Martensitic Phase Transformations

Reference: W. C. Kerr, M. G. Killough, A. Saxena, P. J. Swart and A. R. Bishop, Phase Transitions 69, 247-270 (1999)

This page contains results from research on martensitic transformations conducted by Avadh Saxena, Pieter Swart, Alan Bishop, Matt Killough, and me.  The first three people are Staff Members at Los Alamos National Laboratory;  Avadh and Alan are in  the Condensed Matter Theory and Statistical Physics group (T-11), and  Pieter is in the Mathematical Modelling and Analysis group (T-7).  Matt is a graduate student at the Courant Institute of Mathematical Sciences of New York University.

We have written a paper entitled Role of Elastic Compatibility in Martensitic Texture Evolution (LA-UR 97-4297).  Here is the abstract of the paper:

We have employed the time-dependent Ginzburg-Landau (TGDL) method to analyze the time evolution of strain fields in a model for materials with martensitic phase transformations.  The free energy functional is expressed in terms of the components of the strain tensor, and its functional derivatives with respect to these components give their rate of change.  However, the components of the strain tensor are not independent fields;  rather, they are related by the Saint-Venant compatibility condition.  This condition imposes constraints on the variations of the strain tensor components needed to obtain the equations of motion.  We have been able to incorporate these constraints in the TDGL procedure, and they introduce extra terms into the equations that effectively act as long-range, anisotropic elastic interactions.  The latter govern the types of elastic textures that may emerge during a martensitic transformation.  The results from the solution of these evolution equations exhibit fine and coarse tweed, the appearance of twinning, and tip splitting.

Clicking on the title above leads you to a Postscript file of this paper.  Color Postscript files of the figures are in these files:  Figure 1, Figure2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, and Figure 11.

The figures are snapshots from movies which show results from the computer solution of our equations of motion.  The paper describes three different simulations, and the mpeg files for those simulations are here.  Clicking on the names below takes you to those movies.  However, if you try to view the movies on a computer running Windows 95 with a typical viewer, you may not be able to see them.  They are not in the "constrained standard" of 352x240 pixels.  You will need to use a viewer that displays mpeg files with arbitrary dimensions.  Your browser may lead you to a plugin that will work.  If you are viewing them from a Unix computer, you should have no problem.

Here are the three movies:

One of the snapshots from these simulations was selected for the cover illustration of the November 1997 issue of the Notices of the American Mathematical Society.  Click here to see that picture,