Sourav Gur, Venkateswara Rao Manga, Stefan Bringuier, Krishna Muralidharan, Frantziskonis George...
-
Upload
cordelia-hunter -
Category
Documents
-
view
219 -
download
0
Transcript of Sourav Gur, Venkateswara Rao Manga, Stefan Bringuier, Krishna Muralidharan, Frantziskonis George...
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