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.
Issue Section:
Technical Papers
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
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
