Recently developed dislocation dependent equations that describe dense sets of deformation discontinuities and related thermodynamics are applied to the problem of continuous chip formation during metal-cutting. The kinematics of chip formation is represented by dislocations moving on each and every discrete, fixed angle shear plane between the fracture point of the chip separating from the work-piece to the tangent point of the chip and cutting tool. The discontinuum viewpoint of this chip model realistically represents chip deformation for positive rake-angle cutting. An estimate for energy dissipated due to dislocation flux is given in terms of an irreversible thermodynamic work expression. Knowledge of metals manufacture can aid in their conservation.