D.H. Lammlein PhD Dissertation - Vanderbilt University

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constants derived from analytical experiments in Al-6061-T6 were taken (µ ∞ =0, µ 0 =1e8m 2 /s, λ=10, n=1, T 0 =300K) (Tello, Gerlich, & Mendez). For the inlet and outlet zones, a reduced µ 0 of 100m 2 /s was used to aid in solution convergence as flow was not critical in these regions. The total heat input at the interface was determined using the Schmidt heat generation equation. Schmidt’s analytical equation for heat generation approximates the heat generated by the tool based on a sliding contact condition at the interface (Schmidt, Hattel, & Wert, 2004): Qτ contact ωAd where τ contact µP Where Q is heat generated by area, A, whose centroid is distance, D, from the axis of rotation; and is the contact shear stress, µ is the frictional coefficient, P is the contact pressure, ω is the radial velocity of the tool. For a simple tool with a cylindrical probe the equation becomes: Q total 2 3 πτ contactωR 3 3r 2 h where R is the radius of the shoulder, r is the radius of the probe, and h is the height of the probe. For the present case the equation must be slightly modified to account for the portion of the shoulder not in contact with the work. This portion of the shoulder is a circular section on the shoulder defined by an inclusive angle of approximately 100º. The area of this non-contact, circular section is calculated by: 1 2 sin 1 2 5 16 " 1.745 sin 1.745 0.037 2.40 5 where R is the shoulder radius in inches, and θ is the inclusive angle which defines the circular section (100º), in radians. The centroid of this non-contact area is located a distance, , from the tool axis of rotation: 182
4 2 3 4 5 16 " 1.745 2 0.246" 0.0063 31.745 sin1.745 where R is the shoulder radius, in inches, and theta is the angle which defines the circular section, in radians. The contact pressure, P, can be calculated by dividing the axial force by the horizontal tool area: Using the experimental axial force for the 1000rpm, 5.2ipm parameter, the setting contact pressure, P, can be calculated for the width probe and narrow probe tools. Axial force readings were not taken during the narrow probe welds so the value obtained for the wide probe will be used for both cases. The calculated contact pressure for both experimental tools at the 1000rpm, 5.2ipm setting is: ,. 2880.5 . 0079 2.40 5 1.66 7 For the experimental contact condition the general Schmidt equation becomes: µPω 2 3 πR3 3r 2 h For the 1000rpm, 5.2ipm setting and the narrow probe tool using a frictional coefficient of 0.5 the heat generated by the narrow probe tool, , : 0.71.66 7104.72 2 3 π. 00793 ‐3.0024 2 . 0046 2.4e 5. 0063 =1,287 Watts where 0.7 is the friction coefficient, 1.66e-7Pa is the contact pressure, 1000rpm(104.72rad/s) is the tool rotation rate, 5/16”(0.0079m) is shoulder radius, 3/32”(0.0024m) is the probe radius, 0.18”(0.0046m) is the probe height, 0.037in 2 (2.4e- 183
Page 1 and 2:
FRICTION STIR WELDING OF SPHERES, C
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TABLE OF CONTENTS TABLE OF FIGURES
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Appendix ..........................
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Figure 16: Left(FE streamline), Mid
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Figure 51: A thermal camera image t
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for a similar conventional weld (3/
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Figure 102: Tapered retraction proc
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setting are indicated. Note that st
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Unsupported welds of this kind with
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Figure 157: A thermal camera image
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ottom sample is a tungsten inert ga
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N - newton (force unit) n - visco-p
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INTRODUCTION Friction Stir Welding,
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educed conduction lengths. In small
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CHAPTER I LITERATURE REVIEW: COMPUT
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frictional condition at the interfa
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contact. The contact area can inclu
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For horizontal sections, a heat inp
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(1.11) where r p is the probe (pin)
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This efficiency term, η pd , is kn
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The heat input on the tool surface
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The added complication of these met
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Figure 5: Lateral cross sections of
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Flow stress in aluminum alloys is d
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Figure 8: Three flow fields a) rota
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and post-weld cool-down. This model
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Williams et al. [60] use a 2D-axisy
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Figure 16: Left(FE streamline), Mid
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Figure 18: Temperature contour over
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Figure 22: Temperature distribution
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Figure 24: Lateral velocity contour
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Figure 26: Experimental(white) vers
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Figure 28: Top view schematic of tu
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[5] Taylor RE, Groot H, Goerz T, Fe
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[41] Heinz B., Skrotzki B., Eggler
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CHAPTER II COMPUTATIONAL ANALYSIS O
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Figure 30: Blind t-joint setup with
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Figure 33: Process forces and later
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Figure 35: Experimental Welds, Axia
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Figure 37: FEA boundary conditions
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A 4500 N axial force is applied eve
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axial force with lateral offset dur
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Figure 42: Contour plot of von Mise
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Figure 44: Deformation contour for
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Figure 46: Quarter-plate model for
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Figure 49: Contour plot of deflecti
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where P is the weld power (W), Q is
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Figure 52: Fluent CFD model zones.
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Figure 55: Thermal contour of weld
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Figure 59: Thermal contour of weld
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Figure 61: Velocity vectors for 0.0
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Figure 65: Contour of velocity magn
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CHAPTER III THE APPLICATION OF SHOU
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Figure 66: A shoulder-less, conical
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Figure 68: Typical axial(Z-axis) fo
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Figure 71: 90° conical tool macros
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Figure 75: Run 3, 80° conical tool
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Figure 79: (90º tool) Ultimate ten
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Figure 83: (90º tool) Lateral forc
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Figure 87: (80º tool) Lateral forc
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The Eulerian, finite volume, CFD so
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Figure 92 shows the increasing elem
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Figure 91: CFD model geometry consi
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Figure 95: Lateral cross-section of
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Figure 96: Attempts a probe tapered
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CHAPTER IV THE FRICTION STIR WELDIN
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applications for its high strength
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Figure 97: Experimental weld sample
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Figure 99: Split protrusion type de
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with a cupped recess. It is however
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of tapered retraction (i.e. move th
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The adjustments in vertical positio
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manners the assigned depth was main
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Figure 108: Lateral macrosections f
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Figure 110: (Supported, cupped tool
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Page 153 and 154:
Page 155 and 156: apparent strength of 26% parent whi
Page 157 and 158: with a 100º conical tool (0.025”
Page 159 and 160: Figure 119: Macrosection view of an
Page 161 and 162: and tooling. Torque is highly depen
Page 163 and 164: locally in proportion to the local
Page 165 and 166: Figure 126: (threaded tool) Contour
Page 167 and 168: Figure 128: (conical tool) Geometry
Page 169 and 170: Figure 131: (threaded tool) Lateral
Page 171 and 172: The results presented here show tha
Page 173 and 174: Figure 136:(from left: Tapered retr
Page 175 and 176: [8] Metallurgical analysis of ablat
Page 177 and 178: CHAPTER V FRICTION STIR WELDING OF
Page 179 and 180: Collaboration between Advanced Meta
Page 181 and 182: eccentricity, the method of interio
Page 183 and 184: gas tungsten arc welding of small d
Page 185 and 186: Full penetration welds of 4.2” (1
Page 187 and 188: Figure 143: The curvature of the pi
Page 189 and 190: Figure 144: Experimental axial forc
Page 191 and 192: Together, a fine wall thickness tol
Page 193 and 194: Figure 147: Axial force history for
Page 195 and 196: The weld macrosections show complet
Page 197 and 198: Figure 154: Macrosections of welds
Page 199 and 200: Figure 157: A thermal camera image
Page 201 and 202: Figure 159: Average tool shank temp
Page 203 and 204: 471,146 faces. The meshes are fine
Page 205: Figure 162: A closeup view of mesh
Page 209 and 210: applied heat locally in proportion
Page 211 and 212: Figure 164: Modeled temperature con
Page 217 and 218: Figure 172: Model pathlines for the
Page 219 and 220: Figure 174: Model pathlines for the
Page 221 and 222: later speed setting, the tool welds
Page 223 and 224: Figure 178: Zoom view of a macro ta
Page 225 and 226: Figure 180: The superficial appeara
Page 227 and 228: Figure 182: The rotary welding appa
Page 229 and 230: Figure 185: A diagram illustrating
Page 231 and 232: CONCLUSION AND FUTURE WORK Conclusi
Page 233 and 234: new FSW process environment is reso
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D.H. Lammlein PhD Dissertation - Vanderbilt University

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