2. REVIEW AND THEORY
2.2 Deformation of ‘Normal’ and ‘Anomalous’ Glasses
Doremus28 lists five different types of deformations that can occur in materials. They are elastic, anelastic, viscous, plastic, and faulting.
According to Doremus, densification in indentation testing of glass is anelastic deformation, in which part or all of the densification can be removed by heating, but that network bonds are not broken.28 Since the viscosity of glass at room temperature is greater than 1059 P, Doremus dismisses viscous flow as a possible deformation mechanism in indentation of glass at room temperature.28 Since glass lacks dislocations, plasticity can not operate either. Doremus28 believes the permanent impressions in ‘normal’
glasses are due to ‘faulting’ of the material, after the work of Hagan.29 Faulting is a type of deformation that is non-recoverable and non-uniform.
The ‘flow’ in normal glasses can thus be described as ‘faulting,’ since it resembles geologic faulting.28 The fact that fault lines follow high shear stress trajectories suggests the high shear stresses associated with sharp indentation cause the faulting.18
Hagan29 has shown that a series of lines, which he termed ‘flow’ lines, occurs beneath indentations in ‘normal’ glasses. The lines intersect one another at ~ 110°, not at 90°, as observed in materials undergoing pure plastic flow.29 According to Hagan, this is evidence the ‘flow’ is not like that occurring in metals, possibly due to the effects of densification. Further, he believed the ‘flow’ lines were caused by genuine shear displacements, and were not cracks, judging by the small width of the lines, ~ 2 µm. Doremus28
points out the fault planes are distorted regions of the structure, and that not all bonds may reform back into the original structure. Evidence of these faults also appears on the surfaces of indentations, where they are observed to lie parallel to the indentation sides, and are the continuations of the sub- surface faults.7,30
As noted by Ernsberger31, the nature of the actual deformation in ‘normal’
glasses is still a matter of controversy. Plasticity at room-temperature, such as can occur in metals, is due to the motion of dislocations. Thus movement by plasticity in glasses, which lack dislocations, is not possible. In addition, Neely32 has shown that viscous flow is unlikely to occur during room- temperature indentation of silicate glass, since the glass viscosity is too high in spite of the large shear stresses present. Nonetheless, network modifiers and associated non-bridging oxygen’s (NBO’s) facilitate shear movement due to the weakness they introduce into the structure, providing easy ‘slip’ paths, since in vitreous silica few faults are observed.7 Peter12 has shown convincing evidence of material ‘pile-up’ around indentation edges of ‘normal’
glass indented with a sharp indenter. It is hard to imagine shear faulting causing this behavior, with the only other possible mechanism being viscous flow.
Although the deformation in normal glasses is assumed to occur at constant volume, i.e., be volume conserving, Ernsberger31 has shown that densification does occur beneath Vickers indentations in soda-lime-silica
glass, and in borosilicate and vitreous silica glasses as well. In high-pressure experiments, Bridgman and Simon33 found that additions of Na2O, up to 33 mol % in vitreous silica, still resulted in densification of the glass. Increasing the molar amount of Na2O from 10 to 23 to 31% caused the percent increase in density to decrease from 8.7% to 3.5% to 0.7%, respectively, for a pressure of ~ 110,000 atmospheres (~ 11.1 GPa). In comparison, the densification of vitreous silica at 100,000 atmospheres was about 0.1%, much less than for the 10% Na2O glass, where the threshold pressure for densification was about 40,000 atmospheres (~ 4.1 GPa). Mackenzie34 showed that the amount of shear deformation taking place in glass strongly affects the amount of densification achievable. Increasing shear results in increasing densification.
This may help explain why the addition of 10% Na2O increases the percent densification relative to vitreous silica, i.e., the Na+ ions facilitate the shear taking place. However, further additions of Na+ ions take up interstitial space which would otherwise compact (densify), and occurs to the extent that it dominates the shear effect, with the result that percent densification begins to decrease. Bridgman and Simon33 also found that increasing the cation radius decreased the percent densification achievable, likely because of the greater reduction in interstitial space with the larger cations. For 23 mol
% additions of Li2O, Na2O, and K2O to vitreous silica, the percent densification was 6.9%, 3.5%, and 1.2% , respectively.33
2.2.2 ‘Anomalous’ Glasses
‘Anomalous’ glasses in indentation testing are those whose main mode of permanent deformation is a pressure-induced densification (compaction) of a relatively open network.7 The term ‘anomalous’ was first used to describe glasses having a low coefficient of thermal expansion, a negative dependence of bulk modulus on pressure (for pressures up to ~ 40 Kbar for vitreous silica (v-SiO2), after which normal behavior occurs), and a positive dependence of bulk modulus on temperature (between 0 and 60 K for v-SiO2).27,35 The structural change can be described as a displacement transformation in which individual structural units, e.g., SiO4 tetrahedra, become closer.7 Spatial rearrangement of the structural units occurs, but few bonds are broken. Vitreous silica is the prototypical ‘anomalous’ glass. ‘Anomalous’
glasses tend to have open network structures. For v-SiO2, it is believed the transverse bending vibrational modes of the Si-O-Si linkages between SiO4
tetrahedra are primarily responsible for its ‘anomalous’ behavior7. Ernsberger31 and Arora et al.7 have observed densification in vitreous silica around Vickers indentations. Other glasses that behave ‘anomalous’ include v-GeO2, v-BeF2, and v-Zn(PO3)2.7
Bridgman and Simon33 have found that vitreous silica begins to densify starting at pressures around 100,000 atmospheres (~ 10.1 GPa). The percent densification rose rapidly to about 7% at 200,000 atmospheres. According to Neely32 the Vickers hardness of vitreous silica is around 6.2 GPa (200 g
indentation load); thus, based on the threshold pressure for densification from Bridgman and Simon33 densification would not be expected to occur under Vickers indentation. However, Mackenzie34 has shown that increasing the amount of shear stress present facilitates the densification process, making higher densities achievable. Thus, the high shear stresses present in indentation testing must lower the threshold for densification.