AbstractThis study presents incremental finite element computations of creep‐fatigue crack growth in Alloy 718 at in air. Alloy 718 is representative of creep‐brittle materials, in which viscoplastic deformation is restricted near the tip of a growing crack. The computations predict crack growth using a unique combination of an irreversible cohesive zone formulation and a strain gradient viscoplastic material model based on the Kocks–Mecking formulation. Cohesive zone damage parameters are estimated using sustained loading and constant‐amplitude cyclic loading experiments. Computations of crack extension under three different waveforms containing overloads all predict post‐overload retardation. The amount of retardation depends strongly on the overload ratio, consistent with experiments in the literature using similar waveforms. Analysis of the crack‐tip fields demonstrates retardation is associated with unloading in the highly deformed material near the advancing crack tip. Dynamic recovery and geometrically necessary dislocations are shown to significantly influence post‐overload crack extension.