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Numerical stress analysis in resistance spot-welded nugget due to post-weld shear loading
Journal of Manufacturing Processes 27 (2017) 284–290
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Full Length Article
Numerical stress analysis in resistance spot-welded nugget due to post-weld shear loading Rasoul Moharrami ∗ , Behzad Hemmati Mechanical Engineering Department, University of Zanjan, Iran
a r t i c l e
i n f o
Article history: Received 3 October 2016 Received in revised form 25 April 2017 Accepted 8 May 2017 Keywords: Resistance spot weld Stress analysis Residual stress Shear loading Numerical
a b s t r a c t The magnitude and state of residual stress has a great influence on the fatigue life of sheet metal joints used in the automobile and aircraft industries. The present study developed a parametric 3D finite element model for simulation of welding and post-weld loading on the specimen. Electro-thermo-mechanical analysis is utilized to estimate the residual stress distribution at the nuggets and their surroundings at different stages of welding and post-weld mechanical loading. The results show that at the end of postweld loading, the maximum tensile residual stress location moves nearer to the edge of the weld nugget and the residual stress magnitude and distribution change. Also, residual stress have sufficiently effects on stress distribution at the weld joint due to mechanical loading. To accurately estimate the fatigue life of resistance spot-welded joints, moreover external stresses, residual stress and local strain hardening of the material near the edge must be considered. © 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction Resistance spot-welding was invented in 1877 and has been widely used since then in the automobile, aircraft and electronic industries because it is quick, produces good quality joints and is low cost [1]. During resistance spot-welding, a high electric current passes through the sheets and the temperature increases in the contact region until the metal fuses and a weld nugget is formed. The current is then switched off and weld nugget is allowed to cool down slowly to solidify under electrode force. Residual stress is self-equilibrating stress existing in materials or components under uniform temperature conditions with no applied loads. Residual stress occurs in materials and mechanical components during manufacturing, such as in plastic deformation, heat-treating or thermo-chemical treatment. During resistance spot-welding, heterogeneous deformation is induced by temperature gradients, phase changes in the solidifying metal and electrode force, resulting in the development of internal residual stress. When the current is off, the weld zone begins to shrink upon cooling, but is restricted by the surrounding cooler base metal, which produces tensile stress in the joint. During the welding and holding step, the electrode force causes the development of compressive stress in the weld nugget area.
∗ Corresponding author. E-mail address: r [email protected] (R. Moharrami).
Residual stresses effects the mechanical properties of components such as tensile strength, fatigue strength and fracture toughness. Tensile residual stress is the opposite of compressive stress and is undesirable because it accelerates fatigue crack growth [2]. To study the effect of residual stress on fatigue behavior, stress intensity and residual stress ratio should be considered [3]. Long [4] simulated the residual stress generated in resistance spot-welding and compared the numerical results with residual stress measured using an optical technique of high sensitivity called moiré interferometry [5]. Cha [6] studied the effect of welding parameters and hardening of the tangent module on residual stress distribution. Nodeh [7] used a two-dimensional mathematical model to investigate the effect of applied voltage and welding time on the welding residual stress and compared the simulation results with experimental data from x-ray diffraction. Fatigue is the most critical failure mode of spot-welded joints in automobiles [8]. The fatigue life of mechanically-fastened structures strongly depends on the local state of stress at the fastener and the surface condition of the sheets. After welding, a notch is formed at the periphery of the spot weld which concentrates the stress and produces excessive local deformation. Fatigue crack propagation in highly-stressed regions depends on stress level. At a low stress level, the crack initiates some distance away from the nugget and then propagates around the nugget to a large width before propagating through the thickness. At high stress levels, the crack initiates closer to the nugget and propagates through the thickness without growing wider [9].
http://dx.doi.org/10.1016/j.jmapro.2017.05.007 1526-6125/© 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
R. Moharrami, B. Hemmati / Journal of Manufacturing Processes 27 (2017) 284–290
285
Nomenclature ∅ k c q˙ dij e dij ␦ij E
dij p Q d ␣ d U
Electric potential Electric conductance Thermal conductivity Density Specific heat Internal heat generation rate per unit volume Elastic strain increment Stress increment Kroenke delta Young’s modulus Poisson’s ratio Shear modulus Plastic strain increment Plastic potential function Proportionality constant term Thermal expansion coefficient Temperature increment Displacement Fig. 1. Considered area in numerical simulation.
The grain structure of steel sheets alters due to rapid annealing from the electrodes. The grain structure in the nugget is considerably coarser than that of the parent metal. It can be observed that an increase in grain size generally results in a reduction in the fatigue endurance limit. On the other hand, a coarse grain structure can lead to a decrease in the rate of fatigue crack propagation [10]. The fatigue behavior of a spot weld has been investigated by many authors. Rathbun [11] examined the fatigue behavior of highstrength and low-strength steel under different loading conditions. Long [12] investigated the dislocation density and residual stress under low and high fatigue loading and their relationship with the fatigue behavior of spot-welded joints. Tanegashima [13] observed internal fatigue crack propagation around the spot-weld area in detail and studied the fracture type of the joint at different stress levels. Vural [14] experimentally analyzed the effect of the combination of materials and nugget diameter on fatigue life of a spot weld. Rahman [15] studied the effect of spot diameter, sheet thickness and fatigue load on the fatigue life of spot-welded joints. Kang [16] investigated the effects of electrode tip geometry, surface indentation level and base metal strength on fatigue life under tensile shear loading. Radaj [17] used notch stress as an alternative to fatigue testing because the notch is often the location for crack development. Pan [18] studied the stress and strain in spot welds using a FE model and predicted the fatigue life using theh cyclic strain range method. Kang [19] used a mesh-insensitive structural stress parameter for determining the fatigue life of spot-welded joints under different loading conditions. Ertas [20] studied the effects of design variables such as spot-weld diameter and plate thickness on the fatigue life of spot welds using a 3D FE model. Wang [21] predicted the fatigue life of spot welds using elasto-plastic FE analysis and considering the effect of hardness distribution on cyclic material constants after welding. Despite the effect of residual stress on fatigue life, only a few studies have investigated the fatigue life of spot-welded joints under residual stress. Bae [22] calculated the stress amplitude while considering welding residual stress at the edge of a spot weld. They found that the fatigue strength at a fatigue cycle limit for which welding residual stress was assumed was about 25% lower than that without of residual stress. Hassanifard [23] studied the effect of residual stress on fatigue life for different electrode forces using the modified Morrow damage equation. Mirsalehi [24] employed a crack propagation-based fatigue life estimation approach that con-
Table 1 Standard chemical composition of steel H180Y. C
Si
Mn
P
S
Al
Ti
Ti+Nb+V+B
0.01
0.3
0.7
0.06
0.025
0.01
0.12
0.22
sidered residual stress at the nugget edge of the spot weld. Triyono [25] predicted the S-N curve for spot-welded joints under residual stress at the edge of spot weld and found it resulted in the reduction of fatigue strength. In this research, an appropriate 3D finite element model was developed using ANSYS software to simulate resistance spotwelding. Electrode force was first applied to determine the initial contact condition between the electrode-sheet and the sheet–sheet interface. Fully-coupled electro-thermal analysis was used to determine the electrical current and temperature distribution. Next, the residual stress distribution was evaluated in the squeezing, heating and cooling steps. Post-weld tensile loading and unloading on the welds was done to determine the effects of external loading on the welded joint in a FE model. 2. Finite element analysis In this study, welding and post-weld tensile loading of a shear tension specimen as a standard fatigue test sample was considered numerically. The specimen was made of two flat steel sheets joined using a spot welds. A schematic of a section of the joint, sheets and electrodes is shown in Fig. 1. For the numerical simulation, the material properties of H180Y, a cold-rolled steel strip of high strength, were used. The chemical composition of H180Y steel is shown in Table 1. Steel offers excellent forming and aging properties is widely used in the automobile industry. Because the alloying elements in H180Y steel sheets are low, the thermal and electrical properties of AISI 1100 steel were used for numerical simulation of welding. The tensile test on H180Y steel was done at room temperature and test result is shown in Fig. 2. The physical and mechanical properties of the material will be changed at the weld nugget area and heat affected zone (HAZ) during welding sequence because its temperature dependency. Fig. 3 shows the trend of mechanical and physical properties at different temperature which were taken into account in the study.
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Fig. 2. Engineering stress-strain curve of H180Y sheet at diagonal directions. Fig. 4. Three dimension FE model used for simulation.
The bilinear isotropic hardening model was used to determine the plastic behavior of the material. The slope of the first segment in the curve is equivalent to the Young’s modulus of the material and the slope of the second segment is the tangent modulus. The tangent modulus was scaled from the experimental obtained stress-strain curve. Fig. 4 shows the 3D FE model developed to numerical analysis the resistance spot welding and welding residual stress assessment. Because of the weld nugget diameter is small in comparison with the plate dimension and distance between the adjacent spot welds, results of this study will be general results. ANSYS was used to simulate welding and post weld mechanical loading. In the FE simulation, the SOLID45 and SOLID69 element types were used for mechanical and electro-thermal analysis, respectively. The TARGE170 and CONTAC173 contact pair elements were employed to represent the two contact areas on the electrode-sheet interface and one on the sheet–sheet interface. The governing equation for electric potential distribution is:
ε,i
,i
=0
(1)
where ∅ is the electric potential and is electrical conductance. The governing differential equation for the heat transfer problem is:
kT,i
,i
− c
∂T + q˙ = 0 ∂t
(2)
where k is thermal conductivity, is density and c is specific heat. The term q˙ refers to the rate of the internal heat generation per unit volume within the boundaries of the region of analysis. Assuming
small strains, the complete incremental relationship for thermoelastic-plastic deformation is: dεij t = dεij e + dεij p + dεij th where dij e is the elastic strain increment according to Hooke’s law: dεij e =
dij 2
+
(1 − 2) ıij dkk E
(4)
where dij is the stress increment, ␦ij is the Kronecker delta, E is the Young’s modulus, is the Poisson’s ratio, is the shear modulus and dij p is the plastic strain increment which is assumed proportional to the stress gradient of a plastic potential such that: dεij p = d
∂Q ∂ij
(5)
where Q is the plastic potential function, d is the proportionality constant (termed the plastic multiplier) and the thermal strain is calculated as:
dεij th = ˛ d ıij
(6)
where ␣ and d denote the thermal expansion coefficient and temperature increment, respectively. Resistance spot-welding is a complicated process involving the interaction of electrical, thermal and mechanical fields. Fig. 5 shows the numerical simulation flowchart used to predict the fatigue strength of the resistance spotwelded joint. This procedure considers both welding residual stress and residual stress arising from non-uniform plastic deformation during loading.
Fig. 3. The trend of used mechanical and physical properties at different temperature [26].
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Table 3 Welding parameters utilized for numerical results validation. Electrode force(kN)
electrodes face Welding diameter (mm) current(kA)
Welding time(ms)
Holding time(ms)
2.5
5.5
160
200
7.3
Table 4 Difference between obtained results from experimental study and FE models.
Element Number Nugget Dimeter mm Difference%
Experimental
Main FE model
Finer Meshes
Corse Meshes
– 3.82 –
30,604 3.92 2.6
61,348 3.95 3.4
13,860 3.57 7.8
Fig. 5. The FE procedure for predicting the temperature and residual stress distribution. Table 2 Boundary conditions used in RSW simulation. Boundary
Coolant Symmetry Plane Upper Electrode Lower Electrode Lateral side
Conditions Mechanical
Thermal
Electrical
=0 Ur = 0 P Electrode Force Uz = 0 =0
25 ◦ C Adiabatic 25 ◦ C
I=0 I=0 I = IW Welding Current V=0 I=0
25 ◦ C Air Cooling
First, the electrode force is applied to the electrodes to determine initial contact at the electrode-sheet and sheet–sheet interfaces. The contact information is the input for electro-thermal analysis to determine the temperature distribution. The temperature was then calculated for an increment in fully-coupled electro-thermal analysis. Next, the temperature distribution serves as the body load during thermo-mechanical analysis. The new contact conditions gained through thermo-mechanical analysis are used during electro-thermal analysis to update the contact conditions for analysis of the next increment. This iterative procedure continues until the welding time is complete. After welding is complete, the FE model is loaded by applying tension at one side of the model and fixing the other side to determine the residual stress distribution after unloading. To represent the connection between two sheets after electrode removal, the nodes located in the weld nugget zone are overlapped and coupled. The FE model with coupled nodes and without simulated welding is loaded to determine the residual stress arising from only non-uniform plastic deformation. The convection heat transfer coefficient was assumed to be 15 W/m2 k and at each step of analysis, the appropriate boundary conditions from Table 2 are assumed for numerical analysis. The accuracy of the numerical solution was verified using two models with finer and coarser meshes for FE analysis. Also, comparison of nugget size obtained by numerical simulations and experimental values in a definite welding parameters were used to numerical results validation. Table 3 shows welding parameters utilized for numerical results validation and Table 4 shows elements number and nugget diameter in FE models. The differences between the results of the experimental value and the FE models with different meshes were
Fig. 6. Cross sectional view of the nugget prepared in experiment and temperature field obtained from numerical analysis.
insignificant. Fig. 6 shows cross sectional view of spot welded joint prepared by an optical microscope beside same section obtained from numerical simulation. 3. Results The spot weld area first expanded as the temperature increased, but was restricted by the surrounding cold metal resulting in the development of compressive stress in the welding zone. After cutting off the current, the temperature fell abruptly and the welding zone began to shrink. Because it was restricted by the surrounding cold base metal, tensile residual stress dominated the welded joint area. Fig. 7 shows the distribution of the XX stress component on the inner surface of the flat sheet post-welding. A significant difference was found only between the stress distribution alone line L-R because of difference in geometric boundary condition. As seen, the residual stress distribution in the weld zone was tensile and the maximum tensile residual stress was located near the edge of weld nugget. Fig. 8 shows the distribution of the xx stress component along the B-T line and Fig. 9 shows the zz stress component along the L-R line (B-T and L-R lines cross at the center of the weld nugget). The stress field was tensile throughout the weld nugget zone. The tensile stress decreased toward the edge of the nugget and then
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Fig. 7. Stress distribution on the inner surface of sheet at the end of welding process.
Fig. 10. Distribution of XX and ZZ stress through the thickness at center of nugget. Fig. 8. Distribution of XX stress component along the line B-T at the end of welding process.
Fig. 9. Distribution of zz stress component along the line L-R at the end of welding process.
increased sharply. The maximum tensile residual stress was located outside the weld nugget zone near the edge of the spot weld. Fig. 10 shows the residual stress distribution through the thickness of the sheets along a line passing through the center of the weld nugget. As seen, the tensile stress decreases toward the outer surface of the sheets. The model was then statically loaded after welding. Fig. 11 shows the distribution of XX on the inner surface of the sheet
Fig. 11. Distribution of ZZ stress (in Pa) on the inner surface after unloading with considering welding residual stress.
after unloading assuming welding residual stress. The maximum tensile residual stress was located at the edge of the spot weld. Plastic deformation occurred around the weld nugget due to the high stress concentration even at low load levels. Tensile residual stress dominated on one side of the spot weld and compressive stress governed the other side. Figs. 12 and 13 compare the residual stress distribution before and after shear loading along the Q-P and M-N lines (which cross at the center of the weld nugget).
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Fig. 15. Effect of welding residual stress on distribution of xx stress component along the line Q-P after unloading. Fig. 12. Distribution of XX stress component along the line Q-P before and after loading.
Fig. 16. Effect of welding residual stress on distribution of xx stress component along the line M-N after unloading.
Fig. 13. Distribution of xx stress component along the line M-N before and after loading.
Fig. 14 shows the stress field after unloading without residual stress and indicates that the maximum tensile residual stress was located at the edge of weld nugget. The maximum tensile stress was lower than that of the model for the welding residual stress. Figs. 15 and 16 show the effect of welding residual stress on the stress distribution along the Q-P line and M-N line after unloading the resistance spot-welded joint. As seen, the level of tensile residual stress is increased by the welding residual stress both inside and outside the weld nugget zone. The maximum tensile residual stress was located along the M-N line at the edge of weld nugget. 4. Conclusions The effect post weld shear loading on the residual stress redistribution on a resistance spot-welded joint was investigated. A 3D finite element simulation were used to determine the residual stress distribution before and after the mechanical loading. The following conclusions can be drawn from the results:
Fig. 14. Distribution of xx stress component (in Pa) on the inner surface of sheet after unloading without considering welding residual stress.
After loading, the stress distribution had significantly altered along the M-N line, which coincides with the direction of loading. The tensile stress increased on one side of the spot weld and decreased on the other side due to the bending of the joined sheets.
• Post weld tensile residual stresses are dominant in the weld nugget zone, decreases toward the edge of the weld nugget and then increases. The maximum tensile residual stress occurs near the edge of the weld nugget. • At the end of loading, plastic deformation was observed at the edge of the nugget because of the stress concentration. The residual stress arising from welding and the stress concentration aggregated. The maximum tensile residual stress after unloading as located at the edge of the weld nugget.
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Acknowledgments The authors wish to thank Dr. Saeid Saber, Dr. Wolfgang Ernst and Dr. Rudolf Vallent from Graz University of Technology for their constant support for this research. References [1] Gupta OP, De A. An improved numerical modeling for resistance spot welding process and its experimental verification. J Manuf Sci Eng 1998;120:246–51. [2] Fleck NA, Shin CS, Smith RA. Fatigue crack growth under compressive loading. Eng Fract Mech 1985;21(1):173–85. [3] Liljedahl CDM, Brouard J, Zanellato O, Lin J, Tan ML, Ganguly S, et al. Weld residual stress effects on fatigue crack growth behaviour of aluminium alloy 2024-T351. Int J Fatigue 2009;31:1081–8. [4] Khanna SK, Long X. Residual stresses in resistance spot welded steel joints. Sci Technol Weld Join 2008;13:278–88. [5] Khanna SK, He C, Agrawal HN. Residual stress measurement in spot welds and the effect of fatigue loading on redistribution of stresses using high sensitivity moiré interferometry. ASME J Eng Mater Technol 2001;123:132–8. [6] Cha BW, NA SJ. A study on the relationship between welding conditions and residual stress of resistance spot welded 304-type stainless steels. J Manuf Syst 2003;22:181–9. [7] Nodeh IR, Serajzadeh S, Kokabi AH. Simulation of welding residual stresses in resistance spot welding, FE modeling and X-ray verification. J Mater Process Technol 2008;205:60–9. [8] Kim D, Han Q, Gong S, Kang H, Shin CW, Lee TS. Fatigue Life Prediction of Spot Welds with Direct Strain Measurement. Detroit: SAE world Congress; 2011, paper no. 2011-01-0480. [9] Ertas AH, Vardar O, Sonmez FO, Solim z. Measurement and assessment of fatigue life of spot-weld joints. J Eng Mater Technol 2009;131(1):160–5. [10] Hanlon T. Grain size effect on the fatigue response of Nano crystalline materials, PhD thesis. The Massachusetts Institute of Technology; 2004. [11] Rathbun RW, Matlock DK, Speer JG. Fatigue behavior of spot-welded highstrength sheet steels. Weld J 2003;82(8):207–18.
[12] Long X, Khanna SK, Allard L. Effect of fatigue loading and residual stress on microscopic deformation mechanisms in a spot welded joint. Mater Sci Eng 2007;455:398–406. [13] Tanegashima R, Akebono H, Kato M, Miyagaki A, Sugeta A. 3-Dimensional observation of fatigue crack propagation on spot welded joints using high strength steel. Int J Automot Eng 2011;2:61–7. [14] Vural M, Akkus A, Eryurek B. Effect of welding nugget diameter on the fatigue strength of the resistance spot welded joints of different steel sheets. J Mater Process Technol 2006;176:127–32. [15] Rahman MM, Bakar RA, Noor MN, Rejab MRM, Sani MSM. Fatigue life prediction of spot-welded structures: a finite element analysis approach. Eur J Sci Res 2008;22(3):444–56. [16] Kang HT, Dong p, Hong JK. Fatigue analysis of spot welds using a meshinsensitive structural stress approach. Int J Fatigue 2007;29(8):1546–53. [17] Radaj D. Fatigue assessment of spot welds by approximated local stress parameters. Int J Fract 2000;102(1):1–8. [18] Pan N, Sheppard S. Spot welds fatigue life prediction with cyclic strain rang. Int J Fatigue 2002;24:519–28. [19] Kang HT, Dong p, Hong JK. Fatigue analysis of spot welds using a meshinsensitive structural stress approach. Int J Fatigue 2007;29:1546–53. [20] Ertas AH, Sonmez FO. A parametric study on fatigue strength of spot-weld joint. Fatigue Fract Eng Mater Struct 2008;31(9):766–76. [21] Wang RJ, Shang DG. Low-cycle fatigue life prediction of spot welds based on hardness distribution and finite element analysis. Int J Fatigue 2009;31:508–14. [22] Bae DH, Sohn IS, Hong JK. Assessing the effects of residual stresses on the fatigue strength of spot welds. Weld J 2003;82:18–23. [23] Hassanifard S, Zehsaz M. The effects of residual stresses on the fatigue life of 5083-O aluminum alloy spot welded joints. Procedia Eng 2010;2(1):1077–85. [24] Mirsalehi SE, Kokabi AH. Fatigue life estimation of spot welds using a crack propagation-based method with consideration of residual stresses effect. Mat Sci Eng 2010;527(23):6359–63. [25] Triyono J, Ilman MN, Soekrisno R. Comparative study of fatigue assessment methods with and without considering residual stress on resistance spot-welded unequal sheet thickness stainless steel. Int J Eng Technol 2011;11(3):133–7. [26] Handbook Metals. Properties and Steels Selection: Irons and High-Performance Alloys. 10th ed. ASM International; 1990.
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Full Length Article
Numerical stress analysis in resistance spot-welded nugget due to post-weld shear loading Rasoul Moharrami ∗ , Behzad Hemmati Mechanical Engineering Department, University of Zanjan, Iran
a r t i c l e
i n f o
Article history: Received 3 October 2016 Received in revised form 25 April 2017 Accepted 8 May 2017 Keywords: Resistance spot weld Stress analysis Residual stress Shear loading Numerical
a b s t r a c t The magnitude and state of residual stress has a great influence on the fatigue life of sheet metal joints used in the automobile and aircraft industries. The present study developed a parametric 3D finite element model for simulation of welding and post-weld loading on the specimen. Electro-thermo-mechanical analysis is utilized to estimate the residual stress distribution at the nuggets and their surroundings at different stages of welding and post-weld mechanical loading. The results show that at the end of postweld loading, the maximum tensile residual stress location moves nearer to the edge of the weld nugget and the residual stress magnitude and distribution change. Also, residual stress have sufficiently effects on stress distribution at the weld joint due to mechanical loading. To accurately estimate the fatigue life of resistance spot-welded joints, moreover external stresses, residual stress and local strain hardening of the material near the edge must be considered. © 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction Resistance spot-welding was invented in 1877 and has been widely used since then in the automobile, aircraft and electronic industries because it is quick, produces good quality joints and is low cost [1]. During resistance spot-welding, a high electric current passes through the sheets and the temperature increases in the contact region until the metal fuses and a weld nugget is formed. The current is then switched off and weld nugget is allowed to cool down slowly to solidify under electrode force. Residual stress is self-equilibrating stress existing in materials or components under uniform temperature conditions with no applied loads. Residual stress occurs in materials and mechanical components during manufacturing, such as in plastic deformation, heat-treating or thermo-chemical treatment. During resistance spot-welding, heterogeneous deformation is induced by temperature gradients, phase changes in the solidifying metal and electrode force, resulting in the development of internal residual stress. When the current is off, the weld zone begins to shrink upon cooling, but is restricted by the surrounding cooler base metal, which produces tensile stress in the joint. During the welding and holding step, the electrode force causes the development of compressive stress in the weld nugget area.
∗ Corresponding author. E-mail address: r [email protected] (R. Moharrami).
Residual stresses effects the mechanical properties of components such as tensile strength, fatigue strength and fracture toughness. Tensile residual stress is the opposite of compressive stress and is undesirable because it accelerates fatigue crack growth [2]. To study the effect of residual stress on fatigue behavior, stress intensity and residual stress ratio should be considered [3]. Long [4] simulated the residual stress generated in resistance spot-welding and compared the numerical results with residual stress measured using an optical technique of high sensitivity called moiré interferometry [5]. Cha [6] studied the effect of welding parameters and hardening of the tangent module on residual stress distribution. Nodeh [7] used a two-dimensional mathematical model to investigate the effect of applied voltage and welding time on the welding residual stress and compared the simulation results with experimental data from x-ray diffraction. Fatigue is the most critical failure mode of spot-welded joints in automobiles [8]. The fatigue life of mechanically-fastened structures strongly depends on the local state of stress at the fastener and the surface condition of the sheets. After welding, a notch is formed at the periphery of the spot weld which concentrates the stress and produces excessive local deformation. Fatigue crack propagation in highly-stressed regions depends on stress level. At a low stress level, the crack initiates some distance away from the nugget and then propagates around the nugget to a large width before propagating through the thickness. At high stress levels, the crack initiates closer to the nugget and propagates through the thickness without growing wider [9].
http://dx.doi.org/10.1016/j.jmapro.2017.05.007 1526-6125/© 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
R. Moharrami, B. Hemmati / Journal of Manufacturing Processes 27 (2017) 284–290
285
Nomenclature ∅ k c q˙ dij e dij ␦ij E
dij p Q d ␣ d U
Electric potential Electric conductance Thermal conductivity Density Specific heat Internal heat generation rate per unit volume Elastic strain increment Stress increment Kroenke delta Young’s modulus Poisson’s ratio Shear modulus Plastic strain increment Plastic potential function Proportionality constant term Thermal expansion coefficient Temperature increment Displacement Fig. 1. Considered area in numerical simulation.
The grain structure of steel sheets alters due to rapid annealing from the electrodes. The grain structure in the nugget is considerably coarser than that of the parent metal. It can be observed that an increase in grain size generally results in a reduction in the fatigue endurance limit. On the other hand, a coarse grain structure can lead to a decrease in the rate of fatigue crack propagation [10]. The fatigue behavior of a spot weld has been investigated by many authors. Rathbun [11] examined the fatigue behavior of highstrength and low-strength steel under different loading conditions. Long [12] investigated the dislocation density and residual stress under low and high fatigue loading and their relationship with the fatigue behavior of spot-welded joints. Tanegashima [13] observed internal fatigue crack propagation around the spot-weld area in detail and studied the fracture type of the joint at different stress levels. Vural [14] experimentally analyzed the effect of the combination of materials and nugget diameter on fatigue life of a spot weld. Rahman [15] studied the effect of spot diameter, sheet thickness and fatigue load on the fatigue life of spot-welded joints. Kang [16] investigated the effects of electrode tip geometry, surface indentation level and base metal strength on fatigue life under tensile shear loading. Radaj [17] used notch stress as an alternative to fatigue testing because the notch is often the location for crack development. Pan [18] studied the stress and strain in spot welds using a FE model and predicted the fatigue life using theh cyclic strain range method. Kang [19] used a mesh-insensitive structural stress parameter for determining the fatigue life of spot-welded joints under different loading conditions. Ertas [20] studied the effects of design variables such as spot-weld diameter and plate thickness on the fatigue life of spot welds using a 3D FE model. Wang [21] predicted the fatigue life of spot welds using elasto-plastic FE analysis and considering the effect of hardness distribution on cyclic material constants after welding. Despite the effect of residual stress on fatigue life, only a few studies have investigated the fatigue life of spot-welded joints under residual stress. Bae [22] calculated the stress amplitude while considering welding residual stress at the edge of a spot weld. They found that the fatigue strength at a fatigue cycle limit for which welding residual stress was assumed was about 25% lower than that without of residual stress. Hassanifard [23] studied the effect of residual stress on fatigue life for different electrode forces using the modified Morrow damage equation. Mirsalehi [24] employed a crack propagation-based fatigue life estimation approach that con-
Table 1 Standard chemical composition of steel H180Y. C
Si
Mn
P
S
Al
Ti
Ti+Nb+V+B
0.01
0.3
0.7
0.06
0.025
0.01
0.12
0.22
sidered residual stress at the nugget edge of the spot weld. Triyono [25] predicted the S-N curve for spot-welded joints under residual stress at the edge of spot weld and found it resulted in the reduction of fatigue strength. In this research, an appropriate 3D finite element model was developed using ANSYS software to simulate resistance spotwelding. Electrode force was first applied to determine the initial contact condition between the electrode-sheet and the sheet–sheet interface. Fully-coupled electro-thermal analysis was used to determine the electrical current and temperature distribution. Next, the residual stress distribution was evaluated in the squeezing, heating and cooling steps. Post-weld tensile loading and unloading on the welds was done to determine the effects of external loading on the welded joint in a FE model. 2. Finite element analysis In this study, welding and post-weld tensile loading of a shear tension specimen as a standard fatigue test sample was considered numerically. The specimen was made of two flat steel sheets joined using a spot welds. A schematic of a section of the joint, sheets and electrodes is shown in Fig. 1. For the numerical simulation, the material properties of H180Y, a cold-rolled steel strip of high strength, were used. The chemical composition of H180Y steel is shown in Table 1. Steel offers excellent forming and aging properties is widely used in the automobile industry. Because the alloying elements in H180Y steel sheets are low, the thermal and electrical properties of AISI 1100 steel were used for numerical simulation of welding. The tensile test on H180Y steel was done at room temperature and test result is shown in Fig. 2. The physical and mechanical properties of the material will be changed at the weld nugget area and heat affected zone (HAZ) during welding sequence because its temperature dependency. Fig. 3 shows the trend of mechanical and physical properties at different temperature which were taken into account in the study.
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Fig. 2. Engineering stress-strain curve of H180Y sheet at diagonal directions. Fig. 4. Three dimension FE model used for simulation.
The bilinear isotropic hardening model was used to determine the plastic behavior of the material. The slope of the first segment in the curve is equivalent to the Young’s modulus of the material and the slope of the second segment is the tangent modulus. The tangent modulus was scaled from the experimental obtained stress-strain curve. Fig. 4 shows the 3D FE model developed to numerical analysis the resistance spot welding and welding residual stress assessment. Because of the weld nugget diameter is small in comparison with the plate dimension and distance between the adjacent spot welds, results of this study will be general results. ANSYS was used to simulate welding and post weld mechanical loading. In the FE simulation, the SOLID45 and SOLID69 element types were used for mechanical and electro-thermal analysis, respectively. The TARGE170 and CONTAC173 contact pair elements were employed to represent the two contact areas on the electrode-sheet interface and one on the sheet–sheet interface. The governing equation for electric potential distribution is:
ε,i
,i
=0
(1)
where ∅ is the electric potential and is electrical conductance. The governing differential equation for the heat transfer problem is:
kT,i
,i
− c
∂T + q˙ = 0 ∂t
(2)
where k is thermal conductivity, is density and c is specific heat. The term q˙ refers to the rate of the internal heat generation per unit volume within the boundaries of the region of analysis. Assuming
small strains, the complete incremental relationship for thermoelastic-plastic deformation is: dεij t = dεij e + dεij p + dεij th where dij e is the elastic strain increment according to Hooke’s law: dεij e =
dij 2
+
(1 − 2) ıij dkk E
(4)
where dij is the stress increment, ␦ij is the Kronecker delta, E is the Young’s modulus, is the Poisson’s ratio, is the shear modulus and dij p is the plastic strain increment which is assumed proportional to the stress gradient of a plastic potential such that: dεij p = d
∂Q ∂ij
(5)
where Q is the plastic potential function, d is the proportionality constant (termed the plastic multiplier) and the thermal strain is calculated as:
dεij th = ˛ d ıij
(6)
where ␣ and d denote the thermal expansion coefficient and temperature increment, respectively. Resistance spot-welding is a complicated process involving the interaction of electrical, thermal and mechanical fields. Fig. 5 shows the numerical simulation flowchart used to predict the fatigue strength of the resistance spotwelded joint. This procedure considers both welding residual stress and residual stress arising from non-uniform plastic deformation during loading.
Fig. 3. The trend of used mechanical and physical properties at different temperature [26].
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Table 3 Welding parameters utilized for numerical results validation. Electrode force(kN)
electrodes face Welding diameter (mm) current(kA)
Welding time(ms)
Holding time(ms)
2.5
5.5
160
200
7.3
Table 4 Difference between obtained results from experimental study and FE models.
Element Number Nugget Dimeter mm Difference%
Experimental
Main FE model
Finer Meshes
Corse Meshes
– 3.82 –
30,604 3.92 2.6
61,348 3.95 3.4
13,860 3.57 7.8
Fig. 5. The FE procedure for predicting the temperature and residual stress distribution. Table 2 Boundary conditions used in RSW simulation. Boundary
Coolant Symmetry Plane Upper Electrode Lower Electrode Lateral side
Conditions Mechanical
Thermal
Electrical
=0 Ur = 0 P Electrode Force Uz = 0 =0
25 ◦ C Adiabatic 25 ◦ C
I=0 I=0 I = IW Welding Current V=0 I=0
25 ◦ C Air Cooling
First, the electrode force is applied to the electrodes to determine initial contact at the electrode-sheet and sheet–sheet interfaces. The contact information is the input for electro-thermal analysis to determine the temperature distribution. The temperature was then calculated for an increment in fully-coupled electro-thermal analysis. Next, the temperature distribution serves as the body load during thermo-mechanical analysis. The new contact conditions gained through thermo-mechanical analysis are used during electro-thermal analysis to update the contact conditions for analysis of the next increment. This iterative procedure continues until the welding time is complete. After welding is complete, the FE model is loaded by applying tension at one side of the model and fixing the other side to determine the residual stress distribution after unloading. To represent the connection between two sheets after electrode removal, the nodes located in the weld nugget zone are overlapped and coupled. The FE model with coupled nodes and without simulated welding is loaded to determine the residual stress arising from only non-uniform plastic deformation. The convection heat transfer coefficient was assumed to be 15 W/m2 k and at each step of analysis, the appropriate boundary conditions from Table 2 are assumed for numerical analysis. The accuracy of the numerical solution was verified using two models with finer and coarser meshes for FE analysis. Also, comparison of nugget size obtained by numerical simulations and experimental values in a definite welding parameters were used to numerical results validation. Table 3 shows welding parameters utilized for numerical results validation and Table 4 shows elements number and nugget diameter in FE models. The differences between the results of the experimental value and the FE models with different meshes were
Fig. 6. Cross sectional view of the nugget prepared in experiment and temperature field obtained from numerical analysis.
insignificant. Fig. 6 shows cross sectional view of spot welded joint prepared by an optical microscope beside same section obtained from numerical simulation. 3. Results The spot weld area first expanded as the temperature increased, but was restricted by the surrounding cold metal resulting in the development of compressive stress in the welding zone. After cutting off the current, the temperature fell abruptly and the welding zone began to shrink. Because it was restricted by the surrounding cold base metal, tensile residual stress dominated the welded joint area. Fig. 7 shows the distribution of the XX stress component on the inner surface of the flat sheet post-welding. A significant difference was found only between the stress distribution alone line L-R because of difference in geometric boundary condition. As seen, the residual stress distribution in the weld zone was tensile and the maximum tensile residual stress was located near the edge of weld nugget. Fig. 8 shows the distribution of the xx stress component along the B-T line and Fig. 9 shows the zz stress component along the L-R line (B-T and L-R lines cross at the center of the weld nugget). The stress field was tensile throughout the weld nugget zone. The tensile stress decreased toward the edge of the nugget and then
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Fig. 7. Stress distribution on the inner surface of sheet at the end of welding process.
Fig. 10. Distribution of XX and ZZ stress through the thickness at center of nugget. Fig. 8. Distribution of XX stress component along the line B-T at the end of welding process.
Fig. 9. Distribution of zz stress component along the line L-R at the end of welding process.
increased sharply. The maximum tensile residual stress was located outside the weld nugget zone near the edge of the spot weld. Fig. 10 shows the residual stress distribution through the thickness of the sheets along a line passing through the center of the weld nugget. As seen, the tensile stress decreases toward the outer surface of the sheets. The model was then statically loaded after welding. Fig. 11 shows the distribution of XX on the inner surface of the sheet
Fig. 11. Distribution of ZZ stress (in Pa) on the inner surface after unloading with considering welding residual stress.
after unloading assuming welding residual stress. The maximum tensile residual stress was located at the edge of the spot weld. Plastic deformation occurred around the weld nugget due to the high stress concentration even at low load levels. Tensile residual stress dominated on one side of the spot weld and compressive stress governed the other side. Figs. 12 and 13 compare the residual stress distribution before and after shear loading along the Q-P and M-N lines (which cross at the center of the weld nugget).
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Fig. 15. Effect of welding residual stress on distribution of xx stress component along the line Q-P after unloading. Fig. 12. Distribution of XX stress component along the line Q-P before and after loading.
Fig. 16. Effect of welding residual stress on distribution of xx stress component along the line M-N after unloading.
Fig. 13. Distribution of xx stress component along the line M-N before and after loading.
Fig. 14 shows the stress field after unloading without residual stress and indicates that the maximum tensile residual stress was located at the edge of weld nugget. The maximum tensile stress was lower than that of the model for the welding residual stress. Figs. 15 and 16 show the effect of welding residual stress on the stress distribution along the Q-P line and M-N line after unloading the resistance spot-welded joint. As seen, the level of tensile residual stress is increased by the welding residual stress both inside and outside the weld nugget zone. The maximum tensile residual stress was located along the M-N line at the edge of weld nugget. 4. Conclusions The effect post weld shear loading on the residual stress redistribution on a resistance spot-welded joint was investigated. A 3D finite element simulation were used to determine the residual stress distribution before and after the mechanical loading. The following conclusions can be drawn from the results:
Fig. 14. Distribution of xx stress component (in Pa) on the inner surface of sheet after unloading without considering welding residual stress.
After loading, the stress distribution had significantly altered along the M-N line, which coincides with the direction of loading. The tensile stress increased on one side of the spot weld and decreased on the other side due to the bending of the joined sheets.
• Post weld tensile residual stresses are dominant in the weld nugget zone, decreases toward the edge of the weld nugget and then increases. The maximum tensile residual stress occurs near the edge of the weld nugget. • At the end of loading, plastic deformation was observed at the edge of the nugget because of the stress concentration. The residual stress arising from welding and the stress concentration aggregated. The maximum tensile residual stress after unloading as located at the edge of the weld nugget.
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Acknowledgments The authors wish to thank Dr. Saeid Saber, Dr. Wolfgang Ernst and Dr. Rudolf Vallent from Graz University of Technology for their constant support for this research. References [1] Gupta OP, De A. An improved numerical modeling for resistance spot welding process and its experimental verification. J Manuf Sci Eng 1998;120:246–51. [2] Fleck NA, Shin CS, Smith RA. Fatigue crack growth under compressive loading. Eng Fract Mech 1985;21(1):173–85. [3] Liljedahl CDM, Brouard J, Zanellato O, Lin J, Tan ML, Ganguly S, et al. Weld residual stress effects on fatigue crack growth behaviour of aluminium alloy 2024-T351. Int J Fatigue 2009;31:1081–8. [4] Khanna SK, Long X. Residual stresses in resistance spot welded steel joints. Sci Technol Weld Join 2008;13:278–88. [5] Khanna SK, He C, Agrawal HN. Residual stress measurement in spot welds and the effect of fatigue loading on redistribution of stresses using high sensitivity moiré interferometry. ASME J Eng Mater Technol 2001;123:132–8. [6] Cha BW, NA SJ. A study on the relationship between welding conditions and residual stress of resistance spot welded 304-type stainless steels. J Manuf Syst 2003;22:181–9. [7] Nodeh IR, Serajzadeh S, Kokabi AH. Simulation of welding residual stresses in resistance spot welding, FE modeling and X-ray verification. J Mater Process Technol 2008;205:60–9. [8] Kim D, Han Q, Gong S, Kang H, Shin CW, Lee TS. Fatigue Life Prediction of Spot Welds with Direct Strain Measurement. Detroit: SAE world Congress; 2011, paper no. 2011-01-0480. [9] Ertas AH, Vardar O, Sonmez FO, Solim z. Measurement and assessment of fatigue life of spot-weld joints. J Eng Mater Technol 2009;131(1):160–5. [10] Hanlon T. Grain size effect on the fatigue response of Nano crystalline materials, PhD thesis. The Massachusetts Institute of Technology; 2004. [11] Rathbun RW, Matlock DK, Speer JG. Fatigue behavior of spot-welded highstrength sheet steels. Weld J 2003;82(8):207–18.
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