Large scale 3D atomistic simulations are performed to study the interaction between a curved dislocation with a dominant screw character and a Coherent Twin Boundary (CTB). Three FCC metals (Al, Cu and Ni) are addressed using 6 embedded-atom method (EAM) potentials. The reaction mechanisms are studied first under uniaxial stress showing that transmission mechanism and critical transmission stress depend on the material considered and differ from results reported in quasi- 2D simulations. Then, the influence of multiaxial stresses including shear components in the CTB is investigated. It is shown that the influence of the loading conditions, which can be represented in terms of the Escaig stress, is material dependent. In Al and Cu, the critical transmission stress is largely dependent on the Escaig stress while only mildly for Ni. The presence of a shear component in the CTB tends to increase the critical transmission stress for all three materials. The absorption and desorption mechanisms of the screw dislocation are correlated with a potential energy barrier.