Constitutive Law for the Densification of Fused Silica, with Applications in Polishing and Microgrinding

We discuss a constitutive model describing the permanent densification of fused silica under large applied pressures and shear stresses. The constitutive law is assumed to be rate‐independent and uses a yield function coupling hydrostatic pressure and shear stress, a flow rule describing the evolution of permanent strains after initial densification, and a hardening rule describing the dependence of the incremental densification on the levels of applied stresses. Normality, or lack thereof, of the permanent strain increments to the current yield surface in stress space allows for various relative contributions of densification and shear flow in the ensuing deformation. The constitutive law accounts for multiaxial states of stress, since during polishing and grinding operations complex stress states, with large shear components due to friction and abrasion, occur in a thin surface layer due to the action of abrasive particles. We apply the constitutive law in estimating the extent of the densified layer during the mechanical interaction of an abrasive grain and a flat surface under polishing and grinding conditions. The grain is assumed to be spherical and in Hertz contact with the surface, or sharp and in point contact. The effect on the densified depth of stress relaxation due to densification is discussed.