D. Discussion
3. Strain Models
Figure 33. Elastic FEM stress profiles σyy(z) along the thickness centerline versus z-position from the edge for SAS-450 series. Note, only the tensile portion of the profile is shown.
average alkali site expansion is decreasing with increasing temperature, which is unlikely as similar behavior would then be anticipated for the SLS series, or there is a temperature-dependent component influencing the xxtot that is not being adequately captured by the SPS model. A second indication of potential difficulties with the SPS model is the time dependence of the xxtot (Figure 27A). These problems are addressed with the introduction of densification in the DSPS model. Despite these shortcomings of the SPS model relative to the SAS series, the aggregate plastic-to-total strain ratios Rpla with increasing temperature (Figure 29) appear qualitatively reasonable, where the SLS series has a notably greater slope than the SAS series. The greater rate of increase of the Rpla with increasing temperature for SLS compared to SAS is expected in terms of the proximity of the chemical strengthening temperatures to the glass transition temperatures (for 400-500 °C, 0.75-0.94Tg for SLS and 0.64-0.80Tg for SAS). Finally, the maximum initial stress xxmax (Figure 30) obtained from the maximum total strain produces values that, while high relative to traditional chemical strengthening, are attainable by low- temperature electric field-assist chemical strengthening5,48 and by compaction prior to chemical strengthening.49 Thus, overall, the SPS model appears to generate reasonable Rpla values and xxmax values for glasses with larger fractions of shear plastic flow during chemical strengthening, such as SLS, but produces questionable results for glasses with lower fractions of shear plastic flow, such as SAS.
Incorporating densification into the SPS model generated the DSPS model.
Within the DSPS model a maximum total strain must be assumed and, for the present analysis, the maximum total strain values were obtained from MD simulations as detailed in the results. The average total strain is constant within this model, thus outputs of the deviatoric Rpla-D (shear) and the hydrostatic Rpla-H (densification) plastic-to-total strain ratios are of primary interest. The time-dependence of the average total strain from the SPS model is now evident in the Rpla-H (Figure 31B) in the DSPS model. Interestingly, near-Tg indentation creep experiments of Shang, et al.55 have also noted an increase of densification relative to shear viscous flow with increasing time under load as determined by residual indentation volume and pile-up volume measurements, although this observation was for a soda-lime silicate glass. These authors ascribe this as possibly due
to shear- or pressure-thinning that occurs under the high initial stress of indentation and decays as stress is relaxed, causing an increase in the relative densification to be observed at longer loading times. Based upon the fact that the initial compressive stress magnitudes by chemical strengthening exceed 1 GPa as predicted by the SPS model and MD simulations (Section II), a shear-thinning mechanism56 could potentially be present at early times during traditional chemical strengthening, limited to layers that have high concentrations of stuffing alkali ions that have been exchanged rapidly due to a high chemical potential gradient. If present, the mechanism would be localized to the first few microns of ion-exchanged layers and is not captured by the present Rpla-D trends which are representative averages throughout the ion-exchanged depth (Figure 31A).
Collectively examining the deviatoric and hydrostatic plastic-to-total strain ratios for each temperature (Figure 32), both the SLS series and the SAS series are observed to display an increasing Rpla-D with increasing temperature. This is expected on the basis of increasing shear flow with increasing temperature during sub-Tg indentation55 and sub-Tg
three-point bend and uniaxial compression experiments.50 On the other hand, no trends of the Rpla-H with temperature were identified for either glass series. The wide range of observed values allows much room for interpretation of a trend for this component versus temperature. As noted earlier, the source of the wide range is, in part, attributable to the time dependence of this quantity. Again turning to sub-Tg microindentation experiments for soda-lime silicate,55 the ratio of densification to shear flow, from residual indentation volume and pile-up volume measurements, was reported to be consistently in favor of densification by at least a factor of about three or greater in the 400-500 °C temperature range. In separate, but similar, studies of room temperature microindentation with post- annealing recovered volume measurements, ratios for volume of densification to volume of shear flow were roughly 2:1 for SLS57 and 1:1 for SAS-like glasses.58 Here, the ratio of densification to shear flow is generally around 0.9:1 for SLS and 0.7:1 for SAS as averages across all temperatures (Figure 32). The lower tendency for densification by ion-exchange stuffing compared to microindentation is understandable as the introduction of the larger alkali ion into the silicate network lowers the capacity for network densification.
Comparison of the magnitudes of the Rpla-D and the Rpla-H between the SLS series and SAS series reveals the SLS series has higher Rpla-D and Rpla-H than SAS. Given that the glasses have similar Poisson’s ratios and thus presumably similar atomic packing density,59 the higher degree of network cross-polymerization in the SAS may be responsible for its lower plastic ratios than SLS. Overall, plastic contributions to total strain, averaged throughout the ion-exchanged layers, are about 70% for the SLS series and about 40% for SAS series within the DSPS model, and are slightly lower within the SPS model. In either instance, this represents about half of the total strain, which could potentially be retained as elastic strain, i.e. alkali oxide glass compositions could potentially regularly generate in excess of -1,200 MPa by chemical strengthening if the various relaxation mechanisms could be removed. Future developments in chemical strengthening technology, particularly in glass composition and in ion-exchange technique development, may preserve this elastic strain, providing some room for improvement of glass mechanical strength.24,60
The SPS and DSPS models are highly sensitive to the inputs. Refined techniques for determining step height and stress profiles would improve the quality of the outputs from the models. For step height measurement, potential improvement may be obtained from use of a thicker substrate that is less apt to deform during the chemical strengthening process, thus remedying that described in Appendix C. As for stress profiles, quantification of retardation with a manual birefringence compensator is somewhat subjective as it involves positioning the darkest portion of a fringe at the center of a crosshair. Automated compensation quantification via use of a liquid crystal compensator, for example, may yield improved accuracy of the measured stress profiles.