Quasistatic propagation of steps along a phase boundary. (English) Zbl 1160.74397
Summary: 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.
MSC:
| 74N20 | Dynamics of phase boundaries in solids |
| 74N05 | Crystals in solids |
| 80A22 | Stefan problems, phase changes, etc. |
References:
| [1] | 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 · doi:10.1007/BF02595429 |
| [2] | 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 · Zbl 0917.34052 · doi:10.1137/S0036139996312703 |
| [3] | Celli V., Flytzanis N. (1970). Motion of a screw dislocation in a crystal. J. Appl. Phys. 41(11): 4443–4447 · doi:10.1063/1.1658479 |
| [4] | Duffin R.J. (1953). Discrete potential theory. Duke Math. J. 20: 233–251 · Zbl 0051.07203 · doi:10.1215/S0012-7094-53-02023-7 |
| [5] | Fedelich B., Zanzotto G. (1992). Hysteresis in discrete systems of possibly interacting elements with a two well energy. J. Nonlinear Sci. 2: 319–342 · Zbl 0814.73004 · doi:10.1007/BF01208928 |
| [6] | Hirth J. (1994). Ledges and dislocations in phase transformations. Metall. Mat. Trans. A 25: 1885–1894 · doi:10.1007/BF02649036 |
| [7] | Hirth J.P., Lothe J. (1982). Theory of Dislocations. Wiley, New York · Zbl 1365.82001 |
| [8] | Hobart R. (1962). A solution to the Frenkel–Kontorova dislocation model. J. Appl. Phys. 33(1): 60–62 · doi:10.1063/1.1728528 |
| [9] | Hobart R. (1965). Peierls-barrier minima. J. Appl. Phys. 36(6): 1948–1952 · doi:10.1063/1.1714380 |
| [10] | Hobart R. (1965). Peierls stress dependence on dislocation width. J. Appl. Phys. 36(6): 1944–1948 · doi:10.1063/1.1714379 |
| [11] | Hobart R. (1966). Peierls-barrier analysis. J. Appl. Phys. 37(9): 3572–3576 · doi:10.1063/1.1708904 |
| [12] | Maradudin A.A. (1958). Screw dislocations and discrete elastic theory. J. Phys. Chem. Solids 9(1): 1–20 · doi:10.1016/0022-3697(59)90084-8 |
| [13] | Truskinovsky L., Vainchtein A. (2003). Peierls-Nabarro landscape for martensitic phase transitions. Phys. Rev. B 67: 172–103 · doi:10.1103/PhysRevB.67.172103 |
| [14] | 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 · Zbl 1171.74401 |
| [15] | 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 · Zbl 1171.74402 |
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