The macroscale behavior is often affected by microstructural features of the medium. This is also the case for damages and fractures, which are usually governed by microscale processes. These kinds of phenomena can be suitably modeled with nonlocal theories, where the multiscale response is taken into account by considering an internal length scale. Thus, taking advantage of the possibility of naturally considering discontinuities in the displacement field, nonlocal models are widely employed to investigate fracture processes in both novel fields and classical problems. In this context, the goal of this work is to analyze the role of a specific nonlocal microstructure in a classical study of fracture mechanics, notably a plate with a central circular hole under tension. The chosen microstructure is the discrete lattice representation of bond-based peridynamics, which allows us to perform calculations using this well-established theory. To minimize the computational efforts due to the nonlocal problem, a proposed nonlocal dimensionally reduced model has been employed. The plate has been studied for three different measures of the horizon, a peridynamic parameter that corresponds to the internal length scale, which provides a well-defined microstructure. Each microstructure preserves the same overall elastic stiffness and critical energy, and the chosen failure criterion for the bonds is stress-based. The results of this research show a progressive shift of the onset of damage, which becomes more distal as the internal length scale increases. In addition, an analysis of the peridynamic stress and its concentration factor, together with its distribution, has been performed. Preliminary results emerging from the displacement field analysis seem to indicate that, by increasing the horizon, the stress peak becomes more diffuse, and the stress concentration factor decreases.