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
-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. 3000 P = Po[1 + 0.005(T - 20)] (7) O and _i E 2000 u p = 1.5 pfi-mm > 0 UJ 6) The contact resistance at the faying a interface varies with electrode force as 1000 x o shown in Fig. 4D (Ref. 14). At relatively cc low electrode forces, this resistance is so < large that the bulk resistance of the sheet UJ metal is neglected. The empirical equa tn tion that was derived from the informa tion provided by Fig. 4D for the low- UJ S carbon steel is: 500 a. p' = p'0 (1 - 0.0004754 P) (8) o Temperature (*C) p'o = 15 p.Q-mm 100 where P is the electrode force on the 10 15 20 5 workpiece in units of pounds. a Electrode Force. Lbs. (xlOO) ~-> 7) Since the tip surfaces of the copper x electrodes are not only easily deformed, Fig. 4 — Physical properties of low-carbon steels of conductivity, specific heat, bulk resistivity and o contact resistance as a function of temperature and electrode force (Refs. 14, 16-19) tr but also polished before welding, the < electrode/sheet metal interface resis UJ tances, RT and R5, are assumed to be tn T(r,z,t0) = ^ (constant) (11) 3T UJ negligible. CC The adiabatic boundary conditions on the = (TT + '/2,J-TT-./2,J)/£ (19) dx i,),n 8) Since the metal undergoes a phase workpiece, as shown in Fig. 1, are z change, a latent heat of fusion evolves dl/dr = 0 at r = 0 for 0_< z < b (12) UJ which is assumed to be isothermally 3T/dz ^0 at z = L for R,< absorbed. = (TV + i,j + TV _ ,,j - 2TV,j)/S2 s r< R (13) dr2 a 9) The initial temperature of the metal 2 i,j,n <9T/d0 = 0 everywhere (14) (20) O is the ambient temperature, Too- —i The convective boundary conditions on >ui the workpiece are UJ 2 Mathematical Model -KdT/dr = hoo (T - TOT) at r = w for ^1 . =(TV,j + 1 + TV,j-l-2TT,j)/5 2 a 0 WELDING RESEARCH SUPPLEMENT 1365-s approaches zero (1/r) (3T/3r) would be undefined. To deal with this situation, we have that for r = 0 •OJ-1 w. IM. ti lim [(1/r)(3T/dr)] = d2T/dr2 (28) A r^O i.i-1/2 then the heat-conduction Equation 9 at the location r = 0 takes the form '0.1 I! T ILJ 2d2T/<3r2 + 32T/3z2 + (1/K)g = (29) A^ (1/a)3T/at similar formulations are also developed for points along the boundaries. Howev er, for simplicity their development is 'QK TM,H Tu-1 TM. r •V omitted. Numerical Method <" -> -> The governing differential equation Fig. 5-Rectangular T0l Tr-1.0 TM. was written in finite difference form and nef mes/i of s/ze 7 solved using an explicit method. The 7 n ana a node (ij) \ explicit method is relatively straightfor /ns/rJe f/ie matrix ward but requires a large amount of computing time because of the stringent where gVj is the energy generation term stability condition which is expressed as >0 for 0 < i < 4, 0 < j < 2 2 2 2 at node i,j and moment n. Applying the (25) At < (p"Cp/2Ar) /[1 + (Ar) /(rAt) ]. In ??.i{ = 0 everywhere else above formulation to those nodes on this study, the minimum time step used is boundaries, we can develop a general 0.00015 s. for node i, j located on outer surface, we expression to obtain the temperature I"' value at any node i,j and moment n + 1 Experimental Procedures as follows At h0 qV, = ^(TT,j-Too) (26) A cold-rolled HSLA sheet steel, 2.18 KAt P CpV mm (0.086 in.) thick was used in this Tn. + ) _ 1 i i TV + , i + TV - . i + investigation. Its composition is given in P"C C2" P t g?,i = o Table 1. The material was cut to small coupons of dimensions of 101.6 X 25.4 Ti/T+1 + Ttf-nl and finally, for node i, j located on the mm (4.0 X 1.0 in.). The surfaces of the specimens were previously cleaned with 4 inner surface of the electrodes, we At KAt 1 n have acetone. The spot welds were produced +— g?,i + I by placing two specimens into a special P Cp [ (24) At K welding fixture —Fig. 6. The fixture at qv.) = (27) taches to the lower copper electrode. The spot welding was done on a where qV,, is related to convective pro Sciaky press-type 100-kVA single-phase cess. If node i, j is located within the gV.i = 0 resistance welding machine. The elec system or on adiabatic boundaries, then trode force on welding was 1600 Ibf At the origin, r = 0, Equation 9 would (7120 N). The electrodes used were a have a singularity because as r Class II copper alloy (99.2% Cu, 0.8% Cr) based on the Resistance Welder Manu Fig. 6 - Welding facturers' Association (RWMA) standard. fixture used for Thermocouple Location The electrode tips have a contact diame production of spot ter of 7.9 mm (0.31 in.) and 45-deg welds truncated cone nose in accordance to ? the Ford Motor Company manufacturing standards. The welding time was held fixed at 23 cycles (0.38 s) and the current JL varied between 11 and 12 kA. ZL -f^^? The thermal cycle measurements dur E U5 ing resistance welding were measured by I 1.5'- spot welding a 0.254-mm (0.010-in.) ther mocouple (either a chromel/alumel or a WELDING FIXTURE platinum/platinum-10% rhodium) onto a 0.8-1.1-mm (0.032-0.045-in.) wide slot machined on the upper coupon as shown in Fig. 7. The slot was machined so as to end in the HAZ, and its length was estimated by performing a metallograph ic analysis on several preliminary spot Electrode welds. The welds were sectioned through the nugget normal to the plane 366-s I SEPTEMBER 1989 of the sheet. Samples were mechanically polished and etched with a solution of picric acid plus sodium tridecylbenzene I- sulfonate. This etchant was very effective Z UJ in revealing the solidification structure of it E the weld nugget. Samples were charac Q. terized with a Leco 300 metallograph. o The nugget size, as well as HAZ measure _l UJ ments, were made from the resulting > micrographs and Fig. 8 shows one of 5? several photo composites that were o assembled for the metallographic analy oc < ses. The HAZ was observed to be the UJ widest at the faying interface. The ther 30172" tn ^E ut mocouples were placed very close to this ac faying surface, and its exact location was *>. later determined by metallographic eval uation after welding. The thermal mea L-0.346' to 0.365" surements were collected using a Hew Fig. 7 —Sheet steel o. lett-Packard Series 3000 personal com W= 0.032" to 0.045" coupons for the o puter with a 3852 data acquisition unit spot welds and a Xerox 6060 personal computer interphased with a metrobyte data acqui sition system. The thermocouple output Table 1--Composition of the HSLA-Sheet Steel wt-% X o signal was distorted during the heating cc cycle, but then it remained very smooth C Mn Si Nb Ti Al N s P < during cooling, immediately after the end Ul 0.06 0.96 0.03 0.10 0.002 0.060 0.006 0.012 0.009 tn of the weld cycle. The peak temperature UJ was obtained by extrapolating the cool ac ing curve to a time coinciding with the z end of the weld time. Effect of Current Level on Nugget Formation ment of welding lobes to define the UJ current and time ranges where optimum 2 Results and Discussion Automotive companies' spot weld spot welds can consistently be produced. Q. qualification procedures (Refs. 1, 2) spec However, this reproducibility is ham o pered by inconsistencies in metal compo > The heat transfer model developed in ify measuring the size of the weld nugget ui this study includes in its formulation the in terms of one or more welding vari sition, variation in surface finish and by a ~~^ independent process parameters such as ables, depending on the specification electrode tip mushrooming. x current, electrode force and time, the applied. The correlations of nugget size The heat transfer model proposed o oc material's thermally dependent physical with current or with current and time are defines the temperature of any location < properties and the weld efficiency factor. some of the most popular for qualifica in the workpiece as a function of time UJ The analytical results predicted by the tion procedures. The importance of the from the start of the process. Conse tn ui model are compared with those obtained current's influence on the soundness of quently, it can also define the time when ac experimentally. the weld nugget has led to the develop the weld nugget begins to form. Figure 9 Fig. 8 —Micrograph a. of a spot weld O cross-section CROSS SECTION Or WELD o cc < UJ tn UJ oc a. O ECHANT: PICRIC ACID + SODIUM TRIDECYLBENZENE SULFONATE x o rr «*^BwVVYT* .H*ffl^?SWf||jS% < UJ CA : UJ '"• " *^mw CC WELDING RESEARCH SUPPLEMENT 1367-s 3000 3000 At the Center of At the Center of Tr=29°c Tw = 14b Tr = 29*c, Tw = 14fc Weld Nugget Weld Nugget P=1600Lbs. P= 1600Lbs. EF=70% I =11.93KA 2500 EF=90% l = 14KA EF= 80% l= 11.93KA 0 0.15 0.3 0.45 0.6 0.75 0 0.15 0.3 0.45 0.6 0.75 TIME (Sec.) TIME (Sec.) Fig. 9 - Theoretical temperature distributions as a function of time for Fig. 10— Theoretical temperature distributions as a function of time three different currents for different efficiencies presents temperature versus time predic time of 0.21 s for 14.0 kA versus 0.33 s corresponds to a constant temperature tions at the center of the weld nugget at for 11.93 kA, as seen in Fig. 9. (melting point) of the workpiece (where the faying surface. Computation of this The welding efficiency factor is an the nugget would be formed) as a result information was done with the assump important consideration in this model of the heat absorption prior to melting. tion of a fixed electrode force of 1600 Ib because of its effect on the accuracy of The time at which such drop occurs and efficiency factor of 70%. the model's predictions. Figure 10 reflects coincides with the time to reach the At low currents, undersize and brittle its significance. The use of an incorrect melting temperature as seen in Fig. 11. nuggets are formed because of the insuf efficiency factor could either lengthen or ficient heat supplied to cause the asperity shorten the period for start of nugget Effect of Electrode Force on Nugget collapse and surface film breakdown. formation. The theoretical curves gener Formation From the results observed in Fig. 9, it ated in Fig. 10 assume a constant elec seems that a welding current of 14.0 kA trode load of 1600 Ib and current of In order to examine the effect of will produce a larger nugget than 11.93 11.93 kA. electrode force on the start of the nugget kA, since the supply of heat for the high This heat transfer model has also been formation, temperature-time curves current is larger not only because of the used to determine the heating and cool were calculated with this model using higher current, but also because of the ing rate as a function of time for any three different electrode forces —Fig. 12. time spent at melting temperature or location in the workpiece (Appendix B). All these curves correspond to a location above the melting point, as denoted by Figure 11 shows the heating and cooling at the center of the weld nugget and right AtLow i and AtHigh i- Correspondingly, the rate curves superimposed with the tem at the faying interface. time to reach the melting temperature perature-time curve corresponding to As the electrode force was increased, will be shorter for the high current than the center of the weld nugget. Notice the time to reach the melting tempera for the low current. The model predicts a that the sudden drop in the heating rate ture was delayed because of the general decrease in the resistance level. Such reduction in total resistance is expected Fig. 11— Theoretical At the Center of Weld Nugget Tr = 28 C because the increase in the applied pres temperature Tw=14*C 10000 sure will decrease the thickness of the distributions and . P=1600Lbs. material between the electrodes and the heating and cooling \ 1=11.79KA \ EF=0.75 rates versus time at 2 contact area, primarily at the faying inter Heating Rate /—^ the weld center s 5000 \ Melting Point face, will increase in view of the defor nugget 1 mation of the asperities. Recall that the 6 resistance is proportional to the length of 0 the conductor and inversely proportional to the cross-sectional area (R a L/A). / ' Since all the curves were calculated at -5000 the same current (11.93 kA and efficiency / Cooling Rate value 70%), decreasing resistance results in a decrease in the rate at which energy 2 10000 is supplied to the weld (P = r/l R). Thus 0.3 0.45 the time to reach the temperature for Time (Sec.) melting is shifted to longer times and, 368-s | SEPTEMBER 1989 2500 At the Center of Tr » 2Sfb, Tw=14b 50 Weld Nugget 1 At the Center of Tr= 23b, Tw=14fc P = 1600,Lbs., Weld Nugget EF =70% EF=70% 2000 P = 1300Lbs. £•"""* 1 = 11.93KA A 1=1 1.93KA UJ P = 1600Lbs. i \ FAYING SURFACE rr P = 1900Lbs. 1 < 1500 -MELTING POINT f j 1 /\\ \ <^/ INNER LAYER a LrUr w / / \ \ / 0. / / [5 15001- MELTING POINT i / / \ \ / LU / / \ V \JA ELECTRODE-SHEET F 1000 / / ""L \ INTERFACE / / N I / // / >v / / / \.//v>. ^ 500 // \ / \S '/ // • s 2_ 1 L 1 1 1 0.15 0.3 0.45 0.6 0.75 0.9 TIME (SecJ TIME (Sec.) Fig. 12 — Theoretical temperature distributions as function of time for Fig. 13 - Predicted temperature distributions as a function of time at different electrode forces different positions from the faying interface along the electrode axis consequently, nugget formation is perature as a function of time for any from the center of the weld nugget. delayed as electrode force is increased. location in the workpiece. Figure 13 Although the agreement is very reason Lower electrode forces, therefore, shows the peak temperatures reached able, discrepancies were found primarily should favor nugget formation and larger along the vertical axis of the electrodes during the cooling cycle that could be nugget size in view of the longer time and for different locations through the thick attributed to some of the original at or above the melting temperature for ness of the sheet metal. Similar distribu assumptions made in the model's formu the same current, as observed in Fig. 12. tion of temperatures have been calculat lation. The selection of a relatively large At higher forces, the nuggets would be ed along the faying interface at 1.0-mm grid size (1.0 mm) and the lack of an smaller, which could affect the ductility (0.04-in.) steps from the electrode axis, as efficiency factor were some of the prob and soundness of the spot weld. shown in Fig. 14. lems thought to be responsible for such A direct correlation between experi deviations. Reduction in the mesh size mental and theoretical temperature-time and the step time, as well as the use of a Correlations of Theoretical and curves is presented in Figs. 15 and 16. higher efficiency factor (75%) improved Experimental Results The thermocouple for the experimental the agreement between the experimen It has been indicated that this thermal curve was placed along the faying inter tal and theoretical curves, as shown in model is capable of predicting the tem face at a distance of 53.8 mm (0.15 in.) Figs. 15 and 16 for two different samples. 3000 Tr-28fc Tw = 14fc L-3.8 (mm) Tr-29t;> Tw-14C P=1600Lbs. From Weld Nugget P-1600Lbs, EF=70% Center on Faying Surface ... __ . 2500 I =11.93KA - 2500 2000 WELDING CENTER 2000 rr / L-1 i- < fKV L-2 or. LU UJ 1500 - MELTING POINT lj o. "A\/ L-3 1500 < UJ K \Z cr if LU o. EF=75 % bO.2 mm 1000 l/ 4W).0OO15 S«c, \. 1000 ' /// / \ A- \ EF=70% //"v^ Experiment /~^\ /\ >\ I- 1 mrt 7^-/ • ^^^ 500 • />'/ 500 ^s ^^ J-^s^l~~ l ss" '^~-~^~~~~~~- 0.15 0.3 0.45 0.6 0.75 TIME (Sec.) 0.15 0.3 0.45 0.6 0.75 L: DISTANCE FROM WELDING CENTER TIME (SecJ ON FAYING SURFACE (mm) Fig. 15 — Comparison of theoretical and experimental temperature Fig. 14 —Predicted temperature distributions as a function of time in distributions for a point on the faying interface and 3.8 mm from the the workpiece for different points along the faying interface weld nugget centerline WELDING RESEARCH SUPPLEMENT 1 369-s 3000 The differences between the two curves L-4(mm) Tr=28C, Tw-KfC are more noticeable during cooling and FROM WELDING CENTER P-1600Lbs, at the longer times, with the experimental ON FAYING SURFACE M1.79KA curve having a slower cooling rate — Figs. 2500 EF=75 % 15 and 16. This is probably caused by the • Model fact that material was removed to make a Experimental notch where the thermocouple was spot welded. 2000 The model was used to map constant temperature curves for the spot weld at LU 0.38 s into the welding cycle, when the CC current was stopped at that instant. 500 Si These curves were plotted for one of the tr LU quadrants of the spot welding system as 0. LU shown in Fig. 17. The temperature distri bution allows us to define the regions 1000 that underwent melting (weld nugget) and those that were affected by the heat Fig. 16 — Comparison of the process (HAZ). Based on this, the weld nugget size and HAZ were estimat of theoretical and 500 experimental ed, and these results have been schemat temperature ically compared in Fig. 18 for a spot distributions for a weld. point on the faying interface and 4.0 0.15 0.3 0.45 0.75 mm from the weld Conclusions nugget centerline TIME (Sec.) 1) A finite difference thermal model was developed for resistance spot weld h -Electrode- ing, capable of predicting the tempera I ture as a function of time and location for T-=700'C T=600"C T=300-C T=100*C any position in the workpiece, and for T=500'C T=400"C T=200'C any low-carbon sheet steel. This model could also be applied to any other metal provided the physical properties of given material are included in the model. 2) Acceptable correlations between the theoretical and experimental temper atures have been made. The tempera tures in the spot welds were measured using fine thermocouples imbedded in the sheet-steel coupons near the faying 7 (mm) r interface. 3) Improvement in the experimental Tr=28C, Tw=14C . P=1600Lbs.. 1=11.79KA, EF=75% t=0.38 Sec. techniques to monitor the thermal cycles, Fig. 17-Predicted temperature profiles around the weld nugget and heat-affected zone of the as well as the introduction of empirical spot weld data in the model should reduce the deviations that exist between the pre Tr-28"C, Tw-V4C dicted and the experimental values. Model P-1600LDS, 4) This model can also predict indirect M1.79KA Experiment ly the weld nugget size and the width of EF=75 % the HAZ. Work continues to improve the model to predict the microstructures and corresponding strengths of the HAZ. A ckno wledgments The authors wish to acknowledge the financial support provided by Inland Steel Company for the work performed at the University of Illinois at Chicago. We are also grateful to Michael Bjornson for the extensive metallography and measure ments performed on this project. Mr. Dan Caliher and Mr. Neal Saboff, who carried out the spot welds at Inland Steel Research Laboratories also are acknowl edged. This project could have not been 1 (mm) Distance from Weld Center started without the tremendous support Fig. 18 —Schematic comparing the predicted and experimental weld nugget cross-section and encouragement from the late William dimensions Schumacher. 370-s | SEPTEMBER 1989 Appendix A instant n, at a location i, j, either for niques. Welding lournal 66(1):1-s to 10-s. heating or cooling, can be defined as 7. Goldak, )., Bibby, M., Moore, ]., House, The Drop to Zero: an Explanation R., and Patel, B. 1986. Computer modeling of dT/dt|j,j,n- This can be approximated as AT/At around the moment n, as shown heat flow in welds. Metallurgical Transactions The existence of a finite contact resis B, 17B(9):587. in the following expression tance is due principally to surface rough 8. Rice, W., and Funk, E. ). An analytical ness effects. Heat transfer is therefore investigation of the temperature distributions due to conduction across the actual con AT _ Tjj.n + 5 ' Tj,j,n - 5 during resistance welding. Welding Journal 46 (4):175-s to 186-s. tact area and to conduction (or natural At ti,j,n + 5 — ti,j,n - 5 convection) and radiation across the 9. Krutz, C. W., and Segerlind, L. ). 1978. TU WRC Bulletin 343 May 1989 Destructive Examination of PVRC Weld Specimens 202, 203 and 251J This Bulletin contains three reports: (1) Destructive Examination of PVRC Specimen 202 Weld Flaws by JPVRC By Y. Saiga (2) Destructive Examination of PVRC Nozzle Weld Specimen 203 Weld Flaws by JPVRC By Y. Saiga (3) Destructive Examination of PVRC Specimen 251J Weld Flaws By S. Yukawa The sectioning and examination of Specimens 202 and 203 were sponsored by the Nondestructive Examination Committee of the Japan Pressure Vessel Research Council. The destructive examination of Specimen 251J was performed at the General Electric Company in Schenectady, N.Y., under the sponsorship of the Subcommittee on Nondestructive Examination of Pressure Components of the Pressure Vessel Research Committee of the Welding Research Council. The price of WRC Bulletin 343 is $24.00 per copy, plus $5.00 for U.S., or $8.00 for overseas, postage and handling. Orders should be sent with payment to the Welding Research Council, Room 1301, 345 E. 47th St., New York, NY 10017. WELDING RESEARCH SUPPLEMENT 1371-s