propagation stage. Numerical results were compared with the experimental results in theliterature. It is found that numerical analysis is reliable and the boundary element method

nnecelines

Close form solutions for stress intensity factors are often insufcient for complicated practical components such as the cir-analysis is usuallye modelingptions or

e a semi-elcrack with a xed aspect ratio [10,11]. This is not true since the crack shape can change with the crack propagation. Ftests of transverse welded joints under bending revealed that the ratio of the crack depth to crack length on the surfaies with fatigue loading cycles [12]. The boundary element method (BEM) has been employed as an efcient numericalmethod to solve crack propagation together with the technique of dual boundary element method (DBEM) [1315]. This

0013-7944/$ - see front matter 2012 Elsevier Ltd. All rights reserved.

Corresponding author.E-mail addresses: t.chen@tongji.edu.cn, brucecht@gmail.com (T. Chen).

Engineering Fracture Mechanics 98 (2013) 4451

Contents lists available at SciVerse ScienceDirect

Engineering Fracture Mechanicshttp://dx.doi.org/10.1016/j.engfracmech.2012.12.010cular hollow steel tubes [8]. To solve this problem, numerical analysis has been employed. The numericalconducted with the nite element method and the crack shape and crack path have to be determined beforIt requires a very extensive 3D element mesh with crack tip elements. Therefore, different kinds of assumtests have to be conducted to nd out the crack shape and crack path. The crack is usually assumed to b[9,10].fatiguelipticalatiguece var-ally employed for design purpose [5]. However, small defects and initial cracks are inevitable for these welded connections.Fatigue life of the welded connections is identied as the crack propagation life [6]. Consider the fact that it is expensive tomanufacture specimens and conduct fatigue tests, numerical analysis for crack propagation is necessary to have a betterunderstanding of the welded connections. It is accepted that the fracture mechanics method is a reliable approach for thecrack growth life prediction under fatigue loading.

The crack propagation analysis is usually conducted with Paris law [7], and a reliable stress intensity factor (K) is required.Previous researches show that the stress intensity factors are difcult to obtain through experimental or theoretical analysis.Keywords:Boundary element methodCrack growth lifeWelded connectionsBending

1. Introduction

Fatigue performance of welded coloading. Based on fatigue tests, guidis suitable for estimating the fatigue crack growth life. 2012 Elsevier Ltd. All rights reserved.

tions is essential to the integrity of metallic structures that are subjected to fatiguehave been established for the welded connections [14]. Structural stress is usu-A boundary element analysis of fatigue crack growth for weldedconnections under bending

Tao Chen a,, Zhi-Gang Xiao b, Xiao-Ling Zhao c, Xiang-Lin Gu aaDepartment of Building Engineering, Tongji University, Shanghai 200092, Chinab School of Applied Sciences and Engineering, Monash University, Churchill, VIC 3842, AustraliacDepartment of Civil Engineering, Monash University, Clayton, VIC 3800, Australia

a r t i c l e i n f o

Article history:Received 5 July 2012Received in revised form 21 November 2012Accepted 20 December 2012

a b s t r a c t

Transverse llet welded joints and circular hollow section (CHS)-to-plate welded connec-tions were analyzed to obtain crack growth life under bending. Based on a 3D boundaryelement model, an initial semi-elliptical surface crack was embedded at the weld toe.Thereafter, crack propagation was performed with Paris law and strain energy density cri-terion. This method discards the assumption of constant aspect ratio of crack shape during

journal homepage: www.elsevier .com/locate /engfracmech

marking.

Nomenclature

a, c crack lengths in two directions for semi elliptical crackC, m material constants for Paris lawd tube diameter of CHS-to-plate welded connectionD bolt hole diameter of base plate in CHS-to-plate welded connectionh transverse attachment height of transverse welded jointK stress intensity factorKeff effective stress intensity factorKI stress intensity factor in (opening) mode IKII stress intensity factor in mode IIKIII stress intensity factor in mode III

T. Chen et al. / Engineering Fracture Mechanics 98 (2013) 4451 452. Geometry of the specimens

2.1. Transverse welded joints

The basic geometry of welded joint is shown in Fig. 1 [12]. It consists of a base plate with a thickness T and a width W. Atransverse attachment, which has a thickness ta and a height h, is welded to one side by llet welding with a 6 mm weld legmethod can efciently solve the crack growth problem since re-meshing is signicantly reduced during the crack growthprocess.

The purpose of this research is to numerically determine realistic crack growth lives for an initial surface crack at the weldtoe of transverse llet welded plate and circular hollow section (CHS)-to-plate welded connection under bending. Stressintensity factors were quantied at the crack tip. With Paris law and strain energy density criterion, fatigue crack growthlives were calculated and compared with fatigue test results. Crack patterns were also compared with available beach

W base plate width of transverse welded jointL base plate length of transverse welded jointN number of fatigue cyclesS nominal stresst tube thickness of CHS-to-plate welded connectionta transverse attachment thickness of transverse welded jointT base plate thickness of transverse welded jointlength. Four point bending fatigue tests were conducted on transverse llet welded joints to study the effect of the base platethickness. The middle part of the specimen was subjected to pure bending moment. Two specimens with the main platethickness of 9 mm and 34 mm, respectively, were selected to analyze. Values of 2.0 105 MPa and 0.3 were assumed forYoungs modulus and Poissons ratio in following simulations.

2.2. Circular hollow section (CHS)-to-plate welded connections

Circular hollow sections are popular in civil engineering for their superior structural properties [3,5]. Mashiri and Zhao[16,17] conducted fatigue tests in plane bending for CHS-to-plate welded connections. The welded connections were madefrom tubes of grade C350LO, which conform to the Australian Standard for Structural Steel Hollow Sections, AS1163-1991

L

T

ta6

h

W

a2c

Specimen

PC9PC34

T ta L W h

9 16 180 50 4034 16 400 90 40

Fig. 1. Geometry congurations of transverse welded joint (unit: mm).

plate of 10 mm thickness is bolted to the strong ground oor (Fig. 2). The tube is llet welded to the base plate with a

20 0

46 T. Chen et al. / Engineering Fracture Mechanics 98 (2013) 44514 mm weld leg length.

3. Fatigue life prediction[18]. The tubes have a specied Youngs modulus of 2.0 105 MPa and a specied Poissons ratio of 0.3. Three wall thick-nesses, which were 2.0 mm, 2.6 mm and 3.2 mm, respectively, of the circular hollow section were chosen. A square base

Cross section A-A

20 12

200

Weld bead

Fig. 2. Geometry congurations of CHS-to-plate welded connection (unit: mm).3.1. Fa

Thing. Wcommthe stThis msity fa

Th

wherethe ef

where

Keff,mastress

Wicalcul

DuplacemD =18

Tension side Compression side10A A450

t C8P 42.4 2.6C9P 42.4 2.0Loading pointP

12

62

d

Specimen

C7P

d t

48.3 3.2tigue crack growth analysis with boundary element method (BEM)

e boundary element method has been employed as an efcient way of numerical analysis for its boundary only mesh-ith DBEM technique, it can solve the cracked single domain and predict crack propagation without re-meshing. Theercial software package BEASY [15] has a wizard named Crack Growth that can fulll these functions. In this study,ress intensity factors are determined by J-integral approach [19]. The crack propagation life is integrated with Paris law.ethod can accurately predict the fatigue behavior and it is only dependent on material constants and the stress inten-ctors.e crack growth is predicted by Paris law, expressed as follows:

dadN

CDKeff m 1

a is the crack depth, N is the number of cycles for crack propagation life, C and m are the material constants, 4Keff isfective stress intensity factor range.

DKeff Keff;max Keff ;min 2

Keff is the effective stress intensity factor for mixed-mode problems, which is represented as [20]:

DKeff K I jK IIIj2 2K2II

q3

x and Keff,min are the maximum and the minimum effective stress intensity factor at the crack tip. KI, KII and KIII areintensity factors of mode I, mode II and mode III, respectively.th the previous equations, fatigue crack growth lives of the cracked specimens in mixed-mode conditions can beated with Paris law.ring the calculation, the crack propagation direction should be determined. It is dependent on the local stress and dis-ent eld under mixed loading conditions. It changes continuously with each step. The method to compute the growth

angle is based on strain energy density criterion [21]. The criterion assumes that a fracture spreads in the direction of theminimum strain energy density.

3.2. Model generation process

Model establishment is jointly fullled by ABAQUS nite element package and BEASY boundary element package. In therst step, nite element models are created and analyzed on un-cracked specimens. A critical node can be tracked after anal-ysis. Thereafter, the ABAQUS les of these models are transferred to BEASY model les with special BEASYABAQUS Wizard.Special care should be taken to check the loads and other boundary conditions. If some boundary conditions are lost duringthe transference, they need to be added in BEASY manually. Quadrilateral surface element is specied during modeling. ABA-QUS is used in creating the pre-crack models mainly because of its user-friendly and powerful preprocessing platform.

Compared to the complicated nite element modeling of crack shape [22], it is relatively easy to dene a crack in theBEASY. An initial crack can be dened in the un-cracked specimen with the special Crack Wizard module in the BEASY pack-age. The location of the crack is determined with the numerical analysis in ABAQUS. The maximum principal stress wasfound located on one node at the weld toe. This is consistent with the test results, in spite of the fact that several fatiguecracks emerged at the initial stage and coalesced into a single crack. For simplication, the initial crack is assumed to ema-nate from the node with the maximum principal stress at the weld toe. A semi-elliptical crack can be dened by initial cracksizes, a and c (Fig. 1). Here, a is crack depth and c is half crack length. The crack propagates with Paris law in depth andlength directions without xed ratio a/c. This is more reasonable compared to the xed aspect ratio in conventional niteelement analysis. Material parameters C and m are inputted before numerical analysis. Increment steps and increment sizeare also dened after several trials. The les of results in BEASY are converted to the le format that can be displayed in theABAQUS. This is convenient for display of crack pattern in the post process.

T. Chen et al. / Engineering Fracture Mechanics 98 (2013) 4451 47Table 1Fatigue crack growth results of transverse llet welded joints (nominal stress range = 100 MPa).

Increment PC9 PC34

N DN a (mm) c (mm) N DN a (mm) c (mm)

0 0 0 0.10 0.10 0 0 0.10 0.101 989460 989460 0.43 1.17 1426821 1426821 0.90 2.642 1417797 428338 0.96 1.60 1736207 309386 1.72 3.473 1988565 570768 1.35 2.52 2148541 412334 2.81 5.174 2642860 654295 1.78 3.39 2525813 377272 3.96 7.285 3255278 612418 2.14 4.30 2829809 303996 5.00 9.226 3820917 565639 2.47 5.32 3105025 275216 5.98 11.257 4417627 596710 2.84 6.32 3361359 256334 6.98 13.198 4889065 471438 3.14 7.27 3633375 272016 7.93 15.449 5257618 368553 3.42 8.22 3897456 264081 8.81 17.81

10 5703636 446017 3.76 9.23 4149273 251817 9.67 20.1011 6082890 379255 3.94 10.19 4382042 232769 10.46 22.5212 6386468 303577 4.11 11.10 4547593 165551 11.05 26.2813 6646182 259715 4.19 11.96 4684380 136787 11.65 29.1714 6918448 272266 4.33 12.85 4810922 126542 12.42 31.6315 7403647 485198 4.49 13.64 4916492 105570 13.13 34.0116 8046777 643131 4.59 14.43 5007478 90986 13.70 36.4117 8549238 502461 4.70 15.15 5084611 77133 14.10 38.3018 9370276 821038 4.85 15.97 5138779 54168 14.48 40.3419 NA NA NA NA 5172276 33497 14.92 42.234. Results and discussions

4.1. Fatigue life of transverse welded joints under bending

As described in the previous section, the transverse welded joint models were created and analyzed. Material related con-stants, C and m, for Paris law were taken as 3.98 1013 (da/dN in mm/cycle and K in N/mm3/2) and 2.88 [4,23]. The con-stants were chosen for consistency with the previous work of the authors [23]. An initial semi-elliptical crack ofa = c = 0.1 mm was dened at a location based on numerical analysis by ABAQUS.

Table 1 gives the total number of cycles, incremental cycles and crack sizes at each increment for specimens PC9 and PC34under a pure bending moment that can introduce the maximum nominal tensile stress range of 100 MPa on the plate sur-face. It is observed that cracks propagated faster in the surface direction than in the depth direction. With regard to specimenPC9, the crack depth propagated to 3.76 mm, i.e. 42% of the thickness, after 10th increment and terminated at 4.85 mm (54%of the thickness) after 18th increment. The numerical analysis terminated due to convergence problems. With regard tospecimen PC34, the crack depth propagated to 9.67 mm (28% of the thickness) after 10th increment and terminated at

14.92 mm (44% of the thickness) after 19th increment. The crack propagated very fast in the nal stage, and fatigue failure ofwelded joints is dened when the crack propagates to 40% of the plate thickness in Ref. [24]. It is therefore appropriate totake the numerical results when 4050% of the plate thickness has cracked as the nal fatigue life.

The SIFs determined by the J-integral approach, which are essential to estimate the crack propagation analytically, wereplotted with the normalized crack fronts for specimen PC9 in Fig. 3. The stress intensity factors of KI and Keff were nearlysymmetrical with respect to the crack center and reached the maximum values at crack ends on the surface. The stress inten-sity factors of KII and KIII were negligibly small in comparison with KI. Similar trend was also observed for specimen PC34. Theresults indicate that mode I (opening mode) is the primary fracture mode.

A comparison of measured and simulated crack shapes near the weld seam is given in Fig. 4. The ratio between two semi-axes, a/c, changed from the initial value of 1.0 to 0.4 (in the 10th increment) and 0.3 (in the 18th increment). This indicatedthat the crack aspect ratio kept changing instead of being constant as assumed by most researches. The nding was veriedby comparison with the beach marks taken from experimental observations [12].

The results of LEFM calculations are plotted with the fatigue test data of transverse llet welded joints under bending inFig. 5. The estimated results are in agreement with the thickness effect, i.e., the fatigue strength decreases with the increaseof plate thickness. The predicted SN curve of PC9 is below all the fatigue data of this series while the predicted SN curve ofPC34 is close to the mean value of the fatigue test data.

4.2. Fatigue life of CHS-to-plate welded connections under in plane bending

300

48 T. Chen et al. / Engineering Fracture Mechanics 98 (2013) 4451Normalized crack front0.0 0.2 0.4 0.6 0.8 1.0

Stre

ss in

tens

ity fa

ctor

(MPa

mm1

/2)

-50

0

50

100

150

200

250Keff

KI

KII

KIII

10th increment (a=3.76mm, c=9.23mm)

Normalized crack front0

1

Fig. 3. SIFs along the crack fronts for PC9 (nominal stress range = 100 MPa).In this section, thin-walled CHS-to-plate welded connections were analyzed with the boundary element method. Basedon the fatigue test results of Mashiri and Zhao [16,17], cracks initiated along the weld toe on the tube tension side surface oftube plate weld connection and were observed as surface cracks. With the fatigue loading being applied, the cracks propa-gated into the thickness of the tube and became through-thickness cracks. Finally, cracks extended along the circumferenceof tube and broke the weld connection. In the numerical modeling, only one surface crack was dened before it reachedthrough thickness. Corresponding fatigue life was calculated and compared to the fatigue test results of the joints underin-plane bending at a stress ratio of 0.1.

The values for material constants of Paris law were chosen from the conservative curves as recommended by the Japa-nese Society of Steel Construction. They were taken as C = 2.02 1012 (da/dN in mm/cycle and K in N/mm3/2) and m = 2.75[1]. The constants are chosen to include the high tensile residual stress induced by welding process which is critical to thin-walled tubular connections. An initial semi-elliptical crack with a = c = 0.1 mm was dened as in the previous sections.

The total number of cycles, incremental cycles and crack sizes were tabulated in Table 2 for three series of CHS-to-platewelded connections under in plane bending. The surface crack propagated with the increments. With regard to specimenC7P, the crack depth propagated to 2.06 mm after 5th increment, being about 64% of the thickness, and terminated at3.02 mm after 8th increment, being about 94% of the thickness. With regard to specimen C8P, the crack depth propagatedto 1.71 mm after 5th increment, being about 66% of the thickness, and terminated at 2.48 mm after 8th increment, beingabout 95% of the thickness. With regard to specimen C9P, the crack depth propagated to 1.33 mm after 5th increment, beingabout 67% of the thickness, and terminated at 1.99 mm after 8th increment, being about 99.5% of the thickness.

Stress intensity factors are important to crack growth rate and fatigue mechanism in the welded connections. They werecalculated with J-integral method and graphed in Fig. 6. Comparisons with various stress intensity factors indicated that themixed mode crack growths are mainly dominated by mode I crack growth.

(a) Numerical simulations (Nominal stress range =100MPa)

10th

a=3

(b) Beach marks from Mikis fatigue tests

in.76

cre

m

men

m, c

t

=9.23 mm

10mm

1a

8th i=4.

ncr

85 em

mm,

ent

c=15.97 mm

Fig. 4. Fracture modes of specimen PC9 (nominal stress range = 100 MPa).

Number of cycles105 106 107

Nom

inal

stre

ss ra

nge

(MPa

)

100

Transverse weled joints PC9 (T=9 mm)Transverse weled joints PC34 (T=34 mm)

PC9PC34

200

300

400

80

60

40

20

Fig. 5. Test data and BEM simulations of transverse welded joints.

Table 2Fatigue crack growth results of CHS-to-plate welded connections (nominal stress range = 70 MPa).

Increment C7P C8P C9P

N DN a (mm) c (mm) N DN a (mm) c (mm) N DN a (mm) c (mm)

0 0 0 0.10 0.10 0 0 0.10 0.10 0 0 0.10 0.101 460732 460732 0.43 1.15 491896 491896 0.37 0.94 515209 515209 0.30 0.752 655492 194760 0.91 1.66 705817 213921 0.77 1.34 752575 237366 0.60 1.063 828399 172907 1.30 2.55 903789 197972 1.07 2.03 960106 207531 0.86 1.634 986144 157744 1.69 3.31 1075585 171796 1.40 2.73 1133822 173716 1.10 2.125 1119154 133010 2.06 4.32 1225766 150181 1.71 3.49 1296476 162654 1.33 2.736 1234466 115312 2.41 5.19 1350140 124373 1.97 4.17 1434193 137717 1.55 3.247 1339597 105131 2.72 6.19 1454838 104698 2.21 4.95 1552160 117968 1.77 3.878 1429313 89716 3.02 7.19 1552251 97414 2.48 5.73 1661794 109634 1.99 4.45

T. Chen et al. / Engineering Fracture Mechanics 98 (2013) 4451 49

50 T. Chen et al. / Engineering Fracture Mechanics 98 (2013) 4451Pa m

m1/2

)

200

250Keff

KIWith illustrations of simulated crack patterns for specimen C9P in Fig. 7, it was observed that the surface crack propa-gated with the number of fatigue cycles. The crack patterns are in good agreement with the results of the experimental study[17]. It nearly penetrated through the thickness at the last step.

The results obtained with the aforementioned procedure have been compared with fatigue test data as graphed in Fig. 8.Due to the unavailability of through-thickness fatigue lives for the three series of specimens, the estimated fatigue lives were

Stre

ss in

tens

ity fa

ctor

(M

Normalized crack front0.0 0.2 0.4 0.6 0.8 1.0

-50

0

50

100

150

KII

KIII5th increment (a=1.33 mm, c=2.73mm)

Normalized crack front

01

Fig. 6. SIFs along the crack fronts for C9P (nominal stress range = 70 MPa).

5t

a

th in

=1.3ncre

33 memen

mm

nt

m, c==2.773 mmm 8a

8th ina=1.

ncre

99 memen

mm

nt

m, c==4.445 mmm

Fig. 7. Fracture modes of specimen C9P (nominal stress range = 70 MPa).

Number of Cycles104 105 106 107

Nor

min

al st

ress

rang

e (M

Pa)

100

CHS-to-plate welded connections C7P (t=3.2 mm)CHS-to-plate welded connections C8P (t=2.6 mm)CHS-to-plate welded connections C9P (t=2.0 mm)

C8PC7P

C9P

Mean

Mean-2S

200

300

400

80

60

40

20

Fig. 8. Test data and BEM simulations of CHS-to-plate welded connections.

compared with the nal fatigue lives. The nal fatigue live was dened as the number of cycles when the crack propagated to

T. Chen et al. / Engineering Fracture Mechanics 98 (2013) 4451 51a length equal to half of the circumference of the tube during the fatigue experiments [16,17].It was observed that the fatigue test data points were mostly above the predicted SN curves. This is reasonable since the

predicted fatigue lives were obtained with the surface crack model. The model cannot obtain the further crack propagationlife after penetration of the tube thickness. The other reason is that conservative material constants were used in Paris law.Comparison with the tting curves of the fatigue test data obtained with the least squares method shows that the predictedSN curves are located between the mean curve and the mean-2s (mean-2 standard deviation) curve of the test data. It wasalso shown by the simulation that the increase of tube wall thickness resulted in fatigue strength decrease. This is in agree-ment with the previous researches [2,25]. The conclusion is that fatigue assessment on the crack propagation life of thiswelded connection can be determined by using the boundary element method.

5. Conclusions

In this paper, the boundary element method was employed to analyze the fatigue crack growth lives of welded connec-tions under bending. Paris law and strain energy density criterion were adopted during analysis. Thereafter, crack patternsand fatigue crack growth life were calculated and compared with available experimental results.

The fatigue crack growth simulations of transverse llet welded joints under bending revealed that the surface crack atweld toe propagated faster in the surface direction than in the thickness direction. The aspect ratio decreased as the crackdeveloped. The assumption of constant aspect ratio is not valid for the transverse llet welded joints under bending. CHS-to-plate welded connections under in plane bending were also analyzed with 3D BEM models. The estimated SN curveswere between the mean curve and the mean-2s curve obtained from fatigue test data. The numerical results also reectthe thickness effect.

Acknowledgments

This project was supported by ARC Discovery Project, Australia and Kwang-Hua Fund for College of Civil Engineering, Ton-gji University. The rst author was partially supported by the China Scholarship Council during his visiting to the Depart-ment of Civil Engineering, Monash University, Australia.

References

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[2] Hobbacher A. Recommendations for fatigue design of welded joints and components. IIW document XIII-2151-07/XV-1254-07. WRC bulletin 520, TheWelding Research Council, New York; 2009.

[3] Zhao XL, Herion S, Packer JA, Puthli RS, Sedlacek G, Weynand K, et al. Design guide for circular and rectangular hollow section joints under fatigueloading. Cologne, Germany: Verlag TUV Rheinland GmbH; 2001.

[4] British standards institution (BSI). BS 7910:2005 Guide to methods for assessing the acceptability of aws in metallic structures. British StandardInstitution, London; 2005.

[5] van Wingerde AM, Packer JA, Wardenier J. Criteria for the fatigue assessment of hollow structural section connections. J Constr Steel Res1995;35(1):71115.

[6] Hobbacher AF. The new IIW recommendations for fatigue assessment of welded joints and components a comprehensive code recently updated. Int JFatigue 2009;31(1):508.

[7] Paris P, Erdogan F. A critical analysis of crack propagation laws. Trans ASME, J Basic Engng 1963;85(4):52834.[8] Hobbacher A. Stress intensity factors of welded joints. Engng Fract Mech 1993;46(2):17382.[9] Lee MM, Bowness D. Estimation of stress intensity factor solutions for weld toe cracks in offshore tubular joints. Int J Fatigue 2002;24(8):86175.[10] Newman J. An empirical stress-intensity factor equation for the surface crack. Eng Fract Mech 1981;15(12):18592.[11] Ferreira JM, Pereira AH, Branco CM. A fracture mechanics based fatigue life prediction for welded joints of square tubes. Thin Wall Struct

1995;21(2):10720.[12] Miki C, Mori T, Sakamoto K, Kashiwagi H. Size effect on the fatigue strength of transverse llet welded joints. J Struct Eng, JSCE 1987;33A:393402.[13] Yang ZM, Lie ST, Gho WM. Fatigue crack growth analysis of a square hollow section T-joint. J Constr Steel Res 2007;63(9):118493.[14] Citarella R, Cricr G. Comparison of DBEM and FEM crack path predictions in a notched shaft under torsion. Eng Fract Mech 2010;77(11):173049.[15] BEASY. BEASY V10r12 documentation, computational mechanics. BEASY Ltd., Southampton; 2009.[16] Mashiri FR, Zhao XL. Thin circular hollow section-to-plate T-joints: stress concentration factors and fatigue failure under in-plane bending. Thin Wall

Struct 2006;44(2):15969.[17] Mashiri FR, Zhao XL. Fatigue tests and design of thin CHS-plate T-joints under cyclic in-plane bending. Thin Wall Struct 2007;45(4):46372.[18] Standards Association of Australia (SAA). Structural steel hollow sections, Australian standard AS1163-1991. Standards Association of Australia,

Sydney, Australia; 1991.[19] Anderson TL. Fracture mechanics: fundamentals and applications. Florida: CRC Press; 2005.[20] Mi Y. Three-dimensional analysis of crack growth. Southampton UK and Boston: Computational Mechanics Publications; 1996.[21] Sih G. Mechanics of fracture initiation and propagation: surface and volume energy density applied as failure criterion. Dordrecht: Kluwer Academic

Publishers; 1991.[22] Lee C, Chiew S, Lie S, Ji H. Fatigue behaviors of square-to-square hollow section T-joint with corner crack. II: numerical modeling. Eng Fract Mech

2007;74(5):72138.[23] Xiao ZG, Chen T, Zhao XL. Fatigue strength evaluation of transverse llet welded joints subjected to bending loads. Int J Fatigue 2012;38(1):5764.[24] Mori T, Zhao XL, Grundy P. Fatigue strength of transverse single-sided llet welded joints. Aust Civ/Struct Trans 1997;1(2):95105.[25] Berge S. On the effect of plate thickness in fatigue of welds. Eng Fract Mech 1985;21(2):42335.

A boundary element analysis of fatigue crack growth for welded connections under bending1 Introduction2 Geometry of the specimens2.1 Transverse welded joints2.2 Circular hollow section (CHS)-to-plate welded connections

3 Fatigue life prediction3.1 Fatigue crack growth analysis with boundary element method (BEM)3.2 Model generation process

4 Results and discussions4.1 Fatigue life of transverse welded joints under bending4.2 Fatigue life of CHS-to-plate welded connections under in plane bending

5 ConclusionsAcknowledgmentsReferences