The objective of this paper is the development of a multiscale, mechanistic based intergranular crack growth model, which considers creep, fatigue and environment interactions in a nickel disk material, ME3. In this model, the basic cracking mechanism involves grain boundary (GB) sliding and dynamic embrittlement, which are identified by examining the apparent activation energy, as well as, the slip/GB interactions in both air and vacuum environments. Modeling of the damage events is achieved by adapting a cohesive zone approach (an interface with internal singular surfaces) in which the GB dislocation network is smeared into a Newtonian fluid element. The deformation behavior of this element is controlled by the continuum in both far field (internal state variable model) and near field (crystal plasticity model) regions and the intrinsic GB viscosity which is able to define the mobility of the element by scaling up the motion of dislocations into a mesoscopic scale. This process is characterized by the rate at which the time-dependent sliding reaches a critical displacement and as such, a damage criterion is introduced by considering the GB mobility limit in the tangential direction leading to strain incompatibility and failure. Results of simulated intergranular crack growth rate, at different temperatures in both air and vacuum, are compared with those obtained experimentally. The model sensitivity is examined by performing case studies of materials with varying GB viscosity and different partial pressures of oxygen.