The superelastic model is based on the uniaxial stress-strain response of phase transforming
materials. Such materials (e.g., Nitinol) are in the austenite phase under no loading
conditions. Austenite is assumed to follow isotropic linear elasticity. On loading the
material, the austenite phase starts transforming into martensite beyond a certain stress.
Martensite is also assumed to follow isotropic linear elasticity. During the phase
transformation, elastic properties are calculated from the elastic constants of austenite and
martensite, following the rule of mixtures:
E=EA+ζ(EM−EA)
ν=νA+ζ (νM−νA)
where
ζ
is the fraction of martensite,
EA
is the Young's modulus of austenite,
EM
is the Young's modulus of martensite,
νA
is the Poisson's ratio of austenite, and
νM
is the Poisson's ratio of martensite. After a certain stress, austenite is
completely transformed into martensite, which deforms elastically thereafter. Therefore, the
deformation follows the elastic constants of austenite when the fraction of martensite is zero
and follows the elastic constants of martensite if the fraction of martensite is one (full
transformation). On unloading, martensite transforms back into austenite and the
transformation strain is fully recovered. However, the stress at which the reverse
transformation occurs is different from the stress at which the austenite to martensite
transformation occurred.
Superelasticity
You can define the elastic properties of martensite, the critical stress levels for forward
and reverse transformation, and the variation of transformation plateau with temperature.
You can define elastic properties of austenite in the elastic material option.
Superelasticity supports both associated and nonassociated flow rules:
- Associated: When using associated flow the volumetric transformation strain,
εLV
, is assumed to be equal to the uniaxial transformation strain,
εL
.
- Nonassociated: When using nonassociated flow the volumetric transformation strain,
εLV
, must be specified independently from the uniaxial transformation
strain,
εL
.
Table 1. Flow rule=Associated
Input Data |
Description |
E_m |
Young's modulus of martensite,
EM
. |
Nu_m |
Poisson's ratio of martensite,
νM
. |
Episilon_L |
Uniaxial transformation strain,
εL
. |
Stress_S_tL |
Stress at which the transformation begins during loading in
tension,
σStL
|
Stress_E_tL |
Stress at which the transformation ends during loading in
tension,
σEtL
|
Stress_S_tU |
Stress at which the reverse transformation begins during
unloading in tension,
σStU
|
Stress_E_tU |
Stress at which the reverse transformation ends during unloading
in tension,
σEtU
|
Stress_S_cL |
Stress at which the transformation begins during loading in
compression, as a positive value,
σScL
|
T_0 |
Reference temperature,
T0
|
DeltaS/DeltaT_L |
Slope of the stress versus temperature curve for loading,
(δσδT)L
|
DeltaS/DeltaT_U |
Slope of the stress versus temperature curve for loading,
(δσδT)U
|
Table 2. Flow rule=Nonassociated
Input Data |
Description |
E_m |
Young's modulus of martensite,
EM
. |
Nu_m |
Poisson's ratio of martensite,
νM
. |
Episilon_L |
Uniaxial transformation strain,
εL
. |
Episilon_VL |
Volumetric transformation strain,
εLV
. |
Stress_S_tL |
Stress at which the transformation begins during loading in
tension,
σStL
|
Stress_E_tL |
Stress at which the transformation ends during loading in
tension,
σEtL
|
Stress_S_tU |
Stress at which the reverse transformation begins during
unloading in tension,
σStU
|
Stress_E_tU |
Stress at which the reverse transformation ends during unloading
in tension,
σEtU
|
Stress_S_cL |
Stress at which the transformation begins during loading in
compression, as a positive value,
σScL
|
T_0 |
Reference temperature,
T0
|
DeltaS/DeltaT_L |
Slope of the stress versus temperature curve for loading,
(δσδT)L
|
DeltaS/DeltaT_U |
Slope of the stress versus temperature curve for loading,
(δσδT)U
|
Superelastic Hardening
The plasticity model for superelastic materials is based on the uniaxial stress-strain
response. Such materials (e.g., Nitinol) are in the austenite phase under no loading
conditions. Austenite is assumed to follow isotropic linear elasticity. On loading the
material, the austenite phase starts transforming into martensite beyond a certain stress.
Martensite is assumed to follow an elastoplastic response, with elasticity characterized by
the linear elastic model and the plastic behavior represented by the Drucker Prager model.
Martensite exhibits plastic behavior after full transformation.
Note:
The hardening data for superelastic materials is specified by providing the yield stress
as a function of total strain. This is in contrast to hardening
data for many other types of materials that specify yield stress as a function of
plastic strain.
Input Data |
Description |
Yield Stress |
The true - or logarithmic - stress value at the corresponding
total strain. |
Total Strain |
Total stran . |
Superelastic Hardening Modifications
It is observed that the transformation stress levels decrease with an increase in the
plastic strain. There are two ways to specify this variation in the transformation plateau
with plastic strain. You can either specify the data describing the change in transformation
stress levels as a function of the plastic strain, using the built-in functionality, or you
can use a user subroutine to specify this dependency.
Table 3. Builtin
Input Data |
Description |
Stress_S_tl |
Stress at which the transformation begins during loading in
tension,
σStL
|
Stress_E_tl |
Stress at which the transformation ends during loading in
tension,
σEtL
|
Stress_S_tU |
Stress at which the reverse transformation begins during
unloading in tension,
σStU
|
Stress_E_tU |
Stress at which the reverse transformation ends during unloading
in tension,
σEtU
|
Plastic Strain |
Stress at which the transformation begins during loading in
compression, as a positive value,
σScL
|
The user subroutine USUPERELASHARDMOD is used for implicit time integration
simulations and VUSUPERELASHARDMOD is used for explicit time integration
simulations.
Table 4. User
Input Data |
Description |
User parameters |
User defined material parameters. |