journal article·2018-06Open access

Effect of Pore Size, Morphology and Orientation on the Bulk Stiffness of a Porous Ti35Nb4Sn Alloy

Carmen Torres-Sanchez, John McLaughlin, Ross Bonallo

Abstract

The metal foams of a titanium alloy were designed to study porosity as well as pore size and shape independently. These were manufactured using a powder metallurgy/space-holder technique that allowed a fine control of the pore size and morphology; and then characterized and tested against well-established models to predict a relationship between porosity, pore size and shape, and bulk stiffness. Among the typically used correlations, existing power-law models were found to be the best fit for the prediction of macropore morphology against compressive elastic moduli, outperforming other models such as exponential, polynomial or binomial. Other traditional models such as linear ones required of updated coefficients to become relevant to metal porous sintered macrostructures. The new coefficients reported in this study contribute toward a design tool that allows the tailoring of mechanical properties through porosity macrostructure. The results show that, for the same porosity range, pore shape and orientation have a significant effect on mechanical performance and that they can be predicted. Conversely, pore size has only a mild impact on bulk stiffness.
Source: openalex_inverted_index · Quality: baseline

Research context

OpenAlex topics: Cellular and Composite Structures · Titanium Alloys Microstructure and Properties · Orthopaedic implants and arthroplasty

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (46)

Show source-provided references
1. J.M. Dewey, The Elastic Constants of Materials Loaded with Non-Rigid Fillers, J. Appl. Phys., 1947, 18(6), p 578–58110.1063/1.1697691 ↗
2. D.P.H. Hasselman and R.M. Fulrath, Effect of Small Fraction of Spherical Porosity on Elastic Moduli of Glass, J. Am. Ceram. Soc., 1964, 47(1), p 52–5310.1111/j.1151-2916.1964.tb14644.x ↗
3. M.Y. Balshin, Relation of Mechanical Properties of Powder Metals and their Porosity and the Ultimate Properties of Porous Metal-Ceramic Materials, in Dokl Akad Nauk SSSR, 1949, pp. 831–834
4. A.K. Maitra and K.K. Phani, Ultrasonic Evaluation of Elastic Parameters of Sintered Powder Compacts, J. Mater. Sci., 1994, 29(17), p 4415–441910.1007/BF00376263 ↗
5. L.J. Gibson and M.F. Ashby, Cellular Solids: Structure and Properties, 2nd ed., Cambridge University Press, Cambridge, 199710.1017/CBO9781139878326 ↗
6. M. Eudier, The Mechanical Properties of Sintered Low-Alloy Steels, Powder Metall., 1962, 5(9), p 278–29010.1179/pom.1962.5.9.005 ↗
7. O. Ishai and L.J. Cohen, Elastic Properties of Filled and Porous Epoxy Composites, Int. J. Mech. Sci., 1967, 9(8), p 539–54610.1016/0020-7403(67)90053-7 ↗
8. R.M. Spriggs, Expression for Effect of Porosity on Elastic Modulus of Polycrystalline Refractory Materials, Particularly Aluminum Oxide, J. Am. Ceram. Soc., 1961, 44(12), p 628–62910.1111/j.1151-2916.1961.tb11671.x ↗
9. F.P. Knudsen, Effect of Porosity on Young’s Modulus of Alumina, J. Am. Ceram. Soc., 1962, 45(2), p 94–9510.1111/j.1151-2916.1962.tb11089.x ↗
10. R.W. Rice, Extension of the Exponential Porosity Dependence of Strength and Elastic Moduli, J. Am. Ceram. Soc., 1976, 59, p 536–53710.1111/j.1151-2916.1976.tb09434.x ↗
11. B. Paul, Prediction of Elastic Constants of Multiphase Materials. Technical Report No. 3, Brown Univ., Providence, 1959
12. D.P.H. Hasselman, On the Porosity Dependence of the Elastic Moduli of Polycrystalline Refractory Materials, J. Am. Ceram. Soc., 1962, 45(9), p 452–45310.1111/j.1151-2916.1962.tb11191.x ↗
13. D.P. Mondal, N. Ramakrishnan, K.S. Suresh, and S. Das, On the Moduli of Closed-Cell Aluminum Foam, Scrip. Mater., 2007, 57(10), p 929–93210.1016/j.scriptamat.2007.07.021 ↗
14. S. Spinner, F.P. Knudsen and L. Stone, Elastic Constant- Porosity Relations for Polycrystalline Thoria. J. Res. Natl. Bur. Stand. C Eng. Instrum., 1963, Medium: X; Size: Article No. 3910.6028/jres.067C.005 ↗
15. J.K. Mackenzie, The Elastic Constants of a Solid containing Spherical Holes, Proc. Phys. Soc. Lond. B, 1950, 63(1), p 210.1088/0370-1301/63/1/302 ↗
16. L.F. Nielsen, Strength and Stiffness of Porous Materials, J. Am. Ceram. Soc., 1990, 73(9), p 2684–268910.1111/j.1151-2916.1990.tb06746.x ↗
17. T.T. Wu, The Effect of Inclusion Shape on the Elastic Moduli of a Two-Phase Material, Int. J. Solids Struct., 1966, 2(1), p 1–810.1016/0020-7683(66)90002-3 ↗
18. C.W. Bert, Prediction of Elastic Moduli of Solids with Oriented Porosity, J. Mater. Sci., 1985, 20(6), p 2220–222410.1007/BF01112307 ↗
19. L. Griffiths, M.J. Heap, T. Xu, C.-F. Chen, and P. Baud, The Influence of Pore Geometry and Orientation on the Strength and Stiffness of Porous Rock, J. Struct. Geol., 2017, 96, p 149–16010.1016/j.jsg.2017.02.006 ↗
20. A.R. Boccaccini, G. Ondracek et al., On the Effective Young’s Modulus of Elasticity for Porous Materials: Microstructure Modelling and Comparison Between Calculated and Experimental Values, J. Mech. Behav. Mat., 1993, 4, p 119–12610.1515/JMBM.1993.4.2.119 ↗
21. D.S. Li, Y.P. Zhang, X. Ma, and X.P. Zhang, Space-Holder Engineered Porous NiTi Shape Memory Alloys with Improved Pore Characteristics and Mechanical Properties, J. Alloys Compd., 2009, 474(1–2), p L1–L5
22. J. Xiong, Y. Li, X. Wang, P. Hodgson, and C.E. Wen, Mechanical Properties and Bioactive Surface Modification via Alkali-Heat Treatment of a Porous Ti-18Nb-4Sn Alloy for Biomedical Applications, Acta Biomater., 2008, 4(6), p 1963–196810.1016/j.actbio.2008.04.022 ↗
23. B. Jiang, N.Q. Zhao, C.S. Shi, X.W. Du, J.J. Li, and H.C. Man, A Novel Method for Making Open Cell Aluminum Foams by Powder Sintering Process, Mater. Lett., 2005, 59(26), p 3333–333610.1016/j.matlet.2005.05.068 ↗
24. W. Niu, C. Bai, G. Qiu, and Q. Wang, Processing and Properties of Porous Titanium Using Space Holder Technique, Mater. Sci. Eng. A, 2009, 506(1–2), p 148–15110.1016/j.msea.2008.11.022 ↗
25. A. Bansiddhi and D.C. Dunand, Shape-memory NiTi Foams Produced by Solid-State Replication with NaF, Intermetallics, 2007, 15(12), p 1612–162210.1016/j.intermet.2007.06.013 ↗
26. Y. Torres, J.J. Pavón, and J.A. Rodríguez, Processing and Characterization of Porous Titanium for Implants by Using NaCl as Space Holder, J. Mater. Process. Technol., 2012, 212(5), p 1061–106910.1016/j.jmatprotec.2011.12.015 ↗
27. J. Jakubowicz, G. Adamek, and M. Dewidar, Titanium Foam Made with Saccharose as a Space Holder, J. Porous Mater., 2013, 20(5), p 1137–114110.1007/s10934-013-9696-0 ↗
28. M. Köhl, T. Habijan, M. Bram, H.P. Buchkremer, D. Stöver, and M. Köller, Powder Metallurgical Near-Net-Shape Fabrication of Porous NiTi Shape Memory Alloys for Use as Long-Term Implants by the Combination of the Metal Injection Molding Process with the Space-Holder Technique, Adv. Eng. Mater., 2009, 11(12), p 959–96810.1002/adem.200900168 ↗
29. M.E. Gomes, J.S. Godinho, D. Tchalamov, A.M. Cunha, and R.L. Reis, Alternative Tissue Engineering Scaffolds Based on Starch: Processing Methodologies, Morphology, Degradation and Mechanical Properties, Mater. Sci. Eng. C, 2002, 20(1–2), p 19–2610.1016/S0928-4931(02)00008-5 ↗
30. A. Mansourighasri, N. Muhamad, and A.B. Sulong, Processing Titanium Foams Using Tapioca Starch as a Space Holder, J. Mater. Process. Technol., 2012, 212(1), p 83–8910.1016/j.jmatprotec.2011.08.008 ↗
31. Z. Esen and Ş. Bor, Processing of Titanium Foams Using Magnesium Spacer Particles, Scrip. Mater., 2007, 56(5), p 341–34410.1016/j.scriptamat.2006.11.010 ↗
32. H. Matsumoto, S. Watanabe, and S. Hanada, Beta TiNbSn Alloys with Low Young’s Modulus and High Strength, Mater. Trans., 2005, 46(5), p 1070–107810.2320/matertrans.46.1070 ↗
33. Y.F. Zheng, B.L. Wang, J.G. Wang, C. Li, and L.C. Zhao, Corrosion Behaviour of Ti-Nb-Sn Shape Memory Alloys in Different Simulated Body Solutions, Mater. Sci. Eng. A, 2006, 438–440, p 891–89510.1016/j.msea.2006.01.131 ↗
34. A. Nouri, P.D. Hodgson, and C. Wen, Effect of Ball-Milling Time on the Structural Characteristics of Biomedical Porous Ti-Sn-Nb Alloy, Mater. Sci. Eng. C, 2011, 31(5), p 921–92810.1016/j.msec.2011.02.011 ↗
35. A. Nouri, P.D. Hodgson, and C.E. Wen, Effect of Process Control Agent on the Porous Structure and Mechanical Properties of a Biomedical Ti-Sn-Nb Alloy Produced by Powder Metallurgy, Acta Biomater., 2010, 6(4), p 1630–163910.1016/j.actbio.2009.10.005 ↗
36. R.E. Fryxell and B.A. Chandler, Creep, Strength, Expansion, and Elastic Moduli of Sintered BeO as a Function of Grain Size, Porosity, and Grain Orientation, J. Am. Ceram. Soc., 1964, 47(6), p 283–29110.1111/j.1151-2916.1964.tb14417.x ↗
37. F. Gatto, Influence of Small Cavities on Velocity of Sound in Metals, Alluminio, 1956, 19(1), p 19–26
38. A.S. Wagh, R.B. Poeppel, and J.P. Singh, Open Pore Description of Mechanical Properties of Ceramics, J. Mater. Sci., 1991, 26(14), p 3862–386810.1007/BF01184983 ↗
39. R.B. Martin and R.R. Haynes, Confirmation of Theoretical Relation Between Stiffness and Porosity in Ceramics, J. Am. Ceram. Soc., 1971, 54(8), p 410–41110.1111/j.1151-2916.1971.tb12333.x ↗
40. N. Ramakrishnan and V.S. Arunachalam, Effective Elastic Moduli of Porous Solids, J. Mater. Sci., 1990, 25(9), p 3930–393710.1007/BF00582462 ↗
41. Z. Hashin, The Elastic Moduli of Heterogeneous Materials, J. Appl. Mech., 1962, 29(1), p 143–15010.1115/1.3636446 ↗
42. C.E. Wen, M. Mabuchi, Y. Yamada, K. Shimojima, Y. Chino, and T. Asahina, Processing of Biocompatible Porous Ti and Mg, Scrip. Mater., 2001, 45(10), p 1147–115310.1016/S1359-6462(01)01132-0 ↗
43. C.E. Wen, Y. Yamada, K. Shimojima, Y. Chino, T. Asahina, and M. Mabuchi, Processing and Mechanical Properties of Autogenous Titanium Implant Materials, J. Mater. Sci. Mater. Med., 2002, 13(4), p 397–40110.1023/A:1014344819558 ↗
44. N. Tuncer, G. Arslan, E. Maire, and L. Salvo, Influence of cell aspect ratio on architecture and compressive strength of titanium foams, Mater. Sci. Eng. A, 2011, 528(24), p 7368–737410.1016/j.msea.2011.06.028 ↗
45. M. O’Neill, M.K. Haas, B.K. Peterson, R.N. Vrtis, S.J. Weigel, D. Wu, M.D. Bitner, E.J. Karwacki, Impact of Pore Size and Morphology of Porous Organosilicate Glasses on Integrated Circuit Manufacturing, MRS Proceedings 914 (2011).10.1557/PROC-0914-F01-02 ↗
46. C.T. Herakovich and S.C. Baxter, Influence of Pore Geometry on the Effective Response of Porous Media, J. Mater. Sci., 1999, 34(7), p 1595–160910.1023/A:1004528600213 ↗