Mean, normalized concentration integration for potassium versus square root of time for (A) SLS series and (B) SAS series. DSPS model: Plastic to total strain ratios for SAS for (A) deviatoric Rpla-D and (B) hydrostatic Rpla-H components versus the natural logarithm of time.
INTRODUCTION
Of these, the most critical point in terms of advancing science and technology is improving understanding of the inherent ability to develop compressive stress. As such, the current set of investigations aims to understand what dictates the maximum magnitude of compressive stress generated during chemical toughening of glass.
MOLECULAR DYNAMICS SIMULATIONS OF ALKALI STUFFED
Introduction
Basic Principles
Particle velocities are scaled to maintain a constant relationship between the rate of change of temperature with time and the temperature difference between the system and the heat bath. In this case, the system volume is scaled instead of particle velocities to maintain a constant relationship between the rate of pressure change with time and the pressure difference between the system and the pressure bath.
Background
Previous studies of the filling of alkali accommodation (SAA) in silicate networks by molecular dynamics (MD) simulations revealed a lower molar volume for the filled glass than its CEAM glass for three binary sodium silicate glasses,12 various mixed sodium -potassium silicates,13 and various mixed sodium-potassium aluminosilicates,14,15 where potassium was the filling ion in all cases. It is observed that general features of SAL are similar between these two types of studies, but specific details of SAL may differ due to differences in the structural features of binary sodium silicate and mixed sodium-potassium silicate hosts.
Foundation
By examining the network topology, the ring size distributions for the 100% filled glasses remained significantly closer to that of the host glass after SAA (Figure 4). Displacement of the oxygen atoms is partly made possible by Si-O-Si bond angle changes.
Simulation and Analysis Methods
Taken together, the results suggested that the potassium SAA process in silicate glasses involves expansion of the host alkali site, during which time the average (K)O-CN increases from ca. 6 to approx. . Filled" configurations were formed starting with the configuration at the end of the "host" relaxation step, relabeling all Na ions as K ions.
Results
- Molar Volume and LNDC
- Range I: Structural Unit
- Range II: Interconnection of Adjacent Structural Units
- Range III: Network Topology
- Elastic Properties
- NVT Stuffing
For the SMAS series, the host and CEAM (M)M CN differ by approx. one, and the loaded (M)M CN remains near the host. For the SMAS series, the (Mg)BO CN is slightly lower for the filled and CEAM configurations than the host.
Discussion
- A Note on Timescale, Temperature, and Boundary Conditions
- What Influences LNDC?
- Network Features of Stuffing Alkali Accommodation
- LNDC and Compression Maximum
Examining systemic LNDC with a diverse host composition allows identification of network characteristics that significantly affect LNDC size. A notable difference between SMAS and other glasses currently being studied is the construction of the alkali sites. In light of this study, the advantage of this chemical hardening technique is that the diffusion front is completely replaced and pushed into the glass.
Further examination of the ERM hypothesis against the literature references in Table X allows the following observations to be drawn.
Conclusions
DIMENSIONAL SWELLING CHARACTERIZATION OF CHEMICALLY
- Background
- Dimensional Changes and Models
Changing the glass by ion exchange at elevated temperature, but using the glass at room temperature, thus makes it possible for thermal expansion factors to be relevant. Step height measurements made with a roughness meter were somewhat unreliable, but allowed an estimated expansion in the diffusion direction (free) of about 10-4 per mol% K2O relative to LNDC. Letting the z-axis be the diffusion direction, then within the x-plane the total (or initial) strain xxtot z is equal to the sum of the elastic strain elaxx z and plastic strain.
Integrating over all the chemically reinforced layers in the z direction, the integral of Eq.
Method
Using a reference profile and calibrating to a stair height standard, the profiler created height measurement accuracy. A 5x 0.4x zoom objective (11.3 μm pixel resolution) was used to assemble whole-area profiles of 16 mm x 8 mm areas. The height at each position along the profile was an average height of 25 pixels by 0.28 mm width.
10 mm x 10 mm x 1 mm microscope slide feet at each of the four corners of the backplane.
Results
Laboratory Dimensional Changes
While the typical replacement depth does not exceed 40 μm and 125 μm for SLS and SAS, respectively, the deformed edge portion of the glass is comparatively quite deep, often extending to around 500 μm. Edge profiles after edge chemical enhancement determined by white light profilometer for (A) SLS 450 °C series and (B) SAS 450 °C series. The step height, also determined by white light profilometry, shows an increasing trend with the square root of time for each temperature series of both glass types (Figure 18), indicating a strong correlation with the underlying filler ion.
Step height versus square root of time after selective surface chemical enhancement determined by white light profilometer for (A) SLS series and (B) SAS series.
Laboratory Chemical Diffusion and Stress Profiles
Where possible, a chemical diffusion profile was determined from each of the opposite 8 mm edges of coupon #4, such that the majority of chemical reinforcement conditions had two chemical diffusion profiles determined, one from each edge. This relationship is predicted from the form of the solution to Fick's second law in one-dimension with constant source when integrated across position and where the interdiffusion coefficient D is constant:41. Two stress profiles were measured using optical birefringence, one from each of the 8 mm edges of coupon #4.
Compressive stress magnitudes for SLS generally agree with those reported in the literature. 42 , 43 Most SLS stress profiles show a compression maximum below the surface, a feature often observed in the chemical hardening literature. Compressive stress magnitudes for SAS show reasonable agreement with literature values allowing for the different curing times and temperatures used.45,46 Each selected profile was converted from stress to elastic strain by dividing by the corresponding Young's modulus given in Table XI and is was then integrated from the surface to the depth of the casing for use as model input called "integrated elastic strain" or.
Laboratory Combined Results
The elastic strain integrand also exhibits an approximately linear relationship with increasing normalized concentration integrand (Figure 23). The collective slope for the SLS and SAS series is 5.6x10-3 μm/μm and 8.2x10-3 μm/μm, respectively, indicating that the SAS series generates a larger elastic strain integration for the amount of potassium filler, which is expected.
Finite Element Method Elastic Dimensional Changes
Laboratory edge profiles are consistently shorter near the edge than the elastic FEM profiles (Appendix F). Dimensional swelling perpendicular to the edge surface (swelling along the z dimension) of the FEM model was used for comparisons with step heights obtained by the arrangement depicted for Coupon #3 in Figure 16C. As such, the dimensional swelling perpendicular to the edge surface was used for comparison with the laboratory measured step height, allowing an error of ±20 nm for the FEM "step height." Simulated step height difference in percent compared to the laboratory measurement for the same stress profile is given in figure 26.
Similar to the edge swelling equation above, higher exchange temperatures and longer exchange times lead to stress relaxation.
Strain Model with Shear Flow (SPS model)
The averages of the chemical cure times for each temperature series for totxx and xxpla are given in Figure 28, where the error bars represent the range. SPS model: Average cure times for average total strain xxtot and average plastic strain xxpla versus cure temperature for (A) SLS series and (B) SAS series. SPS model: Average cure times for Rpla plastic to total strain ratio versus cure temperature.
SPS model: Average cure times for maximum initial load xxmax versus cure temperature for (A) SLS series and (B) SAS series.
Strain Model with Densification and Shear Flow (DSPS model)
The deviatoric and hydrostatic plastic-to-total strain ratios averaged over chemical strengthening times for each temperature series are given in Figure 32, where the error bars represent the observed range. In view of the large ranges observed for this quantity, it is likely that there is little significance in the movement of its mean over temperature. For both glass series, there is a noticeable spread in the plastic-to-total strain components, especially for the hydrostatic component, suggesting that the model is very sensitive to input.
DSPS model: Deviatoric Rpla-D and hydrostatic Rpla-H plastic ratios to total strain versus chemical hardening temperature for (A) SLS series and (B) SAS series.
Discussion
General Dimensional Swelling
Elastic Finite Element Method
Regardless of the stress relaxation mechanism, elastic incompatibility between the filled ion exchange layers and the substrate dictates the edge deformation. This interval is too wide to provide further insight into the source of the difference in edge swelling at short times. This suggests that the source of the short-time edge swelling difference, related to elastic properties or otherwise, is largely absent at intermediate times.
Examination of the stress profile σyy(z) in this dimension shows the maximum internal stress from 25 MPa to 60 MPa for the SAS-450 series (Figure 33).
Strain Models
A second indication of potential problems with the SPS model is the time dependence of the xxtot (Figure 27A). Despite these shortcomings of the SPS model relative to the SAS series, the total plastic to total strain ratios Rpla with increasing temperature (Figure 29) appear qualitatively reasonable, where the SLS series has a significantly greater slope than the SAS series have. The time dependence of the mean total stress from the SPS model is now evident in the Rpla-H (Figure 31B) in the DSPS model.
As mentioned earlier, the source of the wide range is due in part to the time dependence of this quantity.
Conclusions
Comparison of the sizes of the Rpla-D and the Rpla-H between the SLS series and SAS series shows that the SLS series has higher Rpla-D and Rpla-H than SAS. In both cases, this represents approximately half of the total deformation, which may be retained as elastic deformation, i.e. refined techniques for determining step height and stress profiles will improve the quality of the outputs of the models.
For example, automated quantification of compensation through the use of a liquid crystal compensator can lead to improved accuracy of measured stress profiles.
SUMMARY AND CONCLUSIONS
A combination of molecular dynamics simulations and laboratory measurements of dimensional changes were used to study elastic-plastic processes during glass chemical strengthening. Measurement of edge deformation generated by selective surface chemical enhancement produced deformation profiles broadly representative of the underlying stress state as determined by elastic finite element analysis. For both compositions, the fraction of deviatoric plastic strain relative to the total strain was observed to increase with increasing chemical strengthening temperature.
The results showed that traditional chemical reinforcement produces much lower maximum compressive stress than that suggested by total loading.
FUTURE WORK
Finally, further investigation of surface compression loss upon cooling from the chemical strengthening temperature to room temperature would be of interest. Determining whether this is a universal feature of chemically enhanced glasses will help improve quantitative comparisons between laboratory and molecular dynamics studies, as well as potentially shed light on the source of the phenomenon.
MD Simulation Cutoff Distances
MD Simulation Q n Distributions
Surface Profile Notes
Substrate Deformation
Edge Profile Averaging
Substrate deformation at different stages of preparation for a preliminary trial coupon, (A) hill side and (B) valley side. The line profiles were shifted along the y-axis such that the profile minimum was moved to the y-position zero (see “Valley Side” and “Hill Side” in Figure 35). Finally, the new average profile was shifted along the y-axis to realign the minimum with the y-position of zero (“Average” in Figure 35).
This procedure was used for all cases where reliable hill and valley profiles were available.
Edge Profiles After Chemical Strengthening
Stress Profiles After Chemical Strengthening
Edge Profile Comparisons with Elastic FEM
SPS Model Inputs and Outputs Tables
DSPS Model Inputs and Outputs Tables
