We numerically investigate the role of plastic strain accumulation on the mechanical response of a planar strike-slip fault. Our models show that fault-zone strength significantly impact the ensuing sequence of earthquakes. Weaker fault zones accumulating more plastic strain promote more complexity in the seismicity pattern through aperiodic earthquake occurrences and intermittent episodes of rupture and arrest. However, if the fault zone strength is high enough, the overall earthquake sequence is characterized by periodic fault-spanning events. We find that both the fault normal stress and the fault surface profile evolve throughout the earthquake sequence, suggesting a self-roughening mechanism. Despite the significant impact of plasticity on the fault response, the width of the plastically deforming region in the fault zone is small compared to the fault length. Our results suggest a rich behavior in dynamically evolving fault zones and support the need for further high-resolution studies of the highly non-linear near-fault region.