This study examines the elastic recovery (springback) of a porous tantalum foam after sheet forming operations. The foam and sheet-like form is applicable to bone ingrowth surfaces on orthopedic implants and is desirable due to its combination of high strength, low relative density, and excellent osteoconductive properties. Forming of the foam improves nestability during manufacture and is essential to have the material achieve the desired shape. Experimentally, bending about a single axis using a wiping die is studied by observing cracking and measuring springback. Die radius and clearance strongly affect the springback properties, while punch speed, embossing, die radius, and clearance all influence cracking. To study the effect of the foam microstructure, bending also is examined numerically. A horizontal hexagonal mesh comprised of beam elements is employed, which allows for the densification that occurs during forming. The flow strength of individual tantalum struts is directly measured in an atomic force microscope. The numerical results show that as the hexagonal cells are elongated along the sheet length, elastic springback decreases. By changing the material properties of the struts, the models can be modified for use with other open-cell metallic foams.

References

References
1.
Bobyn
,
J.
,
Stackpool
,
G.
,
Hacking
,
S.
,
Tanzer
,
M.
, and
Krygier
,
J.
, 1999, “
Characteristics of Bone Ingrowth and Interface Mechanics of a New Porous Tantalum Biomaterial
,”
J. Bone Joint Surg.
,
81-B
, pp.
907
913
.
2.
Bobyn
,
J. D.
,
Toh
,
K.-K.
,
Hacking
,
S. A.
,
Tanzer
,
M.
, and
Krygier
,
J. J.
, 1999, “
Tissue Response to Porous Tantalum Acetabular Cups
,”
J. Arthroplasty
,
14
, pp.
347
353
.
3.
Nebosky
,
P. S.
, and
Schmid
,
S. R.
, 2007, “
Formability of Porous Tantalum Sheet Metal
,”
Trans. NAMRI
,
35
, pp.
57
64
.
4.
Kalpakjian
,
S.
, and
Schmid
,
S. R.
, 2010,
Manufacturing Engineering and Technology
,
6th ed.
,
Prentice-Hall
,
Upper Saddle River (NJ)
.
5.
Sturm
,
R.
, and
Fletcher
,
B.
, 1941, “
Determining Springback-I: Calculating Die Radius to Bend Desired Curve
,”
Prod. Eng.
,
12
, pp.
526
528
.
6.
Sturm
,
R.
, and
Fletcher
,
B.
, 1941 “
Determining Springback-II: Calculating Die Radius to Bend Desired Curve
,”
Prod. Eng.
,
12
, pp.
590
594
.
7.
Chapman
,
F.
,
Hazlett
,
T.
, and
Schroeder
,
W.
, 1942, “
Springback in Flanging: Curves and Table for Determining Die-Block Angle
,”
Prod. Eng.
,
13
, pp.
382
383
.
8.
Schroeder
,
W.
, 1943, “
Mechanics of Sheet-Metal Bending
,”
Trans. ASME
,
65
, pp.
817
827
.
9.
Sachs
,
G.
, 1951,
Principles and Methods of Sheet-metal Fabricating
,
Reinhold Publishing Corporation
,
New York
.
10.
Gardiner
,
F.
, 1957, “
The Spring Back of Metals
,”
Trans. ASME
,
79
, pp.
1
9
.
11.
Queener
,
C.
, and
DeAngelis
,
R.
, 1968, “
Elastic Springback and Residual Stresses in Sheet Metal Formed by Bending
,”
Trans. ASME
,
61
, pp.
757
768
.
12.
Sidebottom
,
O.
, and
Gebhardt
,
C.
, 1979, “
Elastic Springback in Plates and Beams Formed by Bending
,”
Exp. Mech.
,
19
, pp.
371
377
.
13.
Johnson
,
W.
, and
Yu
,
T.
, 1981, “
Springback After the Biaxial Elastic-Plastic Pure Bending of a Rectangular Plate-I
,”
Int. J. Mech. Sci.
,
23
, pp.
619
630
.
14.
Wang
,
C. T.
,
Kinzel
,
G.
, and
Altan
,
T.
, 1993, “
Mathematical Modeling of Plane-Strain Bending of Sheet and Plate
,”
J. Mater. Process. Technol.
,
39
, pp.
279
304
.
15.
Kim
,
H.
,
Nargundkar
,
N.
, and
Altan
,
T.
, 2007, “
Prediction of Bend Allowance and Springback in Air Bending
,”
J. Manuf. Sci. Eng.
,
129
, pp.
342
351
.
16.
Panthi
,
S. K.
,
Ramakrishnan
,
N.
,
Pathak
,
K. K.
, and
Chouhan
,
J. S.
, 2007, “
An Analysis of Springback in Sheet Metal Bending Using Finite Element Method (FEM)
,”
J. Mater. Process. Technol.
,
186
, pp.
120
124
.
17.
Cho
,
J. R.
,
Moon
,
S. J.
,
Moon
,
Y. H.
, and
Kang
,
S. S.
, 2003, “
Finite Element Investigations on Springback Characteristics in Sheet Metal U-Bending Process
,”
J. Mater. Process. Technol.
,
141
, pp.
109
116
.
18.
Lee
,
Y. E.
,
Lee
,
H. P.
, and
Cheok
,
B. T.
, 2005, “
Finite Element Analysis of Springback in L-Bending of Sheet Metal
,”
J. Mater. Process. Technol.
,
168
, pp.
296
302
.
19.
Bralla
,
J.
, 1998,
Design for Manufacturability Handbook.
McGraw-Hill
,
New York.
20.
Zhou
,
J.
,
Mercer
,
C.
, and
Soboyejo
,
W.
, 2002, “
An Investigation of the Microstructure and Strength of Open-Cell 6101 Aluminum Foams
,”
Metall. Mater. Trans. A
,
33A
, pp.
1413
1427
.
21.
Black
,
J.
, 1994, “
Biological Performance of Tantalum
,”
Clin. Mater.
,
16
, pp.
167
173
.
22.
Hector
,
L. G.
, and
Schmid
,
S. R.
, 1998, “
Simulation of Asperity Plowing in an Atomic Force Microscope. Part I: Experimental and Theoretical Models
,”
Wear
,
215
, pp.
247
256
.
23.
Burnett
,
P. J.
, and
Rickerby
,
D. S.
, 1984, “Surface Softening in Silicon by Ion Implantation,”
J. Mater. Sci.
,
19
, pp.
845
860
.
24.
Ashby
,
M. F.
,
Evans
,
A.
,
Fleck
,
N. A.
,
Gibson
,
L. J.
,
Hutchinson
,
J. W.
, and
Wadley
,
H. N. G.
, 2000,
Metal Foams: A Design Guide
,
Butterworth-Heinemann
, Oxford, UK.
25.
Gibson
,
L. J.
, and
Ashby
,
M. J.
, 1997,
Cellular Solids: Structures and Properties
,
2nd ed.
Pergamon
, Oxford, UK.
26.
Gibson
,
L. J.
, and
Ashby
,
M. J.
, 1982, “
The Mechanics of Three-Dimensional Cellular Materials
,”
Proc. R. Soc. London
,
382
, pp.
43
59
.
27.
Gibson
,
L. J.
, 1989, “
Modelling the Mechanical Behavior of Cellular Materials
,”
Mater. Sci. Eng. A
,
110
, pp.
1
36
.
28.
Gioux
,
G.
,
McCormiack
,
T. M.
, and
Gibson
,
L. J.
, 2000, “
Failure of Aluminum Foams Under Multiaxial Loads
,”
Int. J. Mech. Sci.
,
42
, pp.
1097
1117
.
29.
McCullough
,
K. Y. G.
,
Fleck
,
N. A.
, and
Ashby
,
M. F.
, 1999, “
Toughness of Aluminum Alloy Foams
,”
Acta Mater.
,
47
, pp.
2231
2343
.
30.
Harte
,
A. M.
,
Fleck
,
N. A.
, and
Ashby
,
M. F.
, 1999, “
Fatigue Failure of an Open Cell and a Closed Cell Aluminum Alloy Foam
,”
Acta Mater.
,
47
, pp.
2511
2524
.
31.
Sugimura
,
Y.
,
Rabiei
,
A.
,
Evans
,
A. G.
,
Harte
,
A. M.
, and
Fleck
,
N. A.
, 1999, “
Compression Fatigue of a Cellular Al Alloy
,”
Mater. Sci. Eng. A
,
269
, pp.
38
48
.
32.
Smith
,
A.
,
Niebur
,
G.
, and
Schmid
,
S. R.
, 2002, “
Forming of Metal Foams
,”
Trans. NAMRI
,
30
, pp.
3
8
.
33.
Deshpande
,
V. S.
, and
Fleck
,
N. A.
, 2000, “
Isotropic Constitutive Models for Metallic Foams
,”
J. Mech. Phys. Solids
,
48
, pp.
1253
1283
.
34.
Meguid
,
S. A.
,
Cheon
,
S. S.
, and
El-Abbasi
,
N.
, 2002, “
FE Modelling of Deformation Localization in Metallic Foams
,”
Finite Elem. Anal. Design
,
38
, pp.
631
643
.
35.
Santosa
,
S.
, and
Wierzbicki
,
T.
, 1998, “
On the Modeling of Crush Behavior of a Closed-Cell Aluminum Foam Structures
,”
J. Mech. Phys. Solids
,
46
, pp.
645
669
.
36.
Santosa
,
S.
, and
Wierzbicki
,
T.
, 1998, “
Crash Behavior of Columns Filled With Aluminum Honeycomb or Foam
,”
Comput. Struct.
,
68
, pp.
343
367
.
37.
Young
,
W. C.
, and
Budynas
,
R. G.
, 2002,
Roark’s Formulas for Stress and Strain
,
7th ed.
,
McGraw-Hill
,
New York
.
38.
Nebosky
,
P. S.
, 2006, “
Porous Metal Scaffolds for Bone Ingrowth
,” Ph.D. thesis,
University of Notre Dame
.
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