

Preprint 42/2002
Reconstructive phase transformations, maximal Ericksen-Pitteri neighborhoods, dislocations and plasticity in crystals
Sergio Conti and Giovanni Zanzotto
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Submission date: 21. May. 2002
Pages: 23
Bibtex
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Abstract:
We study the reconstructive phase
transformations in crystalline solids (i.e. transformations in
which the parent and product lattices have arithmetic symmetry groups
admitting no finite supergroup), the best known example of which is
the bcc-to-fcc transformation in iron. We first describe the maximal
Ericksen-Pitteri neighborhoods in the space of lattice metrics, thereby obtaining a
quantitative characterization for weak transformations. Then, focussing
for simplicity on a two-dimensional setting, we construct a class of
strain-energy functions which admit large strains in their domain and
are invariant under the full symmetry group of the lattice; in particular,
we give an explicit energy suitable for the square-to-hexagonal
reconstructive transformation in planar lattices. We present a numerical scheme
based on atomic-scale finite elements and use it to analyze the effects
of transformation cycling on a planar crystal, by means of our constitutive
function. This example illustrates the main phenomena related to
reconstructive phase changes: in particular, the formation of dislocations,
vacancies and interstitials in the lattice.