The Structural Strength of Glass: Hidden Damage
Исследуется “скрытое повреждение” стекла в процессе прокатки из-за неравномерного
 распределения микротрещин в торцевых поверхностях стеклянных конструкционных элементов, которые снижают их прочность и приводят к разрушению. Показано, что при устранении указанных торцевых повреждений существ...
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| Опубліковано в: : | Проблемы прочности |
|---|---|
| Дата: | 2011 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/112766 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Structural Strength of Glass: Hidden Damage / F.A. Veera, Yu.M. Rodichevb // Проблемы прочности. — 2011. — № 3. — С. 93-109. — Бібліогр.: 8 назв. — ангд. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860022955135729664 |
|---|---|
| author | Veera, F.A. Rodichevb, Yu.M. |
| author_facet | Veera, F.A. Rodichevb, Yu.M. |
| citation_txt | The Structural Strength of Glass: Hidden Damage / F.A. Veera, Yu.M. Rodichevb // Проблемы прочности. — 2011. — № 3. — С. 93-109. — Бібліогр.: 8 назв. — ангд. |
| collection | DSpace DC |
| container_title | Проблемы прочности |
| description | Исследуется “скрытое повреждение” стекла в процессе прокатки из-за неравномерного
распределения микротрещин в торцевых поверхностях стеклянных конструкционных элементов, которые снижают их прочность и приводят к разрушению. Показано, что при устранении указанных торцевых повреждений существенно повышается конструкционная прочность стекла. С помощью подхода “скрытого повреждения” выполнен статистически
обоснованный расчет прочности для наиболее поврежденных образцов с использованием
надежного инженерного параметра.
Досліджується “приховане пошкодження” скла у процесі прокатки через
нерівномірний розподіл мікротріщин у торцевих поверхнях скляних конструкційних елементів, які, знижуючи їх міцність, зумовляють руйнування.
Показано, що усунення вказаних торцевих пошкоджень суттєво підвищує
конструкційну міцність скла. За допомогою підходу “прихованого пошкодження” виконано статистично обгрунтований розрахунок міцності для найбільш пошкоджених зразків із використанням надійного інженерного параметра.
|
| first_indexed | 2025-12-07T16:48:18Z |
| format | Article |
| fulltext |
UDC 539.3
The Structural Strength of Glass: Hidden Damage
F. A. Veer
a,1
and Yu. M. Rodichev
b,2
a Delft University of Technology, Delft, the Netherlands
1 f.a.veer@tudelft.nl, www.glass.bk.tudelft.nl
b Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine,
Kiev, Ukraine
2 rym@ipp.kiev.ua
ÓÄÊ 539.3
Êîíñòðóêöèîííàÿ ïðî÷íîñòü ñòåêëà: ñêðûòîå ïîâðåæäåíèå
Ô. À. Âååð
à
, Þ. Ì. Ðîäè÷åâ
á
à Äåëôòñêèé òåõíîëîãè÷åñêèé óíèâåðñèòåò, Äåëôò, Íèäåðëàíäû
á Èíñòèòóò ïðîáëåì ïðî÷íîñòè èì. Ã. Ñ. Ïèñàðåíêî ÍÀÍ Óêðàèíû, Êèåâ, Óêðàèíà
Èññëåäóåòñÿ “ñêðûòîå ïîâðåæäåíèå” ñòåêëà â ïðîöåññå ïðîêàòêè èç-çà íåðàâíîìåðíîãî
ðàñïðåäåëåíèÿ ìèêðîòðåùèí â òîðöåâûõ ïîâåðõíîñòÿõ ñòåêëÿííûõ êîíñòðóêöèîííûõ ýëåìåí-
òîâ, êîòîðûå ñíèæàþò èõ ïðî÷íîñòü è ïðèâîäÿò ê ðàçðóøåíèþ. Ïîêàçàíî, ÷òî ïðè óñòðà-
íåíèè óêàçàííûõ òîðöåâûõ ïîâðåæäåíèé ñóùåñòâåííî ïîâûøàåòñÿ êîíñòðóêöèîííàÿ ïðî÷-
íîñòü ñòåêëà. Ñ ïîìîùüþ ïîäõîäà “ñêðûòîãî ïîâðåæäåíèÿ” âûïîëíåí ñòàòèñòè÷åñêè
îáîñíîâàííûé ðàñ÷åò ïðî÷íîñòè äëÿ íàèáîëåå ïîâðåæäåííûõ îáðàçöîâ ñ èñïîëüçîâàíèåì
íàäåæíîãî èíæåíåðíîãî ïàðàìåòðà.
Êëþ÷åâûå ñëîâà: ñòåêëî, ïðîöåññ ïðîêàòêè, ñêðûòîå ïîâðåæäåíèå, èíæåíåð-
íûé ïàðàìåòð, ìèêðîòðåùèíû.
Introduction. Glass is commonly used in engineering, when a transparent,
durable, and stiff material is needed. Although glass is not usually used for
load-bearing applications, in most cases glass still carries a load. In an automobile,
the front and rear windows are an integral part of the structure responsible for a
significant part of the total stiffness and resisting the considerable forces generated
by the air pressure at high-speed driving.
However, the reliable value for the glass strength is an open issue: the tensile
strength cannot easily be determined, since glass in direct tensile test will break at
the grip. In certain cases, bending test results provide scattered values of the
bending strength with a spread of 30 to 50% of the mean strength.
For glass fibers and cast glass the distribution can be adequately described
using the Weibull statistic approach leading to a probabilistic strength for the glass
used [1, 2]. For the more common float glass this is more complicated. Results of
bending experiments by various authors suggest that the processing and specimen
size influence the results and suggest systematic data deviation from the Weibull
statistic distribution [3–5].
© F. A. VEER, Yu. M. RODICHEV, 2011
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 93
A likely explanation for this is that the usual processing of float glass results
in multiple types of defects which provides a multilinear Weibull plot [6, 7].
To investigate this systematically it was decided to look in more depth at the
effect of processing on float glass strength. The initial step, which is described in
this paper, deals with the effect of cutting and breaking quality on the strength of
processed float glass.
Float glass is produced as 6�3.21 m “jumbo” plates. These are cut into the
required size and the cut edges are usually grinded and polished. The cutting is
usually done by scratching the glass with a glazier’s diamond or rolling it with a
tungsten carbide roller producing a cut on the upper surface. This is schematically
shown in Fig. 1. By bending the plate slightly, as is shown by the arrows, tension is
generated at the cut resulting in an unstable crack-cut growing down on the figured
straight arrow through the thickness separating the glass parts. Surface damages
such as crumbled arrises and cross microcracks are forming on edges of both glass
parts under the contact cutter action.
The depth values of these specific cross microcracks are larger than those of
the initial surface microcracks which form the cracked surface layer on both sides
of float glass. The length of transversal microcracks is typically larger than the
width of the cut with the crumbled arrises as seen in Figs. 1 and 2.
Therefore these “invisible” and practically uncontrolled microcracks are root
cause for the low strength of cut glass elements. Their sizes may be so large that
the deepest of them may remain partially or fully after grinding and polishing of
the glass element edges.
For this research 190 pieces of glass with a size of 400�50 mm were cut from
a single 6 mm “jumbo” panel using an automated cutting table. The length axis of
the specimens corresponds to the width axis of the jumbo plate. These specimens
were carefully removed, stacked and shipped.
Specimens were subjected to flat tests with the cut up (i.e., with the cut in the
compression zone) and with the cut down ( i.e., with the cut in the tension zone).
F. A. Veer and Yu. M. Rodichev
94 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
Fig. 1. Diamond cutting and cross microcracks in glass plate elements.
In the standing tests, the specimens were tested with the cut left or the cut right
relative to the front of the machine. The purpose of the tests was to systematically
study the effect of the orientation.
The additional specimens were made more precisely and carefully protected to
prevent handling damaging of the edges. These specimens were tested flat with a
cut up. Their high quality broken edge arrises were in the tension zone.
Test results were compared with previous data on size effects on glass bending
strength with the grinded and polished specimens up to 3.2 m length [8].
Methodology. All four-point bending tests were conducted using a Zwick
Z100 universal testing machine under displacement control. Table 1 gives the
relevant data. The rig for the standing tests was equipped with friction less
antibuckling supports. All glass was wrapped in self adhesive plastic foil for safety.
Before test commencement all orientations (top, bottom, left, and right) were
indicated on the specimens. After testing specimens were inspected for breakage
between the loading span, relative crack origin and number of cracks emanating
from the failure point. The tests were conducted in a single week to ensure
reasonably constant climatic conditions. During testing no changes were made to
the testing machines and the supports. The tests setups are shown in Figs. 3 and 4.
Testing of additional specimens was made with flat test orientation under the
same testing conditions using a ZD-4 universal hydraulic testing machine under
displacement, test speed and loading speed control. Table 2 gives the relevant data.
The test setup is shown in Fig. 5.
The Structural Strength of Glass: Hidden Damage
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 95
Fig. 2. Transversal microcracks in diamond cut.
T a b l e 1
Testing Conditions
Orientation Height
(mm)
Width
(mm)
Load span
(mm)
Support span
(mm)
Test speed
(mm/min)
Standing test 40 6 175 350 1
Flat test 6 40 175 350 5
Results. The results of the flat tests are given in Table 3. Figure 6 shows a
Weibull plot of the flat results with the cut in the compression zone. Figure 7
shows a Weibull plot of the flat test results with the cut in the tensile zone.
The results from the standing tests are given in Table 4. Figure 8 shows a
Weibull plot of the standing results with the cut left. Figure 9 shows a Weibull plot
of the standing results with the cut right.
Statistical Analysis. As there is doubt about the suitability of the Weibull
distribution, the data has been analyzed using the following distributions:
(i) normal;
(ii) lognormal;
(iii) extreme value;
(iv) exponential;
(v) Rayleigh;
(vi) Weibull.
96 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
F. A. Veer and Yu. M. Rodichev
T a b l e 2
Testing Conditions for Additional Flat Test Specimens with the Cut in Compression
Height
(mm)
Width
(mm)
Load span
(mm)
Support span
(mm)
Average test
speed (mm/min)
Average loading
speed (MPa/s)
Number
of specimens
6 40 175 350 4.80 1.590 6
0.49 0.162 5
Fig. 3. Test setup for flat tests. Fig. 4. Test setup for standing tests.
Fig. 5. Test setup for additional specimens in flat tests.
No. F
cut
down
(N)
�b, max
cut
down
(MPa)
Break
between
loading
span
(yes/no)
Crack
from
left or
right
Number
of
cracks
F
cut up
(N)
�b, max
cut up
(MPa)
Break
between
loading
span
(yes/no)
Crack
from
left or
right
Number
of
cracks
1 2 3 4 5 6 7 8 9 10 11
1 357 52.06 yes left 13 259 37.77 yes left 3
2 335 48.85 yes right 6 447 65.19 yes right 14
3 351 51.19 yes right 5 413 60.23 yes left 17
4 382 55.71 yes left 9 373 54.40 yes right 15
5 405 59.06 yes right 11 414 60.38 yes right 13
6 352 51.33 yes right 9 365 53.23 yes right 8
7 364 53.08 yes right 6 463 67.52 yes right 12
8 356 51.92 yes right 5 467 68.10 yes left 16
9 386 56.29 yes left 8 470 68.54 yes right 10
10 347 50.60 yes right 6 400 58.33 yes left 9
11 328 47.83 yes left 7 431 62.85 yes left 14
12 248 36.17 yes left 1 360 52.50 yes left 6
13 340 49.58 yes right 8 381 55.56 yes left 10
14 350 51.04 yes left 10 361 52.65 yes right 8
15 377 54.98 yes left 9 398 58.04 yes right 8
16 368 53.67 yes right 13 375 54.69 yes right 14
17 382 55.71 yes right 9 408 59.50 yes right 23
18 380 55.42 yes right 8 432 63.00 yes left 15
19 375 54.69 yes left 18 343 50.02 yes left 5
20 396 57.75 yes right 7 301 43.90 yes left 4
21 340 49.58 yes right 9 442 64.46 yes left 11
22 361 52.65 yes left 7 290 42.29 yes right 4
23 343 50.02 yes right 9 369 53.81 yes right 10
24 383 55.85 yes left 17 467 68.10 yes right 15
25 366 53.38 yes right 8 512 74.67 yes left 19
26 305 44.48 yes left 10 275 40.10 yes right 7
27 341 49.73 yes left 14 485 70.73 yes middle* n.a.
28 397 57.90 yes middle n.a. 434 63.29 yes right 16
29 286 41.71 yes right 11 554 80.79 yes left 33
30 384 56.00 no* right n.a. 683 99.60 yes right 36
31 303 44.19 yes left 12 402 58.63 yes right 8
32 354 51.63 yes right 10 656 95.67 yes middle* n.a.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 97
The Structural Strength of Glass: Hidden Damage
T a b l e 3
Results of Flat Tests
1 2 3 4 5 6 7 8 9 10 11
33 395 57.60 yes right 3 302 44.04 yes right 4
34 238 34.71 yes right 14 364 53.08 yes middle* n.a.
35 329 47.98 yes right 2 470 68.54 yes right 17
36 378 55.13 yes right 14 349 50.90 yes right 8
37 337 49.15 yes right 15 396 57.75 yes left 20
38 327 47.69 yes right 14 532 77.58 yes left 16
39 335 48.85 yes left 12 383 55.85 yes left 9
40 379 55.27 yes left 15 539 78.60 yes right 21
41 – – – – – 559 81.52 yes left 23
42 – – – – – 418 60.96 yes left 9
43 – – – – – 455 66.35 yes left 29
44 – – – – – 257 37.48 yes right 3
45 – – – – – 469 68.40 yes right 17
46 – – – – – 440 64.17 yes left 21
47 – – – – – 544 79.33 yes left 29
48 – – – – – 505 73.65 yes middle* n.a.
49 – – – – – 517 75.40 yes left 16
50 – – – – – 446 65.04 yes right 18
Mean 51.6 left 38% 61.4 left 47.8%
std/mean 10.6% 20.5%
maximum 59.1 99.6
minimum 34.7 37.5
98 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
F. A. Veer and Yu. M. Rodichev
Continued Table 3
Fig. 6. Weibull plot of flat test results with the cut upwards.
Note. Here and in Table 4: results with * are excluded from calculations and graphs.
No. F
cut left
(N)
�b, max
cut left
(MPa)
Break
between
loading
span
(yes/no)
Number
of cracks
F
cut right
(N)
�b, max
cut right
(MPa)
Break
between
loading
span
(yes/no)
Number
of cracks
1 2 3 4 5 6 7 8 9
1 2770 48.48 yes 5 3730 65.28 yes 4
2 2800 49.00 yes 5 3620 63.35 yes 9
3 2450 42.88 yes 4 3450 60.38 yes 7
4 2430 42.53 no* n.a. 3550 62.13 yes 7
5 2860 50.05 yes 7 3010 52.68 yes 5
6 2830 49.53 yes 4 2890 50.58 yes 7
7 3290 57.58 yes 6 2780 48.65 yes 5
8 2970 51.98 yes 5 2900 50.75 yes 6
9 2860 50.05 yes 5 2530 44.28 yes 6
10 2750 48.13 yes 5 3560 62.30 yes 9
11 2260 39.55 yes 5 2740 47.95 no* n.a.
12 2740 47.95 yes 6 2950 51.63 yes 5
13 1820 31.85 yes 2 2500 43.75 no* n.a.
14 2510 43.93 yes 4 3020 52.85 yes 6
15 2560 44.80 yes 5 2790 48.83 yes 6
16 2500 43.75 yes 4 3010 52.68 yes 5
17 2970 51.98 yes 5 2730 47.78 yes 5
18 2710 47.43 yes 4 2130 37.28 yes 4
19 2240 39.20 no* n.a. 3120 54.60 yes 7
20 2590 45.33 no* n.a. 3350 58.63 no* n.a.
21 1990 34.83 yes 3 2650 46.38 no* n.a.
22 3120 54.60 yes 6 3950 69.13 yes 9
23 3190 55.83 yes 6 3110 54.43 yes 6
24 2240 39.20 yes 3 2710 47.43 yes 6
25 2470 43.23 yes 4 3050 53.38 yes 5
26 3080 53.90 yes 7 3340 58.45 yes 7
27 2440 42.70 yes 4 3190 55.83 yes 7
28 2800 49.00 yes 6 2930 51.28 no* n.a.
29 2320 40.60 yes 5 2760 48.30 no* n.a.
30 2310 40.43 yes 4 2260 39.55 yes 4
31 3150 55.13 yes 8 3420 59.85 yes 8
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 99
The Structural Strength of Glass: Hidden Damage
T a b l e 4
Results of Standing Tests
1 2 3 4 5 6 7 8 9
32 2890 50.58 yes 5 3140 54.95 yes 7
33 2930 51.28 yes 6 3370 58.98 yes 6
34 2600 45.50 yes 4 3250 56.88 yes 7
35 2290 40.08 yes 5 1870 32.73 yes 2
36 2400 42.00 yes 4 3960 69.30 yes 8
37 2660 46.55 yes 5 3400 59.50 yes 7
38 3080 53.90 yes 6 3400 60.20 yes 9
39 3610 63.18 no* n.a. 3480 60.90 yes 9
40 3460 60.55 yes 6 3200 56.00 yes 8
41 2680 46.90 yes 5 3540 61.95 yes 9
42 2640 46.20 yes 6 3270 57.23 yes 7
43 3500 61.25 yes 9 3180 55.65 yes 8
44 2120 37.10 no* n.a. 2380 41.65 yes 6
45 3120 54.60 yes 6 3090 54.08 yes 7
46 2970 51.98 yes 6 2810 49.18 yes 6
47 2330 40.78 no* n.a. 3000 52.50 yes 5
48 2690 47.08 yes 4 3550 62.13 yes 10
49 3120 54.60 yes 6 2910 50.93 yes 7
50 2380 41.65 yes 3 2960 51.80 yes 6
Mean 47.9 54.3
std/mean 13.5% 14.3%
maximum 61.3 69.3
minimum 31.9 32.7
100 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
F. A. Veer and Yu. M. Rodichev
Continued Table 4
Fig. 7. Weibull plot of flat test results with the cut downwards.
These are analyzed using normal probability plots for the best fit of the
distribution. If the points fall on the straight line the distribution fits. In general, the
problem lies at the maximum and minimum values. Only in some cases a
reasonable fit occurs. This is given in Table 5 and Figs. 10–12. In practice. there is
no single statistical descriptor that gives a universal fit on all valid test results.
Analysis of Partial Data Sets. By splitting the cut up and cut down data sets
for flat tests into subsets with fracture from the left or from the right we obtain the
Weibull plot shown in Fig. 13. The partial data sets seem to fit the Weibull function
better than the mixed data sets. The extremes at top and bottom are again the
problem.
Figure 14 shows the cut left data (standing tests), separated to failure from the
cut and failure not from the cut. The partial data set for failure not from the cut fits
the Weibull function much better (Fig. 14a and curve 1 in Fig. 14b). For the failure
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 101
The Structural Strength of Glass: Hidden Damage
Fig. 8. Weibull plot of standing test results with the cut left.
Fig. 9. Weibull plot of standing test results with the cut right.
from the cut (curves 2 and 3 in Fig. 14b) the bimodal Weibull function is better on
account of three lowest strength values deviate (curve 3 in Fig. 14b).
Fractography. A microscope was used to look at the failure origins. For the
standing cut right series all failures started at the cut. This is shown in Fig. 15. The
depth of cut as well as crumbled arris of cut are clearly visible in the butt of the cut
glass specimen.
102 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
F. A. Veer and Yu. M. Rodichev
T a b l e 5
Fits to Different Statistical Functions
Distribution Cut up Cut down Cut left Cut right
Normal no no yes no
Lognormal no no yes no
Extreme value no yes no yes
Exponential no no no no
Rayleigh no no no no
Weibull no no yes yes
a b
Fig. 10. Normal (a) and lognormal (b) distribution plot for cut left data set (standing).
a b
Fig. 11. Extreme value distribution probability plot for cut down – flat tests (a) and cut right data
set – standing tests (b).
Fractographic analysis of the cut left data shows that of 44 valid results 34
specimens failed from the cut and 10 from the other side. Figure 16 shows a failure
from the damaged arris on the uncut side of specimen.
Relation between Number of Cracks and Failure Stress. Figure 17 shows a
plot between the number of cracks branching from the failure point and the failure
stress. There is an approximately linear relation with very large deviations. However,
the slopes of flat and standing tests differ by a factor of three.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 103
The Structural Strength of Glass: Hidden Damage
a b
Fig. 12. Weibull distribution probability plot for cut left (a) and cut right (b) data set (standing tests).
a b
c d
Fig. 13. Weibull plot of data subdivided into: fracture from left (a) or right (b) for the cut down data
sets and from left (c) or right (d) for the cut up data sets (flat tests).
104 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
F. A. Veer and Yu. M. Rodichev
a b
Fig. 14. Weibull plot of cut left data (standing tests) subdivided into: fracture not from cut (a) and (b,
curve 1), and fracture from cut (b, curves 2 and 3).
Fig. 15 Fig. 16
Fig. 15. Failure point of cut right standing specimen No. 50 (Table 5), �30.
Fig. 16. Failure from the damaged arris in the uncut side in cut left specimen No. 30 (Table 5).
Fig. 17. Relation between the number of cracks and the failure stress.
Strength of Cut Specimens with a High-Quality Broken Arris of the Edge.
The results from the flat tests of additional specimens with a high-quality cut glass
edge working and safely handled are given in Table 6. The undamaged broken
edge arris of these specimens was in the tension zone.
Discussion. A significant amount of results have been presented. There are
several possible conclusions that can be drawn from this. The most important is
that the cutting process produces unequal sides. There is a significant effect if the
cut is the source of failure. The average strength is some 20% less compared with
the tests where the cut is on the compression side. The data is however much more
homogeneous. The relative standard deviation is half compared to the tests where
the cut is on the compression side. Even if both sides would follow a perfect
Weibull distribution, the mixed data would not give a good Weibull distribution.
As the Weibull distribution of both sets is considerably less than perfect, any
resultant combination of course should totally deviate.
The statistical analyses initially suggest that there is no single distribution that
fits all data. Of course this would only be valid if the data sets are really the result
of a single causative operation and are independent. At best the statistical results
can indicate that there is no single valid parameter or that the Weibull parameter is
better or worse than any other parameter.
More interesting is the good fit for the standing tests with the cut on the right.
There can be a deterministic explanation for this. Glass is an unyielding material
and it is very unlikely that the test setup places the specimen perfectly straight.
More likely is a small misalignment such as shown, exaggerated, in Fig. 18. This
would explain the relatively high number of failures from the upper loading which
go outside of the area between the loading span as the load would be transferred
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 105
The Structural Strength of Glass: Hidden Damage
T a b l e 6
Results of the Flat Tests for Specimens with High-Quality Broken Arris
No. �b max ,
MPa
Test speed,
mm/min
Loading
speed,
MPa/s
Mean value
of �b max ,
MPa
std/mean,
%
Maximum
value of
�b max , MPa
Minimum
value of
�b max , MPa
1 148 4.900 1.560 146 15 160 114
2 151 4.920 1.600
3 114 4.660 1.520
4 157 4.930 1.600
5 160 4.770 1.600
6 145 4.950 1.610
7 137 0.494 0.161 149 11 170 131
8 131 0.488 0.158
9 162 0.526 0.170
10 147 0.492 0.160
11 170 0.497 0.161
mostly onto an edge. In the tensile zone, the cut would be the most highly stressed
part, especially the corner edge. Apparently the misalignment forces the specimens
to fail from a single geometrical position and thus results in a single Weibull
distribution.
If we compare the Weibull plots of the partial flat specimen data sets,
separated to failure from the left and from the right in Fig. 13 an improved Weibull
fit is visible, especially for the bur-down tests (Fig. 13a and b). The higher
homogeneity of damages under glass cutting is the cause of that.
Presumably by separating the data further to source of fracture we might be
able to obtain a series of single Weibull lines. The inherent multilinear Weibull
behavior of cut float glass is thus the result of combining incomparable data sets.
If the cut glass is grinded and polished, the edges should become more equal.
The reality of any process is of course that it has statistical results. The authors
have regularly seen glass that has been grinded and polished, even tempered, on
which parts of the cut or original crumbled arris of cut are still visible. In one case
glass went into a tempering furnace with the cut surface still visible on about 50%
of the edge surface.
Even if just enough of the glass was grinded to remove the bur and the
protruding edge areas, the excess forces applied during the grinding could easily
cause further surface microcrack growth and microdamage at areas of very poor
surface quality. In any case, it would be impossible to see the original orientationon
the grinded surface. As the data sets for grinded and polished large-size glass
specimens are similar to those of cut glass, it is reasonable to assume that invisible
damage from the cutting process influences the failure process of grinded and
polished glass as shown in Fig. 19.
The standing test results allow us to evaluate the most probable lower value of
glass plate strength as they include damages on all edge surfaces – on the Tin,
nitrogen sides and bur as well as damages on both arrises. The Weibull plots of
diamond cut specimens standing test results based on the data of Table 5 together
with previous experimental data on size effect influence on grinded and polished
glass strength (Table 2, Fig. 10 [8]) are given in Fig. 19.
106 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
F. A. Veer and Yu. M. Rodichev
Fig. 18. Proposed alignment problem for the cut right standing tests.
Curves 1–4 show the test results for 8 mm float glass grinded and polished
specimens series A, B, C and D with a load span l � 0.9, 0.45, 0.225, and 0.1125 m
[8]. For comparison with these data the curves 5 and 6 for diamond cut 6 mm
specimens with cut left and cut right are given. It is obvious that angle of slope of
lower part of multilinear curves 4, 5, and 6 is closer to angle of slope of single
Weibull line 1 for large-size specimens. But the minimal strength value for small
grinded and polished specimens (curve 4) is significantly larger than the minimal
value of large specimens (curve 1) as a result of large difference of their edge
“hidden damages.” Quite the contrary, curves 5 and 6 are close to curve 1 for
probability of fracture less than 0.05. Thus, low-quality processing and rough
handling are the reasons for “hidden damage” effect on engineering strength of
float glass.
This approach is corroborated by the new test results on the strength of
specimens with a high-quality edge given in Table 6. The minimal strength values
for both series of specimens of 6 mm float glass tested at various loading speeds
are within the range of 115–130 MPa, which is more than twice higher than that of
the grinded and polished specimen series C and D in flat tests (60 and 50 MPa) [8].
Standard deviation for these specimens' strength was comparable with series S and
D – within the range of 10–15% of average. Average values 145–150 MPa and the
maximal values of strength 160–170 MPa reach the level of fully tempered glass
strength. In contrast to tempered glass, fracture of these high-strength specimens
was localized around the fracture source. Very small “central” surface defects –
microcracks on side face are typical for tested high-quality float glass specimens.
Just these initial microcracks in the thin cracked surface layer of high-quality sheet
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 107
The Structural Strength of Glass: Hidden Damage
Fig. 19. Weibull plot of standing test results with cut edge left and right in reference to roller cut,
grinded, and polished specimens with different load span: (1) l � 0 9. m; (2) l � 0 45. m; (3) l � 0 225. m;
(4) l � 01125. m, roller cut, grinded, and polished [1]; (5) l � 0175. m, diamond cut, cut edge left;
(6) l � 0175. m, diamond cut, cut edge right.
glass are the fracture source in the absence of large edge or side face “hidden
damages” of glass elements.
These results show that “hidden damages” are the reason for the low structural
strength of glass in usual practice. But these damages may be controlled and
eliminated using the proposed approach and experimental data on glass structural
strength together with advanced glass processing technology and industrial methods
of structural glass strength control.
C o n c l u s i o n s
1. The side of the glass that is rolled or scratched to create the cut is on
average by 20% weaker than the other side.
2. The failure stress of the side of the glass that was rolled to create the bur is
much more consistent than the results obtained with specimen failure from the
other side.
3. The failure stress of the side opposite to the bur can be much higher than
strength of specimens with cut edge in tension as well as than strength of ordinary
mechanically treated specimens, reaching values of heat-strengthened and even
fully tempered glass.
4. If failure is forced from a single part of the cut area, a single mode Weibull
distribution is obtained.
5. If the data are sorted out according to failure from left or right and from cut
side or uncut side, the Weibull distributions of the partial data sets are better than
those of the combined data sets.
6. The multilinear Weibull pattern of the mixed data of the cut glass is similar
to that of grinded and polished glass.
7. It is suggested that invisible damage from the cutting process remains after
grinding and polishing and is the underflat cause of the multilinear Weibull
behavior.
Acknowledgments. The work of the students who did the experiments for this
work as part of their MSc1 materials science course is acknowledged.
Ð å ç þ ì å
Äîñë³äæóºòüñÿ “ïðèõîâàíå ïîøêîäæåííÿ” ñêëà ó ïðîöåñ³ ïðîêàòêè ÷åðåç
íåð³âíîì³ðíèé ðîçïîä³ë ì³êðîòð³ùèí ó òîðöåâèõ ïîâåðõíÿõ ñêëÿíèõ êîíñò-
ðóêö³éíèõ åëåìåíò³â, ÿê³, çíèæóþ÷è ¿õ ì³öí³ñòü, çóìîâëÿþòü ðóéíóâàííÿ.
Ïîêàçàíî, ùî óñóíåííÿ âêàçàíèõ òîðöåâèõ ïîøêîäæåíü ñóòòºâî ï³äâèùóº
êîíñòðóêö³éíó ì³öí³ñòü ñêëà. Çà äîïîìîãîþ ï³äõîäó “ïðèõîâàíîãî ïîøêîä-
æåííÿ” âèêîíàíî ñòàòèñòè÷íî îáãðóíòîâàíèé ðîçðàõóíîê ì³öíîñò³ äëÿ íàé-
á³ëüø ïîøêîäæåíèõ çðàçê³â ³ç âèêîðèñòàííÿì íàä³éíîãî ³íæåíåðíîãî ïàðà-
ìåòðà.
1. J. G. R. Kingston and R. J. Hand, “Compositional effects on the fracture
behaviour of alkali-silicate glasses,” Fatigue Fract. Eng. Mater. Struct., 23,
No. 8, 685–690 (2000).
108 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3
F. A. Veer and Yu. M. Rodichev
2. M. K. Keshavan, G. A. Sargent, and H. Conrad, “Statistical analysis of the
Hertzian fracture of pyrex glass using the Weibull distribution function,”
Mater. Sci., 15, No. 4, 839–844 (1980).
3. F. A. Veer, F. P. Bos, J. Zuidema, and T. Romein, “Strength and fracture
behaviour of annealed and tempered float glass,” in: A. Carpinteri (Ed.), Proc.
of 11th Int. Conf. on Fracture (Turin, Italy) (2005), pp. 1–6 (cd-rom).
4. F. A. Veer, F. P. Bos, and P. C. Louter, “The strength of annealed, heat
strengthened and fully tempered float glass,” Fatigue Fract. Eng. Mater.
Struct., 32, No. 1, 18–25 (2009).
5. F. A. Veer, C. Louter, F. Bos, et al., “The strength of architectural glass,” in:
Proc. of Challenging Glass Conf. (Delft) (2008), pp. 419–428.
6. F. A. Veer, “The strength of glass, a nontransparent value,” Heron, 52, No. 1,
87–104 (2007).
7. Y. M. Rodichev, “Problems of technological and constructional strengthening
of glass for architecture and new fields of glass industry,” in: Proc. of Glass
Processing Days Conf. (Tampere) (1999), pp. 162–165.
8. F. A. Veer and A. C. Riemslag, “The strength of glass, size effects,” in: Proc.
of Glass Performance Days Conf. (2009), pp. 851–853.
Received 15. 01. 2010
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 3 109
The Structural Strength of Glass: Hidden Damage
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| id | nasplib_isofts_kiev_ua-123456789-112766 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T16:48:18Z |
| publishDate | 2011 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Veera, F.A. Rodichevb, Yu.M. 2017-01-27T09:41:21Z 2017-01-27T09:41:21Z 2011 The Structural Strength of Glass: Hidden Damage / F.A. Veera, Yu.M. Rodichevb // Проблемы прочности. — 2011. — № 3. — С. 93-109. — Бібліогр.: 8 назв. — ангд. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112766 539.3 Исследуется “скрытое повреждение” стекла в процессе прокатки из-за неравномерного
 распределения микротрещин в торцевых поверхностях стеклянных конструкционных элементов, которые снижают их прочность и приводят к разрушению. Показано, что при устранении указанных торцевых повреждений существенно повышается конструкционная прочность стекла. С помощью подхода “скрытого повреждения” выполнен статистически
 обоснованный расчет прочности для наиболее поврежденных образцов с использованием
 надежного инженерного параметра. Досліджується “приховане пошкодження” скла у процесі прокатки через
 нерівномірний розподіл мікротріщин у торцевих поверхнях скляних конструкційних елементів, які, знижуючи їх міцність, зумовляють руйнування.
 Показано, що усунення вказаних торцевих пошкоджень суттєво підвищує
 конструкційну міцність скла. За допомогою підходу “прихованого пошкодження” виконано статистично обгрунтований розрахунок міцності для найбільш пошкоджених зразків із використанням надійного інженерного параметра. The work of the students who did the experiments for this
 work as part of their MSc1 materials science course is acknowledged. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел The Structural Strength of Glass: Hidden Damage Конструкционная прочность стекла: скрытое повреждение Article published earlier |
| spellingShingle | The Structural Strength of Glass: Hidden Damage Veera, F.A. Rodichevb, Yu.M. Научно-технический раздел |
| title | The Structural Strength of Glass: Hidden Damage |
| title_alt | Конструкционная прочность стекла: скрытое повреждение |
| title_full | The Structural Strength of Glass: Hidden Damage |
| title_fullStr | The Structural Strength of Glass: Hidden Damage |
| title_full_unstemmed | The Structural Strength of Glass: Hidden Damage |
| title_short | The Structural Strength of Glass: Hidden Damage |
| title_sort | structural strength of glass: hidden damage |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112766 |
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