FUNDAMENTAL STUDY OF CONTACT RESISTANCE BEHAVIOR IN RSW ALUMINUM DISSERTATION. Presented in Partial Fulfillment of the Requirements for

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1 FUNDAMENTAL STUDY OF CONTACT RESISTANCE BEHAVIOR IN RSW ALUMINUM DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ta-chien Sun, M.A. ***** The Ohio State University 2003 Dissertation Committee: Approved by Professor Chon L. Tsai, Adviser Professor Dave W. Dickinson Professor Dave F. Farson Professor Herman Shen Adviser Welding Engineering Graduate Program

2 ABSTRACT The contact resistance behavior at the joint faying surface in resistance spot welding aluminum alloys is critical to the basic understanding of the process and the development of numerical models to analyze the process. This dissertation study has developed such a fundamental understanding of the contact resistance behavior using the virtual contact volume concept and the equivalent contact resistivity definition. In this research, an integrated experimental-numerical approach was used to demonstrate the proposed equivalent contact resistivity versus temperature relationship. Such relationship was further used to study the expulsion behavior of the resistance spot welding aluminum alloy. A concept of using constriction ring was proofed to be effective in preventing weld expulsion in resistance spot aluminum welds. ii

3 The a-spot model simulated a single ball contact to define the equivalent contact resistivity. It was found that, for a loading range from 500 lbs to 900 lbs, the contact area versus bulk temperature relationship may be written as: A c = 8x x10-4 Exp (5.8483x10-3 T) The electrical analysis defined the electrical potential field in the a-spot model with given contact deformations. A generic equivalent contact resistivity versus temperature relationship was established. The generic equivalent contact resistivity versus temperature relationship was derived as follows: ρ c = (4.53x10-8 ) βt Exp [(-6.53x10-3 )γ(t - T 0 )] The proportionality term including βt represents the increasing contact resistivity with temperature reflecting the Wiedemann-Franz-Lorentz behavior. The exponential term including γ(t-t o ) represents the softening effect of the contact surface as temperature increases. This was derived from the simple a-spot contact analysis. With the generic equivalent contact resistivity versus temperature relationship established, an a-spot welding model was conducted. This welding model incorporated the contact pairs with the resistivity relationship leaving the β, γ, and iii

4 T o factors as parametric variables. Experiment a-spot welding model was also conducted. Both the numerical and experimental analyses show the same relationship that is defined by the theoretical hypothesis of a-spot model. The β factor may be defined as bulk contact resistivity factor, which reflects the Wiedemann-Franz-Lorentz effect. Physically the reference temperature (T 0 ) diminishes the magnitude of softening temperature (T-T 0 ) and hence reduces the slope of the resistivity-temperature relation. This means that the effective softening temperature depends on the temperature rise from the reference temperature, instead of the absolute temperature. Numerically, the reference temperature (T 0 ) is simply a factor reducing the effect of γ and hence reduces the decreasing slope. The peak value of equivalent contact resistivity increases with the raise of the reference temperature (T 0 ). The contact area correction factor (γ) is assumed to depict the softening effect of asperities under different loading condition and is proportional to the applied load. For constant values of β and T 0, varying γ values changes the slope of the resistivity-temperature curve. iv

5 Based on the resistivity-temperature curve, it was observed that the contact resistivity would be affected by the combination of the bulk material effect and the contact softening effect. The equation can be divided into two parts. The first part, (4.53x10-8 ) βt, represents the bulk effect, which increases the equivalent contact resistivity when temperature rises. The second part, Exp [(-6.53x10-3 )γ(t - T 0 )], depicts the softening effect, which enlarges the contact area and then reduces the dynamic contact resistivity with increasing temperature. The dynamic contact resistivity rises initially with temperature because the bulk effect is dominant; and reaches a peak value at the critical temperature; then drops down to a lower constant value because of the softening effect. Numerical simulation of RSW was used to verify the equivalent contact resistivity versus temperature relationship. The FEA simulation models used both a quarter model and a half model. The quarter model was used to validate the mesh design and the numerical procedures. The half model, which has more realistic electrical boundary condition, was used for the parametric study. Observations based of the parametric study results on weld nugget dimensions may be summarized as follows: v

6 i. Weld nugget is larger when higher bulk contact resistivity factor, β, is used in the analysis. ii. The predicted weld nugget dimensions are sensitive to the contact area correlation factor, γ. The greater the value of this factor it shows more significant softening effect of the contact surface, and hence the smaller the nugget size. The most reasonable value of γ is unity, as demonstrated by the parametric study results. iii. The reference temperature reduces the effect of γ by reducing the softening temperature, which is the difference between the contact temperature and the reference temperature (T-T o ). The liquidus nugget is sensitive to this reference temperature, but the solidus nugget is insensitive to this reference temperature. Larger liquidus nugget would be predicted with a higher reference temperature value. The solidus nugget predictions are insensitive to welding current, nor the bulk contact resistivity factor, β. The liquidus nugget predictions are significantly influenced by both the current and the β factor. The appropriate range of the β values is from 800 to Similar relationship between equivalent contact vi

7 resistivity versus contact temperature was assumed for the electrode/workpiece interface. For Cu/Al interface, the equivalent contact resistivity factors: β = 200, γ = 1, and T 0 = 32 o F enable reasonable predictions of nugget size. The parametric study was conducted to quantify the parametric factors based on comparisons on nugget size and electrical potential drops across the electrodes. When the equivalent contact resistivity curve is in the range between the boundaries with parametric inputs of β = 800, γ = 1, T 0 = 70 o F, and β = 2500, γ = 1, T 0 = 32 o F; the nugget size comparison is acceptable. When β = 800, γ = 1, T 0 = 70 o F (21 o C) at Al/Al interface and β = 200, γ = 1, T 0 = 32 o F (0 o C) at Cu/Al interface, both the comparisons of weld nugget size and potential drops are satisfactory. The mechanical analysis proposed a concept in the prediction of expulsion based on the crack tip distance (CTD) with respect to the instantaneous location of the solidus front. It is assumed that expulsion would occur when the crack tip is within the solidus nugget zone at any instant during the welding process. With the application of the external constriction ring, expulsion can be prevented; and electrode indentation and workpiece distortion can be improved. vii

8 In this research, in order to simply the analysis of contact phenomenon, a single-spot contact pairs, called the a-spot model, was employed. In the future work, a model with regularly arranged multi-spot contact pairs and their random nature in the RSW process would be necessary for more quantities description of the actual contact behaviors under various process conditions. The resistivity-temperature relationship derived in this study was under a specific loading range and a given surface condition (unmilled surface). More researches, including experimental studies, are suggested to cover broader areas of loading situations and interface conditions. The FEA mechanical simulation has demonstrated the concept of CTD in the prediction of expulsion. Stresses should also be determined in order to predict the cracking sensitivities of the aluminum alloys under the resistance spot welding process. In order to prevent the occurrence of expulsion, the external ring constriction model was demonstrated to be an effective method. However, experimental verifications would be needed. viii

9 Dedicated to My Adviser, Prof. Chon L. Tsai, My Dear Wife, Duan-Mei Chen, and My Families ix

10 ACKNOWLEDGMENTS I would like to express my deeply sincere appreciation to my advisor, Prof. Chon L. Tsai, for his strong support and encouragement during the past 10 years. If I can reach any achievement in my future life, I want to dedicate all the glory to him. I am also grateful to other members of my advisory committee, Prof. Dave Farson, Prof. Herman Shen, and Prof. Dave Dickinson, for their instruction and suggestion. This dissertation cannot be accomplished without many nice people, especially, Mr. Choong-Yuh Kim and Jeff Lu, who assisted me to handle all numerical and experimental problems, stimulated discussions on various aspects of my research, and provided a lot of valuable information. I also wish to thank my families and my dear wife, Duan-Mei Chen. With the power of their love, I never give up on the long way to achieve my dream even when I face those tough difficulties and challenges. x

11 VITA August 28, 1969.Born-Taipei, Taiwan, R.O.C B.S. Chemical Engineering, Taiwan University, Taipei, Taiwan, R.O.C M.A. International Relationship (One-of-a-kind Program), The Ohio State University, Columbus, Ohio, U.S.A Graduate Research Associate, Dept. of Industrial, Welding, and Systems Engineering, The Ohio State University, Columbus, Ohio, U.S.A Spokesman, The People First Party, Taipei, Taiwan, R.O.C. Present.Senator, Taiwan, R.O.C. xi

12 PUBLICATIONS Research Publication 1. Dynamic Contact Resistivity at Aluminum/Aluminum Interface during Resistance Spot Welding. Proceedings of TIWC 98, Sept. 1998, pp Dynamic Contact Resistivity in Resistance Spot Welding Aluminum. Paper presented at the 80 th AWS Annual Convention, St. Luis, Missouri, Aprial 2-15, 1999, pp Modeling and Design for Resistance Spot Welding of Aluminum Alloy. Paper to be presented at the Sheet Metal Conference XI, Detroit, Michigan, May FIELDS OF STUDY Major Field: Welding Engineering Welding Design, Finite Element Analysis xii

13 TABLE OF CONTENTS Page Abstract...ii Dedication...ix Acknowledgement...x Vita...xi List of Tables......xvii List offigures......xviii List of Symbols...xxviii Chapters: 1. Introduction Background Resistance Spot Welding (RSW) Process Resistance Weldability Issues of Aluminum Objectives Method of Approach Anticipated Accomplishments...16 xiii

14 2. Literature Review and Critical Issues Dynamic Contact Resistance Numerical Procedure Effect of Electrode Force Equivalent Contact Resistivity: A-Spot Model Analysis Electric Contact and Physical Model Basic Definition of an Electric Contact Physical Model Electrical and Mechanical Analysis of A-Spot Model Mechanical Analysis Electrical Analysis Equivalent Contact Resistivity Definition of Evaluation Procedure Equivalent Contact Resistivity versus Temperature Relationship Effect of Contact Surface Condition and Softening Summary Experimental Observations and Analysis Experimental Procedure FEA Analysis of the Experimental Results FEA A-Spot Welding Model Determination of Equivalent Contact Resistivity Summary Numerical Simulation Procedure for RSW Aluminum Alloys Finite Element Quarter Model The Quarter Model Results/Discussion xiv

15 4.2 Finite Element Half Model The Half Model Determination of Nugget Size Effect of AC/DC Current Input Temperature Evolution at Joint Faying Surface Parametric Study Effect of Current Level Consideration of Cu/Al Interface Summary Parametric Calibration Experiment of RSW AA2024-T3 Aluminum Alloys Experimental Background Equipment Set-Up Experimental Procedure Experimental Observations Parametric Calibration Nugget Diameter Comparison Numerical Simulation of Electrical-Thermal-Mechanical Behaviors Potential Drop Comparison Summary Mechanical Analysis for Expulsion Phenomenon Background FEA Mechanical Simulation Case Study I: RSW without Expulsion Case Study II: RSW with Expulsion External Ring Constriction Model Effect of Constriction Ring on Gap (β = 800) Effect of Constriction Ring on Expulsion xv

16 and Gap (β = 2500) Split-Force Electrode Design Concept Conclusions and Recommendations Conclusions A-Spot Model A-Spot Welding Model Numerical Simulation of RSW Parametric Calibration Mechanical Analysis for Expulsion Phenomenon Recommendations References xvi

17 LIST OF TABLES Table Page 3.1 Welding schedule of a-spot model experiment Nugget size comparison results in FEA case study Potential drop comparison results in FEA case study xvii

18 LIST OF FIGURES Figure Page 3.1 Contact surfaces Lines of current flow and equipotential surfaces of a current constriction Physical model Meshed finite element model Stress distribution in thermal-mechanical analysis (70 o F, 512 lbs) Stress distribution in thermal-mechanical analysis (700 o F, 512 lbs) Dependency of contact areas on temperature Current density distribution in electrical analysis: (a) 5% of sphere radius, (b) 10% of sphere radius Current density distribution from the centerline at interface for three different contact area percentages Electrical potential distribution for 5% and 10% contact area percentages Electrical potential distribution along centerline...52 xviii

19 3.12 (δv/l) Calculation method Contact resistivity determination procedure Equivalent contact resistivity for different β Values (γ = 1, T 0 = 0 o F) Equivalent contact resistivity for different T 0 Values (β = 2500, γ = 1) Contact surface in resistance spot welding Equivalent contact resistivity for different γ values (β = 2500, T 0 = 0 o F) Equivalent contact resistivity for γ = 1 to 5 (β = 2500, T 0 = 0 o F) Equivalent contact resistivity for γ = 0.5 to 1 (β = 800, T 0 = 70 o F) Picture of a-spot specimens before and after experiment Specific points on the hemispherical surface of the specimen for temperature and potential drop measurement Specimens and data acquisition system arrangement Picture of specimens and data acquisition system arrangement Recorded current Input in the experiment Recorded voltage input in the experiment Potential distribution along y-axis from experiment data Dynamic contact resistance determined from the experimental current and voltage data of a-spot aluminum welding model...90 xix

20 3.28 Potential history of four points in the bottom portion of the a-spot (V1 to V4) Voltage drop at interface (V5-V4) and current input (RMS = 13 ka) Predicted changes of contact area during the weld cycles Potential distributions along y-axis of experimental and numerical results at different weld time Calculated dynamic contact resistivity in FEA simulation Temperature history of four nodes at interface Correlation between dynamic contact resistance and average temperature at contact determined from the FEA simulation Mesh of the entire geometry of the quarter model Equivalent contact resistivities calculated from equation (9) with different β values (γ = 1, T 0 = 0 o F) Electrical and thermal properties of aluminum alloy 2024-T3: (a) thermal conductivity (b) specific heat (c) electrical resistivity Mechanical properties of aluminum alloy 2024-T3: (a) Young s modulus (b) yield stress (c) thermal expansion coefficient Electrical and thermal properties of copper electrodes: (a) thermal conductivity (b) specific heat (c) electrical resistivity Mechanical properties of copper electrodes: (a) Young s modulus (b) yield stress (c) thermal expansion coefficient Electrical potential distribution during welding cycles (β = 1200, xx

21 γ = 1, and T 0 = 0 o F) Weld nugget growth of FEA quarter model simulation (β = 1200, γ = 1, and T 0 = 0 o F) Nugget size growth with various values of β in FEA quarter model simulation (γ = 1, T 0 = 0 o F) Electrode indentation and residual stresses distribution in FEA quarter model simulation (β = 1200, γ = 1, and T 0 = 0 o F) Cross-section of aluminum alloys 2024-T3 weld nugget (26.2 ka with 0.2 in. tip diameter, dome type electrode, squeeze time: 60 cycles; weld time: 8 cycles; hold time: 60 cycles, electrode force: 750 lbs) Mesh of entire geometry of the half model Welding schedule of AC current input model Temperature contour of AC current input Model (β=800, γ=1, T o =70 o F, 33 ka RMS): (a) Time A: 0.4 cycles ( sec.) (b) Time B: 0.8 cycles ( sec.) (c) Time C: 2.35 cycles ( sec.) (d) Time D: 2.88 cycles (0.048 sec.) Temperature history of AC and DC current input simulations at the center point of the weld nugget Temperature history of AC and DC current input simulations at the solidus front point Temperature history of AC current input model at three different points in weld nugget Temperature profile of AC current input model at the interface xxi

22 4.19 Comparison of nugget size between AC and DC current input models Temperature evolution along a faying surface during first one and half cycles (β=800, γ=1, T o =70 o F, RMS current 33 ka) Temperature evolution along a faying surface during first half cycle (β=800, γ=1, T o =70 o F, RMS current 33 ka) Effect of β on weld nugget size (γ = 1, T 0 = 32 o F (0 o C), and I RMS = 33 ka): (a) β = 400 (b) β = 600 (c) β = 800 (d) β = 1600 (e) β = Effect of β on weld nugget size (γ = 1, T 0 = 70 o F (21 o C), and I RMS = 33 ka): (a) β = 800 (b) β = 1600 (c) β = Effect of β on temperature history at the center point of weld nugget (γ = 1, T 0 = 0 o F, and I RMS = 33 ka) Effect of β on temperature history at the solidus front point (γ = 1, T 0 = 0 o F, and I RMS = 33 ka) Nugget size determination for different β values (γ = 1, T 0 = 0 o F, and I RMS = 33 ka) Effect of γ on weld nugget size (β = 5000, T 0 = 32 o F (0 o C), and I RMS = 33 ka): (a) γ = 1.5 (b) γ = Effect of γ on weld nugget diameter (RMS: 33 ka, T o = 32 o F for β=5000 and T o =70 o F for other β values) Effect of γ on weld nugget depth (RMS: 33 ka, T o = 32 o F for β=5000 and T o =70 o F for other β values) Effect of T 0 on weld nugget size (β = 800, γ= 1.0, and I RMS = 33 ka): (a) T 0 = 32 o F (0 o C) (b) T 0 = 70 o F (21 o C) 186 xxii

23 4.31 Weld nugget diameters as defined by liquidus and solidus temperatures versus the RMS welding current (γ=1 and T o =70 o F) Weld nugget depths as defined by liquidus and solidus temperatures versus the RMS welding current (γ=1 and T o =70 o F) Effect of the Cu/Al interface parameters on temperature contours. (The Al/Al interface factors are β = 800, γ = 1, T 0 = 70 o F (21 o C) and I RMS = 33 ka): (a) Cu/Al: β = 200, γ = 1, and T 0 = 32 o F (0 o C) (b) Cu/Al: β = 10, γ = 1, and T 0 = 70 o F (21 o C) (c) Cu/Al: β = 1, γ = 1, and T 0 = 70 o F (21 o C) Experimental arrangement of dynamic contact resistance measurement Current and calibrated voltage inputs Experimental nugget size growth Variation of dynamic contact resistance Measured potential drops between workpieces within half cycle: (a) original curve (b) calibrated curve Comparison between numerical nugget sizes and electrode diameter with various current levels and values of β when γ = 1 and T 0 = 0 o F (β = 200, γ = 1, and T 0 = 32 o F (0 o C) at Cu/Al interface) Ideal range of dynamic contact resistivity Weld nugget growth of FEA half model simulation (β = 2500, γ = 1, and T 0 = 0 o F): (a) 1 st cycle (b) 2 nd cycle (c) 3 rd cycle Electrical potential distribution during welding process (β = 2500, xxiii

24 γ = 1, and T 0 = 0 o F): (a) 1 st cycle (b) 2 nd cycle (c) 3 rd cycle Electrical current density during welding process (β = 2500, γ = 1, and T 0 = 0 o F): (a) 1 st cycle (b) 2 nd cycle (c) 3 rd cycle Electrode indentation phenomenon during the whole process (β = 2500, γ = 1, and T 0 = 0 o F): (a) squeeze cycles (b) 1 st cycle (c) 2 nd cycle (d) 3 rd cycle (e) hold cycles (f) cool cycles Stress Distribution (β = 2500, γ = 1, and T 0 = 32 o F): (a) squeeze cycles (b) 1 st cycle (c) 2 nd cycle (d) 3 rd cycle Comparison of numerical potential drops and experimental results, with β = 800, γ = 1, T 0 = 70 o F (21 o C) at Al/Al interface and β = 200, γ = 1, and T 0 = 32 o F (0 o C) at Cu/Al interface Effect of Cu/Al interface on potential drop comparison when β = 800, γ = 1, T 0 = 70 o F (21 o C) at Al/Al interface Definition of Terminologies Welding schedule in case study I Variations of CTD in case study I: (a) total time = 16.2 cycles (0.27 sec.), weld time = 1.2 cycles (b) total time = cycles (0.273 sec.), weld time = 1.38 cycles (c) total time = cycles (0.276 sec.), weld time = 1.58 cycles (d) total time = cycles (0.281 sec.), weld time = 1.86 cycles (e) total time = cycles (0.283 sec.), weld time = 2.00 cycles (f) total time = cycles (0.285 sec.), weld time = 2.10 cycles (g) total time = cycles (0.290 sec.), weld time = 2.36 cycles (h) total time = cycles (0.298 sec.), weld time = 2.88 cycles (i) total time = 18 cycles (0.3 sec.), weld time = 3 cycles (j) total time = cycles (0.301 sec.) (k) total time = cycles (0.306 sec.) (l) total time = cycles (0.310 sec.) (m) total xxiv

25 time = cycles (0.315 sec.) (n) total time = sec Variations of CTD in case study II: (a) total time = cycles (0.261 sec.), weld time = 0.65 cycles (b) total time = cycles (0.268 sec.), weld time = 1.08 cycles (c) total time = cycles (0.273 sec.), weld time = 1.37 cycles (d) total time = cycles (0.277 sec.), weld time = 1.60 cycles (e) total time = cycles (0.281 sec.), weld time = 1.87 cycles (f) total time = cycles (0.285 sec.), weld time = 2.10 cycles (g) total time = cycles (0.290 sec.), weld time = 2.37 cycles (h) total time = cycles (0.294 sec.), weld time = 2.62 cycles (i) total time = cycles (0.298 sec.), weld time = 2.88 cycles (j) total time = cycles (0.3 sec.), weld time = 3.00 cycles (k) total time = cycles (0.301 sec.) (l) total time = cycles (0.306 sec.) (m) total time = sec Occurrence of expulsion in case study II: (a) weld time = 2.88 cycles (b) weld time = 3 cycles FEA model of case study I with an external constriction ring Variations of CTD and CL in case study I with the application of a constriction ring: (a) total time = cycles (0.270 sec.), weld time = 1.19 cycles (b) total time = cycles (0.273 sec.), weld time = 1.37 cycles (c) total time = cycles (0.276 sec.), weld time = 1.58 cycles (d) total time = cycles (0.282 sec.), weld time = 1.90 cycles (e) total time = cycles (0.285 sec.), weld time = 2.11 cycles (f) total time = cycles (0.290 sec.), weld time = 2.37 cycles (g) total time = cycles (0.294 sec.), weld time = 2.61 cycles (h) total time = cycles (0.298 sec.), weld time = 2.88 cycles (i) total time = 18 cycles (0.3 sec.), weld time = 3 cycles (j) total time = cycles (0.301 sec.) (k) total time = cycles (0.306 sec.) (l) total time = cycles (0.310 sec.) (m) total time = cycles (0.317 sec.) (n) total time = sec..269 xxv

26 6.8 Variations of CTD and SFL in case study I with and without the external constriction ring Weld nugget size and electrode indentation in case study I with and without the application of an external ring: (a) without the application of an external ring (b) with the application of an external ring FEA model of case study II with an external constriction ring Variations of CTD in case study II with the application of a constriction ring: (a) total time = cycles (0.261 sec.), weld time = 0.65 cycles (b) total time = cycles (0.268 sec.), weld time = 1.08 cycles (c) total time = cycles (0.273 sec.), weld time = 1.37 cycles (d) total time = cycles (0.277 sec.), weld time = 1.60 cycles (e) total time = cycles (0.281 sec.), weld time = 1.87 cycles (f) total time = cycles (0.285 sec.), weld time = 2.10 cycles (g) total time = cycles (0.290 sec.), weld time = 2.37 cycles (h) total time = cycles (0.294 sec.), weld time = 2.62 cycles (i) total time = cycles (0.298 sec.), weld time = 2.88 cycles (j) total time = cycles (0.3 sec.), weld time = 3.00 cycles (k) total time = cycles (0.301 sec.) (l) total time = cycles (0.306 sec.) (m) total time = sec Variations of CTD and SFL in case study II with and without the external constriction ring Weld nugget size and electrode indentation in case study II with and without the application of an external ring: (a) without the application of an external ring (b) with the application of an external ring 287 xxvi

27 LIST OF SYMBOLS A a Apparent contact area (in. 2 ) A b Load bearing contact area (in. 2 ) A c Contact area (in. 2 ) A e CL CMOD CTD dv F FEA I I RMS Equipotential end-surfaces Crack length (in. or mm) Crack mouth opening distance (in. or mm) Crack tip distance (in. or mm) Potential drop (volts) Applied load (lbs) Finite element analysis Electric current (ka) RMS current input level (ka) L Wiedemann-Franz Law constant (V/ o K) 2 l Contact thickness (in.) R 1, R 2 Constriction resistance of contact members (ohm) R c R f RSW SFL Contact resistance (ohm) Film resistance (ohm) Resistance spot welding Solidus front location T Temperature ( o F) T 0 Reference temperature ( o F) T liquidus Liquidus temperature ( o F) T solidus Solidus temperature ( o F) β Bulk contact resistivity factor γ Contact area correction factor. xxvii

28 λ Thermal conductivity (BTU/in.-sec.- o F) λ c Contact thermal conductivity (BTU/in.-sec.- o F) ρ c ρ e Contact resistivity (ohm-in.) Equivalent contact resistivity (ohm-in.) xxviii

29 CHAPTER 1 INTRODUCTION 1.1 Background Aluminum and its alloys have good inherent corrosion resistance and need little additional surface protection, unlike mild steel, which must be galvanized. Adding this advantage to its light weight, aluminum alloys have been used in the automotive industry since the 1920s. However, its applications have primarily been in low-volume vehicles and for closure panels. In the past decade, driven by the need to reduce weight and fuel consumption while improving handling, performance, and safety, a number of major automobile 1

30 companies are evaluating or already producing aluminum-intensive vehicles (AIVs) as a means for dramatically reducing vehicle weight without downsizing. Some recent examples are the Acura NSX, the Neon Lite, and the Audi A8. Aluminum sheet with a thickness one-and-a-half-time the gauge of steel sheet results in a structure that possesses 70% of the torsional stiffness but only 50% of the weight. It is reasonable to believe that a material with the same stiffness as the steel structure with a mass of about 60% of the steel structure can be achieved by a combination of up-gauging and optimization of the sheet gauges. A well-designed aluminum vehicle can perform as well as one made of steel yet weigh as much as 50% less and can provide a more rigid body structure. Through significant weight savings, aluminum structures provide a new flexibility in vehicle design-lighter cars do not need to be smaller, larger cars do not need to be heavier, and more options can be offered without increasing weight. Another important aspect of this new design flexibility is the secondary weight savings from the appropriate downsizing of the engine, drive train, and suspension; these savings could be as large as the primary weight savings, while still enhancing vehicle performance. 2

31 While the weight savings from aluminum are significant for a particular vehicle model, an automaker would need to apply aluminum to one or more high-volume production vehicle lines to make an appreciable impact on its manufacturing cost. Thus, the technology adopted for AIVs must be suitable for high-volume production; automated resistance welding is such a technology. Automated resistance welding offers a number of advantages as a joining process for aluminum-vehicle body assembly. It is a high-speed technology that adapts well to the automation needed for high-volume production of sheet-metal assemblies. It also offers low energy consumption, minimum weld distortion, and minimum metallurgical disturbance. Finally, the technology consumes no materials, requires less skill to perform, and is environmentally clean. With all of these advantages, aluminum is a potentially important material for the automotive industry. Limitations in current resistance-welding technology, however, have made automakers reluctant to replace steel with aluminum. The major obstacles are primarily associated with material weldability and electrode life. In addition, aluminum is usually more expensive than steel, although high-volume production can compensate for the cost disadvantage. (Refs. 1-8) 3

32 This dissertation study addresses an integrated numerical and experimental approach to the material weldability issues and develops a new concept of process design to improve the process efficiency while eliminating expulsion. The new design also provides a strategy for reducing the cracking susceptibility of some heat-sensitive aluminum alloys (e.g. multispot AA5754 resistance welds). The integrated approach is used in this study to (1) understand the resistance spot welding process for aluminum; (2) develop a credible numerical modeling scheme and procedure; and (3) verify the new process design concept via numerical modeling and analysis of the welding process. 4

33 1.2 Resistance Spot Welding (RSW) Process Resistance welding was invented a century ago, and has evolved into a simple, straightforward manufacturing process that is fast, easily automated and easily maintained. These characteristics make resistance welding a preferred process in mass production manufacturing situations. Resistance spot welding is one of the most common methods of the resistance welding processes. It is used widely in the automotive, appliance, furniture and aircraft industries to join sheet materials. In automotive applications, resistance spot welding is used to manufacture small reinforcing bracket as well as complete outer panels. It is conservatively estimated that several thousands of resistance spot welds are used in an average size vehicle. Because of the extensive usage, even a small process improvement would bring significant economic benefits. This large potential payoff has attracted a significant amount of research in general resistance spot welding and in specific sub-field of resistance spot welding control. 5

34 The basic sequence of resistance spot welding is as follows. Water-cooled copper electrodes are used to clamp the sheets to be welded into place. Then, the force applied to the electrodes ensures intimate contact between all the parts in the weld configuration. An electric current is passed across the electrodes through the workpieces. Because of the imperfect contact condition, there is an extremely high contact resistance at the faying surface of the workpieces. This resistance generates a substantial amount of joule heat on the contact interface which melts the metal to make a weld. Several authors have reported the electrical parameters vary continuously during the welding of mild steel sheet. At the end of the first cycle, there is an increase in voltage across the copper electrodes and a reduction in current flowing through the weld zone until a peak stage is reached. Throughout the remaining portion of the weld cycle, the voltage decreases to a constant value as the current increases also to a constant value. These changes in voltage and current have also been represented as dynamic resistance. 6

35 The contact resistance, which is the electrical resistance at the joint faying surface, is relatively high compared to the bulk material resistance of the joint material causing fast heating at this contact interface. The combination of heat extraction by the chilled electrodes and rapid contact surface heating causes the maximum temperature to occur roughly around the faying surface. As the material near the faying surface heats up, the bulk resistance rises rapidly, and the contact resistance falls. Again, the peak resistance is at the faying surface, resulting in the highest temperatures. Eventually melting occurs at the faying surface, and a molten nugget develops. On termination of the welding current, the weld cools rapidly under the influence of the chilled electrodes and causes the nugget to solidify, joining the two sheets. In general, the control parameters of the resistance spot welding process are the electrode force, electric current, weld time, and surface conditions. (Refs. 1-18) 7

36 1.3 Resistance Weldability Issues of Aluminum The resistance spot welding process can join steel, cast iron, aluminum and others. In the past, steel is the major material encompassing over 70% of all joining materials in resistance spot welding. Thus, most researches in resistance spot welding try to solve the joining problems of bare or coated steels. Resistance welding of aluminum alloys is different from welding sheet steels, due in part to the large variations in the interfacial physical properties. These variations include: plastic condition temperature range, thermal conductivity, bulk electrical resistivity, expansion and contraction, and surface conditions. As a result, aluminum alloys are typically more difficult to be resistance spot welded and require tighter controls. Plastic Condition Temperature Range Aluminum reaches its plastic range at a much lower temperature than steel due to the lower melting point of aluminum (480 to 640 o C compared to 1480 to 1540 o C). This is the temperature range wherein the aluminum softens, then melts. Therefore, a much smaller amount of heat to generate fusion 8

37 temperatures for an equivalent volume of aluminum is required. However, consideration of the plastic temperature range for aluminum directly affects the resistance welding process. Aluminum has a plastic temperature range of about 93 o C or less compared to steel which has a much wider range of about 538 o C. Heating aluminum up to its plastic temperature but not exceeding its maximum plastic temperature is a critical point. Thermal Conductivity The thermal conductivity of aluminum is greater than that of steel. As a result, the rate of heat loss from the weld region is much greater in aluminum. Since the amount of heat loss is also a function of time, the welding process must be accomplished in a very short time so that thermal conduction does not dissipate welding energy away from the weld. Therefore, both short welding times and high current levels are required. 9

38 Bulk Electrical Resistivity The bulk electrical resistivity of aluminum is quite low (approximately 5 micro-ohm-cm compared to about 15 micro-ohm-cm for steel), and the specific heat and heat of fusion are both high. These factors further indicate that short welding times and high current levels are required to develop the necessary resistance heating. Three to five times the current is required to weld an equivalent thickness of aluminum compared to steel. The low electrical resistance of aluminum governs the optimum distance between individual spot welds and the distance between rows of spot welds through shunting. For aluminum alloys, shunting losses are more of a problem than for steel. Hence, weld current must be increased for aluminum to compensate for the shunting problem. Thermal Expansion and Contraction Aluminum alloys also undergo greater expansion and contraction during melting and solidification processes than does steel. These pronounced dimensional changes are greater in the weld zone and commonly result in weld cracking and shrinkage stresses. 10

39 Surface Condition The variability of the sheet surface in the as-received condition is a key factor in the fabrication of an AIV. Surface-condition issues revolve around the aluminum oxide film that forms on the surface of the aluminum. This oxide has high electrical resistance and a high melting point (2040 o C). As the oxide film grows, the effective contact resistance of the aluminum changes. This, in turn, strongly affects the required current level of the material. In addition, as the electrode comes in contact with the sheet surface, this oxide fractures non-uniformly and creates only small areas for the passage of electric current. When high current level is forced through these scattered points, the electrode face becomes excessively heated and expulsion. The electrode face will also be deteriorated due to the resulting erosion and excessive alloying. (Refs. 1, 2, 4, 17-28) For given material properties of aluminum, the weldability issues in the resistance spot welding aluminum are largely associated with the dynamic characteristics of the interfacial phenomenon at the faying surface and the electrode/workpiece interface. The dynamic contact resistance changes with 11

40 temperature, pressure, and surface conditions of the contact surface. The contact resistance at the faying surface between workpieces determines the heat generation during welding and the subsequent nugget formation. (Refs ) Aluminum resistance weld quality is dominated by the spatial uniformity of current along the electrode contact and interfacial surfaces rather than bulk resistances traditionally associated with steel. However, when considering the time-based variability of a production welding application, the faying surface resistance is spatially variant, meaning the resistance has a non-uniform distribution within the contact area. Actual heat generation at the faying surface is locally spatial and a function of the time-varying current distribution, so as the temperature distribution especially during the initial period of weld cycles. This leads to two demands: (a) a temperature-dependent spatial contact resistance (or equivalent contract resistivity) for optimum process design, and (b) a more efficient electrode design reducing the electrode contact area (or electrode force), or increasing the contact pressure to homogenize the current distribution. Along a similar line, the electrode design may split the force into lower electricity-carrying force and the remaining force for nugget enclosure and 12

41 compressive strains suppressing the cracking susceptibility. The weld current requirement would also be reduced due to smaller electrode contact area, lower electrode force, or higher contact resistance. To date, these two demands in resistance spot welding aluminum alloys and their associated fundamentals have not been fully studied by the researchers or discussed in the literatures. 1.4 Objectives The objectives of this research are threefold: 1. To fundamentally understand the dynamic nature of the contact resistance behaviors at the faying surface in resistance spot welding aluminum alloys, and to define and develop a basic correlation between the equivalent dynamic contact resistivity and local interface temperature for numerical modeling and analysis. 2. To develop a credible numerical modeling scheme and analysis procedure, verified by the experimental data, to investigate the electrical, thermal, and mechanical phenomena in resistance spot welding aluminum alloys. 13

42 3. To develop and verify a new process design concept through numerical modeling and analysis of the resistance spot welding process to eliminate weld expulsion and to recommend a strategy for reducing the cracking tendency of heat-sensitive aluminum alloys. 1.5 Method of Approach An integrated numerical and experimental approach is applied to accomplish the three objectives in this dissertation study. The method of approach is summarized as follows: 1. Study the fundamental electric contact behavior using an a-spot model by an integrated theoretical/numerical (FEA) and experimental procedure. This study defines the equivalent contact resistivity by the virtual contact volume concept, which provides a means to incorporate the temperature dependency of the dynamic contact resistance in the numerical model. This a-spot model study derives a functional correlation between the equivalent contact 14

43 resistivity and temperature during RSW process. The correlation is verified by both a-spot welding model and numerical spot welding model. 2. Conduct a parametric study of the resistance spot welding process using the FE modeling scheme and the process simulation method to determine the weld nugget growth behavior and the electrical potential changes across the faying surface during welding. The predicted results are then compared with the experimental data to determine the best-fit coefficients in the functional relationship between the equivalent contact resistivity and the local temperature at the faying surface. 3. Conduct thermo-mechanical FEA analysis of a new process design, which splits the electrode force into (a) electrical-coupling force and (b) decoupling mechanical force. The reduced electrical-coupling force increases the interfacial contact resistance and hence reduces the need for high amperages. The decoupling mechanical force, which is not associated with the electricity flow, provides the nugget enclosure force, which prevents expulsion and suppresses the cracking tendency by introducing the compressive strains surrounding the peripheral edge of the weld nugget. 15

44 1.6 Anticipated Accomplishments This dissertation study will obtain the following significant results to address the dynamic contact resistance issues and the new electrode design concept. More specifically, these results may be summarized in the following three categories: 1. Under a specific electrode force range, the correlation between dynamic equivalent contact resistivity and temperature to be developed from the a-spot model as shown by an equation with three physical parameters, β, γ, and T 0 (i.e. to be defined later in the text) will be developed. 2. For a given process condition, the three physical parameters in the functional relationship between the dynamic equivalent contact resistivity and the local temperature will be quantified. 3. A new electrode design concept will be demonstrated using the FEA process simulation technique, which predicts and monitors the nugget growth during weld cycles with a special emphasis in the peripheral edge opening displacement and the strain field surrounding the nugget edge. 16

45 CHAPTER 2 LITERATURE REVIEW AND CRITICAL ISSUES In the study of resistance spot welding process using the numerical and experimental approach three research issues are usually encountered. They are (a) quantification of the interfacial contact resistance, (b) numerical procedure that incorporates nonlinear thermo-mechanical properties and the interfacial contact behaviors, and (c) effect of the electrode force on the interfacial contact behaviors under the influence of thermal and mechanical variations. Lack of the fundamental knowledge in these areas has slowed the progress in optimizing the resistance welding process for aluminum. This chapter presents a state-of-the-art review on the current status of these research issues and the approaches developed and used in this dissertation study. 17

46 2.1 Dynamic Contact Resistance Many papers have reported the significance of the dynamic contact resistance behaviors at the aluminum faying surface in relationship to weld nugget formation process and the resulting weld quality (Refs ). However, to date, the time-based interaction between the contact resistance and the thermal-mechanical conditions at the aluminum faying surface is not fully understood. In this section, this issue is discussed by comparing different observations in the resistance spot welding of steel and aluminum. The dynamic contact resistance at the interface is one of the most critical physical properties in resistance welding. The electrical energy generated and the heat dissipated in the joint is influenced by this interfacial property. Depending upon the contact resistance variation with temperature, pressure, and workpiece yield strength, a donut-shaped weld nugget may initiate from the interfacial area under the periphery of the electrode contract and grow toward the center and then outward in the thickness direction. The weld nugget may also initiate from the center of the faying surface and grow simultaneously in both radial and thickness directions. 18

47 The contact resistance at the electrode/workpiece interface is also important to create a thermal blanket effect that keeps the resistance heating generated from the workpiece faying surface within the workpiece. Without this thermal blanket effect, a cold nugget will develop because the heat quickly dissipated into the electrode and is carried away by the cooling water in the electrode. Assuming the electrode geometry and electrode force are held constant, the remaining major process variables are the electric current and weld time. Resistance spot welding steel traditionally uses weld time as the major control parameter, holding the weld current constant. Acceptable weld times for steel can range from 12 to 24 cycles within a 2 to 3 kilo-amperes current window, essentially a six-to-one time to current control ratio. The majority of fusion occurs during the later 25% of steel's weld time. During this late period of time when fusion occurs, the contact interface is pretty much of uniform temperature and pressure. Therefore, the dynamic contact resistance may be experimentally determined by measuring the electrical voltage drop across a contact surface between two pieces of electrodes and the weld current during the weld cycles. The interfacial temperature and pressure may be determined by in-situ measurements, which are very difficult. 19

48 Process modeling and simulation method using the FEA procedure has been the usual method to determine the interfacial temperatures and pressures. However, these interfacial parameters evolve from mutual dependence with the contact resistance, which varies with temperature and pressure during the weld cycles. An inverse method using the FEA modeling and simulation scheme, which can be verified by measurable electrical, thermal, and mechanical experimental data, has been successfully applied to quantitatively determine the dynamic interfacial properties of resistance steel weld at the Ohio State University (Refs. 48, 49, 74). On a contrast to the steel resistance welding, an aluminum resistance weld is in general controlled by current level, not the weld time as in steel. It has been found that the combination of aluminum's high thermal conductivity and rapid drop in dynamic resistance necessitates energy densities exceed a threshold level for weld formation. Extending the weld time will provide little assistance to weld nugget formation if insufficient current density levels are not attained. The majority of the weld forms within the first 25% weld time, as compared with that the majority of fusion occurs during the later 25% weld time of steel. The acceptable weld times for aluminum are 3 to 6 cycles and weld currents are from 20

49 approximately 20 to 35 kilo-amperes depending upon the joint thickness. When weld pressure reaches a particular level (13 to 15 ksi), the weld lobe does not appreciably change with the exception of increased electrode indentation (Ref. 75). One major difference between resistance weld of steel and aluminum is the time-based spatial variability of the contact resistance prior to the formation of the weld nugget. This is particularly true during the initial few cycles in welding aluminum. The contact resistance is non-uniform and local temperature and pressure variant. For resistance spot welding of aluminum, due to the application of high current level and short welding time, the dynamic contact resistance is an important factor of considerable concern. The surface of an aluminum worksheet can exhibit a wide range of characteristics, depending on the processing and storage situations as well as the alloy content. 21

50 Many different measurement methods for the dynamic contact resistance of steels and aluminum alloys have been proposed and published. The effect of various welding parameters and surface conditions on the dynamic contact resistance has also been discussed. (Refs ) An interesting research was studied by Rice, et al. (Ref. 25). In that research, the temperature dependence of the dynamic contact resistance was introduced as an empirical equation. The variation of the base metal resistance was incorporated in the equation based on a one-dimensional thermal analysis. However, due to the nonlinear nature of the geometrical and material properties, it is difficult to directly measure the dynamic contact resistance at the faying surface from a resistance spot welding process. The dynamic contact resistance values studied by those previous researchers are calculated by dividing the measured voltage drops across the contact surfaces by the electric current passing through the interface. Therefore, this calculated contact resistance differs from the actual dynamic contact resistance at the interface during spot welding. Also, because the dynamic contact resistance is a global term and changes with different geometries and thermal-mechanical conditions, local spatial variation of the dynamic contact resistance would have to be 22

51 quantified for a meaningful analysis. An equivalent resistivity concept may be defined assuming a virtual volume of electrical resistant materials at the interface. This dissertation will define and quantify this term using an a-spot contact model and a numerical modeling and simulation procedure to study the resistance spot welding process for aluminum. 2.2 Numerical Procedure Numbers of FEA models on resistance spot welding in both steels and aluminum alloys have been used in the analysis that incorporates the concept of equivalent dynamic contact resistivity by researchers. (Refs ) The basic idea is to assign the electric resistivity values of many times the substrate material to the contact elements in the numerical implementation. However, all these published literatures estimated the contact resistance from the characteristic relationship between the voltage drop across the interface and the estimated maximum interface temperature, which has worked well for resistance steel welds but not the aluminum welds due to the difference in the time-based variations of contact conditions prior to weld fusion. 23

52 Li, Dong, and Kimchi (Ref. 53) used Khlrausch model (Ref. 76) to calculate the contact resistance in the ABAQUS FEA simulation of resistance spot welding of steels. The Khlrausch model states that the voltage drop across the contact interface can be estimated by V 2 =4L(T s 2 -T o 2 ); where V is the voltage drop across the contact interface. T s and T o are the maximum temperature at the interface and the bulk temperature, respectively. L is Lorentz constant. This model is valid for metallic contacts and contact members that obey the Wiedemann-Franz-Lorentz law (i.e. κρ=lt, where κ is the thermal conductivity; ρ is the electric resistivity; and T is the temperature). Diesselhorst (Ref. 77), Bowden and Williamson (Ref. 78), Greenwood and Williamson (Ref. 79) published strict proofs under well defined conditions to substantiate this model for resistance steel welds. Deviations from Kohlrausch model caused by geometry and material variations were discussed by Holms (Ref. 80). In the FEA analysis of resistance spot welding of bare steels, T s was specified as the solidus temperature of bare steel at the faying surface. The effective contact area in the thermoelectric analysis was assumed equal to the mechanical area. For the electrode/steel interface, T s was set to the eutectoid temperature of Fe-Cu alloy. The equivalent contact resistivity was estimated 24

53 from the resistance calculated by dividing the measured voltage drop, which varies with the interface bulk temperature, by the specific welding current. An iterative numerical procedure was used to estimate the numerical convergence between the equivalent contact resistivity and the bulk temperature. In the FEA analysis of galvanized steel, the melting temperature of pure zinc, 420 o C was used as the base for equivalent contact resistivity. For zinc-coated steel weld, the effective contact area was assumed to be the actual solid to solid contact (i.e. enlarged by the molten zinc at the periphery of mechanical contact area) if the contact temperature is within the temperature range for liquid zinc to exist, 420 o C (melting point) to 911 o C (evaporation point). Although implementing the Khlrausch model in Li's study used many assumptions without vigorous theoretical verifications, the reported nugget sizes by calculation agreed well with the experimental measurements. This is due to the fact that the nugget formation process in resistance steel weld occurs within the later 25% weld time, at which moment the contact resistance and the interfacial temperature have both reached constant values. However, the Khlrausch model suffers a setback when used in the resistance welding aluminum alloys due to local geometric and temperature variations. The bulk 25

54 temperature-based equivalent contact resistivity is insufficient to describe the spatial contact variance phenomenon in the resistance aluminum welds. Tsalf (Ref. 81) in his paper described the behavior of interfacial resistivity based on hardness variations as a function of the interface temperatures. His study demonstrated a variation of the contact resistance in direct proportion to the square root of the corresponding hardness values. As the hardness to temperature relationship is defined the contact resistance can be estimated indirectly from the temperature-hardness function. Cho (Ref. 27) incorporated Tsalf model and an iterative procedure in his finite difference analysis predicting the thermal behavior in resistance spot steel welds. The predicted temperature field in the weldment, nugget diameter growth, and nugget penetration were reported in good agreement with the experimental data. From the studies of aforementioned two papers it seems that the thermal conditions at the interface of steel welds may be insensitive to the contact resistance model. However, neither contact resistance model implemented in the numerical analysis could lead to any credible results for aluminum welding. To date, almost all the reported contact resistance models are inappropriate for describing the contact resistance behaviors of the aluminum welds. This has 26

55 hindered the numerical modeling efforts by many researchers. This dissertation proposes a contact resistance model based on an analysis of an a-spot contact model and an integrated numerical modeling and experimental procedure. 2.3 Effect of Electrode Force The electrode force in resistance spot welding functions to ensure electrical contact and to retain weld nuggets from expulsion. In the process, the force reaches a preset value during the squeeze stage, theoretically remains constant during weld cycles, holds for a short period after the current terminates, and is then released. In reality, however, the force varies during weld cycles primarily due to thermal expansion of the weld joint. It is also affected by the mechanical characteristics of the welding machine, the process parameters and the thermal and mechanical characteristics of the workpiece material. 27

56 In resistance spot welding of aluminum, a constant electrode force may not be sufficient to compress a weld nugget to an extent where the nugget would be free of internal porosity, or cracking. In these instances, a variable force has been suggested to supply additional forging pressure during the solidification of welds (Ref. 82). It was suggested that the forging pressure be applied at, or close to, the terminating point of current flow (Ref.83). The numerical control and servomotor techniques (Ref. 84) have been used to supply the forging pressure, which can be altered during the welding cycle using an electric or servo welding gun. In the numerical modeling procedure, most of the reported work assumed constant electrode force during the weld cycles (force control). Using force control experimental procedure (i.e. used low amperage avoiding any heating and softening at the contact interface), Thornton et. al. (Ref. 33) conducted experimental study on the effect of load on the contact resistance for AA5182 aluminum alloy with mill finished surfaces using the standard test method in accordance with ASTM B (current used was 0.1A). It showed decreasing contact resistance as the load increases. The measured contact resistance was reduced from more than 20 micro-ohms at light contact to 0.1 micro-ohm at

57 lbs force. In the same reference studying the effect of surface condition in an experiment on AA 5754 aluminum alloy contact surface, the contact resistance reduced from 500 micro-ohms at light contact to 3 micro-ohms at 900 lbs force for abraded surfaces. The contact resistance reduced from micro-ohms to 3000 micro-ohms for degreased surfaces. The above referenced papers explain that, for resistance spot welding aluminum, high electrode force would be required to prevent expulsion or formation of weld discontinuities, which results in the requirement for high welding current due to much reduced contact resistance. In addition, the contact resistance is highly sensitive to the surface condition of the contact interfaces in resistance spot welding aluminum. The resistance welding process for aluminum would be improved if both the electrode force and weld current could be reduced to a level comparable to steel welding while the contact resistance could be kept at high values during the initial 25% weld time. In this dissertation study, a new concept of electrode design, which splits the electrode force into electrical-coupling force and decoupling mechanical force, is investigated using the numerical modeling tool developed in this dissertation study. The reduced electrical-coupling force increases the interfacial contact resistance 29

58 and hence reduces the need for high amperages. The decoupling mechanical force, which is not associated with the electricity flow, provides the nugget enclosure force and suppresses the cracking tendency by introducing the compressive strains. The numerical process modeling and analysis presented in this dissertation will demonstrate the new design concept. 30

59 CHAPTER 3 EQUIVALENT CONTACT RESISTIVITY: A-SPOT MODEL ANALYSIS In order to define and determine the equivalent contact resistivity for an aluminum contact interface in resistance spot welding, this chapter presents the conceptual flow of the idea on the spatial-variant contact resistance from a fundamental discussion of electric contact and it physically model of a single contact, dubbed "a-spot model", to a numerical procedure quantifying the equivalent resistivity of a single contact. With the equivalency defined the functional relationship between the equivalent contact resistivity and the local contact temperature in resistance spot welding aluminum will be determined in Chapter 4. 31

60 3.1 Electric Contact and Physical Model Basic Definition of an Electric Contact The term electric contact means a releasable junction between two conductors, called contact members, which are apt to carry electric current. This term is defined in a textbook by Holm (Ref. 80). Because the interface of the contact members is characterized by a certain roughness and waviness, these characteristic features cause surfaces in contact to rest on those asperities forming micro-contact points. If the contact members were infinitely hard, the load could not bring them to touch each other in more than three points. But because actually materials are deformable, the contact points become enlarged to small areas. The sum of all these areas is called the load bearing contact area, A b, under a specific loading pressure, which is much smaller than the apparent contact area (Figure 3.1). 32

61 Based on the different types of current conduction, the load bearing area can be categorized into three parts: metallic contact areas, quasi-metallic spots, and insulating film areas. The short name a-spot for the conducting contact areas, referring to the radius a of a circular contact area, is a widely accepted term. To sum up, not only is the load bearing contact area very small, but also that only a fraction of it may be electrically conducting. The current lines of flow will be bent together through narrow areas, causing an increase of resistance beyond the case of a fully conducting contact area. Figure 3.2 shows the system of equipotential surfaces and current flow lines when both members are of the same metals. The term, A c, represents a single circular a-spot in the middle of the apparent contact area. Practically, the constriction of current flow can be seen and assumed as limited in the members by certain equipotential end-surfaces, A e. This constriction resistance at the interface results in a voltage drop and generates heat to fuse the contact members. (Refs ) 33

62 Load-bearing contact surface (A b ) a-spots Apparent contact surface (A a ) Figure 3.1: Contact surfaces (Ref. 74) Figure 3.2: Lines of current flow and equipotential surfaces of a current constriction (Ref. 80) 34

63 The constriction resistance can be calculated as a function of the conducting contact area, and when the measured resistance is greater than the calculated one for a known area, the area must be covered by a film that produces an additional resistance. If there is no film in the contact, the contact resistance, R c, is simply a constriction resistance. If a film is present and both sides have different metals, the contact resistance is the sum of the constriction resistances R 1 and R 2 in the two members respectively and the film resistance, R f (Ref. 80), thus R c = R 1 + R 2 + R f (1) As the electric current flows across the interface of two contact points, voltage distribution in a plane normal to the interface seems to be discontinuous. Actually, this is not true, and the sharp voltage drop between extrapolated voltage values on either side of the interface can be treated as a fictitious interface voltage drop. Therefore, it is reasonable to assume linear variation in voltage within the distribution zone, thus maintaining the continuity in the voltage potential field. Then, idealization of the interface of current flow can be done by assigning an equivalent contact resistivity, ρ e, from the microscopic point of view. (Ref. 80) 35

64 3.1.2 Physical Model Figure 3.3 shows a multi-spot metallic contact area referring to a semi-infinite member. It can be simplified by assuming all the a-spots to be circular with equal radii and to lie close to each other and uniformly over the apparent contact area. Specified electric current and squeeze load are applied. The contact resistance at the interface consists of constriction resistance and film resistance. 3.2 Electrical and Mechanical Analyses of a-spot Model In order to establish the fundamental understanding of the contact resistance behavior of an a-spot model, a single a-spot, ball contact is simulated and analyzed using the FEA method. This simple model enables decoupled electrical and mechanical analyses using the same mesh model, which incorporates the temperature-dependent thermal and mechanical properties. 36

65 This numerical simulation work is presented in two steps. At first, the mechanical analysis associated with the a-spot model was employed to establish the relationship between the contact area and the applied force at various temperatures. Three force magnitudes: 128, 512 and 900 pounds, which represent low, typical or high loads associated with the resistance spot welding process were investigated. The 128-pound force is usually beyond the practical steel lobe. The other two load magnitudes are used for resistance spot steel or aluminum welds. In the virtual experiments by FEA simulation, the initially assumed point-contact would deform due to elastic and plastic straining at the contact interface. The deformed contact areas at different temperatures obtained in the deformation analysis were then used to study the electrical characteristics of the contact when the electric current was allowed to pass through the contact interface. 37

66 In this study, three different contact areas were depicted to study the interfacial electrical characteristics. The electrical potential fields were generated for the three contact areas. The material used in this simulation was 2024-T3 aluminum alloys. The size of the ball is 1 inch in radius. Isotropic, temperature-dependent mechanical and electrical properties of 2024-T3 aluminum alloys were used in the analyses. These properties were specified over a temperature range from room temperature, 70 o F, to above the melting temperature, 1200 o F. 38

67 3.2.1 Mechanical Analysis An axisymmetric, finite element half model was developed in order to reduce the number of elements and computation time. This finite element mesh model, consisted of 4940 nodes and 4780 elements, is shown in Figure 3.4. Element types of DCAX4 and CAX4 were employed, for electrical-thermal and thermal-mechanical analyses, respectively. In the mechanical analysis the boundary condition included a pressure-load flat surface, a simply supported flat surface, and free curved surfaces (excluding the contact interface). Bulk temperatures were assumed constant over the materials at different levels. 39

68 I P T δv A c Apparent Area Bearing Area Contact Area (a-spot) Contact Resistance Bulk Resistance Constriction Resistance Film Resistance Constriction Resistance Bulk Resistance Figure 3.3: Physical model 40

69 For the three different mechanical loading conditions of 128 lbs, 512 lbs, and 900 lbs, nine different temperature levels, 100 o F, 200 o F, 300 o F, 400 o F, 500 o F, 600 o F, 700 o F, 800 o F, and 900 o F, were applied in order to understand the deformation characteristics of the contact surface under different load magnitudes and the effect of bulk temperature. When temperature level was higher than 900 o F, numerical divergence occurred due to material softening, which caused the numerical model to collapse. Figures 3.5 and 3.6 summarize the stress distribution in the a-spot model under 512 lbs of force at 70 o F and 700 o F, respectively. The maximum compressive stresses at the contact point are 8.68 x 10 4 psi and 1.23 x 10 4 psi at the respective temperatures. The deformed contact areas were determined from the displacement field at the contact, which are 0.01 and 0.07 square inches at 70 o F and 700 o F, respectively. 41

70 Figure 3.7 summarizes the predicated contact areas with respect to material's bulk temperatures at three load levels. It shows that, under the 512 and 900 lb loads, a correlation is observed. For the lower force magnitude, a complete difference correlation exists. This load level is not really of any interest to the resistance spot welding of steel or aluminum and, therefore, is not to be analyzed further. The functional relationship between contact area and material's bulk temperature shown in Figure 3.7 may be correlated using the Sigma-Plot curve-fitting program and presented as follows: A c = 8x x10-4 Exp (5.8483x10-3 T) (2) The mechanical contact area decreases exponentially with the increasing bulk temperature. This relationship follows pretty much the same softening effect of the aluminum alloy by the increasing temperature. 42

71 Figure 3.4: Meshed finite element model 43

72 2 3 1 Figure 3.5: Stress distribution in thermal-mechanical analysis (70 o F, 512 lbs) Figure 3.6: Stress distribution in thermal-mechanical analysis (700 o F, 512 lbs) 44

73 2.00E-01 Contact Area (inch 2 ) 1.80E E E E E E E-02 F=512 lb F=128 lb F=900 lb A c = 8x x10-4 Exp(5.8483x10-3 T) 4.00E E E Temperature ( 0 F) Figure 3.7: Dependency of contact areas on temperature 45

74 3.2.2 Electrical Analysis For the electrical analysis, the same FEA model with three different contact mesh configurations that represent three different contact areas, which are shown in percentage of the sphere radius (5%, 10%, and 20%), were modeled. The applied electrical current was 33 ka and the potential at the bottom boundary was set to be zero. The current density field for the 5% and the 10% contact areas are shown in Figure 3.8. The maximum current densities are 1.51 x 10 2 ka/in. 2 for the 10% contract area and 4.38 x 10 2 ka/in. 2 for the 5% contact area. The electrical constriction effect (i.e. high current density concentration) is shown due to the decreasing contact area. 46

75 Current Density (Amperes/in 2 ) 5% of Sphere Radius (a) Current Density (Amperes/in 2 ) 10% of Sphere Radius (b) Figure 3.8: Current density distribution in electrical analysis: (a) 5% of sphere radius, (b) 10% of sphere radius 47

76 25000 Current Density (Amps/inch 2 ) R c = 5%R R c = 10%R R c = 20%R E E E E E E E E E-01 Distance from the Centerline (inch) Figure 3.9: Current density distribution from the centerline at interface for three different contact area percentages (R c : radius of contact area) 48

77 Figure 3.9 illustrates the current density distributions from the centerline at the interface for those three different contact areas. For the 5% and 10% contact areas, the current density is not evenly distributed at the interface. The maximum current density is at the periphery of the contact interface. However, if the contact area is large (i.e. 20%), the electric constriction effect is unnoticeable and the current density distribution is approximately uniform along the contact interface. The electrical potential fields for the 5% and 10% contact areas are shown in Figure This figure also shows the geometrical constriction effect of the 5% contact area. Figure 3.11 shows the electrical potential distribution curves along the centerline of the sphere for three different contact areas (dashed lines). It clearly shows the geometric constriction effect resulting in the sudden slope change at the contact interface (i.e. near the one inch location from the bottom surface). Figure 3.11 also shows the effect of higher resistance at the interface when the contact mesh elements incorporate a higher value of resistivity, which simulates the existence of an oxide film on the contact surface. The actual 49

78 magnitudes of the film resistivity values are not of significance here. The purpose of this exercise is to demonstrate that with existence of this simulated film, the predicted results show discontinuous slope changes at the contact interface. This would be expected when the surface condition is incorporated in the resistance welding analysis of aluminum alloys. In this FEA simulation, the same film thickness and film resistivity were incorporated in the numerical analyses for the three contact areas. It appears that the film resistance effect becomes less significant when the geometric constriction effect decreases (i.e. larger contact area). 50

79 Figure 3.10: Electrical potential distribution for 5% and 10% contact areas 51

80 Electrical Potential (volt) 4.50E E E E E E E-03 Rc = 5%R0, with oxide film on the contact suface Rc = 10%R0, with oxide film on the contact suface Rc = 20%R0, with oxide film on the contact suface Rc = 5%R0, without oxide film on the contact suface Rc = 10%R0, without oxide film on the contact suface Rc = 20%R0, without oxide film on the contact suface 1.00E E E E E E E E E E E E E E+00 Distance from the Bottom (inch) Figure 3.11: Electrical potential distributions along centerline 52

81 3.3 Equivalent Contact Resistivity Definition and Evaluation Procedure The equivalent resistivity for a single spot contact, ρ e, may be written as: RA ρ e c c c l dv A l I = = (3) where R c is the contact resistance; l is the contact thickness (i.e. to be defined later as the length of a linear portion of the electric potential curve); A c is the contact area; dv is the voltage drop at the interface; and I represents the electric current. The value of (dv/l) for three deformed contact areas can be interpreted by employing the respect slopes of the three potential curves shown in Figure The interpretation procedure may be illustrated in Figure For a given bulk material temperature, the contact area can be estimated using Equation (2). The potential drop is taken from the slope at the contact (i.e. Figure 3.11). The equivalent contact resistivity is then estimated using Equation (3). Figure 3.13 shows a graphic flow chart summarizing the procedure. 53

82 Using the above described procedure, for the force range studied here (512 and 900 lbs); the equivalent contact resistivity may be estimated for various bulk temperatures. This enables a plot of the resistivity versus the contact area curve. Using Equation (2), the equivalent contact resistivity versus the bulk temperature relationship can be constructed from the resistivity-contact area curve. The general relationship between the equivalent contact resistivity and the contact temperature developed from the simple a-spot model analysis may be explained using the Wiedemann-Franz-Lorentz Law, which may be expressed as Equations (4) and (5). ρλ = LT (4) where ρ is electrical resistivity; λ is thermal conductivity; L is Lorentz constant which is regarded independent of both metal and temperature. Actually, L is not quite the same for all metals used in contact, but a fairly good approximation expressed by Equation (5) has been reported (Refs. 80). L = 2.4 x 10-8 (V/ o K) 2 (5) 54

83 Electrical Potential (volt) 1.80E E E E E E E E E-04 dv 1 ρ = x dl I / A dl dv 0.00E E E E E E E E E E E E +00 Distance from the Bottom (inch) Figure 3.12: (δv/l) Calculation method 55

84 P I A c Load Range y Asymmetric T Asymmetric V l Temperature V = 0 δv ρ e ρ e A c T Figure 3.13: Contact resistivity determination procedure 56

85 When two metallic surfaces are pressed together, contact is made only at a few discrete points. Since the thermal conductivity of the metals in contact is in general much greater than the thermal conductivity of the fluid filling the interstices, heat flow will tend to channel through the small size points of contact. A number of studies have been done on heat transfer phenomenon in the resistance spot welding and on thermal conduction in contact. (Refs ) The common engineering approach to this contact problem has been visualizing the contact interface as a finite layer of virtual thickness, which has equivalent volumetric properties with respect to electrical, thermal or mechanical contact behaviors. This approach enables the numerical analysis treating the contact interface as a virtual volume (or actual mesh in the numerical models) of material that posses hypothetical property values. These hypothetical properties can usually be explained and estimated in good proximity to the physical phenomena of the contact surfaces. 57

86 3.3.2 Equivalent Contact Resistivity versus Temperature Relationship Based on the virtual volume concept, the correlation between the contact thermal conductivity, λ c, and the contact area, A c, may be written as: λ c A c (6) Substituting the virtual contact conductivity by the contact area using Equation (6), the Wiedemann-Franze-Lorentz Law may be rewritten in a proportional relationship as follows: ρ c LT LT = (7) λ A c c Further substituting the contact area by the contact temperature using Equation (2), the equivalent contact resistivity may be defined in a generic format as shown by Equation (8), with the proportional constants written as ρ o /T o, β, C, and γ. ρ c = ρ 0 T 0 βt Exp [-Cγ(T - T 0 )] (8) The β factor is added to be associated with the contact temperature in Equation (7) incorporating the potential effect of oxidation and other conditions at the contact surface. The γ factor is inserted in Equation (2) to encounter the softening effect of contact points at the interface. The equivalent contact resistivity is assumed 58

87 proportional to a reference value, ρ o, at a reference temperature, T o. Using this proportionality format, the Lorentz constant is eliminated. The contact thermal conductivity, λ c, is lumped into the proportional constant. Using the definition of equivalent contact resistivity (Figure 3.12) and the numerical analysis results of the a-spot model with the force range between 512 and 900 lbs, the equivalent contact resistivity for an 2024-T3 aluminum alloy a-spot contact may be written as shown in Equation (9). The proportional constants, ρ o /T o and C are estimated using the Sigma-Plot curve-fitting program. ρ c = (4.53x10-8 ) βt Exp [(-6.53x10-3 )γ(t - T 0 )] (9) where β is the bulk contact resistivity factor, γ is the contact area correction factor, T 0 is the reference temperature, and (T T 0 ) is defined as the effective softening temperature. In Equation (9) β and γ are inserted for calibration purpose and determined by an iterative numerical and experimental procedure in the analysis of the resistance spot welding process (Chapter 4). 59

88 Equation (9) practically implies two physical phenomena at the contact interface in the resistance spot welding process. The equivalent contact resistivity in the virtual contact volume would be affected by the bulk material resistivity (may include the effect of surface oxidation) and spot contact area enlargement due to material softening as temperature increases under a given load (may also include the mechanical restriction effect of the surrounding contact spots). In Equation (9), the proportional term of (4.53x10-8 ) βt represents the bulk resistivity effect, which would increase the equivalent contact resistivity when temperature increases, as shown in the Wiedemann-Franz-Lorentz relationship. The exponential term of Exp [(-6.53x10-3 )γ(t - T 0 )] depicts the softening effect, which will enlarge the contact area and then reduce the equivalent contact resistivity with increasing temperature, as shown by Equation (2). Considering a combined effect of these two conflicting phenomena, the equivalent contact resistivity is expected to rise initially with temperature because the bulk resistivity effect would be a dominant factor due to surface roughness and oxidation. As soon as the interface temperature reaches the softening 60

89 temperature, further increase in temperature would reduce the equivalent contact resistivity rather quickly due to softening effect. Mechanical restriction effect from those neighboring contact spots would reduce the contact softening effect. The a-spot model can study the bulk resistivity effect and the softening effect, but not capable of including the effect of mechanical restriction. Because of the complexity of the actual contact conditions and the welding process, the factors of β and γ are left in Equation (9) as the calibration constants to be determined from modeling and analysis of the resistance spot welding process. The β factor may be called "bulk contact resistivity factor" and the γ factor may be dubbed "contact area correction factor" for the following analysis Effect of Contact Surface Condition and Softening The bulk contact resistivity factor (β) is related to applied load and surface condition, like grease, dirt, oxide film, and preparation. Figure 3.14 plots a series of equivalent contact resistivity versus temperature curves of four different β values. In these curves, γ is assumed to be unity (neglecting the softening and 61

90 restriction effect) and the reference temperature is taken as 0 o F. At this moment, all these values for β, γ and T o are arbitrarily chosen. The purpose of this exercise is to observe the functional relationship and effect of β. It is interesting to observe the dominance of the initial bulk resistivity effect, which shows resistivity increase with temperature. This reflects the Wiedemann-Franz-Lorentez phenomenon. As the temperature reaches a plateau, the contact surface enlargement becomes dominant due to rapid softening of the contact spot at temperatures above the softening temperature. The observation shows that the peak resistivity values occur at approximately 200 o F, which is the plastic temperature of aluminum alloys, for all four curves studied. At these high temperatures, the initial surface condition would have been altered to become less effective in determining the equivalent contact resistivity. 62

91 Increasing the β value would increase the contact resistance, which phenomenon should also be reflected in the equivalent resistivity of the virtual contact volume. This β-dependency diminishes as the contact temperature increases beyond the contact softening temperature. Figure 3.14 also shows that the resistivity-temperature relationship is more sensitive to β variation at smaller values. This β sensitivity reduces as its value increases. Since Equation (9) is defined relative to the resistivity value at a reference temperature, which is derived by proportionality. Therefore, the reference temperature, T o, in the exponential term is shown in the difference between the actual contact temperature and the reference temperature. Physically, this reference temperature alone does not have any significance. It simply reflects the definition of the equivalent contact resistivity influenced by the softening temperature in a relative matter. Contact spot softening actually depends on this relative temperature in the original definition. In order to parametrically investigate the effect of the reference temperature on the equivalent contact resistivity versus temperature relationship, Figure shows five curves at temperatures from 0 o F to 70 o F, assuming β=2500 and γ=1. 63

92 Increasing the reference temperature would reduce the relative temperature of softening. This not only increases the resistivity magnitude but also increases its sensitivity of the temperature dependency (slope change). 64

93 Contact Resistivity (ohm-in.) 3.50E E E E E E E-04 ρ = β(4.53x10-8 )T Exp(-6.532x10-3 )γt β = 400 β = 800 β = 1000 β = E Temperature (DegF) Figure 3.14: Equivalent contact resistivity for different β Values (γ = 1, T 0 = 0 o F) 65

94 The physical significance of the reference temperature is really not a concern. It could be lumped into the contact area correction factor (γ). By re-grouping the softening temperature as shown in Equation (10) and redefining the contact correction factor, Equation (11) retains the same resistivity versus temperature relationship by replacing γ by γ'=γ(1-t o /T). ρ c = (4.53x10-8 ) βt Exp [(-6.53x10-3 )γ(1 - T 0 /T)T] (10) ρ c = (4.53x10-8 ) βt Exp [(-6.53x10-3 ) γ T] (11) Since γ' would be determined, together with β, by modeling and analysis of the resistance spot welding process (Chapter 4), it would make no difference if we chose γ or γ' in this original relationship derived from the a-spot model. However, the reference temperature would disappear from the equation if the modified contact area correction factor were interpreted in the relationship. 66

95 1.20E E-02 T 0 = 70 o F T 0 = 50 o F β = 2500, γ = 1 Contact Resistivity (ohm-in.) 8.00E E E-03 T 0 = 32 o F T 0 = 20 o F T 0 = 0 o F 2.00E E Temperature (degf) Figure 3.15: Equivalent contact resistivity for different T 0 Values (β = 2500, γ = 1) 67

96 Figure 3.16 is an actual contact surface taken by an electronic imaging device. It demonstrates the actual surface that is rough and irregular, which would result in many contact spots when two of these surfaces are brought together to bear. When the force is applied to close the two surfaces, those asperities would collapse and the contact area would enlarge. The contact resistance or the equivalent contact resistivity at the interface would decrease. The contact area correction factor is assumed to depict the softening and constriction effect of the asperities, which is also influenced by the load magnitude. Figure 3.17 illustrates how the γ-factor influences the resistivity versus temperature relationship, assuming β=2500 and T o =0 o F. For small γ values, the bulk contact resistivity or contact surface condition is a dominant factor over the entire temperature range. This is because the contact area does not increase due to lack of softening effect even at high temperature, which should be not true in a practical sense. However, on the other hand, when γ becomes a value greater than 1, the softening effect over rides the contact surface condition effect, which is also not realistic from the past experiences in resistance spot welding of 68

97 aluminum alloys, or even in the steel welding case. Figure 3.18 shows the resistivity versus temperature relationships for high γ values (γ= 1 through 5, β=2500 and T o =0). This clearly shows that any values greater than one would result in a decreasing resistivity way before reaching the softening temperature. Therefore, it is judged that the realistic range for γ values would be best estimated as between 0.5 and 1. Figure 3.19 shows a series of curves for the equivalent resistivity versus temperature relationships for the γ range between 0.5 and 1.0, assuming β=800 and T o =0 o F. Increasing γ would reduce the overall magnitude (shift the curve to lower magnitude) and move its maximum value towards lower temperature. 69

98 Figure 3.16: Contact surface in resistance spot welding 70

99 7.00E-02 γ = E E-02 Resistivity (ohm-inch) 4.00E E E-02 γ = 0.3 γ = 0.2 γ = E-02 γ = 0.9 γ = 1 γ = E Temperature (degf) Figure 3.17: Equivalent contact resistivity for different γ values (β = 2500, T 0 = 0 o F) 71

100 7.00E E-03 γ = 1 β = 2500, T o = 0 o F 5.00E-03 Contact Resistivity (ohm-in.) 4.00E E E E-03 γ = 2 γ = 3 γ = 4 γ = E Temperature (degf) Figure 3.18: Equivalent contact resistivity for γ = 1 to 5 (β = 2500, T 0 = 0 o F) 72

101 1.20E-02 β = 800, γ = 1, Τ0 = 70 β = 800, γ = 0.9, Τ0 = E-02 β = 800, γ = 0.8, Τ0 = 70 β = 800, γ = 0.7, Τ0 = 70 Contact Resistivity (ohm-in.) 8.00E E E-03 Peak electrical resistivity Increasing γ value β = 800, γ = 0.6, Τ0 = 70 β = 800, γ = 0.5, Τ0 = E E Temperature (degf) Figure 3.19: Equivalent contact resistivity for γ = 0.5 to 1 (β = 800, T 0 = 70 o F) 73

102 3.3.4 Summary 1. For a load range from 500 lbs to 900 lbs, the a-spot contact area-temperature correlation is: A c = 8x x10-4 Exp (5.8483x10-3 T) 2. The electrical constriction effect decreases as the contact area increases. This current constriction is evidenced by the current density concentration at the periphery of the contact interface. 3. In the numerical simulation of a-spot model, the interfacial potential drop is inversely proportional to the contact area due to the diminishing electrical constriction effect. When the artificial oxide film resistance is incorporated in the contact model, the potential drop across the contact surfaces shows a discontinuous slop increase, which would be anticipated from a physical point of view. 74

103 4. The generic correlation between the equivalent contact resistivity of AA2024-T3 a-spot contact and contact temperature under a load range from 500 to 900 lbs is determined to be ρ c = (4.53x10-8 ) βt Exp [-6.53x10-3 γ (T-T o )] or ρ c = (4.53x10-8 ) βt Exp [-6.53x10-3 γ' T] where β is the bulk contact resistivity factor, γ or γ' is the originally defined or modified contact area correction factor, T 0 is the reference temperature, and (T T 0 ) is defined as the effective softening temperature. 5. The equivalent contact resistivity increases with the bulk contact resistivity, assuming existence of a virtual volume of a contact substance at the interface. The bulk contact resistivity depends on surface condition, including oxidation. A bulk contact resistivity factor (β) is defined reflecting the bulk contact resistivity or local contact resistance variation with temperature. 75

104 6. The contact area correction factor (γ) is assumed to depict the softening effect of asperities under load. Increasing γ value would lower the overall resistivity versus temperature curve (magnitude) and move the maximum resistivity point towards lower temperature region, even below the material softening temperature for γ values, which becomes practically unrealistic. The realistic range of γ values would be between 0.5 and The reference temperature (T 0 ) reduces the magnitude of the effective softening temperature (T-T 0 ) and hence reduces the slope of the contact resistivity-temperature relation. In the numerical analysis, the reference temperature (T 0 ) can be lumped into the surface correction factor (γ) and replaced by the modified surface correction factor (γ') without any difference in the determining equivalent contact resistivity for the resistance spot welding analysis. 8. The generic equivalent contact resistivity versus temperature relationship consists of two parts. The first part, (4.53x10-8 ) βt, shows the proportionality relationship with the bulk contact resistivity and follows the Wiedemann-Franz-Lorentz law. The second part, Exp[(-6.53x10-3 )γ(t - T 0 )], 76

105 is shown in the exponential term that reflects the relationship between the contact area and temperature determined from the a-spot analysis. The equivalent contact resistivity is influenced by a combined effect of these two parts. The equivalent contact resistivity initially increases with temperature, reaches a peak plateau at materials softening temperature (or plastic temperature which is 200 o F for aluminum alloys), and quickly decreases as the temperature passing over this material softening temperature. The proportionality term (first part) of Equation (9) increases the contact resistivity, however, the exponential term (second part) in the same equation decreases the contact resistivity due to contact area enlargement. 77

106 3.4 Experimental Observations and Analysis The a-spot model analysis defines the generic relationship between the equivalent contact resistivity and temperature with two parameters β and γ to be determined. In order to quantify these two parameters, an experimental and numerical approach was conducted to evaluate the relationship based on a physical a-spot model Experimental Procedure Two AA 2024-T3 bars were machined to form a semispherical surface (1 inch radius) on one end of the bars. This semispherical surface was used to simulate an asperity. Brining two curved surfaces together forms an a-spot contact. The specimen geometry is shown in Figure This experiment was designed to measure the electrical potential and temperature histories at specified points, which are illustrated in Figure 3.21, on the surface of the hemispherical portion of the specimens and to investigate the 78

107 axial displacement. Voltage probes were welded to eight specified points to record the potential levels and thermal couples were welded to two points to observe the temperature variation. The location of these two temperature measurement points in y-axie is also shown in Figure The measurement data values were used to compare with the predicted results obtained from the numerical FEA model. 79

108 Before After Figure 3.20: Picture of a-spot specimens before and after experiment 80

109 Point 2 (y = inch) Point 1 (y = inch) Thermal Couples y Voltage Probes Point 8 (y = 1.80 inch) Point 7 (y = inch) Point 6 (y = inch) Point 5 (y = inch) Point 4 (y = inch) Point 3 (y = inch) Point 2 (y = inch) Point 1 (y = inch) Ground (y = 0.00 inch) Figure 3.21: Specific points on the hemispherical surface of the specimen for temperature and potential drop measurement 81

110 A single-phase 150 kva AC Taylor-Winfield press-type resistance welder and a Medar programmable resistance welding control were used to apply the weld current and squeeze force in this experiment. Two electrode holders of the resistance welder were replaced with the specimens as shown in Figure A data acquisition system, including a personal computer, an AD converter board, voltage probes, a displacement transducer, a weld checker and K-type thermal couples, as shown in Figure 3.22 and pictured in Figure 3.23, was used in the experimental study. In order to avoid melting and large deformation of the specimen, which would invalidate the measurement data; low electrical current level (13 ka RMS) and small squeeze force (450 lbs) were selected at the beginning of this experiment. In order to collect the full waveform of current input for dynamic contact resistance calculation, the current input was selected as L-1 level with 95% heat percentage. The weld schedule is listed in Table 3.1. The weld time was 3 cycles. 82

111 Upper Platform Specimens Power Supply Displacement Transducer AD Converter Lower Platform Weld Checker Figure 3.22: Specimens and data acquisition system arrangement 83

112 Figure 3.23: Picture of specimens and data acquisition system setup Squeeze Time Weld Time Hold Time Squeeze RMS Current (cycles) (cycles) (cycles) Force (lbs) Input (ka) Table 3.1: Welding schedule of a-spot model experiment 84

113 In the experiment the current and voltage inputs were recorded and presented in Figures 3.24 and 3.25, respectively. The voltage drops were measured at 8 points as numbered in the brackets. Figure 3.26 shows the measured distributions of the potential drops along y-axis in the experiment when the weld time equals to 0.25, 1.25, and 2.25 cycles, respectively. The shapes of those potential distribution curves are similar to the theoretical hypothesis and FEA results of a-spot model, as shown in Figure However, the magnitude is about two orders of magnitude higher. This is due to the smaller contact area due to low current (13 ka vs. 33 ka) and the resulting low contact temperature. As shown in Figure 3.7, the contact area may be less than 2% (0.02 ) ball radius as compared to 5% (0.05 ) contact radius shown in Figure Another possible reason for this difference between the experimental data and the predicted results using the simple a-model analysis would be the oxidation surface. Nevertheless, the sharp increase in the potential drops across the interface demonstrates the predicted contact resistance behavior in the physical a-spot model. 85

114 30 20 Current (ka) Weld Time (Cycles) Figure 3.24: Recorded current Input in the experiment 86

115 Voltage (Volts) V(1) V(2) V(3) V(4) V(5) V(6) V(7) V(8) Weld Time (Cycles) Figure 3.25: Recorded voltage input in the experiment 87

116 In Figure 3.26, the voltage drops at 0.25 cycles is larger than those at 1.25 and 2.25 cycles because the contact resistance was expected to reach its peak within the first half cycle and then dropped off during the remaining weld cycles in resistance spot welding aluminum alloys. This phenomenon has been reported in many literatures (Ref.) and in the later chapter discussing the experimental study of the actual resistance spot welding of the AA2024-T3 sheet joints in this dissertation. Figure 3.27 shows the dynamic contact resistance of the a-spot welding sample interpreted from the voltage and current plots. The resistance values were calculated by dividing the momentary voltage by the momentary current. This enabled a plot of the contact resistance versus weld time relationship. It is shown that high contact resistance occurred within the first half of the weld cycle. The resistance remained at the 15 µohms level until 2.5 weld cycle time. After this time, the contact resistance drops very quickly indicating loss of contact due to weld nugget formation. 88

117 7.00E E-01 Expt. (0.25 cycles) Expt. (1.25 cycles) Expt. (2.25 cycles) 5.00E-01 Potential Drop (volts) 4.00E E E E E Global Y Coordinate (in.) Figure 3.26: Potential distribution along y-axis from experiment data 89

118 Dynamic Contact Resistance (µomh) Weld Time (cycles) Figure 3.27: Dynamic contact resistance determined from the experimental current and voltage data of a-spot aluminum welding model 90

119 The initial surge of the contact resistance within the 0.5 weld cycle time demonstrates the typical characteristic of the resistance spot aluminum welds, which has been reported in many literatures. However, whether or not the dipping shape of the curve reflects the true behavior needs to be further studied. This observation could also be influenced by the limitation of instrument sensitivity and dynamic response during the very first second weld period. Interpreting the current observation and behavior may suggest the following: (a) The initial contact resistance value of about 22 µohms is the contact resistance at room temperature. (b) The temperature of the contact interface starts to rise at approximately 0.2 weld cycle, which increases the contact resistivity in accordance to the Wiedemann-Franz-Lorentz law. (c) When the contact temperature reaches the materials softening temperature, contact area quickly enlarges, which causes the sharp drop of the contact resistance at approximately 0.3 weld cycle. 91

120 (d) The contact resistance remains at approximately 17 µohms after 0.3 weld cycle until weld nugget starts to form. The contact temperature is uniform and the resistance remains constant and does not follow the Wiedemann-Franz-Lorentz law. The temperature measurement at two locations, as shown in Figure 3.21, was not successful due to lack of responsiveness and sensitivity of the thermocouples within the very small initial time duration. Therefore, numerical simulation of the a-spot welding model was used to determine the temperatures for further analysis of the equivalent contact resistivity versus temperature relationship. Because of the uncertainty of the resistance curve during the most critical initial period in resistance spot aluminum welding, the a-spot experimental results are primarily used for qualitative analysis of the contact behavior and to validate the numerical model based on a comparison of the electrical potential drops, which is discussed in the following section. 92

121 3.4.2 FEA Analysis of the Experimental Results FEA A-Spot Welding Model In order to quantify the experimental observations, a FEA analysis of the experimental results was conducted. The analysis first developed a FEA model simulating the spot welding process as conducted in the experimental study. Electrical potential drops, temperature variations, and contact area changes were predicted for the 3 weld cycles. This FEA analysis results were also used to evaluate the equivalent contact resistivity versus temperature relationship. An axisymmetric, finite element half model (Figure 3.4) was established to simulate this a-spot model. The meshed geometry of this half model consists of 4940 nodes and 4780 elements. One contact pair was used to simulate the contact surfaces between two specimens. Element types of DCAX4 and CAX4 were employed for the electrical-thermal and thermal-mechanical analyses of the a-spot welding model, respectively. 93

122 In addition to the thermal mechanical properties and the electrical bulk resistivity, which are temperature-dependent functions assigned to the elements, the equivalent contact resistivity, also a temperature-dependent function, is assigned to the contact elements on both sides of the faying surface. The two factors, β and γ', are assigned with values of 2500 and 1, respectively. These are more or less judgmental values for the purposes to analyze the experimental observations and to validate the equivalent contact resistivity relationship as developed using the a-spot model. More detailed analysis of these two factors will be discussed in Chapter 4. In the numerical simulations, the applied force will cause the contact point to deform during the initial squeezing cycle. With this contact area determined by the mechanical analysis, the electrical field, including potential drops, can be calculated by the electrical-thermal analysis module. Temperature field is also calculated from the joule heating of the bulk material and the interfacial contact resistance, which is assigned automatically by the equivalent contact resistivity equation. Due to material softening, the contact area would be enlarged with the increasing contact temperature. The electrical and temperature fields are 94

123 changing as the temperature of the analysis domain varies during the weld cycle. The FEA procedure incorporates both geometrical and materials nonlinearity using an iterative routing. Boundary Conditions Mechanical Condition. A constant 450-lb. mechanical load was applied as a pressure condition at the nodes on the top surface of the upper spot. The bottom surface of the lower spot was simply supported. All other surfaces, except the contact interface, were at numerically default values (stress free surfaces). Radial displacement was restricted along the entire central axis due to axisymmetry. Electrical Condition. The electrical current flow was assumed to be uniformly distributed on the top surface of the upper spot and was permitted across the contact nodes at interfaces, while no current flow was permitted along the lateral surfaces and centerline of the model. On the bottom surface of the lower spot the electrical potential was set to be zero. A 60 Hz AC current input 95

124 was used and the RMS current strength was calculated as 13 ka. Symmetric boundary condition of zero radial potential gradients in the radial direction was imposed along the centerline of the a-spot model. Thermal Condition. Convective heat transfer was allowed along the lateral surfaces of the model and surfaces that were not in contact. The outer surfaces were subject to convective heat loss to the ambient environment. The symmetric boundary condition was imposed by setting zero radial thermal gradient along the centerline. Material Properties The material of the a-spot model used in this simulation was AA 2024-T3 aluminum alloy. Isotropic, temperature-dependent material properties of AA2024-T3 were used for both electrical-thermal and thermal-mechanical modules. These properties were specified over a temperature range from 70 o F, to 1200 o F. Mechanical, thermal, and electrical material properties of AA2024-T3 are presented in Figure 4.3 and Figure

125 Determination of Equivalent Contact Resistivity The basic idea in the determination of the equivalent contact resistivity versus temperature relationship is to use Equation (3) and the procedure shown in Figure The equivalent contact resistivity is proportional to the gradient of the potential drop across the contact interface and inversely proportional to the average current density, which is the current divided by the contact area. Using this procedure, the voltage gradient can be determined from the electrical potential drop distribution along the centerline of the a-spot model. This potential drop distribution may be approximated by plotting the measured voltage drops at the exterior sensor points in the hemispherical surfaces, which is shown in Figure The contact area cannot be determined experimentally; therefore, the calculated contact area changes may be used in the calculation of the contact resistivity values. 97

126 Figure 3.28 shows the predicted potential drop history at four points on the bottom hemispherical portion, shown as V1, V2, V3 and V4 in Figure Point 4 is close to the contact point (0.012" from the contact point before welding). The bulk resistivity of the a-spot material is responsible for the voltage drops. They follow the current cycles from the AC input. Figure 3.29 shows the potential drop between two points across the contact interface (V5 - V4). The initial distance between these two points are approximately 0.07". The RMS current input is 13 ka. The current alternation shows a phase shift from the voltage variations, which are also shown in Figure The potential drop at the interface shows its peak value of 0.82 volts at approximately 0.3 weld cycle time, as compared to approximately 0.6 volts at 0.25 weld cycle time from the experimental data (Figure 3.26). The variations of contact area during the weld cycles are shown in Figure The contact area gradually enlarged before the first half weld cycle and maintained approximately a constant value of in 2. The rate of area enlargement was particularly fast up to approximately 0.3 weld cycle. 98

127 0.03 V Voltage Drop (Volts) V V2 V Weld Time (Cycles) Figure 3.28: Potential drop history at four points in the bottom portion of the a-spot (V1 to V4) 1.00E Votage Drop at the Interface (V5-V4) (Volts) 8.00E-01 Current Input E E-01 Voltage Drop at Interface (V5-V4) E E E-01 Current Input (x 10, ka) (RMS=13KA) -4.00E-01 Weld Time (Cycles) -1.5 Figure 3.29: Voltage drop at contact interface (V5-V4) and current input (RMS = 13 ka) 99

128 Contact Area (inch 2 ) Weld Time (cycles) Figure 3.30: Predicted changes of contact area during the weld cycles 100

129 The potential drop distributions along the axial axis in the a-spot model, at three moments of 0.25, 1.25 and 2.25 weld cycle times, are shown in Figure The predicted distribution is along the centerline of the a-spot model. In the same figure, the experimental data (Figure 3.26) at the same moments are plotted for comparison purpose. One difference between the numerical and experimental models is that the measured data are taken from the surface points in the axial direction. The comparison results may be summarized as follows: (a) At the beginning of the weld cycles, the predicted voltage drop is greater than the measurement. This is probably due to the difference in initial surface condition between the two models. In the FEA model, the bulk contact resistivity factor β is chosen to be 2500, which is probably too high. It is also possible that the measurement at this early stage is inaccurate due to instrument limitations. (b) When welding continues into 1.25 and 2.25 cycle times, the comparison reverses the trend between the predicted and experimental data. The predicted voltage drops at this later stage of weld cycles are almost half of the magnitude of the measured values. This may indicate the γ factor of one is too high. As 101

130 suggested by Figure 3.19, reducing the γ factor would substantially increase the resistivity value. Nevertheless, the functional relationship of the equivalent contact resistivity holds well as demonstrated by this comparison. To determine the equivalent contact resistivity from the FEA a-spot welding simulations, the basic definition and procedure as specified in Figure 3.12 was again used. Figure 3.29 defines the potential gradient by dividing the voltage drops by the distance between V5 and V4, which is a function of weld time. Figure 30 defines the contact area also as a function of weld time. The equivalent contact resistivity can therefore be plotted as a function of time using Equation (3). Figure 3.32 shows such a plot. The equivalent contact resistivity reaches its peak value of 7.0 µohm-inch at approximately 0.35 weld cycle time, which is 3 orders of magnitude lower than the equivalent contact resistivity values as shown in Figures from 14 through 19. Since the FEA a-spot welding model uses a specific pair of values for β and γ factors, the results shown in Figure 3.32 clearly indicates a non-convergent answer by these arbitrary chosen values. An iterative numerical procedure must be adopted to establish the convergence between the resistivity values and the 102

131 values of β and γ. This iterative procedure was conducted using the actual resistance spot welding model and experimental analysis to determine the convergence. Although the order of magnitude of the calculated equivalent contact resistivity is off by 3 orders of magnitude, the curve still reflects the characteristic feature of the welding process. High contact resistivity exists before the initial half weld cycle, which is expected to be the norm for resistance spot aluminum welding. Figure 3.33 plots changes in contact area and the temperatures at four nodal points (# ) at the faying surface. Node #4182 is the contact center and other nodal points are 0.028" (#4181), 0.056" (#4180) and 0.085" (#4179) from the contact center. The initial contact area prior to welding is approximately in 2 or 0.028" radius. Therefore, nodes #4181 and #4182 are always within the contact area. The maximum contact area is at the end of the third weld cycle, in 2 or 0.064" radius. At the first half weld cycle, the contact area is about in 2 or 0.062" radius. By examining these numbers, node #4179 is always outside the contact area. Because the contact area enlarges 103

132 during welding, node #4180 (0.056" from center), which is originally not in contact, becomes a contact point at approximately 0.2 weld cycle time (when the contact area reaches 0.01 in 2 or 0.057" radius). Figure 3.33 shows an interesting observation that the weld nugget starts at a small distance from the contact center (e.g " at approximately 0.3 weld cycle time). This donut-shape weld nugget moves inward very quickly to reach the center in about 0.05 weld cycle. Nodes #4179 and #4180 never become melted during the entire weld cycles because the peak temperature never goes beyond the melting temperature of the material. The nodal temperatures fluctuate with the AC current form and are unevenly distributed over the contact surface, especially during the initial first half cycle. Temperatures within the contact area become close to uniform after the first half weld cycle because of high conductivity of aluminum. Average temperature curve is plotted to be the reference temperature for determining the dynamic contact resistance versus temperature relationship. Dynamic contact resistance is determined by dividing the voltage drops between V5 and V4 (Figure 3.29) by the welding current for the duration of 3 weld 104

133 cycles. Since both the voltage drop-time and the average temperature-time curves are plotted on the same time scale, the voltage drop-time relationship can therefore be translated into the contact resistance versus average temperature relationship (Figure 3.34). It is an interesting observation that the resistance-temperature relationship is almost a linear-increasing curve with temperature up to approximately 0.3 weld cycle time. This reflects the Wiedemann-Franz-Loretz law that is represented by the proportional temperature term in Equation (9). After that weld time, the contact resistance does not change with temperature, which is within the range between 500 o F and 800 o F. This phenomenon reflects the contact area softening term in Equation (9). Beyond this softening temperature, the a-spot model does not show numerical convergence and the model starts to collapse. 105

134 0.80 Voltage Drop (volts) FEM W eld Time=0.25 Cycle Expt. Weld Time=0.25 Cycle Expt. Weld Time=1.25 Cycle Expt. Weld Time=2.25 Cycle FEM W eld Time=1.25 Cycle FEM W eldtime=2.25 Cycle Location (inch) Figure 3.31: Potential distributions along y-axis of experimental and numerical results at different weld time 106

135 8.0E E-06 Dynamic Contact Resistivity (ohm-inch 6.0E E E E E E E Weld Time (cycles) Figure 3.32: Calculated dynamic contact resistivity in FEA simulation 107

136 Contact Area (inch 2 ) Node 4181 Contact Area Contact Center (Node 4182) Temperature ( 0 F) Node 4180 Average Temperaure Node Weld Time (cycles) Figure 3.33: Temperature history of four nodes at interface 108

137 Resistance (µohm) Before Reaching the Maximum Resistance ( <0.3 Cycle ) 10.0 After the Maximum Resistance Reached ( >0.3 Cycle ) Temperature ( 0 F) Figure 3.34: Correlation between dynamic contact resistance and average temperature at contact determined from the FEA simulation 109

138 3.4.3 Summary 1. For the numerical analysis, the equivalent contact resistivity must be used because the contact resistance does not provide the mechanism to be incorporated in the numerical model. The virtual contact volume concept is an engineering approach to most of the contact problems in the numerical analysis. 2. The a-spot welding model validates the generic relationship between the equivalent contact resistivity and the contact temperature derived from the base model. Both the numerical and experimental analyses show the same relationship that is defined by the theoretical hypothesis of a-spot model. 3. The magnitude of the equivalent contact resistivity values determined from the a-spot welding model is 3 orders of magnitude lower than the theoretical predictions. This is due to the arbitrary values of β and γ factors. However, the characteristic relationship is demonstrated consistency with the theoretical hypothesis of the a-spot model. 4. Under the conditions defined for the a-spot model studied, the contact areas melt from a distance from the center and form an initial donut-shape weld 110

139 nugget. This molten nugget grows towards center and then outwards. Contact resistance plays the critical role within the first 0.3 weld cycle duration. The resistance increases with temperature due to the Wiedemann-Franz-Lorentz phenomenon. However, once softening of the contact area starts this phenomenon diminishes and the contact resistance becomes a constant value. 5. The β and γ factors are to be further investigated using an integrated numerical and experimental approach, which is discussed in Chapter

140 CHAPTER 4 NUMERICAL SIMULATION PROCEDURE FOR RSW ALUMINUM ALLOYS In order to calibrate and quantify those parameters, β, γ, and T 0 in Equation (9), a FEA model was developed to simulate the process of resistance spot welding aluminum alloys. First, a FEA quarter model (preliminary study) with different dynamic contact resistivity inputs, calculated by Equation (9), was established for numerical procedure development using respective constant value for the contact area correlation factor (γ = 1) and the reference temperature (T 0 = 0 o F). The bulk resistivity factor, β was incorporated as a variable in the simulation analysis. This FEA quarter model simulated the weld nugget growth under the influence of different β values. 112

141 With the basic numerical procedure validated by the quarter model analysis, the resistance welding process was analyzed using a half model with the joint faying surface implemented as a contact pair. The weld nugget was defined by the liquidus and solidus temperatures, which simulated fully molten and partially molten zones. The effects of AC/DC current input and current level were studied. The influences of parameters (β, γ, and T 0 ) in Equation (9) were analyzed. The Cu/Al interface behavior was also taken into consideration. 4.1 Finite Element Quarter Model The Quarter Model An axisymmetric finite element, quarter model for electrical-thermal and thermal-mechanical modules was developed to simulate resistance spot welding aluminums. In order to reduce the element numbers and calculation time, the quarter model was analyzed for the numerical validation purpose. Figure 4.1 presents the mesh for the entire geometry of the electrode and aluminum sheet 113

142 generated by IDEAS software and consisted of 2841 elements and 2973 nodes. The face diameter of the truncated electrodes (FA25Z00) was 0.25 in. and the aluminum workpiece (AA2024-T3) was 0.05 in. thick. In this model, a layer of contact elements (virtual contact volume) with 10-3 in. thickness was used to simulate the contact surface between electrode and workpiece and the faying surface between workpieces. The ABAQUS software was employed for this finite element simulation model and the element types of DCAX4 and CAX4 were chosen for electrical-thermal and thermal-mechanical modules, respectively. 114

143 Figure 4.1: Mesh of the entire geometry of the quarter model 115

144 Boundary Conditions Mechanical Condition. The mechanical load, 800 lbs, was applied as a pressure input on the nodes at the end of the electrode. This load was made time-dependent during the analysis, increased linearly during squeeze period, and was held constant during welding, holding, and cooling periods. The bottom surface of the workpiece (joint faying surface) was assumed to be simply supported. All other lateral surfaces, except the electrode-workpiece contact surface, were specified as stress-free. Radial displacement was restricted along the entire central axis due to axisymmetry. Electrical Condition. The electrical current flow was assumed to be uniformly distributed on the top surface of the electrode and flowed through the contact areas at both the electrode/workpiece and workpiece/workpiece (bottom of the workpiece in this quarter model) interfaces. The current strength was given according to the actual welding cycles used in the experimental study. The potential boundary condition was imposed as a voltage drop between the end of the electrode and the joint faying surface (bottom of the workpiece in the model). The reference potential boundary was located at the faying surface and assumed 116

145 to be zero along the entire length during the entire weld cycles. Symmetry boundary condition was incorporated as zero radial potential gradient along the axisymmetry centerline. Thermal Condition. The thermal boundary condition assumed in natural convention with air along all electrode and workpiece free surfaces. A forced cooling condition was simulated for the electrode inner surfaces due to water coolant in the electrode cavity. Symmetry boundary condition was specified as zero radial thermal gradient along the model centerline. Material Properties Isotropic, temperature-dependent material properties of 2024-T3 aluminum alloys, copper electrodes, and contact elements were used in the FEA model and the electrical-thermal and thermal-mechanical analysis procedures. These properties were specified over a temperature range from room temperature, 70 o F, to above melting temperature, 1200 o F. Four sets of equivalent contact resistivity 117

146 correlation (Figure 4.2), which were calculated from Equation (9) with different β values, 400, 800, 1000, and 1200 while the respective values of γ and T 0 being 1 and 0 o F, respectively, were studied. In the numerical procedure, the inverse values of the equivalent contact resistivity were used as the electrical conductivity of the contact elements. The electrical conductivity values were applied through a tabulation format in the numerical procedure. The thermal and bulk electrical material properties of both 2024-T3 aluminum alloy and copper electrode are presented in Figure 4.3 through Figure

147 3.50E E-03 β = 1200 ρ = β(4.53x10-8 )T Exp(-6.532x10-3 )T Contact Resistivity (ohm-in.) 2.50E E E E-03 β = 1000 β = 800 β = E E Temperature (DegF) Figure 4.2: Equivalent contact resistivities calculated from equation (9) with different β values (γ = 1, T 0 = 0 o F) 119

148 Initial Condition At the beginning of the squeeze time, the initial values of stress and electrical potential were set to be zero over the entire model region, while the temperature was specified as room temperature, 70 o F. After applying the electrode force, the electrode indentation and the contact was established at the faying surface. The equivalent contact resistivity was activated when the weld cycle started. 120

149 Weld Schedule The weld schedule and parameters in this FEA quarter model simulation are listed as follows: Squeeze time: 15 cycles Weld time: 4 cycles Hold time: 24 cycles Current level: 33 ka (RMS) Electrode force: 800 lbs During the weld cycles, the weld nugget development was recorded by plotting the nugget isotherms. 121

150 Thermal Conductivity (BTU/in.-sec-DegF, 10E-3) Temperature (DegF) (a) Continued Figure 4.3: Electrical and thermal properties of aluminum alloy 2024-T3: (a) thermal conductivity (b) specific heat (c) electrical resistivity 122

151 Figure 4.3 continued Specific Heat (BTU/lb-DegF) Temperature (DegF) (b) Electrical Resistivity (ohm-in. 10E-6) Temperature (DegF) (c) 123

152 Young's Modulus (psi, 10E6) Temperature (DegF) (a) Continued Figure 4.4: Mechanical properties of aluminum alloy 2024-T3: (a) Young s modulus (b) yield stress (c) thermal expansion coefficient 124

153 Figure 4.4 continued Yield Stress (ksi) Temperature (DegF) (b) Thermal Expansion Coefficient (10E-5) Temperature (DegF) (c) 125

154 5.40E E-03 Thermal Conductivity (BTU/in.-sec-DegF) 5.00E E E E E E Temperature (DegF) (a) Thermal conductivity Continued Figure 4.5: Electrical and thermal properties of copper electrodes: (a) thermal conductivity (b) specific heat (c) electrical resistivity 126

155 Figure 4.5 continued Specific Heat (BTU/lb-DegF) Temperature (DegF) (b) Electrical Resistivity (ohm-in., 10E-6) Temperature (DegF) (c) 127

156 2.00E E E E+07 Young's Modulus (psi) 1.20E E E E E E E Temperature (DegF) (a) Continued Figure 4.6: Mechanical properties of copper electrodes: (a) Young s modulus (b) yield stress (c) thermal expansion coefficient 128

157 Figure 4.6 continued Yield Stress (ksi) Temperature (DegF) (b) Thermal Expansion Coefficient (10E-6) Temperature (DegF) (c) 129

158 4.1.2 Results/Discussion The validations of the FEA numerical procedure including the mesh design, boundary values, and the nonlinearity of material may be demonstrated by evaluating the general behaviors of the predicted electrical, thermal and mechanical responses from the resistance spot welding process. For this purpose, the equivalent contact resistivity factors, β, γ, and T o, are assigned values of 1200, 1 and 0 o F, which are still arbitrary at this time. Electrical Potential Figure 4.7 shows the predicted electrical potential fields at the end of each weld cycle (1-4 cycles). Five iso-potential lines (0.002, 0.004, 0.006, and volts) are plotted in each graph. The electrical potential field shifts away from the workpiece-to-workpiece contact surface as its contact resistance reduces with increasing weld time. 130

159 Figure 4.7: Electrical potential distribution during weld cycles (β = 1200, γ = 1, and T 0 = 0 o F) 131

160 At the end of first weld cycle, the voltage drop (0.002 volts) across the contact surface is obvious. This potential drop line moves away from the contact surface and becomes flattened during the 2nd and 3rd weld cycles. This indicates the diminishing significance of the contact resistance as the contact area enlarges due to softening. The bulk contact resistivity and the bulk material resistivity maintain the volts potential line, but the potential drop near the contact is reduced. The potential drop across the electrode-to-workpiece contact surface remains at volts at all weld cycles with a slight tendency of drifting upwards. Since the electrode is water cooled, the electrode-workpiece contact interface maintains at relative lower temperature than the workpiece-to-workpiece contact interface, change in the contact resistance at this interface is relatively small. After the 2nd weld cycle, the voltage drops across the electrode-workpiece interface has somewhat stabilized. The electrical potential lines of 0.006, and (volts) shift up during the first two weld cycles and move down a little during the latter two weld cycles. This phenomenon is due to diminishing contact resistance at the workpiece-to- workpiece interface after the 2nd weld cycle. 132

161 Weld Nugget Growth Weld nugget is defined by an iso-thermal contour of melting temperature (850 o F). Figure 4.8 shows the iso-thermal contours of the temperature field at end of each weld cycle. The temperature field expands as the weld time increases. The weld nugget has already formed at the end of the first weld cycle. This nugget grows in both radial direction and the axial (thickness) direction. This also indicates disappearing workpiece-to-workpiece contact interface. This phenomenon is already incorporated in the equivalent contact resistivity versus temperature relationship, as shown in Equation (9). When contact interface temperature is higher than the plastic temperature of aluminum (>200 o F), the equivalent contact resistivity has the same order of magnitude as the bulk material resistivity. This would reflect the diminishing contact interface in the numerical analysis procedure. 133

162 Weld Nugget (a) 1st Cycle (b) 2nd Cycle (c) 3rd Cycle (d) 4th Cycle (Expulsion) Figure 4.8: Weld nugget growth of FEA quarter model simulation (β = 1200, γ = 1, and T 0 = 0 o F) 134

163 At end of the 4th weld cycle, the nugget thickness has reached the electrode-to-workpiece contact interface. This would indicate a condition for nugget expulsion. In this dissertation, nugget expulsion will be defined by the opening displacement at the nugget periphery, which will be discussed in Chapter 5. In the development of a weld lobe for resistance spot welding, the nugget diameter is often used as the basis for weld strength, provided that the weld is sound. Figure 4.9 summarizes the predicted nugget growth behavior of four different β values (γ=1 and T o =0 o F) used for the equivalent contact resistivity incorporated in the quarter-model analysis. For a smaller β of 400, the nugget actually starts to form at end of the 2nd cycle. For other higher values, weld nugget has already started developing at end of the 1st weld cycle. The weld nugget continues to grow as the weld time increases. Figure 4.9 also shows an observation that the effect of β value on the weld nugget development reduces as the value increases. Comparing the rate of increase due to increase of β (β=400, 800 and 1200 and β=800, 1000, and 1200), 135

164 it appears an asymptotic trend when β approaches This behavior is also shown in the generic equivalent contact resistivity versus temperature relationship, Equation (9) and Figure Joint Indentation and Residual Stresses The thermal-mechanical analysis is decoupled from the electrical-thermal analysis. It retrieves the temperature data from the electrical-thermal analysis at incremental time intervals. The temperature field at each time interval results in a strain field, which may or may not include both elastic and plastic components depending the temperature distribution and gradients. Two iterative numerical procedures are incorporated in this mechanical analysis. The temperature dependent thermal and mechanical nonlinearities are iterated on the given temperature dependent functions. The incremental plastic strains are iterated based on the plastic strain-total strain plasticity relations. The Prandtl-Reuss plasticity constitutive equations (Ref.) are used. 136

165 Figure 4.10 shows typical, predicted results of electrode indentation and residual stress distribution in the workpiece after welding and electrode removal. The indentation is caused by the plastic deformation of the workpiece. Von Mises equivalent stresses are plotted as iso-stress contours. The residual stresses vary from below 10 ksi to greater 40 ksi. The maximum stress is in an annual-ring area along the edge of the nugget periphery and at the edge of the electrode-to-workpiece contact area (cusped zone). Figure 4.11 shows an experimental weld nugget with the electrode indentation similar to the predicted shape shown in Figure. 4.10, although the welding conditions of the two cases were not quite identical. AA2024-T3 was studied in both cases. Summary The quarter model predicted the behaviors of the resistant spot aluminum weld reasonable well in accordance with the expected physical behaviors. A more rigorous FEA half model will be studied using the same mesh design, numerical procedure, and equivalent contact resistivity versus temperature relationship. 137

166 0.25 Belta = Belta = 800 Belta = 1000 Nugget Diameter (in.) Belta = Weld Time (cycles) Figure 4.9: Nugget size growth with various values of β in FEA quarter model simulation (γ = 1, T 0 = 0 o F) 138

167 Figure 4.10: Electrode indentation and residual stresses distribution in FEA quarter model simulation (β = 1200, γ = 1, and T 0 = 0 o F) 139

168 Figure 4.11: Cross-section of aluminum alloys 2024-T3 weld nugget (26.2 ka with 0.2 in. tip diameter, dome type electrode, squeeze time: 60 cycles; weld time: 8 cycles; hold time: 60 cycles, electrode force: 750 lbs) 140

169 4.2 Finite Element Half Model In Section 4.1, the simple FEA quarter model validated the numerical procedure. The generic equivalent contact resistivity versus temperature relationship, Equation (9), was evaluated again based on the predicted results and the anticipated physical responses. In this section, an axisymmetric, FEA half model was used to perform a parametric study on the β, γ and T o factors. The reasons for using the half-model are the following: (1) The reference potential boundary is set along the bottom surface of the workpiece, which is the joint faying surface. Since the electrical potential actually varies at this interface during the critical first weld cycle, this assumption may cause inaccuracy in the predicted results, especially in the electrical potentials. (2) The simply supported boundary condition along the bottom of the single workpiece in the quarter model would be too rigid for the contact area to deform as it would be if both workpieces are modeled. The half model includes both workpieces and the electrodes. 141

170 4.2.1 The Half Model The meshed geometry of the half model with 5798 nodes and 5257 elements is illustrated in Figure This axisymmetric finite element model consisted of two truncated electrodes (FA25Z00, RWMA Class 2) with 0.25-inch face diameter and the aluminum workpieces with 0.05-inch thickness. Three contact pairs were used to simulate the electrode-workpiece contact surfaces and the workpiece-workpiece faying surface. Element types of DCAX4 and CAX4 were employed for electrical-thermal and thermal-mechanical modules, respectively. Boundary Conditions Mechanical Condition. An 800-lb. mechanical load was applied as a pressure condition at the nodes on the top face of the upper electrode. This load was applied in accordance with the weld schedule. It was increased linearly during the squeeze period and was held constant during the welding, holding, and cooling periods. All the exterior surfaces including the electrodes and the workpieces and the interior surface in the electrode cavity, except the top and 142

171 bottom faces of the electrode and the contact interface, were stress-free surfaces. The contact elements were used for the contact pairs along the faying surface. These contact pairs will automatically determine the contract area since the contact pairs would allow the other surfaces not in contact to move freely. The radial displacement was restricted along the central axis for the axisymmetry condition. 143

172 Figure 4.12: Mesh of entire geometry of the half model 144

173 Electrical Condition. The electrical current flow was assumed to be uniformly distributed at the top surface of the upper electrode and was permitted to flow across the contact areas at both the electrode/workpiece and workpiece/workpiece interfaces and, eventually reaching the bottom surface of the lower electrode. All other surfaces were at numerical default value (zero gradient normal to the surface). The current form was either AC or DC following the designed current variation used in the experimental study. The bottom of the lower electrode was set to be zero for the reference electrical potential. The centerline of the model was again axysemmetric with zero potential gradient in the radial direction. Thermal Condition. The thermal boundary condition was the same as that used in the quarter model, except that the boundary condition on the upper electrode was applied to the lower electrode surfaces. 145

174 Material Properties Isotropic, temperature-dependent material properties of 2024-T3 aluminum alloys and copper alloy (RWMA Class 2) were used for both electrical-thermal and thermal-mechanical modules. These properties were specified over a temperature range from room temperature, 70 o F, to above melting temperature, 1200 o F. Mechanical, thermal, and electrical material properties of both 2024-T3 aluminum alloy and copper electrodes are presented in Figure 4.3 through Figure 4.6. Due to the application of contact pairs, special gap material properties, such as gap conductance and gap electrical conductance were required for the electrical-thermal module. In ABAQUS software, gap conductance, k, and gap electrical conductance, σ g, are defined as: q = k(θ A θ B ) = λ (θa θ B ) (12) t J = σ g (ϕ A ϕ B ) = 1 (ϕa ϕ B ) (13) ρt In Equation (12), q is the heat flux per unit area crossing the interface from point A on one surface to point B on the other; θ A and θ B are the temperatures of 146

175 the points on the surfaces; λ is the thermal conductivity; t is the gap thickness; and k is the gap conductance. Gap conductance, k, can be obtained by dividing thermal conductivity, λ,with gap thickness, t. In Equation (13), J is the electrical current density flowing across the interface from point A on one surface to point B on the other; ϕ A and ϕ B are the electrical potentials at points A and B; ρ is the electrical resistivity; t is the gap thickness; and σ g is the gap electrical conductance which is equal to the inverse value of electrical resistivity, ρ, multiplied by gap thickness, t. In this model, the gap thickness, t, was assumed as 10-3 in. Various values of dynamic contact resistivity calculated by Equation (9) with different values of parameters were inputted through a tabular form. The inverse values of the product of the electrical resistivity and the gap thickness for the temperature range from room temperature, 70 o F, to above melting temperature, 1200 o F, were used as the gap electrical conductance of contact pairs and were inputted as equations. Due to the programming bugs inherited in the function of the contact pairs, ABAQUS software program is unable to track peak temperatures automatically 147

176 (i.e. this problem was recognized by ABAQUS at the time when this dissertation study was conducted). In this simulation, a user's subroutine was developed to retrieve the peak temperature automatically as a field variable to overcome this problem. Initial Conditions At the beginning of the squeeze time, the initial values of stress and electrical potential were set to be zero, while the temperature was specified as room temperature, 70 o F. After the electrode force application, the electrode indentation and the contact established at the faying surface became the geometric boundary conditions for welding cycle. Welding Schedule The welding schedule and parameters used in this FEA half model are almost the same as those for the quarter model, except for the electrical current input. In this half model, electrical current input was applied in accordance with the actual AC function and in a DC form with the RMS current. 148

177 4.2.2 Determination of Nugget Size One of the special characteristics of AA2024 alloy is the existence of a wide solidus-liquidus gap, which is defined as the difference between liquidus temperature (1180 o F/638 o C) and solidus temperature (936 o F/502 o C). Initially, it melts when temperature reaches the solidus temperature. When temperature increases from the solidus temperature to the liquidus temperature, the alloy melts partially. The alloy is fully melted when temperature exceeds the liquidus temperature. It is common to define the weld nugget by the liquidus temperate in numerical simulations. Figure 4.10 shows an experimental weld nugget cross-section of aluminum alloy 2024-T3, which defines both fully molten and partially molten regions. These regions are distinctly presented due to the wide solidus-liquidus gap. 149

178 4.2.3 Effect of AC/DC Current Input Traditionally AC current is used for the resistance spot welding. Recently, the mid-frequency DC or simply DC current has been used and studied by the industrial users or the academic researchers. When resistance welding aluminum alloys using the DC current, a Peltier effect due to the electrode polarity has been reported. In this half-model study, both AC and DC current inputs were investigated. However, the Peltier effect was not considered in this study. Figure 4.13 illustrates the welding schedule of the AC current input model. The maximum current was amps, as converted from RMS current. When the values of β, γ, and T 0 were selected as 800, 1, and 70 o F, the temperature contours at times indicated by A, B, C, and D are shown in Figure 4.14(a)-(d). These times are at approximately 0.4, 0.8, 2.35 and 2.88 weld cycle, respectively. No mechanical deformation was analyzed in this simulation. Because of the low β value (800) assumed in this simulation, weld nugget as defined by the liquidus temperature did not start until after completion of the 2nd weld cycle (C). However, partial melting is shown to start in distance from the 150

179 joint center as a donut ring at 0.8 weld cycle (B). The peak temperature was reached at 2.88 cycles (D), which was almost at end of the weld schedule. At this time, the solidus temperature contour reached the edge beneath the electrode contact. In additional to the completed molten nugget zone (light gray color), the partially molten zone occupied almost the entire volume of the joint beneath the electrode because of the large temperature gap between the liquidus and solidus temperatures of the AA2024 alloy. This predicted weld nugget situation would suggest an expulsion condition. Figure 4.15 and Figure 4.16 compare the temperature evaluations at two points at the contact interface predicted by the AC and DC current input simulations. Figure 4.15 shows the temperatures at the center point of weld nugget. Figure 16 shows the temperatures at an interface location where reaches the solidus temperature at 1.2 weld cycle time. The DC current input level was set to the RMS value (33 ka) of the AC current input (46.68 ka max.). 151

180 In both figures, it is shown that local temperature fluctuations existed in the AC current input model. Due to the cyclic variation of current input, the peak temperature of simulation with AC current input did not occur at the end of heating, unlike DC current input model. It occurred before the end of weld cycles and showed higher temperatures than that predicted with DC current. The same two figures also show a peak temperature difference of approximately 40 o F between these two locations at the contact interface. Both locations completely melted near the end of the weld cycles. Figure 4.17 presents the temperature evaluation at three points as indicated by A, B and C along model s centerline. These three points represent the nugget center (C), the location where melting starting at 1.5 weld cycle (B), and the location where melting starting at 2.3 weld cycle (A). The temperature fluctuations reflected the AC variations. Point A was within the partial molten zone and points B and C were within the completely melted weld nugget. The peak temperatures were reached just prior to the end of the weld cycles. 152

181 A (0.4 cycles) (2.35 cycles) C (3 cycles) B D (0.8 cycles) (2.88 cycles) Figure 4.13: Welding schedule of AC current input model 153

182 (a) Continued Figure 4.14: Temperature contour of AC current input Model (β=800, γ=1, T o =70 o F, 33 ka RMS): (a) Time A: 0.4 cycles ( sec.) (b) Time B: 0.8 cycles ( sec.) (c) Time C: 2.35 cycles ( sec.) (d) Time D: 2.88 cycles (0.048 sec.) 154

183 Figure 4.14 continued (b) (c) Continued 155

184 Figure 4.14 continued (d) 156

185 ºC End of weld Liquidus temp Solidus temp sec ( 1 sec. = 60 cycles) Figure 4.15: Temperature history of AC and DC current input simulations at the center point of the weld nugget (β=800, γ=1, T o =70 o F, 33 ka RMS) 157

186 ºC End of weld Liquidus temp Solidus temp sec (1 sec. = 60 cycles) Figure 4.16: Temperature history of AC and DC current input simulations at the solidus front point (β=800, γ=1, T o =70 o F, 33 ka RMS) 158

187 ºC End of weld Liquidus temp Solidus temp A B C sec (1 sec. = 60 cycles) Figure 4.17: Temperature history of AC current input model at three different points in weld nugget (β=800, γ=1, T o =70 o F, 33 ka RMS) 159

188 Figure 4.18 shows the temperature distributions along the joint faying surface at four instants: 0.4, 0.8, 2.4 and 3 weld cycles, respectively. The weld nugget started to melt after about 1 weld cycle time. The nugget reached its maximum dimension near the end of the weld cycles. The completely molten nugget diameter was less than 3mm (0.118 ); however, the diameter of the partially molten zone was approximately 6mm (0.236 ). Temperatures dropped quickly as the distance increased from the weld nugget. Figure 4.19 illustrates the comparison of nugget size predicted by the AC and DC current input models. The weld nugget as defined by the liquidus temperature is larger in AC analysis (diameter: and depth: ), as compared to that predicted by DC analysis (diameter: and depth: ). However, both AC and DC models predict the same boundary location of partially molten zones, which are beneath the peripheral edge of the electrodes. The current form does not appear to influence the temperature fields outside the weld nugget. 160

189 ºC Liquidus temp Solidus temp mm (1 in. = 25.4 mm) Figure 4.18: Temperature profile of AC current input model at interface (β=800, γ=1, T o =70 o F, 33 ka RMS) 161

190 Solidus Temp. D DC CURRENT LiquidusTemp. AC CURRENT Nugget depth: mm (0.048 in.) Nugget diameter: 2.977mm (0.117 in.) Nugget depth: mm (0.056 in.) Nugget diameter: mm (0.141 in.) Figure 4.19: Comparison of nugget size between AC and DC current input models (β=800, γ=1, T o =70 o F, 33 ka RMS) 162

191 4.2.4 Temperature Evolution at Joint Faying Surface Figure 4.20 shows temperature evolution along the joint faying surface under the condition of: β=800, γ=1, T o =70 o F, and 33 ka RMS for the first 1.5 weld cycle period. The temperature curves are plotted at each quarter cycle increment. The general trend shows that higher temperature is at the contact interface, which is confined within the electrode periphery boundary. The faying surface temperature drops quickly across this electrode edge over a short distance and continues to decrease at slower rate as the distance further increases. At the end of the first quarter cycle, the maximum temperature (390 o F or 200 o C) is at the center of the contact interface. Between the 1st quarter cycle and the 2nd quarter cycle, the rate of temperature increase slow down due to the decreasing current magnitude. The rate of temperature increase is picked up the speed again due to increasing current strength as indicated in Figure This trend continues for the remaining quarter cycles. However, the differential speed of the temperature increase is reduced due to softening of the contact surface, which reflects the down turn slope of the equivalent contact resistivity 163

192 versus temperature relationship. At the end of the 1.5 weld cycle, partial melting has already started. The solidus nugget diameter is approximately 0.09" (2.3mm). Since most of the contact resistance would change during the first half cycle, it is of interest to observe the temperature evolution over this half weld cycle. Figure 4.21 shows that temperature at the contact interface continuously increases up to 0.4 weld cycle (0.006 second) and then begins to decrease, although the current magnitude still is on the rise. This phenomenon is due to much reduced equivalent contact resistivity when the contact temperature is higher than 200 o F as shown by the equivalent contact resistivity versus temperate relationship, Equation (9). The reduction in the contact resistance overcomes the effect of current increase. 164

193 ( x 1000 o C) 5 Q 6 Q 3 Q 4 Q Q: quarter cycle Temperature 2 Q 1 Q mm (1 in. = 25.4 mm) Figure 4.20: Temperature evolution along a faying surface during first one and half cycles (β=800, γ=1, T o =70 o F, RMS current 33 ka) 165

194 1000 C (1 sec. = 60 cycles) Temperature sec sec sec Electrode radius (3.2 mm) sec sec sec sec sec mm (1 in. = 25.4 mm) Figure 4.21: Temperature evolution along a faying surface during first half cycle (β=800, γ=1, T o =70 o F, RMS current 33 ka) 166

195 4.2.5 Parametric Study To this section, the FEA model and the numerical procedure have been validated, so as the equivalent contact resistivity versus temperature relationship, Equation (9). In order to establish the parametric database for the correlation factors (β, γ, and T o ), a parametric study on these factors, which consists of a total of 30 combinations, were performed. The axisymmetriic half-model with AC current input was used in this parametric study. The experimental comparison study will be discussed in Chapter 5. The ranges of the three factors for the Al/Al interface studied are as follows: β factor: 400, 600, 800, 1600, 2500, and γ factor: 0.5, 1.0, 1.5 and 2.0 T o reference temperature: 32 o F and 70 o F For the Cu/Al contact interface, the equivalent contact resistivity versus temperature relationship, Equation (9) was also assumed and applied with the three factors as follows: β factor: 1, 10,

196 γ factor: 1.0 T o reference temperature: 32 o F and 70 o F The parametric studies are evaluated based on the predicted results of (1) weld nugget size as defined by the liquidus temperature and (2) the maximum electrical potential drop between the electrodes. The predicted results are compared with the experimentally measured data to assess the quantity of factors, which will be discussed in Chapter 5. Bulk Contact Resistivity Factor, β It is known that the magnitude of the equivalent contact resistivity will increase with increasing value of the Bulk Contact Resistivity Factor (β). When the RMS current input is equal to 33 ka and the values of γ and T 0 were set to 1 and 32 o F (0 o C), the effect of β on the peak temperature contour is presented in Figure 4.22(a)-(e). Figure 4.23(a)-(c) show the effect of β on peak temperature contour when the RMS current input is equal to 33 ka and the values of γ and T 0 were set to 1 and 70 o F (21 o C). The analysis of these temperature maps suggests the following general phenomena: 168

197 (1) The higher the reference temperature (32 o F versus 70 o F), the larger the nugget size. However, the increase is insignificant as compared to the effect of the β factor. (2) The β factor has significant influence on the nugget size as defined by the liquidus temperature. However, its effect on the solidus boundary is much less significant. This is due to the flow path of electrical current restricted within the electrode tip diameter. Temperature drops off very quickly in the workpiece material outside this electrode-bounded region. 169

198 (a) Continued Figure 4.22: Effect of β on weld nugget size (γ = 1, T 0 = 32 o F (0 o C), and I RMS = 33 ka): (a) β = 400 (b) β = 600 (c) β = 800 (d) β = 1600 (e) β =

199 Figure 4.22 continued (b) (c) Continued 171

200 Figure 4.22 continued (d) (e) 172

201 (a) Continued Figure 4.23: Effect of β on weld nugget size (γ = 1, T 0 = 70 o F (21 o C), and I RMS = 33 ka): (a) β = 800 (b) β = 1600 (c) β =

202 Figure 4.23 continued (b) (c) 174

203 Figure 4.24 and Figure 4.25 illustrate the effect of β on temperature evolution at the center point of weld nugget and a point near the electrode edge with the other two factors being 1 and 32 o F, respectively. Figure 4.24 shows that nugget center location reaches liquidus temperature earlier during the weld cycles when β is large. For β=400 this central point barely reaches the liquidus temperature at almost the end of the weld cycles. Figure 4.25 further suggests that β=400 or 600 results in cold weld nugget. The liquidus temperature contour approaches to the electrode edge point only when β equals to or greater than 800. When β=2500 the electrode edge point reaches liquidus temperature at end of the 1st weld cycle. However, this edge solidifies and remelts as the electrical current fluctuates. For β=800 this electrode edge point melts at end of the 3rd weld cycle. Figure 4.26 summarizes the diameters and depths of the weld nugget predicted using different β values. The nugget dimensions are defined by both liquidus and solidus temperatures to identify complete melting and partial melting. The electrode diameter and the workpiece thickness are also indicated in the figure for comparison purpose. For the weld schedule analyzed, the solidus 175

204 diameter of all β values are greater than 85% of the electrode diameter. However, the liquidus diameters are about 80%, 50%, 40%, and 0% of the electrode diameter for β=2500, 800, 600 and 400, respectively. The nugget size is also evaluated by its thickness to workpiece thickness ratio. The solidus depth covers the entire workpiece thickness for all β values. However, the liquidus depth is less than 40% when β is smaller than 600. The liquidus depths are 100% and 60% of the workpiece thickness for β=2500 and 800, respectively. From these observations of the nugget dimensions, It is apparent that the β values would probably be equal to or greater than

205 ºC End of weld Liquidus temp Solidus temp sec (1 sec. = 60 cycles) Figure 4.24: Effect of β on temperature history at the center point of weld nugget (γ = 1, T 0 = 32 o F, and I RMS = 33 ka) 177

206 ºC End of weld Liquidus temp Solidus temp sec (1 sec. = 60 cycles) Figure 4.25: Effect of β on temperature history at the solidus front point (γ = 1, T 0 = 32 o F, and I RMS = 33 ka) 178

207 Diameter (mm) Electrode diameter Joint thickness solidus diameter solidus depth liquidus diamter liquidus depth (1 in. = 25.4 mm) β B Figure 4.26: Nugget size determination for different β values (γ = 1, T 0 = 32 o F, and I RMS = 33 ka) 179

208 Contact Area Correction Factor, γ The contact area correction factor (γ) is assumed to depict the softening effect of asperities and is proportional to the applied load. For constant β and T 0, varying γ values will change the slope of the dropping section of the equivalent contact resistivity curve, as shown by Equation (9) and Figures 3.18 and 19. When γ increases, the effect of softening is stronger and then the equivalent contact resistivity decreases. Figure 4.27 illustrates the effect of γ on temperatures based on the conditions of: current RMS 33 ka, β=5000, and T o =32 o F. The extreme β value and γ values are chosen in this comparison. It is observed that even with high β value weld nugget does not form when γ is also large. Figure 4.27(b) does not show any liquidus nugget when γ=2.0. When γ = 1.5 is chosen, Figure 4.27(a) shows small liquidus nugget. In either case, the solidus nugget approaches to the edge of the electrode periphery. This observation demonstrates the significance of the γ factor (soften effect). The γ values would be probably around 1, which is consistent with the conclusion derived from the a-spot model (Figure 3.19). 180

209 Figures 4.28 and 4.29 summarize the effect of γ value on the predicted nugget diameter and depth using four different β values (800, 1600, 2500 and 5000). The reference temperature, T o, is 70 o F, except that it is 32 o F when β=5000. The nugget dimensions are compared with the electrode diameter and workpiece thickness to judge the validity of the equivalent contact resistivity factors. Figure 4.28 suggests that γ<1 would result in excessive melting. For β=5000 with a reference temperature of 32 o F γ>1 would cause insufficient nugget size. Figure 4.29 shows that β=800, γ=1 and T o =70 o F shows a reasonable nugget would be established with the RMS current equals to 33kA for 3 weld cycle time. It must be noted that this observation is purely numerical. The parametric study results will have to be compared with the experimental study results in order to derive a recommendation on the equivalent contact resistivity factors. This will be discussed in Chapter

210 (a) (b) Figure 4.27: Effect of γ on weld nugget size (β = 5000, T 0 = 32 o F (0 o C), and I RMS = 33 ka): (a) γ = 1.5 (b) γ =

211 18 16 Weld Diameter (mm) Electrode Diameter β Values solidus 5000 solidus 2500 solidus 1600 solidus 800 liquidus 5000 liquidus 2500 liquidus 1600 liquidus 800 (1 in. = 25.4 mm) γvalues Figure 4.28: Effect of γ on weld nugget diameter (RMS: 33 ka, T o = 32 o F for β=5000 and T o =70 o F for other β values) 183

212 3 2.5 Joint Thickness Weld Depth (mm) β Values solidus 5000 solidus 2500 solidus 1600 solidus 800 liquidus 5000 liquidus 2500 liquidus 1600 liquidus 800 (1 in. = 25.4 mm) γvalues Figure 4.29: Effect of γ on weld nugget depth (RMS: 33 ka, T o = 32 o F for β=5000 and T o =70 o F for other β values) 184

213 Reference Temperature, T 0 Physically the reference temperature (T 0 ) diminishes the magnitude of effective softening temperature (T-T 0 ) and hence reduces the softening effect. The peak value of equivalent contact resistivity will increase with the rise of the reference temperature (T 0 ). The effect of T 0 on temperature contours is illustrated in Figure 4.30(a)-(b), which is based on the following conditions: β=800, γ=1.0 and current RMS=33 ka. Higher reference temperature increases the nugget size by both liquidus and solidus temperatures in the analysis. Figure 4.30 shows that the nugget size is larger when T 0 = 70 o F than that when T 0 = 32 o F. 185

214 (a) (b) Figure 4.30: Effect of T 0 on weld nugget size (β = 800, γ= 1.0, and I RMS = 33 ka): (a) T 0 = 32 o F (0 o C) (b) T 0 = 70 o F (21 o C) 186

215 4.2.6 Effect of Current Level In order to cover the practical range of welding currents in the parametric study, a series of process simulations with the RMS currents from 24 ka to 33 ka and β values from 400 through 2500 were conducted. Other resistivity parameters were kept constant for γ=1 and T o =70 o F. The predicted nugget diameter and depth are evaluated. Figures 4.31 and 4.32 summarize the effect of RMS current on the nugget dimensions for various β values. The nugget dimensions are represented by both liquidus and solidus temperatures. Electrode diameter is shown in the figure for comparison purpose. Figure 4.31 shows that the solidus diameters are relatively insensitive to the welding current. They are pretty much the same as the electrode diameter when the RMS current level is about 33 ka. The solidus diameters are insensitive to the β values, especially at the high current level (e.g. 33 ka). The liquidus diameter is more sensitive to the current level. The liquidus diameter increases as the RMS current increases. From a practical point of view, it expects that the 187

216 lliquidus nugget diameter would reach at least 50% of the electrode diameter in resistance spot welding of aluminum. Therefore, the low β values (e.g. 400 and 600) are not reasonable values for the equivalent contact resistivity versus temperature relationship. Similar observations are shown in Figure 4.32 with respect to the nugget depth variations with the RMS current. The low β values are inappropriate to be considered for further qualitative evaluation of the equivalent contact resistivity factors. 188

217 diameter (mm) Electrode diameter 6 4 liquidus 800 liquidus liquidus (1 in. = 25.4 mm) RMS (amp) β solidus 2500 solidus 1600 solidus 800 solidus 600 solidus 400 liquidus 2500 liquidus 1600 Figure 4.31: Weld nugget diameters as defined by liquidus and solidus temperatures versus the RMS welding current (γ=1 and T o =70 o F) 189

218 depth (mm) Joint thickness β solidus 2500 solidus 1600 solidus 800 solidus 600 solidus 400 liquidus 2500 liquidus 1600 liquidus 800 liquidus 600 liquidus 400 (1 in. = 25.4 mm) RMS (amp) Figure 4.32: Weld nugget depths as defined by liquidus and solidus temperatures versus the RMS welding current (γ=1 and T o =70 o F) 190

219 4.2.7 Consideration of Cu/Al Interface The dynamic contact resistance at the Cu/Al interface has been neglected in many researches. It expects that a similar equivalent contact resistivity versus temperature relationship to the Al/Al interface would exist in the resistant spot welding process. In order to evaluate the possible values, three sets of assumed conditions for the Cu/Al interface were studied. They are (1) (β=1; γ=1; T o =70 o F), (2) (β=10; γ=1; T o =70 o F), and (3) (β=200; γ=1; T o =32 o F). These conditions were investigated for the Al/Al interface condition of (β=800; γ=1; T o =70 o F), except that the Cu/Al condition of (β=10; γ=1; T o =32 o F) was used for all parametric conditions of the Al/Al interface. Figure 4.33 illustrates the temperature contours and the nugget dimensions. It is shown that low β values or high reference temperature would cause insufficient nugget growth at 33 ka RMS welding current. Therefore, the equivalent contact resistivity factors for Cu/Al interface was assumed to be (β = 200; γ = 1; T 0 = 32 o F) for all the parametric study cases. 191

220 (a) Continued Figure 4.33: Effect of the Cu/Al interface parameters on temperature contours. (The Al/Al interface factors are β = 800, γ = 1, T 0 = 70 o F (21 o C) and I RMS = 33 ka): (a) Cu/Al: β = 200, γ = 1, and T 0 = 32 o F (0 o C) (b) Cu/Al: β = 10, γ = 1, and T 0 = 70 o F (21 o C) (c) Cu/Al: β = 1, γ = 1, and T 0 = 70 o F (21 o C) 192

221 Figure 4.33 continued (b) (c) 193

222 4.3 Summary 1. The FEA simulation models used both a quarter model and a half model. The quarter model was used to validate the mesh design and the numerical procedures. The half model, which has more realistic electrical boundary condition, was used for the parametric study. 2. The weld nugget was determined based on the liquidus temperature, dubbed "liquidus nugget" and the solidus temperature, dubbed "solidus nugget". Because of the large temperature difference between the liquid and solidus temperatures, the partially molten zone was predicted fairly large in the weld nugget. The solidus nugget is relatively insensitive to the equivalent contact resistivity variations and the welding current within the practical range for aluminum welding. However, the liquidus nugget growth is strongly influenced by both the equivalent contact resistivity factors and the welding current. 3. Due to the cyclic variation of AC current input, which causes local temperature fluctuations along the contact interface, the predicted peak 194

223 temperature occurs prior to the end of the weld time. The nugget size is also a little larger than that predicted using the DC current input of equivalent RMS current level. 4. The temperature evolution analysis shows that the contact temperature increases as the welding current increases during each AC cycle. However, the rate of temperature rise is reduced when the current is on the downturn cycle. It picks up again upon upswing of the current cycle. However, the changes become smaller as the contact resistance reduces due to the softening effect at raised temperatures. 5. Observations based of the parametric study results on weld nugget dimensions may be summarized as follows: i. Weld nugget is larger when higher bulk contact resistivity factor, β, is used in the analysis. ii. The predicted weld nugget dimensions are sensitive to the contact area correlation factor, γ. The greater the value of this factor it shows more significant softening effect of the contact surface, and hence the smaller 195

224 the nugget size. The most reasonable value of γ is unity, as demonstrated by the parametric study results. iii. The reference temperature reduces the effect of γ by reducing the softening temperature, which is the difference between the contact temperature and the reference temperature, (T-T o ). The liquidus nugget is sensitive to this reference temperature, but the solidus nugget is insensitive to this reference temperature. Larger liquidus nugget would be predicted with a higher reference temperature value. 6. The solidus nugget predictions are insensitive to welding current, nor the bulk contact resistivity factor, β. The liquidus nugget predictions are significantly influenced by both the current and the β factor. The appropriate range of the β values is from 800 to Similar relationship between equivalent contact resistivity versus contact temperature was assumed for the electrode/workpiece interface. For Cu/Al interface, the equivalent contact resistivity factors: β = 200, γ = 1, and T 0 = 32 o F enable reasonable predictions of nugget size. 196

225 CHAPTER 5 PARAMETRIC CALIBRATION In order to calibrate the parameters in Equation (9), bulk contact resistivity factor (β), contact area correction factor (γ), and reference temperature (T 0 ) were calibrated by comparing with the experimental data and their proximity behaviors. The weld nugget size and the interfacial potential drop were used as the basis for comparison. This chapter presents the experimental procedure and analysis, as well as the parametric calibration procedure and results. 197

226 5.1 Experiment of RSW AA2024-T3 Aluminum Alloy The experimental study included measuring the electrical potential drop between the two electrode tips in contact with the workpiece surface and the welding current. The transient weld nugget areas were determined by sectioning the weld coupons with weld cycle time equal to 1, 2, 3, and 4 cycles, respectively Experimental Background There have been a number of researches made to quantify contact resistance of sheet steel and aluminum. Five of the most famous studies were performed by Studer (Ref. 29), Savage, et al. (Ref ), Kim and Eager, Sheppard and Vogler (Ref. 39), and Thornton, Krause, and Davies (Refs , 36). Studer s experiment (Ref. 29), performed in the 1930s, was primarily concerned with contact between uncoated low-carbon and stainless steels. Contact resistance measurements were made by welding fine lead wires to 198

227 specimens near the interface. The effect of load in the range of 50 to 800 lbs and temperatures between 68 o F and 752 o F on contact resistance between steel sheets was studied. Studer s work did not discuss coated steels or contact between dissimilar materials, such as electrode and workpiece. Furthermore, Studer stated that his test results were highly variable. Savage, et al. (Ref ) experimentally studied the effect of load on contact resistance between the electrodes and steel sheet, and at the workpiece-to- workpiece interface. Both bare and coated mild steel sheets were considered, but the influence of temperature on contact resistance was not addressed. Kim and Eager carried out extensive testing by using infrared imaging to measure thermal contact resistance between a copper electrode and galvanized mild steel sheet. By using an iterative numerical technique they backed out electrical contact resistance. Implicit in this approach is the assumption that both the electrical and thermal contact areas are the same. Due to the presence of contaminants, such as oxides, it is more likely that the thermal contact area will be greater than the electrical contact area. 199

228 The research, conducted by Sheppard and Vogler (Ref. 39), was focused on characterizing electrical contact resistance involved in resistance spot welding of thin sheet steels. A special test fixture has been fabricated that allows contact resistance at both the electrode-to-sheet and the sheet-to-sheet interfaces to be measured under typical welding pressures and from room temperature to elevated temperatures. This experiment examined the bare and galvanized mild as well as HSLA steels. Thornton, Krause, and Davies (Refs , 36) measured the contact resistance of electrode-workpiece and faying surface for a variety of aluminum alloys with different surface finishes. Standard spot weld electrode tips with a 50-mm-radius spherical contact surface were inserted in stainless steel holders attached to the top and bottom crossheads of an Instron testing machine. The tip holders were designed so that the electrode tips could be internally water-cooled. The sheet samples, 50mmx25 mm, were placed upon a micarta loading guide mounted on the bottom electrode holder at such a height that the samples lay flat and parallel to one another on the bottom electrode tip with 25-mm overlap. Current was passed between the electrodes through cables 200

229 attached to the electrode tips. The contact voltages at the electrode-workpiece and faying interfaces were detected via alligator clips that had one insulated jaw. This simulated experimental instrument is used to measure quasi-static change of contact resistance with different current levels and loads. In this experiment, dynamic resistance measurements were made in situ on a Taylor Winfield pedestal spot welding machine equipped with a WTC Nadesco controller and recorder. The effect of welding parameters on both quasi-static and dynamic contact resistance has been well discussed. 201

230 5.1.2 Equipment Set-Up Resistance Spot Welding Tests were conducted in the laboratory using a 200 kva NEWCOR AC resistance spot welding machine. The electrodes and machine were instrumented for spot welding tests conducted on 2024-T3 aluminum alloy specimens: 0.05 inch thick, 2 inch wide, and 6 inch long. The surface condition of the specimens was as received. Truncated electrodes with 0.25 inch diameter (FA25Z00) were used. Dynamic Contact Resistance and Potential Drop Measurement In order to experimentally measure the dynamic contact resistance during resistance spot welding aluminum alloys, an instrumentation system, including an NEWCOR 200kVA AC resistance welder and a data acquisition circuit, has been arranged. Alligator clips, toroidal coils, a passive integrator, a conditioning modulus, a digital storage oscilloscope, and a personal computer were included to develop the data acquisition circuit in order to quantify the electrical data from the 202

231 welding process, which was believed to contain the most potentially useful information. This instrumentation arrangement is schematically shown in Figure

232 di/dt Conditioning Modulus Secondary Voltage Digital Storage Oscilloscope Interface Current Passive Integrator Figure 5.1: Experimental arrangement of dynamic contact resistance measurement 204

233 5.1.3 Experimental Procedure Welding Schedule The welding schedule and parameters in this experiment are listed as follows: Squeeze time: 15 cycles Welding time: 4 cycles Hold time: 24 cycles Current level: 33 ka (RMS) Electrode force: 800 lbs Nugget Size Determination Experiments were conducted by employing the welding schedule listed above with the welding time from 1 cycle to 4 cycles in order to calibrate the 205

234 parameters in Equation (9). The cycle times for squeeze, weld and hold were set on the welding unit controls. The current setting was made on the percent heat control and tap switch. The welded samples were peeled and the nugget sizes were measured and recorded. Dynamic Contact Resistance and Potential Drop Measurement The voltage drop across two electrodes was measured by using the alligator clips and the acquisition circuit. Both the current level and secondary current were also sampled via the toriodal coils and the acquisition system. Before beginning the welding process, the preset electrode force was confirmed by using the hydraulic force-measuring unit. Because the AC power supply was used, the dynamic contact resistance could not be calculated only by dividing the weld voltage by the current flowing through the workpieces. Because inductance always cause a phase shift between the welding voltage and current waveforms, simply dividing these waveforms point by point will not yield the correct results. The voltage across an inductive load is related the current and expressed by 206

235 di V = IR + L dt (14) Where R is the resistance of the load and L is the inductance. The phase shift between voltage and current is a function of R and L. In the past, no universal correction scheme had been developed that could provide dynamic contact resistance data more frequently than once per half cycle, because di/dt is zero at the peak. However, because the dynamic contact resistance of aluminum alloys will drop to a constant level during the first cycle, the traditional approach obviously cannot meet the need. An more accurate correction method for this phase shift has to be developed. In this experiment, a computer program was developed in order to calculate the inductance by using the measured electrical data, such as voltage drop, secondary voltage drop, current, and secondary current. Based on this program, the phase shift between the welding voltage and current waveforms was removed. Figure 5.2 shows the current and calibrated voltage inputs which were recorded by the instrumentation system. Then, the dynamic contact resistance can be obtained by dividing the calculated voltage drop by the current level point by point. 207

236 5.1.4 Experimental Observations The nugget size growth was recorded and plotted in Figure 5.3. Melting initiated at the first cycle and expulsion happened at the fourth cycle. It was found that weld nugget diameter and depth are almost equal to the electrode diameter and the workpiece thickness, respectively. 208

237 60 40 Current (ka) Voltage (volts) Current (ka) Voltage (volts) Weld Time (cycles) -1.5 Figure 5.2: Current and calibrated voltage inputs 209

238 0.300 Nugget Diameter (inch) Weld Time (Cycles) Figure 5.3: Experimental nugget size growth 210

239 Figure 5.4 presents the dynamic contact resistance measured during the welding cycles. The dynamic contact resistance drops steeply and reaches a constant minimum value just within the first quarter cycle. This phenomenon is probably due to the collapse of micro-asperities and the breakup of oxide film. Missing points and sharp sparks in this curve occurred when the current values were zero or close to zero. In addition to dynamic contact resistance, the potential drops between workpieces were also obtained in this experimental measurement. The variation of potential drops at interface within the first half cycle is plotted in Figure 5.5 (a)-(b). Due to the existence of a time delay of instrumentation, the curve of experimental results shown in Figure 5.5 (a) has to be calibrated. The final calibrated curve is plotted in Figure 5.5 (b). 211

240 0.4 Dynamic Contact Resistance (milliohms) T3 Aluminum Alloy 800 lbs, 33 ka, 4 cycles 0.05 in. thick Weld Time (cycles) Figure 5.4: Variation of dynamic contact resistance 212

241 Potential Drop (volts) Experiment Results Weld Time (cycles) (a) Experimental Results Potential Drop (volts) Calibrated Experiment Results Weld Time (cycles) (b) Figure 5.5: Measured potential drops between workpieces within half cycle: (a) original curve (b) calibrated curve 213

242 5.2 Parametric Calibration The nugget size comparison was the first step of the parametric calibration process. In this section, the numerical nugget sizes calculated from FEA simulation were compared with the experimental results Nugget Diameter Comparison Twenty FEA case studies with different sets of parameters and current inputs were performed in an attempt to compare the simulated weld nugget size to experimental results. The FEA half model established in Chapter 4.2 and the welding schedule listed in Section were employed. The numerical nugget size was defined from the weld center to the point at which peak temperature exceeds the liquidus temperature. The dynamic contact resistivity at Cu/Al interface in this simulation was quantified from Equation (9) with the parametric input of β = 200, γ = 1, and T 0 = 32 o F (0 o C). 214

243 Table 5.1 summarizes the results of nugget size comparison. Figures 4.31 and 4.32 show the numerical liquidus/solidus nugget sizes, which diameter and depth are compared with the electrode diameter and the workpiece thickness, respectively. The experimental nugget diameters (Figure. 5.3) were superimposed in Figure 4.31 and replotted in Figure 5.6. It is observed from Table 5.1 that when the equivalent contact resistivity factors being in combinations of (β = 800, γ = 1, T 0 = 70 o F), (β = 1600, γ = 1, T 0 = 32 o F), (β = 2500, γ = 1, T 0 = 70 o F) and (β = 2500, γ = 1, T 0 = 32 o F) as the parametric inputs the numerical model predicted acceptable nugget dimensions. Among these four combinations, (β = 800, γ = 1, T 0 = 32 o F) predicted the best fit (based on the liquidus nugget diameter) with the experimental nugget diameter at end of 3 weld cycles (Figure 5.6). The ideal range of equivalent contact resistivity is presented in Figure

244 5.2.2 Numerical Simulation of Electrical-Thermal-Mechanical Behaviors With the four acceptable combinations of the equivalent resistivity factors, this section presents a complete simulation of the electrical, thermal, and mechanical behaviors of the resistance spot welding AA2204-T3 alloy using (β = 2500, γ = 1, T 0 = 32 o F). The predicted nugget growth is shown in Figure 5.8(a)-(c). Three different states of electrical potential and current density during welding cycles are shown in Figure 5.9(a)-(c) and Figure 5.10(a)-(c), respectively. Figure 5.11(a)-(f) illustrates the electrode indentation phenomenon during the whole welding process; including squeeze cycles, welding cycles, hold cycles, and cool cycles. The induced stress distribution is also presented in Figure 5.12(a)-(d). 216

245 5.2.3 Potential Drop Comparison Another parametric calibration is based on the potential drop comparison. The experimental potential drops, measured in Section 5.1, were used to compare with the FEA numerical results in this section in order to determine the most optimal assembly of parameters from the ideal range of parametric combinations, obtained. The same twenty FEA simulation cases established in the process of nugget size comparison were employed in this section. The numerical potential drops at interface, recorded by the FEA half model with the equivalent contact resistivity with various inputs of parameters in Table 5.1, were compared with experimental results. The potential drop comparison results are summarized in Table 5.2. From Table 5.1 and Table 5.2, it is found when β = 800, γ = 1, T 0 = 70 o F (21 o C) at Al/Al interface and β = 200, γ = 1, and T 0 = 32 o F (0 o C) at Cu/Al interface, both the comparisons of weld nugget size and potential drops are satisfactory. Figure 5.13 illustrates the comparison of numerical potential drops and experimental results, when the parametric inputs were: β = 800, γ = 1, T 0 = 70 o F 217

246 (21 o C) at Al/Al interface and β = 200, γ = 1, and T 0 = 32 o F (0 o C) at Cu/Al interface. Figure 5.14 presents the effect of Cu/Al interface on the potential drop comparison. It is verified that the equivalent contact resistivity at Cu/Al interface cannot be neglected in FEA numerical simulation. 218

247 5.3 Summary 1. When the equivalent contact resistivity curve is in the range between the boundaries with parametric inputs of β = 800, γ = 1, T 0 = 70 o F, and β = 2500, γ = 1, T 0 = 32 o F; the nugget size comparison is acceptable. 2. When β = 800, γ = 1, T 0 = 70 o F (21 o C) at Al/Al interface and β = 200, γ = 1, T 0 = 32 o F (0 o C) at Cu/Al interface, both the comparisons of weld nugget size and potential drops are satisfactory. 219

248 Cu/Al Interface No. Al/Al Interface (β-γ-i RMS -T 0 ) β Value γ Value T o, o F Nugget Size Comparison No Nugget Insufficient Size Acceptable Weld Expulsio n kA-32 o F X kA-32 o F X kA-70 o F X kA-70 o F X kA-70 o F X kA-70 o F X kA-32 o F X kA-32 o F X kA-32 o F X kA-32 o F X Continued Table 5.1: Nugget size comparison results in FEA case study 220

249 Table 5.1 continued kA-70 o F X kA-70 o F X kA-70 o F X kA-32 o F X kA-70 o F X kA-32 o F X kA-32 o F X kA-32 o F X kA-32 o F X kA-32 o F X 221

250 solidus 2500 diameter (mm) Electrode diameter solidus 1600 solidus 800 solidus 600 solidus 400 liq uid us 2500 liq uid us 1600 liq uid us 800 liq uid us 600 liq uid us ( 1 in. = 25.4 mm) RMS (amp) Figure 5.6: Comparison between numerical nugget sizes and electrode diameter with various current levels and values of β when γ = 1 and T 0 = 0 o F (β = 200, γ = 1, and T 0 = 32 o F (0 o C) at Cu/Al interface) 222

251 9.00E E-03 β = 2500, γ = 1, T 0 = 32 o F 7.00E-03 Resistivity (ohm-in.) 6.00E E E E-03 β = 2500, γ = 1, T 0 = 0 o F 2.00E E-03 β = 800, γ = 1, T 0 = 70 o F 0.00E Temperature (degf) Figure 5.7: Ideal range of dynamic contact resistivity 223

252 (a) 1st Cycle (b) 2nd Cycle Continued Figure 5.8: Weld nugget growth of FEA half model simulation (β = 2500, γ = 1, and T 0 = 32 o F): (a) 1 st cycle (b) 2 nd cycle (c) 3 rd cycle 224

253 Figure 5.8 continued (c) 3rd Cycle 225

254 (a) 1st Cycle (b) 2nd Cycle Continued Figure 5.9: Electrical potential distribution during welding process (β = 2500, γ = 1, and T 0 = 32 o F): (a) 1 st cycle (b) 2 nd cycle (c) 3 rd cycle 226

255 Figure 5.9 continued (c) 3rd Cycle 227

256 (a) 1st Cycle (b) 2nd Cycle Continued Figure 5.10: Electrical current density during welding process (β = 2500, γ = 1, and T 0 = 32 o F): (a) 1 st cycle (b) 2 nd cycle (c) 3 rd cycle 228

257 Figure 5.10 continued (c) 3rd Cycle 229

258 (a) Squeeze Cycles (b) 1st Cycle Continued Figure 5.11: Electrode indentation phenomenon during the whole process (β = 2500, γ = 1, and T 0 = 32 o F): (a) squeeze cycles (b) 1 st cycle (c) 2 nd cycle (d) 3 rd cycle (e) hold cycles (f) cool cycles 230

259 Figure 5.11 continued (c) 2nd Cycle (d) 3rd Cycle Continued 231

260 Figure 5.11 continued (e) Hold Cycles (f) Cool Cycles 232

261 (a) Squeeze Cycles (b) 1st Cycle Continued Figure 5.12: Stress Distribution (β = 2500, γ = 1, and T 0 = 32 o F) : (a) squeeze cycles (b) 1 st cycle (c) 2 nd cycle (d) 3 rd cycle 233

262 Figure 5.12 continued (c) 2nd Cycle (d) 3rd Cycle 234

263 Case No. Al/Al Interface Cu/Al Interface β Value γ Value T o Interfacial Potential Drop Comparison kA-32 o F Low kA-32 o F Low kA-70 o F OK kA-70 o F Low kA-70 o F Low kA-70 o F Low kA-32 o F Low kA-32 o F Low kA-32 o F Low kA-32 o F High Continued Table 5.2: Potential drop comparison results in FEA case study 235

264 Table 5.2 continued kA-70 o F High kA-70 o F High kA-70 o F High kA-32 o F High kA- 0 o F Low kA-32 o F Low kA-32 o F Low kA-32 o F Low kA-32 o F High kA-32 o F Low 236

265 Amps Potential Drop (volts) Calibrated Experiment Results Weld Time (cycles) Figure 5.13: Comparison of numerical potential drops and experimental results, with β = 800, γ = 1, T 0 = 70 o F (21 o C) at Al/Al interface and β = 200, γ = 1, and T 0 = 32 o F (0 o C) at Cu/Al interface 237

266 Volt Cu/Al Interface ρ Potential drop Experimental Data V Quarter cycle Half cycle. Time 1 cycle: sec X10-3 sec Figure 5.14: Effect of Cu/Al interface on potential drop comparison when β = 800, γ = 1, T 0 = 70 o F (21 o C) at Al/Al interface 238

267 CHAPTER 6 MECHANICAL ANALYSIS FOR EXPULSION PHENOMENON 6.1 Background It is known that cracking and expulsion are the two most encountered problems in resistance spot welding aluminum and are complicated issues due to the complex nature of RSW. The cracking phenomenon is related to the nature of wider solidus-liquidus gap, the presence of low melting point eutectics or impurities, high solidification shrinkage, large coefficient of thermal expansion, and a rapid drop of mechanical properties at elevated temperatures. (Ref ) The expulsion issue is caused by softening of the workpieces or electrode indentation and large partially molten nugget, which extends to the peripheral 239

268 boundary of the electrodes. High electrode force is usually required to provide an enclosure force containing the partially or completely molten metal from expulsion. This force requirement reduces the contact resistance, constituting one of the reasons for demanding high welding current. (Ref ) There are limited publications on the cracking mechanisms in resistance spot welding aluminum, although this topic has been studied extensively for arc welding aluminum alloys. Cracking in resistance spot welding aluminum has been reported recently by Wu, Zhang and Senkara (Ref ), and Michie and Renaud (Ref. 104), Watanabe and Tachikawa (Ref.105), and Thornton (Ref.33). In researches performed by Wu, Zhang and Senkara (Ref ), the cracking phenomenon in single and multiple resistance spot welding AA5754 was investigated experimentally and analyzed by using simplified thermal-mechanical models. Several important findings related to the cracking mechanisms may be summarized as follows: (1) Tensile thermal stress is developed on the non-constrained side of the weldment in the cooling stage of welding in multi-spot welds and on both sides of single spot welds. 240

269 (2) A high probability of crack formation and propagation exists in the region adjacent to the nugget, where solid and liquid phases co-exist. (3) Unlike fusion welding processes, constraining the peripheral edge of the nugget in RSW is preferred for minimizing cracking, because it reduces the tendency of generating tensile stresses in the heat affected zone (HAZ) during welding. It is oblivious that applying the constraining force along the peripheral edge would be a method to reduce the cracking tendency and weld expulsion. A new electrode design that splits the electrode force into a lower electricity-carrying force and the remaining force for nugget enclosure and compressive strains could suppress the cracking susceptibility and contain the weld nugget from expulsion. Because the electrical coupling force is reduced that will increase the contact resistance, the welding current requirement can be reduced. The electrical decoupling force is used to generate compressive strains and enclose nugget's peripheral edge. 241

270 This chapter presents the mechanical analysis of the resistance spot aluminum weld using the equivalent contact resistivity versus temperature relationship and the numerical modeling and analysis procedure demonstrated in the previous chapters. The expulsion condition is defined by the nugget tip opening displacement. Nugget expulsion is set to occur when the opening displacement is inside the growing nugget at any instant during the weld cycles. 242

271 6.2 FEA Mechanical Simulation A thermal-mechanical FEA module with the equivalent contact resistivity input in the ideal range obtained in Chapter 5 was established to simulate the mechanical phenomenon at interface in order to predict and prevent expulsion. Two case studies with different parametric inputs were conducted to investigate the formation of expulsion. Those terminologies used to predict the initiation of expulsion in this analysis are introduced in Figure 6.1. The peripheral edge of the nugget is defined as the tip of a circular crack. The terms, crack tip distance (CTD) and crack mouth opening displacement (CMOD), are defined as the distance from the nugget center to the crack tip at interface and the opening gap between the workpieces at the end of the workpiece, respectively. When CTD is less than the solidus front location (SFL) before the end of welding, expulsion is said to happen. 243

272 6.2.1 Case Study I: RSW without Expulsion The parametric inputs in case study I are listed as follows: β = 800, γ = 1, T 0 = 32 o F at Al/Al interface and β = 200, γ = 1, and T 0 = 32 o F at Cu/Al interface. The welding schedule in this case study is shown in Figure 6.2. The electrode force increases linearly to 800 lbs within 15 squeeze cycles and is kept at this force level until the end of the cooling cycle (42 cycles from beginning of the process). The electrode force is then removed at this time (i.e. the electrode elements remain in the model). Cooling continues for additional one hour. 33 ka AC current is applied when the electrode force reaches 800 lbs and is maintained for 3 weld cycles. Figures 6.3 (a)-(n) illustrate the variations of crack tip distance (CTD) and crack mouth opening distance (CMOD) during the weld cycles. The electrode force causes a contact at the faying surface. The initial contact diameter is approximately 0.008" (0.2mm) larger than the electrode diameter (0.25" or 6.4mm). It also causes an opening at end of the workpiece, approximately 0.005" (0.137 mm). Both the contact area and the end opening increase as the 244

273 during the weld cycles. The maximum contact area (0.277" or mm in diameter) is reached just before the end of the weld time (0.3 second from the beginning of the squeeze cycle). The contact diameter shrinks inwards during the cooling cycles and becomes smaller than electrode diameter. However, when the weld completely cools off to room temperature, due to weld shrinkage the contact area increases to a diameter (0.262" or mm) that is greater than the electrode. During the weld cycles, the solidus front location (SFL) is always inside of the contact area. As the solidus weld nugget solidifies during the cooling cycles, the edge of the contact area also moves inward, but at a slower rate than the nugget shrinkage. Therefore, no expulsion would be expected using this weld schedule. The final gap between the workpieces is 0.005" (0.126mm) Case Study II: RWS with Expulsion In this case study, the bulk contact resistivity factor is increased from β=800 to β=2500, with all other parameters remained the same as Case I. Figures

274 (a)-(m) summarize the evolutions of crack tip distance (CTD) and crack mouth opening displacement (CMOD) during welding. Similar behaviors in the contact area evolution can be seen in this case as to the previous case. However, the contact diameter does not drop below the electrode diameter. Unlike the case I situation, the higher contact resistance assigned to the equivalent contact resistivity function results in the contact edge inside the solidus weld nugget just prior to end of the 3rd weld cycle. The numerical analysis predicts expulsion of this weld schedule. At 2.88 weld cycle time, the predicted CTD intersects with the SFL, which indicates a condition for expulsion. Figure 6.5 presents a roomed-in picture showing the expulsion condition. It clearly shows that the contact tip or crack tip is inside the solidus nugget. The electrode force would push the molten weld metal out of the weld nugget. The final gap between the workpieces is unreasonably high due to large electrode indentation (1.523" or mm). The opening shown in the figure is reduced by 40 times. 246

275 6.3 External Ring Constriction Model In RSW aluminum, large electrode force is usually required to contain the molten nugget in order to prevent expulsion when excessive weld current and/or duration are applied. By constraining the molten nugget using a closure force from a restricting ring attached to the electrode would prevent expulsion. This concept is analyzed using the same weld schedule as studied in Section 6.2. Both contact resistance values (β=800 and β=2500) are investigated to consider the effect of the external ring constriction on the expulsion condition and the final gap between the workpieces. 247

276 6.3.1 Effect of Constriction Ring on Gap (β=800) Figure 6.6 shows a schematic diagram of an axisymmetric RSW model with the constriction ring. In this model, the electrode force is kept the same as the model without the ring. This is to maintain the same pressure condition for the contact resistance between the electrodes. An addition ring force, approximately 12% of the electrical coupling force is applied surrounding the electrodes in order to establish the constriction effect. The outer diameter of the ring is 0.52" (13.2mm). The clearance between the electrode face contact and the ring contact is 0.02" (0.5mm). The annular distance of the ring contact is one quarter of the electrode diameter. The ring dimensions and the constriction force are arbitrary. Optimum parametric study of the ring design is beyond the scope of current study. Figures 6.7 (a)-(n) illustrate the variations of crack tip distance (CTD) and crack length (CL) during welding with an external constriction ring. It is obvious that the gap between he workpieces has been pretty much closed during the 248

277 entire welding duration. The electrode contact area is also increased by this constriction force. The resistivity-temperature relationship is assumed to be valid in this case. Figure 6.8 plots the crack tip distance (CTD) evolution for models with and without the constriction ring. The solidus front location (SFL) evolution and the radius of the electrode are also plotted in the same figure. It is seen that in either case the SFL is always smaller than CTD. The gap between the workpieces is reduced from 0.005" (0.126mm) to almost zero (Figure 6.9) Effect of Constriction Ring on Expulsion and Gap (β=2500) In this model, the outer diameter of the external ring is 0.78" (19.8mm). The ring force is also increased to 56% of the electrode force (800 lbs) in order to maintain similar constriction pressure to low contact resistance case. The FEA model is schematically graphed in Figure The welding schedule remains the unchanged. The variations of crack tip distance (CTD) and crack length (CL) during 249

278 welding with an external constriction ring are presented in Figure 6.11 (a)-(m). Although the contact area changes, the gap between the workpieces does not exist during the entire welding cycles. The contact diameter increases at a much higher rate than the model without the constriction ring. The maximum contact diameter (0.344" or 8.744mm) is reached prior to the end of the 3rd weld cycle. It drops quickly to 0.289" (7,348mm) diameter at the end of the weld cycles (0.3 seconds). The contact area is further reduced with a fluctuation as the weld nugget shrinkages and the joint cools off. Nevertheless, the contact tip is always outside the solidus nugget diameter. No expulsion would be expected. Figure 6.12 plots CTD evolution for models with and without the constriction ring. It clearly shows the constriction effect with the ring, especially during the weld cycles. The SFL intersects with the CTD curve of without the constriction ring, but never intersects with the CTD curve with the constriction effect. Figure 6.13 shows a comparison of the joint geometry and the weld nugget after removal of the electrodes. Without the constriction ring, very significant electrode indentation and gap between the workpieces are observed. With the constriction ring, indentation is much reduced and the joint gap is eliminated completely. 250

279 6.4 Split-Force Electrode Design Concept The concept of using the constriction ring is effective to enclose the weld nugget from expulsion. The idea is to reduce the electrical coupling electrode force, which would also increase the electrical contact resistance due to reduction of the contact area. The originally required large electrode force may split into a secondary forging force through the constriction ring. This nonelectrical coupling force provides the enclosure force and compressive strains surrounding the weld nugget. It would expect that an optimum electrode force design exists for RSW aluminum. The reduced electrical coupling force would increase the contact resistance. The electrical current requirement may also be reduced. Because the equivalent contact resistivity versus temperature relationship, as presented by Equation (9), may be subject to force variation, it would be necessary to quantify the force effect before a meaningful investigation could be conducted. The constriction analysis presented in this chapter provides an initial guide for further studies on this subject. 251

280 Crack mouse opening distance (CMOD) Crack length (CL) Crack tip distance (CTD) Figure 6.1: Definition of Terminologies ( 1 sec. = 60 cycles) ( 1 lb. = kg) A C E G I (RMS) CURRENT (AMP) B D F H WELDING FORCE (kg) COOLING FREE WITH ELECTRODE SQUEEZE ELECTRODE A~I J~M N TIME(SEC) Figure 6.2: Welding schedule in case study I 252

281 mm CMOD = mm (a) Continued Figure 6.3: Variations of CTD in case study I: (a) total time = 16.2 cycles (0.27 sec.), weld time = 1.2 cycles (b) total time = cycles (0.273 sec.), weld time = 1.38 cycles (c) total time = cycles (0.276 sec.), weld time = 1.58 cycles (d) total time = cycles (0.281 sec.), weld time = 1.86 cycles (e) total time = cycles (0.283 sec.), weld time = 2.00 cycles (f) total time = cycles (0.285 sec.), weld time = 2.10 cycles (g) total time = cycles (0.290 sec.), weld time = 2.36 cycles (h) total time = cycles (0.298 sec.), weld time = 2.88 cycles (i) total time = 18 cycles (0.3 sec.), weld time = 3 cycles (j) total time = cycles (0.301 sec.) (k) total time = cycles (0.306 sec.) (l) total time = cycles (0.310 sec.) (m) total time = cycles (0.315 sec.) (n) total time = sec. 253

282 Figure 6.3 continued mm CMOD = mm (b) mm CMOD = mm (c) mm CMOD = mm (d) Continued 254

283 Figure 6.3 continued mm CMOD = mm (e) mm CMOD = mm (f) Continued 255

284 Figure 6.3 continued mm CMOD = mm (g) mm CMOD = mm (h) Continued 256

285 Figure 6.3 continued mm CMOD = mm (i) mm CMOD = mm (j) Continued 257

286 Figure 6.3 continued mm CMOD = mm (k) mm CMOD = 0.481mm (l) Continued 258

287 Figure 6.3 continued mm CMOD = mm (m) mm CMOD = mm (n) Continued 259

288 3.175 mm mm (a) Continued Figure 6.4: Variations of CTD in case study II: (a) total time = cycles (0.261 sec.), weld time = 0.65 cycles (b) total time = cycles (0.268 sec.), weld time = 1.08 cycles (c) total time = cycles (0.273 sec.), weld time = 1.37 cycles (d) total time = cycles (0.277 sec.), weld time = 1.60 cycles (e) total time = cycles (0.281 sec.), weld time = 1.87 cycles (f) total time = cycles (0.285 sec.), weld time = 2.10 cycles (g) total time = cycles (0.290 sec.), weld time = 2.37 cycles (h) total time = cycles (0.294 sec.), weld time = 2.62 cycles (i) total time = cycles (0.298 sec.), weld time = 2.88 cycles (j) total time = cycles (0.3 sec.), weld time = 3.00 cycles (k) total time = cycles (0.301 sec.) (l) total time = cycles (0.306 sec.) (m) total time = sec. 260

289 Figure 6.4 continued mm mm (b) mm mm (c) Continued 261

290 Figure 6.4 continued mm mm (d) mm mm (e) Continued 262

291 Figure 6.4 continued mm mm (f) mm mm (g) Continued 263

292 Figure 6.4 continued mm mm (h) mm mm Expulsion (i) Continued 264

293 Figure 6.4 continued mm mm Expulsion (j) mm mm (k) Continued 265

294 Figure 6.4 continued mm mm (l) mm mm (m) 266

295 (a) (b) Figure 6.5: Occurrence of expulsion in case study II: (a) weld time = 2.88 cycles (b) weld time = 3 cycles 267

296 Force to electrode: kg 0.5 mm Electrode 6.6 mm Ring Al 2024-T3 Force to ring: kg Axisymmetric axis ( 1 in. = 25.4 mm, 1 lb = kg) Boundary condition Figure 6.6: FEA model of case study I with an external constriction ring 268

297 mm mm (a) Continued Figure 6.7: Variations of CTD and CL in case study I with the application of a constriction ring: (a) total time = cycles (0.270 sec.), weld time = 1.19 cycles (b) total time = cycles (0.273 sec.), weld time = 1.37 cycles (c) total time = cycles (0.276 sec.), weld time = 1.58 cycles (d) total time = cycles (0.282 sec.), weld time = 1.90 cycles (e) total time = cycles (0.285 sec.), weld time = 2.11 cycles (f) total time = cycles (0.290 sec.), weld time = 2.37 cycles (g) total time = cycles (0.294 sec.), weld time = 2.61 cycles (h) total time = cycles (0.298 sec.), weld time = 2.88 cycles (i) total time = 18 cycles (0.3 sec.), weld time = 3 cycles (j) total time = cycles (0.301 sec.) (k) total time = cycles (0.306 sec.) (l) total time = cycles (0.310 sec.) (m) total time = cycles (0.317 sec.) (n) total time = sec. 269

298 Figure 6.7 continued mm mm (b) mm mm (c) mm mm (d) Continued 270

299 Figure 6.7 continued mm mm (e) mm mm (f) Continued 271

300 Figure 6.7 continued mm mm (g) mm mm (h) Continued 272

301 Figure 6.7 continued mm mm (i) mm mm (j) Continued 273

302 Figure 6.7 continued mm mm (k) mm mm (l) Continued 274

303 Figure 6.7 continued mm mm (m) mm mm (n) 275

304 Figure 6.8: Variations of CTD and SFL in case study I with and without the external constriction ring 276

305 (a) (b) Figure 6.9: Weld nugget size and electrode indentation in case study I with and without the application of an external ring: (a) without the application of an external ring (b) with the application of an external ring 277

306 Force to electrode: kg 0.5 mm Electrode 9.9 mm Ring Al 2024-T3 Force to ring: kg Axisymmetric axis ( 1 in. = 25.4 mm, 1 lb = kg) Boundary condition Figure 6.10: FEA model of case study II with an external constriction ring 278

307 mm mm (a) Continued Figure 6.11: Variations of CTD in case study II with the application of a constriction ring: (a) total time = cycles (0.261 sec.), weld time = 0.65 cycles (b) total time = cycles (0.268 sec.), weld time = 1.08 cycles (c) total time = cycles (0.273 sec.), weld time = 1.37 cycles (d) total time = cycles (0.277 sec.), weld time = 1.60 cycles (e) total time = cycles (0.281 sec.), weld time = 1.87 cycles (f) total time = cycles (0.285 sec.), weld time = 2.10 cycles (g) total time = cycles (0.290 sec.), weld time = 2.37 cycles (h) total time = cycles (0.294 sec.), weld time = 2.62 cycles (i) total time = cycles (0.298 sec.), weld time = 2.88 cycles (j) total time = cycles (0.3 sec.), weld time = 3.00 cycles (k) total time = cycles (0.301 sec.) (l) total time = cycles (0.306 sec.) (m) total time = sec. 279

308 Figure 6.11 continued mm mm (b) mm mm (c) Continued 280

309 Figure 6.11 continued mm mm (d) mm mm (e) Continued 281

310 Figure 6.11 continued mm mm (f) mm mm (g) Continued 282

311 Figure 6.11 continued mm mm (h) mm mm (i) Continued 283

312 Figure 6.11 continued mm mm (j) mm mm (k) Continued 284

313 Figure 6.11 continued mm mm (l) mm mm (m) 285

314 Figure 6.12: Variations of CTD and SFL in case study II with and without the external constriction ring 286

315 (a) (b) Figure 6.13: Weld nugget size and electrode indentation in case study II with and without the application of an external ring: (a) without the application of an external ring (b) with the application of an external ring 287