Skip to main content
SpringerLink
Log in

Numerical analysis of crack tip fields in interface fracture of SMA/elastic bi-materials

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The problem of an interface crack between a shape memory alloy and an elastic layer is numerically addressed. The shape memory alloy behavior is modeled with a continuum thermodynamics based constitutive model embedded within the finite element method. With the help of the boundary layer approach, and the assumption of small scale transformation zone, the K-dominated region in the tip of the interface crack is loaded under general mixed-mode condition. Both slow and fast loading rates are considered to study the effects of thermo-mechanical coupling on the interface crack tip fields, especially the crack tip energy release rate within a history-dependent J-integral framework, the stress/strain curve during the loading process, and the shape and size of the transformation zone and the heated zone. A special effort is made to investigate how changing the rate of applied loading, the mode-mixity, and the material properties of SMA and elastic layer modify the crack tip fields.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Ahmadian H, Hatefi Ardakani S, Mohammadi S (2015) Strain-rate sensitivity of unstable localized phase transformation phenomenon in shape memory alloys using a non-local model. Int J Solids Struct 63:167–183

    Article  Google Scholar 

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

  • 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 175:151–166

    Article  Google Scholar 

  • Baxevanis T, Landis CM, Lagoudas DC (2014) On the fracture toughness of pseudoelastic shape memory alloys. J Appl Mech 81(4):041005

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

    Article  Google Scholar 

  • Boyd JG, Lagoudas DC (1996) A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy. Int J Plast 12:805–842

    Article  Google Scholar 

  • Brinson LC (1993) One-dimensional constitutive behavior of shape memory alloys: thermomechanical derivation with non-constant material functions and redefined martensite internal variable. J Intell Mater Syst Struct 4:229–242

    Article  Google Scholar 

  • Carka D, Landis CM (2011) On the path-dependence of the J-integral near a stationary crack in an elastic-plastic material. J Appl Mech 78:011006

    Article  Google Scholar 

  • Carka D, McMeeking RM, Landis CM (2012) A note on the path-dependence of the J-integral near a stationary crack in an elastic-plastic material with finite deformation. J Appl Mech 79:044502

    Article  Google Scholar 

  • 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  Google Scholar 

  • Freed Y, Banks-Sills L, Aboudi J (2008) On the transformation toughening of a crack along an interface between a shape memory alloy and an isotropic medium. J Mech Phys Solids 56:3003–3020

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Hatefi Ardakani S, Afshar A, Mohammadi S (2015a) Numerical study of thermo-mechanical coupling effects on crack tip fields of mixed-mode fracture in pseudoelastic shape memory alloys (under revision)

  • Hatefi Ardakani S, Ahmadian H, Mohammadi S (2015b) Thermo-mechanically coupled fracture analysis of shape memory alloys using the extended finite element method. Smart Mater Struct 24:045031

    Article  Google Scholar 

  • Helm D, Haupt P (2003) Shape memory behavior: modelling within continuum thermomechanics. Int J Solids Struct 40:827–849

    Article  Google Scholar 

  • Hu Z, Xiong K, Wang X (2005) Study on interface failure of shape memory alloy (SMA) reinforced smart structure with damages. Acta Mech Sin 21:286–293

    Article  Google Scholar 

  • Juhasz L, Schnack E, Hesebeck O, Andra H (2002) Macroscopic modeling of shape memory alloys under non-proportional themo-mechanical loadings. J Intell Mater Syst Struct 13:825–836

    Article  Google Scholar 

  • Lagoudas DC, Entchev PB (2004) Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense SMAs. Mech Mater 36:865–892

    Article  Google Scholar 

  • Lagoudas DC, Moorthy D, Qidwai MA, Reddy JN (1997) Modeling of the thermomechanical response of active laminates with SMA strips using the layerwise finite element method. J Intell Mater Syst Struct 8:476–488

    Article  Google Scholar 

  • Leclercq S, Lexcellent C (1996) A general macroscopic description of the thermomechanical behavior of shape memory alloys. J Mech Phys Solids 44:953–980

    Article  Google Scholar 

  • Maletta C, Bruno L, Corigliano P, Crupi V, Guglielmino E (2014) Crack-tip thermal and mechanical hysteresis in shape memory alloys under fatigue loading. Mater Sci Eng A 616:281–287

    Article  Google Scholar 

  • 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  Google Scholar 

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

    Article  Google Scholar 

  • Neuser S, Michaud V, White SR (2012) Improving solvent-based self-healing materials through shape memory alloys. Polymer 53:370–378

    Article  Google Scholar 

  • Paiva A, Savi MA, Bragra AMB, Pachec PMCL (2005) A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity. Int J Solids Struct 42:3439–3457

    Article  Google Scholar 

  • Popov P, Lagoudas DC (2007) 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of selfaccommodated martensite. Int J Plast 23:1679–1720

    Article  Google Scholar 

  • Qidwai MA, Lagoudas DC (2000) On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material. Int J Plast 16:1309–1343

    Article  Google Scholar 

  • Reese S, Christ D (2008) Finite deformation pseudo-elasticity of shape memory alloys—constitutive modelling and finite element implementation. Int J Plast 24:455–482

    Article  Google Scholar 

  • 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-di raction analysis. Acta Mater 55:6198–6207

    Article  Google Scholar 

  • Shimamoto A, Ohkawara H, Nogata F (2004) Enhancement of mechanical strength by shape memory effect in TiNi fiber-reinforced composites. Eng Fract Mech 71:737–746

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Sun QP, Hwang KC (1983a) Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys-II. Study of individual phenomena. J Mech Phys Solids 41:19–33

    Article  Google Scholar 

  • Sun QP, Hwang KC (1983b) Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys-I. Derivation of general relations. J Mech Phys Solids 41:1–17

    Article  Google Scholar 

  • Suo Z (1989) Mechanics of interface fracture. PhD Thesis, Harvard University, Cambridge, p 103

  • Wang G, Xuan F, Tu S, Wang Z (2010) Effects of triaxial stress on martensite transformation, stress-strain and failure behavior in front of crack tips in shape memory alloy NiTi. Mater Sci Eng A 527:1529–1536

  • 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

  • Wei ZG, Tang CY, Lee W (1997) Design and fabrication of intelligent composites based on shape memory alloys. J Mater Process Technol 69:68–74

    Article  Google Scholar 

  • 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 

Download references

Acknowledgments

The authors wish to acknowledge the technical support of the High Performance Computing Lab, School of Civil Engineering, University of Tehran. The financial support of Iran National Science Foundation (INSF) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. High Performance Computing Laboratory, School of Civil Engineering, University of Tehran, Tehran, Iran

    Arman Afshar, Saeed Hatefi Ardakani, Sepideh Hashemi & Soheil Mohammadi

Authors
  1. Arman Afshar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saeed Hatefi Ardakani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sepideh Hashemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Soheil Mohammadi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Soheil Mohammadi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Afshar, A., Hatefi Ardakani, S., Hashemi, S. et al. Numerical analysis of crack tip fields in interface fracture of SMA/elastic bi-materials. Int J Fract 195, 39–52 (2015). https://doi.org/10.1007/s10704-015-0047-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-015-0047-9

Keywords

Search

Navigation