Dislocation phenomena described with free volume concept and Eyring's rate process theory

Dislocation phenomena in solids under simple shear stress are theoretically addressed with the free volume concept and Eyring's rate process theory for obtaining a generic and unified description. The obtained equations do not have any restrictions to specific materials and are compared with various theories and empirical equations like the Hall-Petch and its inverse forms. Moreover, our equations are used to fit experimental data of mechanical properties and dislocation density against grain sizes available in the literature. A good agreement with observations is achieved, indicating that our theoretical framework is sound. Our findings provide a theoretical foundation for the very common dislocation phenomena observed among many solid materials including pure metals, metallic alloys, ceramics, and even geological scale entities, potentially clearing out many inconsistencies and puzzles in the literature.