A Plastic-Flow Problem Arising in the Theory of Discontinuous Machining

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Abstract
Plastic flow is analyzed adjacent to the nose of the tool in the initial stages of the formation of a discontinuous-chip segment. It is assumed on the basis of experimental evidence that fracture of the previous chip segment occurred across a plane through the cutting edge of the tool. The present solution applies only while the fracture surface is being deformed, before plastic flow spreads to the initial work surface. The solution demonstrates the influence of the plastic-stress distribution in determining the chip-formation process. It shows that simple shear across a plane between two undeforming regions cannot satisfy stress conditions in typical cases. It is shown that the inclination of the plane of equivalent simple shear is remarkably insensitive to the coefficient of friction at the tool face. The variation to be expected as a result of spread of plastic flow to the initial work surface is discussed briefly. The choice between alternative types of slip-line fields which arise in certain cases is considered.

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