Functionally graded materials (FGMs) in which the elemental composition intentionally varies with position can be fabricated using directed energy deposition additive manufacturing (AM). This work examines an FGM that is linearly graded from V to Invar 36 (64 wt% Fe, 36 wt% Ni). This FGM cracked during fabrication, indicating the formation of detrimental phases. The microstructure, composition, phases, and microhardness of the gradient zone were analyzed experimentally. The phase composition as a function of chemistry was predicted through thermodynamic calculations. It was determined that a significant amount of the intermetallic σ-FeV phase formed within the gradient zone. When the σ phase constituted the majority phase, catastrophic cracking occurred. The approach presented illustrates the suitability of using equilibrium thermodynamic calculations for the prediction of phase formation in FGMs made by AM despite the nonequilibrium conditions in AM, providing a route for the computationally informed design of FGMs.