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Research Papers

On the Fracture Toughness of Pseudoelastic Shape Memory Alloys

[+] Author and Article Information
Theocharis Baxevanis

Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843–3141
e-mail: theocharis@tamu.edu

Chad M. Landis

Department of Aerospace Engineering
and Engineering Mechanics,
The University of Texas at Austin,
Austin, TX 78712-0235
e-mail: landis@utexas.edu

Dimitris C. Lagoudas

Department of Aerospace Engineering,
Texas A&M University,
College Station, TX 77843–3141
e-mail: lagoudas@tamu.edu

Manuscript received May 13, 2013; final manuscript received July 10, 2013; accepted manuscript posted July 29, 2013; published online September 23, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(4), 041005 (Sep 23, 2013) (8 pages) Paper No: JAM-13-1195; doi: 10.1115/1.4025139 History: Received May 13, 2013; Revised July 10, 2013; Accepted July 29, 2013

A finite element analysis of quasi-static, steady-state crack growth in pseudoelastic shape memory alloys is carried out for plane strain, mode I loading. The crack is assumed to propagate at a critical level of the crack-tip energy release rate. Results pertaining to the influence of forward and reverse phase transformation on the near-tip mechanical fields and fracture toughness are presented for a range of thermomechanical parameters and temperature. The fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip energy release rate. A substantial fracture toughening is observed, in accordance with experimental observations, associated with the energy dissipated by the transformed material in the wake of the growing crack. Reverse phase transformation, being a dissipative process itself, is found to increase the levels of toughness enhancement. However, higher nominal temperatures tend to reduce the toughening of an SMA alloy—although the material's tendency to reverse transform in the wake of the advancing crack tip increases—due to the higher stress levels required for initiation of forward transformation.

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Figures

Grahic Jump Location
Fig. 1

Stress–temperature phase diagram. A pseudoelastic loading path.

Grahic Jump Location
Fig. 2

Uniaxial stress–strain response for a range of the nondimensional parameters (As-Ms)/(T-Ms), (Af-As)/(T-Ms), and (Ms-Mf)/(T-Ms)

Grahic Jump Location
Fig. 3

Martensite volume fraction, ξ, close to the steadily advancing crack tip for a range of values of the nondimensional parameters (As-Ms)/(T-Ms) and (Af-As)/(T-Ms). The values of the other nondimensional parameters used in the calculations are (EAH/σMs) = 5,((Ms-Mf)/(T-Ms)) = 1,(EM/EA) = 0.5,(CM/CA) = 0.8,νM = νA = 0.33.

Grahic Jump Location
Fig. 4

Angular distribution of stresses close to the crack tip. The markers are the numerical results and the solid lines are the components of the isotropic elastic stress field. The numerical results plotted are for all integration stations within the radial distance 5×10-3Rξ < r < 7 × 10-3Rξ. The 1/r radial dependence has been accounted for within the normalization. The parameters used are those of Fig. 3(c).

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Fig. 5

The toughness enhancement, Gss/Gtip, as a function of EAH/σMs for a range of the nondimensional parameter (As-Ms)/(T-Ms)

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Fig. 6

The toughness enhancement, Gss/Gtip, as a function of EAH/σMs for a range of the nondimensional parameter (Af-As)/(T-Ms)

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Fig. 7

The toughness enhancement, Gss/Gtip, as a function of EAH/σMs for a range of the nondimensional parameter (Ms-Mf)/(T-Ms)

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Fig. 8

Toughness enhancement, Gss/Gtip, during steady crack growth as a function of EAH/σMs for a range of the material parameter EM/EA

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Fig. 9

Toughness enhancement, Gss/Gtip, during steady crack growth as a function of EAH/σMs for a range of the material parameter CM/CA

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Fig. 10

Toughness enhancement, Gss/Gtip, during steady crack growth as a function of EAH/σMs for a range of Poisson's ratio, ν

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Fig. 11

Toughness enhancement, Gss/Gtip, as a function of temperature T for values of the nondimensional parameters chosen so as to conform with those of a pseudoelastic SMA characterized in Ref. [34] (Table 1)

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