Numerous experimental studies in the field of mechanical processing of composite materials for individual materials and tools made it possible to formulate particular models for describing tool wear, changing its microgeometry during operation and predicting durability. There are significant difficulties in measuring current wear and recalculation in mathematical models, since they include a large number of parameters. This does not allow for simple technical control of cutting edge wear and predicting tool life. The formulation of the wear-contact problem of the tool tip and the material interaction during turning of reinforced composite plastics is presented. Based on known studies, it is assumed that wear occurs along the flank of the tool, and is accompanied by an asymmetric change in the geometry of its tip. A model of abrasive wear during sliding of a tool tip rear surface with a polymer composite reinforcement material and fracture products is considered. It is assumed that the wear law is hereditary and there is a linear dependence of the wear rate on the rate of contact interaction and pressure. Shear stresses through the contact pressure and the coefficient of friction nonlinearly depend on the operating time of the tool due to the change due to wear in the geometric shape of the tool and the processing parameters of the product over time. The volumetric wear factor is a tool run time function. It reflects the fact that the interaction of the “tool-workpiece” pair with time should, as it were, forget about the running-in stage, which has a high wear rate, and the fact that the dependence of wear on the load (contact pressure) is characterized by the presence of aftereffect. A simplified relationship is obtained for the wear law under the assumption that there is no change in the coefficient of friction, temperature and contact pressure over time. Ultimately, to describe the wear law and predict the tool life, it is necessary to know a number of empirical constants, the values of which are determined by the change in the microgeometry of the tool tip during interaction during cutting.