Fractal coupled theory of drilling and wear

Drilling perforations and tool wear are intimately and mutually connected by fracture propagations at different size-scales. To study this interaction phenomenon, we propose an ad hoc developed fractal coupled theory. Describing the two processes in terms of drilling and wear velocities, the theory is able to predict the relation between these two quantities. The result is represented by a power law between wear and drilling velocities with exponent comprised between 2/3 and 3/2. Some experimental tests on different materials like mortar, concrete and reinforced concrete have also been performed. Theoretical predictions and experimental results agree satisfactorily.