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Shock–induced martensitic phase transitions: critical stresses, Riemann problems and applications

Bruno, Oscar and Vaynblat, Dimitri (2001) Shock–induced martensitic phase transitions: critical stresses, Riemann problems and applications. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 457 (2016). pp. 2871-2920. ISSN 1364-5021. https://resolver.caltech.edu/CaltechAUTHORS:20181106-145235963

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Abstract

In this paper we develop a theory for phase transitions in solids under shock loading. This theory applies, in particular, to a class of experiments which, as a result of solid–to–solid phase transitions, give rise to certain characteristic patterns consisting of two shock–like waves. We show that the single assumption that stresses in a phase cannot lie beyond its transition boundaries leads to a complete model for the physical systems at hand. This model is different from others proposed in the literature: it does not make use of kinetic relations and it accounts for the observed wave histories without parameter fitting. The first part of this paper focuses on the basic mathematical description of our model and it presents solutions to the complete set of Riemann problems which could arise as a result of dynamic interactions, including the basic two–wave structures mentioned above. In the second part of the paper we use our Riemann solver to construct general solutions for the piecewise constant initial–value problems usually arising in experiment, and we specialize our solutions to two widely studied polymorphic phase changes: the graphite–diamond transition and the α–∈ transition in iron. We show that, in the presence of well–accepted quations of state for the pure phases, our model leads to close quantitative agreement with a wide range of experimental results; possible sources of disagreement in certain fine features are also discussed. Interestingly, in some cases our theory predicts sequences of events which differ from those generally accepted. In particular, our model predicts a variety of regimes for the iron experiments which previous theoretical investigations had not surmised, and it indicates the existence of certain unexpected transformation domains in the graphite systems.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1098/rspa.2001.0829DOIArticle
ORCID:
AuthorORCID
Bruno, Oscar0000-0001-8369-3014
Additional Information:© 2001 The Royal Society. Received 2 June 2000; revised 4 December 2000 and 12 March 2001; accepted 29 March 2001. The authors acknowledge the support of the DOE through contract W-7405-ENG-48. O.B. gratefully acknowledges support from the NSF, under contract nos DMS-9523292 and DMS-9816802, and the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant nos F49620-96-1-0008, F49620-99-1-0010 and F49620-99-1-0193. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-ENG-48
NSFDMS-9523292
NSFDMS-9816802
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0008
Air Force Office of Scientific Research (AFOSR)F49620-99-1-0010
Air Force Office of Scientific Research (AFOSR)F49620-99-1-0193
Subject Keywords:martensitic phase transitions; shocks; Riemann problems
Issue or Number:2016
Record Number:CaltechAUTHORS:20181106-145235963
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181106-145235963
Official Citation:Shock–induced martensitic phase transitions: critical stresses, Riemann problems and applications. Oscar Bruno, Dimitri Vaynblat. Proc. R. Soc. Lond. A 2001 457 2871-2920; DOI: 10.1098/rspa.2001.0829. Published 8 December 2001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90677
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Nov 2018 21:17
Last Modified:03 Oct 2019 20:27

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