Acta Mechanica Solida Sinica, Vol. 19, No. 1, March, 2006 Published by AMSS Press, Wuhan, China. DOI: 10.1007/s10338-006-0610-z ISSN 0894-9166 A MULTI-COUPLED FINITE ELEMENT ANALYSIS OF RESISTANCE SPOT WELDING PROCESS Hou Zhigang1,2 Wang Yuanxun1 Li Chunzhi2 Chen Chuanyao1 (1 School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China) (2 School of Mechtronic and Automobile Engineering, Yantai University, Yantai 264005, China) Received 13 January 2005; revision received 28 December 2005 ABSTRACT A two-dimensional axisymmetric finite element model is developed to analyze the transient thermal and mechanical behaviors of the Resistance Spot Welding (RSW) process using commercial software ANSYS. Firstly a direct-coupled electrical-thermal Finite Element Analysis (FEA) is performed to analyze the transient thermal characteristics of the RSW process. Then based on the thermal results a sequential coupled thermo-elastic-plastic analysis is conducted to determine the mechanical features of the RSW process. The thermal history of the whole process and the temperature distribution of the weldment are obtained through the analysis. The mechanical features, including the distributions of the contact pressure at both the faying surface and the electrode-workpiece interface, the stress and strain distributions in the weldment and their changes during the RSW process, the deformation of the weldment and the electrode displacement are also calculated. KEY WORDS Finite Element Analysis (FEA), Resistance Spot Welding (RSW), electrical-thermal coupling, thermo-elastic-plastic analysis, thermal behavior, mechanical feature I. INTRODUCTION The RSW process has been widely employed in sheet metal fabrication owing to its high speed, suitability for automation and inclusion in high-production assembly lines with other fabricating operations. It is a complex process in which coupled interactions exist between electrical, thermal, mechanical, metallurgical phenomena, and even surface behaviors. In order to well understand the mechanism of such a complex process, numerous researches have been performed on all kinds of welding conditions and materials, using both theoretical and experimental methods. In recent years, numerical method provides a powerful tool in studying these interactions, and much related work has been done on the numerical modeling of RSW. In particular, the FEA, which can deal with nonlinear behaviors and complex boundary conditions, has become the most important method for the analysis of RSW process. Nied[1] developed the first FEA model for RSW process, investigated the effect of the geometry of electrode on workpiece and predicted the deformation and stresses as a function of temperature. However, the model developed was restricted to elastic deformation, and not calculated the contact areas at the electrode-workpiece and faying surface. Furthermore, many researchers developed more sophisticated FEA models that considered temperature dependent material properties, contact status, phase changing, and coupled field effects on the simulation of RSW[2−−4] . To solve a common coupled problem, the iterative solution procedure is an often-adopted method, in which the equations describing different domains are solved separately using dedicated solvers, and the data exchanged at every time-step until : A Multi-coupled Finite Element Analysis · 87 · convergence of iteration is reached. {ε} is the strain vector. {Q} the heat flow vector. [K v ] the electric coefficient matrix. For the structural analysis. The governing equation of the electrical analysis is q = −k ∂ ∂r Ce ∂φ ∂r + Ce ∂φ ∂ + r ∂r ∂z Ce ∂φ ∂z =0 On the boundary surface. {T } the temperature vector. 7] . GOVERNING EQUATIONS The RSW process can be simulated as an axisymmetric problem. and qv the rate of internal heat generation. .Vol. The calculated temperature field is then passed back to the thermal-structural analysis to update the stress field and contact status. 19. and structural fields of the RSW process[6. Even if the iterative method can provide the temperature field. 1 Hou Zhigang et al. The objective of this paper is to develop a multicoupled method to analyze the thermal and mechanical behaviors of RSW process. improve the quality monitoring and process control of RSW. The coupled thermal electrical problem is solved by the following matrix equation: [C t ] [0] [0] [0] ˙ {T } ˙} {V + [K t ] [0] [0] [K v ] {T } {V } = {Q} {I} (5) where [C t ] is the thermal specific heat matrix. there is (3) (4) where Ce is the electrical conductivity. and {I} is the current vector. Initially the stress field and contact status are obtained from the thermal-mechanical analysis. The governing equation for axisymmetric transient thermal analysis is given by ρC ∂T ∂ = ∂t ∂r k ∂T ∂r + k ∂T ∂ + r ∂r ∂z k ∂T ∂z + qv (1) where ρ is the density of the material. thermal. reduce the computing time with the minimum loss of accuracy and get more adequate information of the process. and {α} the coefficient of thermal expansion. {V } the electric potential vector. the stress equilibrium equation is given by ∇σ(r. and then the temperature field is obtained from the fully coupled thermal-electrical analysis based on the contact area at the electrode-workpiece interface and faying surface. C the specific heat capacity. the modeling of transient processes with such a methodology would probably require tremendous computing time. [D] the elastic-plastic matrix. n is the outward normal to the surface. [K t ] the thermal conductivity matrix. φ is the electrical potential. T the temperature. This iterative method can also be employed to simulate the interactions between coupled electrical. t) + b(r. k the thermal conductivity. No. II. This information is transferred forward to the next time step and the numerical scheme of study repeated[5] . t the time. b is the body force. the stress and strain distributions in one calculation. The thermal boundary conditions can be decomposed from the nonlinear isotropic Fourier heat flux constitutive relation: q = −k∇T (2) ∂T ∂n where q is the heat flux through the boundary surface. r is the coordinate vector. The constructive equation of the materials based on the thermo-elastic-plastic theory is given by d {σ} = [D]d {ε} − {C} dT {C} = −[De ] {α} + ∂ [D ] ∂T e −1 (7) {σ} (8) where {σ} is the stress vector. t) = 0 (6) where σ is the stress. the electric potential field. [De ] the elastic matrix. Element types and degree of freedom options analysis electrical-thermal thermo-elastic-plastic solid PLANE67 PLANE42 element type contact CONTA171/TARGE169 CONTA171/TARGE169 degree of freedom (for contact element) TEMP. 13 cycles (0.2 kA. In each analysis. while the meshes of other areas are relatively coarse. Model dimensions Dimensions Values OE = HI 1. electrical and mechanical properties of electrode and workpiece are given in Table 3 and Table 4. 50 Hz sine wave AC current of 12.26 s).2. as shown in Fig. the model is meshed using three types of elements. UY 3. the model must have identical mesh both in the electrical-thermal analysis and in the thermo-elastic-plastic analysis. Contact areas 1 and 2 represent the electrode-workpiece interface and contact area 3 represents the faying surface.2. In order to obtain reliable results. 3000 N. Fig.5 mm ED 3 mm OP 32 mm α 30◦ Fig. The FEA model of RSW process. only the values of the upper half of the model are listed. 1. The thermal. The solid element is employed to simulate the coupled interaction between the sheets and electrodes. There are three contact areas in the model. as shown in Table 2. Its corresponding dimensions are tabulated in Table 1. 2.1. Model and Mesh Figure 1 illustrates the 2-dimensional axisymmetric FEA model of RSW process built in ANSYS program. The contact pair elements are employed to simulate the contact areas. Mesh of the model. Table 2. 3 cycles (0.· 88 · ACTA MECHANICA SOLIDA SINICA 2006 III. whereas the element types are different or have different degree of freedom options. electrode force. where x and y represent the faying surface and the axisymmetric axis respectively. weld time. . Because the materials are subjected to a wide range of temperatures.5 mm OI = EH 15 mm PA = FG 5mm PB 11 mm AG 18 mm EF 12. most of these properties are considered as temperature dependent. VOLT UX. Since the model is also mirror symmetric about the faying surface. MODELING AND PARAMETERS 3. In order to correctly couple and transfer data. Welding Parameters and Material Properties The welding parameters used in this analysis are: welding current. fine meshes are generated near these contact areas. hold time.06 s). Table 1. 1 8 contact resistivity Ω·m2 ×10−7 faying surface specific heat J/(kg·◦ C) mild copper steel electrode 443.1 8.2 611.31 204 2.0 464.8 418. the yield strength of the materials.66 305 115.9 34. latent heat-2.75 390. related to the interface resistivity.5 101.4 39.7 4 37.77 334.5 6.8 6.9 * mild steel: solidus-1482◦ C. temperature.26 density (kg/m3 ) mild copper steel electrode 7800 8900 The most important property in the simulation of RSW process is the contact resistivity of faying surface.05 49.3 63.24 17.48 0.64 18.79 649 1.1 44.5 17.: A Multi-coupled Finite Element Analysis Table 3.33 370.32 coefficient of thermal expansion (/◦ C)×10−6 mild copper steel electrode 10. .82 14. This simplification is reasonable because. the temperature dependent contact resistance is imposed on the faying surface.98 16.98 0.567 774 799 871 28.52 16. this is a highly non-linear problem involving the complex interaction between thermal.04 18.0 431. 1 Hou Zhigang et al.6 661.56 11. In Ref.12 427 1.31 732 760 30.417 1093 28.342 1204 120.25 316 2.2 2.3 1004 1189 1189 502. and average yield strength of two contact materials.1 49. the computing time can be greatly reduced.04 18.Vol.3 439.93 538 1. electrical and mechanical phenomena.2 401. 19. many researchers take the contact resistivity as a function of temperature[2.492 982 27. secondly.25 380.41 310.[8] that the contact resistance decreases as the contact pressure increases. firstly.19 64. 6] . Mechanical properties of materials thermal conductivity W/(m·◦ C) mild copper steel electrode 64.94 355.9 0.[9] an empirical model is developed for the pressure and temperature dependence of electrical contact resistance. which determines the contact status in the contact area.6 55. in the present research. which affects the temperature field through Joule heating.3 0. No. It is pointed out in Ref.4 temperature ( C) ◦ 21 93 204 316 427 538 649 760 871 982 Young’s modulus (GPa) mild copper steel electrode 206 124 196 105 194 93 186 82 169 55 117 38 55 25 16 14 7 yield stress (MPa) mild copper steel electrode 248 238 224 200 172 83 145 76 Poisson’s ratio mild steel copper electrode 0.91 320 resistivity Ω·m×10−8 mild copper steel electrode 14. During the RSW process.5 19. the contact resistivity is a dependent function of contact pressure.74 12. a curve fitting procedure is used and the desired relationship between contact resistance and pressure and temperature is established. liquidus-1521◦ C.50 315.98 0. Generally speaking.72×105 J/kg Table 4.38 93 2.5 9. To simplify the problem.96 17. Therefore.46 13. the load is constant in a specified RSW process. Therefore.8 9.9 13.6 3 26. the contact resistivity distribution influences the current density pattern.7 561.1 117.99 81. while the temperature field then influences the mechanical pressure distribution through thermal expansion.8 452.2 762. Thermal and electrical properties of materials∗ · 89 · temperature (◦ C) 21 2.3 111.5 452.36 14.86 345. is essentially influenced by temperature.8 397.56 300.58 18.1 12. With this simplification.54 14.6 5.7 1004 2386 477.9 510. the faying surface throughout the whole welding process. the temperature at the center of faying surface increases very fast. Temperature distributions at four different times of RSW process.· 90 · ACTA MECHANICA SOLIDA SINICA 2006 IV. the center and the edge of the electrode-workpiece interface. and the nugget geometry has completely formed at this instant.4(c). the highest temperature reaches 1500◦C and the nugget starts to form at this temperature. The nugget is in the shape of a very flat ellipse. At the start of the welding process. 3 Temperature changing histories of three points. The temperature distribution of this time is shown in Fig. as shown in Fig. It can be seen that the Joule heat generated along the contact line of faying surface and electrode-workpiece interface due to the contact resistance. and then expand to the material near it. Fig. The maximum temperature of nugget center. At the second half of the eighth cycle. 2096◦C. Melting will first occur at the faying surface. As the temperature rises. from which we can get their dimensions. RESULTS OF THE ELECTRICAL-THERMAL ANALYSIS The temperature fields and its changing of the whole weldment are obtained through the coupled electrical-thermal analysis. . 4. occurs at the last AC cycle. the nugget keeps growing. Figure 5 illustrates the geometry of the nugget and the Heat Affected Zone (HAZ). The highest temperature remains at the center of Fig. Figure 3 shows the temperature changing histories at three key points: the center of the weld nugget. Figure 4(a) shows the temperature distribution of the first calculated substep.4(b). Fig. The contact pressure distributions on the faying surface. and then keeps this temperature for a while due to the latent heat of phase change being released.4(d). 6. At the same time.Vol. Illustration of nugget and HAZ. the squeeze step is marked as cycle 0). 5. Contact Pressure Figure 6 shows the contact pressures on the faying surface versus radial distance at different welding cycles. The contact pressure distribution on the electrode-workpiece interface. RESULTS OF THE THERMO-ELASTIC-PLASTIC ANALYSIS 5. During the squeeze step (for the convenience of describing. 7. the temperature of nugget center is 937◦ C. and the peak value of 162 MPa appears at cycle 7. At cycle 2. the weldment starts to cool down. while the pressure at the center increases quickly. 1 Hou Zhigang et al.1. The high contact pressure near the edge of the contact area is beneficial to the RSW process because it can prevent liquid metal expulsion during welding. At the end of the simulation. V. and is 236◦ C at the end of simulation. Then the pressure near the edge begins to increase.: A Multi-coupled Finite Element Analysis · 91 · As the electric current ceases at 0. the location of the maximum value moves outward of the contact area. the maximum contact pressure at the center of faying surface reaches 155 MPa. In a very short time. The contact area on the faying Fig. as shown in Fig. becomes and remains larger than that of the center during the subsequent cycles. No.26 s. . a maximum contact pressure of 90 MPa is attained near the edge of contact area. The temperature at the center of electrode-workpiece interface decreases more slowly but continuously. Fig. 19. and the pressure at the center is a little less than this value. As the heating cycles start. the temperature of the nugget center decreases to l500◦ C. the pressure near the edge decreases. The radius of the contact area varies in a narrow range from 3 mm to 3. Probably the main reason for such a change is that the temperature at the center of faying surface increases quickly. is very important to the residual stress and deformation of the weldment. the pressure curves change. . while the temperature at the edge starts to increase and leads to thermal expansion. Fig. It can be seen that there is mainly compressive stress in the contact area. there is a stress concentration at the edge of the electrode. and forms a ‘plastic annulus’ around the contact area. The ‘plastic annulus’ is helpful to preventing liquid metal expulsion during welding[11] . Stress and Strain The stress and strain field in the weldment during the RSW process is very complex.· 92 · ACTA MECHANICA SOLIDA SINICA 2006 surface is nearly constant during the welding cycles. i. It can be seen that lager plastic strain occurs near the edge of the contact area through the thickness of sheets. which could be a vital cause for the wear of the electrode tip. This status is kept for 4 cycles.2. Fig. In other words. During the squeeze step. The distribution of normal stress σy at squeeze step. The welding residual stress is produced in welded joint as a result of plastic deformation caused by non-uniform thermal expansion and contraction due to non-uniform temperature distribution in the welding process[10] . while the temperature at the edge is still low and the material remains unchanged. which results in the increase of the pressure. making the material along the axisymmetric axis expand. and then another change occurs. the pressure is relatively uniform near the center of the contact area but very steep at the edge. As the heating cycles start. Figure 8 shows the distribution of normal stress σy at the squeeze step. This is probably because the temperature near the center has become so high that the Young’s modulus decreases. Figure 10 shows the distribution of plastic strain at the time of maximum temperature. The distribution of normal stress σy at the time of nugget started to form. The contact pressure distribution keeps this status up to the end of the hold step. low and uniform near the center while very large and steep at the edge. Figure 9 shows the distribution of normal stress σy at cycle 9. The stress field became more complex due to the generation of thermal stress. The contact pressure distribution on the electrode-workpiece interface is shown in Fig. 5. 8. 9. it has a different pattern from that on the faying surface. especially the plastic strain. which means the electrode edge keeps working under large stress. Fig. The distribution and change of the strain. The pressure near the center increases while that at the edge decreases quickly.7. 10 The distribution of plastic strain at the time of maximum temperature. The distribution pattern became similar to that of the squeeze step.e. when the weld nugget starts to form. and the maximum stress is about 172 MPa at the edge of the electrode-workpiece interface.5 mm. Obviously. 3. Deformation of weldment Figures 11 and 12 show the deformation of the weldment at the squeeze step and the end of hold step. VI. For example. No.Vol. The deformation of the weldment during the squeeze step (amplified by 100 times). the electrodes move apart during welding and close together upon cooling. 12. Figure 13 shows the predicted variations of the electrode displacement during weld and hold cycles.[11]. The deformation of the weldment at the end of hold step (amplified by 10 times). The deformation will affect the properties of the welded joint since it cannot be completely eliminated after welding. also shown in Fig. Thus the electrode displacement can be utilized as a suitable parameter for quality monitoring and Fig. 5.12. CONCLUSIONS A multi-coupled electro-thermal and thermo-elastic-plastic analysis is developed and carried out on the transient thermal and mechanical behaviors of the RSW process.4. Tsai[12] developed a real-time process. though the value according to this paper is a little lower. Based on the ANSYS program. Displacement of Electrode Owing to the thermal expansion and contraction of the weldment. respectively. Fig. Through the thermal histories and temperature distributions obtained from the electro-thermal analysis. This means much deformation is produced in the RSW process owing to the thermal expansion. this multi-coupled method can efficiently provide sufficient details of the RSW process and be of benefit to the quality monitoring and process control of RSW. This indicates a direct correlation between the electrode displacement and the temperature.: A Multi-coupled Finite Element Analysis · 93 · 5.11 is amplified by 100 times and 10 times in Fig. Results acquired from the thermo-elastic-plastic analysis show that the contact pressure value remains high near the edge of the faying surface and is beneficial to preventing liquid metal expulsion during welding. Fig. the geometry and dimensions of the nugget and HAZ are drawn and calculated. The curve has a profile similar to that of the temperature shown in Fig. the deformation shown in Fig. It can be observed that the calculated expansion displacement and expansion rate given in this paper agree well with that of Ref. In other words. The contact pressure at the edge of the electrode-workpiece is very large and could be a key . For the clarity of illustration.13. 11. the electrode displacement due to joint expansion and contraction reflects the direct thermal responses of the joint material to the welding conditions during the nugget formation. control method in RSW and obtained direct correlations between nugget formation and expansion displacement of electrodes. 1 Hou Zhigang et al. a fatigue crack or failure notch may initiate at the end of the gap between the two sheets. So it is obvious that the deformation at the end of hold step is much lager than that of the squeeze step.3. 13 The electrode displacement during the RSW process control in RSW. 19. . Vol.Y..18..T.B. it can be used as a suitable parameter for quality monitoring and process control in RSW. Welding Journal.. No. [3] Browne. [11] Zou.W. and Cho. Analysis and development of a real-time control methodology in resistance spot welding. 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