Thermodynamics and kinetics of nucleation of a spherical gas bubble inside an elastoplastic material due to sublimation

General thermodynamic and kinetic approaches for sublimation inside an elastoplastic material developed in Levitas (2012) are applied to the problem of a nucleation of a spherical gas bubble inside an infinite elastoplastic sphere. A large-strain solution of the mechanical problem on a spherical void formation is generalized for the case with internal pressure and surface tension. Nucleation via homogeneous transformation in the nucleus of a fixed mass and nucleation via continuous interface propagation are studied in detail. For both paths, the explicit expressions for the thermodynamic driving forces and activation energies are derived. Using a kinetic nucleation criterion, the kinetic relationships between tensile sublimation pressure and temperature are derived. For both transformation paths, three different regions are present on the kinetic temperature-stress curve. For small stresses, elastic deformation of a sphere takes place, and the results for both paths coincide. For large stresses, nucleus size is equal to the minimum radius for which one still can distinguish between solid and gas, and for the intermediate stresses the radius of the critical nucleus maximizes the activation energy. For all cases with plastic expansion, nucleation via homogeneous transformation is more probable for small stresses and significantly more probable for large stresses. However, such a homogeneously transformed nucleus cannot grow. It is necessary to slightly increase temperature or tensile pressure (to a value well below that for nucleation via interface propagation) to cause growth. Below some critical temperature θin, while the nucleus cannot grow because of solid–gas transformation, it expands like a balloon due to loss of mechanical stability. To our knowledge, this is the only known example of transformation of a subcritical nucleus into a supercritical one due to mechanical instability. The thermodynamics and the kinetics of evaporation are considered as well, and similar mechanical instability is found. Also, homogeneously transformed nucleus, while it starts to shrink, does not completely disappear; it represents a metastable rather than a critical nucleus. All of these results do not have counterparts in nucleation in elastic materials.

► Nucleation of a spherical bubble inside due to sublimation in elastoplastic material.
► Concept of a critical nucleus inside elastoplastic material and its path-dependence.
► Growth of a critical nucleus via interface propagation and mechanical instability.
► Arrhenius-type kinetic equation and principle of the minimum of transformation time.
► Tensile pressure–temperature nucleation diagram is determined.