Abstract
We study quasistatic propagation of steps along a phase boundary in a two-dimensional lattice model of martensitic phase transitions. For analytical simplicity, the formulation is restricted to antiplane shear deformation of a cubic lattice with bi-stable interactions along one component of shear strain and harmonic interactions along the other. Energy landscapes connecting equilibrium configurations with periodic and non-periodic arrangements of steps are constructed, and the energy barriers separating metastable states are calculated. We show that a sequential one-by-one step propagation along a phase boundary requires smaller energy barriers than simultaneous motion of several steps.
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Bray D., Howe J. (1996). High-resolution transmission electron microscopy investigation of the face-centered cubic/hexagonal close-packed martensite transformation in Co-31.8 Wt Pct Ni alloy: Part I. Plate interfaces and growth ledges. Metall. Mat. Trans. A 27: 3362–3370
Cahn J.W., Mallet-Paret J., Vleck E.S.V. (1998). Traveling wave solutions for systems of odes on a two-dimensional spatial lattice. SIAM J. Appl. Math. 59(2): 455–493
Celli V., Flytzanis N. (1970). Motion of a screw dislocation in a crystal. J. Appl. Phys. 41(11): 4443–4447
Duffin R.J. (1953). Discrete potential theory. Duke Math. J. 20: 233–251
Fedelich B., Zanzotto G. (1992). Hysteresis in discrete systems of possibly interacting elements with a two well energy. J. Nonlinear Sci. 2: 319–342
Hirth J. (1994). Ledges and dislocations in phase transformations. Metall. Mat. Trans. A 25: 1885–1894
Hirth J.P., Lothe J. (1982). Theory of Dislocations. Wiley, New York
Hobart R. (1962). A solution to the Frenkel–Kontorova dislocation model. J. Appl. Phys. 33(1): 60–62
Hobart R. (1965). Peierls-barrier minima. J. Appl. Phys. 36(6): 1948–1952
Hobart R. (1965). Peierls stress dependence on dislocation width. J. Appl. Phys. 36(6): 1944–1948
Hobart R. (1966). Peierls-barrier analysis. J. Appl. Phys. 37(9): 3572–3576
Maradudin A.A. (1958). Screw dislocations and discrete elastic theory. J. Phys. Chem. Solids 9(1): 1–20
Truskinovsky L., Vainchtein A. (2003). Peierls-Nabarro landscape for martensitic phase transitions. Phys. Rev. B 67: 172–103
Zhen, Y., Vainchtein, A.: Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution. J. Mech. Phys. Solids (2007). Published online, doi:10.1016/j.jmps.2007.05.017
Zhen, Y., Vainchtein, A.: Dynamics of steps along a martensitic phase boundary II: Numerical simulations. J. Mech. Phys. Solids (2007). Published online, doi:10.1016/j.jmps.2007.05.018
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Communicated by R. Abeyaratne
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Sharma, B.L., Vainchtein, A. Quasistatic propagation of steps along a phase boundary. Continuum Mech. Thermodyn. 19, 347–377 (2007). https://doi.org/10.1007/s00161-007-0059-4
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DOI: https://doi.org/10.1007/s00161-007-0059-4