The ARIES project is currently proposing an all-tungsten divertor for their tokamak designs. In designing such a component, fracture will be a critical failure mechanism, due to the limited ductility of the tungsten. Hence, this paper presents a series of fracture mechanics-based analyses to demonstrate the feasibility of using an all-tungsten divertor in a commercial device. The analyses presented here employ a commercial finite element code (ANSYS) to carry out three-dimensional thermal, mechanical, and fracture calculations. Due to the inelastic deformations produced by the high temperatures and stresses in the component, the fracture calculations employ the J-Integral, a path-independent contour integral that estimates the strain energy release rate for a crack of assumed geometry. Elliptical surface cracks are introduced both inside and outside the coolant channel and steady state calculations are carried out for both full power and cold shutdown conditions. It is determined that the critical crack is on the inside of the coolant channel and the largest forcing is during full power. In addition, transient calculations are carried out to simulate edge localized modes (ELMs) in the plasma and conclusions are drawn with respect to the severity of these events and their effect on the lifetime of the component. Finally, thermal creep is considered as a potential failure mode.