- Email: [email protected]
Fatigue Crack Growth Behaviour of an Out-of –Plane Gusset Welded Joints under Biaxial Tensile Loadings with Different Phases
Available online at www.sciencedirect.com
ScienceDirect Procedia Materials Science 3 (2014) 1536 – 1541
20th European Conference on Fracture (ECF20)
Fatigue crack growth behaviour of an out-of –plane gusset welded joints under biaxial tensile loadings with different phases *Koji Gotoha*, Toshio Niwab and Yosuke Anaic a
Department of Marine Systems Engineering Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan Maintenance Research Technology Group, National Maritime Research Institute, 6-38-1, Shinkawa, Mitaka, Tokyo, Japan c Structural Analysis and Processing Research Group, National Maritime Research Institute, 6-38-1, Shinkawa, Mitaka, Tokyo, Japan b
Abstract Most of in-service welded built-up structures, which contain many welded joints as fatigue crack initiation sites, are subjected to many types of loading and these loadings have different axial components with different phases. However, the structural integrities are evaluated according to design codes based on theoretical and experimental investigations under a uniaxial loading condition. Most of these codes are based on the S-N curves approach. On the other hand, authors proposed the numerical simulation method of fatigue crack propagation histories of a cracked plate subjected biaxial loadings with phase difference of each loading component. Fracture mechanics approach is applied to establish our method. In this study, fatigue crack growth behaviour of an out-of-plane gusset welded joint under biaxial loading with two different phase conditions were investigated. The phase difference effect for fatigue crack shape evolution under biaxial loading was confirmed by measured ones. Besides, comparisons of measured crack evolution with the numerical simulation results were performed to validate of our fatigue crack growth simulation for welded joints. © 2014 2014Published The Authors. Published by Elsevier Ltd. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department Engineering. Structuraland of Structural Engineering Keywords: Fatigue; Biaxial loading with phase difference; Numerical simulation of fatigue crack growth; RPG stress; Out-of-plane gusset welded joints
* Corresponding author. Tel.:+81-92-802-3457; fax:+81-92-802-3368. E-mail address: [email protected]
2211-8128 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering doi:10.1016/j.mspro.2014.06.248
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
1. Introduction
200
500
80 R
75 75 75
120
0R 12
2. Specimen configuration and loading condition
50 50
120
In general, most of in-service welded structures and vehicles are subjected to many types of loading which contain different axial components with different phases. However, the structural integrity of most working structures and vehicles are assessed by the design codes of each structure, which are based on theoretical and experimental investigations under uniaxial loading conditions from a practical point of view. Fatigue strength under biaxial loading has been investigated via the S–N curves approach and the fracture mechanics approach. The researches based on the fracture mechanics approach (Hoshide et al. 1981, Yuuki et al. 1984 1988, Brown and Miller 1985) could not reach a definite conclusion regarding the effect of biaxial loading on fatigue crack growth behavior because of conflicting results. The researches based on the S–N curves (Sonsino 1995, Takahashi et al. 1997, 1999) merely gave measured S-N curves for individual loading conditions. Hence, it is very important to establish a quantitative evaluation procedure for fatigue crack growth under biaxial loading conditions. On the other hand, we have been using our developed numerical simulation code of fatigue crack propagation to evaluate the fatigue crack growth under arbitrary loading histories. This code enables to consider the fatigue crack opening / closing phenomena caused by crack wake over crack surfaces and implements the Re-tensile Plastic zone Generating (RPG) stress criterion (Toyosada et al. 2004a) as the fatigue crack propagation law. The validity of the estimated fatigue crack propagation histories for the following objects were confirmed by comparing measured results. x A cracked plate under uniaxial variable loadings (Toyosada et al. 2004a), including superimposed loadings with two different frequencies (Gotoh et al. 2012) x Welded joints under uniaxial variable loadings (Toyosada et al. 2004b, Nagata et al. 2009) x A cracked plate under biaxial loadings with phase difference (Gotoh et al. 2013) The aim in this study is to verify the applicability of our numerical approach to estimate the fatigue crack growth histories of welded joints under biaxial loadings with phase difference from a practical point of view. We performed fatigue crack propagation tests using the out-of-plane gusset welded joints under biaxial loading with two different phase conditions, highlighting the effect of the phase difference under biaxial loading on the fatigue crack growth behavior. Applicability of the numerical simulation method of fatigue crack growth based on the RPG criterion under biaxial loading with different loading phases is 75 75 75 75 verified by comparing the estimated fatigue crack growth histories with measured ones.
10
100
100
160
500
200
400
Cruciform-shaped out-of-plane gusset welded joints specimens shown in Fig.1 were prepared for fatigue crack propagation tests under biaxial loading conditions. All the specimens were formed from the same mild Stiffener steel plate (ClassNK grade KA). The chemical composition and Rolling direction mechanical properties of the tested steel are listed in Table 1. In y general, the fatigue crack in out-of-plane gusset joints initiates at toes x of boxing fillet weld. Because of restricting the fatigue crack initiation 400 site, three toe regions of the boxing fillet shown in Fig.1 were 100 processed by grinding to relieve the stress concentration. The fatigue z crack in both specimens initiated from the as welded boxing fillet weld as welded x toe. Rolling direction toe dressed We performed fatigue crack propagation tests under biaxial loading by grinder 500 500 conditions using a testing system that consisted of four independent servo loading actuators that enabled controlled variable loading under Fig.1 Configuration of the cruciform-shaped outdifferent phases, see Fig.2. of-plane gusset welded joint. The applied loading conditions for each specimen are listed in Table 2. Because our study focused on the effects of the phase difference between the applied stresses in the two perpendicular directions, the stress amplitudes in both directions were kept equal.
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
Table 1 Mechanical properties and Chemical composition of tested material (ClassNK grade KA). Mechanical properties Yield strength
Tensile strength
Elongation
[MPa]
[MPa]
[%]
439
30
298
Chemical composition [%] C
Si
Mn
P
S
0.14
0.23
0.86
0.018
0.005 Fig.2 Set-up of fatigue test under biaxial tensile loading.
Table 2 Loading conditions. Specimen ID
Stress ratio: R = Vxmax/Vxmin
Stress amplitude: [MPa]
Vx / Vy
Phase difference: I
G-1 G-2
0.05
110
1
S
0
3. Results of fatigue crack propagation tests Figures 3 and 4 shows observed fractured surface of each specimen.
(a) Overview of fracture surface
(b) Enlarged view near the crack initiation site
Fig.3 Observed fracture surface (Specimen ID: G-1)
(a) Overview of fracture surface (b) Enlarged view near the crack initiation site Fig.4 Observed fracture surface (Specimen ID: G-2)
In case of specimen G-1, plurality of fatigue cracks occur near the as welded boxing fillet weld regions. These cracks grew while repeating coalescence and became a large single surface crack. Continue, this surface crack penetrated the base plate thickness. Followed by the penetration, a fatigue crack continue to propagate as a through thickness crack. In case of specimen G-2, the evolution process of plural surface fatigue cracks was the same to specimen G-1. It is, however, two different fatigue cracks propagate through different cross section of base plate. The step of fracture surface was confirmed from Fig.4. Figure 5 shows measured aspect ratio evolutions of each surface crack in the specimens. Aspect ratios were identified by approximating the elliptical shape of a surface crack. Measurement was performed with respect to the single surface crack after coalescence. It is confirmed from Fig.5 that the shape evolution of a surface crack is affected by the phase difference of biaxial loading.
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
Figures 6 (a) and (b) shows measured fatigue crack growth histories. It is also confirmed that fatigue crack growth rate under biaxial loading is affected by the phase difference of loading components. Fatigue crack in specimen G-2 with S phase difference of biaxial loading component grew faster than specimen G-1 with zero phase difference. This tendency related to the phase difference effect is the same as the measured results at the center cracked cruciform shaped specimen (Gotoh et al. 2013). 1.0
0.6
0.4 2b
0.2
0.0 0
10mm
Aspect ratio: a/b
0.8
a
2
4 6 Crack depth: a (mm)
8
10
100 Specimen G-1 (I=0䠅
Crack depth: a , Half crack length: b [mm]
Crack depth: a , Half crack length: b [mm]
100 G-1 (I= 0) G-2 (I S)
Crack depth: a Crack length: b 1 Crack length: b 2
80
2b1
60
a
40
2b2
20
0 0
Specimen G-2 (I S䠅
60
2b1 a
40 2b2
20
1 2 3 6 Number of cycles: N [ x 10 cycle ]
Fig.5 Measured aspect ratio evolutions of each defect.
Crack depth: a Crack length: b 1 Crack length: b 2
80
(a) Specimen G-1
0 0
1 2 3 6 Number of cycles: N [ x 10 cycle ]
(b) Specimen G-2
Fig.6 Measured fatigue crack growth histories.
4. Numerical simulation of fatigue crack growth 4.1. Overview of the Equivalent Distributed Stress method We performed the numerical simulation of the fatigue crack propagation using our numerical simulation code which models the fatigue crack opening/closing behavior and estimates the relationship between the fatigue crack shape, e.g. the depth or the width of a planer shape defect, and the number of applied loading cycles. Details of the theoretical background for our code can be found in reference (Toyosada et al. 2004a). On the other hand, our numerical simulation code of fatigue crack propagation cannot be applied directly to arbitrary geometrical-shaped joints with a crack because explicit expressions of the weight function of the stress intensity factor for such cracked joints have not yet been established. An alternative method, the Equivalent Distributed Stress (EDS) method (Toyosada et al. 2004b) for estimating the fatigue crack propagation histories was proposed. Calculation flow by applying EDS method is as follows. 1) 2)
Obtaining the relationship between the fatigue crack length (a) and stress intensity factor (K). Transformation of a-K relationship into the EDS as a function of crack length. EDS enables the stress field near the crack tip of planar cracks in an infinite wide plate with a through thickness crack to reproduce. EDS must satisfy the following equation, Where, VEDS(x): Kobject(a):
3)
2
Sa
³ ^V a
0
EDS
x
`
1 x a dx Kobject a 2
(1).
EDS at crack length x and Stress intensity factor at crack length a. Performing the numerical simulation of fatigue crack growth for an infinite wide plate with a through thickness crack the condition that EDS is distributed along a crack line
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
Before applying the EDS method to estimate the fatigue crack propagation in the welded joints to be evaluated, the relationship between the fatigue crack shape and stress intensity factor must be determined. The superposition procedure for a cracked body, which is illustrated in Fig. 7, were applied to obtain SIF in this research. Detailed explanation for these SIF estimation procedure including the consideration method of the case where stress is distributed in the crack width direction was introduced in the references (Toyosada et al., 2004b, Nagata et al. 2009). Approximated conversion method of biaxial loading condition to uniaxial loading to the normal direction to the crack surface (a) (b) (c) (d) (Gotoh et al., 2013) is applied for the SIF calculations. That is, the (a) Surface crack in stress concentration field. (b) Surface crack in a plate subjected to tensile loading biaxial loading effect is incorporated in the SIF evolutions. and out-of bending. Commercial FE software MSC Nastran 2012 was applied to (c) Through thickness edge crack in stress concentration calculate the stress distribution for no cracked specimen under field. (d) Through thickness edge crack in plate subjected to external applied biaxial loading conditions. Inherent stress method tensile loading and out-of bending. (Matsuoka and Yoshii, 1998) for the out-of-plane gusset joint was Fig.7 Approximate method to estimate the SIF at the applied to calculate the residual stress distribution for no cracked deepest point of a surface crack in an arbitrary stress specimen. distributed field. Figure 8 shows the relation of the reference crack length (X) (Toyosada et al., 2004b) defined by Eq. (2) and the stress intensity factor (K) of specimen G-1 as an example. Several weld toe radus conditions were set to estimate SIFs under external loading conditions because the exact value of the toe radii for each specimen had not been measured. Figure 9 shows the EDS distributions derived from Fig.8. Definition of the reference crack length is shown in Eq. (2). EDS of specimen G-2 was obtained according to the same procedure for specimen G-1.
° a >for a surface crack @ ® °¯ c c penetration t > for a through thickness crack @ , where a :crack depth, t :plate thickness, c:half crack length and c penetration : c at crack penetrating through thickness.
(2)
X
5
1500
1000
500
U: Radius of weld toe 0 0
5 10 Reference crack length X [mm]
15
0 0
5 10 Reference crack length X [mm]
Fig.8 Relationship between Stress intensity factor (K) and Reference crack length (X) for specimen G-1.
15
2
9 8 7 6
2
2
2000
500
VEDS [N/mm ]
1.5
0.2mm 0.3mm 0.7mm 1.0mm
10
Equivalent distributed stress VEDS [N/mm ]
: U= : U= : U= : U=
2
Specimen G-1 Under residual stress field
Equivalent distributed stress
10
Stress intensity factor K [N/mm ]
Vx=Vy=1 N/mm
Equivalent distributed stress VEDS [N/mm ]
2500 Specimen G-1 Under unit external loading:
1.5
Stress intensity factor K [N/mm ]
15
10
Specimen G-1 Under unit external loading:
9 8 7 6 5
Vx=Vy=1 N/mm
4
2
3 2
300
1 0 0
0.5 Reference crack lenght:
X [mm]
1
5 4 3 2
: U= : U= : U= : U=
200
0.2mm 0.3mm 0.7mm 1.0mm
100
1 0 0
Specimen G-1 Under residual stress field
400
5 10 Reference crack lenght: X [mm]
15
0 0
5 10 Reference crack lenght: X [mm]
15
Fig.9 Relationship between Equivalent Distributed Stress (VEDS) and Reference crack length (X) for specimen G-1.
4.2. Numerical simulation of fatigue crack growth Fig.10 shows a comparison between the fatigue crack growth histories obtained by the numerical simulation and the measured ones. Note the horizontal axis (Number of cycles) is drawn by the normal scale, not logarithmic one.
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
Considering the ambiguity in the SIF estimation procedure shown in Fig.7, we could conclude that the numerical simulation method proposed in this paper could give fair estimation result. It is also confirmed from Fig.10 that the fatigue life is strongly affected the phase difference of biaxial loading and that the effect on the fatigue crack growth through the total life of weld toe radius could be negligible. 100 Specimen G-1 (Phase difference : I=0)
Fatigue tests for the out-of-plane gusset joint under biaxial loading with two different phase conditions were performed. It is confirmed that the shape evolution of surface fatigue is affected by the phase difference of the biaxial loading. A numerical simulation method of fatigue crack growth for welded joints under biaxial load with different loading phases, which is based on the Equivalent Distributed Stress (EDS) method, is proposed and the method was validated by comparing the estimated fatigue crack growth histories with the measured ones.
Reference crack length: X [mm]
5. Concluding remarks.
Acknowledgements
References
60
40
20
0 0
: U= : U= : U= : U=
0.2mm 0.3mm 0.7mm 1.0mm
Symbols: measurement : Before penetration : After penetration Crack penetrates base plate
1 2 3 6 Number of cycles: N [ x10 cycles]
100 Specimen G-2 (Phase difference: I S䠅 Reference crack length: X [mm]
This research was funded by a Grant-in-Aid for Young Scientists (S) (No. 21676007) from the Japan Society for the Promotion of Science. The authors would like to express their appreciation to Nippon Steel & Sumitomo Metal Corporation for supplying the steel plates for the specimens. Mr. Kouki Sugino (Master course student, Kyushu University) and Mr. Yoshihisa Tanaka, (Maintenance Research Technology Group, National Maritime Research Institute, Japan) contributed to the numerical and experimental works for this research.
80 Curves: Numerical simulation
80 Curves: Numerical simulation
60
40
20
: U= : U= : U= : U=
0.2mm 0.3mm 0.7mm 1.0mm
Symbols: Measurement : Before penetration : After peneteration Crack penetrates base metal.
Brown, M.W. and Miller, K.J., 1985. Mode I Fatigue Crack Growth under Biaxial Stress at 0 Room and Elevated Temperature, ASTM STP 853, 135-152. 0 2 4 6 8 5 Number of cycles: N [ x 10 cycles] Gotoh, K., Matsuda, K. and Kitamura, O, 2012. Numerical Simulation of Fatigue Crack Propagation under Superposed Loading Histories with Two Different Frequencies, Proc. Fig.9 Comparison between estimated fatigue crack growth histories and measured of Hydroelasticity in Marine Technology, 287-297. values. Gotoh, K., Niwa, T., Anai, Y. Omori, T., Tanaka, Y. and Murakami, K., 2013. Fatigue Crack Propagation under Biaxial Tensile Loading, Proc. of OMAE 2013, OMAE 2013-10980. Hoshide, T., Tanaka, K. and Yamada, A. 1981. Stress-Ratio Effect of Fatigue Crack Propagation in a Biaxial Stress Field, Fatigue Eng. Mater. Struc. , 4, 4, 355-366. Matsuoka, K. and Yoshii, T., 1998. Weld Residual Stress in Corner Boxing Joints, ClassNK technical bulletin, 16, 1-10. Nagata, Y., Gotoh, K. and Toyosada, M., 2009. Numerical Simulations of Fatigue Crack Initiation and Propagation Based on Re-tensile Plastic Zone Generating (RPG) Load Criterion for In-plane Gusset Welded Joints, J. Marine Sci. Tech., 14, 1, 104-114. Sonsino, C.M., 1995, Multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses, Int. J. Fatigue, 17, 1, 55-70. Takahashi, I., Takada, A., Akiyama, S., Ushijima, M. and Maenaka, H., 1998. Fatigue behavior of box welded joint under biaxial cyclic loads, J SNAJ, 184, 321-327, (in Japanese). Takahashi, I., Ushijima, M., Takada, A., Akiyama, S. and Maenaka, H., 1999. Fatigue behavior of a box-welded joint under biaxial cyclic loads, Fatigue Eng. Mat. Struc., 22, 10, 869-877. Toyosada, M., Gotoh, K. and Niwa, T., 2004a. Fatigue crack propagation for a through thickness crack, Int. J. Fatigue, 26, 9, 983-992. Toyosada, M., Gotoh, K. and Niwa, T., 2004b. Fatigue life assessment for welded structures without initial defects, Int. J. Fatigue, 26, 9, 9931002. Yuuki, R., Kitagawa, H., Tohgo, K. and Tanabe, M., 1984. Effect of Bi-Axial Stress on Fatigue Crack Growth, Mat. Sci. Research, 33, 373, 12711277, (in Japanese) Yuuki, R., Akita, K. and Kishi, N., 1988. Effect of Biaxial Stress Condition and its Change on Fatigue Crack Growth Properties, Mat. Sci. Research, 37, 420, 1084-1089, (in Japanese).
ScienceDirect Procedia Materials Science 3 (2014) 1536 – 1541
20th European Conference on Fracture (ECF20)
Fatigue crack growth behaviour of an out-of –plane gusset welded joints under biaxial tensile loadings with different phases *Koji Gotoha*, Toshio Niwab and Yosuke Anaic a
Department of Marine Systems Engineering Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan Maintenance Research Technology Group, National Maritime Research Institute, 6-38-1, Shinkawa, Mitaka, Tokyo, Japan c Structural Analysis and Processing Research Group, National Maritime Research Institute, 6-38-1, Shinkawa, Mitaka, Tokyo, Japan b
Abstract Most of in-service welded built-up structures, which contain many welded joints as fatigue crack initiation sites, are subjected to many types of loading and these loadings have different axial components with different phases. However, the structural integrities are evaluated according to design codes based on theoretical and experimental investigations under a uniaxial loading condition. Most of these codes are based on the S-N curves approach. On the other hand, authors proposed the numerical simulation method of fatigue crack propagation histories of a cracked plate subjected biaxial loadings with phase difference of each loading component. Fracture mechanics approach is applied to establish our method. In this study, fatigue crack growth behaviour of an out-of-plane gusset welded joint under biaxial loading with two different phase conditions were investigated. The phase difference effect for fatigue crack shape evolution under biaxial loading was confirmed by measured ones. Besides, comparisons of measured crack evolution with the numerical simulation results were performed to validate of our fatigue crack growth simulation for welded joints. © 2014 2014Published The Authors. Published by Elsevier Ltd. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department Engineering. Structuraland of Structural Engineering Keywords: Fatigue; Biaxial loading with phase difference; Numerical simulation of fatigue crack growth; RPG stress; Out-of-plane gusset welded joints
* Corresponding author. Tel.:+81-92-802-3457; fax:+81-92-802-3368. E-mail address: [email protected]
2211-8128 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Norwegian University of Science and Technology (NTNU), Department of Structural Engineering doi:10.1016/j.mspro.2014.06.248
1537
Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
1. Introduction
200
500
80 R
75 75 75
120
0R 12
2. Specimen configuration and loading condition
50 50
120
In general, most of in-service welded structures and vehicles are subjected to many types of loading which contain different axial components with different phases. However, the structural integrity of most working structures and vehicles are assessed by the design codes of each structure, which are based on theoretical and experimental investigations under uniaxial loading conditions from a practical point of view. Fatigue strength under biaxial loading has been investigated via the S–N curves approach and the fracture mechanics approach. The researches based on the fracture mechanics approach (Hoshide et al. 1981, Yuuki et al. 1984 1988, Brown and Miller 1985) could not reach a definite conclusion regarding the effect of biaxial loading on fatigue crack growth behavior because of conflicting results. The researches based on the S–N curves (Sonsino 1995, Takahashi et al. 1997, 1999) merely gave measured S-N curves for individual loading conditions. Hence, it is very important to establish a quantitative evaluation procedure for fatigue crack growth under biaxial loading conditions. On the other hand, we have been using our developed numerical simulation code of fatigue crack propagation to evaluate the fatigue crack growth under arbitrary loading histories. This code enables to consider the fatigue crack opening / closing phenomena caused by crack wake over crack surfaces and implements the Re-tensile Plastic zone Generating (RPG) stress criterion (Toyosada et al. 2004a) as the fatigue crack propagation law. The validity of the estimated fatigue crack propagation histories for the following objects were confirmed by comparing measured results. x A cracked plate under uniaxial variable loadings (Toyosada et al. 2004a), including superimposed loadings with two different frequencies (Gotoh et al. 2012) x Welded joints under uniaxial variable loadings (Toyosada et al. 2004b, Nagata et al. 2009) x A cracked plate under biaxial loadings with phase difference (Gotoh et al. 2013) The aim in this study is to verify the applicability of our numerical approach to estimate the fatigue crack growth histories of welded joints under biaxial loadings with phase difference from a practical point of view. We performed fatigue crack propagation tests using the out-of-plane gusset welded joints under biaxial loading with two different phase conditions, highlighting the effect of the phase difference under biaxial loading on the fatigue crack growth behavior. Applicability of the numerical simulation method of fatigue crack growth based on the RPG criterion under biaxial loading with different loading phases is 75 75 75 75 verified by comparing the estimated fatigue crack growth histories with measured ones.
10
100
100
160
500
200
400
Cruciform-shaped out-of-plane gusset welded joints specimens shown in Fig.1 were prepared for fatigue crack propagation tests under biaxial loading conditions. All the specimens were formed from the same mild Stiffener steel plate (ClassNK grade KA). The chemical composition and Rolling direction mechanical properties of the tested steel are listed in Table 1. In y general, the fatigue crack in out-of-plane gusset joints initiates at toes x of boxing fillet weld. Because of restricting the fatigue crack initiation 400 site, three toe regions of the boxing fillet shown in Fig.1 were 100 processed by grinding to relieve the stress concentration. The fatigue z crack in both specimens initiated from the as welded boxing fillet weld as welded x toe. Rolling direction toe dressed We performed fatigue crack propagation tests under biaxial loading by grinder 500 500 conditions using a testing system that consisted of four independent servo loading actuators that enabled controlled variable loading under Fig.1 Configuration of the cruciform-shaped outdifferent phases, see Fig.2. of-plane gusset welded joint. The applied loading conditions for each specimen are listed in Table 2. Because our study focused on the effects of the phase difference between the applied stresses in the two perpendicular directions, the stress amplitudes in both directions were kept equal.
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
Table 1 Mechanical properties and Chemical composition of tested material (ClassNK grade KA). Mechanical properties Yield strength
Tensile strength
Elongation
[MPa]
[MPa]
[%]
439
30
298
Chemical composition [%] C
Si
Mn
P
S
0.14
0.23
0.86
0.018
0.005 Fig.2 Set-up of fatigue test under biaxial tensile loading.
Table 2 Loading conditions. Specimen ID
Stress ratio: R = Vxmax/Vxmin
Stress amplitude: [MPa]
Vx / Vy
Phase difference: I
G-1 G-2
0.05
110
1
S
0
3. Results of fatigue crack propagation tests Figures 3 and 4 shows observed fractured surface of each specimen.
(a) Overview of fracture surface
(b) Enlarged view near the crack initiation site
Fig.3 Observed fracture surface (Specimen ID: G-1)
(a) Overview of fracture surface (b) Enlarged view near the crack initiation site Fig.4 Observed fracture surface (Specimen ID: G-2)
In case of specimen G-1, plurality of fatigue cracks occur near the as welded boxing fillet weld regions. These cracks grew while repeating coalescence and became a large single surface crack. Continue, this surface crack penetrated the base plate thickness. Followed by the penetration, a fatigue crack continue to propagate as a through thickness crack. In case of specimen G-2, the evolution process of plural surface fatigue cracks was the same to specimen G-1. It is, however, two different fatigue cracks propagate through different cross section of base plate. The step of fracture surface was confirmed from Fig.4. Figure 5 shows measured aspect ratio evolutions of each surface crack in the specimens. Aspect ratios were identified by approximating the elliptical shape of a surface crack. Measurement was performed with respect to the single surface crack after coalescence. It is confirmed from Fig.5 that the shape evolution of a surface crack is affected by the phase difference of biaxial loading.
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
Figures 6 (a) and (b) shows measured fatigue crack growth histories. It is also confirmed that fatigue crack growth rate under biaxial loading is affected by the phase difference of loading components. Fatigue crack in specimen G-2 with S phase difference of biaxial loading component grew faster than specimen G-1 with zero phase difference. This tendency related to the phase difference effect is the same as the measured results at the center cracked cruciform shaped specimen (Gotoh et al. 2013). 1.0
0.6
0.4 2b
0.2
0.0 0
10mm
Aspect ratio: a/b
0.8
a
2
4 6 Crack depth: a (mm)
8
10
100 Specimen G-1 (I=0䠅
Crack depth: a , Half crack length: b [mm]
Crack depth: a , Half crack length: b [mm]
100 G-1 (I= 0) G-2 (I S)
Crack depth: a Crack length: b 1 Crack length: b 2
80
2b1
60
a
40
2b2
20
0 0
Specimen G-2 (I S䠅
60
2b1 a
40 2b2
20
1 2 3 6 Number of cycles: N [ x 10 cycle ]
Fig.5 Measured aspect ratio evolutions of each defect.
Crack depth: a Crack length: b 1 Crack length: b 2
80
(a) Specimen G-1
0 0
1 2 3 6 Number of cycles: N [ x 10 cycle ]
(b) Specimen G-2
Fig.6 Measured fatigue crack growth histories.
4. Numerical simulation of fatigue crack growth 4.1. Overview of the Equivalent Distributed Stress method We performed the numerical simulation of the fatigue crack propagation using our numerical simulation code which models the fatigue crack opening/closing behavior and estimates the relationship between the fatigue crack shape, e.g. the depth or the width of a planer shape defect, and the number of applied loading cycles. Details of the theoretical background for our code can be found in reference (Toyosada et al. 2004a). On the other hand, our numerical simulation code of fatigue crack propagation cannot be applied directly to arbitrary geometrical-shaped joints with a crack because explicit expressions of the weight function of the stress intensity factor for such cracked joints have not yet been established. An alternative method, the Equivalent Distributed Stress (EDS) method (Toyosada et al. 2004b) for estimating the fatigue crack propagation histories was proposed. Calculation flow by applying EDS method is as follows. 1) 2)
Obtaining the relationship between the fatigue crack length (a) and stress intensity factor (K). Transformation of a-K relationship into the EDS as a function of crack length. EDS enables the stress field near the crack tip of planar cracks in an infinite wide plate with a through thickness crack to reproduce. EDS must satisfy the following equation, Where, VEDS(x): Kobject(a):
3)
2
Sa
³ ^V a
0
EDS
x
`
1 x a dx Kobject a 2
(1).
EDS at crack length x and Stress intensity factor at crack length a. Performing the numerical simulation of fatigue crack growth for an infinite wide plate with a through thickness crack the condition that EDS is distributed along a crack line
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Before applying the EDS method to estimate the fatigue crack propagation in the welded joints to be evaluated, the relationship between the fatigue crack shape and stress intensity factor must be determined. The superposition procedure for a cracked body, which is illustrated in Fig. 7, were applied to obtain SIF in this research. Detailed explanation for these SIF estimation procedure including the consideration method of the case where stress is distributed in the crack width direction was introduced in the references (Toyosada et al., 2004b, Nagata et al. 2009). Approximated conversion method of biaxial loading condition to uniaxial loading to the normal direction to the crack surface (a) (b) (c) (d) (Gotoh et al., 2013) is applied for the SIF calculations. That is, the (a) Surface crack in stress concentration field. (b) Surface crack in a plate subjected to tensile loading biaxial loading effect is incorporated in the SIF evolutions. and out-of bending. Commercial FE software MSC Nastran 2012 was applied to (c) Through thickness edge crack in stress concentration calculate the stress distribution for no cracked specimen under field. (d) Through thickness edge crack in plate subjected to external applied biaxial loading conditions. Inherent stress method tensile loading and out-of bending. (Matsuoka and Yoshii, 1998) for the out-of-plane gusset joint was Fig.7 Approximate method to estimate the SIF at the applied to calculate the residual stress distribution for no cracked deepest point of a surface crack in an arbitrary stress specimen. distributed field. Figure 8 shows the relation of the reference crack length (X) (Toyosada et al., 2004b) defined by Eq. (2) and the stress intensity factor (K) of specimen G-1 as an example. Several weld toe radus conditions were set to estimate SIFs under external loading conditions because the exact value of the toe radii for each specimen had not been measured. Figure 9 shows the EDS distributions derived from Fig.8. Definition of the reference crack length is shown in Eq. (2). EDS of specimen G-2 was obtained according to the same procedure for specimen G-1.
° a >for a surface crack @ ® °¯ c c penetration t > for a through thickness crack @ , where a :crack depth, t :plate thickness, c:half crack length and c penetration : c at crack penetrating through thickness.
(2)
X
5
1500
1000
500
U: Radius of weld toe 0 0
5 10 Reference crack length X [mm]
15
0 0
5 10 Reference crack length X [mm]
Fig.8 Relationship between Stress intensity factor (K) and Reference crack length (X) for specimen G-1.
15
2
9 8 7 6
2
2
2000
500
VEDS [N/mm ]
1.5
0.2mm 0.3mm 0.7mm 1.0mm
10
Equivalent distributed stress VEDS [N/mm ]
: U= : U= : U= : U=
2
Specimen G-1 Under residual stress field
Equivalent distributed stress
10
Stress intensity factor K [N/mm ]
Vx=Vy=1 N/mm
Equivalent distributed stress VEDS [N/mm ]
2500 Specimen G-1 Under unit external loading:
1.5
Stress intensity factor K [N/mm ]
15
10
Specimen G-1 Under unit external loading:
9 8 7 6 5
Vx=Vy=1 N/mm
4
2
3 2
300
1 0 0
0.5 Reference crack lenght:
X [mm]
1
5 4 3 2
: U= : U= : U= : U=
200
0.2mm 0.3mm 0.7mm 1.0mm
100
1 0 0
Specimen G-1 Under residual stress field
400
5 10 Reference crack lenght: X [mm]
15
0 0
5 10 Reference crack lenght: X [mm]
15
Fig.9 Relationship between Equivalent Distributed Stress (VEDS) and Reference crack length (X) for specimen G-1.
4.2. Numerical simulation of fatigue crack growth Fig.10 shows a comparison between the fatigue crack growth histories obtained by the numerical simulation and the measured ones. Note the horizontal axis (Number of cycles) is drawn by the normal scale, not logarithmic one.
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Koji Gotoh et al. / Procedia Materials Science 3 (2014) 1536 – 1541
Considering the ambiguity in the SIF estimation procedure shown in Fig.7, we could conclude that the numerical simulation method proposed in this paper could give fair estimation result. It is also confirmed from Fig.10 that the fatigue life is strongly affected the phase difference of biaxial loading and that the effect on the fatigue crack growth through the total life of weld toe radius could be negligible. 100 Specimen G-1 (Phase difference : I=0)
Fatigue tests for the out-of-plane gusset joint under biaxial loading with two different phase conditions were performed. It is confirmed that the shape evolution of surface fatigue is affected by the phase difference of the biaxial loading. A numerical simulation method of fatigue crack growth for welded joints under biaxial load with different loading phases, which is based on the Equivalent Distributed Stress (EDS) method, is proposed and the method was validated by comparing the estimated fatigue crack growth histories with the measured ones.
Reference crack length: X [mm]
5. Concluding remarks.
Acknowledgements
References
60
40
20
0 0
: U= : U= : U= : U=
0.2mm 0.3mm 0.7mm 1.0mm
Symbols: measurement : Before penetration : After penetration Crack penetrates base plate
1 2 3 6 Number of cycles: N [ x10 cycles]
100 Specimen G-2 (Phase difference: I S䠅 Reference crack length: X [mm]
This research was funded by a Grant-in-Aid for Young Scientists (S) (No. 21676007) from the Japan Society for the Promotion of Science. The authors would like to express their appreciation to Nippon Steel & Sumitomo Metal Corporation for supplying the steel plates for the specimens. Mr. Kouki Sugino (Master course student, Kyushu University) and Mr. Yoshihisa Tanaka, (Maintenance Research Technology Group, National Maritime Research Institute, Japan) contributed to the numerical and experimental works for this research.
80 Curves: Numerical simulation
80 Curves: Numerical simulation
60
40
20
: U= : U= : U= : U=
0.2mm 0.3mm 0.7mm 1.0mm
Symbols: Measurement : Before penetration : After peneteration Crack penetrates base metal.
Brown, M.W. and Miller, K.J., 1985. Mode I Fatigue Crack Growth under Biaxial Stress at 0 Room and Elevated Temperature, ASTM STP 853, 135-152. 0 2 4 6 8 5 Number of cycles: N [ x 10 cycles] Gotoh, K., Matsuda, K. and Kitamura, O, 2012. Numerical Simulation of Fatigue Crack Propagation under Superposed Loading Histories with Two Different Frequencies, Proc. Fig.9 Comparison between estimated fatigue crack growth histories and measured of Hydroelasticity in Marine Technology, 287-297. values. Gotoh, K., Niwa, T., Anai, Y. Omori, T., Tanaka, Y. and Murakami, K., 2013. Fatigue Crack Propagation under Biaxial Tensile Loading, Proc. of OMAE 2013, OMAE 2013-10980. Hoshide, T., Tanaka, K. and Yamada, A. 1981. Stress-Ratio Effect of Fatigue Crack Propagation in a Biaxial Stress Field, Fatigue Eng. Mater. Struc. , 4, 4, 355-366. Matsuoka, K. and Yoshii, T., 1998. Weld Residual Stress in Corner Boxing Joints, ClassNK technical bulletin, 16, 1-10. Nagata, Y., Gotoh, K. and Toyosada, M., 2009. Numerical Simulations of Fatigue Crack Initiation and Propagation Based on Re-tensile Plastic Zone Generating (RPG) Load Criterion for In-plane Gusset Welded Joints, J. Marine Sci. Tech., 14, 1, 104-114. Sonsino, C.M., 1995, Multiaxial fatigue of welded joints under in-phase and out-of-phase local strains and stresses, Int. J. Fatigue, 17, 1, 55-70. Takahashi, I., Takada, A., Akiyama, S., Ushijima, M. and Maenaka, H., 1998. Fatigue behavior of box welded joint under biaxial cyclic loads, J SNAJ, 184, 321-327, (in Japanese). Takahashi, I., Ushijima, M., Takada, A., Akiyama, S. and Maenaka, H., 1999. Fatigue behavior of a box-welded joint under biaxial cyclic loads, Fatigue Eng. Mat. Struc., 22, 10, 869-877. Toyosada, M., Gotoh, K. and Niwa, T., 2004a. Fatigue crack propagation for a through thickness crack, Int. J. Fatigue, 26, 9, 983-992. Toyosada, M., Gotoh, K. and Niwa, T., 2004b. Fatigue life assessment for welded structures without initial defects, Int. J. Fatigue, 26, 9, 9931002. Yuuki, R., Kitagawa, H., Tohgo, K. and Tanabe, M., 1984. Effect of Bi-Axial Stress on Fatigue Crack Growth, Mat. Sci. Research, 33, 373, 12711277, (in Japanese) Yuuki, R., Akita, K. and Kishi, N., 1988. Effect of Biaxial Stress Condition and its Change on Fatigue Crack Growth Properties, Mat. Sci. Research, 37, 420, 1084-1089, (in Japanese).