Numerous investigations have de'alt with the influence of various factors on the strength of glass, but still not enough is known about the strength of commercial glasses owing ~o the fact that most of the studies were on ~lasses the compositions of which differed significantlyfrom industrialproducts. In addition, the significance ef individual factors could not always be taken into account because of the lack of unified methods for deter~ ~lination of the mechanical properties of glass. In the majority of instances, with the exception of glass fibers, glass is subjected to bending stresses i n use2 Therefore the principal characteristic of glass strength commonly adopted is tensile strength under bending de~grmation, or bending strength. In our experiments on the testing of glass specimens for bending strength two types of glass were used -vertically drawn and continuous-r, olled. The time' of action of the 10ad to rupture was about 1 minute. It was first desired to determine the influence of the shape o f the supporting prisms on the strength Values cbtained in the tests. These experiments were carried out on the testing machine with different arrangements cf the supporting and loading prisms: cylindrical, of 5 mm radius, and triangular with an acute angle and 8 m m s~des. Vertically drawn glass specimens 100• 26x 6 t a m i n size were used. The edges of the speeimem were finely ground. 25 specimens were tested in each batch. . 9 The results, shown in Table 1, indicate that the shape of the supports has no appreciable influence on the value obtained for glass strength. The effect of storage time on strength was determined on specimens of vertically drawn glass 150x30x :~ 5.5 a-rim in size. The edges of the specimens ,were not subjected to any additional treatment after cutting. The plane along which the diamond cuts were made was in a state of extensfon during the tests. All the specimens were cut simultaneously and divided into batches of 15. The tests were carded out ever a period of 5 months. The results are illustrated in Fig. 1. 27A BLE 1
~;hape of Supports and batch of specimens
Bending strength, kg/em ~
Arithmetic ~ne hour one o n e .mot~th mean error p~ Kg/ci az ' in batch, qo 6t~___.cm.mr ~._._~~
on, re~lJ[: 1
first batch second batch
Three -sided third batch fourth batch
tLs lo g0 25 Storage time, log t hours
It is seen from the diagram that the strength of glass does not change during storage. Consequently. the slight variations of the temperature andhumidity of the surrounding medium, inevitable during prolonged ino vestigations, have no appreciable influence on the test result1. The maximum strains during bending under the action of a load arise on the surface o f the plate opposite to the application of the load; the magnitude of the strains varies along the length of the specimen. Since the maximum extension occurs at the central point of the underside of the plate, rupture should be expected to occur at that point, In reality, however, as our observations showed, rupture does not always occur in the region of the m a x i mum strains caused by the load. This confirms once again that strength is determined by flaws present in tlm specimens, and its Value is greater at some points than at others. This has been noted earlier by some workers , but the effect has not been quantitatively evaluated. The bending strength of glass is usually c a l c u l a t e d from the formula:
P ~ 2--~-"
where Q is the load on the specimen causing destruction, ~g;1 is the distance between supports, cm; b is the width of the specimen, cm; d is the thickness of the specimen, crn. As was pointed out above, destruction does not always occur at the poi m of m a x i m u m stress(Ij~) and therefore it is more correct to use the formula : p, = -~-c~ - - ,
where c is the distance from the point of destruction to the nearer support. In the ideal ease it should be equal to
In determinations of glass strength the point of destruction was recorded. The value of c was c a l c u l a t e d as due arithmetical mean for each batch. 50 specimens were ~ested in each batch. The results of ~he rest are shown in Table 2. Examination of the data in Table 2 shows that the strength values c a l c u l a m d from Formula TABLE 2 (1) ate about 10% higher than the strains which actually caused destruction. Batch No.
c, m m I P > ~'~ % 69 54 48 33 22
9 II 5 15. 13
For a correct determination of the strengfla of a material, i t is necessary to determine e x a c t l y the nature and magnitude o f the forces, and ~aen to apply the formula appropriate in the given i n stance in accordance to the forces acting on abe specimen.
W e , 1 i k e o t h e r s, used Formula (1) for calculation of the bending strengfll of glass. It was necessary to establish the dimensions of glass specimens the strength of which c a n be calculated with the use o f this formula. The simplest formula for calculation of strain on bending slaows that the bending s~resses in a b e a m arc p r o portional to the diztance from the neutral axis. This is valid for beams the cross-section of which is small in comparison with the length, and if points at considerable distances from the ends are considered. Formula (1) is applicable to tiae calculation of the strength of thhl elastic plazes when, as A c a d e m i c i a n B. G. Galerkin has shown, the distance between the suppor~ is more than 10 times the thickness'of the plate, while the bending deflection does not exceed half the thickness. We have studied the effect of fl~e length/width ratio of the specimens on the strength. The rcsutts o f these experiments are shown in Fig. 2.
I t is seen that the strength of glass c a l c u l a t e d from For mula (1) r e m a i m p r a c t i c a l l y unchanged a t the 1.;./b ratio vades from 1 to 6. O
According to experimental results published in the literature, the value o f the bending strength greatly depends on the dimensions of the speeimera tested. These investigations covered a range o f specimen areas from 1 to 10 e m z and over 200 e m 2. In our experiments specimens from 15 to 150 e m z were used. The results are shown in Table 3.
Ratio of length to width of specimen lpa
The results indicate that the strength both of annealed and of toughened glass is practically l a dy,pendent of the area of the specimens in file range 15"150 em='., TABLE 3 _
II .mber o, /l egr. of IArea | of stm .-t
ge Ispeeimem i tougllening / =/ .~. t . . , I _ q ... leilx~en, c m t s t r e n ~ , " S t i oaten for. a n n e a u n ~ l = t
, i 1 2 3 4 5
15 14 16 14 15
"2 16 2.2 2.12 2- ! 7 2.12
151" 84.5 40.0 40.0 42.0 .k
I0 11 12 13 14 15
Average dimenrdom of speeimem
1890 1790 1860 1720 . 1740
150 84.5 84.5 90,0 900
] Mean arithmetle error,
100.5 100,0 47.2 44.5 46,5
6.71 6,67 6.68 6.38 6.68
7 13, 10 7 12
97.0 I01.5 45.8 46.4
6.63 6.63 6.67 6,66
14 25 13 ll
17.5 30.5 37-0 49.0 63-0 61.5
5,8 5,76 5.82 5.78 5.79 5.84
15 16 14 15
0,12 0,12 0,12 0,12
145.0 85.0 39.0 23.2
430 525 5t0 585
150.0 84.5 84,5 500
30 '20 '20 19 20 18
0.1 0.1 0.1 0.1 0.1 0-1
17.5 30.5 37.0 49.0 115.0 111.0
6'20 645 650 645 635 620
-100 I00 100 100 180 180
10 8 7 9.5 9 10
A l l the authors note that the strength values obtained increase with decreasing thickness of the specimen. The effect of glass thickness ou strength has been studied least for glass between 4 and ! 6 m m thick. It is generally not stated in the literature by what process the glass had been made and whether the methods o f m~uufaeture and preparation of the specimens were the same for a l l tlie uhieknesses tested. The results of determinations of the e f f e c t of thickness of the specimens on the strength of vertieaUy drawn glass are illustrated by the graph in Fig, 3; for e o m p a r i ~ n , the graph also shows the results of other i n vcstigations (1 - g l a s s from K0nstantinovka works, 2 - from the Dzerzhinsky works, Gusevo, 3 " - f r o m the Gork7 works, 4 - from Lyubertsy works, 5 - Graf's data , 6 - Petrov's data , 7 - Tyuremnova and Lioznyanslo]a's d~ta [ 5 ] ) . It is seen from Fig. 3 that as the thickness of glass decreases in the range from 16 t o 3 turn, the strength increases from 550 to 750 k g / c m z, and then begins to rise rapidly with further decrease o f thickness. Similar re~,;ults were obtained in tests o f stmeimens with ground and polished surfaces. Our findings are in agreement with the literature d a m . Only the side which undergoes extension in the test is considered. 313
~m t o:
a-f A-2 ,z,-3
Speeimen thiekness d, m m
A comparison of the variation of the szrength of specimens with their dimensions (Table 3) and their thickness (Fig. 3) shows that file strength d e pends more on the thielmess than on the other dimensions.
Fig. 8 TABLE 4
Method of production of glass Thickness, inln
Strength, k g /
7.3 6,93 4.60 2.50 2.15
6O5 590 595 ~95 74O
6~0 700 6;0 7(O 7~0 89O 850 965
I t was especially interesting to determine the strength o f speeimera of different thickness obtained from the same origiiml glass by grinding and polishing. Specimens of less thickness were made from ' / - m i l l i m e t e r rolled glass by grinding and polishing for this purpose. The same was done with 5-mLUmeter vertically drawn glasL The results o f tests on 25 x lP.J) m m specimem of different thicknesses are shown in Table 4. 20 specimens were tested in each batch.
3-16 3.20 2.9.5 i-~ - i,76 !.30
Oar hypothesis that the different strength values obtained for thin and thick glasses are the consequence of the insufficient accuracy of the formulas as applied to thin glass does not fully explain the phenomenon described above, as c a n be seen from the following eonsideratiom. In the bending o f a block or b e a m  l o n g i tudinal extension is accompanied by transverse d e formation. In consequence, the shape of a l l crosssections of the bent beam is distorted. In the ease o f bending, the normal stresses will be: P
=EX" p '
where: .Z is the distance of an elementary plate from the neutral axis; p is the radius of curvatm'e of the neutral layer; E is young's modulus.
i f a thin strip is bent, transverse deformations occur only near the edges. In this c a s e the equation rakes the form: p =
Ey (1---//) p
wheie p is Poisson's ratio. This means that the strength of a plate during bending along a cylindrical surface is increased in the ratio 1 - -1#
" For glass /t = 0.22. and ~ e n ' i L P = L 0 5 .
It follows from this calculation that the value o f the strength of very thin glass plates, c a l c u l a t e d from the formula for a beam, exceeds the true value by 5~m~ Fig. 3 shows that the strength of thin glass specimens is several times as g r e a t a s that of thick specimens, and not only 5% greamr. The dependence of the strength of glass on the thickness of the specimen may to some extent be explained by the fact ~ a t destruction of glass commences at the edges, places which have been most weakened by cutting and mechanical treatment of the ends. Therefore the most dangerous flaws arc present on tim end faces, and the area of these faces depend~ on the uhiekness. The strength is also probably affected by ~ e rate of cooling during r~he formation of thick and thin glasses . 314
In determinations of glass steength and in comparisons of different types of glass it Is necessa~ to take into sideration the influence of the factors discussed above on the strength of glass and to maintain constant conc,ns of testing, selection, and preparation of the samples. LITERATURE CITED  Littleton and Preston, J. Soc. Glass Technol~ 13,336 (1929); G. M. Bartenev, J. Tech, Phys. 2 1 , 6 ~ 51); PrOCoAcad. Sci. USSR 71,23(1950),  N. N. Davidenko, I. Tech. Phys. 13, 281 (1943).  O. Graf, Glastech. Ber. 13.23~ (1936).  S.P. Pe~ov, Production of Stalinit Glass (Ind. Constr. Press, 195~ o  N. A. Tyurernnova and S. G. Lioznyanska)ra; Glass and Ceramics 1950, No, 11.  S.P. Timoshen.~o and Les~l, Applied Theory of Elasticity (State Sci. Tech. Press, 1931) o  G. M. Bar~nev and A. I. Ivanova, Glass and Ceramics 19fi5, No. 12.