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Resistance Spot Welding: a Heat Transfer Study

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Resistance Spot Welding: a Heat Transfer Study Resistance Spot Welding: A Heat Transfer Study Real and simulated welds were used to develop a model for predicting temperature distribution BY Z. HAN, J. OROZCO, J. E. INDACOCHEA AND C. H. CHEN ABSTRACT. A heat transfer study of resis­ quate weld nugget size is still the primary ing boundary conditions are expressed in tance spot welding has been conducted concern for spot welding qualification finite difference forms. The solution to both theoretically and experimentally. A procedures (Refs. 1, 2). Weld nugget the equations includes an explicit formu­ numerical solution based on a finite dif­ sizes have been estimated conventional­ lation which incorporates the physical ference formulation of the heat equation ly, using a number of destructive tests, properties of the HSLA (high-strength has been developed to predict tempera­ and recently using more sophisticated low-alloy) sheet steel, the base metal. ture distributions as a function of both techniques, such as ultrasonic and The analytical thermal results have time and position during the welding dynamic resistivity profiles (Refs. 3-5). been correlated with the information process. The computer model also pre­ However, it has been pointed out by obtained from real and simulated weld dicts the temperature distribution other investigators (Ref. 6) that seldom heat-affected zones (HAZ). The real resis­ through the copper electrodes. One has the nugget size been directly and tance spot welds were processed at the important feature of the program is that it methodically correlated with the different Inland Steel Research Laboratories, while allows for variations in the physical prop­ welding process parameters. the simulated weld HAZ's were pro­ erties of the metal workpiece. A survey of the literature on resistance duced at the University of Illinois at Chi­ Temperature measurements have welding (Refs. 7-11) reveals that most of cago Welding and joining Laboratories. been made in real and simulated welds of the thermal models currently available to The temperature computations were a high-strength low-alloy (HSLA) sheet describe the resistance spot welding pro­ performed for different power levels, steel. Excellent agreement is obtained cess are either too basic (one-dimension­ several welding efficiencies, various elec­ between the numerical solution and the al) or do not include some of the funda­ trode forces and corresponding material experimental measurements. The heat- mental variables. For instance, the varia­ contact resistances. The model also affected zone (HAZ) obtained by plotting tion of contact resistance with applied accounts for the temperature depen­ the lines of constant temperature is very electrode force is not included in the heat dence of the physical properties of the similar to that measured from actual transfer formulation, nor is it the effect of base metal. welds. temperature on physical properties of the material. Physical and Mathematical Formulation Introduction This investigation has been undertaken to address some of these issues. Basically, The weld nugget in resistance spot Resistance spot welding is character­ in this work a heat transfer model is welding is produced by the melting and ized as a rapid and clean process for proposed for predicting the temperature subsequent coalescence of a small vol­ joining sheet steel. Despite its long and as a function of time, from the start of the ume of material due to the heating wide commercial application, an ade- weld, and as a function of position, for caused by the passage of the electric any location within the weld nugget, current and the high contact resistance adjacent heat-affected regions or elec­ between the sheet metals joined. Such trodes. This heat transfer model takes heating per unit time (Q) is defined as the KEY WORDS into account the following considera­ product of the current intensity (I) Resistance Spot Weld tions: conduction in the solid, convection, squared, times the total resistance (R), Spot Welding heat of fusion due to solid-liquid phase times the welding efficiency (17). HSLA Steels change, element heat content as a func­ Several authors (Refs. 12-14) have Heat Transfer Model tion of time and temperature, conduction reported continuous variations in the Temperature Spread in the weld pool, and heat of fusion on electrical parameters during welding of Copper Electrodes resolidification. mild steel sheet. After about the first Nugget Size For the analysis of the temperature cycle, there is an increase in voltage Heat Conduction distribution in the sheet metal, it is known across the copper electrodes and a Heat of Fusion that there is a symmetrical distribution of reduction in current flowing through the Computer Model temperatures through the thickness of weld zone until a "peak state" is reached. the material and along the interface Throughout the remaining portion of the where the two sheet pieces meet. Con­ weld cycle, the voltage decreases to a sequently, a cylindrical coordinate system constant value while the current was selected (Fig. 1) with radial as well as increases also to a constant value. These Z. HAN, J. OROZCO and). E. INDACOCHEA changes in voltage and current have also are with the University of Illinois at Chicago, vertical variations in temperature and the Chicago, III. C. H. CHEN is with inland Steel assumption of azimuthai symmetry in </>. been represented as dynamic resistance Laboratories, East Chicago, Ind. The basic equations and the correspond­ (Refs. 12-14). Basic welding mechanisms WELDING RESEARCH SUPPLEMENT I 363-s 6T/<5z=0 6T/6*=0 ST/6<t>=0 • -KdT/Sr^d-T,,,), K6T/6r=h„(T-Tj -KST/Sz-huCT-T^)^ 6T/6r=0 . 6T/6z=0 Fig. 1 —Schematic describing thermal boundary conditions Fig. 2 - Schematic of the resistance spot welding process can be altered by changes in welding large current flow is needed to produce a 1) A cylindrical coordinate system was variables such as weld time, electrode high-Joule heating effect in the work- selected as illustrated in Fig. 1. The por­ force and overall weld current. piece. The largest voltage drop occurs in tions of the coupon affected by the heat The components of the system for the workpiece, because the resistivity of and the immediate-adjacent areas of the resistance spot welding are schematically the copper electrodes is an order of unaffected base metal have been repre­ represented in Fig. 2. The copper elec­ magnitude lower than that of the carbon sented by a disk of radius o> (w = 25 mm), trodes are water cooled; they exert a steel (Ref. 16). This generates the highest because of the temperature symmetry. concentrated force on the outer surfaces internal heat production in the work- This selection reduces the geometrical of the metals to be joined. Because of piece, and melting takes place at the dependency to two dimensions, hence their low electric resistance, these elec­ common interface of the workpiece and T = T(r,z,4>) (1) trodes can conduct high currents to the spreads to produce the weld nugget. This 2) The temperature of the inner sur­ workpiece without significant )oule heat­ phase change from solid to liquid will face of the electrodes is that of the ing losses. Further, their high thermal cause a drastic change in the physical cooling water, Tw. conductivity permits closer control of the properties of the sheet steel. 3) Natural convection is the dominant nugget formation as well as the cooling The total resistance across the elec­ mechanism on the outer surface of the rate, by conducting heat away from the trodes could be considered as the sum of electrodes as well as on the surface of workpiece (Ref. 15). five resistors in the series schematically the workpiece. The resistances of the sheet steels to represented in Fig. 3. R-i and R5 are the 4) Symmetry with respect to 4>, the be joined are relatively small, so that a interface resistances between the elec­ azimuthal angle, permits heat transfer in trodes and the sheet metal; R2 and R4 the radial and vertical directions only. The represent the metals' bulk resistance. R3 is boundary conditions created by symme­ defined as the contact resistance at the try are indicated in Fig. 1. faying interface and is affected by the 5) The materials are subjected to a electrical, mechanical and thermal condi­ wide range of temperatures. Properties tion of the surface. Since melting occurs such as thermal conductivity (K), thermal at this last interface, heat production is diffusivity (a), specific heat (Cp) and resis­ the greatest at this location, implying that tivity (p) must then be considered as Rl R3 is much larger than the other resis­ functions of temperatures. For our study, R3 R4 tances. However, this value drops to the thermal properties considered were R5 zero (Appendix A) as the weld nugget is those of low-carbon steel, as shown in formed. Fig. 4 (Refs. 14, 16-19). Equations have been developed for these properties as function of temperature from the data in Model Assumptions Fig. 4. In modeling the resistance spot weld­ The thermal conductivity is expressed ing process, several boundary conditions as: and physical phenomena must be consid­ K = K0[1 - 0.0004528(T - 20)] (2) Fig. 3 —Simplification of the resistance across ered. In simplifying this thermal model, where 7 the electrodes the following assumptions are made: K0 = 5.4 X 10 erg/s • mm • °C 364-s | SEPTEMBER 1989 The equations for the specific heat were derived taking into consideration four temperature ranges as noted below Z (i) T < 520°C, Cp = CPo [1+ 0.000688(T - 20)] (3) a and o 8 CPo = 4.65 X 10 erg/g • °C (ii) 520°C < T < 770°C, CP CPo T"' (4) and X 3 o CPo = 8.55 X 10 erg/f tr (iii) 770°C < T < 850°C, < 4 8 Cp = Cpo(T - 850) + 7.118 X 10 (5) 2 6 10 14 tn and 400 800 1200 Temperature'C (xlOO) CPo = 13.716 erg/g • °C (iv) T > 850°C Temperature (*C) 8 z Cp = 6.25 X 10 erg/g • "C (6) UJ The equation developed for the resistivi­ 5000 s ty is: a.
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