free weld) upper fillet weld

6

chord (notch free weld)

4

brace (notched weld) in notch bottom

2

chord (notched weld)

0 0

30

Φ i (degrees)

60

90

Fig. 11. kt(rV+) on brace and chord members respectively, for the weld with and without a notch, in the case of axial loading.

45 40

kt

35 30

ε =0.005

25

ε =0.05

20

ε =0.1

15

ε =0.2

10

ε =0.5

5

notch free weld

0 0

15

30

45

60

75

90

Φ i (degrees) Fig. 12. kt(rV+) in the bottom of the U-notch vs. notch width, in the case of axial loading.

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5 4.5 4 3.5

ε = 0.2 mm

kt

3 2.5

ε = 0.7 mm

2 1.5

ε = 1 mm

1 0.5

notch free weld

0 0

15

30

45

60

75

90

Φ i (degrees) Fig. 13. kt(rV+) in the bottom of the U-notch vs. notch width, in the case of IPB loading.

12 10 ε = 0.2 mm

kt

8 6

ε = 0.7

4

ε = 1 mm

2 notch free weld

0 0

15

30

45

60

75

90

Φ i (degrees) Fig. 14. kt(rV+) in the bottom of the U-notch vs. notch width, in the case of OPB loading.

kt

50 45 40 35 30 25 20 15

kt (σv+) in the U-notch kt (σyy) in the U-notch

10 5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ε (mm) Fig. 15. kt(rV+) and kt(ryy) in the notch bottom at the peak hot-spot stress vs. width e, for axial loading.

factors rise as width e decreases. In general, Figs. 11–14 reveal that stress concentration factors increase significantly when the weld element is notched for axial, IPB and OPB loadings. Stresses in the notch bottom as a function of notch width have been plotted in Fig. 15. From this figure, it can be concluded that: – kt(rV+) and kt(ryy) decrease from e = 0.1 mm, e = 0.2 mm(prediction – fatigue crack initiation); and – kt(rV+) and kt(ryy) are quasi stable over the range of e = 0.2 mm to e = 1 mm (effective fatigue crack). 5. Conclusion Offshore structures are submitted to the combined action of axial, bending and dynamic loadings, which results in peak stresses forming at the joint between the chord and brace members. These

zones often serve as the initiation point for fatigue cracks. The first part of this study has shown that the static and dynamic SCFs are both higher on the brace than on the chord, and the dynamic SCFs are higher on the brace and chord than in the static loading case. We have noticed that for the static as well as dynamic loading cases, SCF increases sharply in the vicinity of the fillet weld, on the brace and chord members, and particularly at the hot-spot stress (HSS). Generally speaking, the increase of dynamic SCFs can accelerate the appearance of fatigue damage through cracking at the HSS and, consequently, may prove dangerous for offshore tubular T-joints. The second part of the study has revealed that when the fillet weld is notched, stress concentration factors decrease slightly on the brace member and more extensively on the chord member; they increase significantly in the notch bottom. These SCFs increase as width e decreases. In general, the results obtained in this second part of the study show that small width

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notches, i.e. e 6 0.2 mm, are greater at higher SCF (HSS phase prediction and fatigue crack initiation) than those with width e P 0.2 mm (effective fatigue crack phase). These phenomena undeniably diminish in both cases, especially the fatigue life of welded tubular T-joints. The localization of these hot-spot stress zones, which are susceptible to cracking by means of fatigue, allows identifying the reinforcement solutions that ensure a long life cycle for offshore structures. Acknowledgements The present study has been made possible through a research fellowship from AER&DCS – Industries (specialised in structural analysis), at Metz University and the Douai Mining School. The authors would also like to thank Professor G. Pluvinage and the British industrialist for guidance provided and valuable suggestions made throughout the course of this research work. References [1] ARSEM. Guides pratiques sur les ouvrages en mer. Assemblages tubulaires soudés, Editions Technip; 1985. [2] Radenkovic D. Analysis of stresses in tubular joints. In: International conference, CECA-IRSID: l’Acier dans les structures marines, Paris; 1981. [3] Recho N, Brozzetti J. Concentration de contraintes dans les piquages de Tubes due à des sollicitations axiales. Rapport No. 10 – 002 – 6 CTICM; 1982. [4] Robert A, Bourdon C, Meziere Y. Analyse Photo-élastique et Numérique de la Concentration des contraintes dans les Noeuds Tubulaires. CECA-IRSID: l’Acier dans les structures marines, Paris; 1981. [5] Potvin AB, Kuang JG, Leick RD, Kahlich JL. Stress concentrations in tubularjoints. SPE Journal; 1977. [6] Ryan I. Comparaisons des diverses formules paramétriques de Coefficients de concentration de Contraintes. Rapport No. 10.002-2, CTICM; 1981. [7] Ryan I. Comparaisons Statistiques entre les CCC expérimentaux et les CCC selon les diverses formules paramétriques. Rapport No. 10.002-5, CTICM; 1982. [8] Rapport CNEXO-CTICM. Calcul Statique des Assemblages Tubulaires. Concentration des Contraintes dans les Assemblages Tubulaires. [9] Recommended practice for planning, designing and constructing fixed offshore platforms API RP2A. 19th ed. American Petroleum Institute: Washington DC; 1991. [10] Pang HLJ, Lee CW. Three-dimensional finite element analysis of a tubular Tjoint under combined axial and bending loading, Nanyang Technological University, MPE School, Elsevier. Int J Fatigue 1995;17(5):313–20. [11] Chang E, Dover WD. Stress concentration factor, parametric equations for tubular X and DT joints, Department of Mechanical Engineering, University College, London, WC1E 7JE, Elsevier. Int J Fatigue 1996;18(6):363–87. Jan.

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