Open Access Peer-reviewed Research Article

Load-induced local phase transformation and modulus of shape memory alloys under spherical indentation by finite element method

Main Article Content

Sayed Ehsan Saghaian corresponding author
Y. C. Lu
Sayed M. Saghaian
Haluk E. Karaca

Abstract

Shape memory alloys are a unique class of materials that are capable of large reversible deformations under external stimuli such as stress or temperature. The present study examines the phase transformations and mechanical responses of NiTi and NiTiHf shape memory alloys under the loading of a spherical indenter by using a finite element model. It is found that the indentation unloading curves exhibit distinct changes in slopes due to the reversible phase transformations in the SMAs. The normalized contact stiffness (F/S2) of the SMAs varies with the indentation load (depth) as opposed to being constant for conventional single-phase materials. The load-induced phase transformation that occurred under the spherical indenter was simulated numerically. It is observed that the phase transformation phenomenon in the SMA induced by an indentation load is distinctly different from that induced by a uniaxial load. A pointed indenter produces a localized deformation, resulting in a stress (load) gradient in the specimen. As a result, the transformation of phases in SMAs induced by an indenter can only be partially completed. The overall modulus of the SMAs varies continuously with the indentation load (depth) as the average volumetric fraction of the martensite phase varies. For NiTi (E> Em), the modulus decreases with the depth, while for NiTiHf (E< Em), the modulus increases with the depth. The predicted young modules during indentation modeling agree well with experimental results. Finally, the phase transformation of the SMAs under the indenter is not affected by the post-yield behavior of the materials.

Keywords
shape memory alloys, nanoindentation, spherical indenter, phase transformation, finite element method

Article Details

How to Cite
Saghaian, S. E., Lu, Y. C., Saghaian, S. M., & Karaca, H. E. (2023). Load-induced local phase transformation and modulus of shape memory alloys under spherical indentation by finite element method. Materials Engineering Research, 5(1), 256-264. https://doi.org/10.25082/MER.2023.01.002

References

  1. Oliver WC and Pharr GM. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of materials research, 1992, 7(6): 1564-1583. https://doi.org/10.1557/JMR.1992.1564
  2. Doerner MF and Nix WD. A method for interpreting the data from depth-sensing indentation instruments. Journal of Materials Research, 1986, 1(4): 601-609. https://doi.org/10.1557/JMR.1986.0601
  3. Mayo MJ, Siegel RW, Liao YX, et al. Nanoindentation of nanocrystalline ZnO. Journal of Materials Research, 1992, 7: 973-979. https://doi.org/10.1557/JMR.1992.0973
  4. Cheng L, Xia X, Yu W, et al. Flat-punch indentation of viscoelastic material. Journal of Polymer Science Part B: Polymer Physics, 2000, 38(1): 10-22. https://doi.org/10.1002/(SICI)1099-0488(20000101)38:1<10::AID-POLB2>3.0.CO;2-6
  5. Lu YC and Shinozaki DM. Characterization and modeling of large displacement micro-/nano-indentation of polymeric solids. Journal of Engineering Materials and Technology, 2008, 130(4): 041001. https://doi.org/10.1115/1.2969250
  6. Pharr GM, Harding DS and Oliver WC. Measurement of fracture toughness in thin films and small volumes using nanoindentation methods. Mechanical properties and deformation behavior of materials having ultra-fine microstructures. NATO ASI Series, 1993, 233: 449-461. https://doi.org/10.1007/978-94-011-1765-4_29
  7. Volinsky AA, Moody NR and Gerberich WW. Nanoindentation of Au and Pt/Cu thin films at elevated temperatures. Journal of Materials Research, 2004, 19(9): 2650-2657. https://doi.org/10.1557/JMR.2004.0331
  8. Zhang Q, Lu YC, Du F, et al. Viscoelastic creep of vertically aligned carbon nanotubes. Journal of physics D: Applied physics, 2010, 43(31): 315401. https://doi.org/10.1088/0022-3727/43/31/315401
  9. Fulcher JT, Lu YC, Tandon GP, et al. Thermomechanical characterization of shape memory polymers using high temperature nanoindentation. Polymer Testing, 2010, 29(5): 544-552. https://doi.org/10.1016/j.polymertesting.2010.02.001
  10. Bansiddhi A, Sargeant TD, Stupp SI, et al. Porous NiTi for bone implants: a review. Acta biomaterialia, 2008, 4(4): 773-782. https://doi.org/10.1016/j.actbio.2008.02.009
  11. Elahinia MH, Hashemi M, Tabesh M, et al. Manufacturing and processing of NiTi implants: A review. Progress in materials science, 2012, 57(5): 911-946. https://doi.org/10.1016/j.pmatsci.2011.11.001
  12. Jani JM, Leary M, Subic A, et al. A review of shape memory alloy research, applications and opportunities. Materials & Design (1980-2015), 2014, 56: 1078-1113. https://doi.org/10.1016/j.matdes.2013.11.084
  13. Saedi S, Saghaian SE, Jahadakbar A, et al. Shape memory response of porous NiTi shape memory alloys fabricated by selective laser melting. Journal of Materials Science: Materials in Medicine, 2018, 29: 1-12. https://doi.org/10.1007/s10856-018-6044-6
  14. Saghaian SE, Nematollahi M, Toker G, et al. Effect of hatch spacing and laser power on microstructure, texture, and thermomechanical properties of laser powder bed fusion (L-PBF) additively manufactured NiTi. Optics & Laser Technology, 2022, 149: 107680. https://doi.org/10.1016/j.optlastec.2021.107680
  15. Moghaddam NS, Saedi S, Amerinatanzi A, et al. Influence of SLM on compressive response of NiTi scaffolds. Behavior and Mechanics of Multifunctional Materials and Composites XII. SPIE, 2018, 10596: 60-66.
  16. Frâemond M and Miyazaki S. Shape Memory Alloys. Springer, New York, 1996. https://doi.org/10.1007/978-3-7091-4348-3
  17. Otsuka K. and Wayman CM. Shape memory materials. Cambridge university press, 1999.
  18. Fu Y, Du H, Huang W, et al. TiNi-based thin films in MEMS applications: a review. Sensors and Actuators A: Physical, 2004, 112(2-3): 395-408. https://doi.org/10.1016/j.sna.2004.02.019
  19. Zhang L, Xie C and Wu J. Progress in research on shape memory alloy films in MEMS field. Materials Review, 2006, 2: 109-113.
  20. Saedi S, Saghaian SE, Jahadakbar A, et al. Shape memory response of porous NiTi shape memory alloys fabricated by selective laser melting. Journal of Materials Science: Materials in Medicine, 2018, 29: 1-12. https://doi.org/10.1007/s10856-018-6044-6
  21. Saghaian SE, Amerinatanzi A, Moghaddam NS, et al. Mechanical and shape memory properties of triply periodic minimal surface (TPMS) NiTi structures fabricated by selective laser melting. Biol Eng Med, 2018, 3: 1-7. https://doi.org/10.15761/BEM.1000152
  22. Moghaddam NS, Saedi S, Amerinatanzi A, et al. Influence of SLM on compressive response of NiTi scaffolds. Behavior and Mechanics of Multifunctional Materials and Composites XII. SPIE, 2018, 10596: 60-66.
  23. Gall K, Juntunen K, Maier HJ, et al. Instrumented micro-indentation of NiTi shape-memory alloys. Acta Materialia, 2001, 49(16): 3205-3217. https://doi.org/10.1016/S1359-6454(01)00223-3
  24. Liu R, Li DY, Xie YS, et al. Indentation behavior of pseudoelastic TiNi alloy. Scripta Materialia, 1999, 41(7): 691-696. https://doi.org/10.1016/S1359-6462(99)00199-2
  25. Ni W, Cheng YT and Grummon DS. Recovery of microindents in a nickel–titanium shape-memory alloy: a ``self-healing'' effect. Applied Physics Letters, 2002, 80(18): 3310-3312. https://doi.org/10.1063/1.1476064
  26. Ni W, Cheng YT and Grummon DS. Microscopic superelastic behavior of a nickel-titanium alloy under complex loading conditions. Applied Physics Letters, 2003, 82(17): 2811-2813. https://doi.org/10.1063/1.1569984
  27. Amini A, Yan W and Sun Q. Depth dependency of indentation hardness during solid-state phase transition of shape memory alloys. Applied Physics Letters, 2011, 99(2): 021901. https://doi.org/10.1063/1.3603933
  28. Kang G and Yan W. Scaling relationships in sharp conical indentation of shape memory alloys. Philosophical Magazine, 2010, 90(5): 599-616. https://doi.org/10.1080/14786430903213346
  29. Kan Q, Yan W, Kang G, et al. Oliver–Pharr indentation method in determining elastic moduli of shape memory alloys—a phase transformable material. Journal of the Mechanics and Physics of Solids, 2013, 61(10): 2015-2033. https://doi.org/10.1016/j.jmps.2013.05.007
  30. Tabor D. The hardness of metals. Oxford university press, 2000.
  31. Karaca HE, Saghaian SM, Ded G, et al. Effects of nanoprecipitation on the shape memory and material properties of an Ni-rich NiTiHf high temperature shape memory alloy. Acta Materialia, 2013, 61(19): 7422-7431. https://doi.org/10.1016/j.actamat.2013.08.048
  32. Andani MT, Moghaddam NS, Haberland C, et al. Metals for bone implants. Part 1. Powder metallurgy and implant rendering. Acta biomaterialia, 2014, 10(10): 4058-4070. https://doi.org/10.1016/j.actbio.2014.06.025
  33. Pattanayak DK, Fukuda A, Matsushita T, et al. Bioactive Ti metal analogous to human cancellous bone: Fabrication by selective laser melting and chemical treatments. Acta Biomaterialia, 2011, 7(3): 1398-1406. https://doi.org/10.1016/j.actbio.2010.09.034
  34. Yan C, Hao L, Hussein A, et al. Ti–6Al–4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting. Journal of the mechanical behavior of biomedical materials, 2015, 51: 61-73. https://doi.org/10.1016/j.jmbbm.2015.06.024
  35. Lindner M, Hoeges S, Meiners W, et al. Manufacturing of individual biodegradable bone substitute implants using selective laser melting technique. Journal of Biomedical Materials Research Part A, 2011, 97(4): 466-471. https://doi.org/10.1002/jbm.a.33058
  36. Saghaian SM, Karaca HE, Tobe H, et al. High strength NiTiHf shape memory alloys with tailorable properties. Acta Materialia, 2017, 134: 211-220. https://doi.org/10.1016/j.actamat.2017.05.065
  37. Nematollahi M, Toker G, Saghaian SE, et al. Additive manufacturing of ni-rich nitihf 20: Manufacturability, composition, density, and transformation behavior. Shape Memory and Superelasticity, 2019, 5: 113-124. https://doi.org/10.1007/s40830-019-00214-9
  38. Bae JW, Jung J, Kim JG, et al. On the phase transformation and dynamic stress–strain partitioning of ferrous medium-entropy alloy using experimentation and finite element method. Materialia, 2020, 9: 100619. https://doi.org/10.1016/j.mtla.2020.100619
  39. Johnson KL and Johnson KL. Contact mechanics. Cambridge University Press, 1987.
  40. Joslin DL and Oliver WC. A new method for analyzing data from continuous depth-sensing microindentation tests. Journal of Materials Research, 1990, 5: 123-126. https://doi.org/10.1557/JMR.1990.0123
  41. Biwa S and Storåkers B. An analysis of fully plastic Brinell indentation. Journal of the Mechanics and Physics of Solids, 1995, 43(8): 1303-1333. https://doi.org/10.1016/0022-5096(95)00031-D
  42. Sneddon IN. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. International Journal of Engineering Science, 1965, 3(1): 47-57.