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Research Papers

On the Effect of Latent Heat 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

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 27, 2014; final manuscript received July 31, 2014; accepted manuscript posted August 7, 2014; published online August 13, 2014. Editor: Yonggang Huang.

J. Appl. Mech 81(10), 101006 (Aug 13, 2014) (6 pages) Paper No: JAM-14-1230; doi: 10.1115/1.4028191 History: Received May 27, 2014; Revised July 31, 2014; Accepted August 07, 2014

A finite element analysis of steady-state crack growth in pseudoelastic shape memory alloys under the assumption of adiabatic conditions 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 and the fracture toughness is obtained as the ratio of the far-field applied energy release rate to the crack-tip critical value. Results related to the influence of latent heat on the near-tip stress field and fracture toughness are presented for a range of parameters related to thermomechanical coupling. The levels of fracture toughness enhancement, associated with the energy dissipated by the transformed material in the wake of the growing crack, are found to be lower under adiabatic conditions than under isothermal conditions [Baxevanis et al., 2014, J. Appl. Mech., 81, 041005]. Given that in real applications of shape memory alloy (SMA) components the processes are usually not adiabatic, which is the case with the lowest energy dissipation during a cyclic loading–unloading process (hysteresis), it is expected that the actual level of transformation toughening would be higher than the one corresponding to the adiabatic case.

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Figures

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Fig. 1

Stress–temperature phase diagram. A pseudoelastic loading path.

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Fig. 2

Martensite volume fraction, ξ, and temperature, (T-Ms)/(T0-Ms), close to the steadily advancing crack tip for isothermal and adiabatic conditions. The values of the other nondimensional parameters used in the calculations are EAH/σMs=14, ρc/CM=0.7,  Ms+As/T0-Ms=14, As-Ms/T0-Ms=-2,Af-As/T0-Ms=3.5,Ms-Mf/T0-Ms=5,EM/EA=0.7,CM/CA=0.8, ν=0.33. (a) Martensite volume fraction, ξ, close to the steadily advancing crack tip under isothermal heat conditions. (b) Martensite volume fraction, ξ, close to the steadily advancing crack tip under adiabatic conditions. (c)Temperature, T˜=(T-Ms)/(T0-Ms), close to the steadily advancing crack tip under adiabatic conditions.

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Fig. 3

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. 2(b).

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Fig. 4

The toughness enhancement, Gss/Gtip, as a function of EAH/σMs for a range of the nondimensional parameter ρc/CM

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Fig. 5

The toughness enhancement, Gss/Gtip, as a function of EAH/σMs for a range of the nondimensional parameter (Ms+As)/(T0-Ms)

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Fig. 6

Uniaxial mechanical response of an NiTi material system characterized in Ref. [31] (Table 1) under isothermal and adiabatic conditions for T0 = 270 (K). For this material, the exponents ni (i = 1, 2, and 3) that capture the gradual transition from the elastic to transformation response and vice versa assume the following values, n1 = 0.17, n2 = 0.27, n3 = 0.25, and n4 = 0.35. (a) Stress–strain response for a uniaxial loading–unloading sequence. (b) Stress–temperature response for a uniaxial loading–unloading sequence.

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Fig. 7

Toughness enhancement, Gss/Gtip, as a function of ambient temperature T0 for values of the nondimensional parameters chosen so as to conform with those of a pseudoelastic NiTi material system characterized in Ref. [31] (Table 1). The values of the exponents ni (i = 1, 2, and 3) that capture the gradual transition from the elastic to transformation response and vice versa are n1 = 0.17, n2 = 0.27, n3 = 0.25, and n4 = 0.35.

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