×

zbMATH — the first resource for mathematics

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.
PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.