Solid Freeform Fabrication (SFF) processes allow the automated building of three-dimensional shapes by successively depositing material in layers. Residual stress-induced tolerance losses are principal concerns in using these processes to create functional parts. Thermomechanical models of temperatures and stresses are presented, which are relevant to controlling residual stress effects in SFF processes. Models are applied to a particular SFF process; however, insights and conclusions are applicable to a large number of related processes. The temporal evolution of temperatures and stresses is investigated at two levels of detail. The successive deposition of layers of material is investigated first using one-dimensional simulations, approximating the build-up of residual stress in a multi-layered part. The successive deposition of a column of molten metal droplets (a technique used to create thick layers) is then modeled using two-dimensional axisymmetric simulations. Insights are given into process changes that can minimize residual stress-related effects in manufactured parts, including part constraint and localized preheating near the point of deposition. Results for thermomechanical interactions between droplets deposited in a column provide the foundation for studying interactions between adjacently deposited droplets, which is addressed in Part 2.

1.
Bourell, D. L., Beaman, J. J., Crawford, R. H., Marcus, H. L., and Barlow, J. W., eds., 2000, Solid Freeform Fabrication Proceedings, Proc. 2000 Solid Freeform Fabrication Symposium, Austin, August 2000.
2.
Beuth
,
J. L.
, and
Narayan
,
S. H.
,
1996
, “
Residual Stress-Driven Delamination in Deposited Multi-layers
,”
Int. J. Solids Struct.
,
33
, No.
1
, pp.
65
78
.
3.
Narayan
,
S. H.
, and
Beuth
,
J. L.
,
1997
, “
Axisymmetric Delamination in Deposited Multi-Layers
,”
Int. J. Solids Struct.
,
34
, Nos.
35–36
, pp.
4617
4631
.
4.
Griffith, M. L., Keicher, D. L., Atwood, C. L., Romero, J. A., Smugeresky, J. E., Harwell, L. D., and Greene, D. L., 1996, “Free Form Fabrication of Metallic Components Using Laser Engineered Net Shaping (LENS),” Solid Freeform Fabrication Proceedings (D. L. Bourell, J. J. Beaman, H. L. Marcus, R. H. Crawford, and J. W. Barlow, eds.), Proc. 1996 Solid Freeform Fabrication Symposium, Austin, August 1996, pp. 125–132.
5.
Das, S., Fuesting, T. P., Danyo, G., Brown, L. E., Beaman, J. J., Bourell, D. L., and Sargent, K., 1998, “
Direct Laser Fabrication of a Gas Turbine Engine Component - Microstructure and Properties - Part I and Part II,” Solid Freeform Fabrication Proceedings (D. L. Bourell, J. J. Beaman, R. H. Crawford, H. L. Marcus, and J. W. Barlow, eds.), Proc. 1998 Solid Freeform Fabrication Symposium, Austin, August 1998, pp. 1–18.
6.
Merz, R., Prinz, F. B., Ramaswami, K., Terk, M., and Weiss, L. E., 1994, “Shape Deposition Manufacturing,” Solid Freeform Fabrication Proceedings (H. L. Marcus, J. J. Beaman, D. L. Bourell, J. W. Barlow, and R. H. Crawford, eds.), Proc. 1994 Solid Freeform Fabrication Symposium, Austin, August 1994, pp. 1–8.
7.
Amon
,
C. H.
,
Beuth
,
J. L.
,
Merz
,
R.
,
Prinz
,
F. B.
, and
Weiss
,
L. E.
,
1998
, “
Shape Deposition Manufacturing with Microcasting: Processing, Thermal and Mechanical Issues
,”
ASME J. Manuf. Sci. Eng.
,
120
, No.
3
, pp.
656
665
.
8.
Chin
,
R. K.
,
Beuth
,
J. L.
, and
Amon
,
C. H.
,
2001
, “
Successive Deposition of Metals in Solid Freeform Fabrication Processes Part II: Thermomechanical Models of Adjacent Droplets
,”
ASME J. Manuf. Sci. Eng.
,
123
, pp.
632
638
.
9.
Brown
,
S.
, and
Song
,
H.
,
1992
, “
Finite Element Simulation of Welding of Large Structures
,”
ASME J. Manuf. Sci. Eng.
,
114
, pp.
441
451
.
10.
Brown
,
S.
, and
Song
,
H.
,
1992
, “
Implications of Three-Dimensional Numerical Simulations of Welding of Large Structures
,”
Weld. J. (Miami)
,
71
, pp.
55s–62s
55s–62s
.
11.
Michaleris
,
P.
, and
DeBiccari
,
A.
,
1997
, “
Prediction of Welding Distortion
,”
Weld. J. (Miami)
,
76
(
4
), pp.
172s–181s
172s–181s
.
12.
Ueda
,
Y.
,
Murakawa
,
H.
,
Gu
,
S. M.
,
Okumoto
,
Y.
, and
Kamichika
,
R.
,
1992
, “
Simulation of Welding Deformation for Precision Ship Assembling (Report I): In-Plane Deformation of Butt Welded Plate
,”
Trans. JWRI
,
21
, pp.
265
275
.
13.
Chakravarti, A., Malik, L. M., and Golak, J., 1986, “
Prediction of Distortion and Residual Stresses in Panel Welds,” Symposium on Computer Modeling of Fabrication Processes and Constitutive Behavior of Metals, Ottawa, Ontario, pp. 547–561.
14.
El-Kaddah
,
N.
,
McKelliget
,
J. W.
, and
Szekely
,
J.
,
1984
, “
Heat Transfer and Fluid Flow in Plasma Spraying
,”
Metall. Trans. B
,
15
, pp.
59
70
.
15.
Trapaga
,
G.
,
Matthys
,
E. F.
,
Valencia
,
J. J.
, and
Szekely
,
J.
,
1992
, “
Fluid Flow, Heat Transfer, and Solidification of Molten Metal Droplets Impinging on Substrates: Comparison of Numerical and Experimental Results
,”
Metall. Trans. B
,
23B
, pp.
701
718
.
16.
Zhao
,
Z.
, and
Poulikakos
,
D.
,
1996
, “
Heat Transfer and Fluid Dynamics During the Collision of a Liquid Droplet on a Substrate - I Modeling
,”
Int. J. Heat Mass Transf.
,
39
, pp.
2771
2789
.
17.
Pasandideh-Fard
,
M.
,
Bhola
,
R.
,
Chandra
,
S.
, and
Mostaghimi
,
J.
,
1998
, “
Deposition of Tin Droplets on a Steel Plate: Simulations and Experiments
,”
Int. J. Heat Mass Transf.
,
41
, pp.
2929
2945
.
18.
Gill
,
S. C.
, and
Clyne
,
T. W.
,
1990
, “
Stress Distributions and Material Response in Thermal Spraying of Metallic and Ceramic Deposits
,”
Metall. Trans. B
,
21B
, pp.
377
385
.
19.
Weiner
,
J. H.
, and
Boley
,
B. A.
,
1963
, “
Elasto-plastic Thermal Stresses in a Solidifying Body
,”
J. Mech. Phys. Solids
,
11
, pp.
145
154
.
20.
Landau
,
H. G.
,
Weiner
,
J. H.
, and
Zwicky
, Jr.,
E. E.
,
1960
, “
Thermal Stress in a Viscoelastic-Plastic Plate with Temperature-dependent Yield Stress
,”
ASME J. Appl. Mech.
,
27
, pp.
297
302
.
21.
Thomas
,
B. G.
,
Samarasekera
,
I. V.
, and
Brimacombe
,
J. K.
,
1987
, “
Mathematical Modeling of the Thermal Processing of Steel Ingots: Part I. Heat Flow Model
,”
Metall. Trans. B
,
18B
, pp.
119
130
.
22.
Thomas
,
B. G.
,
Samarasekera
,
I. V.
, and
Brimacombe
,
J. K.
,
1987
, “
Mathematical Modeling of the Thermal Processing of Steel Ingots: Part II. Stress Model
,”
Metall. Trans. B
,
18B
, pp.
131
147
.
23.
Zabaras
,
N.
,
Ruan
,
Y.
, and
Richmond
,
O.
,
1991
, “
On the Calculation of Deformations and Stresses during Axially Symmetric Solidification
,”
ASME J. Appl. Mech.
,
58
, pp.
865
871
.
24.
Chin
,
R. K.
,
Beuth
,
J. L.
, and
Amon
,
C. H.
,
1996
, “
Thermomechanical Modeling of Molten Metal Droplet Solidification Applied to Layered Manufacturing
,”
Mech. Mater.
,
24
, pp.
257
271
.
25.
Chin, R. K., Beuth, J. L., and Amon, C. H., 1995, “
Control of Residual Thermal Stresses in Shape Deposition Manufacturing,” Solid Freeform Fabrication Proceedings (H. L. Marcus, J. J. Beaman, D. L. Bourell, J. W. Barlow, and R. H. Crawford, eds.), Proc. 1995 Solid Freeform Fabrication Symposium, Austin, August 1995, pp. 221–228.
26.
Chin, R. K., Beuth, J. L., and Amon, C. H., 1996, “
Thermomechanical Modeling of Successive Material Deposition in Layered Manufacturing,” Solid Freeform Fabrication Proceedings (D. L. Bourell, J. J. Beaman, H. L. Marcus, R. H. Crawford, and J. W. Barlow, eds.), Proc. 1996 Solid Freeform Fabrication Symposium, Austin, August 1996, pp. 507–514.
27.
Klingbeil, N. W., Zinn, J. W., and Beuth, J. L., 1997, “
Measurement of Residual Stresses in Parts Created by Shape Deposition Manufacturing,” Solid Freeform Fabrication Proceedings, (D. L. Bourell, J. J. Beaman, R. H. Crawford, H. L. Marcus, and J. W. Barlow, eds.), Proc. 1997 Solid Freeform Fabrication Symposium, Austin, August 1997, pp. 125–132.
28.
Klingbeil, N. W., Beuth, J. L., Chin, R. K., and Amon, C. H., 1998, “
Measurement and Modeling of Residual Stress-Induced Warping in Direct Metal Deposition Processes,” Solid Freeform Fabrication Proceedings (D. L. Bourell, J. J. Beaman, R. H. Crawford, H. L. Marcus, and J. W. Barlow, eds.), Proc. 1998 Solid Freeform Fabrication Symposium, Austin, August 1998, pp. 367–374.
29.
Fessler, J. R., Merz, R., Nickel, A. H., and Prinz, F. B., 1996, “
Laser Deposition of Metals for Shape Deposition Manufacturing,” Solid Freeform Fabrication Proceedings, (D. L. Bourell, J. J. Beaman, H. L. Marcus, R. H. Crawford, and J. W. Barlow, eds.), Proc. 1996 Solid Freeform Fabrication Symposium, Austin, August 1996, pp. 117–124.
30.
Nickel, A. H., Barnett, D. M., and Prinz, F. B., 2001, “
Deposition Pattern Effects in Layered Manufacturing,” submitted to Materials Science and Engineering.
31.
Yao, W. L., and Leu, M. C., 1998, “
Shell Cracking in Investment Casting with Laser Stereolithography Patterns,” Solid Freeform Fabrication Proceedings (D. L. Bourell, J. J. Beaman, R. H. Crawford, H. L. Marcus, and J. W. Barlow, eds.), Proc. 1998 Solid Freeform Fabrication Symposium, Austin, August 1998, pp. 427–434.
32.
Amon
,
C. H.
,
Schmaltz
,
K. S.
,
Merz
,
R.
, and
Prinz
,
F. B.
,
1996
, “
Numerical and Experimental Investigation of Interface Bonding via Substrate Remelting of an Impinging Molten Metal Droplet
,”
ASME J. Heat Transfer
,
118
, pp.
164
172
.
33.
Zarzalejo
,
L. J.
,
Schmaltz
,
K. S.
, and
Amon
,
C. H.
,
1999
, “
Molten Droplet Solidification and Substrate Remelting in Microcasting Part I: Numerical Modeling and Experimental Verification
,”
Int. J. Heat Mass Transf.
,
34
, pp.
477
486
.
34.
Schmaltz
,
K. S.
,
Zarzalejo
,
L. J.
, and
Amon
,
C. H.
,
1999
, “
Molten Droplet Solidification and Substrate Remelting in Microcasting Part II: Parametric Study and Effect of Dissimilar Materials
,”
Int. J. Heat Mass Transf.
,
35
, pp.
17
23
.
35.
Orme
,
M. E.
,
Huang
,
C.
, and
Courter
,
J.
,
1996
, “
Precision Droplet-Based Manufacturing and Material Synthesis: Fluid Dynamics and Thermal Control Issues
,”
Atomization Sprays
,
6
, pp.
305
329
.
36.
Orme
,
M. E.
, and
Huang
,
C.
,
1997
, “
Phase Change Manipulation for Droplet-Based Solid Freeform Fabrication
,”
ASME J. Heat Transfer
,
119
, pp.
818
823
.
37.
Schmaltz, K. S., 1997, The Impinging Behavior of a Molten Metal Droplet: Integration of Analytical, Numerical and Experimental Techniques, Doctoral Thesis, Carnegie Mellon University, Department of Mechanical Engineering.
38.
Schmaltz, K. S., and Amon, C. H., 1995, “
Experimental Verification of an Impinging Molten Metal Droplet Numerical Simulation,” Modeling of Heat Transfer in Multi-Phase Systems, ASME HTD-Vol. 317-1, pp. 219–226
39.
Peckner, D., and Bernstein, I. M., 1977, Handbook of Stainless Steels, McGraw-Hill, pp. 19-3, 19-7, 21-5, and 21-6.
40.
Ryan, N. D., and McQueen, H. J., 1987, “
Strain Rate and Temperature Dependence of Hot Strength in 301, 304, 316, and 317 Steels in As-cast and Worked Conditions,” Stainless Steels’ 87, Institute of Metals, London.
41.
McQueen
,
H. J.
,
Jin
,
N.
, and
Ryan
,
N. D.
,
1994
, “
Relationship of Energy Dissipation Efficiency to Microstructural Evolution in Hot Working of AISI 304 Steel
,”
Mater. Sci. Eng., A
,
190
, pp.
43
53
.
42.
Klingbeil, N. W., 1998, Residual Stress-Induced Warping and Interlayer Debonding in Layered Manufacturing, Doctoral Thesis, Carnegie Mellon University, Department of Mechanical Engineering.
43.
Touloukian, Y. S., ed., 1967, Thermophysical Properties of High Temperature Solid Materials, Volume 3: Ferrous Alloys, MacMillan, New York.
44.
Incropera, F. P., and DeWitt, D. P., 1985, Fundamentals of Heat and Mass Transfer, Second Edition, John Wiley & Sons, Appendix A. Thermophysical Properties of Matter.
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