The evolution of voids (damage) in friction stir welding processes was simulated using a void growth model that incorporates viscoplastic flow and strain hardening of incompressible materials during plastic deformation. The void growth rate is expressed as a function of the void volume fraction, the effective deformation rate, and the ratio of the mean stress to the strength of the material. A steady-state Eulerian finite element formulation was employed to calculate the flow and thermal fields in three dimensions, and the evolution of the strength and damage was evaluated by integrating the evolution equations along the streamlines obtained in the Eulerian configuration. The distribution of internal voids within the material was qualitatively compared with experimental results, and a good agreement was observed in terms of the spatial location of voids. The effects of pin geometry and operational parameters such as tool rotational and travel speeds on the evolution of damage were also examined.
1.
Thomas
, W. M.
, Nicholas
, E. D.
, Needham
, J. C.
, Murch
, M. G.
, Temple-Smith
, P.
, and Dawes
, C. J.
, 1991, “Friction Stir Butt Welding
,” GB Patent No. 9125978.8 and International Patent No. PCT∕GB92∕02203.2.
Collier
, M.
, Steel
, R.
, Nelson
, T.
, Sorensen
, C.
, and Packer
, S.
, 2003, “Grade Development of Polycrystalline Cubic Boron Nitride for Friction Stir Processing of Ferrous Alloys
,” Mater. Sci. Forum
0255-5476, 426–432
(4
), pp. 3011
–3016
.3.
Thomas
, W. M.
, Threadgill
, P. L.
, and Nicholas
, E. D.
, 1999, “Feasibility of Friction Stir Welding Steel
,” Sci. Technol. Weld. Joining
1362-1718, 4
(6
), pp. 365
–372
.4.
Lienert
, T. J.
, and Gould
, J. E.
, 1999, “Friction Stir Welding of Mild Steel
,” Proceedings of the First International Symposium on Friction Stir Welding
, TWI
, Thousand Oaks, CA
, paper on CD.5.
Sorensen
, C. D.
, Nelson
, T. W.
, and Packer
, S. M.
, 2001, “Tool Material Testing for FSW of High-Temperature Alloys
,” Proceedings of the Third International Symposium on Friction Stir Welding
, TWI
, Kobe, Japan
, paper on CD.6.
Konkol
, P. J.
, Mathers
, J. A.
, Johnson
, R.
, and Pickens
, J. R.
, 2003, “Friction Stir Welding of HSLA-65 Steel for Shipbuilding
,” J. Ship Prod.
8756-1417, 19
(3
), pp. 159
–164
.7.
Packer
, S. M.
, Nelson
, T. W.
, Sorensen
, C. D.
, Steel
, R.
, and Matsunaga
, M.
, 2003, “Tool and Equipment Requirements for Friction Stir Welding of Ferrous and Other High Melting Temperature Alloys
,” Proceedings of the Fourth International Symposium on Friction Stir Welding
, TWI
, Park City, UT
, paper on CD.8.
Posada
, M.
, DeLoach
, J.
, Reynolds
, A. P.
, Skinner
, M.
, and Halpin
, J. P.
, 2001, “Friction Stir Weld Evaluation of DH-36 and Stainless Steel Weldments
,” Friction Stir Welding and Processing, TMS
, pp. 159
–171
.9.
Posada
, M.
, DeLoach
, J.
, Reynolds
, A. P.
, and Halpin
, J. P.
, 2002, “Mechanical Property and Microstructural Evaluation of Friction Stir Welded AL-6XN
,” Trends in Welding Research, Proceedings of the Sixth International Conference
, ASM International
, Pine Mountain, GA
.10.
Reynolds
, A. P.
, Tang
, W.
, Gnaupel-Herold
, T.
, and Prask
, H.
, 2003, “Structure, Properties and Residual Stress of 304L Stainless Steel Friction Stir Welds
,” Scr. Mater.
1359-6462, 48
(9
), pp. 1289
–1294
.11.
Sorensen
, C. D.
, and Nelson
, T. W.
, 2007, “Friction Stir Welding of Ferrous and Nickel Alloys
,” Friction Stir Welding and Processing
, R. S.
Mishra
and M. W.
Mahoney
, eds., ASM International
, Materials Park, OH
, pp. 111
–121
.12.
Li
, Y.
, Murr
, L. E.
, and McClure
, J. C.
, 1999, “Solid-state Flow Visualization in the Friction Stir Welding of 2024 Al to 6061 Al
,” Scr. Mater.
1359-6462, 40
(9
), pp. 1041
–1046
.13.
Colligan
, K. J.
, 1999, “Material Flow Behavior During Friction Stir Welding of Aluminum
,” Weld. J. (Miami, FL, U.S.)
0043-2296, 78
(7
), pp. 229
–237
.14.
Seidel
, T. U.
, and Reynolds
, A. P.
, 2001, “Material Flow Behavior During Friction Stir Welding of Aluminum
,” Metall. Mater. Trans. A
1073-5623, 32A
, pp. 2879
–2884
.15.
Feng
, Z.
, Wang
, X. L.
, David
, S. A.
, and Sklad
, P. S.
, 2004, “Modeling of Residual Stresses and Property Distributions in Friction Stir Welds of Aluminum Alloy 6061-T6
,” Proceedings of the Fifth International Symposium on Friction Stir Welding
, TWI
, Metz, France
, paper on CD.16.
Schmidt
, H.
, and Hattel
, J.
, 2005, “A Local Model for the Thermomechanical Conditions in Friction Stir Welding
,” Modell. Simul. Mater. Sci. Eng.
0965-0393, 13
, pp. 77
–93
.17.
Nandan
, R.
, Roy
, G. G.
, Lienert
, T. J.
, and Debroy
, T.
, 2007, “Three-Dimensional Heat and Material Flow During Friction Stir Welding of Mild Steel
,” Acta Mater.
1359-6454, 55
, pp. 883
–895
.18.
Chao
, Y. J.
, Qi
, X.
, and Tang
, W.
, 2003, “Heat Transfer in Friction Stir Welding-Experimental and Numerical Studies
,” ASME J. Manuf. Sci. Eng.
1087-1357, 125
, pp. 138
–145
.19.
Seidel
, T. U.
, and Reynolds
, A. P.
, 2003, “Two-Dimensional Friction Stir Welding Process Model Based on Fluid Mechanics
,” Sci. Technol. Weld. Joining
1362-1718, 8
(3
), pp. 175
–183
.20.
Buffa
, G.
, Hua
, J.
, Shivpuri
, R.
, and Fratini
, L.
, 2006, “A Continuum Based FEM Model for Friction Stir Welding-Model Development
,” Mater. Sci. Eng., A
0921-5093, 419
, pp. 389
–396
.21.
Cho
, J. H.
, Boyce
, D. E.
, and Dawson
, P. R.
, 2007, “Modeling of Strain Hardening During Friction Stir Welding of Stainless Steel
,” Int. J. Numer. Methods Eng.
0029-5981, 15
, pp. 469
–486
.22.
Prangnell
, P. B.
, and Heason
, C. P.
, 2005, “Grain Structure Formation During Friction Stir Welding Observed by the ‘Stop Action Technique’
,” Acta Mater.
1359-6454, 53
, pp. 3179
–3192
.23.
Fonda
, R. W.
, Bingert
, J. F.
, and Colligan
, K. J.
, 2004, “Development of Grain Structure During Friction Stir Welding
,” Scr. Mater.
1359-6462, 51
, pp. 243
–248
.24.
Oh-Ishi
, K.
, Zhilyaev
, A. P.
, and McNelley
, T. R.
, 2006, “A Microtexture Investigation of Recrystallization During Friction Stir Processing of As-Cast NiAL Bronze
,” Metall. Mater. Trans. A
1073-5623, 37A
(7
), pp. 2239
–2251
.25.
Cho
, J. H.
, Boyce
, D. E.
, and Dawson
, P. R.
, 2005, “Modeling Strain Hardening and Texture Evolution in Friction Stir Welding of Stainless Steel
,” Mater. Sci. Eng., A
0921-5093, 398
, pp. 146
–163
.26.
Chen
, Y. C.
, Liu
, H. J.
, and Feng
, J. C.
, 2006, “Friction Stir Welding Characteristics of Different Heat-Treated-State 2219 Aluminum Alloy Plates
,” Mater. Sci. Eng., A
0921-5093, 420
, pp. 21
–25
.27.
James
, M. N.
, Bradley
, G. R.
, Lombard
, H.
, and Hattingh
, D. G.
, 2005, “The Relationship Between Process Mechanisms and Crack Paths in Friction Stir Welded 5083-H321 and 5383-H321 Aluminium Alloys
,” Fatigue Fract. Eng. Mater. Struct.
8756-758X, 28
, pp. 245
–256
.28.
Adams-Hughes
, M.
, Kalu
, P. N.
, Khraisheh
, M. K.
, and Chandra
, N.
, 2005, “Microstructure Refinement and Void Evolution Via Friction Stir Processing of AA 5052
,” Microsc. Microanal.
1431-9276, 11
(Suppl 2
), pp. 1698
–1699
.29.
Zhang
, H.
, Lin
, S. B.
, Wu
, L.
, Feng
, J. C.
, and Ma
, S. L.
, 2006, “Defects Formation Procedure and Mathematic Model for Defect Free Friction Stir Welding of Magnesium Alloy
,” Mater. Des.
0264-1275, 27
(9
), pp. 805
–809
.30.
Bendzsak
, G. J.
, North
, T. H.
, and Smith
, C. B.
, 2000, “An Experimentally Validated 3D Model for Friction Stir Welding
,” Proceedings of the Second International Symposium on Friction Stir Welding
, TWI
, Gotherburg, Sweden
.31.
McClintock
, F. A.
, 1968, “A Criterion for Ductile Fracture by Growth of Holes
,” ASME J. Appl. Mech.
0021-8936, 35
, pp. 363
–371
.32.
Rice
, J. R.
, and Tracey
, D. M.
, 1969, “On the Ductile Enlargement of Voids in Triaxial Stress Fields
,” J. Mech. Phys. Solids
0022-5096, 17
, pp. 201
–217
.33.
Gurson
, A. L.
, 1975, “Plastic Flow and Fracture Behavior of Ductile Materials Incorporating Void Nucleation, Growth and Interaction
,” Ph.D. thesis, Brown University, Providence, RI.34.
Tvergaard
, V.
, 1990, “Material Failure by Void Growth to Coalencence
,” Adv. Appl. Mech.
0065-2156, 27
, pp. 83
–151
.35.
Budiansky
, B.
, Hutchinson
, J. W.
, and Shutsky
, S.
, 1982, “Void Growth and Collapse in Viscous Solids
,” Mechanics of Solids
, H. G.
Hopkins
and M. J.
Sewell
, eds, Pergamon
, Oxford, UK
, pp. 13
–45
.36.
Cocks
, A. C. F.
, and Ashby
, M. F.
, 1982, “On Creep Fracture by Void Growth
,” Prog. Mater. Sci.
0079-6425, 27
, pp. 189
–244
.37.
Huang
, Y.
, 1991, “Accurate Dilatation Rates for Spherical Voids in Triaxial Stress Fields
,” ASME J. Appl. Mech.
0021-8936, 58
, pp. 1084
–1086
.38.
Lee
, Y. S.
, and Dawson
, P. R.
, 1993, “Modeling Ductile Void Growth in Viscoplastic Materials: Parts I and II
,” Mech. Mater.
0167-6636, 15
, pp. 21
–52
.39.
Hart
, E. W.
, 1976, “Constitutive Relations for the Nonelastic Deformation of Metals
,” ASME J. Eng. Mater. Technol.
0094-4289, 98
, pp. 193
–202
.40.
Eggert
, G. M.
, and Dawson
, P. R.
, 1987, “On the Use of Internal Variable Constitutive Equations in Transient Forming Processes
,” Int. J. Mech. Sci.
0020-7403, 29
(2
), pp. 95
–113
.41.
Davison
, L.
, Stevens
, A. L.
, and Kipp
, M. E.
, 1977, “Theory of Spall Damage Accumulation in Ductile Metals
,” J. Mech. Phys. Solids
0022-5096, 25
, pp. 11
–28
.42.
Coffin
, L. F.
, and Rogers
, H. C.
, 1967, “Influence of Pressure on the Structural Damage in Metal Forming Processes
,” ASME J. Appl. Mech.
0021-8936, 60
, pp. 672
–686
.43.
Murakami
, S.
, and Ohno
, N.
, 1981, “A Continuum Theory of Creep and Creep Damage
,” Creep in Structures
, A. R. S.
Ponter
and D. R.
Hayhurst
, eds, Springer
, New York
, pp. 422
–444
.44.
Fisher
, E. S.
, 1966, “Temperature Dependence of the Elastic Moduli in Alpha Uranium Single Crystals. PT. 4. 298to923K
,” J. Nucl. Mater.
0022-3115, 18
, pp. 39
–54
.45.
Dawson
, P. R.
, 1984, “A Model for the Hot or Warm Forming of Metals With Special Use of Deformation Mechanism Maps
,” Int. J. Mech. Sci.
0020-7403, 26
, pp. 227
–244
.46.
Dawson
, P. R.
, 1987, “On Modeling of Mechanical Property Changes During Flat Rolling of Aluminum
,” Int. J. Solids Struct.
0020-7683, 23
, pp. 947
–968
.47.
Balay
, S.
, Buschelman
, K.
, Eijkhout
, V.
, Gropp
, W.
, Kaushik
, D.
, Knepley
, M.
, McInnes
, L. C.
, Smith
, B.
, and Zhang
, H.
, 2006, PETSc User Manual, Argonne National Laboratory, Argonne, IL.48.
Okamoto
, K.
, Hirano
, S.
, Inagaki
, M.
, Park
, S. H. C.
, Sato
, Y. S.
, and Kokawa
, H.
, 2003, “Metallurgical and Mechanical Properties of Friction Stir Welded Stainless Steels
,” Proceedings of the Fourth International Symposium on Friction Stir Welding
, TWI
, Park City, UT
.49.
Park
, S. H. C.
, Sato
, Y. S.
, Kokawa
, H.
, Okamoto
, K.
, Hirano
, S.
, and Inagaki
, M.
, 2003, “Rapid Formation of the Sigma Phase in 304 Stainless Steel During Friction Stir Welding
,” Scr. Mater.
1359-6462, 49
, pp. 1175
–1180
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
