BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Models for self-similarity and disclinations in martensite - Pierl uigi Cesana (Kyushu University) DTSTART:20190320T150000Z DTEND:20190320T160000Z UID:TALK121846@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:The austenite-to-martensite phase-transformation is a first-or der diffusionless transition occurring in elastic
crystals and characte rized by an abrupt change of shape of the underlying crystal lattice. It m anifests itself
to what in materials science is called a martensitic mi crostructure\, an intricate highly inhomogeneous
pattern populated by s harp interfaces that separate thin plates composed of mixtures of differen t martensitic
phases (i.e.\, rotated copies of a low symmetry lattice) possibly rich in defects and lattice mismatches. In
this talk we review a series of separate results on the modeling of inter-connected phenomena observed in
martensite\, which are self-similarity (criticality) and d isclinations.
Inspired by Bak&rsquo\;s cellular automaton model for san d piles\, we introduce a conceptual model for a
martensitic phase trans ition and analyze the properties of the patterns obtained. Nucleation and evolution
of martensitic variants is modeled as a fragmentation process in which the microstructure evolves via
formation of thin plates of ma rtensite embedded in a medium representing the austenite. While the
ori entation and direction of propagation of the interfaces separating the pla tes is determined by kinematic
compatibility of the crystal phases\, th eir nucleation sites are inevitably influenced by defects and disorder\,which are encoded in the model by means of random variables. We investig ate distribution of the lengths
of the interfaces in the pattern and es tablish limit theorems for some of the asymptotics of the interface
pro file. We also discuss numerical aspects of determining the behavior of the density profile and power
laws from simulations of the model and prese nt comparisons with experimental data.
Turning our attention on defects \, we investigate wedge disclinations\, high-energy rotational defects cau sed
by an angular lattice mismatch that were predicted by Volterra in h is celebrated 1907 paper. Unlike
dislocations\, which have received con siderable attention since the 1930s\, disclinations have received
dispr oportionally less interest. However\, disclinations are not uncommon as th ey accompany\, as a relevant
example\, rotated and nested interfaces se parating (almost) kinematically compatible variants as in
martensitic a valanche experiments. Here we follow two modeling approaches. First\, we i ntroduce a few
recent results on the modeling of planar wedge disclinat ions in a continuum\, purely (non-linear) elastic
model that describes disclinations as solutions of some differential inclusion. Secondly an ato mistic model
of nearest-neighbor interactions over a triangular lattice inspired by the literature on discrete models for
dislocations.
Som e of these results are from a collaboration with J.M. Ball and B. Hambly ( Oxford) and P. Van Meurs
(Kanazawa).
LOCATION:Seminar Room 2\, Newton Institute END:VEVENT END:VCALENDAR