It is well established that the mechanical properties of polycrystalline materials depend on the interaction between lattice dislocations and grain boundaries (GBs). However, in spite of extensive numerical and experimental studies, the mechanisms behind these interactions are not yet fully understood. To study these complex interaction mechanisms, we recently performed large scale 3D Molecular Dynamics simulations of a screw dislocation interacting with Coherent Twin Boundaries, in a range of face-centered cubic metallic bicrystals modeled with 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. Following these first results, we extended this study on two fronts. First, we evaluated the impact of the boundary structure on the interaction mechanism and on the critical stress for transmission, by considering the case of Incoherent Twin Boundaries (ITB) containing ledges. Second, we investigated the influence of multiaxial stresses including shear components in the CTB. We could evidence that the influence of the loading conditions, which can be represented in terms of the Escaig stress is materail dependent. In Al and Cu, the critical transmission stress is largely dependent on the Escaig stress while only mildly for Ni. Additionally, 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 discussed in terms of a potential energy barrier. The simulation results are captured in a mechanistic analytic models aiming to provide input for constitutive equations to be used in mesoscopic simulation schemes.