Once the chip has developed a mixed mode of side-curl and up-curl, it would generally curl to strike the tool flank. The development of the bending stresses and sheat in the chip would ultimately lead to chip failure. This paper approach this problem from a mechanics-based approach, by treating the chip as a 3-D elastic curved beam, and applying appropriate constraints and forces. The expressions for bending, shear and direct stresses are developed through an energy-based criterion. The location of the maximum stresses is also identified and explained for simulated test conditions.