As the renewable energy industry moves towards deep water, mooring chains play an irreplaceable role in position keeping. The geometrical and material nonlinearity of the mooring chains significantly affects moored platform responses and mooring responses. To investigate local mooring stress evolution under wave loads, a simulation method was proposed, combining hydrodynamic loads derived from fully coupled simulations of floating offshore wind turbines (FOWTs). The simulation method, embedding the lumped mass mooring model, was validated by comparing the experimental data from OC4 semi-submersible wind turbines. Their reasonable segment numbers and the mooring structural damping ratio were also discussed. Based on the validated simulation technology, a coupled 3D-mooring analysis was performed, replacing linear mooring stiffness suggested in FAST tutorials with nonlinear mooring stiffness calculated by axial stretching the real-sized 3D chains. The nonlinear mooring stiffness is assumed, taking into account detailed geometry, nonlinear material properties, and contact behavior between chains. The nominal diameter of the real-sized 3D-chains was determined, so that the chains had the same volume per unit length as the validated case, ensuring a similar Morison's force on the mooring line. Then, the local mooring stresses were investigated by loading the derived nonlinear fairlead tension onto both sides of real-sized 3D chains in an explicit finite element software. The evolution of local mooring stresses under design wave loads with different wave headings of 0, 30, 60° was compared and discussed. As wave direction increases, this study indicated that the amplitude of local maximum principal stress decreases and its phase leads. Additionally, its magnitude is mainly influenced by axial tension force and contact behavior.