Researchers have performed studies with the addition and dispersion of a few weight percent of nanoscale particles in polymer matrices to mitigate the brittleness and microcracking of polymer matrices without incurring weight penalty and improve their strain to failure and fracture toughness. This thesis aims at studying these length scale effects in nano-fillers, identifying the existence of a lower bound on flaw-size that marks the transition from brittle fracture to strength-based failure in nanocomposites, resulting in a deviation from linear elastic fracture mechanics (LEFM) predictions. Crack-tip bond-order based prediction of critical value of stress intensity factor is also addressed in this work. The objective of this work also includes employment of an atomistic J-integral as a suitable metric for the evaluation of fracture behaviour in materials at nanoscale. Good agreement is observed between atomistic and LEFM predictions using far-field stress and J-integral computations. While the far-field stress based atomistic data enables global prediction of the system undergoing fracture, the J-integral around the crack tip sheds light on local near-crack-tip stress state. Both far-field and near tip predictions are seen to deviate from LEFM predictions below a certain length-scale. In addition, effects such as nonlocality in molecular dynamics (MD) computations and entropic effects at the atomistic scale add to the discrepancy with LEFM. The fracture study on crystalline (graphene) was performed to lay the foundation for atomistic predictions of fracture in amorphous (polymer) nanocomposite systems.