Weatherwax, John and Vaynblat, Dimitri and Bruno, Oscar and Rosales, Ruben (2007) On a viscous critical-stress model of martensitic phase transitions. Journal of Applied Physics, 102 (6). Art. No. 064905. ISSN 0021-8979 http://resolver.caltech.edu/CaltechAUTHORS:WEAjap07
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The solid-to-solid phase transitions that result from shock loading of certain materials, such as the graphite-to-diamond transition and the alpha-epsilon transition in iron, have long been subjects of a substantial theoretical and experimental literature. Recently a model for such transitions was introduced which, based on a CS condition (CS) and without use of fitting parameters, accounts quantitatively for existing observations in a number of systems [Bruno and Vaynblat, Proc. R. Soc. London, Ser. A 457, 2871 (2001)]. While the results of the CS model match the main features of the available experimental data, disagreements in some details between the predictions of this model and experiment, attributable to an ideal character of the CS model, do exist. In this article we present a version of the CS model, the viscous CS model (vCS), as well as a numerical method for its solution. This model and the corresponding solver results in a much improved overall CS modeling capability. The innovations we introduce include: (1) Enhancement of the model by inclusion of viscous phase-transition effects; as well as a numerical solver that allows for a fully rigorous treatment of both, the (2) Rarefaction fans (which had previously been approximated by “rarefaction discontinuities”), and (3) viscous phase-transition effects, that are part of the vCS model. In particular we show that the vCS model accounts accurately for well known “gradual” rises in the alpha-epsilon transition which, in the original CS model, were somewhat crudely approximated as jump discontinuities.
|Additional Information:||©2007 American Institute of Physics. (Received 26 February 2007; accepted 21 July 2007; published online 19 September 2007)|
|Subject Keywords:||critical phenomena; martensitic transformations; shock wave effects|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||25 Sep 2007|
|Last Modified:||26 Dec 2012 09:43|
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