ON LOCKING STRAINS IN MECHANOCHEMISTRY OF CHEMICAL REACTIONS FRONTS

The influence of stresses and strains on the chemical reaction rate is studied basing on the concept of the chemical affinity tensor. The  reaction between a deformable solid and diffusive gaseous  constituents is considered. The reaction is localized at the reaction  front and consumes all the matter supplied by the diffusion. Silicon  oxidation and lithiation are examples of such a reaction. Tensorial  nature of the chemical reaction is manifestation of the fact that in  the case of deformable material the reaction is to be considered not  in a point but at an oriented area element. A kinetic equation takes  the form of the dependence of the reaction rate at the oriented area element on the normal component of the chemical affinity  tensor. Stressstrain state affects the reaction rate as it affects the  chemical affinity tensor. If the normal component of the affinity tensor is negative then the reaction at the oriented area element is  impossible. Strains and stresses at which the normal component of  the affinity tensor cannot be positive at any orientation or  concentration of the diffusive constituent form forbidden zones in  strain or stress space. A procedure for forbidden zones construction is developed. The use of the jump relationships for  stresses and strains allows to present the normal component of the  chemical affinity tensor as a dependence on strains/stresses on one  side of the reaction front and the normal to the front. Then it is shown that the boundaries of the zone are determined by maximum  and minimum of a quadratic form that was earlier studied for phase  transitions zones construction. The location and sizes of the zone  depend on the input of the chemical energies of the constituents relatively to strain energies. Besides the deformations  which correspond to forbidden regions, blocking deformations are  also considered which can be unblocked and started-up due to inelastic strains or diffusion.

1. Freidin, A. 2014, “Chemical affinity tensor and stress-assist chemical reactions front propagation in solids” ASME 2013 International Mechanical Engineering Congress and Exposition, November 13-21, 2013, San Diego, California, USA.

2. Freidin, A., Vilchevskaya, E., Korolev, I. 2014, “Stress-assist chemical reactions front propagation in deformable solids” Int. J. Engineering Science. vol. 83, pp. 57–75.

3. Freidin, A.B. 2015, “On a chemical affinity tensor for chemical reactions in deformable solids.” Mechanics of Solids vol. 50, no. 3, pp. 260–285.

4. Freidin, A., Morozov, N., Petrenko, S., Vilchevskaya, E. 2016, “Chemical reactions in spherically symmetric problems of mechanochemistry” Acta Mech. vol. 227, no. 1, pp. 43–56.

5. Freidin, A.„ Korolev, I., Aleshchenko, S., Vilchevskaya, E. 2016, “Chemical affinity tensor and chemical reaction front propagation: theory and FEsimulations” Int. J. Fract. vol. 202, no. 2, pp. 245–259.

6. Grinfeld, M., Thermodynamic methods in the theory of heterogeneous systems. Longman, New York, 1991.

7. Abeyaratne, R., Knowles, J. Elovution of phase transitions. A continuum theory. Cambridge University Press. 2006. 242 p.

8. Levitas V.I., Levin V.A., Zingerman K.M., Freiman E.I. 2009, “Displacive phase transitions at large strains: phase-field theory and simulations ” Physical Review Letters. vol. 103, no. 2, pp. 025702.

9. Levin V.A., Levitas V.I., Lokhin V.V., Zingerman K.M., Sayakhova L.F., Freiman E.I. 2010, “Solid-state stress-induced phase transitions in a material with nanodimensional inhomogeneities: model and computational experiment” Doklady Physics. vol. 55, no. 10, pp. 507-511.

10. Levin V.A., Levitas V.I., Zingerman K.M., Freiman E.I. 2013, “Phasefield simulation of stress-induced martensitic phase transformations at large strains” International Journal of Solids and Structures. vol. 50, pp. 2914–2928.

11. Glansdorff, P., Prigogine, I. 1971, Thermodynamic theory of stability and fluctuation. Wiley-Interscience. New York.

12. Rusanov, A.I. 2005, “Surface thermodynamics revisited” // Surface Science Reports. vol. 58, pp. 111–239.

13. A. I. Rusanov 2006, Thermodynamic foundations of mechanochemistry. Nauka, Saint-Petersburg. 222 p. (Russian)

14. Morozov, N. F.,Freidin, А.Б. 1998, "Phase transition zones and phase transformations of elastic solids under different stress states"Proc. Steklov Mathe. Inst. vol. 223, pp. 220–232. (Russian)

15. Freidin, A.B. 2007, “On new phase inclusions in elastic solids” ZAMM. vol. 87, no. 2, pp. 102–116.

16. Kunin, I. 1983, Elastic Media with Microstructure. Springer-Verlag, Berlin, New York, etc .

17. Freidin, A.B., Vilchevskaya, E.N., Sharipova, L.L. 2002, “Two-phase deformations within the framework of phase transition zones” Theoretical and Applied Mechanics. vol. 28–29, pp. 149–172

18. Freidin, A.B., Sharipova, L.L. 2006, “On a model of heterogenous deformation of elastic bodies by the mechanism of multiple appearance of new phase layers” Meccanica. 2006. vol. 41, no. 2, pp. 321–339.

19. Antimonov, M.A., Cherkaev, A., Freidin 2016, “A.B. Phase transformations surfaces and exact energy lower bounds” International Journal of Engineering Science. vol. 98, pp. 153–182.