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The effects of residual stresses on the fatigue life of 5083-O aluminum alloy spot welded joints
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Procedia Engineering
Procedia Engineering 00 (2009) 000–000 Procedia Engineering 2 (2010) 1077–1085 www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Fatigue 2010
The effects of residual stresses on the fatigue life of 5083-O aluminum alloy spot welded joints Soran Hassanifarda, * and Mohammad Zehsazb a,b
Building No. 8, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran. Received 25 February 2010; revised 10 March 2010; accepted 15 March 2010
Abstract In this study, resistance spot welding (RSW) process of 5083-O Aluminum alloy has been simulated numerically using an axisymmetric model of electrodes and sheets, and then the effects of residual stresses have been investigated on the fatigue life of the joints. All process parameters except electrode clamping force have been considered to be constant during RSW. Three different electrode force level have been considered and then dimensions of nuggets, HAZ and gaps have been obtained numerically. Three kinds of spot welded models with three different gap values between sheet joints have been simulated using Ansys code. Non-linear analysis was performed to obtain the local stress and strain ranges and then, Morrow equation with particular consideration of residual stress and gap distance effects has been applied to estimate fatigue lives. The results show that, with increasing the electrode force, the gap values between sheet joints increase. The results also reveal that the center region and the roots of nuggets have surrounded by the relatively large amounts of tensile residual stresses and also increasing the electrode force, reduce the amounts of residual stresses. The comparison between numerical results of fatigue lives and experimental data provided good agreement between numerical predictions and experiments. c 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license.
Keywords: Resistance spot welding; Electrode clamping force; Residual stresses; Fatigue life.
1. Introduction Resistance spot welding is widely used in industry especially in vehicle manufacturing field and the electronic instruments due to having good rate of welding process, good quality of joints and low cost. Nowadays, the use of aluminium alloys in automotive industry is very common and is used instead of steel alloys because of their advantages like low weight. Aluminum alloys are usually more difficult to weld. This is because of their narrow plastic range, low bulk resistance and greater thermal conductivity. Although several papers have been published dealing with the fatigue life of spot welded joints [1-8], it seems that because of very complex and maybe unknown mechanical and metallurgical parameters, further attempts are required for better understanding the behavior of the joints subjected to the repetitive loading. In this paper, a complete investigation about the simulation of resistance
* Corresponding author. Tel.: +98-411-339-3057; fax: +98-411-335-4153. E-mail address: [email protected].
c 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. 1877-7058 doi:10.1016/j.proeng.2010.03.116
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spot welding and the fatigue life prediction in spot welded joints has been studied numerically and then the results have been compared with the available experimental data. 2. Resistance Spot Welding Simulation The selected material in this investigation is 1.5 mm thick 5083-O aluminum alloy sheets whose chemical composition and mechanical properties have been presented in Tables 1 and 2, respectively. Three different load levels of electrode force (2500N, 3000N, and 3500 N) had been used to prepare the test samples in the previous investigation which had been called A Type, B Type, and C Type samples [9]. These three kinds of spot welded joints have been considered to numerically simulate the welding process and to obtain the spot weld attributes such as nugget diameters, sheet spacing values as well as the amounts of welding residual stresses. In the second part of the present study, the effects of welding residual stresses on the fatigue crack initiation lives of spot welded joints have been investigated based on the Morrow’s damage equation and then the results have been compared with the available experimental data. Welding electric current and time have been considered to be fixed during RSW process and their values are 20kA and 5 cycles (0.1 sec), respectively. The holding cycle is 0.25 second and mechanical electrode forces of 2500N, 3000N and 3500N have been applied at the top of the electrode during the welding and holding stages. The cooling period has been considered about 10 seconds. Thermal and mechanical boundary conditions of electrodes and sheets in the RSW process have been presented in Figure 1. It should be noted that the temperature in the water cooling chamber has been considered constant at 25 degree of Celsius. Nugget sizes and the amounts of gap distance between sheets of spot welded joints were measured by micrograph observation of the cut-off samples from the centre line of the spot welds. Details of experiments are available in reference [9]. Table 1. Chemical composition of the 5083-O Aluminum alloy Cu 0.1 Values are given in percentages
Si 0.4
Fe 0.4
Mn 0.4-1
Mg 4-4.9
Zn 0.25
Ti 0.15
Al bal
Table 2. Mechanical properties of the 5083-O Aluminum alloy Young’s modulus (GPa) 70
Yield stress (MPa) 145
Tensile strength (MPa) 290
Elongation (%) 22
Electrode Force
25 D C h 10 W / m 2 C
25 D C Upper Sheet
Ux = 0 Faying Surface
h
Electrode
h Lower Sheet
Uy = 0
Fig. 1. Thermal and mechanical boundary conditions of electrodes and sheets
Poisson’s ratio (Q ) 0.33
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Figure 2 shows the plastic deformations of the aluminum alloy 5083-O at different temperatures which have been simulated using bilinear isotropic hardening model. 200
Stress (MPa)
160
21D C 93D C 149D C 204D C
120
80
260D C 316D C
40
u103
0 0
1.6
3.2
4.8
6.4
8
Strain
Fig. 2. Bi-linear model of the plastic deformations of aluminium alloy 5083-O at different temperatures
Temperature dependent electric and contact resistances of copper and Aluminum alloy 5083-O have been presented in Table 3. Table 3. Electric and contact resistances of Copper and Aluminum alloy 5083-O
Temperature
,D C
20
200
300
400
500
Aluminium alloy resistance, u108 :m
5.8
7.7
8.8
9.8
20.5
Copper electrode resistance, u108 :m
2.64
3.99
5.19
6.01
7.48
Contact resistance (E/W), u108 :m
580
370
280
98
20.5
Contact resistance (W/W), u108 :m
290
190
140
49
20.5
3. Results of RSW Simulation The temperature profile in the spot weld sheet joints after welding cycle has been presented in Figure 3. Figure 4 show some attributes of spot weld joint which have been obtained from FE analysis and have compared with a photograph of a cut-off section from the centre line of a corresponded spot weld. The amount of gap between two sheets has been measured from the nodal displacement of the end of each sheet joint. Electrode
Upper Sheet
Half of Penetration Half of Fusion Zone Width 25
93
161
229
297
365
434
501
570
638
Fig. 3. The temperature profile in the sheet joint after welding cycle for all kinds of spot welds
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The numerical results of spot weld attributes have been compared with the available experimental data and have summarized in Table 4.
Gap
Fusion Zone Width
Fig. 4. Comparison of spot weld attributes between numerical results and experimental morphology
Table 4. Comparison between numerical results of spot weld attributes and experimental data Type of specimens A type
Electrode force [kN] 2.5
B type
3
C type
3.5
Nugget diameter [mm] (Experimental)
Nugget diameter [mm] (Numerical)
7.48 (6.10
t
)
7.34(6.00
t
)
7.53 (6.14
t
)
7.34(6.00
t
)
6.08 (4.96
t
)
7.34(6.00
t
)
Gap distance [mm] (Experimental) 0.09
Gap distance [mm] (Numerical) 0.09
0.11
0.10
0.13
0.11
The transient temperature distribution at the end of holding cycle has been presented in Figure 5. Figures 6-8 show the stress distribution in the longitudinal direction of all kinds of spot weld joints after the cooling cycle. It can be seen from Figures 6-8 that the areas near the nugget have been surrounded by the relatively large amount of tensile stresses. It can also be seen that the maximum values of tensile residual stresses reduce with increasing the electrode force level.
1250
End of Welding Cycle
Temperature
1000
Melting Point of Aluminum Alloy 5083-O
750
638D C
500
End of Holding Cycle 250
Cooling 0
0.1
0.2
0.3
0.4
0.5
Time (sec)
Fig. 5. Temperature distribution at the end of holding cycle of RSW process
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Electrode Upper Sheet
-16.9
3.5
23.8
44.1
64.5
84.8
105.2
125.5
145.8
166.2
Fig. 6. Stress distribution in the longitudinal direction of A type spot welded joint (electrode force=2500N) Electrode Upper Sheet
-9.1
10
29.1
48.2
67.3
86.4
105.4
124.5
143.6
162.7
Fig. 7. Stress distribution in the longitudinal direction of B type spot welded joint (electrode force=3000N)
Electrode Upper Sheet
-15.4
3.3
21.9
40.5
59.1
77.8
96.4
115
133.7
152.3
Fig. 8. Stress distribution in the longitudinal direction of C type spot welded joint (electrode force=3500N)
The welding residual stress profiles after the cooling cycle in the longitudinal directions of the sheets for all kinds of spot welded joints have been shown in Figure 9. As it can be seen in Figure 9, the welding residual stresses at whole nugget region reduce with increasing the electrode clamping pressure level. A Type (Electrode Force=2500N)
Residual stress (MPa)
200
B Type (Electrode Force=3000N) C Type (Electrode Force=3500N)
150
100
50
0 0
0.5
1
1.5
2
2.5
3
3.5
4
Distance from nugget center (mm) Fig. 9. Welding residual stress profiles after the cooling cycle in the longitudinal directions of the sheets for all kinds of spot welded joints
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Figures 10-12 show the welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle in the longitudinal directions of the sheets for all kinds of spot welded joints, together.
End of Cooling Cycle (10sec)
Residual stress (MPa)
200 150 100
End of Holding Cycle (0.35sec)
50
Electrode Removal (after 1.1sec)
0 0
0.5
1
1.5
2
2.5
3
3.5
4
-50 End of Welding Cycle (0.1sec)
-100
Distance from nugget center (mm) Fig. 10. Welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle for A type spot weld (electrode force=2500N)
200
End of Cooling Cycle (10sec)
Residual stress (MPa)
150 100 End of Holding Cycle (0.35sec)
50
Electrode Removal (after 1.1sec)
0 0
1
2
3
4
-50 End of Welding Cycle (0.1sec)
-100
Distance from nugget center (mm)
Fig. 11. Welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle for B type spot weld (electrode force=3000N)
End of Cooling Cycle (10sec)
Residual stress (MPa)
150 100 50
End of Holding Cycle (0.35sec) Electrode Removal (after 1.1sec)
0 0
0.5
1
1.5
2
2.5
3
3.5
4
-50 -100
End of Welding Cycle (0.1sec)
Distance from nugget center (mm) Fig. 12. Welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle for C type spot weld (electrode force=3500N)
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4. Fatigue Analysis The most commonly referenced spot weld fatigue life prediction method based on structural stresses and strains near the spot welds are: stress based approach, strain based approach, structural stress method and fracture mechanics approach. In this paper the strain-based method has been employed for fatigue analysis. For this reason, the modified Morrow’s damage equation has been employed which can be written as follows: 'H 2
V f Vm 2E
(2 N f ) b H f (2 N f ) c ,
in which:
Vm
V m * V m res ,
where 'H is the total strain amplitude, V f is the fatigue strength coefficient, V m is the mean stress, b is the fatigue strength exponent, N f is the number of cycles, H f is the fatigue ductility coefficient, c is the fatigue ductility exponent and E is the Young’s modulus. It should be noted that V m * is the amount of mean stress which has been obtained from the non-linear 3D analysis due to applying external loads, and V m res is the corresponding residual stress value which has been obtained from the transient analysis of RSW simulation. To obtain the fatigue life of the joints with three different gaps listed in Table 4, three dimensional models of the joints were simulated using Ansys finite element software. Structural 8-node element was used to perform the nonlinear analysis for obtaining the amounts of stress and strain values near the roots of nuggets. Fatigue parameters of 5083-O aluminium alloy which have been obtained based on the Uniform Materials Law [10], have been presented in Table 5. Table 5. Fatigue parameters of 5083-O aluminum alloy obtained from the Uniform Materials Law [10] Cyclic Material Properties
Vf
Aluminium Alloy
1.67Su
484 MPa
b
-0.095
Hf
0.35
c
-0.69
Non-linear analyses for different loads at the approximate range of 30%-80% of static fracture load were applied on the models and the values of equivalent mean stress and strain range were obtained during one complete loadingunloading cycle. Loading data, the values of mean stress and strain amplitude for all kinds of spot weld specimens have been listed in Table 6. The results indicate that increasing the gap distance between sheets decrease the values of mean stress and strain range. Figure 13 shows the stress range versus fatigue crack initiation lives for all kinds of spot weld specimens obtained from the strain-based fatigue life prediction based on the modified Morrow’s damage equation. Experimentally fatigue test results for three different types of spot welded joints have been re-called in Figure 14 [9]. As it can be seen in Figure 13, smaller gaps predict the smaller lives for the joints, because the small distance can behave as a sharp crack. This Figure also shows very good agreement and similar pattern with experimental S-N curve shown in Figure 14.
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Table 6. Mean stress and strain range values for all kinds of the joints at different external loads
A-Type (Gap=0.09mm)
B-Type (Gap=0.11mm)
C-Type (Gap=0.13mm)
Load (kN)
V m (MPa)
'H
V m (MPa)
'H
V m (MPa)
'H
1.6
108.62
0.0028
103.4
0.0023
101.34
0.0022
2
109.65
0.0048
108.1
0.0045
106.03
0.0042
2.4
119.82
0.007
118.5
0.0067
114.58
0.0062
2.8
129.03
0.0091
128.4
0.0086
125.36
0.0082
3.2
143.53
0.0141
141.6
0.0138
141.54
0.0131
Power (C-Type with residual stress (Gap=0.13mm)) Power (B-Type with residual stress (Gap=0.11mm)) Power (A-Type with residual stress (Gap=0.09mm))
Stress range (MPa)
120 100 80 60 40 20 0 1.E+01
1.E+02
1.E+03
1.E+04
Fatigue crack initiation life (Ni)
Fig. 13. Stress range versus fatigue crack initiation lives for all kinds of spot weld specimens predicted from the strain-based approach
120
Stress Range (MPa)
Electrode Force=3500 N 100
Electrode Force=3000 N Electrode Force=2500 N
80 60 40 20 0 1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
Number of cycles to failure (N f )
Fig. 14. Fatigue test results for three different types of spot welded joints
5. Conclusions In the present study, three kinds of spot welded models with three different gap values between sheet joints have been simulated using Ansys FE code. Morrow’s damage equation with particular consideration of residual stress and gap distance effects has been applied to predict fatigue crack initiation lives of spot weld models. The following conclusions have been drawn. The results show that, the welding residual stresses at whole nugget regions reduce with increasing the electrode clamping force level. The results also reveal that the areas near the nuggets have been surrounded by the relatively
S. Hassanifard, M. Zehsaz / Procedia Engineering 2 (2010) 1077–1085 S. Hassanifard et al. / Procedia Engineering 00 (2010) 000–000
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large amount of tensile stresses. The comparison between numerical results of fatigue crack initiation lives and experimental fatigue data provided good agreement between numerical predictions and experiments.
References [1] Long X, Khanna SK. Fatigue properties and failure characterization of spot welded high strength steel sheet. Int J Fatigue 2007; 29: 879-886. [2] Spitsen R., Kim D, Flinn B, Ramulu M, Easterbrook ET. The effects of post-weld cold working processes on the fatigue strength of low carbon steel resistance spot welds. J Manufact Sci and Eng Trans ASME 2005; 127, 718-723. [3] Gean A., Westgate SA, Kucza JC, Ehrstrom JC. Static and fatigue behavior of spot welded 5182-O aluminum alloy sheet. Weld J 1999; 78, No. 3, pp. 80-86. [4] Sun X, Stephens EV, Davies RW, Khaleel MA, Spinella DJ. Effects of fusion zone size on failure modes and static strength of aluminum resistance spot welds. Weld J 2004; 83, No. 11, pp. 308-318. [5] Chang BH, Zhou Y. Numerical study on the effect of electrode force in small-scale resistance spot welding. J Materials Processing Technol 2003; 139, 635-641. [6] Ni K, Mahadevan S. Strain-based probabilistic fatigue life prediction of spot-welded joints. Int J Fatigue 2004; 26, 763-772. [7] Adib H, Gilgert J, Pluvinage G. Fatigue life duration prediction for welded spots by volumetric method. Int J Fatigue 2004; 26, 81-94. [8] Hassanifard S, Zehsaz M, Tohgo K, Ohguma T. The prediction of fatigue crack initiation life in spot welds. J Strain 2009; 45, 489-497. [9] Hassanifard S, Zehsaz M, Tohgo K. The effects of electrode force on the mechanical behavior of resistance spot-welded 5083-O aluminum alloy joints. J Strain 2009; DOI: 10.1111/j.1475-1305.2008.00554.x. [10] Lee YL, Pan J, Hathaway R, Barkey M. Fatigue testing and analysis (Theory and Practice). Elsevier Inc; 2005, Amsterdam.
Procedia Engineering
Procedia Engineering 00 (2009) 000–000 Procedia Engineering 2 (2010) 1077–1085 www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Fatigue 2010
The effects of residual stresses on the fatigue life of 5083-O aluminum alloy spot welded joints Soran Hassanifarda, * and Mohammad Zehsazb a,b
Building No. 8, Faculty of Mechanical Engineering, University of Tabriz, Tabriz, Iran. Received 25 February 2010; revised 10 March 2010; accepted 15 March 2010
Abstract In this study, resistance spot welding (RSW) process of 5083-O Aluminum alloy has been simulated numerically using an axisymmetric model of electrodes and sheets, and then the effects of residual stresses have been investigated on the fatigue life of the joints. All process parameters except electrode clamping force have been considered to be constant during RSW. Three different electrode force level have been considered and then dimensions of nuggets, HAZ and gaps have been obtained numerically. Three kinds of spot welded models with three different gap values between sheet joints have been simulated using Ansys code. Non-linear analysis was performed to obtain the local stress and strain ranges and then, Morrow equation with particular consideration of residual stress and gap distance effects has been applied to estimate fatigue lives. The results show that, with increasing the electrode force, the gap values between sheet joints increase. The results also reveal that the center region and the roots of nuggets have surrounded by the relatively large amounts of tensile residual stresses and also increasing the electrode force, reduce the amounts of residual stresses. The comparison between numerical results of fatigue lives and experimental data provided good agreement between numerical predictions and experiments. c 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license.
Keywords: Resistance spot welding; Electrode clamping force; Residual stresses; Fatigue life.
1. Introduction Resistance spot welding is widely used in industry especially in vehicle manufacturing field and the electronic instruments due to having good rate of welding process, good quality of joints and low cost. Nowadays, the use of aluminium alloys in automotive industry is very common and is used instead of steel alloys because of their advantages like low weight. Aluminum alloys are usually more difficult to weld. This is because of their narrow plastic range, low bulk resistance and greater thermal conductivity. Although several papers have been published dealing with the fatigue life of spot welded joints [1-8], it seems that because of very complex and maybe unknown mechanical and metallurgical parameters, further attempts are required for better understanding the behavior of the joints subjected to the repetitive loading. In this paper, a complete investigation about the simulation of resistance
* Corresponding author. Tel.: +98-411-339-3057; fax: +98-411-335-4153. E-mail address: [email protected].
c 2010 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. 1877-7058 doi:10.1016/j.proeng.2010.03.116
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spot welding and the fatigue life prediction in spot welded joints has been studied numerically and then the results have been compared with the available experimental data. 2. Resistance Spot Welding Simulation The selected material in this investigation is 1.5 mm thick 5083-O aluminum alloy sheets whose chemical composition and mechanical properties have been presented in Tables 1 and 2, respectively. Three different load levels of electrode force (2500N, 3000N, and 3500 N) had been used to prepare the test samples in the previous investigation which had been called A Type, B Type, and C Type samples [9]. These three kinds of spot welded joints have been considered to numerically simulate the welding process and to obtain the spot weld attributes such as nugget diameters, sheet spacing values as well as the amounts of welding residual stresses. In the second part of the present study, the effects of welding residual stresses on the fatigue crack initiation lives of spot welded joints have been investigated based on the Morrow’s damage equation and then the results have been compared with the available experimental data. Welding electric current and time have been considered to be fixed during RSW process and their values are 20kA and 5 cycles (0.1 sec), respectively. The holding cycle is 0.25 second and mechanical electrode forces of 2500N, 3000N and 3500N have been applied at the top of the electrode during the welding and holding stages. The cooling period has been considered about 10 seconds. Thermal and mechanical boundary conditions of electrodes and sheets in the RSW process have been presented in Figure 1. It should be noted that the temperature in the water cooling chamber has been considered constant at 25 degree of Celsius. Nugget sizes and the amounts of gap distance between sheets of spot welded joints were measured by micrograph observation of the cut-off samples from the centre line of the spot welds. Details of experiments are available in reference [9]. Table 1. Chemical composition of the 5083-O Aluminum alloy Cu 0.1 Values are given in percentages
Si 0.4
Fe 0.4
Mn 0.4-1
Mg 4-4.9
Zn 0.25
Ti 0.15
Al bal
Table 2. Mechanical properties of the 5083-O Aluminum alloy Young’s modulus (GPa) 70
Yield stress (MPa) 145
Tensile strength (MPa) 290
Elongation (%) 22
Electrode Force
25 D C h 10 W / m 2 C
25 D C Upper Sheet
Ux = 0 Faying Surface
h
Electrode
h Lower Sheet
Uy = 0
Fig. 1. Thermal and mechanical boundary conditions of electrodes and sheets
Poisson’s ratio (Q ) 0.33
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Figure 2 shows the plastic deformations of the aluminum alloy 5083-O at different temperatures which have been simulated using bilinear isotropic hardening model. 200
Stress (MPa)
160
21D C 93D C 149D C 204D C
120
80
260D C 316D C
40
u103
0 0
1.6
3.2
4.8
6.4
8
Strain
Fig. 2. Bi-linear model of the plastic deformations of aluminium alloy 5083-O at different temperatures
Temperature dependent electric and contact resistances of copper and Aluminum alloy 5083-O have been presented in Table 3. Table 3. Electric and contact resistances of Copper and Aluminum alloy 5083-O
Temperature
,D C
20
200
300
400
500
Aluminium alloy resistance, u108 :m
5.8
7.7
8.8
9.8
20.5
Copper electrode resistance, u108 :m
2.64
3.99
5.19
6.01
7.48
Contact resistance (E/W), u108 :m
580
370
280
98
20.5
Contact resistance (W/W), u108 :m
290
190
140
49
20.5
3. Results of RSW Simulation The temperature profile in the spot weld sheet joints after welding cycle has been presented in Figure 3. Figure 4 show some attributes of spot weld joint which have been obtained from FE analysis and have compared with a photograph of a cut-off section from the centre line of a corresponded spot weld. The amount of gap between two sheets has been measured from the nodal displacement of the end of each sheet joint. Electrode
Upper Sheet
Half of Penetration Half of Fusion Zone Width 25
93
161
229
297
365
434
501
570
638
Fig. 3. The temperature profile in the sheet joint after welding cycle for all kinds of spot welds
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The numerical results of spot weld attributes have been compared with the available experimental data and have summarized in Table 4.
Gap
Fusion Zone Width
Fig. 4. Comparison of spot weld attributes between numerical results and experimental morphology
Table 4. Comparison between numerical results of spot weld attributes and experimental data Type of specimens A type
Electrode force [kN] 2.5
B type
3
C type
3.5
Nugget diameter [mm] (Experimental)
Nugget diameter [mm] (Numerical)
7.48 (6.10
t
)
7.34(6.00
t
)
7.53 (6.14
t
)
7.34(6.00
t
)
6.08 (4.96
t
)
7.34(6.00
t
)
Gap distance [mm] (Experimental) 0.09
Gap distance [mm] (Numerical) 0.09
0.11
0.10
0.13
0.11
The transient temperature distribution at the end of holding cycle has been presented in Figure 5. Figures 6-8 show the stress distribution in the longitudinal direction of all kinds of spot weld joints after the cooling cycle. It can be seen from Figures 6-8 that the areas near the nugget have been surrounded by the relatively large amount of tensile stresses. It can also be seen that the maximum values of tensile residual stresses reduce with increasing the electrode force level.
1250
End of Welding Cycle
Temperature
1000
Melting Point of Aluminum Alloy 5083-O
750
638D C
500
End of Holding Cycle 250
Cooling 0
0.1
0.2
0.3
0.4
0.5
Time (sec)
Fig. 5. Temperature distribution at the end of holding cycle of RSW process
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Electrode Upper Sheet
-16.9
3.5
23.8
44.1
64.5
84.8
105.2
125.5
145.8
166.2
Fig. 6. Stress distribution in the longitudinal direction of A type spot welded joint (electrode force=2500N) Electrode Upper Sheet
-9.1
10
29.1
48.2
67.3
86.4
105.4
124.5
143.6
162.7
Fig. 7. Stress distribution in the longitudinal direction of B type spot welded joint (electrode force=3000N)
Electrode Upper Sheet
-15.4
3.3
21.9
40.5
59.1
77.8
96.4
115
133.7
152.3
Fig. 8. Stress distribution in the longitudinal direction of C type spot welded joint (electrode force=3500N)
The welding residual stress profiles after the cooling cycle in the longitudinal directions of the sheets for all kinds of spot welded joints have been shown in Figure 9. As it can be seen in Figure 9, the welding residual stresses at whole nugget region reduce with increasing the electrode clamping pressure level. A Type (Electrode Force=2500N)
Residual stress (MPa)
200
B Type (Electrode Force=3000N) C Type (Electrode Force=3500N)
150
100
50
0 0
0.5
1
1.5
2
2.5
3
3.5
4
Distance from nugget center (mm) Fig. 9. Welding residual stress profiles after the cooling cycle in the longitudinal directions of the sheets for all kinds of spot welded joints
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Figures 10-12 show the welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle in the longitudinal directions of the sheets for all kinds of spot welded joints, together.
End of Cooling Cycle (10sec)
Residual stress (MPa)
200 150 100
End of Holding Cycle (0.35sec)
50
Electrode Removal (after 1.1sec)
0 0
0.5
1
1.5
2
2.5
3
3.5
4
-50 End of Welding Cycle (0.1sec)
-100
Distance from nugget center (mm) Fig. 10. Welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle for A type spot weld (electrode force=2500N)
200
End of Cooling Cycle (10sec)
Residual stress (MPa)
150 100 End of Holding Cycle (0.35sec)
50
Electrode Removal (after 1.1sec)
0 0
1
2
3
4
-50 End of Welding Cycle (0.1sec)
-100
Distance from nugget center (mm)
Fig. 11. Welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle for B type spot weld (electrode force=3000N)
End of Cooling Cycle (10sec)
Residual stress (MPa)
150 100 50
End of Holding Cycle (0.35sec) Electrode Removal (after 1.1sec)
0 0
0.5
1
1.5
2
2.5
3
3.5
4
-50 -100
End of Welding Cycle (0.1sec)
Distance from nugget center (mm) Fig. 12. Welding residual stress distributions after the end of welding cycle, holding cycle, electrode removal period and cooling cycle for C type spot weld (electrode force=3500N)
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4. Fatigue Analysis The most commonly referenced spot weld fatigue life prediction method based on structural stresses and strains near the spot welds are: stress based approach, strain based approach, structural stress method and fracture mechanics approach. In this paper the strain-based method has been employed for fatigue analysis. For this reason, the modified Morrow’s damage equation has been employed which can be written as follows: 'H 2
V f Vm 2E
(2 N f ) b H f (2 N f ) c ,
in which:
Vm
V m * V m res ,
where 'H is the total strain amplitude, V f is the fatigue strength coefficient, V m is the mean stress, b is the fatigue strength exponent, N f is the number of cycles, H f is the fatigue ductility coefficient, c is the fatigue ductility exponent and E is the Young’s modulus. It should be noted that V m * is the amount of mean stress which has been obtained from the non-linear 3D analysis due to applying external loads, and V m res is the corresponding residual stress value which has been obtained from the transient analysis of RSW simulation. To obtain the fatigue life of the joints with three different gaps listed in Table 4, three dimensional models of the joints were simulated using Ansys finite element software. Structural 8-node element was used to perform the nonlinear analysis for obtaining the amounts of stress and strain values near the roots of nuggets. Fatigue parameters of 5083-O aluminium alloy which have been obtained based on the Uniform Materials Law [10], have been presented in Table 5. Table 5. Fatigue parameters of 5083-O aluminum alloy obtained from the Uniform Materials Law [10] Cyclic Material Properties
Vf
Aluminium Alloy
1.67Su
484 MPa
b
-0.095
Hf
0.35
c
-0.69
Non-linear analyses for different loads at the approximate range of 30%-80% of static fracture load were applied on the models and the values of equivalent mean stress and strain range were obtained during one complete loadingunloading cycle. Loading data, the values of mean stress and strain amplitude for all kinds of spot weld specimens have been listed in Table 6. The results indicate that increasing the gap distance between sheets decrease the values of mean stress and strain range. Figure 13 shows the stress range versus fatigue crack initiation lives for all kinds of spot weld specimens obtained from the strain-based fatigue life prediction based on the modified Morrow’s damage equation. Experimentally fatigue test results for three different types of spot welded joints have been re-called in Figure 14 [9]. As it can be seen in Figure 13, smaller gaps predict the smaller lives for the joints, because the small distance can behave as a sharp crack. This Figure also shows very good agreement and similar pattern with experimental S-N curve shown in Figure 14.
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Table 6. Mean stress and strain range values for all kinds of the joints at different external loads
A-Type (Gap=0.09mm)
B-Type (Gap=0.11mm)
C-Type (Gap=0.13mm)
Load (kN)
V m (MPa)
'H
V m (MPa)
'H
V m (MPa)
'H
1.6
108.62
0.0028
103.4
0.0023
101.34
0.0022
2
109.65
0.0048
108.1
0.0045
106.03
0.0042
2.4
119.82
0.007
118.5
0.0067
114.58
0.0062
2.8
129.03
0.0091
128.4
0.0086
125.36
0.0082
3.2
143.53
0.0141
141.6
0.0138
141.54
0.0131
Power (C-Type with residual stress (Gap=0.13mm)) Power (B-Type with residual stress (Gap=0.11mm)) Power (A-Type with residual stress (Gap=0.09mm))
Stress range (MPa)
120 100 80 60 40 20 0 1.E+01
1.E+02
1.E+03
1.E+04
Fatigue crack initiation life (Ni)
Fig. 13. Stress range versus fatigue crack initiation lives for all kinds of spot weld specimens predicted from the strain-based approach
120
Stress Range (MPa)
Electrode Force=3500 N 100
Electrode Force=3000 N Electrode Force=2500 N
80 60 40 20 0 1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
Number of cycles to failure (N f )
Fig. 14. Fatigue test results for three different types of spot welded joints
5. Conclusions In the present study, three kinds of spot welded models with three different gap values between sheet joints have been simulated using Ansys FE code. Morrow’s damage equation with particular consideration of residual stress and gap distance effects has been applied to predict fatigue crack initiation lives of spot weld models. The following conclusions have been drawn. The results show that, the welding residual stresses at whole nugget regions reduce with increasing the electrode clamping force level. The results also reveal that the areas near the nuggets have been surrounded by the relatively
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large amount of tensile stresses. The comparison between numerical results of fatigue crack initiation lives and experimental fatigue data provided good agreement between numerical predictions and experiments.
References [1] Long X, Khanna SK. Fatigue properties and failure characterization of spot welded high strength steel sheet. Int J Fatigue 2007; 29: 879-886. [2] Spitsen R., Kim D, Flinn B, Ramulu M, Easterbrook ET. The effects of post-weld cold working processes on the fatigue strength of low carbon steel resistance spot welds. J Manufact Sci and Eng Trans ASME 2005; 127, 718-723. [3] Gean A., Westgate SA, Kucza JC, Ehrstrom JC. Static and fatigue behavior of spot welded 5182-O aluminum alloy sheet. Weld J 1999; 78, No. 3, pp. 80-86. [4] Sun X, Stephens EV, Davies RW, Khaleel MA, Spinella DJ. Effects of fusion zone size on failure modes and static strength of aluminum resistance spot welds. Weld J 2004; 83, No. 11, pp. 308-318. [5] Chang BH, Zhou Y. Numerical study on the effect of electrode force in small-scale resistance spot welding. J Materials Processing Technol 2003; 139, 635-641. [6] Ni K, Mahadevan S. Strain-based probabilistic fatigue life prediction of spot-welded joints. Int J Fatigue 2004; 26, 763-772. [7] Adib H, Gilgert J, Pluvinage G. Fatigue life duration prediction for welded spots by volumetric method. Int J Fatigue 2004; 26, 81-94. [8] Hassanifard S, Zehsaz M, Tohgo K, Ohguma T. The prediction of fatigue crack initiation life in spot welds. J Strain 2009; 45, 489-497. [9] Hassanifard S, Zehsaz M, Tohgo K. The effects of electrode force on the mechanical behavior of resistance spot-welded 5083-O aluminum alloy joints. J Strain 2009; DOI: 10.1111/j.1475-1305.2008.00554.x. [10] Lee YL, Pan J, Hathaway R, Barkey M. Fatigue testing and analysis (Theory and Practice). Elsevier Inc; 2005, Amsterdam.