Interior stress for axisymmetric abrasive indentation in the free abrasive machining process: Slicing silicon wafers with modern wiresaw

In wiresaw manufacturing processes, such as those in slicing silicon wafers for electronics fabrication, abrasive slurry is carried by high-speed wire (5 to 15 m/s), which exerts normal load to the surface via hydrodynamic effects arul bow of taut wire. As a result, the abrasives carried by slurry arc constrained to indent onto and roll over the surface of substrate. In this paper, the axisymmetric indentation problem in the free abrasive machining (FAM) is studied by modeling a rigid abrasive of different shapes pushing onto an elastic half space. Based on the harmonic property of dilatation, the closed-form solution of stress distribution inside the cutting material for three different indentation processes in common FAM process are presented: cylindrical and conical abrasives as well as uniform pressure distribution. Along the symmetrical axis, von-Mises stress is two times larger than that of local maximum shear stress for all three indentation conditions. The von-Mises stress is infinity at the contact point for sharp pointed indentation, a location of crack initiation and nucleation. For indentation by abrasive of flat surface, which also can be provided by the localized effects due to the hydrodynamic pressure acting on the surface, both the von-Mises and local maximum shear stress reach maximum underneath the contact zone.