Sourav Gur, Venkateswara Rao Manga, Stefan Bringuier, Krishna Muralidharan, Frantziskonis George

Dept. of Materials Science and EngineeringUniversity of Arizona

Transformation-induced stress in austenite associated with shape memory effect in NiTi

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

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

ε ij(B2)

strain

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?

On the nature of transformation-induced strain in Austenite

Characteristic internal strain tensor that makes B2 stable in two-phase region

- shape memory effect- superelasticity

B2-B19’ phase transformation as a function of temperature

450 K370 K330 K250 K100% B2100% B19’

B19’ phase fraction as a function of temperature

• Phase fractions from sufficiently large supercells

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

Martensite phase fraction as a function of temperature

Tm --- temperature for maximum transformation rate

g, v – dictate the transformation rate

Zotov et al. Journal of alloys and compounds 616(2014)385Richards J. Exp. Bot 10 (1959) 290

- Richards equation[Richards] – for growth of plant population- Zotov et al. used to describe the evolution of phase fractions [zotov et al]

Strained lattice parameters of Austenite phase as a function of temperature

strained-B2

(001)

(010)

(100)

extrapolatedUnstrained

lattice parameter

εin[100] = (a[100]-aunstrained)/aunstrained

In the two-phase region aunstrained of B2 is obtained by extrapolation

Measured principal strains on Austenite phase as a function of temperature(001)

(010)

(100)

strained-B2

εin[010] = εin[100]

εin[001]• Strain state of austenite in two-

phase region : tetragonal strain

• What equation based on phenomenology best describes the strain as function of T?

The relationship between Martensite fraction and the principal strains in Austenite

Richard equation ?

Martensite phase fraction with internal strain on austenite phase, in [100] or [010] direction:

Martensite phase fraction with temperature [Zotov et al.]

The relationship between Martensite fraction and the principal strains in Austenite

ε0= 0.0119

Strain in austenite as a function of temperature

0

Variation of strain in austenite as a function of temperature

a1= -0.0198, b1=2.451a2= -0.0370, b2=8.643

0

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

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

Acknowledgment

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

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?

ε ij(B2)

strain

superelasticity