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Fracture mechanics of shape memory alloys: review and perspectives

Abstract

Shape memory alloys (SMAs) are intermetallic alloys displaying recoverable strains that can be an order of magnitude greater than in traditional alloys due to their capacity to undergo a thermal and/or stress-induced martensitic phase transformation. Since their discovery, the SMA industry has been dominated by products for biomedical applications with geometrically small feature sizes, especially endovascular stents. For such products the technological importance of fracture mechanics is limited, with the emphasis being placed on preventing crack nucleation rather than controlling crack growth. However, the successful integration of SMAs into commercial actuation, energy absorption, and vibration damping applications requires understanding and practice of fracture mechanics concepts in SMAs. The fracture response of SMAs is rather complex owing to the reversibility of phase transformation, detwinning and reorientation of martensitic variants, the possibility of dislocation and transformation-induced plasticity, and the strong thermomechanical coupling. Large-scale phase transformation under actuation loading paths, i.e., combined thermo-mechanical loading, and the associated configuration dependence complicate the phenomenon even further and question the applicability of single parameter fracture mechanics theories. Here, the existing knowledge base on the fracture mechanics of SMAs under mechanical loading is reviewed and recent developments in actuation-induced SMA fracture are presented, in terms of the micro-mechanisms of fracture, near-tip fracture environments, fracture criteria, and fracture toughness properties.

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Notes

  1. 1.

    On going work that is presented in Sect. 3.1.

  2. 2.

    Private communication with Dr. Karaman’s group at Texas A&M University.

  3. 3.

    Rice (1968, 1967) demonstrated path-independence of the \(J\)-integral for flow theory plasticity near stationary crack tips loaded in mode III in elastic-power-law hardening materials under the small-scale yielding assumption. There is no such proof for in-plane loading modes. Actually, finite element calculations have shown that \(J\) is path-dependent near stationary crack tips for loadings with a mode I component in elastic-power-law hardening materials obeying flow plasticity theory (Carka and Landis 2011).

  4. 4.

    A video of simulated quasi-static stable crack growth in an SMA material and the resulted toughness enhancement measured in the terms of the ratio of the loading parameter, \(K_I\), to its critical value for initiation of crack growth, \(K_{I_c}\) under the small-scale transformation assumption can be found here (Supplementary material 1) (see Baxevanis et al. (2013) for the details of the simulation). \(\delta a\) denotes increments of the crack length \(a\) and \(R_{\xi }\) the approximated size of the transformation zone at initiation of crack growth.

  5. 5.

    The authors would like to acknowledge the help of Kirk, Rohmer, and Wheeler in performing the experiments.

References

  1. Baxevanis T, Chemisky Y, Lagoudas D (2012) Finite element analysis of the plane strain crack-tip mechanical fields in pseudoelastic shape memory alloys. Smart Mater Struct 21. doi:10.1088/0964-1726/21/9/094012

  2. Baxevanis T, Lagoudas D (2012) A mode I fracture analysis of a center-cracked infinite shape memory alloy plate under plane stress. Int J Fract 175(2):151–166

  3. Baxevanis T, Landis C, Lagoudas D (2014a) On the effect of latent heat on the fracture toughness of pseudoelastic shape memory alloys. J Appl Mech Trans ASME 81(10). doi:10.1115/1.4028191

  4. Baxevanis T, Landis C, Lagoudas D (2014b) On the fracture toughness of pseudoelastic shape memory alloys. J Appl Mech Trans ASME 81(4). doi:10.1115/1.4025139

  5. Baxevanis T, Parrinello A, Lagoudas D (2013) On the fracture toughness enhancement due to stress-induced phase transformation in shape memory alloys. Int J Plast 50:158–169

  6. Baxevanis T, Parrinello A, Lagoudas D (2015) On the driving force for crack growth during thermal actuation of shape memory alloys. Submitted

  7. Birman V (1998) On mode I fracture of shape memory alloy plates. Smart Mater Struct 7:433–437

  8. Budniansky B, Hutchinson J, Lambropoulos J (1983) Continuum theory of dilatant transformation toughening in ceramics. Int J Solids Struct 19:337–355

  9. Carka D, Landis C (2011) On the path-dependence of the \({J}\)-integral near a stationary crack in an elastic-plastic material. J Appl Mech Trans ASME 78. doi:10.1115/1.4001748

  10. Creuziger A, Bartol L, Gall K, Crone W (2008) Fracture in single crystal NiTi. J Mech Phys Solids 56:2896–2905

  11. Daymond M, Young ML, Almer J, Dunand D (2007) Strain and texture evolution during mechanical loading of a crack tip in martensitic shape-memory NiTi. Acta Mater 55:3929–3942

  12. Desindes S, Daly S (2010) The small-scale yielding of shape memory alloys under mode III fracture. Int J Solids Struct 47:730–737

  13. Duerig T, Pelton A, Stöckel D (1999) An overview of nitinol medical applications. Mater Sci Eng A 273–275, 149–160

  14. Dugdale D (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104

  15. E1820 (2013) Standard test method for measurement of fracture toughness. ASTM International, West Conshohocken

  16. Freed Y, Banks-Sills L (2007) Crack growth resistance of shape memory alloys by means of a cohesive zone model. J Mech Phys Solids 55:2157–2180

  17. Gall K, Yang N, Sehitoglu H, Chumlyakov Y (2001) Fracture of precipitated NiTi shape memory alloys. Int J Fract 109:189–207

  18. Gollerthan S, Young M, Neuking K, Ramamurty U, Eggeler G (2009a) Direct physical evidence for the back-transformation of stress-induced martensite in the vicinity of cracks in pseudoelastic niti shape memory alloys. Acta Mater 57(19):5892–5897

  19. Gollerthan S, Young ML, Baruj A, Frenzel J, Schmahl W, Eggeler G (2009b) Fracture mechanics and microstructure in NiTi shape memory alloys. Acta Mater 57:1015–1025

  20. Hartl D, Lagoudas D (2007) Aerospace applications of shape memory alloys. In: Proceedings of the institution of mechanical engineers, Part G. J Aerosp Eng SAGE, pp 535–552

  21. Hartl D, Lagoudas D, Calkins F (2011) Advanced methods for the analysis, design, and optimization of sma-based aerostructures. Smart Mater Struct 20(9). doi:10.1088/0964-1726/20/9/094006

  22. Hazar S, Zaki W, Moumni Z, Anlas G (2015) Modeling of steady-state crack growth in shape memory alloys using a stationary method. Int J Plast 67:26–38

  23. He Y, Sun Q (2011) On non-monotonic rate dependence of stress hysteresis of superelastic shape memory alloy bars. Int J Solids Struct 48(11–12):1688–1695

  24. He Y, Yin H, Zhou R, Sun Q (2010) Ambient effect on damping peak of NiTi shape memory alloy. Mater Lett 64(13):1483–1486

  25. Holtz R, Sadananda K, Imam M (1999) Fatigue thresholds of NiTi alloy near the shape memory transition temperature. Int J Fatigue 21:S137–S145

  26. Hutchinson J (1968) Singular behavior at the end of a tensile crack in a hardening material. J Mech Phys Solids 16:13–31

  27. Hutchinson J (1983) Fundamentals of the phenomenological theory of nonlinear fracture mechanics. J Appl Mech Trans ASME 50(4B):1042–1051

  28. Irwin G (1968) Linear fracture mechanics, fracture transition, and fracture control. Eng Fract Mech 1(2):241–257

  29. Jape S, Baxevanis T, Lagoudas D (2014) Stable crack growth during actuation in shape memory alloys, vol 9058. In: Proceedings of SPIE—the international society for optical engineering. doi:10.1117/12.2048590

  30. Jape S, Baxevanis T, Lagoudas D (2015) Actuation-induced toughness enhancement in shape memory alloys. Under preparation

  31. Krueger R (2004) Virtual crack closure technique: history, approach, and applications. Appl Mech Rev 57(2):109–143. doi:10.1115/1.1595677

  32. Lagoudas D (ed) (2008) Shape memory alloys: modelling and engineering applications. Springer, New York

  33. Lagoudas D, Bo Z, Qidwai M (1996) A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites. Mech Compos Mater Struct 4:153–179

  34. Lagoudas D, Entchev P, Popov P, Patoor E, Brinson L, Gao X (2006) Shape memory alloys. Part II: modeling of polycrystals. Mech Mater 38:430–462

  35. Lagoudas D, Hartl D, Chemisky Y, Machado L, Popov P (2012) Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. Int J Plast 32–33, 158–183

  36. Lexcellent C, Laydi MR, Taillebot V (2011a) Analytical prediction of the phase transformation onset zone at a crack tip of a shape memory alloy exhibiting asymmetry between tension and compression. Int J Fract 169(1):1–13

  37. Lexcellent C, Laydi R, Taillebot V (2011b) Impact of the choice of a 3D thermomechanical model for shape memory alloys on the fracture and the delamination predictions. In: Procedia engineering, vol 10. pp 2232–2237

  38. Lexcellent C, Thiebaud F (2008) Determination of the phase transformation zone at a crack tip in a shape memory alloy exhibiting asymmetry between tension and compression. Scr Mater 59:321–323

  39. Loughran G, Shield T, Leo P (2003) Fracture of shape memory CuAlNi single crystals. Int J Solids Struct 40(2):271–294

  40. Machado L (2007) Shape memory alloys for vibration isolation and damping. Ph.D. thesis, Texas A&M University, College Station

  41. Maletta C (2012) A novel fracture mechanics approach for shape memory alloys with trilinear stress–strain behavior. Int J Fract 177(1):39–51

  42. Maletta C, Furgiuele F (2010) Analytical modeling of stress-induced martensitic transformation in the crack tip region of nickel–titanium alloys. Acta Mater 58:92–101

  43. Maletta C, Furgiuele F (2011) Fracture control parameters for NiTi based shape memory alloys. Int J Solids Struct 48:1658–1664

  44. Maletta C, Sgambitterra E, Furgiuele F (2013) Crack tip stress distribution and stress intensity factor in shape memory alloys. Fatigue Fract Eng Mater Struct 36(9):903–912

  45. Maletta C, Young M (2011) Stress-induced martensite in front of crack tips in NiTi shape memory alloys: modeling versus experiments. J Mater Eng Perform 20(4–5):597–604

  46. McMeeking R, Evans A (1982) Mechanics of transformation-toughening in brittle materials. J Am Ceram Soc 65:242–246

  47. Miyazaki S (1990) Engineering aspects of shape memory alloys. Butterworth-Heinemann, London

  48. Miyazaki S, Imai T, Igo Y, Otsuka K (1986) Effect of cyclic deformation on the pseudoelastic characteristics of Ti–Ni alloys. Metall Trans A 17A(1):115–120

  49. Nespoli A, Besseghini S, Pittaccio S, Villa E, Viscuso S (2010) The high potential of shape memory alloys in developing miniature mechanical devices: a review on shape memory alloy mini-actuators. Sens Actuator A Phys 158(1):149–160

  50. Otsuka K, Wayman C (eds) (1999) Shape memory materials. Cambridge University Press, Cambridge

  51. Parrinello A, Baxevanis T, Lagoudas D (2013) On the energy release rate during global thermo-mechanically-induced phase transformation in shape memory alloys, vol. 2 of ASME 2013 conference on smart materials, adaptive structures and intelligent systems, SMASIS 2013. doi:10.1115/SMASIS2013-3187

  52. Patoor E, Lagoudas D, Entchev PB, Brinson L, Gao X (2006) Shape memory alloys. Part I: general properties and modeling of single crystals. Mech Mater 38:391–429

  53. Pelton A, DiCello J, Miyazaki S (2000) Optimisation of processing and properties of medical grade nitinol wire. Minim Invas Ther Allied Technol 9(2):107–118

  54. Petrini L, Migliavacca F (2011)Biomedical applications of shape memory alloys. J Metall. doi:10.1155/2011/501483

  55. Prahlad H, Chopra I (2003) Development of a strain-rate dependent model for uniaxial loading of SMA wires. J Intell Mater Syst Struct 14(14):429–442

  56. Rice J (1967) Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear. ASME J Appl Mech 34:287–298

  57. Rice J (1968) A path independent integral and approximate analysis of strain concentration by notches and cracks. ASME J Appl Mech 35:379–386

  58. Rice J, Rosengren G (1968) Plane strain deformation near a crack tip in a power-law hardening material. J Mech Phys Solids 16:1–12

  59. Robertson S, Mehta A, Pelton A, Ritchie R (2007a) Evolution of crack-tip transformation zones in superelastic Nitinol subjected to in situ fatigue: a fracture mechanics and synchrotron X-ray microdiffraction analysis. Acta Mater 55(18):6198–6207

  60. Robertson S, Metha A, Pelton A, Ritchie R (2007b) Evolution of crack-tip transformation zones in superelastic Nitinol subjected to in situ fatigue: a fracture mechanics and synchrotron X-ray micro-diffraction analysis. Acta Mater 55:6198–6207

  61. Robertson S, Pelton A, Ritchie R (2012) Mechanical fatigue and fracture of nitinol. Int Mater Rev 57(1):1–36

  62. Robertson S, Ritchie R (2007) In vitro fatigue–crack growth and fracture toughness behavior of thin-walled superelastic nitinol tube for endovascular stents: a basis for defining the effect of crack-like defects. Biomaterials 28(4):700–709

  63. Robertson S, Ritchie R (2008) A fracture-mechanics-based approach to fracture control in biomedical devices manufactured from superelastic nitinol tube. J Biomed Mater Res B 84(1):26–33

  64. Rybicki E, Kanninen M (1977) A finite element calculation of stress intensity factors by a modified crack closure integral. Eng Fract Mech 9:931–938

  65. Shaw J, Kyriakides S (1995) A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings. J Mech Phys Solids 43(1):1243–1281

  66. Sreekumar M, Nagarajan T, Singaperumal M, Zoppi M, Molfino R (2007) Critical review of current trends in shape memory alloy actuators for intelligent robots. Ind Robot 34(4):285–294

  67. Stam G, van der Giessen E (1995) Effect of reversible phase transformations on crack growth. Mech Mater 21:51–71

  68. Stoeckel D, Pelton A, Duerig T (2004) Self-expanding nitinol stents: material and design considerations. Eur Radiol 14(2):292–301

  69. Vaidyanathan R, Dunand D, Ramamurty U (2000) Fatigue crack-growth in shape-memory NiTi and NiTi–TiC composites. Mater Sci Engi A 289(1–2):208–216

  70. Vasko G, Leo P, Shield T (2002) Prediction and observation of crack tip microstructure in shape memory CuAlNi single crystals. J Mech Phys Solids 50(9):1843–1867

  71. Wang G (2007a) Effect of martensite transformation on fracture behavior of shape memory alloy NiTi in a notched specimen. Int J Fract 146:93–104

  72. Wang G (2007b) A finite element analysis of evolution of stress–strain and martensite transformation in front of a notch in shape memory alloy NiTi. Mater Sci Eng A 460–461

  73. Wang X, Wang Y, Baruj A, Eggeler G, Yue Z (2005) On the formation of martensite in front of cracks in pseudoelastic shape memory alloys. Mater Sci Eng A 394:393–398

  74. Xie D, Biggers S (2006) Progressive crack growth analysis using interface element based on the virtual crack closure technique. Finite Elem Anal Des 42:977–984

  75. Xiong F, Liu Y (2007) Effect of stress-induced martensitic transformation on the crack tip stress-intensity factor in Ni–Mn–Ga shape memory alloy. Acta Mater 55:5621–5629

  76. Yan W, Mai Y (2006) Theoretical consideration on the fracture of shape memory alloys, vol 127. Springer, Netherlands

  77. Yan Y, Yin H, Sun Q, Huo Y (2012) Rate dependence of temperature fields and energy dissipations in non-static pseudoelasticity. Contin Mech Thermodyn 24(4–6):675–695

  78. Yi S, Gao S (2000) Fracture toughening mechanism of shape memory alloys due to martensite transformation. Int J Solids Struct 37:5315–5327

  79. Yi S, Gao S, Shen S (2001) Fracture toughening mechanism of shape memory alloys under mixed-mode loading due to martensite transformation. Int J Solids Struct 38:4463–4476

  80. Yin H, Yan Y, Huo Y, Sun Q (2013) Rate dependent damping of single crystal CuAlNi shape memory alloy. Mater Lett 109:287–290

  81. Yoon S, Yeo D (2008) Experimental investigation of thermo-mechanical behaviors in Ni–Ti shape memory alloy. J Intell Mater Syst Struct 19(3):283–289

  82. Young M, Gollerthan S, Baruj A, Frenzel J, Schmahl W, Eggeler G (2013) Strain mapping of crack extension in pseudoelastic niti shape memory alloys during static loading. Acta Mater 61(15):5800–5806

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Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant Numbers CMMI-1301139 and DMR-0844082.

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Correspondence to T. Baxevanis.

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Baxevanis, T., Lagoudas, D.C. Fracture mechanics of shape memory alloys: review and perspectives. Int J Fract 191, 191–213 (2015). https://doi.org/10.1007/s10704-015-9999-z

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Keywords

  • Shape memory alloys
  • Fracture mechanics
  • Phase transformation
  • Finite element analysis