1. Dept. of Materials Science and Engineering
Transformation-induced stress in austenite associated with shape memory effect in NiTi
Sourav Gur, Venkateswara Rao Manga, Stefan Bringuier, Krishna Muralidharan, Frantziskonis George
Dept. of Materials Science and Engineering
University of Arizona

2. The induced tetragonal strain Tensor removes the phonon instability
Quantified transformation-induced strain state of Austenite in the two-phase region
The induced tetragonal strain
Tensor removes the phonon instability
Austenite in the two-phase region
- The strain
- Temperature dependence

3. NiTi: Austenite (B2)↔(B19’) Martensite phase transformation is displacive
- Phonon instability
Softening of TA phonons near zone boundaries
- In two-phase (B2+B19’) region:
Transformation stresses stabilize B2

4. On the nature of transformation-induced strain in Austenite
εij(B2)
strain
superelasticity
Characteristic internal strain tensor that makes B2 stable in two-phase region
- shape memory effect
- superelasticity
Objectives:
Using molecular dynamics simulations
What is the internal strain state (i.e. strain tensor) of austenite in the two-phase region associated with the shape memory effect in NiTi?
Temperature dependence of the strain?

5. B2-B19’ phase transformation as a function of temperature
250 K
330 K
370 K
450 K

6. B19’ phase fraction as a function of temperature
Size-I : 25 Å X 25 Å X 200 Å
Size-II: 50 Å X 50 Å X 200 Å
Size-III: 75 Å X 75 Å X 200 Å
Phase fractions from sufficiently large supercells

7. Martensite phase fraction as a function of temperature
- Richards equation[Richards] – for growth of plant population
- Zotov et al. used to describe the evolution of phase fractions
[zotov et al]
Tm --- temperature for maximum transformation rate
g, v – dictate the transformation rate
Zotov et al. Journal of alloys and compounds 616(2014)385
Richards J. Exp. Bot 10 (1959) 290

8. Strained lattice parameters of Austenite phase as a function of temperature
Unstrained
lattice parameter
extrapolated
(001)
(010)
(100)
strained-B2
εin[100] = (a[100]-aunstrained)/aunstrained
In the two-phase region aunstrained of B2 is obtained by extrapolation

9. Measured principal strains on Austenite phase as a function of temperature
(001)
(010)
(100)
strained-B2
εin[010] = εin[100]
Strain state of austenite in two-phase region : tetragonal strain
εin[001]
What equation based on phenomenology best describes the strain as function of T?

10. The relationship between Martensite fraction and the principal strains in Austenite
Richard equation ?

11. Strain in austenite as a function of temperature
The relationship between Martensite fraction and the principal strains in Austenite
Martensite phase fraction with temperature
[Zotov et al.]
Martensite phase fraction with internal strain on austenite phase, in [100] or [010] direction:
ε0=
Strain in austenite as a function of temperature

12. Variation of strain in austenite as a function of temperature
a1= , b1=2.451
a2= , b2=8.643

13. Phonon dispersion of austenite phase with and without lattice strain at 364 K
Austenite at T=364 K with no strain
Austenite at T=364 K with no
calculated strains
- In two-phase region (austenite + martensite):
- the phonon instability dissappears due to the transformation induced strains/stress in austenite
- The principal strains are quantified

14. Summary
The transformation-induced strain state in austenite in the two-phase region associated with shape memory effect in NiTi is quantified
Tetragonal-form strain tensor is found to stabilize the austenite
The strain that removes the phonon instability is found to vary exponentially with temperature

15. Acknowledgment
We thank Dr. Ting Zhu (Woodruff school of mechanical engineering at Georgia Institute of Technology) for the EAM potential

16. The Austenite (B2)↔(B19’)Martensite phase transformation is displacive
- Phonon instability
Softening of TA phonons near zone boundaries
- In two-phase (B2+B19’) region:
Transformation stresses stabilize B2
What is the internal-strain state (i.e. strain tensor) of austenite in the two-phase region associated with the shape memory effect?
Is the strain tensor of a particular type over the entire range?
εij(B2)
strain
superelasticity