The degradation of the railhead on curved tracks stemming from high lateral contact forces between the wheel and the rail imposes high maintenance costs. Consequently, precise forecasts of rail damage under different operational conditions are necessary to carry out cost-effective maintenance strategies and prolong the useful life of the rail. Typical damage mechanisms include plastic deformation, wear, and the appearance of cracks on the surface (or subsurface) due to rolling contact fatigue. The numerical calculations necessary to assess the long-term evolution and degradation of the railhead are computationally demanding. A proposed methodology [1] considers feedback loops that involve dynamic vehicle-track interaction, elastic-plastic wheel-rail contact, and accumulative rail damage attributed to plasticity and surface wear to update the rail profile. The evolution of plastic deformation, specifically, demands numerous degrees of freedom to ensure an accurate 3D description of this nonlinear problem. To increase cost efficiency and predictive accuracy, we propose implementing the reduced-order model Proper Generalized Decomposition (PGD). PGD utilizes separated functions to successively enrich the solution in each iteration, allowing for the introduction of many extra coordinates without affecting the model's solvability. Our model, featuring a 3D rail head with elastoplastic material properties subjected to various contact scenarios, is based on a PGD model explored in [2], which considered linear elastic material with a domain decomposition and parametric load framework. In this work, the model is extended to account for elastoplastic rail material. This involves two main features. First, a stationary contact problem for a single over-rolling is formulated in a convective coordinate system along the rail. Secondly, fixed-point iterations are implemented to solve the displacements caused by a given loading scenario and plastic strains, as well as to solve the plastic strains given the displacement field. This approach facilitates an efficient speed-up of online simulations, particularly in evaluating the accumulated plastic deformation resulting from many over-rollings.