Residual stress distribution in tempered glass with reground edges
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Abstract
Many glass applications require laminated glass to achieve a safe loadbearing behaviour. Beside the structural aspect, glass elements have to meet high aesthetic demands. Laminated glasses often feature an offset between the individual glass panes resulting from the lamination process. With regards to visible or exposed edges, this displacement reduces the aesthetic quality of the glass component. The regrinding of the edge after lamination equalises the offset and thus creates a smooth surface. However, regrinding tempered glass leads to a reduction of the surface compression zone at the edge and may decrease the loadbearing capacity. A research project focuses on the detailed evaluation of the effect of regrinding tempered glass. To attain a precise understanding, three different aspects have to be examined: first the maximum required grinding depth resulting from the edge offset, second the defects on the surface of the edge and third the residual stress distribution. The third part was examined by means of stress measurements at the edge and the surface of different specimens. Glass beams made of fully tempered glass and heat strengthened glass with three different thicknesses (6, 8 and 10 mm) were ground after the tempering process. The regrinding depth was 1, 2 and 3 mm. One group of specimens remain untreated as a reference. The depth of the compression zone and the magnitude of the surface stress at the edge were measured with the help of photoelastic measurements. The experimental approach and the results are the content of this paper. It enables a statement about transformations of the residual stress state at the edge owing to regrinding tempered glass.
Keywords
Edge Tempered glass Regrinding Photoelastic measurements1 Introduction
The regrinding of annealed glass is allowed without restrictions, but thinking about glass with load bearing functions, a regrinding of tempered glass is profitable. As a result of the lamination process, the single glass panes have a residual stress distribution with the tensile zone in the centre and the compression zone at the surface. Regrinding of the tempered glass edge has an influence on the compression zone at the edge. The depth of the compression zone will be reduced and hence, the load bearing capacity of the glass may decrease, which is the subject and motivation of the investigations in this paper. Finally, this could lead to premature failure of the glass component. If we want to regrind the edges of tempered glass anyway, it is important to know exactly what happens with the compression zone at the edge. How deep is the compression zone at the edge after tempering? What is the effect of regrinding in varied regrinding depths on the residual stress state? What are the differences between heatstrengthened glass (HS) and fully tempered glass (FT)?
The parameters that determine the influence of regrinding on tempered glass result from the individual work steps during the processing of glass. Cutting and edge finishing of the annealed glass represent the first manufacturing steps in the production of laminated glass. During the finishing process of the edge (cutting, grinding), flaws on the edge surface may appear. These flaws influence the edge strength. Initial research on the influence of flaws on the edge strength has been conducted and discussed in Vandebroek (2014), Lindqvist (2013), Kleuderlein et al. (2014), Ensslen and MüllerBraun (2017) and Lohr et al. (2016). The results of those studies show a high dependency on the various process parameters, which currently do not provide a clear statement on the correlation between the finishing process and the strength. Recommendations for those parameters of the cutting process which positively influence the edge strength of annealed glass are published in Ensslen and MüllerBraun (2017).
In the second production step of laminated glass, the singleglass panes of annealed glass are tempered to result in heatstrengthened glass (HS) or fully tempered glass (FT). Finally, an interlayer (e.g. polyvinyl butyral (PVB) foil) joins the tempered glass panes. Thus, the finished laminated glass consists of glass panes with an individual distribution of compression and tensile zone near the edge and surface (Fig. 1: \(\hbox {d}_{(),E}\), \(\hbox {d}_{(),S})\) as well as flaws on the surface, resulting from the first grinding process. Because of the lamination process, the glass panes have an edge offset that is unknown beforehand. Optimising the optical quality of the glass edge requires regrinding in the regrinding depth \(\hbox {d}_{gr}\) (Fig. 1). The value of the regrinding depth results from the maximum offset between the glass panes and from the depth of the chamfer of each glass pane. This causes a straight surface of the laminated glass without irregularities, even with regards to the interlayer.
The regrinding in the required regrinding depth leads to a reduction of the compression zone near the edge \(\hbox {d}_{(),E}\). Previous photoelastic analyses indicate that the influence zone near the edge (area until the residual stress equals the parabolic distribution of the inner glass) differs depending on the type of glass (FT or HS) (Laufs 2000). With regard to FT, a depth of 1.0 \(\cdot \) d was determined for the influence zone. In contrast, the depth of the influence zone of heat strengthened glass is 1.5 \(\cdot \) d. As a result, the part of the influence zone of heat strengthened glass that remains after regrinding could be greater than the remaining influence zone of FT. In addition, cracks in the depth \(\hbox {d}_{flaw}\), which occur during the regrinding process on the edge surface, cause an additional reduction of the compression zone.

the depth of the compression zone near the edge resulting from the tempering process,

the maximum edge offset of the singleglass panes and

the flaws occurring during the regrinding process.
2 Method
2.1 Basics
 \(\delta \)

Phase shift [–]
 C

Photoelastic constant [mm\(^{2}\)/N]
 \({\uplambda }\)

Wavelength of light [nm]
 \(\left( {\sigma _1 \sigma _2 } \right) \)

Principle stress difference [N/mm\(^{2}\)]
 d

Glass thickness [mm].
The phase shift is measureable with the aid of polarising filters. After the waves passed through the glass, they reach an analyser, which aligns the light waves emerging from the glass in a direction of oscillation and causes interference. As a result, the areas of the same phase shift and thus the same main difference of the principal stress appear in the same colour. The colours conform with the complementary colours and are termed isochromates. Consequently, it is possible to calculate the principle stress difference from the visible isochromates in the polariscope. The benefit of the measurement of the residual stress at the edge is that the direction of the principle stress is known as the stress perpendicular to the edge equals zero. Consequently, only one component of the principle stress is left and can thus be calculated directly from Eq. 1.
2.2 Measuring device
Within our examination, the measurement device “StrainScope S3/50” by ilis gmbh was used to determine the influence of regrinding on the compression zone at the edge. It works like a polariscope and thus creates a picture of the isochromates of tempered glass. Moreover, it uses the compensation method of Sénarmont to also calculate the stress in the segue between the isochromates to finally obtain exact results at each point (Föppl and Mönch (1972) describes the method in detail). This method includes an additional quarter wave plate between the glass and the analyser. By rotating the analyser, the angle of polarisation \(\alpha \) is measureable at each point. This angle represents the change of the light waves due to the residual stress state. The accuracy of the StrainScope is denoted by means of the resolution of the measurement of 1 nm, this equates < 0.1 N/mm\(^{2}\). Figure 2, left depicts the parts of the measuring device.
 \(\alpha \)

Angle of polarisation [\({^{\circ }}\)]
 \(\sigma \)

Integrated stress [N/mm\(^{2}\)]
 R

Retardation [nm].
The measuring method based on the compensation method of Sénarmont considers a plane stress state with the two principal stresses (x and ydirection). The third principle stress (zdirection) is not measurable. Furthermore, a change in the residual stress within the thickness of the glass cannot be examined. Therefore, the measuring result is the mean stress as integrated stress through the glass thickness of the resultant of the principal stresses depending on the direction of measuring.
At the edge surface, the stress in xdirection equals zero, but there are stresses in ydirection as well as in zdirection (Laufs 2000, pp. 49). For the edge strength, the residual stress in ydirection is the most important. However, the orientation of the principle stresses to the measuring device is not exactly known and it is not possible to transfer the measured resultant stress to the different directions. Thus, the principle stress in zdirection at the edge could lead to overestimated or underestimated stress values. Consequently, the measured resultant stress results from the stresses in all stress directions and the poisson’s ratio. However, the evaluation aims to characterise the influence of different regrinding depths on the residual stress state. Consequently, we assumed that the poisson’s ratio is constant for each specimen. In addition, we ensured that the measuring direction was the same. Thus, the results are comparable.
The chart points a zero crossing of the yaxis at a length of 3.9 mm. Consequently, the compression zone at the edge ends at this point and the residual stress equals the inner parabolic state. After the zero crossing, the integrated stress declines. Consequently, the difference between the zero crossing of the integrated stress and the arrowhead at the glass edge provides the depth of the compression zone (distance between dashed lines in Fig. 5). The apparent offsets at the end of the graph result from the chamfer of the edge. The chamfer has an angle of \(45{^{\circ }}\) and therefore, the light waves are not orientated perpendicular to the glass surface. Consequently, the optical refraction changes and the results will be misjudged. Due to that, the evaluation of the measurement results will not include the area of the chamfer.
Consequently, the results of the StrainScope enables the evaluation of the depth of the compression zone and the calculation of the maximum of the absolute value of the compression stress at the edge until the chamfer. Based on that, the example in Fig. 5 has a maximum of the absolute integrated stress of 45 N/mm\(^{2}\) at the chamfer. The depth of the compression zone has an amount of 12.8 mm – 3.9 mm = 8.9 mm.
2.3 Specimens
The experimental study included 24 different series of specimens in the dimensions of 125 mm in height and 1100 mm in width. The dimensions resulted from the planned four point bending test of the specimens after the photoelastic measurements. In detail, the fracture tests were conducted according to EN 12883 (EN 12883 2000) with load introduction about the strong axis to obtain the edge strength. Figure 6 shows the test setup and the dimensions of the specimens. A detailed description is included in Lohr et al. (2016).
The considered parameters were the type of the glass (HS or FT), the glass thickness (6, 8 or 10 mm) and the regrinding depth (1, 2, 3 mm). Additionally, a reference group with untreated edges was included (0 mm regrinding depth).
Table 1 shows the different series and the number of the tested specimens. All together, the experimental study included 236 specimens.
Different types and number of specimens
Reground depth (mm)  Type  Heat strengthened glass (HS)  Fully tempered glass (FT)  

Thickness  6 mm  8 mm  10 mm  6 mm  8 mm  10 mm  
0  Series 1, 10 pcs.  Series 5, 10 pcs.  Series 9, 10 pcs.  Series 13, 10 pcs.  Series 17, 10 pcs.  Series 21, 10 pcs.  
1  Series 2, 9 pcs.  Series 6, 10 pcs.  Series 10, 10 pcs.  Series 14, 10 pcs.  Series 18, 10 pcs.  Series 22, 10 pcs.  
2  Series 3, 8 pcs.  Series 7, 10 pcs.  Series 11, 10 pcs.  Series 15, 10 pcs.  Series 19, 10 pcs.  Series 23, 10 pcs.  
3  Series 4, 9 pcs.  Series 8, 10 pcs.  Series 12, 10 pcs.  Series 16, 10 pcs.  Series 20, 10 pcs.  Series 24, 10 pcs. 
The second processing step was the grinding of the annealed glass. After that, the specimens were tempered into fully tempered glass or heat strengthened glass, each type in the same oven with the same adjustments. The reference specimens were finished after the third step and the other specimens were ground in 1, 2 or 3 mm regrinding depth. To minimise the damage of the edge, we decided to regrind gradually with 1 mm depth each. Consequently, the specimens with 3 mm reground edges had to be reground 3 times at each edge. The grinding before and after tempering was done with an edger with 13 cup wheels to achieve a constant edge quality.
2.4 Approach
Six of the points (2, 3, 4, 7, 8, 9) were located in the load introduction area of the four point bending test (Fig. 6) and another four measurements were positioned outside (1, 5, 6, 10).
After finishing of the measurements, we had ten distributions of the integral compressive stress as a function of the measuring length per specimen. Each of the 24 series, except series 2, 3, and 4, included ten specimens (Table 1). Consequently, we had to evaluate 2360 data sets. Firstly, the maximum of the absolute value of the compressive stress at the edge was calculated from the distribution. It was defined as the last measured point before the continuous distribution ended and therefore the chamfer began (Fig. 5). As a second part, the depth of the compression zone at the edge was calculated based on the zero crossing of the integrated stress. Because of the missing data in the area of the chamfer, the calculated depth of the compression zone does not include the chamfer.
3 Results
3.1 Basics
The blue box comprises the inter quartile range (IQR) and the difference between the 25% and the 75%quantile. The outliers were defined as experimental results, which deviated more than 1.5 \(\cdot \) IQR off the quantiles. Thus, the maximum and minimum are marked as upper and lower boundaries. Furthermore, the median is depicted within the boxplot.
3.2 Variation of the measuring results
The chart on the right hand side shows, in comparison to the chart on the left hand side, a high difference of both outside measuring points to each other and to the measuring points in the load introduction area considering both edges of the specimens. We were able to confirm the linear trend by choosing a selection of specimens and measuring the residual stress along the whole edge.
To achieve comparable results, we decided to involve the mean value of the results at measuring point 2, 3 and 4 as well as 7, 8 and 9 (Fig. 11). Thus, we included two final mean values \(\bar{\hbox {x}}_{2,3,4}\) and \(\bar{\hbox {x}}_{7,8,9}\) per specimen consisting of three measured results each in the evaluation. Finally, 60 measuring results were considered within each series (10 specimens with 2 mean values calculated from 3 results). This approach was exercised for both: compressive stress at the edge and depth of the compression zone.
3.3 Compressive stress at the edge
As expected, all of the charts in Fig. 12 show a decreasing of the compressive stress with rising regrinding depth. Especially, the series with 6 mm glass thickness point the highest difference between the untreated and the 3 mm reground specimens. Two groups deviate from this tendency, the 8 mm heat strengthened glass with 2 mm regrinding depth and the 10 mm heat strengthened glass with 2 mm regrinding depth.
Looking at the position of the median within the boxplot, some of the series do not have a symmetric statistical distribution, e.g. 8 mm HS with 0 mm regrinding depth or 10 mm HS with 0 mm and 3 mm regrinding depth.
3.4 Depth of the compression zone
The differences between the four results within one chart are not as clearly visible as it was in Fig. 12. There is no apparent dependency of the depth of the compression zone on the regrinding depth recognisable. Most of the groups show a decreasing depth of the compression zone according to the regrinding depth, but some point an increasing of the depth of the compression zone with increasing regrinding depth. Moreover, some of the series had a high variation of the results, e.g. 6 mm heat strengthened glass or 10 mm fully tempered glass with 3 mm regrinding depth.
Furthermore, all of the results of the fully tempered glass series decrease the results of the heat strengthened glass series. Consequently, there is a clear difference between the depth of the compression zone between fully tempered glass and heat strengthened glass. Beyond, there is an increasing depth of the compression zone by increasing glass thicknesses visible.
3.5 Additional results
Calculated mean values and standard deviations of the different series
Thickness  Regrinding depth  Fully tempered glass  Heatstrengthened glass  

Compressive stress [N/mm\(^{2}\)]  Depth of compression zone [mm]  Compressive stress [N/mm\(^{2}\)]  Depth of compression zone [mm]  
Mean value  Standard deviation  Mean value  Standard deviation  Mean value  Standard deviation  Mean value  Standard deviation  
6 mm  0 mm  \(\) 37.58  1.49  4.41  0.24  \(\) 44.05  2.75  9.12  1.23 
1 mm  \(\) 29.04  5.87  4.11  0.49  \(\) 35.22  1.85  9.58  1.52  
2 mm  \(\) 24.56  2.44  3.60  0.38  \(\) 29.31  3.49  9.90  2.16  
3 mm  \(\) 13.25  2.61  2.95  0.35  \(\) 16.57  1.57  8.20  2.62  
8 mm  0 mm  \(\) 43.88  1.75  5.84  0.40  \(\) 50.22  2.38  11.24  1.00 
1 mm  \(\) 39.94  2.94  6.78  1.46  \(\) 43.05  2.10  11.00  1.05  
2 mm  \(\) 31.92  5.76  5.90  1.14  \(\) 45.29  2.79  11.51  1.34  
3 mm  \(\) 25.45  7.70  5.46  1.60  \(\) 33.68  1.54  11.90  1.53  
10 mm  0 mm  \(\) 44.88  2.11  9.11  0.93  \(\) 41.44  2.84  11.27  0.89 
1 mm  \(\) 40.92  3.11  8.39  0.85  \(\) 39.60  2.17  11.06  0.83  
2 mm  \(\) 33.27  1.53  7.48  1.14  \(\) 25.00  4.37  10.39  1.19  
3 mm  \(\) 24.52  2.37  8.78  2.97  \(\) 34.73  2.82  10.38  0.96 
4 Discussion and conclusion
4.1 Approach
Within the discussion, we have to differ between the three main parameters of the study: the glass thickness, the glass type (FT or HS) and the regrinding depth. It is really important to keep in mind that the results represent the value at the beginning of the chamfer. Therefore, the compressive stress at the end of the chamfer reaches higher values. Consequently, we want to concentrate on the comparison of the results of the different groups, not the values itself.
Generally, we expect one main and two other possible transformations of the residual stress state at the edge according to the regrinding process. Figure 14 illustrates our approaches based on the example in Fig. 5.
 \(d_{gr} \)

Regrinding depth
 \(d_{\left(  \right) ,E,0} \)

Depth of the compression zone of the untreated glass before regrinding
 \(\sigma _0 \)

Compressive stress at the edge of the untreated glass before regrinding
Comparison of the compressive stress of the specimens with untreated edges
Thickness [mm]  Compressive stress [N/mm\(^{2}\)]  

6  8  10  
Type  FT  \(\) 37.3  \(\) 44.3 (+ 18.7%)  \(\) 45.1 (+ 1.8%) 
HS  \(\) 44.7 (+ 19.8%)  \(\) 49.7 (+ 11.1%) (+ 12.2%)  \(\) 40.7 (− 18.1%) (− 9.8%) 
 \(\Delta y_0 \)

Displacement of the zero crossing of the stress distribution
4.2 Compressive stress at the edge
Firstly, Table 3 focusses on the comparison of the reference groups, i.e. the glass with untreated edges, to finally characterise the influence of the glass thickness and the glass type. The stated values are the median.
Remaining compressive stress after 3 mm regrinding depth in relation to the reference group
Thickness [mm]  Compressive stress N3 / Compressive stress N0  

6  8  10  
Type  FT  0.36  0.63  0.55 
HS  0.37  0.68  0.83 (0.61 N2) 
Depth of the compression zone of the specimens with untreated edges with and without the chamfer
Thickness [mm]  Depth of compression zone [mm]  

6  8  10  
Chamfer  Without  With  Without  With  Without  With  
Type  FT  4.4  5.4 (\(1.11 \cdot \) d)  5.8  6.8 (\(1.17 \cdot \) d)  9  10 (1.0 \(\cdot \) d) 
HS  8.7  9.7 (1.62 \(\cdot \) d)  10.8  11.8 (1.45 \(\cdot \) d)  11.4  12.4 (1.24 \(\cdot \) d) 
Furthermore, the comparison between the results of fully tempered glass and heat strengthened glass shows a high difference of the 6 mm specimens (19.8%). In contrast, the measured compressive stress of 10 mm heat strengthened glass falls below the results of 10 mm fully tempered glass. These differences could result from changed process parameters during the tempering. For example, a changing of the cooling rate according to the thickness of the glass was suspected to result in a different residual stress state. This has to be discussed with the processor, but will be neglected within this paper. The focus is the analysis of the influence of regrinding.
Figure 15 summarises the results of the compressive stress at the edge of all series by means of the calculated median.
The chart shows a decreasing trend of the compressive stress at the edge with an increasing in regrinding depth. Only the groups 8 mm heat strengthened glass and 10 mm heat strengthened glass show a deviation from this tendency. Unfortunately, we have not yet found the reason for this deviation. The maximum reduction of the compressive stress occurs in the series with 6 mm fully tempered glass specimens. After 3 mm reground depth only 36% of the compressive stress is left. In contrast, after 3 mm regrinding of the heat strengthened glass specimens, 68% of the compressive stress is left. Table 4 points the remaining compressive stress after 3 mm regrinding related to the reference group with untreated edges of the six different types of specimens.
The reduction of the compressive stress of the fully tempered glass and heat strengthened glass specimens with 6 mm and 8 mm thickness are nearly similar. Therefore, we are not able to prefer fully tempered glass or heat strengthened glass based on this result. In contrast, the values of the compressive stress of the heat strengthened glass specimens exceed the fully tempered glass specimens with the same thickness (Fig. 15). These results confirm the assumption that regrinding leads to a reduction of the compressive stress at the edge.
4.3 Depth of compression zone
The measuring of the depth of the compression zone did also not include the chamfer. Indeed, the horizontal width of the chamfer is known and amounts 1 mm. With the assumption of a constant chamfer of each specimen, the final depth of the compression zone was calculated by adding 1 mm to the measured results.
Table 5 shows the median of the calculated depth of the compression zone of the specimens with untreated edges as well as the final results with the added chamfer depth. As mentioned in Sect. 2, Laufs (2000) determined the depth of the compression zone of fully tempered glass as 1.0 \(\cdot \) d and heat strengthened glass as 1.5 \(\cdot \) d. The resultant depth of the compression zone according to the thickness is also given in brackets in Table 5.
The depth of the compression zone of the heat strengthened glass specimens reaches higher values than the depth of fully tempered glass in accordance to the thickness. The experimental results also show a high accordance with the indications of Laufs. Only the results of the heat strengthened glass specimens with 10 mm thickness have a clear difference to the expected depth of 1.5 \(\cdot \) d. This may result from the tempering process, because also the low values of the measured compressive stress (Table 3) of these group attract attention.
Remaining depth of the compression zone after 3 mm regrinding depth in relation to the reference group
Thickness [mm]  Depth compression zone N3 / Depth compression zone N0  

6  8  10  
Type  FT  0.66  0.93  0.94 
HS  0.83  1.06  0.90 
The highest degradation of the depth of the compression zone developed in the group of fully tempered glass specimens with 6 mm thickness. The depth of the compression zone achieves only 66% of the depth of the compression zone of specimens with untreated edges. The reduction of the depth of the 8 mm and 10 mm specimens does not reach 10%.
4.4 Conclusion
Finally, it is important to emphasize that the presented study included specimens of one manufacturer and one size only. Consequently, the results are not sufficient for a general statement. There are additional studies needed to consider the influence of the manufacturer as well as the parameters of the tempering process. Furthermore, the measured compressive stress does not include the chamfer of the edge. To determine the compressive stress at the end of the chamfer, additional research is necessary.
5 Summary and outlook
The main goal of the presented photoelastic studies was to answer the following question: How deep is the compression zone at the edge after tempering? What is the effect of regrinding in varied regrinding depths on the residual stress state? What are the differences between heatstrengthened glass (HS) and fully tempered glass (FT)?
To answer these questions we conducted comprehensive studies on specimens with varied thickness, regrinding depth and glass type (FT or HS). Firstly, we determined in accordance to Laufs (2000) that the depth of the compression zone of fully tempered glass is nearly \(1.0\cdot \)d and \(1.5\cdot \)d of heat strengthened glass. Moreover, the compressive stress at the edge of heat strengthened glass reaches higher values than the results of fully tempered glass. Consequently, if someone intends to regrind the edge of a glass component, heat strengthened glass is more suitable than FT.
Regrinding follows in a reduction of the compressive stress at the edge up to 64%. In contrast, we determined only a small reduction of the depth of the compression zone (max. 34%). Furthermore, the reduction of the depth of the compression zone is not equal to the regrinding depth. The reason for that could be a rearrangement at the edge. This assumption has not been approved and the physical reason for the rearrangements has to be part of future research.
The best results concerning a high absolute value of the compressive stress as well as a high depth of the compression zone before and after regrinding arose within the heat strengthened glass specimens with 8 mm thickness. The influence of the glass thickness and the used settings of the tempering process have to be discussed with the manufacturer. That includes a discussion about the low values of the specimens with 10 mm thickness.
Current research focusses on the evaluation of the residual stress state in the area with the parabolic distribution of the specimens presented in this paper. In the course of that, photoelastic measurements were done and are planned to be presented soon. Furthermore, four point bending tests with load introduction about the strong axis will be done and finally compared with the photoelastic examinations.
Notes
Acknowledgements
The investigations are conducted as part of a research project supported by the German Federal Ministry of Economic Affairs and Energy. The authors would like to thank the project partner Glaswerkstätten Frank Ahne GmbH for the close cooperation, the technical support and the production of the test specimens. Moreover, we would like to thank ilis gmbH for their support and the appropriation of the StrainScope.
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