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

Abstract

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.

Evaluation of Sinking-In and Cracking Behavior of Soda-Lime Glass under Varying Angle of Trigonal Pyramid Indenter

“…However, the response of glass under shear stress is of primary importance to understand threshold of deformation or cracking in glass. For example, these two types of yield criteria are indispensable to obtain the reliable constitutive model for the plastic deformation of glass (Lambropoulos et al, 1997;Lacroix et al, 2012;Keryvin et al, 2014). According to the constitutive models proposed, the yield criterion of glass varies with the type of loading.…”

Mechanical modelling of indentation-induced densification in amorphous silica

“…It should also be noted that the small strain assumption has been implicitly applied to describe the densification in fused silica. This hypothesis is expected to be valid for silica since saturation of the densification is reached around 20 % [5].…”

“…In that respect glasses do not differ from standard materials, except that the characteristic length scale below which volume deformation (plasticity) is energetically more favorable than surface creation (crack propagation) is smaller [3]. Although known for half a century [4] and of primary interest for many micron-scale applications, the plasticity of silicate glasses has up to now remained little studied [5][6][7][8].…”

“…Fused silica, the most anomalous silicate glass of industrial interest, can achieve a significant 20% densification [5].…”

Densification as the Only Mechanism at Stake during Indentation of Silica Glass?

“…As an example, the density of a-SiO 2 (amorphous silica) can be increased by up to 21% and that of window glass by 6% for pressures around 25 GPa [6,7]. Different mechanical models have been proposed these last thirty years [3,8,9,10]. The two more recent ones [11,12] challenged the mechanical response of nano-indentation tests on fused silica with Finite Element Analyses.…”