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Chemical affinity tensor and chemical reaction front propagation: theory and FE-simulations

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Abstract

We develop an approach to studying the influence of stresses and strains on the kinetics of chemical reaction fronts based on the expression of the chemical affinity tensor that determines the configurational force acting at the transformation front. For a chemical reaction between diffusive gaseous and deformable solid constituents we formulate a kinetic equation in a form of the dependence of the reaction front velocity on the normal component of the chemical affinity tensor that in turn depends on stresses. We describe a locking effect—blocking the reaction by stresses at the reaction front and define the forbidden stresses or strains at which the chemical reaction cannot go. We develop a finite-element model to describe how stresses affect a chemical reaction front propagation. To demonstrate how the model works we consider a chemical front propagation in a plate with a groove assuming that the solid constituents are linear elastic. Comparing the front propagation in the vicinity of the groove top and at the bottom of the plate far from the groove we study how the stress concentrations, internal stresses and external loading, material and reaction parameters affect the reaction.

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Acknowledgments

This work was supported by Russian Foundation for Basic Research (Grants 14-01-31433 mol_a, 16-01-00815) and by Russian Federation President Grant Council (Grant MK-6316.2015.1).

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, Bolshoy Pr., 61, V.O., St. Petersburg, Russia, 199178

    Alexander B. Freidin, Igor K. Korolev, Sergey P. Aleshchenko & Elena N. Vilchevskaya

  2. Peter the Great St. Petersburg Polytechnic University, Polytechnicheskaya Str., 29, St. Petersburg, Russia, 195251

    Alexander B. Freidin & Elena N. Vilchevskaya

  3. St. Petersburg University, Universitetsky Pr., 28, Peterhof, St. Petersburg, Russia, 198504

    Alexander B. Freidin

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  1. Alexander B. Freidin
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  2. Igor K. Korolev
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  3. Sergey P. Aleshchenko
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  4. Elena N. Vilchevskaya
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Correspondence to Alexander B. Freidin.

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Freidin, A.B., Korolev, I.K., Aleshchenko, S.P. et al. Chemical affinity tensor and chemical reaction front propagation: theory and FE-simulations. Int J Fract 202, 245–259 (2016). https://doi.org/10.1007/s10704-016-0155-1

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