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The role and effect of γ′ precipitate size on the mechanical properties of Ni-base single crystal superalloy is investigated. The underlying mechanisms are analyzed on the one hand with the help of experiments including hardness and creep tests, and on the other hand with the help of two different simulation approaches by taking the typical γ/γ′ microstructure into account. Simulations, based on the crystal plasticity finite element method (CPFEM) are carried out for the hardness tests, whereas simulations, based on the crystal plasticity coupled phase-field method (CPPFM) are carried out for the creep tests. The hardness test simulation results show that the hardness of material varies inversely with the size of γ′ precipitates for a given γ′ phase volume fraction and it varies directly with the volume fraction of γ′ precipitates for a given precipitate size. These results are qualitatively consistent with the experimental observations. The creep simulation results show that the refinement of γ′ precipitates with a certain volume fraction of precipitates leads to an improvement of creep resistance by delaying the plastic activity in the material.