We have fabricated micro- and nanocrystalline YBa2Cu3O7, Bi2Sr2CaCu2O8 and Bi2Sr2Ca2Cu3O10 superconductors using mechanical ball milling, hot isostatic pressing and oxygen annealing. The fabricated materials were characterised using powder x-ray diffraction, differential scanning calorimetry, thermogravimetry, resistivity, V-I traces, a.c. magnetic susceptibility and d.c. magnetic hysteresis. A new approach for measuring the resistivity of grain boundaries in polycrystalline materials is presented. The average resistivities of the grain boundaries ρ_GB in micro- and nanocrystalline YBa2Cu3O7 are much higher than that of the grains (ρ_G) which leads to huge ρ_GB/ρ_G values of 2 × 10^3 and 1.6 × 10^5 respectively. For nanocrystalline Bi2Sr2CaCu2O8 and both micro- and nanocrystalline Bi2Sr2Ca2Cu3O10 samples, ρ_GB/ρ_G is at least 10^3. Only microcrystalline Bi2Sr2CaCu2O8 has a very low ρ_GB that is similar to ρ_G such that ρ_GB/ρ_G≈1. The values of grain boundary resistivity measured in our samples were used in conjunction with a theoretical framework developed in Durham, to quantitatively calculate how high grain boundary resistivities must be to account for the decrease by several orders of magnitude in transport critical current density J_c in polycrystalline YBa2Cu3O7 and Bi2Sr2Ca2Cu3O10. We conclude that the significant effort made by the research community in texturing samples and removing the grain boundaries is well-founded. For low-temperature superconducting intermetallics such as Nb3Sn, we demonstrate that increases in J_c by two orders of magnitude is still possible by completely removing the grain boundaries from these materials and incorporating additional artificial pinning. Only large-grained polycrystalline Bi2Sr2CaCu2O8 has sufficiently low grain boundary resistivity, that cost constraints for applications may yet lead to high J_c polycrystalline materials that have artificial pinning sites or pinning produced by irradiation
