Thermal fluctuations effects on crack nucleation and propagation

This paper investigates the impact of thermal effects on fracture propagation, a subject that poses significant theoretical and experimental challenges across multiple scales. While previous experimental and numerical studies have explored the relationship between temperature fluctuations and mechanical behavior, a comprehensive theoretical framework in fracture mechanics that rigorously incorporates temperature effects is still absent. Building upon the Griffith energetic approach and equilibrium statistical mechanics, we incorporate entropic effects into the overall energy balance of the system and replace the total mechanical energy with free energies. Indeed, our model captures the energetic interplay between elastic deformation, external loads, fracture energy, and entropic contributions. We propose a simplified approach in which both discrete and continuum representations are formulated concurrently, reflecting a multiscale paradigm. The discrete model leverages statistical mechanics to account for temperature effects, while the continuum model provides a mesoscopic description of the fracture process. This framework provides (temperature dependent) analytical expressions for key mechanical parameters, such as the stress and displacement fracture thresholds, the energy release rate, the fracture surface energy, and the J-integral. Notably, we identify a critical temperature at which the system undergoes a phase transition from an intact to a fractured state in the absence of mechanical loading. We believe that this approach lays the foundation for a new theoretical framework, enabling a rigorous multiscale understanding of thermal fluctuations in fracture mechanics. We finally propose a comparison with numerical data concerning the fracture of graphene as a function of temperature exhibiting the efficiency of the model in describing thermal effects in fracture behavior.