Prediction of Fracture Properties in Nanographene Reinforced Polymers Using Atomistic Simulations

This paper is directed towards understanding damage initiation and failure progression in advanced nanostructured composite materials using molecular dynamics. The critical value of the J-integral (JI) at crack initiation is related to the fracture toughness of the material, where the subscript I denotes the fracture mode (I=1, 2, 3). Therefore, the J-integral could be used as a suitable metric for estimating the crack driving force as well as the fracture toughness of the material as the crack begins to initiate. However, for the conventional macroscale definition of the J-integral to be valid at the nanoscale in terms of the continuum stress and displacement fields and their spatial derivatives requires the construction of local continuum fields from discrete atomistic data, and using these data in the conventional contour integral expression for atomistic J-integral. One such methodology is proposed by Hardy that allows for the local averaging necessary to obtain the definition of free energy, deformation gradient, and Piola-Kirchoff stress as fields (and divergence of fields) and not just as total system averages. Further, the conventional isothermal definition of J-integral does not take into account the entropic contribution to the free energy, and consequently, may lead to significant over- estimation of the J-integral at the atomistic level, especially at finite temperatures. As a case study, the feasibility of computing the dynamic atomistic J-integral over the molecular dynamics (MD) domain at finite is evaluated for a graphene nano-platelet and the values are compared with results from linear elastic fracture mechanics (LEFM) for isothermal crack initiation at 0 K and at 300 K. Good agreement is observed between the atomistic J and the LEFM results at 0 K, with predictable discrepancies at 300 K due to entropic effects, which have been discussed in detail in the paper. Issues regarding concurrent coupling of MD with continuum domain are also discussed in this paper.