Titanium foams of relative density ranging from 0.3 to 0.9 were produced by titanium powder sintering procedures and tested in uniaxial compression at strain rates ranging from 0.01 to 2,000 s ？1. The material microstructure was examined by X-ray tomography and Scanning Electron Microscopy (SEM) observations. The foams investigated are strain rate sensitive, with both the yield stress and the strain hardening increasing with applied strain rate, and the strain rate sensitivity is more pronounced in foams of lower relative density. Finite element simulations were conducted modelling explicitly the material’s microstructure at the micron level, via a 3D Voronoi tessellation. Low and high strain rate simulations were conducted in order to predict the material’s compressive response, employing both rate-dependant and rate-independent constitutive models. Results from numerical analyses suggest that the primary source of rate sensitivity is represented by the intrinsic sensitivity of the foam’s parent material.
References
[1]
Long, M.; Rack, H.J. Titanium alloys in total joint replacement—A material science perspective. Biomaterials 1998, 19, 1621–1639, doi:10.1016/S0142-9612(97)00146-4.
[2]
Nemat-Nasser, S.; Guo, W.G.; Cheng, J.Y. Mechanical properties and deformation mechanisms of commercially pure Titanium. Acta Mater. 1999, 47, 3705–3720, doi:10.1016/S1359-6454(99)00203-7.
[3]
Ashby, M.F.; Evans, A.G.; Fleck, N.A.; Hutchinson, J.W.; Wadley, H.N.G.; Gibson, L.J. Making metal foams. In Metal Foams: A Design Guide; Butterworth-Heinemann: Burlington, MA, USA, 2000.
[4]
Lefebvre, L.P.; Baril, E.; Bureau, M.N. Effect of the oxygen content in solution on the static and cyclic deformation of titanium foams. J. Mater. Sci. Mater. Med. 2009, 20, 2223–2233, doi:10.1007/s10856-009-3798-x.
[5]
Jorgensen, D.J.; Dunand, D.C. Ti-6Al-4V with micro- and macropores produced by powder sintering and electrochemical dissolution of steel wires. Mater. Sci. Eng. A 2010, 527, 849–853, doi:10.1016/j.msea.2009.08.034.
[6]
Guden, M.; Celik, E.; Akar, E.; Cetiner, S. Compression testing of a sintered Ti6Al4V powder compact for biomedical applications. Mater. Char. 2005, 54, 399–408, doi:10.1016/j.matchar.2005.01.006.
[7]
Rouxel, A.; Chiem, C.Y. Strain-rate history effects on TiAl6V4 titanium alloy. Impact Loading Dynam. Behav. Mater. 1988, 2, 601–608.
[8]
Meyer, L.W.; Krüger, L.; Razorenov, S.V.; Kanel, G.I. Investigation of dynamic flow and strength properties of Ti-6-22-22S at normal and elevated temperatures. In. J. Impact Eng. 2003, 28, 877–890, doi:10.1016/S0734-743X(02)00151-3.
[9]
Wen, C.E.; Yamada, Y.; Shimojima, K.; Chino, Y.; Asahina, T.; Mabuchi, M. Processing and mechanical properties of autogenious titanium implant materials. J. Mater. Sci. Mater. Med. 2002, 13, 397–401, doi:10.1023/A:1014344819558.
[10]
Wen, C.E.; Mabuchi, M.; Yamada, Y.; Shimojima, K.; Chino, Y.; Asahina, T. Processing of biocompatible porous Ti and Mg. Scr. Mater. 2001, 45, 1147–1153, doi:10.1016/S1359-6462(01)01132-0.
[11]
Imwinkelried, T. Mechanical properties of open-pore titanium foam. J. Biomed. Mater. Res. A 2007, 81A, 964–970, doi:10.1002/jbm.a.31118.
[12]
Tuncer, N.; Arslan, G. Designing compressive properties of titanium foams. J. Mater. Sci. 2009, 44, 1477–1484, doi:10.1007/s10853-008-3167-z.
[13]
Thelen, S.; Barthelat, F.; Brinson, L.C. Mechanics considerations for microporous titanium as an orthopedic implant material. J. Biomed. Mater. Res. 2004, 69A, 601–610, doi:10.1002/jbm.a.20100.
[14]
Mori, T.; Tanaka, K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 1973, 21, 571–574, doi:10.1016/0001-6160(73)90064-3.
[15]
Ashby, M.F.; Gibson, L.J. Mechanics of foams. In Cellular Solids: Structure and Properties; Cambridge University Press: New York, NY, USA, 1997.
[16]
Deshpande, V.S.; Fleck, N.A. Isotropic constitutive models for metallic foams. J. Mech. Phys. Solid. 2000, 48, 1253–1283, doi:10.1016/S0022-5096(99)00082-4.
[17]
Radford, D.D.; Deshpande, V.S.; Fleck, N.A. The use of metal foam projectile to simulate shock loading on a structure. Int. J. Impact Eng. 2005, 31, 1152–1171, doi:10.1016/j.ijimpeng.2004.07.012.
[18]
Lefebvre, L.P.; Thomas, Y. Method of Making Open Cell Material. U.S. Patent 6,660,224, 9 December 2003.
[19]
Shen, H.; Oppenheimer, S.M.; Dunand, D.C.; Brinson, L.C. Numerical modeling of pore size and distribution in foamed titanium. Mech. Mater. 2006, 38, 933–944, doi:10.1016/j.mechmat.2005.06.027.
[20]
Borovinsek, M.; Ren, Z. Computational modelling of irregular open-cell foam under impact loading. Mater. Sci. Eng. Technol. 2008, 39, 114–120.
[21]
Gray, G.T. Classic Split Hopkinson Pressure Bar Testing; ASM International: Materials Park, OH, USA, 2000; pp. 462–476.
[22]
Voronoi, G. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. J. Pure Appl. Math. 1908, 133, 97–178.
[23]
Beta CAE Systems S.A. Ansa v. 12.1.3 User’s Guide; Makedonia Palace: Thessaloniki, Greece, 2008; Volume Meshing, pp. 503–575. Chapter 10.
[24]
Abaqus Analysis User’s Manual, Classical Metal Plasticity, Rate Dependence-Direct Tabular Data. Simulia Abaqus CAE 6.9 Documentation. Maastricht, The Nethelands, 2009.
