Sublimation, chemical decomposition, and melting inside an elastoplastic material: General continuum thermodynamic and kinetic theory Valery I. Levitas Iowa State University, Departments of Aerospace Engineering, Mechanical Engineering, and Material Science and Engineering, Ames, Iowa 50011, USA article info Article history: Received 5 May 2011 Received in final revised form 23 November 2011 Available online 25 January 2012 Keywords: Sublimation Chemical decomposition Elastoplastic materials Nucleation and growth Mechanical instability abstract General thermodynamic and kinetic approaches for sublimation inside an elastoplastic material are developed for large strains. Various conceptual problems related to the effect of irreversible plastic deformation and dissipation, path-dependence of the appearance of a critical nucleus, and the presence of large strains are considered. Two transformation paths are studied: nucleation via homogeneous transformation in the nucleus of fixed mass and nucleation via continuous interface propagation. For both paths, the expressions for the thermodynamic driving forces and activation energies are derived. The activation energy is equal to the negative driving force for the appearance of a nucleus maximized with respect to nucleus mass and minimized over the nucleus shape, transformation path, and position. This definition corresponds to the principle of the minimum of transforma- tion time and reduces to the traditional one in the limit of elastic materials. An Arrhe- nius-type kinetic equation for nucleation time and kinetic nucleation criterion are formulated. Algorithms for the determination of the critical nucleus are suggested. After appearance of the nucleus via homogeneous transformation, the possibility of its growth should be checked. Growth may occur by further sublimation or by mechanical expansion without phase transformation due to mechanical instability. Because the driving force for forward and reverse transformations maybe different, several scenarios are possible. The nucleus can grow, disappear, or be arrested; in the last case, it represents a stable rather than a critical nucleus. It is demonstrated that with small modifications, our approach to sublimation can be applied to chemical decomposition and melting inside an elastoplastic material. In the accompanying paper (Levitas and Altukhova, 2012) we will apply the developed theory to nucleation of a spherical gas bubble inside an elastoplastic material. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Sublimation is a direct, first-order phase transformation from the solid to the gas phase. Sublimation always occurs from the free surface of the solid until partial gas pressure reaches an equilibrium value for a given temperature. Thermodynamic equilibrium between a gas and a free solid surface and sublimation from a free surface are problems from any advanced ther- modynamics textbook (e.g., Moran and Shapiro, 2008). Evaporation within a liquid is a typical nucleation problem (formally completely similar to melting and solidification), see Landau and Lifshitz (1980) and Porter and Easterling (1992). Thus, the total Gibbs energy change of a system when a spherical nucleus of a radius r appears is DG ¼ Dg 4 3 pr 3  C4pr 2 , where Dg is the change of the local Gibbs energy and C is the surface energy of a nucleus. The plot of DG versus radius r is shown in Fig. 1. Note that the dissipation increment X = DG. Thus, for small radii, dissipation is negative and the nucleus is thermodynamically inadmissible – i.e., it can appear due to thermal fluctuation only. 0749-6419/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijplas.2012.01.006 E-mail address: vlevitas@iastate.edu International Journal of Plasticity 34 (2012) 41–60 Contents lists available at SciVerse ScienceDirect International Journal of Plasticity journal homepage: www.elsevier.com/locate/ijplas