

Preprint 95/2003
Modeling and simulation of martensitic phase transitions with a triple point
Patrick W. Dondl and Johannes Zimmer
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Submission date: 22. Nov. 2003
Pages: 30
published in: Journal of the mechanics and physics of solids, 52 (2004) 9, p. 2057-2077
DOI number (of the published article): 10.1016/j.jmps.2004.03.001
Bibtex
PACS-Numbers: 61.50.Ks, 62.20.-x, 81.30.Kf
Keywords and phrases: microstructures, phase transformations, elastic material
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Abstract:
A framework for modeling complicated global energy landscapes in a
piecewise manner is presented. Specifically, a class of
strain-dependent energy functions is derived for the triple point of
Zirconia (), where tetragonal, orthorhombic (orthoI)
and monoclinic phases are stable. After presenting a simple
two-dimensional framework to deal with this symmetry breaking, an
explicit energy is fitted to the available elastic moduli of Zirconia
in this two-dimensional setting. First, we use the orbit space method
to deal with symmetry constraints in an easy way. Second, we introduce
a modular (piecewise) approach to reproduce or model elastic moduli,
energy barriers and other characteristics independently of each other
in a sequence of local steps. This allows for more general results
than the classical Landau theory (understood in the sense that the
energy is a polynomial of invariant polynomials), since the class of
functions considered here is strictly larger. Finite Element
simulations with the energy constructed here investigate the pattern
formation in Zirconia at the triple point.