We investigate the statistics of intergranular failure of two-dimensional polycrystalline structures. The emergence of mechanically robust two-dimensional materials, such as graphene, and the ability to synthesize them in large-area polycrystalline sheets provides a platform for measuring the strength of the resulting grain boundary distribution directly. Nanoindentation experiments of free-standing circular membranes reveal a non-Gaussian distribution of fracture loads. Herein, we determine a relationship between the fracture load and grain boundary distance by modeling the nanoindentation experiments through the Finite Element Method (FEM). We explore a simple circular membrane domain with a single straight grain boundary at varying distances from the point of indentation. The grain boundary is modeled with a traction-separation relation based on molecular dynamic simulations and is implemented through a membrane-based cohesive zone model (CZM). The FEM model admits two modes of failure: (1) within the grain due to a structure instability and (2) within the grain boundary by reaching the maximum traction of the CZM. The resulting failure load versus grain boundary distance response is fitted with a set of piecewise continuous functions. This response is used to derive a probability density function (PDF) for periodic and random two-dimensional grain structures. Random grain structures that closely resemble experimentally observed ones are generated using a two-dimensional Voronoi Tessellation. For validation, we consider the mechanical properties of polycrystalline graphene. The resulting PDF is convoluted with a Gaussian distribution to account for instrument error and compared against the experimentally measured distributions to validate the mechanical behavior of the CZM.