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A Finite-Strain Phase-Field Description of Thermomechanically Induced Fracture in Shape Memory Alloys

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Abstract

A finite-strain, phase-field model for thermomechanically induced fracture in shape memory alloys (SMAs), i.e., fracture under loading paths that may take advantage of either the superelastic response or the shape memory effect in SMAs, is presented based on the Eulerian logarithmic (Hencky) strain and the logarithmic objective rate. Based on experimental observations suggesting that SMAs fracture in a stress-controlled manner, damage is assumed to be driven by the elastic energy, i.e., phase transformation is assumed to contribute in crack formation and growth indirectly through stress redistribution. The model is restricted to quasistatic mechanical loading (no latent heat effects) and thermal loading sufficiently slow with respect to the time rate of heat transfer by conduction (no thermal gradients), and can describe phase transformation and orientation of martensite variants from a self-accommodated state. A single fracture toughness value is assumed, that of martensite, thus, the temperature range of interest is below \(M_{\text {d}}\), which is the temperature above which the austenite phase is stable. The numerical implementation of the model in an efficient scheme is described and its ability to reproduce experimental observations on the fracture response of SMAs and handle complex geometries and loading conditions is demonstrated.

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Notes

  1. Oriented martensite forms from self-accommodated martensite under mechanical load with or without thermal inputs.

References

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

    Google Scholar 

  2. Otsuka K, Wayman CM (eds) (1999) Shape memory materials. Cambridge University Press, Cambridge

    Google Scholar 

  3. Morgan NB (2004) Medical shape memory alloy applications—the market and its products. Mater Sci Eng A 378:16–23

    Article  Google Scholar 

  4. Lagoudas DC (ed) (2008) Shape memory alloys: modelling and engineering applications. Springer, NewYork

    Google Scholar 

  5. Barbarino S, Flores ES, Ajaj RM, Dayyani I, Friswell MI (2014) A review on shape memory alloys with applications to morphing aircraft. Smart Mater Struct 23(6):063001

    Article  CAS  Google Scholar 

  6. Jani JM, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Mater Des 56:1078–1113

    Article  Google Scholar 

  7. Robertson SW, Metha A, Pelton AR, Ritchie RO (2007) 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

    Article  CAS  Google Scholar 

  8. Gollerthan S, Young ML, Baruj A, Frenzel J, Schmahl WW, Eggeler G (2009) Fracture mechanics and microstructure in Ni Ti shape memory alloys. Acta Mater 57:1015–1025

    Article  CAS  Google Scholar 

  9. Robertson SW, Pelton AR, Ritchie RO (2012) Mechanical fatigue and fracture of Nitinol. Int Mater Rev 57(1):1–36

    Article  CAS  Google Scholar 

  10. Baxevanis T, Lagoudas DC (2015) Fracture mechanics of shape memory alloys: review and perspectives. Int J Fract 191:191–213

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. 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

    Article  Google Scholar 

  14. Wang GZ (2007) Effect of martensite transformation on fracture behavior of shape memory alloy Ni Ti in a notched specimen. Int J Fract 146:93–104

    Article  CAS  Google Scholar 

  15. Wang GZ (2007) A finite element analysis of evolution of stress-strain and martensite transformation in front of a notch in shape memory alloy Ni Ti. Mater Sci Eng A 460–461:460–461

    Google Scholar 

  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

    Article  CAS  Google Scholar 

  17. 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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Baxevanis T, Lagoudas DC (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

    Article  Google Scholar 

  20. Baxevanis T, Chemisky Y, Lagoudas DC (2012) Finite element analysis of the plane-strain crack-tip mechanical fields in pseudoelastic shape memory alloys. Smart Mater Struct 21(9):094012

    Article  Google Scholar 

  21. Özerim G, Anlaş G, Moumni Z (2018) On crack tip stress fields in pseudoelastic shape memory alloys. Int J Fract 212(2):205–217

    Article  Google Scholar 

  22. Baxevanis T, Landis CM, Lagoudas DC (2013) On the fracture toughness of pseudoelastic shape memory alloys. J Appl Mech Trans ASME 81:041005

    Article  Google Scholar 

  23. 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 Plastic 67:26–38

    Article  CAS  Google Scholar 

  24. Jiang D, Landis CM (2016) A constitutive model for isothermal pseudoelasticity coupled with plasticity. Shape Mem Super 2(4):360–370

    Google Scholar 

  25. Yan W, Wang CH, Zhang XP, Mai YW (2002) Effect of transformation volume contraction on the toughness of superelastic shape memory alloys. Smart Mater Struct 11:947–955

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  27. Jape S, Baxevanis T, Lagoudas DC (2017) On the fracture toughness and stable crack growth in shape memory alloy actuators in the presence of transformation-induced plasticity. Int J Fract 209:117–130

    Article  Google Scholar 

  28. Baxevanis T, Landis CM, Lagoudas DC (2014) On the effect of latent heat on the fracture toughness of pseudoelastic shape memory alloys. J Appl Mech Trans ASME. https://doi.org/10.1115/1.4028191

    Article  Google Scholar 

  29. You Y, Gu X, Zhang Y, Moumni Z, Anlaş G, Zhang W (2019) Effect of thermomechanical coupling on stress-induced martensitic transformation around the crack tip of edge cracked shape memory alloy. Int J Fract 216(1):123–133

    Article  CAS  Google Scholar 

  30. Baxevanis T, Parrinello A, Lagoudas DC (2016) On the driving force for crack growth during thermal actuation of shape memory alloys. J Mech Phys Solids 89:255–271

    Article  CAS  Google Scholar 

  31. Illiopoulos A, Steuben J, Kirk T, Baxevanis T, Michopoulos J, Lagoudas DC (2017) Thermomechanical failure response of notched NiTi coupons. Int J Solids Struct 125:265–275

    Article  Google Scholar 

  32. Jape S, Baxevanis T, Lagoudas DC (2016) Stable crack growth during thermal actuation of shape memory alloys. Shape Mem Super 2(1):104–113

    Google Scholar 

  33. Gall K, Yang N, Sehitoglu H, Chumlyakov YI (1998) Fracture of precipitated Ni Ti shape memory alloys. Int J Fract 109:189–207

    Article  Google Scholar 

  34. Olsen JS, Zhang ZL, Lu H, van der Eijk C (2012) Fracture of notched round-bar NiTi-specimens. Eng Fract Mech 84:1–14

    Article  Google Scholar 

  35. Hasan MM, Baxevanis T (2022) Structural fatigue and fracture of shape memory alloy actuators: Current status and perspectives. J Intell Mater Syst Struct 33(12):1475–1486

    Article  Google Scholar 

  36. Makkar J, Baxevanis T (2019) Notes on the experimental measurement of fracture toughness of shape memory alloys. J Intell Mater Syst Struct. https://doi.org/10.1177/1045389X19888730

    Article  Google Scholar 

  37. Ungàr T, Frenzel J, Gollerthan S, Ribárik G, Balogh L, Eggeler G (2017) On the competition between the stress-induced formation of martensite and dislocation plasticity during crack propagation in pseudoelastic niti shape memory alloys. J Mater Res 32(23):4433–4442. https://doi.org/10.1557/jmr.2017.267

    Article  CAS  Google Scholar 

  38. Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–826

    Article  Google Scholar 

  39. Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8):1319–1342

    Article  Google Scholar 

  40. Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comp Methods Appl Mech Eng 199(45–48):2765–2778

    Article  Google Scholar 

  41. Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int J Numer Methods Eng 83(10):1273–1311

    Article  Google Scholar 

  42. Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217–220:77–95

    Article  Google Scholar 

  43. Borden MJ, Hughes TJR, Landis CM, Verhoosel CV (2014) A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng 273:100–118

    Article  Google Scholar 

  44. Kuhn C, Müller R (2010) A continuum phase field model for fracture. Eng Fract Mech 77(18):3625–3634

    Article  Google Scholar 

  45. Shanthraj P, Svendsen B, Sharma L, Roters F, Raabe D (2017) Elasto-viscoplastic phase field modelling of anisotropic cleavage fracture. J Mech Phys Solids 99:19–34

    Article  CAS  Google Scholar 

  46. Ambati M, Gerasimov T, De Lorenzis L (2014) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55(2):383–405

    Article  Google Scholar 

  47. Nguyen KD, Thanh CL, Vogel F, Nguyen-Xuan H, Abdel-Wahab M (2022) Crack propagation in quasi-brittle materials by fourth-order phase-field cohesive zone model. Theoret Appl Fract Mech 118:103236

    Article  Google Scholar 

  48. Lampron O, Therriault D, Lévesque M (2021) An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified newton method. Comput Methods Appl Mech Eng 386:114091

    Article  Google Scholar 

  49. Gerasimov T, De Lorenzis L (2022) Second-order phase-field formulations for anisotropic brittle fracture. Comput Methods Appl Mech Eng 389:114403

    Article  Google Scholar 

  50. Novelli L, Gori L, da Silva Pitangueira RL (2022) Phase-field modelling of brittle fracture with smoothed radial point interpolation methods. Eng Anal Bound Elem 138:219–234

    Article  Google Scholar 

  51. Tanné E, Li T, Bourdin B, Marigo JJ, Maurini C (2018) Crack nucleation in variational phase-field models of brittle fracture. J Mech Phys Solids 110:80–99

    Article  Google Scholar 

  52. Yang L, Yang Y, Zheng H, Wu Z (2021) An explicit representation of cracks in the variational phase field method for brittle fractures. Comput Methods Appl Mech Eng 387:114127

    Article  Google Scholar 

  53. Mandal TK, Nguyen VP, Wu JY (2019) Length scale and mesh bias sensitivity of phase-field models for brittle and cohesive fracture. Eng Fract Mech 217:106532

    Article  Google Scholar 

  54. Xue T, Adriaenssens S, Mao S (2021) Mapped phase field method for brittle fracture. Comput Methods Appl Mech Eng 385:114046

    Article  Google Scholar 

  55. Yun K, Kim MH, Chu PH (2021) A modified phase field model for predicting the fracture behavior of quasi-brittle materials. Int J Numer Methods Eng 122(20):5656–5675

    Article  Google Scholar 

  56. Li B, Peco C, Millán D, Arias I, Arroyo M (2015) Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy. Int J Numer Methods Eng 102(3–4):711–727

    Article  Google Scholar 

  57. Wu JY (2017) A unified phase-field theory for the mechanics of damage and quasi-brittle failure. J Mech Phys Solids 103:72–99

    Article  Google Scholar 

  58. Borden MJ, Hughes TJR, Landis CM, Anvari A, Lee IJ (2016) A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Comput Methods Appl Mech Eng 312:130–166

    Article  Google Scholar 

  59. Miehe C, Aldakheel F, Raina A (2016a) Phase field modeling of ductile fracture at finite strains: a variational gradient-extended plasticity-damage theory. Int J Plast Article in Press

  60. Miehe C, Kienle D, Aldakheel F, Teichtmeister S (2016) Phase field modeling of fracture in porous plasticity: a variational gradient-extended Eulerian framework for the macroscopic analysis of ductile failure. Comput Methods Appl Mech Eng 312:3–50

    Article  Google Scholar 

  61. Miehe C, Hofacker M, Schänzel LM, Aldakheel F (2015) Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids. Comput Methods Appl Mech Eng 294:486–522

    Article  Google Scholar 

  62. Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55(5):1017–1040

    Article  Google Scholar 

  63. Tao Z, Li X, Tao S, Chen Z (2022) Phase-field modeling of 3d fracture in elasto-plastic solids based on the modified gtn theory. Eng Fract Mech 260:108196

    Article  Google Scholar 

  64. Aldakheel F, Noii N, Wick T, Allix O, Wriggers P (2021) Multilevel global-local techniques for adaptive ductile phase-field fracture. Comput Methods Appl Mech Eng 387:114175

    Article  Google Scholar 

  65. Proserpio D, Ambati M, De Lorenzis L, Kiendl J (2021) Phase-field simulation of ductile fracture in shell structures. Comput Methods Appl Mech Eng 385:114019

    Article  Google Scholar 

  66. Han J, Matsubara S, Moriguchi S, Kaliske M, Terada K (2022) Crack phase-field model equipped with plastic driving force and degrading fracture toughness for ductile fracture simulation. Comput Mech 69:151–175

    Article  Google Scholar 

  67. Talamini B, Tupek MR, Stershic AJ, Hu T, Foulk JW, Ostien JT, Dolbow JE (2021) Attaining regularization length insensitivity in phase-field models of ductile failure. Comput Methods Appl Mech Eng 384:113936

    Article  Google Scholar 

  68. Ma PS, Ye JY, Tian K, Chen XH, Zhang LW (2022) Fracture phase field modeling of 3d stitched composite with optimized suture design. Comput Methods Appl Mech Eng 392:114650

    Article  Google Scholar 

  69. Li X, Xu Y (2022) Phase field modeling scheme with mesostructure for crack propagation in concrete composite. Int J Solids Struct 234–235:111259

    Article  Google Scholar 

  70. Pan ZZ, Zhang LW, Liew KM (2022) A phase-field framework for failure modeling of variable stiffness composite laminae. Comput Methods Appl Mech Eng 388:114192

    Article  Google Scholar 

  71. Miehe C, Schänzel LM (2014) Phase field modeling of fracture in rubbery polymers. Part I: finite elasticity coupled with brittle failure. J Mech Phys Solids 65(1):93–113

    Article  CAS  Google Scholar 

  72. Loew PJ, Peters B, Beex LAA (2019) Rate-dependent phase-field damage modeling of rubber and its experimental parameter identification. J Mech Phys Solids 127:266–294

    Article  Google Scholar 

  73. Wu J, McAuliffe C, Waisman H, Deodatis G (2016) Stochastic analysis of polymer composites rupture at large deformations modeled by a phase field method. Comput Methods Appl Mech Eng 312:596–634

    Article  Google Scholar 

  74. Dinachandra M, Alankar A (2022) Adaptive finite element modeling of phase-field fracture driven by hydrogen embrittlement. Comput Methods Appl Mech Eng 391:114509

    Article  Google Scholar 

  75. Martínez-Pañeda E, Golahmar A, Niordson CF (2018) A phase field formulation for hydrogen assisted cracking. Comput Methods Appl Mech Eng 342:742–761

    Article  Google Scholar 

  76. Wilson ZA, Landis CM (2016) Phase-field modeling of hydraulic fracture. J Mech Phys Solids 96:264–290

    Article  Google Scholar 

  77. Lee S, Mikelić A, Wheeler MF, Wick T (2016) Phase-field modeling of proppant-filled fractures in a poroelastic medium. Comput Methods Appl Mech Eng 312:509–541

    Article  Google Scholar 

  78. Lee S, Wheeler MF, Wick T (2016) Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model. Comput Methods Appl Mech Eng 305:111–132

    Article  Google Scholar 

  79. Heider Y, Markert B (2015) A phase-field modeling approach of hydraulic fracture in saturated porous media. Mech Res Commun Article in Press

  80. Ulloa J, Wambacq J, Alessi R, Samaniego E, Degrande G, François S (2022) A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior. J Mech Phys Solids 159:104684

    Article  Google Scholar 

  81. Li Y, Yu T, Natarajan S (2022) An adaptive isogeometric phase-field method for brittle fracture in rock-like materials. Eng Fract Mech 263:108298

    Article  Google Scholar 

  82. Suh HS, Sun W (2021) Asynchronous phase field fracture model for porous media with thermally non-equilibrated constituents. Comput Methods Appl Mech Eng 387:114182

    Article  Google Scholar 

  83. Spetz A, Denzer R, Tudisco E, Dahlblom O (2021) A modified phase-field fracture model for simulation of mixed mode brittle fractures and compressive cracks in porous rock. Rock Mech Rock Eng 54:5375–5388

    Article  Google Scholar 

  84. Fei F, Choo J, Liu C, White JA (2022) Phase-field modeling of rock fractures with roughness. Int J Numer Anal Methods Geomech 46(5):841–868

    Article  Google Scholar 

  85. Liu S, Wang Y, Peng C, Wu W (2022) A thermodynamically consistent phase field model for mixed-mode fracture in rock-like materials. Comput Methods Appl Mech Eng 392:114642

    Article  Google Scholar 

  86. Wang S, Zhang J, Zhao L, Zhang W (2021) Phase field modeling of anisotropic tension failure of rock-like materials. Front Phys 9

  87. Wu JY, Chen WX (2021) Phase-field modeling of electromechanical fracture in piezoelectric solids: analytical results and numerical simulations. Comput Methods Appl Mech Eng 387:114125

    Article  Google Scholar 

  88. Hasan MM, Baxevanis T (2021) A phase-field model for low-cycle fatigue of brittle materials. Int J Fatigue 150:106297

    Article  Google Scholar 

  89. Caputo M, Fabrizio M (2015) Damage and fatigue described by a fractional derivative model. J Comput Phys 293:400–408

    Article  Google Scholar 

  90. Boldrini JL, Barros de Moraes EA, Chiarelli LR, Fumes FG, Bittencourt ML (2016) A non-isothermal thermodynamically consistent phase field framework for structural damage and fatigue. Comput Methods Appl Mech Eng 312:395–427

    Article  Google Scholar 

  91. Amendola G, Fabrizio M, Golden JM (2016) Thermomechanics of damage and fatigue by a phase field model. J Therm Stresses 39:487–499

    Article  Google Scholar 

  92. Alessi R, Vidoli S, De Lorenzis L (2018) A phenomenological approach to fatigue with a variational phase-field model: the one-dimensional case. Eng Fract Mech 190:53–73

    Article  Google Scholar 

  93. Carrara P, Ambati M, Alessi R, De Lorenzis L (2020) A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach. Comput Methods Appl Mech Eng 361:112731

    Article  Google Scholar 

  94. Lo YS, Borden MJ, Ravi-Chandar K, Landis CM (2019) A phase-field model for fatigue crack growth. J Mech Phys Solids 132:103684

    Article  Google Scholar 

  95. Loew PJ, Peters B, Beex LAA (2020) Fatigue phase-field damage modeling of rubber using viscous dissipation: crack nucleation and propagation. Mech Mater 142:103282

    Article  Google Scholar 

  96. Mesgarnejad A, Imanian A, Karma A (2019) Phase-field models for fatigue crack growth. Theoret Appl Fract Mech 103:102282

    Article  Google Scholar 

  97. Seiler M, Linse T, Hantschke P, Kästner M (2020) An efficient phase-field model for fatigue fracture in ductile materials. Eng Fract Mech 224:106807

    Article  Google Scholar 

  98. Ulloa J, Wambacq J, Alessi R, Degrande G, François S (2021) Phase-field modeling of fatigue coupled to cyclic plasticity in an energetic formulation. Comput Methods Appl Mech Eng 373:113473

    Article  Google Scholar 

  99. Haveroth GA, Vale MG, Bittencourt ML, Boldrini JL (2020) A non-isothermal thermodynamically consistent phase field model for damage, fracture and fatigue evolutions in elasto-plastic materials. Comput Methods Appl Mech Eng 364:112962

    Article  Google Scholar 

  100. Khalil Z, Elghazouli AY, Martínez-Pañeda E (2022) A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver. Comput Methods Appl Mech Eng 388:114286

    Article  Google Scholar 

  101. Koutromanos I, Tola-Tola A, Eatherton MR (2022) Phase-field description of ductile fracture in structural steel under cyclic loading. J Struct Eng 148:04022073

    Article  Google Scholar 

  102. Yan S, Schreiber C, Müller R (2022) An efficient implementation of a phase field model for fatigue crack growth. Int J Fract

  103. Seleš K, Aldakheel F, Tonkovic Z, Sorić J, Wriggers P (2021) A general phase-field model for fatigue failure in brittle and ductile solids. Comput Mech 67:1431–1452

    Article  Google Scholar 

  104. Xue F, Cheng TL, Lei Y, Wen YH (2022) Phase-field framework with constraints and its applications to ductile fracture in polycrystals and fatigue. npj Comput Mater 8:1–15

    Article  CAS  Google Scholar 

  105. Reinhardt WD, Dubey RN (1995) Eulerian strain-rate as a rate of logarithmic strain. Mech Res Commun 22(2):165–170

    Article  Google Scholar 

  106. Xiao H, Bruhns OT, Meyers A (1997) Logarithmic strain, logarithmic spin and logarithmic rate. Acta Mech 124(1–4):89–105

    Article  Google Scholar 

  107. Haghgouyan B, Hayrettin C, Baxevanis T, Karaman I, Lagoudas DC (2019) Fracture toughness of NiTi-towards establishing standard test methods for phase transforming materials. Acta Mater 162:226–238

    Article  CAS  Google Scholar 

  108. Olsen JS, Zhang ZL, Lu H, Eijk CVD (2012) Fracture of notched round-bar niti-specimens. Eng Fract Mech 84:1–14

    Article  Google Scholar 

  109. Makkar J, Baxevanis T (2021) On the fracture response of shape memory alloys by void growth and coalescence. Mech Mater 153:103682

    Article  Google Scholar 

  110. Simoes M, Martínez-Pañeda E (2021) Phase field modelling of fracture and fatigue in shape memory alloys. Comput Methods Appl Mech Eng 373:113504

    Article  Google Scholar 

  111. Simoes M, Braithwaite C, Makaya A, Martínez-Pañeda E (2022) Modelling fatigue crack growth in shape memory alloys. Fatigue Fract Eng Mater Struct 45:1243–1257

    Article  Google Scholar 

  112. Gurtin ME (1996) Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92(3):178–192

    Article  CAS  Google Scholar 

  113. Zhang M, Baxevanis T (2022) Tailoring the anisotropic (positive/zero/negative) thermal expansion in shape memory alloys through phase transformation and martensite (re)orientation. Int J Eng Sc 177103687

    Article  CAS  Google Scholar 

  114. Zhang M, Baxevanis T (2021) An extended three-dimensional finite strain constitutive model for shape memory alloys. J Appl Mech 88(11)

  115. 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 32:155–183

    Article  Google Scholar 

  116. Freddi F, Royer-Carfagni G (2010) Regularized variational theories of fracture: a unified approach. J Mech Phys Solids 58(8):1154–1174

    Article  Google Scholar 

  117. Malvern LE (1969) Introduction to the mechanics of a continuous medium. Series in Engineering of the Physical Sciences. Prentice-Hall Inc., Upper Saddle River

    Google Scholar 

  118. Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New York

    Google Scholar 

  119. Wu JY, Huang Y (2020) Comprehensive implementations of phase-field damage models in abaqus. Theoret Appl Fract Mech 106:102440

    Article  Google Scholar 

  120. Navidtehrani Y, Betegón C, Martínez-Pañeda E (2021) A simple and robust abaqus implementation of the phase field fracture method. Appl Eng Sci 6:100050

    Google Scholar 

  121. Wick T (2017) Modified newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation. Comput Methods Appl Mech Eng 325:577–611

    Article  Google Scholar 

  122. Wu JY, Huang Y, Nguyen VP (2020) On the BFGS monolithic algorithm for the unified phase field damage theory. Comput Methods Appl Mech Eng 360:112704

    Article  Google Scholar 

  123. Kristensen PK, Martínez-Pañeda E (2020) Phase field fracture modelling using quasi-newton methods and a new adaptive step scheme. Theoret Appl Fract Mech 107:102446

    Article  Google Scholar 

  124. Bourdin B, Francfort GA, Marigo JJ (2008) The variational approach to fracture. J Elast 91(1):5–148

    Article  Google Scholar 

  125. Jape S, Parrinello A, Baxevanis T, Lagoudas DC (2016) On the fracture response of shape memory alloy actuators. In: Karaman I, Arróyave R, Masad E (eds) TMS Middle East — Mediterranean Materials Congress on Energy and Infrastructure Systems (MEMA 2015), p 165

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Acknowledgements

This study was supported by the National Science Foundation under Grant no. CMMI-1917441. The authors acknowledge the Research Computing Data Core (RCDC) at the University of Houston for the supercomputing resources made available for conducting the research reported in this paper.

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  1. Department of Mechanical Engineering, University of Houston, Houston, TX, 77204-4006, USA

    M. M. Hasan, M. Zhang & T. Baxevanis

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Correspondence to T. Baxevanis.

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This invited article is part of a special issue of Shape Memory and Superelasticity honoring Etienne Patoor for his contributions to the field of phase transforming materials and shape memory alloys. The special issue was organized by Dr. Fodil Meraghni, Ecole Nationale Supérieure d'Arts et Métiers (Arts et Métiers Institute of Technology), and Dr. Dimitris Lagoudas, Texas A&M University.

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Hasan, M.M., Zhang, M. & Baxevanis, T. A Finite-Strain Phase-Field Description of Thermomechanically Induced Fracture in Shape Memory Alloys. Shap. Mem. Superelasticity 8, 356–372 (2022). https://doi.org/10.1007/s40830-022-00393-y

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  • DOI: https://doi.org/10.1007/s40830-022-00393-y

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