With the increased application of micromachining, including micromilling and microdrilling, the need to develop accurate models for machining at the microscale has been recognized. In particular, the crystallographic effects that are generally neglected in the macroscale cutting models must be incorporated into the micromachining models. Diamond turning and mechanical nanomanufacturing techniques also require an understanding of crystallographic effects during material removal. This work presents a rate-sensitive plasticity-based machining (RSPM) model that is used to determine the specific energies (and thus forces) for orthogonal cutting of face-centered cubic (fcc) single-crystals. The RSPM model uses kinematics and geometry of orthogonal cutting for an ideally sharp cutting edge. The total power is expressed in terms of the plastic power, which is spent for shearing the material within a finite shear zone, and the friction power, which is spent for overcoming the friction at the rake face. In calculating the shearing power, rate-sensitive plastic behavior of fcc metals is considered. In addition, realistic effects of lattice rotation and strain hardening are included in the model. Subsequently, the total power is minimized within the space of geometrically allowable shear angles to determine the shear angle solution, and associated cutting and thrust specific energies, as a function of cutting plane orientation, cutting direction (with respect to the crystal orientation), rake angle, and the coefficient of friction. The calibration procedure for and the experimental validation of the model are provided in Part II.