A computational model for the indentation and phase transformation of a martensitic thin film

Abstract We propose a computational model for a stress-induced martensitic phase transformation of a single-crystal thin film by indentation and its reverse transformation to austenite by heating. Our model utilizes a surface energy that allows sharp interfaces with finite energy and a penalty that forces the film to lie above the indenter and undergo a stress-induced austenite-to-martensite phase transformation. We introduce a method to nucleate the martensite-to-austenite phase transformation since in our model the film would otherwise remain in the martensitic phase in a local minimum of the energy.

[1]  M. Luskin,et al.  Stability of microstructure for tetragonal to monoclinic martensitic transformations , 2000 .

[2]  Mitchell Luskin,et al.  On the computation of crystalline microstructure , 1996, Acta Numerica.

[3]  Richard D. James,et al.  Martensitic transformations and shape-memory materials ☆ , 2000 .

[4]  C. M. Wayman,et al.  Electron microscopy of internally faulted Cu-Zn-Al martensite , 1977 .

[5]  R. James,et al.  A theory of thin films of martensitic materials with applications to microactuators , 1999 .

[6]  C. M. Wayman,et al.  Shape-Memory Materials , 2018 .

[7]  Mitchell Luskin,et al.  The computation of the austenitic-martensitic phase transition , 1989 .

[8]  Mitchell Luskin,et al.  Computational Results for a Two-Dimensional Model of Crystalline Microstructure , 1993 .

[9]  R. Kohn,et al.  Branching of twins near an austenite—twinned-martensite interface , 1992 .

[10]  Charles Collins,et al.  Computation of Twinning , 1993 .

[11]  K. Bhattacharya,et al.  Relaxation of some multi-well problems , 2001 .

[12]  Kaushik Bhattacharya,et al.  Relaxed constitutive relations for phase transforming materials , 2000 .

[13]  B. Li,et al.  Theory and computation for the microstructure near the interface between twinned layers and a pure variant of martensite , 1999, Materials Science and Engineering: A.

[14]  A. Love A treatise on the mathematical theory of elasticity , 1892 .

[15]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[16]  C. Palmstrøm,et al.  Molecular beam epitaxy growth of ferromagnetic single crystal (001) Ni2MnGa on (001) GaAs , 1999 .

[17]  M. A. Northrup,et al.  Thin Film Shape Memory Alloy Microactuators , 1996, Microelectromechanical Systems (MEMS).

[18]  L. Delaey,et al.  Elastic constant measurements in β CuZnAl near the martensitic transformation temperature , 1977 .

[19]  K. Hane Bulk and thin film microstructures in untwinned martensites , 1999 .

[20]  Elastic constants of the monoclinic 18R martensite of a CuZnAl alloy , 1993 .

[21]  M. Luskin,et al.  On the numerical modeling of deformations of pressurized martensitic thin films , 2001 .

[22]  R. D. James,et al.  Proposed experimental tests of a theory of fine microstructure and the two-well problem , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[23]  Willard Miller,et al.  The IMA volumes in mathematics and its applications , 1986 .

[24]  C. M. Wayman,et al.  Introduction to the crystallography of martensitic transformations , 1964 .

[25]  Mitchell Luskin,et al.  A total-variation surface energy model for thin films of martensitic crystals , 2002 .