A Theoretical Model to Predict Fatigue Life of Laser Welded Joints H. Remes Ship Laboratory, Helsinki University of Technology.

Espoo, Finland

Introduction During the last decade ship building industry has shown increasing interest in the laser welding techniques and first installations for production have been done. Main advantages of laser welding are low welding distortions, high productivity and easy automation. Additionally, the laser welding techniques open new opportunities for innovative design of steel structures. Laser welding process differs from conventional arc welding which causes metallurgical differences. Previous studies indicate that the fatigue properties of the laser welds differ significantly from those of conventionally welded joints (Kujala et al., 1999; Laitinen et al., 1999; Remes et. al, 2003). Due to this the level of fatigue strength and also the slope of S-N curves for laser welded joints is different compared to existing fatigue design standards for arc welding. At present, the arc welded joints are designed using either the nominal stress, hot spot stress or notch stress approach. There does not exist common understanding of the applicability of these methods for the design of laser welded joints. The earlier studies (Ring and Dahl, 1994; Weichel and Petershagen, 1995; Toivonen, 1998) indicate that the notch stress method is suitable for laser welds at the endurance limit (N≈2·106). In these studies, however, the modeling the fatigue strength at medium high cycle range (N≈104-2·106) is not considered. The fatigue of the laser and laser-hybrid welded ship structures have been studied in Ship Laboratory at Helsinki University of Technology (HUT) since 1987. Focus on the research have been fatigue of all steel sandwich panels, laser stake welded closed structures and the joints of laser welded traditional ship structures. The experimental and theoretical work, carried out in several national and EU funded research projects, has revealed the main parameters affecting fatigue crack initiation and propagation. Additionally, the behavior of laser welds under cyclic loading was investigated to develop design basis for laser and laser-hybrid welded joints.

In this paper a theoretical model to predict fatigue life of laser or laser hybrid welded joints is presented. The model based on material hardness including macro crack initiation and propagation is validated with experiments done by Remes and Tamminen (2003).

Theoretical modeling of Fatigue Life The process of the fatigue failure in the welded joints can be divided into two main periods: micro cracks nucleation, growth and coalescence (stage I fatigue crack) and macro crack propagation to a length, which causes fracture (stage II fatigue crack). The boundaries of the periods are poorly defined, but it is useful to think that the total fatigue life NF consist of macro crack initiation period NI and macro crack propagation period NP: NF = NI + NP .

(1)

The macro crack initiation life of notched component such as welded joint can be estimated from material fatigue strength taking into account a reduction of fatigue strength by notch. A reduction of fatigue strength of notched structures is most commonly defined by fatigue notch factor Kf. It is the ratio between the fatigue strength of the smooth specimen and the fatigue strength of the notched specimen for the same life duration (N=2·106), see Fig. 1. By means of Fuchs’s (1980) suggestion, the S-N curves of smooth specimens and notched specimens intersect at N=500. Macro crack initiation S-NI curve can be now written on the basis of the fatigue strength on N=500 load cycles ∆σ500 and fatigue strength on N=2·106 load cycles ∆σE:  ∆S ⋅ K f N I =   ∆σ E

  

mI

⋅ 2 ⋅10 6 ,

(2)

where ∆S is nominal stress range. The slope of S-NI curve mI is

(

)

log 2 ⋅ 106 − log(500) .  ∆σ E   − log( ∆σ500 ) log   Kf 

∆σ E = 2 ⋅ (σ'f −σ m ) ⋅ 2 ⋅10 b

,

(4)

where σm is the mean stress, σf’ is fatigue-strength coefficient and b is fatigue-strength exponent. The fatigue strength parameters can be determined most accurately by experimental testing. The testing of a narrow HAZ zones is very difficult or impossible. Alternative, the fatigue strength parameters can be estimated from the material tensile properties or hardness values. Lawrence et. all (1981) purposed the Brinell hardness based estimation for steel with hardness between 150 HB and 700 HB: (5)

1  2 ⋅ ( HB + 100)  b ≈ − ⋅ log . 6 HB  

(6)

The relationship between the Brinell hardness HB and Vickers hardness HV can be carried out using the conversion table from Metals handbook (Boyer and Gall, 1985): (7)

A reduction of fatigue strength by notch i.e. fatigue notch factor can be calculated using Peterson’s equation: K f = 1+

K t −1 , ap 1+ ρ

(8)

where Kt is elastic stress concentration factor, ρ is notch root radius and ap is Peterson’s material parameter relating to the material ultimate strength (Peterson, 1974). The notch radius is determined so that Kf gets the maximum value using analytical formulations developed for butt welds (Anthes et al., 1994). The ultimate strength for a narrow HAZ is estimated from material hardness value HV (Boyer and Gall, 1985). Hardness based estimation for steel is: S u ≈ 3.074 ⋅ HV − 25.0 HV < 340.

C ⋅ ∆K n

da ,

(10)

where ∆K is stress intensity factor, ai is initiated crack size, ac critical crack length and C, n are material constants.

1000 ∆σ500

Kf /K f ∆σE100

10

σ'f ≈ 3.42 ⋅ HB + 342 MPa,

HB ≈ 0.98 ⋅ HV 0.994 .

NP = ∫

ai

The material fatigue strength, ∆σ500 and ∆σE can be estimated using Basquin-Morrow equation: ∆σ 500 = 2 ⋅ (σ'f −σ m ) ⋅ 500 b

1− R

ac

(3)

Log(∆σ)

mI =

Paris Law and propagation equation by Forman et al. (1967):

(9)

The advantage of the approach is that S-NI curve for macro crack initiation can be calculated from the material hardness at the macro crack initiation point i.e. weld root or toe. Macro crack propagation period is calculated using

100

500 1000

6 Log(NI ) 2·101E+07 10000 100000 1E+06

S-N curve of smooth S-Ni Icurve of material component

S-NI curve of notches S-Ni curve of the joint component

Fig. 1: Schematic presentation for determination of S-NI curve for notched component.

Experimental Tests Test Plates

The test plates were 12 mm thick laser cutting RAEX S275 LASER steel plates produced on the plate rolling lines with the chemical composition shown in Table 1. The parent material fulfils the requirements for chemical composition according to classification society guidelines (The Classification Societies’ Requirements for Approval of CO2 Laser Welding Procedures”, 1996). For plate thickness up to 12 mm the limits are: C ≤ 0.12 %, S ≤ 0.005 %, P ≤ 0.010 %, CEV ≤ 0.38 % and Pcm ≤ 0.22 %. Welding of Test Plates

C02-laser (laser) and C02-laser MAG hybrid (hybrid) welding was performed in the Welding Laboratory of the FORCE Technology and in Meyer Werft shipyards. In FORCE Technology A Rofin-Sinar SR 170 17 kW CO2-laser and ESAB ARISTO 500 MAG equipment were used. In the hybrid welding (hybrid CH) MAG torch was traveled 1-2 mm behind of the laser beam. Shielding gas was delivered trough laser and MAG welding heads. Shielding gas of the hybrid welding was mixtures of helium, argon and oxygen. Filler wire was 1 mm diameter ESAB 12.51. Gas flow rate was 20 l/min for the laser and 30 l/min for the MAG. Laser welding

b)

Requirements ≤ 0.12 % ≤ 0.005 % No req. ≤ 0.010 % No req. No req. No req. No req. No req. ≤ 0.38 % ≤ 0.22 %

Welding method

Welding place

FORCE FORCE

Hybrid CM

Hybrid CH

Laser and laser hybrid welding parameters.

Laser

Table 2:

wt % 0.08 0.014 1.39 0.008 0.004 0.028 0.003 0.006 0.001 0.32 0.15

Meyer

Travel speed

m/min

1.0

1.4

1.5

Laser: Power

kW

11.0

14.0

10.0

MAG Current Voltage Wire speed

A V m/min

-

193 21.4 6.9

420 40.6 16.2

Table 3:

Hardness HV5 values of the welded joints.

Welding method / test sample Weld zone Maximum Mean value Standard deviation Heat affected zone Maximum Toe: Mean value Toe: Stand. dev. Root: Mean value Root: Stand. dev.

Hybrid CM

a)

Chemical comp. C Si Mn P S Al Nb V Ti CEV Pcm

Hybrid CH

Smooth weld geometry was observed for laser and hybrid but also for SAW welded joints. Macrographs of the joints are given in Fig. 2. Additionally the laser and hybrid welded joints had a narrow weld breadth and a low weld toe and root. Table 3 gives the results of hardness measurements. The peak hardness values of 231 HV5 from the weld and 215 HV5 from the HAZ in the hybrid CH welded joints were lower than the values of 255 HV5 from the weld and 241 HV5 from the HAZ in the laser welded joint. Peak hardness values of hybrid CM welded joints were 248 HV5. This indicates that the weld material and HAZ of hybrid and laser joints were overmatched compared to the parent material (mean: 131 HV5, stand. dev.: 6.1 HV5). Hardness values of the joints were considered acceptable according to classification society guidelines (1996).

Chemical composition (wt %) of the RAEX S275 LASER steel and classification society’s requirements for chemical composition.

Laser

Properties of Welded Joints

Table 1:

SAW

was performed without any filler and helium was used as a shielding gas. Focal length was 300 mm. Table 2 gives the welding parameters for the laser and hybrid welding. Hybrid CM was performed in Meyer Werft shipyards using a Trumpf TLF 1200 10 kW CO2-laser and Fronius TPS 450 MIG equipment. The MAG torch was traveling 5 mm in front of the laser beam. The filler wire was 1.2 mm diameter Hoesch Weko 4. Shielding gas was helium and the gas flow rate was 40 l/min. A fully penetrated butt joints were produced. The edges of the joint were milled. I-type groove shape was used for laser and hybrid CH test plates. Hybrid CM test plates had Y- type groove shape. Before welding the test pieces were tack welded to ensure zero air gap in the joints. Submerged arc welding (SAW) were performed in a panel production line of Kvaener Masa-Yards Turku shipyards. The welding was done from one side only using two wires. A water-cooled Cu-backing rod was used on the root side. During the welding the plates were clamped using vacuum. Travel speed was 0.65 m/min. Current and voltage are 831 + 504 A and 32 + 35 V respectively. Consumable was ESAB OK 15.00S+10.71 for toe side and ESAB OK 15.00S+10.69 for root side.

188 175 9.2

255 238 9.3

231 219 6.6

248 234 11.2

173 165 5.7 157 3.1

241 228 13.3 202 6.4

215 207 7.0 187 16.2

248 222 13.7 179 12.2

Fatigue Test Specimens

c)

d)

Fig. 2: Macrographs of the welded joints: a) SAW, b) Laser, c) Hybrid CH and d) Hybrid CM welded butt joints.

Fatigue properties of different welded joint were studied using plate test specimens. An hourglass design was used to enable the damage process localization to the welded joints. The thinnest cross-section of the test specimen was located in the middle of weld. Fig. 3 shows the dimensions of the test specimen. The width of the thinnest cross-section is 20 mm. The specimen length is 250 mm and the radius R is 160 mm. Test specimen with two different end types were used, see Fig. 4. Type A test specimen was traditional test specimen without any modifications. Ends of Type B

test specimen were machined so that the bending moments of the specimen were eliminated during the gripping. Type B test specimens were used to study fatigue strength of the welded joint, which has high angular misalignment. The distortions of the welded test specimen were measured in the six points along the specimen surface. On the basis of the measured horizontal deflections, the axial and angular misalignments were defined. Table 4 present statistical mean value and standard deviation of the axial and angular misalignments. The angular misalignment of Hybrid CH welded test specimens was significantly higher than that of Laser, Hybrid CM and SAW specimens.

mm. The critical crack length ac was calculated according to limit load of cracked cross-section. Results for Validation

Table 6 shows summary of the results. The main values on the critical location (toe or root) are presented. Additionally, the comparison of predicted and experimentally determined fatigue strength, FAT95% are given. The average error of the prediction is 15 %. Predicted values are somewhat conservative for the hybrid welded joints. This can also be seen in the fatigue life comparison presented in Fig. 5 and 6. Agreement of the prediction is good for SAW and laser test specimens.

Fatigue Test Results

In this area width w is constant

Fig. 3: Dimensions of test specimens (mm).

Type A

Type B Fig. 4: End types of test specimens: Type A and B.

Hybrid CH

Hybrid CM

0.2 0.12

0.3 0.23

0.47 0.05

0.3 0.22

1.5 0.36

0.18 0.02

Hybrid CM

Welded test specimen

Hybrid CH

Misalignments of test specimens.

Laser

Table 4:

SAW

The welded joints were tested by using cyclic axial tension loading with load ratio R = 0. The fatigue tests were force controlled and load amplitude was kept constant for each test specimen. The load frequency was between 5 Hz and 20 Hz. MTS 810 and Instron servo hydraulic machines were used. The ends of the test specimen were mechanically attached to the clampsystem. The clamp-system was rigid without hinge as is usual in this kind of material testing system. Fatigue test results are shown in Table 5. The slope of S-N curve m and fatigue classes FAT on 50% and 95% survival probability levels were calculated according Hobbacher (1996). Fatigue strength of SAW welded joints was observed to be very good compared to the design curve FAT 100. Fatigue strength of laser welded joint was also good, but somewhat lower than that of SAW welded joint. Hybrid CH specimen Type B and Hybrid CM specimen was observed to have very excellent fatigue strength compared to laser and SAW welded joint. A remarkable difference of the fatigue strength for hybrid CH specimen Type A and B was observed. Fatigue strength of the Type A specimen was significantly lower because of the high angular misalignments. The clamped test grip caused static bending stress if high angular misalignments of test specimen appear.

Validation of Theoretical model

Table 5:

Summary of fatigue test results.

Welded test specimen Test specimen type FAT50% FAT95% Slope of S-N curve m

Laser

The fatigue strength approach for the tested hybrid and laser and SAW welded joints were calculated using the initiation and propagation approach. The calculation was made on probability level P=95 % (mean-2⋅stand. dev.) and P=50% (mean). The static bending stress Sb and secondary bending stress concentration factor Km due to the test specimen misalignments were calculated using linear elastic FE-analysis (E=210 GPa, ν=0.3). IDEAS and ABAQUS software were used. The material values from guidelines BS7608 (1993) were used in the macro crack propagation calculation. The BS7608 recommends for ferritic structural steels (base metal, weld metal and HAZ): C = 3·10-13 and n = 3. In the calculations the initiated crack size was assumed to be similar to the dimension of typical weld defects, about 0.25

Axial misalignm. [mm] Mean value 0.2 Standard deviation 0.11 Angular misalignm. [deg] Mean value -0.4 Standard deviation 0.05

SAW

Theoretical Calculations

A A&B A B A 180 174 129 238 200 172 154 107 222 208 5.8 5.8 3.7 27.8 9.6

SAW welded joint Specimen type A

Predicted fatigue life [Cycles]

10 000 000

Laser welded joint Specimen type A 1 000 000

Laser welded joint Specimen type B Nf_Pred.=Nf_obs. Nf,pred.=Nf,obs.

100 000 Nf_Pred.=2*Nf_obs. Nf,pred.=2⋅Nf,obs. Nf_Pred.=1/2*Nf_obs. Nf,pred.=1/2⋅Nf,obs.

10 000 10 000

100 000

1 000 000

10 000 000

Observed fatigue life [Cycles] Fig. 5:

Comparison of theoretically calculated (predicted) and experimentally observed fatigue life of the SAW and laser welded test specimens.

Predicted fatigue life [Cycles]

10 000 000

Hybrid welded joint CH Specimen type A Hybrid welded joint CH Specimen type B

1 000 000

Hybrid welded joint CM Specimen type A

Nf,pred.=Nf,obs. Nf_Pred.=Nf_obs. 100 000 Nf_Pred.=2*Nf_obs. Nf,pred.=2⋅Nf,obs. Nf_Pred.=1/2*Nf_obs. Nf,pred.=1/2⋅Nf,obs.

10 000 10 000

100 000

1 000 000

10 000 000

Observed fatigue life [Cycles]

Welded test specimen Test specimen type

A

A&B

Summary of theoretical calculations Critical location Root Root Static stress Sb.max

67

A

B

Hybrid CM

Summary and comparison of theoretical calculated fatigue strength FAT95%.

Hybrid CH

Table 6:

Laser

Comparison of theoretically calculated (predicted) and experimentally observed fatigue life of the hybrid CH and hybrid CM welded test specimens.

SAW

Fig. 6:

A

Toe Toe Root

19&0 281

0

-29

Km,95%

1.16

1.16

1.36 1.36 1.09

Kf,95%

1.70

2.46

2.15 2.15 2.54

Comparison of prediction and experiments: FAT95% Prediction 175 171 98 150 161 Experiments Difference [%]

172

154

2

10

107 222 -9

-48

200 -29

Conclusions The fatigue strength of hybrid welded butt joints have been found to be very excellent. FAT class of 200-220 is significantly higher than that of the laser and SAW welded joints, 154 and 172 respectively. A gentle slope of S-N curve was indicated for all the welded joints compared to the design codes. Hobbacher gives m value of 3 and FAT class of 100 for transverse loaded butt weld made in shop in flat position. Similar observations for laser welded joints have been done in previous studies. Significantly lower fatigue strength for hybrid CH welded test specimen Type A was found. The clamped test grip caused static bending stress at macro crack initiation point. That was seen to reduce the fatigue strength of laser hybrid welded joint about 85%. Fatigue strength approach for laser welded joint is presented. The crack initiation-propagation approach based on the material hardness gives good fatigue strength and

life prediction for SAW and laser welded specimen. The prediction for hybrid weld specimens is somewhat conservative especially near endurance limit. Present model does not include the effect of material non-linearity and “weld quality”, which might explain differences. Theoretical analysis indicates that excellent fatigue strength of laser and hybrid welded joint is related to the geometrical effects but also to good fatigue properties of welded material.

Acknowledgement The results given in this paper are part of the “Fatigue strength modeling of laser welded joint” -research project. The project has been funded by Finnish Academy. The financial support is here gratefully acknowledged. The experimental fatigue testing was carried out with co-operation between Ship Laboratory of Helsinki University of Technology and Polish Academy of Science. Force Institute, Meyer Werft and Kvaener-Masa Yards are also gratefully acknowledged for the practical and experimental support to carry out welding of the test specimens.

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