Finite element analysis of stresses in Berkovich, Vickers and Knoop indentation for densifying and non-densifying glasses

A constitutive law for fused silica accounting for its permanent densification under large compressive stresses is presented. The implementation of the constitutive equations in the general-purpose finite element code ABAQUS via user subroutine is proposed and carefully verified. The three-dimensional indentation mechanics under Berkovich, Vickers and Knoop indenters is extensively investigated based on the proposed constitutive relation. The results of stress distribution and plastic zone for both densifying and non-densifying optical glasses are systematically compared. These numerical results are in good agreement with the experimental observations of optical manufacturing. That is, fused silica shows lower material removal rate, smaller surface roughness and subsurface damage in contrast to non-densifying optical glasses under the same grinding condition.; Material densification of fused silica is thoroughly studied through numerical simulations of indentation mechanics. The exact amount of densification and shear strain of fused silica under Berkovich indentation is calculated to show the deformation mechanism of glass materials under three-dimensional indentations. The surface profiles show the material “pile-up” around the indenter tip for non-densifying glasses and “sink-in” for fused silica after the indentation load is removed.; An important inverse problem is studied: estimation of abrasive size and indentation load through the examination of residual indentation footprints. A series of 2D axisymmetric spherical indentation simulations generate a wide range of relationships among the indentation load, indenter size, residual indentation depth and size of residual indentation zone for the five selected brittle materials: glass fused silica (FS), BK7, semiconductor Si, laser glass LHG8, and optical crystal CaF_2.. The application of the inverse problem is verified by the good agreement between the estimated abrasive size and the actual abrasive size found during a material removal experiment of magnetorheological finishing (MRF) of fused silica.; The explanation of indentation size effect (ISE) is attempted using numerical indentation simulations. Vickers indentation simulations on the five selected brittle materials (FS, BK7, Si, LHG8 and CaF_2.) show no size dependence of Vickers hardness when the material is modeled as elastic-perfectly plastic (with or without densification). The simulation results on axisymmetric conical indentation also indicate that the bluntness of the indenter tip is not the reason for the indentation size effect. A new constitutive model accounting for the material length scale is needed in order to explain the well-observed indentation size effect during indentation tests.