matematické modelování inteligentních slitin

Matematické modelováníinteligentních slitin

Petr Sedlák, Hanuš Seiner, Miroslav Frost, Barbora Benešová

� výztuhy cév – stenty� „pohaněče“ - aktuátory� textilie� kompozity� ...

Materiálu s tvarovou pamětí– úvod


Rozhraní austenit-martenzit v monokrystalu CuAlNi

Modelování martenzitických mikrostruktur

Modelování šíření rozhraní A-M v monokrystalu CuAlNi

Modelování rozhraní martenzitických dvojčat v monokrystalu NiMnGa

Materiálu s tvarovou pamětí– modelování polykrystalických materiálů

Modelování SMA – experimenty na NiTi drátech

� Wire behavior in tension � Wire behavior in torsion

� Material: FWM#1 superelastic NiTi wire, straight annealed, diameter 0.1mm

Constructed by Jan Pilch, Institute of Physics, AS CR

� Wire behavior in tension � Wire behavior in torsion

� Material: FWM#1 superelastic NiTi wire, straight annealed, diameter 0.1mm

Modelování SMA – experimenty na NiTi drátech

Modelování SMA – formulace modelu

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� Key ingredients: I. state variablesII. (Helmholz) free energyIII. dissipation

� Generalized Standard Materials (Models) framework

• free energy function and dissipation function

• assures thermodynamical consistency if specific conditions on dissipation function are fulfilled

• minimum dissipation potential principle

• phase transformation: volume fraction of martensite,

• martensite structure evolution: mean transformation strain of martensite (tensor),

• total strain (small strain setting):

• R-phase transformation: volume fraction of R-phase,

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� I. state variables:

• temperature (parameter in case of isothermal regimes):

� imposed restrictions on internal variables:


• elastic energy:

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• chemical energy:

� II. Helmholz free energy:


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• novel form, allows to capture various phenomena• rate-independent, asymmetric• state-dependent (dissipative variables, temperature)• can be derived from a set of assumptions inspired by microstructural

findings

� III. Dissipation function:


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Mathematical framework

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� quasistatic mechanical loading of a SMA body with prescribed temperature evolution

� in our case: temperature-dependent dissipation!

� energetic solution concept suitable for rate-independent processes

• conditions on model parameters

• existence of solution(s)

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Numerická implementace – Abaqus UMAT

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Model – Material Parameters

Model – Material Parameters

� Anisotropy of transformation strain

� Tension-compression asymmetry

B. Reedlunn et al. / J. Mech. Phys. Solids

Modelování SMA – 3D model

� simulace SMA drátu

2828


NiTi spring – fatigue tests

Number of cycles to failure for different mean strokes and stroke amplitudes (peak topeak). Contour plot corresponds to periodic change of volume fraction of martensite according to simulations.

� Seiner, H. - Sedlák, P. - Landa, M.: Shape recovery mechanism observed in single crystals of Cu-Al-Ni shape memory alloy. Phase transitions. Vol. 81(2008), No. 6, pp. 537-551.

� Straka, L. - Heczko, O. - Seiner, H. - Lanska, N. - Drahokoupil - J., Soroka - A., Fähler, S. -Sozinov, A: Highly mobile twinned interface in 10 M modulated Ni-Mn-Ga martensite: Analysis beyond the tetragonal approximation of lattice. Acta Materialia Vol.59 (2011) (20) , pp. 7450-7463.

� P. Sedlák - M. Frost - B. Benešová - T. Ben Zineb - P. Šittner: Thermomechanical model forNiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings, International Journal of Plasticity 39 (2012) 132–151

References:

matematické modelování inteligentních slitin

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