Analyses of resistance spot welding lobe curve

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ANALYSES OF RESISTANCE SPOT WELDING

LOBE CURVE

by

Euiwhan Kim

S.M. Massachusetts Institute of Technology (1986)

M. Edu. Seoul National University (1979)

B.Sc. Seoul National University (1977)

SUBMITTED TO THE DEPARTMENTS OF MATERIALS SCIENCE AND ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREES OF

DOCTOR of SCIENCE

in

MATERIALS ENGINEERING

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

June 1989

copyright Euiwhan Kim, 1989

The author hereby grants to the M.I.T. permission to reproduce and to distribute copies of this thesis document in whole or in part.

Signature of author

...

Signature redacted

...

K

...

---

...

Department of Material Science and Engineering

Sianature redacted

May 5, 1989

C ertif ied b y ... ... ... ... (vrofessor Thomas W. Eagar

.017 Thesis Supervisor

Signature redacted

A ccepte d by ... ... ... ... Professor Samuel M. Allen, Chairman Department Committee on Graduate Students IoswgftqS7My erials Science and Engineering

OF TECHNOLOGY

JUN 07 1989

LIBRARIES

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2

-ANALYSES OF RESISTANCE SPOT WELDING LOBE CURVE by

Euiwhan Kim

Submitted to the Departments of Materials Science and Engineering on May 5, 1989 in partial fulfillment of the requirements for the degrees of Doctor of Science in Materials Engineering

ABSTRACT

This study was performed to investigate the fundamental parameters controlling the weld lobe shape. For this purpose, a lumped parameter model was developed. Using this model, characteristic parameters which can influence the shape and the position of lobe curves were derived. To investigate the relative importance of these parameters, a numerical analysis was performed using measured and deduced interface properties. A new method was developed and was used to characterize the contact properties. The electrode temperature was also investigated.

Nine weld characterization parameters were derived from analysis of a lumped parameter model and the contact phenomena. These parameters were categorized into f our groups, i.e. material parameters, electrical parameters, thermal parameters and the geometrical parameters. Using these parameters, welding behavior was explained and compared. A new formula is presented as an index of the sensitivity of nugget growth to various parameters.

It was found that a significant thermal discontinuity exists at the electrode interface. The contact heat transfer coefficient for material with zinc coating ranges from 0.5 W/mm2

*Cto 2.0 W/mm2*Cin the temperature range of 100 to 400 degrees centigrade. The dynamic electrical contact resistance at the faying interface is lower than that at the electrode interface. The thicker materials are less sensitive to contact characteristics due to the decreased ratio of contact resistance to the total resistance.

There is a pressure concentration at the periphery of the faying interface contact and at the edge of the electrode. Due to thermal expansion, the contact size and the pressure concentration decreases during the course of welding. This is believed to lead to expulsion. The electrode force has an effect not only on the contact interface properties but also on the contact area.

The most important factor in determing the variability of nugget growth behavior is the ratio of contact radius to the electrode radius and the ratio of electrode radius to the square of specimen thickness. The ease of bare steel welding is believed to be due to the small electrical contact size at the faying interface rather than the high contact resistance. The sensitivity of the nugget growth curve to each parameter was estimated. In general for a variation of 10%, the geometrical parameters are the most important followed by material parameters. The parameters of lowest importance are the electrical parameters and the thermal parameters.

Thesis Supervisor: Dr. Thomas W. Eagar

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-H

To my wife

Keumja Lee

and to my daughters

Jeeyoon and Jungyoon

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-6-List of Tables

Table 2.1 Proportion of Heat Consumption in Resistancr Spot Welding ... 37

Table 2.2 Typical Electrical Bulk Resistance and Contact Resistance ... 42

Table 2.3 Estimation of Electrical Characteristic Parameter ... 45

Table 2.4 Typical Values for Material Characteristic Parameters ... 48

Table 2.5 Effect of Parameters on the Lobe Width and Energy Input ... 49

Table 2.6 Electrical Characteristic of the Welding Machine ... 52

Table 3.1 Experimental Test M aterials ... 71

Table 3.2 Experim ental Test M atrix ... 75

Table 4.1 Effect of Coating Morphology on the Temperature Evolution 88 Table 5.1 Effect of Coolant Flow Rate and Electrode Face Thickness ... 95

Table 6.1 Effect of Coating Thickness in One-D Simulation Welding ... 111

Table 6.2 Effect of Coating Morphology in One-D Simulation Welding ... 114

Table 6.3 Temperature Changes during Welding of Dissimilar Thickness 118 Table 7.1 Heat Control Angle of the Welding Machine ... 154

Table 8.1 Contact Heat Transfer Coefficient ... 179

Table 8.2 Temperature Dependence of Heat Transfer Coefficient ... 182

Table 9.1 Effect of Electrode Force on Contact Size and Pressure ... 211

Table 9.2 Effect of electrode size on the contact size ... 212

Table 9.3 Effect of Specimen Thickness on the Contact size ... 212

Table 9.4 Twelve Cycle Lobe Width vs. Coating Weight ... 217

Table 9.5 Estimated Contact Size and Expulsion Nugget Size ... 219

Table 10.1 Effect of material characteristic parameter ... 261

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-7-List of Figures

Figure 1.1 The spot welding process (after [1.1]). 21

Figure 1.2 Typical welding lobe curve. 21

Figure 1.3 Generalized resistance curve (after [1.24]). 22 Figure 1.4 Components of dynamic electrical resistance. 23 Figure 1.5 The critical current value which can be passed through

a contact conductor under steady state conditions

(after [1.28]). 24

Figure 2.1 An approximate nugget growth model with temperature

profile. 55

Figure 2.2 Basic lobe curve. 56

Figure 2.3 Effect of heat capacity. 57

Figure 2.4 Typical dynamic resistance behavior and its components. 58 Figure 2.5 Effects of changes in the electrical resistivity. 59

Figure 2.6 Effect of heat loss. 60

Figure 2.7 Steady state temperature distribution near a contact

interface. 61

Figure 2.8 Change of interface temperature profiles due to

geometry changes. 62

Figure 2.9 Characteristics of heat loss. 63

Figure 2.10 Welding data for the calculations (after [2.3]). 63

Figure 2.11 Characteristic nugget growth curve. 65

Figure 2.12 Effect of the geometric characteristic parameter

on the heat loss rate. 65

Figure 2.13 Effect of weld time on the lobe curve. 66

Figure 2.14 Welding machine circuit. 67

Figure 2.15 Characteristic change of weldin$ current and power absorbed by the weld. (a) One dimensional simulation

welding. (b) Actual size welding. 68

Figure 3.1 Thermovision system. 80

Figure 3.2 Infrared monitoring system. 80

Figure 3.3 Emissivity versus temperature for the high temperature

paint. 81

Figure 3.4 One dimensional simulation of spot welding. 82 Figure 3.5 Setup for heat transfer coefficient measurement. 83 Figure 3.6 Electrode geometry used in the electrode

temperature experiment. 84

Figure 3.7 Cinematography on an edge weld. 85

Figure 3.8 Four point probe for bulk resistivity measurements. Body is made from a machinable ceramic. All metal contacts are nickel for high temperature performance

(after [3.10]). 86

Figure 4.1 Heat propagation pattern on an edge weld. 91 Figure 4.2 Effect of electrode shape on the starting location

of glow. 92

Figure 5.1 Two dimensional temperature profile on the

electrode surface. 100

Figure 5.2 Cascade display of a high speed thermal line scan. 101 Figure 5.3 Change in the maximum electrode surface temperature

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-8-Figure 5.4 Change in the maximum electrode temperature with electrode face thickness.

Figure 5.5 Change in the maximum electrode surface temperature during welding.

Figure 5.6 Typical data scatter in the measurement of the

maximum electrode surface temperature during welding. Figure 5.7 Schematic of increased cooling of a thin electrode Figure 5.8 Determination of the electrode temperature from

the electrode thickness, heat input and heat transfer coefficient at the cooling interface.

Figure 5.9 Increased cooling of a thinner electrode.

Figure 6.1 Temperature profile of a high speed line scan during one dimensional simulation of the spot welding process. Figure 6.2 Effect of coating thickness on the induced welding

current (a) and temperature (b) in one dimensional simulation welding.

Figure 6.3 Effect of coating weight on current requirements (after [6.1]).

Figure 6.4 Effect of Zinc coating morphology and electrode

force on the induced welding current in one dimensional simulation welding.

Figure 6.5 Temperature profiles in E70 electrogalvanized steel in one dimensional simulation welding.

Figure 6.6 Temperature profiles in G60 hot dip galvanized steel in one dimensional simulation welding.

Figure 6.7 Temperature profiles in A40 galvanized steel in one dimensional simulation welding.

Figure 6.8 Temperature at the faying interface in the 1-D

simulation welding of workpieces of different coating morphology.

Figure 6.9 Temperature at the electrode interface in the 1-D simulation welding of workpieces of different coating morphology.

Figure 6.10 Electrode face temperature in the 1-D simulation welding of workpieces of different coating morphology.

Figure 6.11 Electrode temperature at 1.6mm from the interface in 1-D simulation welding of workpieces of different coating morphology.

Figure 6.12 Lobe curves of zinc coated materials.

Figure 6.13 Effects of specimen thickness and electrode force on the induced current in one dimensional simulation welding of bare steel.

Figure 6.14 Temperature profiles in 1-D simulation welding of specimens of different thicknesses using 900 lbs of electrode force.

Figure 6.15 Temperature profiles in 1-D simulation welding of specimens of different thicknesses using 650 lbs of electrode force.

Figure 6.16 Temperature profiles in 1-D simulation welding of specimens of different thicknesses using 400 lbs of electrode force.

Figure 6.17 Temperature at the faying interface in 1-D simulation welding of bare steel.

Figure 6.18 Work piece temperature at the electrode interface in the 1-D simulation welding of bare steel.

103 104 105 106 107 108 121 122 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139

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-9-Figure 6.19 Figure 6.20 Figure 6.21 Figure 6.22 Figure 6.23 Figure 6.24 Figure 6.25 Figure Figure Figure Figure Figure 7.1 7.2 7.3 7.4 7.5 Figure 7.6 Figure 7.7 Figure 7.8 Figure 7.9 Figure 7.10 Figure 7.11 Figure 7.12 Figure 7.13 Figure 7.14 Figure 8.1 Figure 8.2 Figure 8.3 Figure 8.4 Figure 8.5 Figure 8.6 Figure 8.7 Figure 8.8 Figure 8.9 Figure 8.10

Temperature at the electrode face in the 1-D simulation welding of bare steel.

Electrode temperature 1.6 mm from the electrode interface in the 1-D simulation welding of bare steel. Temperature changes during 1-D simulation welding of bare steel of different thicknesses.

Change of workpiece temperature at the electrode interface during 1-D simulation welding of bare steel of different thicknesses.

Change of electrode temperature 1.6mm from the interface during 1-D simulation welding of bare steel of different thicknesses.

Change of electrode face temperature during 1-D simulation welding of bare steel of different thicknesses.

Change of faying interface temperature during 1-D simulation welding of bare steel of different

thicknesses.

Current discretization

Electrical resistivity of G60 National steel Electrical resistivity of National steel Electrical resistivity of Armco steel

Comparison of electrical resistivity of National steel and Armco steel

Electrical resistivities of different type steels Piecewise linearized electrical resistivity of low carbon steel

Thermal conductivity Heat Capacity

Temperature dependent mechanical properties of low carbon steel (after [7.5])

Model for one dimensional simulation welding. Axisymmetric two dimensional model

Schematic comparision of the current flowing area and the mechanical contact area

Current distribution model

Schematic of temperature profile during the measurement of contact heat transfer coefficient Typical steady state temperature profile

(high heat transfer coefficient)

Typical steady state temperature profile (low heat transfer coefficient)

Contact heat transfer coefficient of AMBR at 500 lbs electrode force

Contact heat ransfer coefficient of AM35 at 500 lbs electrode force

Contact heat transfer coefficient of AM68 at 500 lbs electrode forca

Contact heat transfer coefficient of AM100 at 500 lbs electrode force

Contact heat transfer coefficient of A40 at 500 lbs electrode force

Contact heat transfer coefficient of E70 at 500 lbs electrode force

Contact heat transfer coefficient of G60 at 500 lbs electrode force 140 141 142 148 149 150 151 161 162 163 164 165 166 167 168 169 170 171 172 173 174 187 188 189 190 191 192 193 194 195 196

l

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Figure 8.11 Figure 8.12 Figure 8.13 Figure 8.14 Figure 8.15 Figure 8.16 Figure 8.17 Figure 8.18 Figure 8.19 Figure 8.20 Figure 8.21 Figure 8.22 Figure 9.1 Figure 9.2 Figure 9.3 Figure 9.4 Figure 9.5 Figure 9.6 Figure 9.7 Figure 9.8 Figure 9.9 Figure 9.10 Figure 9.11 Figure 9.12 Figure 9.13 Figure Figure Figure Figure Figure Figure Figure 9.14 9.15 9.16 9.17 9.18 9.19 9.20

Contact heat transfer coefficient of A40 at 650 lbs electrode force

Contact heat transfer coefficient of E70 at 650 lbs electrode force

Contact heat transfer coefficient of G60 at 650 lbs electrode force

Contact heat transfer coefficient of AMBR at 650 lbs electrode force

Typical temperature dependence of the contact heat transfer coefficient and the electrical contact resistivity at the electrode interface.

Typical temperature dependence of electrical contact resistivity at the faying interface.

Temperature profile for AMIO0 in l-D simulation and the measured temperature.

Temperature profile for AM68 in 1-D simulation and the measured temperature.

Temperature profile for AM35 in 1-D simulation and the measured temperature.

Temperature profile for AMBR in 1-D simulation and the measured temperature.

Electrical contact resistivity at electrode interface Electrical contact resistivity at faying interface Contact pressure distribution at the faying interface at room temperature

Contact pressure distribution at the electrode interface at room temperature.

Deformation in electrode and work piece at room temperature.

Contact pressure distribution and contact size at the faying interface for different electrode sizes. Change of contact pressure at the faying interface during welding.

Change of contact pressure at the electrode interface during welding.

Change of temperature field during weldng. Change of deformation in the electrode and in the work piece during welding.

Change of contact size at the faying interface during weling.

Evolution of halo size and nugget size

Typical nugget growth curves generated in axisymmetric two dimensional simultion.

Evolution of temperature at the center line for welding of nominal size nugget.

Evolution of temperature at the center line for expulsion weld.

Nugget growth curve for AMIOO Nugget growth curve for AM68 Nugget growth curve for AM35 Nugget growth curve for AMBR

Nugget growth curve for expulsion weld Nugget growth curve for nominal size weld

Temperature profiles at the faying interface during welding of bare steel, AMBR

197 198 199 200 201 202 203 204 205 206 207 208 226 227 228 231 232 233 234 237 240 241 242 243 244 245 246 247 248 249 250 251

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11 -Figure 9.21 Figure 9.22 Figure 9.23 Figure 9.24 Figure 9.25 Figure 9.26 Figure Figure Figure Figure Figure Figure 10.1 10.2 10.3 10.4 10.5 10.6 Figure 10.7 Figure 10.8 Figure 10.9 Figure 10.10 Figure 10.11 Figure 10.12 Figure 10.13 Figure 10.14

Temperature profiles at the faying interface during welding of electrogalvanized steel, AM100

Axial temperature distribution during welding of bare steel, AMBR

Axial temperature distribution during welding of electrogalvanized steel AMINO

Axial temperature distributions at the start of nugget formation for different welding conditions

Effect of interface properties on the axial temperature profiles in the welding of materials with small contact area

Effect of interface properties on the axial temperature profiles in the welding of material with large contact area

Effect of changes in the thermal conductivity Effect of changes in the electrical resistivity Effect of changes in the heat capacity

Effect of changes in the electrode diameter Effect of changes in the specimen thickness Effect of changes in the contact diameter at the faying interface

Effect of changes in the current level

Effect of changes in the electrical contact resistivity at the faying interface (small change)

Effect of changes in the electrical contact resistivity at the faying interface (large change)

Effect of changes in the electrical contact resistivity at the faying interface and at the electrode interface Effect of changes in the contact properties at the electrode interf ace

Lobe curve of 0.6 mm thick G40 hot dip galvanized steel Lobe curve of modified 0.6 mm thick G40 hot dip

galvanized steel (coating only on the electrode side)) Effect of coating side on the shape of the heat affected zone (after [10.4]) 252 253 254 255 256 257 274 275 276 277 278 279 280 281 282 283 284 285 286 287

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ACKNOWLEDGEMENT

I have received a lot of help from many sources directly or indirectly during this thesis. It is not possible to adequately express my sincere appreciation to all those people in the space available. I will attempt to acknowledge as many people as possible for their valuable contributions to this project.

The first thanks should be given to professor Thomas W. Eagar for his advice and enlightment the author received during the course of education at MIT. His attitude toward science and engineering has made a lasting impression on me. In addition, his attitude toward the every day life has affected me significantly as worthy to emulate. Words cannot fully express this appreciation.

Special thanks goes to Prof. Stuart Brown, Mr. Bob Frank, Mr. Haoshi Song and Mr. Rakesh Kapoor for help in computer related work. Thanks are also due to my old colleague Prof. Carl Sorensen at Brigham Young University for his great help in many aspects during the stay at MIT. Mr. Tom Natale of National Steel and Mr. Greg Nagle of G.M. are also appreciated for providing specimen materials.

Mr. Cesar Calva and Mr. Bruce Russell deserves my special thanks for their generous help in experiments. Dr. Mansoor Khan, Mr. E. J. Yoon, Mr. Dan Peter and Mr. Rakesh Kapoor should be also acknowledged for their valuable help in preparing this document.

Finally, I would like to give my deepest thanks to my wife Keumja Lee and also to my children Jeeyoon and Jungyoon to whom this thesis is dedicated. Without my wife's love, sacrifice and support none of this would have been possible. My

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-

13-mother, who is always with me in sprit, has been a source of inspiration and encouragement throughout my life. By sharing the satisfaction I have from this thesis I hope I can reward her endless love.

The financial support for this research was provided by General Motors, Ford and International Lead Zinc Research Organization.

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1 INTRODUCTION AND BACKGROUND

1.1 INTRODUCTION

Since its development the process of resistance spot welding has been used widely as one of the major joining processes for sheet metals. The weld nugget is formed by passing high current through a stack of sheet materials to be joined, usually two sheets, between two water cooled copper electrodes as shown in figure 1.1 [1.1]. Heat is generated by joule heating due to the inherent resistance of the materials and the contact resistance. The sheets are heated until the center region melts, thus forming a nugget which then solidifies when the current is halted.

The resistance spot welding process involves complicated interactions between physical and metallurgical properties of the materials and electromagnetic and mechanical phenomena. The thermal history of the weld nugget is controlled by these parameters. From the manufacturing point of view, it is very important to establish consistent welding procedures for practical welding. Due to the complexity of the interactions among all these parameters, the methods of establishing weld procedures for new materials and new equipment have usually been empirical. Even for a material of the same specification, weld parameters sometimes have to be reset due to inconsistencies in the weld behavior [1.2-1.5]

The lobe curve has been used for many years to characterize the weldability during resistance spot welding. The typical shape of this curve is shown in figure 1.2, which shows the regions of acceptable weld nugget formation for different welding parameters. The lower bound is determined by the minimum nugget size required for mechanical strength and the upper bound is determined by the expulsion of liquid material from the work pieces. The weldability of a material in resistance spot welding is determined by two main factors. Firstly, the size of the lobe curve width, which shows the permissible weld current range at a constant weld time and secondarily the wear of the electrodes.

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-These two major factors are controlled by the interplay between the many parameters which govern the temperature distribution in the parts during the welding thermal cycle.

Some analytical and numerical models have been developed to understand the mechanism of nugget formation [1.5-1.13]. Although the models have attempted to incorporate the complexities of the weld parameters, such as temperature dependent material properties and contact resistances, those models offer very limited explanations about the effect of each parameter on the weld lobe curve. This seems to be partly due to the ill-defined parameters such as the contact resistance at the interfaces and also due to the orientation of the research which is mostly aimed at automatic control of the process [1.14-1.19]. Another difficulty of this modelling work is the lack of experimental verification. The previous models usually used the final nugget size as an experimental verification. The transient thermal distribution has not been measured. Such information has to be ascertained experimentally in order to obtain a better understanding of the nugget formation mechanism.

In this research, a parametric study of the weld lobe curve was undertaken to understand the basics of weld lobe shape. The main questions to be addressed are what the important parameters are in determining the lobe curves and how sensitive the lobe curves are to these parameters. A systematic approach to each parameter was taken, starting with an approximate heat balance model to see the effect of each parameter and to derive the important parameters. The electrical and the thermal properties of the contact interfaces were also investigated experimentally and numerically using one dimensional simulation welding. Then a numerical simulation of the full welding process was performed using various variables. The variables included the geometry of the electrodes, the thickness of the work pieces, the type of current (AC or DC), the temperature dependent properties of the materials, the thermal and electrical contact resistances and the like.

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1.2 PREVIOUS WORK

Various models have been developed to achieve a better understanding of the weld nugget formation mechanism. These attempts show various degrees of sophistication and mostly tried to predict temperature fields in the nugget. However, the welding variables studied most often were weld current and weld time. Little work has been done to correlate the variations in the materials properties to nugget development, let alone the characteristics of the electrode/work piece interface and the faying interface.

These models use joule heating generated by the contact resistance and the bulk resistance as a heat source, usually without any experimental confirmation of the results. The electrical contact resistance is very important in the early the stages of welding because of its high magnitude compared to the bulk resistance. Static resistance and dynamic resistance have been investigated with various surface conditions and pressure levels [1.20-1.27]. It was found that the static resistance was quite dependent on surface conditions such as the presence of a coating, the surface roughness, surface cleaning and also the current level and pressure under which the measurements were made. The dynamic resistance was also investigated primarily as a tool for automatic control of the process. Some researchers had interest in correlation of the dynamic resistance change to the weld nugget formation mechanism [1.13,1.23]. Kaiser et al and Dickinson et al tried to relate this dynamic resistance change to the weld lobe shape. They related a large drop in resistance to the onset of expulsion.

Gedeon et al tried to generalize the dynamic resistance curve of zinc coated steels and claimed that the initial drop was caused by the resistance drop at the electrode-work piece interface (figure 1.3) [1.24]. The peak in the dynamic resistance curve was thought to exist due to the resistivity rise in the bulk, with increasing temperature, but this rise was not correlated directly to the bulk material resistivity characteristics. Nagle et al attempted to separate out the components of dynamic resistance for bare steel [1.27]. The results are shown in figure 1.4.

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-17-The first attempt to see the details of current flow and heat generation at the contact interface was made by Greenwood et al [1.28]. The major conclusion of this work is that there exists a certain condition under which a steady solution for the temperature rise at the contact interface is impossible. Below the critical current value it is possible to have a steady temperature rise at the interface. Beyond this limit, melting or vaporization will occur. These results show that there exists a relationship between the temperature dependent thermal conductivity and the electrical resistivity at a critical current value for melting (figure 1.5). These conclusions seem to be very important in that there can be criteria for melting of a interface which is controlled by the temperature dependent physical properties of the materials. They emphasized the spatial distribution of the heat generation pattern which showed a concentration of heat at the periphery of an electrode-work piece interface. This observation was numerically confirmed again by Bowers et al [1.29].

Greenwood developed a two dimensional axisymmetric thermal model for resistance spot welding where he assumed no contact resistance, constant material properties and conduction heat loss into the electrode at a rate proportional to the temperature at the electrode contact [1.7]. He calculated the temperature rise up to 16000C neglecting the heat of fusion. This model showed a generic temperature distribution for a spot weld. In his conclusion Greenwood said that the ratio of the thermal conductivity to the product of sheet thickness and the heat transfer coefficient into the electrode is a parameter which can describe the time scale and the pattern of the isotherm. Thus, Greenwood's work was the first to describe the importance of heat loss to the electrode in nugget formation.

Rice and Funk developed a one dimensional model for multilayer spot welding [1.9]. Here the effect of the temperature dependent material properties are discussed with various stacks of materials. But the results were not related to the lobe curve at all. The heat distribution was calculated in only one dimension. They claimed that the empirical shape of the resistance-time curve was of little importance in welding

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because contact resistance drops to its final value very rapidly. They also claimed that the dissipation of heat at the interface into the electrode is very fast and large temperature discontinuities form across this interface. They also concluded that the thermal resistance across this discontinuity decreases very rapidly and becomes essentially a constant, although there was little experimental evidence to support these conclusions. The prediction of the electrode temperature was attempted by Houchens and Yang [1.8]. However, it was not verified by experiments at all. They concluded that the peak electrode temperature is strongly dependent on the temperature of the coolant and can be reduced by increasing the welding current with a corresponding reduction of weld time. Nied developed a two dimensional axisymmetric finite element model and stressed the thermomechanical response of the welding process [1.6]. He presented the idea of a pressure concentration at the periphery of the contact surfaces. This finding could be related to the expulsion phenomena which seems to be related to a peripheral mechanical seal. Gould recently tried a one dimensional model and compared his calculation with experiment using metallographic techniques, however, his results showed a great discrepancy with his experiments [1.10]. He tried to explain the results by considering heat loss through the electrode and the work piece. He related heat loss to some variables such as work piece thickness, contact area, time and current. The possibility of a steady state thermal equilibrium when the weld current is low and the time is long was described. Some researchers considered the effect of current wave form [1.30,1.31] with the advent of a DC welding machine. They found that the weld lobe width is somewhat increased with the use of DC current. Nishiguchi gave an explanation of this phenomenon in detail and concluded that DC has an effect only when the material thickness is smaller than 0.8 mm [1.30]. It was said that pulsation of the heat input in welding of thin materials causes a narrower weld lobe. From this work it can be seen that the fluctuation of the temperature field is also an important factor in nugget development, partically for very thin materials.

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-Another important factor in defining a lobe curve is the expulsion limit. Kimchi claimed little effect of expulsion on the mechanical property of a weld, yet American industry still considers expulsion as the practical weldability limit [1.32]. Very limited work has been published on this phenomena so far. Dickinson integrated the heat input rate over the weld time until expulsion occurs and calculated the expulsion energy. He tried to relate this energy to the electrical resistivity and the thermal conductivity [1.13]. Kaiser et al tried to understand expulsion by defining a new term 'critical expulsion limit' as the minimum combination of current and time required for a material with a given resistivity to create softening of a mechanical seal around the nugget [1.23]. One other important concept introduced in their work is the optimum ratio of the electrical resistance of a bulk material to the contact electrical resistance. They claimed that the ratio must lie within a certain limit for optimum welding. They related these criteria only to the energy input rate governed by electrical contact resistance and bulk resistance. Nishiguchi et al investigated the mechanism of surface expulsion and the nugget formation process in series spot welding [1.33]. They related expulsion experimentally to the shape of the electrodes.

The subject of electrode life, especially for welding of galvinized steel has been studied extensively. It is known that the rate of increase of the electrode face diameter is a major factor [1.5,1.34]. For a given electrode material, the rate of electrode enlargement was hypothesized to be related to the surface condition of the work piece, such as the presence of the zinc coating, the zinc coating thickness, the coating morphology, the chemical composition of the coating, the presence of an oxide film or lubricant and so forth. These conditions affect the electrical and the thermal contact behavior of the interface and thus the thermal history of the welding process. The enlargement of the electrode face diameter results in a decrease in current density. This will eventually shift the position of the weld lobe curve.

Reviewing all of this literature, it can be said that no attempt has been made to determine the effect of changes in material properties on the welding lobe in a

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comprehensive way. Very little attention has been paid to the geometry of the electrodes and the work piece. As the electrodes play a very important role i) as electrical conductors for current flow, ii) as mechanical constraints for pressure application and, iii) as a heat sink, the geometry of the electrodes along with the specimen thickness should be considered in the mechanism of nugget development. One other important parameter which has been neglected is heat loss through the electrode-work piece interface. The sensitivity of the lobe curve to the aforementioned parameters have yet to be investigated.

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21

-Upper electrode

Workpieces

NuggeI

"-Lower elecirode

Figure 1.1 The spot welding process (after [1.11).

LI) expulsion () acceptable E weld undersize nugget

Welding Current (kiloamperes)

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I

7

2 II

Cm -- II

I

0.0 2..0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

VELD TIME (CYCLES)

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2.0 kN (450 lb) .. Rb RI ( e .T 60 -50 -40 -30 -20. 10 -0 i I i I I I 0 2 4 6 8 10 Time (cycles)

Component resistance for 1.8-mm bare steel at a weld force of 2.0 N.

3.3 kN (750 lb) Rb RR Re C -3 50. 40 30. 20-10 6050 - 40- 30-20 10 -0 0 4.5 kN (1000 lb) Rb Rf Re 2 4 6 8 10 Time (cycle)

Component resistance for 1.8-mm bare steel at a weld force of 4.5 N.

Figure 1.4 Components of dynamic electrical resistance. (after [1.27]).

-I

-t - I I

0 2 4 6 8 10 Time (cycle)

Component resistance for 1.8-mm bare

steel at a weld force of 3.3 N. C

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1.4 4 1-2 1.0 0-8 O-0 0-4 y-S 0.30 01 0 2 4 6 8 10 potential, U*

Theoretical relation between current wnd potential for a conductor having

A = A0(1-NO); Ap = A0p0(1+ MO) for various values of y. (y = NIM). Tho curve for

ARMCO iron is shown dashed. The potential and the current are made non-dimensional

yA dvd] 1 2 0 r1 v

by dividing by 2

L--

and j~-

Jrespectively.

A: thermal conductivity, p: electrical resistivity

Figure 1.5 The critical current value which can be passed through a contact conductor under steady state conditions (after [1.281).

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-2 PRELIMINARY ANALYSIS

2.1 LUMPED PARAMETER MODEL

A linearized lumped parameter heat balance model was developed and is discussed for the general case of resistance welding to see the effects of each parameter on the lobe shape. The parameters include material properties, geometry of electrodes and work piece, weld time and current, and electrical and thermal contact characteristics. These are then related to heat dissipation in the electrodes and the work piece.

2.1.1 Model Development

The model described in figure 2.1 was developed to determine the heat balance in the system as a function of nugget growth. A temperature discontinuity at the electrode-work piece interface is assumed. Conduction heat loss through the electrode-work piece interface and into the work piece is estimated as a function of welding time and weld geometry. The overall thermal equilibrium is established by considering a free boundary at the electrode and the work piece surfaces except where they contact. A fixed temperature T., equal to the cooling water temperature is assumed at the internal water cooling surface of the electrode. The size of the work pieces is assumed to be infinite in the radial direction. The nugget shape is assumed to be a disk growing radially and axially in the same proportions as found in a post mortem examination of the maximum nugget size. This assumption is supported by the computer simulation results found in reference [2.1]. The maximum nugget size is assumed to have 80% penetration and to be equal to the electrode contact diameter. The expulsion limit is assumed to have been reached when the nugget diameter matches the electrode face diameter. The equations are established with lumped quantities.

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= 12

R (2.1)

where, R=R +Rc+R,

Rb work piece bulk resistance

RC c:total contact resistance (R,= Rf+2Re)

f for faying interface, e for electrode interface. R : electrode resistance

At welding time I welding current

The heat of fusion required for nugget formation, H,,, is

HM= HAVn (2.2)

where, H: heat of fusion per unit volume AV,: nugget volume (na2

p)

If the temperature rise in the model is described in the three different regions with lumped quantities, the total heat required for the temperature rise is,

Q~t

=

p+C

AT.AV,+pC,,ATAV,+p

C ,AT =Q n +Q' +Q (2.3) where, p : density CP : specific heat V : volume AT : temperature rise n : in a nugget s : in surroundings e : in electrodes

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-27

-Thus the total heat balance including the total heat loss rate, QL, through the model boundaries (into the cooling water) can be written as follows.

QgAt = Hm + +TL~ (2.4)

2.1.2 Derivation of Parameters

2.1.2.1 Effect of Material Properties

Equation (2.4) can be rearranged as

(I2 _ ₁/ R)At = (Hm ++ Qs + Qi-e, Q,)/R (2.5)

Neglecting both the heat loss and the temperature rise in the electrodes and the temperature rise in the surroundings,

CI2RAt = (H + pC ,AT,)AV, (2.6)

C : efficiency of heat input

This is basically a lobe curve, which is a hyperbola with axes of welding time, At

and the square of the welding current, I . This basic lobe curve may be translated or rotated or distorted by changes in each parameter. The change in one parameter may have effects not only on one term but also on other terms simultaneously. Here the effects are considered in each term separately. The final lobe shape will be a combination of these effects.

The nugget volume, AV,, is constant for a certain size of a nugget. In this case, the right hand side of equation (2.6) can be thought as a constant value for a given

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material. Figure 2.2 represents equation (2.6) with two different nugget sizes. The larger nugget size shifts the lobe curve in the direction of higher currents or longer weld times.

The effect of pC ,and H can be considered in a similar way. Equation (2.6) also shows the effect of these parameters. Higher values of p.C, , and H increase the value of the right hand side of equation (2.6), and as a consequence, the lobe curve shifts in a like manner as does a larger size nugget. The temperature dependence of p.Cnwill

affect the lobe shape as shown in figure 2.3.

Assuming a constant nugget size for the welding of a given material, the effect of electric resistance can be considered as follows.

I2At = constant/R (2.7)

Generally, dynamic resistance changes in the manner shown in figure 2.4, at least for steel. Even though the contact resistance at the faying interface RI drops very fast and eventually becomes nil during the early weld cycles, its contribution to the thermal field seems to be great due to its large magnitude. However, The electrical contact resistivity at the electrode interface, Re, exists all through the welding process and contributes to heat generation and heat transfer. Higher contact resistance, Rc values will shift the lobe curve farther to the left as shown in figure 2.5-a. As the bulk resistance, Rb changes with time (temperature), the slope dRb/dT will be important in nugget formation as shown in figure 2.5-b and 2.5-c. The ratio of Rc to R, may also affect the nugget growth mechanism due to differences in the heat generation pattern. It is also possible to see the effect of electrode pressure in equation (2.7). Since higher electrode pressure results in a lower contact resistance R c , the lobe curve will shift as in figure 2.5-a.

The effect of the heat required to raise the temperature of the material surrounding the nugget, Qt',, and the heat required to raise the temperature of the electrodes, Qe,,

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-29-can be seen in equation (2.5). _{If these terms are added to the right hand side of equation}

(2.6), the lobe curve will be shifted in the direction of higher energy input. In equation

(2.5) _{one can see that the extent of this shift is determined by the ratio of the amount}

of heat required for heating of the electrode and the work piece, divided by the electrical resistance (i.e. the ratio of heat capacity, pc to electrical resistivity, R, as a sum of bulk resistance and contact resistance. This is an important parameter in the characterization of nugget growth mechanisms and the lobe curve.

2.1.2.2 Effect of Geometry and Heat Loss

Considering the total heat loss rate for a given nugget size and material, equation (2.6) changes to

(I2R - QL)At = constant (2.8)

This shifts the lobe curve in the high current direction by QLI/R, which is actually a function of the thermal properties of the material and of the geometry. This is shown in figure 2.6. _{Here, one can see that the ratio of the heat loss rate to the resistance,} , R as a total resistance of bulk electrical resistance and contact electrical resistance, can be a important parameter in the characterization of nugget growth and weld lobe shape. The heat loss rate is dependent on many parameters such as the thermal conductivity of the electrode and/or work piece, and the heat transfer coefficients at the coolant interface and the electrode interface.

The usual time scale of the process is on the order of 1/10 second (5 to 20 AC cycles). If the thermal conductivity of the copper electrode is much greater than that of the work piece material (this is not the case for aluminum welding), the characteristic heat diffusion distance in the electrode is about 6 mm while it is only 2 mm in the steel. When the electrode face thickness is very thin (e.g. less than 6 mm) the heat generated in the electrodes and that transferred from the work piece will be carried

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away by the cooling water while the nugget develops. In this case the nugget development mechanism may be influenced by the heat transfer characteristics of the cooling water. Thus the ratio of heat transfer coefficient at the coolant interface to the electrical resistance, h/R , can be a possible nugget growth characterization parameter.

If the electrode face thickness is greater than 6 mm, the heat transferred from the work pieces and that generated in the electrode itself will be used to heat up the electrodes. Hence a smaller portion of the heat may be carried away by the cooling water during nugget development. For this case heat transfer across the electrode interface or heat transfer in the work piece may influence nugget growth. Here one can derive one more nugget growth characterization parameters, i.e. the ratio of heat transfer coefficient at the electrode interface to the electrical resistance, he/R.

The heat flow out of the nugget, Qg, is important in that the formation of a weld nugget is due to its influence on localized accumulation of heat. Therefore, the characteristics of heat transfer from the highest temperature region, a nugget in this case, is very important in understanding the nugget development mechanism. The total heat loss rate of the nugget, Qb, is the sum of the axial heat loss rate through the electrodes, Q,., and the radial heat loss rate through the work pieces, Q,. If it is assumed that the temperature build up in the electrodes has already been reached when melting starts in the nugget, with TCbas a interface temperature at the work piece side, the heat flux in the axial direction during nugget growth can be considered as follows.

The heat loss in the axial direction is assumed to be proportional to the square of the nugget radius. The temperature profile between the interface and the melting front is assumed to be linear. Then the axial loss rate is,

Qa = kb(T.- T C)na2/lb (2.9)

Where, k- thermal conductivity Tm : melting temperature

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-31-Tcb : interface temperature at work piece

t, : distance from melting interface to electrode contact surface

a nugget radius

The heat required for the temperature rise in the surrounding nugget material, Q t , is thought to be determined by the heat flux out of the nugget, Qr, and the heat

generation in the surrounding material itself. The temperature distribution in this region is assumed to be determined mainly by the radial heat loss rate of the nugget,

Qr, when the nugget has grown to sufficient size. If the heat loss through the work piece is assumed to be proportional to the area of the nugget side wall, then,

r kb(T -

T)2na

p (2.10)

Where, T characteristic surrounding temperature

I : characteristic heat diffusion length

The thermal conductivity, k, , included in the heat loss equations changes with temperature while the interface temperature, T,, , is also affected by geometry and interfacial characteristics. This is also affected by the heat generation pattern due to the electrical resistivity change with temperature.

To see the effect of geometry, a one dimensional model was made in the axial direction as shown in figure 2.7. A steady state heat flux balance near the electrode-work

piece interface is modeled without heat generation included.

For steady state heat flux equilibrium with T,, as a electrode face temperature,

kb(Tm-T Cb)= k,(Tr -T.)/ IQ =hC(T -T,.) (2.11)

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Tb(kbk.+ A) T.+ (B-kbk.)T (212 T cb=(b

~e

w(2.12) A+B Te= Atm+BT. (2.13) A+B AT cb Tc =kbke(T. - T.) (.4 AT = T c-Tce= AB(2.14) A+ B

Where, A=kbhle,B kke+kehclb

Plots of these equations are shown in figure 2.8. This model shows that the interface temperature changes with nugget growth, which is represented by decreasing 1

,o Figure 2.8-b is exactly the same shape as given in reference 2.2. The position of the water jacket may also affect the interface temperature. The electrode-work piece interface exists all through the welding process and causes a temperature discontinuity at the interface with possibly a decreasing heat transfer resistance coefficient. This can be manifested by the easy separation of electrodes and work pieces at the end of the normal weld cycle. As the nugget develops, the distance 1, decreases. For a given water jacket distance, I, , the interface temperature at the work piece side, Teb, approaches Tm and increases the value of AT across the interface. However, as the temperature goes up, a softening of the material will occur and will reduce the interface thermal resistance resulting in a lower TC value. The water jacket distance, Ie, may also affect the temperature rise at the interface, and thus the heat loss across this interface varies in a very complex manner. As was indicated previously, if the value for le is small

enough, the thermal characteristic parameter, h,/R, affects the nugget growth behavior.

A rough comparison of heat loss in two directions can be made by considering growth of the nugget. The ratio of axial heat loss, Qa, to the radial loss, Q,, is,

Q. (T.-Tcb(2)al

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-Assuming nugget size growth is proportional to the geometry of the electrode and the thickness as explained in the model development section,

p = afL/b

where, p penetration

3 : final penetration to work piece thickness ratio (about 0.8) b : electrode radius

Then the final ratio becomes,

Q. (Tm-Tb)b( Q, 2(T.-T)LIb

Assuming the nugget front revises its position at every half cycle (1/120 sec) in AC welding,

r/T,=0.9, when 1=0.2at=Fa/50

where, oc thermal diffusivity of the work piece

Then the equation (2.17) becomes,

Q (TTb)bT&

(2.18)

Qr 1 OTmPLlb

Since lb reaches its final value rather abruptly, the distance between the melting front and the electrode interface, 1,, can be assumed constant after nugget formation commences. Then 1, is proportional to the specimen thickness, L If the interface temperature TCb is further assumed constant, the heat loss ratio in equation (2.18) is proportional to the parameter b/L The effect of this geometric parameter on the heat loss ratio is plotted in figure 2.9-a. The ratio is also a function of the thermal diffusivity, m. The total heat loss can be described as follows using equations (2.9), (2.10) and (2.16).

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Q,= Q,~r kblita2 [(T, Tb)llb+ 1O(Tmj3L)/bJa] (2.19)

As the nugget diameter, a , increases with time, the rate of heat flow from the nugget, Qb, increases in a quadratic manner. But this is compensated by changes in the axial temperature gradient in the work piece, T.- T b, which decreases with time. The thermal conductivity also affects the total heat loss as shown in figure 2.9-b. As the thermal conductivity of a weld specimen increases, the effect of this variable becomes more significant. As kb increases, the temperature difference, Tm - T b, in equation (2.9) approaches a null value due to the thermal barrier at the electrode interface. Thus, more heat will dissipate into the surrounding work piece. This means that there exists a certain threshold where the effect of Q, and Q, change their relative importance in the thermal history of nugget development. This threshold is believed to be related to the relative magnitude of interface heat transfer coefficient h, and the thermal conductivity kb. _{Therefore, one can derive one more thermal characteristic parameter,}

hC/kb.

It is almost certain from this analysis that the electrode geometry and the work piece thickness are very important factors not only in the distribution of the heat generation rate but also in determining heat dissipation characteristics in resistance spot welding. Generally, as one welds thinner sheet metal, the temperature gradients in the sheet become steeper and a greater portion of the total heat is lost to the electrodes as long as the value for the thermal characteristic parameter hc/kb is large enough.

2.1.3 Model Calculation

To see the validity of the model and the heat consumption in spot welding, a model case was calculated with experimental data of galvanized steel welding. The lobe curve data used in this section are shown in figure 2.10 as taken from reference 2.3. The material is G90 galvanized steel with a thickness of 1.5 mm. The electrode is a truncated cone with 120 degrees included angle and 1/4 inch (6.4 mm) contact

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- 35

-diameter with 15 mm face thickness and 16 mm outer -diameter. The minimum acceptable nugget size is 0.22 inches (2.8 mm) diameter. The experimentally determined lobe curve for this material is shown in figure 2.10-(a); the dynamic current curve is shown in figure 2.10-(b) and the dynamic resistances are shown in figure 2.10-(c) and 2.10-(d). Using this data, a calculation was performed for the case of no slope control in figure 2.10-(a). The results are tabulated in table 2.1.

The total heat generated in the system was calculated assuming a linearized current value using the measured dynamic resistance. The heat required for phase changes were included in the calculation. The amount of heat required for nugget heating, Qto ,was calculated using 660 J/Kg*Cfor the heat capacity, C., from reference [2.41. The heat used for the temperature rise in the electrodes was calculated using the simulated electrode surface temperature data from reference 2.2 and the measured surface temperature profile obtained in this research. The measurement of electrode temperature profile will be presented in chapter 5. The highest electrode temperature used in the calculation is 500 0C for a minimum nugget size and 700 0C for a maximum size nugget.

In the calculation of heat loss, QL, it was roughly assumed that no heat is lost through the model boundary till the nugget starts to form. It was also assumed that the temperature build up in the electrodes has already begun when melting starts in the nugget. After that time, the heat loss rate, QLwas assumed to be equal to the axial heat loss rate, Qa. This is due to the fact that the temperature gradient in the axial direction which developed before nugget melting occurs, is low compared to the gradient at later times. The heat loss into the work piece is included in the total amount of heat required for the temperature rise in the surrounding nugget material, Qtot.

The axial heat flow rate, Qa, derived in this section is a function of the interface temperature, Tcb, and the nugget thickness or the nugget radius. The T,, value was estimated from reference 2.2 and was taken from the experimental data. The relationship

Analyses of resistance spot welding lobe curve