In service condition rail joints, especially the weldments are under the action of various loadings which are not only working in multiple axis direction but also time-dependent having a cyclic and mixed-mode in nature and non-relative to each other. The surface of the rail and its weldment is acted by very high repetitive stress through the wheel and because of this contact stress the running surface or subsurface may have cracks or fractures due to fatigue. This work is based on numerical simulation of an aluminum thermite weldment on a UIC 60 rail under multi-axial fatigue crack propagation under the friction with surficial interaction between weldment and wheel with bending load due to vertically applied load through the wheel on the weld. Since contact is highly influenced by vertical load and also for minimizing the simulation time the lateral and longitudinal traction forces are not included in this study. The work formulation and discretization have been done with the finite element method and a non-linear lagrangian algorithm solver is applied. A 3-D rail-weld wheel model assembly and a semi-elliptical crack as a flaw on the weld surface are used to identify 3-Modes of SIFs along with its graphical plot generation. Simulation is performed under multi-axial weld wheel surface contact at different locations on weld running surface, taking into account varying position of fracture crack on weld 3-D model to calculate fracture life of weld joint and observation of fatigue crack propagation. This work involves the numerical and theoretical approach of fracture mechanics on created FE fatigue model using the Linear Elastic Fracture Mechanics (LEFM) method following Paris law for fracture mechanics. All the numerical simulation for critical fracture dimension and cycle count with stress intensity factor for weld failure data is estimated using software ANSYS 2020 academic and plotted, then comparison of predicted and observed transverse crack growth behavior and fatigue life of weld, based on Millions Gross Tonnes (MGT) is discussed.