TY - JOUR

T1 - A theory of thin films of martensitic materials with applications to microactuators

AU - Bhattacharya, K.

AU - James, R. D.

PY - 1999/3/1

Y1 - 1999/3/1

N2 - A direct derivation is given of a theory for single crystal thin films, starting from three-dimensional nonlinear elasticity theory augmented by a term for interfacial energy. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a frame-indifferent Cosserat membrane theory with one Cosserat vector field. The theory is applied to multi-well energy functions appropriate to martensitic materials. It is found that, unlike in bulk materials, which generally only support finely twinned austenite/martensite interfaces as energy minimizing states, the thin film theory predicts the existence of exact, untwinned austenite/martensite interfaces. These are used to construct some simple energy minimizing deformations - "tents" and "tunnels" - that could possibly be the basis of simple large-deformation microactuators. Explicit results are given for martensitic materials in the systems NiMnGa, NiTi, NiTiCu, and NiAl. A certain alloy of precise composition Ni30.5Ti49.5Cu20.0 is predicted to support a four-sided "tent" on an (001) film, which furthermore is predicted to collapse to the substrate upon heating. A formal derivation is given of higher order theories, which yields two additional Cosserat vectors and an explicit form of the bending energy. The derivation indicates an approach to plate-shell-thin film theories that is rather different from the ones usually followed.

AB - A direct derivation is given of a theory for single crystal thin films, starting from three-dimensional nonlinear elasticity theory augmented by a term for interfacial energy. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a frame-indifferent Cosserat membrane theory with one Cosserat vector field. The theory is applied to multi-well energy functions appropriate to martensitic materials. It is found that, unlike in bulk materials, which generally only support finely twinned austenite/martensite interfaces as energy minimizing states, the thin film theory predicts the existence of exact, untwinned austenite/martensite interfaces. These are used to construct some simple energy minimizing deformations - "tents" and "tunnels" - that could possibly be the basis of simple large-deformation microactuators. Explicit results are given for martensitic materials in the systems NiMnGa, NiTi, NiTiCu, and NiAl. A certain alloy of precise composition Ni30.5Ti49.5Cu20.0 is predicted to support a four-sided "tent" on an (001) film, which furthermore is predicted to collapse to the substrate upon heating. A formal derivation is given of higher order theories, which yields two additional Cosserat vectors and an explicit form of the bending energy. The derivation indicates an approach to plate-shell-thin film theories that is rather different from the ones usually followed.

KW - A. Phase transformation

KW - B. Thin films

KW - C. Variational calculus

KW - Microactuator

KW - Shape memory effect

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U2 - 10.1016/S0022-5096(98)00043-X

DO - 10.1016/S0022-5096(98)00043-X

M3 - Article

AN - SCOPUS:0033098284

VL - 47

SP - 531

EP - 576

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 3

ER -