Pressurized shape memory thin films

Richard D. James, Raffaella Rizzoni

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We study the behavior of a martensitic thin film with a hydrostatic pressure applied underneath the film. The problem is formulated in 3-D for a single crystal film of thickness h, and a Cosserat membrane theory is derived by Γ-convergence techniques in the limit h → 0. The membrane theory is further simplified using a second Γ-convergence argument based on hard moduli. The resulting theory supports energy minimizing "tunnels": structures having the shape of part of a cylinder cut by a plane parallel to its axis, obtained by releasing the film from the substrate along a strip with a certain orientation. As the temperature is raised (at fixed pressure) the energy minimizing shape collapses gradually to the substrate, accompanied by a martensite-to-austenite phase transformation. During this process the tunnel supports a microstructure consisting of fine bands of austenite parallel to the axis of the tunnel, alternating with bands of a single variant of martensite. Formulas for the associated volume-temperature-pressure relation are given: in these the latent heat of transformation plays an important role.

Original languageEnglish (US)
Pages (from-to)399-436
Number of pages38
JournalJournal of Elasticity
Volume59
Issue number1-3
DOIs
StatePublished - 2000

Bibliographical note

Funding Information:
The authors thank AFOSR/MURI F49620-98-1-0433 for supporting this research. The work also benefitted from the support of ONR N00014-95-1-1145 and -91-J-4034, ARO DA/DAAG55-98-1-0335, NSF DMS-9505077 and DMS 0074043, and the Isaac Newton Institute for Mathematical Sciences. RR also thanks the Italian M.U.R.S.T. for the financial support provided through the project “Modelli matematici per la scienza dei materiali” Co.fin. (1998).

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