Capturing material toughness by molecular simulation: accounting for large yielding effects and limits

The inherent computational cost of molecular simulations limits their use to the study of nanometric systems with potentially strong size effects. In the case of fracture mechanics, size effects due to yielding at the crack tip can affect strongly the mechanical response of small systems. In this paper we consider two examples: a silica crystal for which yielding is limited to a few atoms at the crack tip, and a nanoporous polymer for which the process zone is about one order of magnitude larger. We perform molecular simulations of fracture of those materials and investigate in particular the system and crack size effects. The simulated systems are periodic with an initial crack. Quasi-static loading is achieved by increasing the system size in the direction orthogonal to the crack while maintaining a constant temperature. As expected, the behaviors of the two materials are significantly different. We show that the behavior of the silica crystal is reasonably well described by the classical framework of linear elastic fracture mechanics (LEFM). Therefore, one can easily upscale engineering fracture properties from molecular simulation results. In contrast, LEFM fails capturing the behavior of the polymer and we propose an alternative analysis based on cohesive crack zone models. We show that with a linear decreasing cohesive law, this alternative approach captures well the behavior of the polymer. Using this cohesive law, one can anticipate the mechanical behavior at larger scale and assess engineering fracture properties. Thus, despite the large yielding of the polymer at the scale of the molecular simulation, the cohesive zone analysis offers a proper upscaling methodology.