A methodology for predicting fracture toughness of nano-graphene reinforced polymers using molecular dynamics simulations
The nano-scale interaction between polymer molecules and nanoparticle is a key factor in determining the macro-scale strength of the composite. In recent years numerous efforts have been directed towards modeling nanocomposites in order to better understand the reasons behind the enhancement of mechanical properties, even with the slight addition (a few weight percent) of nano-materials. In order to better understand the local influence of nanoparticle on the mechanical properties of the composite, it is required to perform nano-scale analysis. In this context, modeling of fracture in nano-graphene reinforced EPON 862 at the nano-scale is discussed in this dissertation. Regarding fracture in polymers, the critical value of the J-integral (JIC), where the subscript I denotes the fracture mode (I=1, 2, 3), at crack initiation could be used as a suitable metric for estimating the crack driving force as well as 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 nano-scale, 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 atomistic J-integral takes into account the effect of reduction in J from continuum estimates due to the fact that the total free energy available for crack propagation is less than the internal energy at sufficiently high temperatures when entropic contributions become significant. In this research, the proposed methodology is used to compute J-integral using atomistic data obtained from LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). Further, a novel approach that circumvents the complexities of direct computation of entropic contributions is also discussed. As a case study, the feasibility of computing the dynamic atomistic J-integral over the MD domain is evaluated for a graphene nano-platelet with a central crack using OPLS (Optimized Potentials for Liquid Simulations) potential. For model verification, the values of atomistic J-integral are compared with results from linear elastic fracture mechanics (LEFM) for isothermal crack initiation at 0 K and 300 K. J-integral computations are also done using ReaxFF force field in order to simulate bond breakage during crack propagation. Good agreement is observed between the atomistic J and LEFM results at 0.1 K, with predictable discrepancies at 300 K due to entropic effects. The J-integral computation methodology was then used to computationally predict fracture toughness in nano-particle reinforced composite material at elevated temperatures using the ReaxFF force field in LAMMPS, which can simulate crack propagation more accurately by breaking and forming bonds on the fly.