FATIGUE CRACK PROPAGATION AND

STRENGTH OF WEB-GUSSET WELDED JOINTS UNDER VARIED PRINCIPAL STRESS DIRECTION

Takeshi MORI1 and Shigeyuki HIRAYAMA2

1Fellow of JSCE, Professor, Dept. of Civil and Environmental Eng., Hosei University (2-33, Ichigaya-tamachi, Shinjuku-ku, Tokyo 162-0843, Japan)

E-mail: mori@hosei.ac.jp 2Member of JSCE, Dept. of Technology Development, Highway Technology Research Center

(3-10-11, Toranomon, Minato-ku, Tokyo 105-0001, Japan) E-mail: s.hirayama@tecmex.or.jp

The direction of the principal stress on web-gusset welded joint connected to a main girder web of steel girder bridges changes instantaneously so that the direction of shear stress reverses when a vehicle passes right above there. It is well known that the fatigue crack initiates and propagates in the direction perpen-dicular to the principal stress one, but fatigue crack propagation behavior and fatigue strength when the direction of principal stress changes have not been studied yet. In this study, to determine the propagation behavior and the fatigue strength in the stress field where the direction of the principal stress changes, fa-tigue tests on girder specimens and fatigue crack propagation analyses have been performed. Key Words : variation in principal stress direction, web-gusset welded joint, fatigue crack propagation

1. INTRODUCTION

According to a document issued by the Japanese Ministry of Land, Infrastructure and Transport1), there are about 160,000 highway bridges that are more than 15m long. Steel bridges accounted for 40%, and girder-type bridges accounted for 90% of these highway bridges. The major cases of fatigue damage that occurred in I-sectioned girder bridges are as follows: 1) the crack initiated from the weld toe of the sole plate, 2) the crack initiated from the Gelber hinge portion, 3) the crack initiated from the girder end cut-out with arc-shaped flange, 4) the crack initiated from the web-gap plate located be-tween the upper flange of the main girder and the upper flange of the crossbeam, and 5) the crack ini-tiated from the gusset plate connected to the main girder web2).

The fatigue crack initiated from the main girder web connected with the lower flange of the cross-beam or the lower lateral member (hereinafter, referred to as intersection) in I-sectioned steel bridges indicates serious damage, because fatigue cracks propagate perpendicular to the direction of main girder stress. If cracks propagated toward the vertical direction, it might cause the collapse of the bridge. In

October 2006, a 1m-long fatigue crack was discov-ered at the intersection. It caused traffic to be closed at Meihan national highway for several months.

Fatigue strength of the intersection has been gen-erally examined through fatigue tests under uni-axial loading condition using web-gusset welded joint specimens. On the basis of these results, the fatigue strength category of welded joints has been specified in “Fatigue Design Recommendations for Steel Structures”3) issued by Japan Society of Steel Con-struction. The intersection is subjected to bi-axial forces induced by cross-beam flange force due to the load distribution function and the main girder web force due to in-plane bending4)6). In addition, the maximum principal stress direction of the main girder web at the intersection changes, because the direction of shear stress is reversed by the passage of trucks.

Fig.1 shows variations in normal stress of the x-direction, shear stress, maximum principal stress, and principal stress direction at the center of the span, when the load of 100kN is running. In this way, the direction of the shear stress is reversed when the load is passing above the center, the principal stress di-rection changes instantly. In the combined stress field of normal stress and shear stress, fatigue cracks

Journal of JSCE, Vol. 3, 128-139, 2015(Originally published in Journal of Japan Society of Civil Engineers, Ser. A1, Vol. 69, No. 2, 245-256, 2013 in Japanese)

128

propagate perpendicular to the direction of maximum principal stress, and stress for fatigue assessment could be evaluated by the variable range of principal stress. However, it has not been clarified how fatigue cracks propagate under the field of changing princi-pal stress direction. In addition, there are few dis-cussions on the fatigue evaluation method under this field.

The authors have studied how varying principal stress directions affect fatigue strength of web-gusset welded joints. This was done through bi-axial fatigue tests under in-phase and anti-phase using web-gusset specimens. The results have indicated that the in-fluence of variations in principal stress direction could be evaluated using principal stress range (range between maximum principal stress and minimum stress along the direction of maximum principal stress)7). When the ratio of shear stress to normal stress is equal to 0.87 (variation in maxium principal stress direction is equal to 60 degrees) or more, the minimum principal stress reflected on the maximum principal stress direction is reversed, and the princi-pal stress range is larger than the variation range of maximum principal stress. However, the fatigue tests using the specimens, even if the bi-axial fatigue tests under anti-phase could be conducted, showed that the

variation of the principal stress direction was limited to 90 degrees. That is to say, it is difficult to simulate the stress field on actual plate-girder bridges.

In this study, for the purpose of confirming fatigue crack propagation property and evaluating the in-fluence of the variation in princip al stress direction on fatigue strength of web-gusset welded joints, fa-tigue tests using different principal stress directions have been performed using girder-type specimens. In the fatigue tests, the stress field in which the direction of principal stress changed was produced by alterna-tive loading at two points across the web-gusset. However, it was not possible to produce a stress field where the direction of principal stress was changed instantaneously. This study seems useful in com-firming fatigue crack propagation property and fa-tigue strength under the stress field. 2. SPECIMENS

Fig.2 shows a fatigue test specimen. The length of specimen is 7.0m, and the height is 424mm. Two specimens (specimens A and B) were manufatuc-tured. The thickness of flange was 12mm, and the thickness of web was 9mm. Seven sets of gusset

Fig.1 Stress variation induced by running load.

y

x

8000

4000

1000

x

y

unit : mm

Focus Point

8000

6.46

6.09

10.131

.0

-31.

0-6

.09

Axial Stress σx (N/mm2)

Shear Stress τxy (N/mm2)

Maximum Principal Stress σmax (N/mm2)

Direction of Maximum Principal Stress φ (deg.)

100kN

794

150

1510

41

300

330

Direction of Maximum Principal Stress (deg.)

φ

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plates were attached to both surfaces (north face and south face) of the web. These gussets from the west side are called WG1 ~ WG7. Each gusset plate has two boxing welds that appear to be fatigue cracks in origin. In this study, each gusset plate is labeled; e.g., WG4-EN (gusset plate:WG4, east side and north face) at each boxing weld.

Steel used for the specimens was SM490YA, 9mm thick (web, gusset) and SM490YB, 12mm thick (flange). Table 1 shows the mechanical properties and chemical composition of the steel. Gusset plates were connected to the web by fillet welding using CO2 arc procedure. Fillet welding was performed using flux-cored wire MX-Z200 (JIS Z 3313) with a diameter of 1.2mm. The welding conditions were as follows: welding voltage = 32V, current = 230A, and speed = 26-27cm/min. Weld profiles at each boxing weld were measured before the fatigue tests. Meas-ured weld profiles were leg length, frank angle and toe radius at weld toe on web side. After removing any dirt or rust, molds of weld bead were taken using

dental impression material (hydrophilic vinyl sili-cone impression material), and sliced to a thickness of about 2mm. Thereafter, these sliced molds were measured using a 20x magnifying projector. The number of measurements was 336. The average of weld leg length was 13.8mm on the web side, and 8.2mm on the gusset side. The average of the frank angle and the toe radius was 130 degrees and 0.75mm, respectively. 3. TEST PROCEDURE

Photo 1 shows the test set-up. Specimens have two loading points as shown in Fig.2. Two loading points were called actuator W and actuator E. In the fatigue test, variations in principal stress at the boxing weld on WG3 ~ WG5 induced by reversing shear force were produced by alternative loading with two actu-ators.

When actuators W and E were applied alternately

250 2250 2000 2250 250

1240

012

200 200 200 200 350 200 350 200 350 200 350 200 200 200 200 1300

WG1 WG2 WG3 WG4 WG5 WG6 WG7

1300 300 100300100A

A

C

C

B

B

250

123

00

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9

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70

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30

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022

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300

A-A B-B C-C

Actuator W Actuator E West Side East Side

North Face

South Face

250

Fig.2 Shape and size of specimen.

Table1 Mechanical properties and chemical composition of steel.

Steel Type Thickness

(mm)

Mechanical Properties Chemical Compositions (%)

Yield Stress

(N/mm2)

Tensile Strength (N/mm2)

Elon- gation

(%)

C ×100

Si ×100

Mn ×1000

P ×1000

S ×100

Cu ×100

Ni ×100

Cr ×100

SM490YA 9 420 550 27 16 24 143 12 3 1 1 2

SM490YB 12 436 559 24 16 22 145 19 6 - - -

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before fatigue tests, the magnitude and direction of principal stress in the vicinity of boxing weld in specimens A and B were measured. These meas-urements used rosette strain gauges (gauge length 3mm) attached 5mm from the weld toe. Strain gauges were attached at both sides (north side, south side) of WG1-W, WG3-W and E, WG4-W and E, WG5-W and E, WG7-W.

The fatigue tests were conducted under the condi-tion that the two actuators alternately loaded 220kN (specimen A) or 200kN (specimen B) as the maxi-mum load. The minimum load was set at 0 in both specimens A and B. Cyclic loading speed was 0.5Hz. Therefore, the time required for one cycle of the alternative loading between actuator E and actuator W was 4 seconds. Fatigue tests were carried out until crack length became 50mm or more and were con-ducted as long as possible. In addition, when the crack length became 70mm or more, it was repaired by drilling a stop-hole with a diameter of 18mm at the crack tip and tightened with high-strength bolt JIS F10T-M16 on the stop-hole. 4. STRESS PROPERTIES (1) Stress properties calculated by beam theory

Table 2 shows nominal longitudinal stress σx, shear stress τxy, and the maximum principal stress σmax, the minimum principal stress σmin, the direc-tion of σmax calculated by the beam theory at the weld toe of each gusset plate (the definition of direction is shown in Fig.1). Here, weld leg length on the web side was set to 14mm, the load was assumed to be 220kN, which was the same as the load in the case of the fatigue test of specimen A. The right-hand col-umn of the table shows the variations in the maxi-mum principal stress direction in the case of alterna-

tive loading with actuators W and E. In WG1, WG2, WG6, and WG7 located outside the loading points, there was no variation in the principal stress direction by alternative loading. Variations in the principal stress direction in WG3 ~ WG5 was about 30 de-grees. As mentioned in Chapter 1, this variation in the maximum principal stress direction made no difference between the maximum principal stress range mentioned above and the variation range in maximum principal stress.

As mentioned above, fatigue tests were conducted by applying alternative load of actuator W and actu-ator E. In other words, cyclic load of 0→220kN→0 was applied by actuator W in specimen A, then the cyclic load was applied by actuator E. Therefore, instantaneous changes in principal stress direction by the moving load as shown in Fig.1 could not be produced in this fatigue test. (2) Influence of presence of gusset plate on stress

properties at weld toe As the direction of principal stress seemed to be

different between theoretical value and the value

Table 2 Stress at weld toe of boxing weld calculated by beam theory (specimen A).

WG1-W 68.2 39.8 86.5 -18.3 -24.7 36.1 21.1 45.8 -9.7 -24.7 0

WG1-E 79.1 39.8 95.6 -16.5 -22.6 41.9 21.1 50.6 -8.8 -22.6 0

WG2-W 87.2 39.8 102.6 -15.4 -21.2 46.2 21.1 54.3 -8.2 -21.2 0

WG2-E 98.1 39.8 112.2 -14.1 -19.5 51.9 21.1 59.4 -7.5 -19.5 0

WG3-W 97.6 -21.1 102 -4.4 11.7 64.9 21.1 71.1 -6.2 -16.5 28.2

WG3-E 93.6 -21.1 98.1 -4.5 12.1 76.8 21.1 82.2 -5.4 -14.4 26.5

WG4-W 83.9 -21.1 88.9 -5 13.3 78.9 21.1 84.3 -5.3 -14 27.3

WG4-E 78.9 -21.1 84.2 -5.3 14 83.9 21.1 88.9 -5 -13.3 27.3

WG5-W 76.8 -21.1 82.2 -5.4 14.4 93.6 21.1 98.1 -4.5 -12.1 26.5

WG5-E 64.9 -21.1 71.1 -6.2 16.5 97.6 21.1 102 -4.4 -11.7 28.2

WG6-W 51.9 -21.1 59.4 -7.5 19.5 98.1 -39.8 112.2 -14.1 19.5 0

WG6-E 46.2 -21.1 54.3 -8.2 21.2 87.2 -39.8 102.6 -15.4 21.2 0

WG7-W 41.9 -21.1 50.6 -8.8 22.6 79.1 -39.8 95.6 -16.5 22.6 0

WG7-E 36.1 -21.1 45.8 -9.7 24.7 68.2 -39.8 86.5 -18.3 24.7 0

Variation ofDirectionDirection

(deg.)Direction

(deg.)σx

(N/mm2)

τxy

(N/mm2)

σmax

(N/mm2)

σmin

(N/mm2)

σx

(N/mm2)

τxy

(N/mm2)

σmax

(N/mm2)

σmin

(N/mm2)

Position ofGusset

Actuator W Actuator E

Variation in Direction

Photo 1 Test set-up.

131

when attaching the gusset plate to the web, 3D FE analyses were performed on the girder-type speci-men. In the analyses, a hybrid model combining solid elements around the gusset plate with shell elements in the other parts was used8). Modeling the weld profile was conducted using the following values. In the web side, leg length was set to 14mm, toe radius was set to 0.75mm and frank angle was set to 130 degrees. In the gusset plate side, leg length was set to 8mm and flank angle was set to 130 degrees. These values were based on the measurement results of the weld profiles. Minimum element size around the weld toe was set to 0.2mm. An example of the ana-lytical model is shown in Fig.3. For comparison, the analysis using the model without gusset plate was also carried out.

Fig.4 shows maximum principal stress in the vi-cinity of the boxing weld of WG5-W. The presence of the gusset plate caused maximum principal stress that increased at the weld toe. Forthermore, the di-rection of maximum principal stress changed due to the presence of the gusset plate. However, the mag-nitude and direction of principal stress at distant point from the weld toe was almost the same regardless of the presence of the gusset plate. (3) Stress measurement results

Fig.5 (a) and (b) show a comparison of the mag-nitude and direction of maximum principal stress obtained from stress measurement with those ob-tained from FE analyses. The magnitude and direc-tion of principal stress in these figures are obtained at 5mm apart from the weld toe. The load applied for specimen A was 220kN, and 200kN for specimen B. Therefore, the magnitude of principal stress in specimen B was converted into the value in the case of 220kN by multiplying by 1.1. The magnitude and direction of the maximum principal stress, which was

obtained from the stress analysis without gussets, were almost identical to those obtained from the beam theory shown in Table 2.

In Fig.5, the vertical axis shows the value obtained from the FE analyses, and the horizontal axis shows the value obtained from stress measurement. The magnitude and direction of the principal stress ob-tained from the FE analyses had good agreement with the stress measurement results in the case of the at-tached gusset plates. This fact could indicate that FE analyses under these conditions could produce the stress properties near the gusset plate. On the other hand, the analytical result in the no-gusset case was remarkably different from the stress measurement results.

5. OUTLINE OF FATIGUE TEST RESULTS

The fatigue test using specimen A was conducted until the number of cyclic load reached 1.33 million cycles. Here, an alternative loading by two actuators was counted as the number of cyclic load.

At WG1-W, the occurrence of fatigue cracks was not observed at the time of 1.33 million cycles. At other gusset plates, the fatigue cracks were observed.

At WG4-W, fatigue cracks of 27mm and 12mm length were detected at the weld toes of the north and south face of the web in 418,000 cycles. In 365,000 cycles after detecting fatigue cracks (the total number of cyclic load was 783,000 cycles), the fatigue crack propagated to 78mm at the south face and 71mm at the north face. Then the stop-hole was drilled at the crack tip of the lower side, and tightened with a high-strength bolt on the stop-hole. Bolt tightening was carried out using the calibrated wrench tighten-ing method in order to introduce the specified axial force. Fatigue test was conducted until 212,000 cy-

10mm

Present Gusset

Absent Gusset

Fig.4 Influence of gusset plate on direction of principal stress.

W

E

Fig.3 Example of FE model.

132

cles (the total number of cyclic load was 995,000 cycles). Then fatigue cracks on the upper side were repaired by drilling and bolting the stop-hole in the crack length of 108mm at the south face and in the crack length of 101mm at the north face. The crack length on the upper side was calculated based on the crack tip on the lower side. The crack length shown here was reflected on the vertical direction of the specimen. At the other cracks, similar repairs were carried out.

For specimen B, the fatigue test was carried out up to about 2 million cycles. Fatigue cracks were initi-ated at the weld toe of the gusset plates except for WG1-W and WG2-E. These cracks were repaired using the same procedure used in specimen A.

Table 3 shows the crack length at each gusset plate at the time of crack detection and repair, and at the completion of fatigue test. In specimen A, 12 fatigue cracks were initiated at the longitudinal welded joint between the web and the lower flange. These cracks were repaired by attaching plates on the cracks. The crack at the longitudinal welded joint between the web and the upper flange was also detected within 520,000 cycles. Photo 2 shows examples of repairing

these cracks. The stress properties of the weld toe of the boxing weld seemed to change with these repairs.

The nominal stress range at the longitudinal welded joint appeared to be twice as large as that at the gusset. Though the longitudinal welded joint in specimen A was connected by fillet welding, weld defects were not seen on the fatigue fracture surface. On the other hand, fatigue cracks did not occur at the longitudinal welded joint in specimen B because the flange was welded to the web with full penetration in order to prevent the fatigue cracks from the weld root. 6. PROPAGATION PROPERTIES OF FA-

TIGUE CRACKS

Some examples of the fatigue cracks that occurred at the web gusset welded joints are shown in Photo 3. Photos 3 (a) and (d) show fatigue cracks initiated at the welded joints under the constant direction of prin-cipal stress. Photos 3 (b), (c), (e), and (f) show the fatigue cracks initiated at the welded joint under

0 20 40 60 80 100 120 140 160 180 2000

20

40

60

80

100

120

140

160

180

200

Stress Obtained from Stress Measurement (N/mm 2)

Stre

ss O

btai

ned

from

Str

ess

Ana

lysi

s (N

/mm2 )

Specimen A

Specimen B

GussetPresent Absent

(a) Magnitude of Principal Stress

−30 −20 −10 0 10 20 30−30

−20

−10

0

10

20

30

Direction Obtained from Stress Measurement (deg.)

Dir

ecti

on O

btai

ned

from

Str

ess

Ana

lysi

s (d

eg.)

Specimen A

Specimen B

GussetPresent Absent

(b) Direction of

Principal Stress

Fig.5 Comparison between stress analyses and stress measurement.

Photo 2 Fatigue crack initiated at longitudinal welded joint and examples of repair.

133

the varied directions of principal stress. The fatigue crack propagating path in these pictures was high-lighted for easy identification of these cracks. At each case, the fatigue crack was initiated at the weld toe of the boxing weld, and propagated to the web. The dotted line shows the direction of the fatigue crack propagating path based on the assumption that the fatigue crack propagated perpendicular to the direction of principal stress. The red dotted line shows the propagating direction of the crack guring the loading at the larger principal stress side. On the other hand, the white dot-ted line shows the propa-gating direction of the crack during the loading at the smaller principal stress side. The direction of prin-cipal stress shown here was calculated using the beam theory without considering the influence of the gusset.

As shown in Photo 3 (a) and (d), the fatigue cracks propagated perpendicular to the direction of principal stress under the constant direction of principal stress. This behaivor was the same as that of the previous

knowledge. In WG5-ES of specimen B, the crack propagating

path was almost the same as the direction predicted from the direction of the larger principal stress (loading at actuator E in this case) as shown in Photo 3 (f). However, the fatigue cracks shown in Photos 3(b), 3(c), and 3(e) propagate in a zigzag direction. These directions were not perpendicular to the di-rection of principal stress. In addition, these cracks diverged into two directions. Furthermore, the propagating paths of some cracks were different from the path predicted by the direction of principal stress. Table 4 shows the feature of the fatigue crack propagating path at the welded joints under variid directions of principal stress. Thus, the assumption that fatigue cracks propagate perpendicular to the direction of principal stress could not explain this behavior.

Photo 4 shows the fatigue fracture surface at WG3-E of specimen A. As shown in Photo 3(b), the steps at the surface are propagated in zigzag form.

Table 3 Crack length in the case of crack detection and crack repair.

Specimen A

In the Case of Crack Detection

In the case of Lower Crack Repair

In the case of Upper Crack Repair

In the case of Completion Fatigue Life

in the Case of 40mm Crack

Length (×104)

Number of Cycles (×104)

Crack Length (S, N) (mm)

Number of Cycles (×104)

Crack Length (S, N) (mm)

Number of Cycles (×104)

Crack Length (S, N) (mm)

Crack Length (S, N) (mm)

WG1-W >133

WG1-E 41.8 5, 5 99.5 119, 111 103.4 127, 122 89.2

WG2-W 41.8 14, 13 54, 56 108.6

WG2-E 41.8 16, 2 70.9 120, 78 62.8

WG3-W 41.8 20, 0 78.3 77, 75 103, 101 63.9

WG3-E 41.8 19, 0 87, 84 91.2

WG4-W 41.8 12, 27 78.3 78, 71 99.5 108, 101 60.7

WG4-E 41.8 16, 10 78.3 73, 77 94, 91 58.4

WG5-W 41.8 15, 23 54, 54 84.6

WG5-E 37.5 0, 32 52.0 85, 78 75.9 112, 107 43.1

WG6-W 41.8 17, 21 56.0 105, 108 59.9 121, 120 50.1

WG6-E 41.8 6, 20 113, 111 97.4

WG7-W 41.8 20, 15 70.9 75, 74 75.9 86, 88 63.5

WG7-E 49.1 0, 24 16, 31 137

Specimen B

WG1-W >200

WG1-E 113.0 0, 9 163.0 82, 84 187.0 110, 112 150.9

WG2-W 77.5 0, 20 110.0 113, 115 95.4

WG2-E >200

WG3-W 47.5 27, 28 72.5 89, 92 113.0 111, 112 52.7

WG3-E 182.0 0, 9 15, 16 230

WG4-W 72.5 46, 26 110.0 84, 81 169.0 121, 118 75.1

WG4-E 52.5 13, 8 39, 38 200

WG5-W 32.5 0, 10 148.0 106, 105 153.0 107, 109 80.1

WG5-E 52.5 0, 14 70, 86 79.4

WG6-W 37.5 9, 20 81.5 104, 106 84.2 119, 125 72.1

WG6-E 77.5 8, 7 23, 37 200

WG7-W 86.5 0, 20 118.0 62, 83 143.0 85, 113 106.1

WG7-E 113.0 0, 8 0, 30 206

134

7. FATIGUE CRACK PROPAGATION ANALYSES

(1) Fatigue crack propagation analyses consider-

ing the inclination of fatigue crack To evaluate the fatigue crack propagating path

under the varied directions of principal stress using the fracture mechanics approach, fatigue crack propagation analyses were carried out using a steel plate of 500mm×500mm. The 10mm-long inclining initial crack was induced at the center of the plate, and forced displacement was applied as normal stress of the plate was set to 100N/mm2 (condition 1). In order to analyze fatigue crack propagating behavior, analyses were performed on the condition that any direction by combining normal stress with shear stress (condition 2) as well. In this study, analyses were carried out using condition 1 to simplify the analytical conditions. However, it had already been

confirmed that almost the same results were obtained between the analyses of conditions 1 and 2.

The propagating direction of fatigue crack was determined by the maximum principal stress theory, and stress intensity factor was calculated by the J-integral method. Therefore, the stress intensity factor of mode II component became substantially 0. In addition, the fatigue crack propagating rate for-mula specified in IIW was applied as the relationship between the fatigue crack propagating rate and the stress intensity factor range9). These analyses were peformed using the crack propagation analysis software FRANC2D/L10). In addition, the element size was 1.0mm, and the crack propagating amount was also set to 1.0mm11). In the software, the ele-ments near the crack tip were remeshed, and the remeshed element size was set to be about 0.1mm. Analyses in this chapter were carried out under the plane stress condition.

(a) Specimen A WG7-WS

(b) Specimen AWG3-ES

(c) Specimen A WG5-WS

(d) Specimen B WG2-WS

(e) Specimen B WG4-WN

(f) Specimen B WG5-ES

Photo 3 Fatigue crack propagation at boxing weld of gusset plate.

Table 4 Features of fatigue crack propagating path.

WG3-WThe bigger crack initiated perpendicular to the direction ofprincipal stress and propagated zigzag.

WG3-WThe bigger crack initiated perpendicular to the direction ofprincipal stress and propagated zigzag.

WG3-EDiverged cracks. Direction of propagating path was larger thandirection of principal stress.

WG3-E The crack along the weld toe propagated about 2mm.

WG4-WDiverged cracks. Direction of propagating path was larger thandirection of principal stress.

WG4-WDiverged cracks. Direction of propagating path was larger thandirection of principal stress.

WG4-EDiverged cracks. Direction of propagating path was larger thandirection of principal stress.

WG4-ESmall crack propagated perpendicular to the direction ofmaximum principal stress

WG5-WDiverged cracks. Direction of propagating path was larger thandirection of principal stress.

WG5-WThe bigger crack initiated perpendicular to the direction ofprincipal stress and propagated zigzag.

WG5-EDiverged cracks. Direction of propagating path was larger thandirection of principal stress.

WG5-EThe bigger crack initiated perpendicular to the direction ofprincipal stress.

Specimen BSpecimen A

135

Fig.6 shows the relationship between stress inten-sity factor range KImax obtained from the analyses and directionα of the initial crack. The definition of α is as shown in the figure. Stress intensity factor de-creases with the increase in the value α. This ten-dency indicates that the crack length perpendicular to the stress direction becomes smaller than the actual crack length due to the inclination. Therefore, fatigue life is deemed to be longer due to deceleration of fatigue crack propagating rate induced by the varia-tions in the direction.

Fig.7 shows the relationship between the propa-gating direction θ of the fatigue crack and the direc-tion α of the initial crack. The propagating direction in this figure is obtained from the coordinates of the original crack tip and the crack tip after extending them by 1mm. The direction of principal stress is transverse direction without the presence of fatigue crack, and the fatigue cracks are deemed to have propagated to the direction of θ=0. In the case of α=0, θ also becomes 0. However, in the case of the incli-nation of the initial fatigue crack, fatigue crack propagate toward the larger direction to the initial crack. Therefore, θ is increases with the increase in α. This fact indicates that the fatigue crack propagating angle increases with the large variation in the direc-tion of principal stress. However, when the direction of initial crack exceeds about 25 degrees, θ becomes small. The inclined crack tended to propagate in a more inclined direction because the shear stress at the crack tip increased due to the stress flow along the inclined crack. Because the direction of principal stress due to shear stress was 0 in the case of α equal to 45 degrees. θ became maximum when the value of α was about 25 degrees.

Fig.8 shows the crack propagating path in the case

of α equal to 30 degrees, which was obtained from the analysis. Though θ became larger at the first step as shown in Fig.7, the inclination gradually became small as the crack length got longer. (2) Analyses of fatigue crack propagating path

observed in fatigue tests Using the same method described in the previous

section, the crack propagating analyses using FRANC2D/L were also performed in order to re-produce the fatigue crack propagating path observed in the fatigue tests. In the analyses, enforced dis-placement was applied to the steel plate with initial crack in order to turn it into a stress field (normal stress and shear stress) similar to the girder-type specimen. In these analyses, the analytical condition

.

0 10 20 30 40 500

90

180

270

360

450St

ress

Int

ensi

ty F

acto

r K

Imax

(N/m

m3/

2 )

Direction of Initial Crack α(deg.)

α Initial Crack

Propagated Crack

θ

Fig.6 Relationship between stress intensity factor and direction of initial crack.

0 10 20 30 40 50

0

4

8

12

16

Dir

ecti

on o

f C

rack

Pro

paga

tion

θ(d

eg.)

Direction of Initial Crackα(deg.)

Fig.7 Relationship between direction of crack propagation and direction of initial crack.

Photo 4 Fatigue fracture surface (specimen A, WG3-E).

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was adjusted so that the magnitude and direction of principal stress were similar to those of the fatigue test. The weld and gusset plate were modeled by increasing the thickness of the web. Fig.9 shows the analytical model in the vicinity of the boxing weld.

Fig.10 shows some examples of fatigue crack propagating paths obtained from the analyses, to-gether with those observed in the fatigue tests. The red bold line in the figure shows the initial crack in-duced in the analyses. In Figs.10 (a) and (b), the variations in principal stress direction were adjusted for the purpose of reproducing the upper crack. Though the analytical result was in good agreement with the experimental result in Fig.10 (a), inclination of fatigue crack obtained from analyses became small compared with the experimental result in Fig.10 (b). Fig.10 (c) and (d) also show the comparison between the analytical and the experimental results. Though the analytical result was in good agreement with the experimental result shown in Fig.10 (c), the inclina-tion of fatigue crack obtained from analyses became small compared with the experimental result as shown in Fig.10 (d).

In these analyses, the direction of principal stress was also varied at the position where the crack changed direction as observed in the fatigue tests. In other words, the condition in which the fatigue crack

changed direction or diverged was still unknown. Considering the variation in the direction of principal stress in each cycle of loading and the stress intensity factor in the case of the inclination of fatigue crack (refer to Fig.6), the fatigue crack propagated per-pendicular to the direction of maximum principal stress. Thus, it is difficult to predict the fatigue crack propagating path using the analyses with fracture mechanics approach at the present stage. 8. FATIGUE STRENGTH EVALUATION

OF WEB-GUSSET WELDED JOINTS Some researchers including the authors had carried

out fatigue tests using girder-type specimens with some web-gusset welded joints12)-16) under the load positions being fixed. Figs.11 (a) and (b) show the relationship between stress range and fatigue life obtained from these test results. In these figures, fatigue design curves categorized in the Fatigue De-sign Recommendations issued by JSSC are also shown. In the recommendations, the fatigue strength category of web-gusset welded joint is specified as grade G. Fig.11(a) shows the fatigue test results ar-ranged by nominal stress range. Fig.11 (b) shows the fatigue tests results arranged by principal stress range. In the arrangement by nominal stress range, the fatigue strength of web-gusset welded joint de-teriorates with the increase in the ratio of shear stress τ to axial stress σ (τ/σ). In the arrangement by prin-cipal stress range, the ratio has no remarkable dif-ference. Therefore, the conventional arrangement of the fatigue test results by maximum principal stress range is appropriate. In addition, the lower line of fatigue test data almost agrees with the fatigue design curve of grade F.

Propagated Crack

Initial Crack 10mm

α＝30deg.

Fig.8 Crack propagating path from inclined crack.

Fig.9 Finite element model.

Red : Analysis Green : Experiment

(a) Specimen A WG3-WS

(b) Specimen A WG4-SW

(c) Specimen BWG3-WS

(d) Specimen B WG4-SW

Fig.10 Comparison between analysis and experiment.

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Fig.12 shows the fatigue test results obtained from this study. The vertical axis of the figure is the larger maximum principal stress range of the two. The horizontal axis represents the number of cyclic load as one cycle counted by a combination of actuator E and actuator W. Marks in the figure indicate the presence or absence of variations in the principal stress direction. Existing data are also shown in the figure. Fatigue strength in the case where there is a variation in principal stress direction was slightly lower than the fatigue strength in the case of constant principal stress direction. Some data are lower than the fatigue design curve specified as grade F. Further, some data are lower than the existing fatigue test data with fixed-point loading.

Fig.13 shows the fatigue test results arranged by equivalent principal stress range of the two maximum principal stress. The equivalent principal stress range was obtained from the following equation:

Δσpeq = {(ΔσpE

3 +ΔσpW3)/2}1/3

Δσpeq : equivalent principal stress range ΔσpE : principal stress range in loading of actuator

E ΔσpW : principal stress range in loading of actuator

W This equation does not consider the variation in

principal stress direction. In addition, the number of cyclic loading was calculated as two cycles of the combination actuator W or actuator E. Arranging fatigue test data by equivalent principal stress range makes a good agreement with the existing fatigue test data with fixed-point loading. Further, the lower limit of the data is almost located on the fatigue design curve of grade F. 9. CONCLUSIONS

In this study, for the purpose of clarifying the fa-tigue strength of web-gusset welded joint under

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Fig.11 S-N Data obtained from fatigue test using girder-type specimen (existing data).

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varied principal stress directions, fatigue tests with alternative loading were carried out using girder-type specimens. In addition, the analyses with fracture mechanics approach has been performed in order to comfirm the fatigue propagating behavior under varied principal stress directions.

The main results obtained here are as follows: (1) When there was no variation in principal stress

directions, fatigue crack propagated perpendic-ular to the principal stress direction under the alternative two-point loading.

(2) In the case of varied principal stress directions, fatigue crack propagated in a zigzag manner. The direction did not match the direction per-pendicular to the principal stress direction. Some branchings of fatigue cracks were also observed.

(3) Fatigue strength under varied principal stress directions almost agreed with existing fatigue test results arranged by equivalent principal stress of each maximum stress range.

(4) The stress intensity factor in the case of the inclined crack was smaller compared to that in the case of the vertical crack. In addition, the crack propagating direction would be more in-clined to be perpendicular to the principal stress because the stress component along the crack caused shear stress at the crack tip.

(5) According to the conclusion (4), fatigue strength under varied principal stress directions seemed to be higher than in the case where there was no variation. Actually, fatigue test results were quite different as mentioned in conclusion (3).

(6) In many cases, it was difficult to reproduce the fatigue crack propagating path using analyses with the fracture mechanics approach.

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(Received December 2, 2014)

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