The Avionic Full-Duplex Switched Ethernet (AFDX) is a data network certified for avionic operations. AFDX closely follows the IEEE 802.3 (Ethernet) standard for packet forwarding. On top of that, bandwidth enforcement using traffic shaping is performed to provide deterministic delivery guarantees. The design of an AFDX network, however, imposes that bandwidth enforcement is performed at a coarse granularity. This, together with the tight requirements on transmission jitter, determines a low utilization of the physical links. In this work, we propose traffic phase shifting (TPS) as a way to increase the granularity of bandwidth assignment to nodes of an AFDX network using logic time synchronization among traffic sources. Specifically, we leverage the periodic nature of real-time traffic and use phase-shifing to prevent link congestion. This in turns allows a more fine-grained bandwidth control via the AFDX protocol. We show that TPS leads to significant improvements in terms of per-link utilization without violating predictability.