The stress–strain relationship for uniaxial compression of a metal hollow sphere material in large strains is obtained using a simplified model for the spheres’ deformation within a 3D block assuming a hexagonal packing pattern. The yield strength and material strain hardening are obtained as functions of the relative density in two characteristic loading directions. The expression for the stress–strain relationship consisting of quadratic and linear terms with respect to the relative density is linked to the partitioning of the deformation energy during compression. The theoretical predictions are compared with limited test results on mild steel hollow sphere material and finite element simulation results obtained by our group.

1.
Gibson
,
L. J.
, and
Ashby
,
M. F.
, 1997,
Cellular Solids: Structure and Properties
,
2nd ed.
,
Cambridge University Press
, Cambridge, UK.
2.
Lu
,
G.
, and
Yu
,
T. X.
, 2003,
Energy Absorption of Structures and Materials
,
Woodhead Publishing Ltd.
, Cambridge, UK.
3.
Hurysz
,
K. M.
,
Clark
,
J. L.
,
Nagle
,
A. R.
,
Hardwicke
,
C. U.
,
Lee
,
K. J.
,
Cochran
,
J. K.
, and
Sanders
,
T. H.
, 1998, “
Steel and Titanium Hollow Sphere Foams
,”
Porous and Cellular Materials for Structural Applications, MRS Proceedings
,
A.
Evans
,
D.
Schwartz
,
D.
Shih
, and
H.
Wadley
, eds.,
Materials Research Society
, Pittsburgh, PA, Vol.
521
, pp.
191
203
.
4.
Clark
,
J. L.
,
Hurysz
,
K. M.
,
Lee
,
K. J.
,
Cochran
,
J. K.
, and
Sanders
,
T. H.
, 1999, “
Stainless Steel Hollow Sphere Foams-Fabrication, Carburization, and Properties
,”
Metal Foams and Porous Metal Structures
,
J.
Banhart
,
M. F.
Ashby
, and
N. A.
Fleck
, eds.,
MIT Publishers
, Bremen, Germany, pp.
171
178
.
5.
Lim
,
T.-J.
,
Smith
,
B.
, and
McDowell
,
D. L.
, 2002, “
Behavior of a Random Hollow Sphere Metal Foam
,”
Acta Mater.
1359-6454,
50
, pp.
2867
2879
.
6.
Zhao
,
H.
,
Elnasri
,
I.
, and
Abdennadher
,
S.
, 2005, “
An Experimental Study on the Behavior Under Impact Loading of Metallic Cellular Materials
,”
Int. J. Mech. Sci.
0020-7403,
47
, pp.
757
774
.
7.
Gao
,
Z. Y.
,
Yu
,
T. X.
, and
Zhao
,
H.
, 2007, “
Mechanical Behavior of Metallic Hollow Sphere (MHS) Materials: An Experimental Study
,”
J. Aerosp. Eng.
0893-1321, submitted.
8.
Sanders
,
W. S.
, and
Gibson
,
L. J.
, 2003, “
Mechanics of Hollow Sphere Foams
,”
Mater. Sci. Eng., A
0921-5093,
347
, pp.
70
85
.
9.
Sanders
,
W. S.
, and
Gibson
,
L. J.
, 2003, “
Mechanics of BCC and FCC Hollow-Sphere Foams
,”
Mater. Sci. Eng., A
0921-5093,
352
, pp.
150
161
.
10.
Gasser
,
S.
,
Paun
,
F.
,
Cayzeele
,
A.
, and
Bréchet
,
Y.
, 2003, “
Uniaxial Tensile Elastic Properties of a Regular Stacking of Brazed Hollow Spheres
,”
Scr. Mater.
1359-6462,
48
, pp.
1617
1623
.
11.
Gasser
,
S.
,
Paun
,
F.
, and
Bréchet
,
Y.
, 2004, “
Finite Elements Computation for the Elastic Properties of a Regular Stacking of Hollow Spheres
,”
Mater. Sci. Eng., A
0921-5093,
379
, pp.
240
244
.
12.
Ruan
,
H. H.
,
Gao
,
Z. Y.
, and
Yu
,
T. X.
, 2006, “
Crushing of Thin-Walled Spheres and Sphere Arrays
,”
Int. J. Mech. Sci.
0020-7403,
48
, pp.
117
133
.
13.
Lekie
,
F. A.
, and
Penny
,
P. K.
, 1968, “
Plastic Instability of a Spherical Shell
,”
Engineering Plasticity
,
J.
Heyman
, and
F. A.
Leckie
, eds.,
Cambridge University Press
, Cambridge, UK, pp.
401
411
.
14.
Morris
,
A.
, and
Calladine
,
C. R.
, 1969, “
The Local Strength of Thin Spherical Shell Loaded Radially Through a Rigid Boss
,”
Proceedings 1st International Conference on Pressure Vessel Technology, Delft, Netherlands
,
I.
Berman
, ed.,
Pergamon
, Oxford, UK, pp.
35
44
.
15.
Updike
,
D. P.
, 1972, “
On the Large Deformation of a Rigid Plastic Spherical Shell Compressed by a Rigid Plate
,”
J. Eng. Ind.
0022-0817,
94
, pp.
949
955
.
16.
De Oliveira
,
J. G.
, and
Wierzbicki
,
T.
, 1982, “
Crushing Analysis of Rotationally Symmetrical Plastic Shells
,”
J. Strain Anal. Eng. Des.
0309-3247,
17
, pp.
229
236
.
17.
Reid
,
S. R.
, and
Reddy
,
T. Y.
, 1983, “
Experimental Investigation of Inertia Effects in One-Dimensional Metal Rings Systems Subjected to Impact - I. Fixed Ended Systems
,”
Int. J. Impact Eng.
0734-743X,
1
, pp.
85
106
.
18.
Shim
,
V. P. W.
, and
Stronge
,
W. J.
, 1986, “
Lateral Crushing of Tightly Packed Arrays of Thin-Walled Metal Tubes
,”
Int. J. Mech. Sci.
0020-7403,
28
, pp.
698
617
.
19.
Karagiozova
,
D.
,
Yu
,
T. X.
, and
Gao
,
Z. Y.
, 2006, “
Modeling of MHS Cellular Solid in Large Strains
,”
Int. J. Mech. Sci.
0020-7403,
48
, pp.
1273
1286
.
20.
Gao
,
Z. Y.
,
Yu
,
T. X.
, and
Karagiozova
,
D.
, 2007, “
Finite Element Simulation on the Mechanical Properties of MHS Materials
,”
Acta Mech. Sinica
,
23
, pp.
65
75
.
You do not currently have access to this content.