STABILITY OF THE MECHANICAL PROPERTIES OF GLASS-CERAMICS

Yu. G. Vazhen­tsev, L. M. Sedokov

(Presented by the scientific seminar of the Department of Strength of Materials)

Glass-ceramics are obtained by fine crystallization occurring throughout the entire volume of a previously formed product. They differ from glasses in that they have a predominantly crystalline structure, and from ceramics in the substantially smaller size of their crystals [1]. In their properties, glass-ceramics surpass many ordinary engineering materials, being distinguished by high strength, hardness, good electrical-insulating properties, a high softening temperature, and good thermal and chemical resistance. They are several times stronger than rolled glass, lighter than aluminum, and may be harder than high-carbon steel. By regulating the size, density, and chemical-mineralogical composition of the crystals, it is possible to obtain glass-ceramics with predetermined properties satisfying special requirements [1].

Glass-ceramics are becoming increasingly widespread in engineering, including as elements of load-bearing structures. However, their mechanical properties have been studied very poorly. These materials are very brittle; therefore, for them the direct determination of such an important mechanical characteristic as the ultimate strength in uniaxial tension is associated with certain difficulties [7].

The present work sets forth the results of studies of the stability of the strength characteristics of the glass-ceramic AS-418. Cylindrical specimens 20 mm in diameter and 5, 10, 15, 20, 25, 35, and 40 mm in height, in a total number of 272 pieces, were subjected to radial-compression testing, and 22 specimens 20 mm in diameter and 30 mm in height were tested in axial compression. The tests were carried out on a universal hydraulic testing machine using a special holder, which made it possible to eliminate tilting and eccentricity in the application of the load during axial compression of the specimens and ensured simultaneous contact of the pressing pads with the specimen along the entire length of the generatrix. Windows in the holder, covered with a transparent material, made it possible to carry out visual observation of the specimen during the loading process and its fracture.

The direct result of testing cylindrical specimens in radial compression is the contact strength $\sigma_{\mathrm{kp}}$, equal to the ratio of the maximum force to the area of the diametral section $(d \cdot l)$ [2]. The changes in the contact strength of the glass-ceramic AS-418 with an increase in the ratio of the geometric dimensions of the specimens $d/l$ from 0.25 to 2 are very insignificant and have the same character as for gray cast irons [2].

A histogram of the results of testing specimens of the material under study in radial compression is shown in Fig. 1, and in axial compression in Fig. 2. As can be seen, the strength characteristics of sitall have rather low stability, which is characterized by the degree

Fig. 1. Histogram of the results of testing sitall in radial compression

of scatter of the experimental data about the mean value \(\sigma\) of the quantity under study. The probability that the value of a mechanical characteristic of the material under the given type of loading will be no lower than

Fig. 2. Histogram of the results of testing sitall in axial compression

the lower limiting value of this characteristic at a specified reliability level \(P\) is estimated by the stability coefficient:

\[ c = 1 - t(P,\kappa)\cdot \Delta . \tag{1} \]

Here \(t(P,\kappa)\) is the Student distribution parameter [6]; \(\Delta\) is the coefficient of variation, determined by the formula

\[ \Delta=\frac{S}{\bar{\sigma}}, \tag{2} \]

where \(S\) is the root-mean-square deviation.

The results of tests of glass-ceramic specimens, processed by methods of mathematical statistics, are given in Table 1. Although the stability coefficient depends on the number of tests (here \(\kappa=n-1\) [6]), nevertheless, for \(n>20\) the error in determining the coefficient by (1) does not exceed 2%. Therefore it is quite obvious that the stability of the test results for the material under study in radial compression is higher than in axial compression.

To assess the stability of the method itself for testing brittle materials in radial compression, 15 cylindrical specimens 20 mm in diameter and 10 to 30 mm high, made of gray cast iron of hardness HB180—a well-studied material known for the comparatively low stability of its mechanical properties—were additionally tested. The stability coefficient of the contact strength for gray cast iron at the specified reliability level proved to be significantly higher than for glass-ceramic AC-418 (Table 1). Consequently, when brittle materials are tested for contact strength in radial compression, the stability of the experimental results depends mainly on the properties of the materials.

Table 1

Results of tests of glass-ceramic AC-418 and gray cast iron HB180 in radial compression and of glass-ceramic AC-418 in axial compression

On the basis of the investigations carried out, it may be concluded that the strength characteristics of such brittle materials as glass-ceramics, which are distinguished by low stability of mechanical properties, cannot be adequately evaluated by a single specific value of the test results for a limited number of specimens; it is necessary additionally to perform a confidence evaluation of these characteristics.

To obtain a confidence estimate of the ultimate strength of glass-ceramic with accuracy \(\varepsilon\)

\[ |\sigma-\bar{\sigma}|<\varepsilon \tag{3} \]

the required number of tests, with a specified reliability, can be determined approximately from the formula [6]

\[ n>\left[\frac{t(P,k)}{\varepsilon}\right]^2 S^2 . \tag{4} \]

Taking into account the rather low stability of the strength characteristics of AS-418 glass-ceramic, engineering calculations should use not the mean value, but the design value of the ultimate strength of the material, determined with a specified reliability \(P\),

\[ \sigma_{\text{pc}}^{\text{des}}=c\cdot \bar{\sigma}_{\text{pc}} . \tag{5} \]

Here the stability coefficient \(c\) plays the role of the minimum permissible safety factor for the strength of the material.

Calculation of the tensile ultimate strength of brittle materials from the contact strength determined under radial compression involves a transition coefficient \(A\), which depends on the selected strength criterion [4]. According to the regular TPI criterion for brittle materials [4],

\[ A=\frac{2}{\pi}\sqrt{1+9\nu^2+0.75\nu}, \tag{6} \]

where the brittleness coefficient \(\nu=\dfrac{\sigma_{\text{p}}}{|\sigma_{\text{c}}|}\) characterizes the different resistance of brittle materials to tension and compression. For glass-ceramics \(\nu=0.04\) [1, 3]; in this case \(A=0.65\). The ultimate strengths of AS-418 glass-ceramic for different reliability levels, calculated by the formula

\[ \sigma_{\text{pc,p}}=0.65\,\sigma_{\text{kp}} \tag{7} \]

are given in Table 2.

Fracture of AS-418 glass-ceramic specimens under radial compression occurred in the form of an “explosion” [3]. Specimens that withstood contact stresses of \((3\text{--}6)\ \text{kg/mm}^2\) fractured in the diametral plane into two halves, with low relief of the fracture surfaces and a small number of fairly large and clearly expressed splitting wedges. Specimens that withstood contact stresses of \((6\text{--}12)\ \text{kg/mm}^2\) fractured, as a rule, into 4–5 large pieces with the formation of a large number of small particles from 0.05 to 2 mm and medium ones—from 2 to 5 mm. Most of the fragments of medium size had a plate-like shape.

Table 2

Calculated values of the ultimate tensile strength of AS-418 glass-ceramic at different reliability levels

Fracture of specimens under axial compression also occurred in the form of an “explosion,” with the formation of many small particles \((0.05\text{--}1\ \text{mm})\), if the specimens withstood compressive stresses on the order of \(100\ \text{kg/mm}^2\) and higher; at smaller values of \(\sigma_{\text{pc.c}}\), the specimens fractured into more

large pieces. Some specimens, however, broke into pieces in the form of columns along planes parallel to the direction of action of the compressive force, with fragmentation of the fracture surfaces.

Upon visual examination of the specimens before and after fracture, spherical bubbles from 1 to 5 mm were often found on the end faces and fracture surfaces. As a rule, such specimens showed low strength values both under axial and under radial compression.

The most probable cause of the low stability of the strength characteristics of AS-418 glass-ceramic may be considered to be the considerable inhomogeneity of their structure and the presence of defects in the form of bubbles and micro- and submicrocracks, arising as a result of instability in the technological processes used to manufacture the specimens [3, 5].

Conclusions

1. The stability of the mechanical properties of AS-418 glass-ceramic proved to be very low. At a reliability level of $P = 0.95$, the stability coefficient $c$ for the contact strength under radial compression is 0.60, and for the ultimate strength under linear compression it is 0.46. The coefficient of variation $\Delta$ is respectively 0.203 and 0.276.

2. The calculated value of the ultimate compressive strength is half the mean value: 44.70 kg/mm² and $(97.03 \pm 12.10)$ kg/mm², respectively, at $P_1 = 0.95$.

3. The calculated value of the tensile strength, obtained from the results of the radial-compression test, was 3.08 kg/mm², with a mean value of this characteristic of $(5.13 \pm 0.13)$ kg/mm² $(P = 0.95)$.

References

1. A. I. Berezhnoy. Glass-ceramics and photositalls. “Mashinostroenie,” 1966.

2. Yu. S. Bogomolov, L. M. Sedokov. Investigation of the strength of cast iron under radial compression. Izvestiya TPI, vol. 133, 1965.

3. V. S. Kamnerskii, N. V. Skvortsov, A. E. Zhuravel. Mechanical properties of glass-ceramic under tension, compression, and bending. Problems of Strength, Kiev, 1971, No. 4.

4. G. L. Kalinichenko, E. M. Mikhailovskii, L. M. Sedokov. Reliability of strength theories for brittle materials. Problems of Strength, Kiev, 1970, No. 6.

5. F. Fanderlik. Defects in Glass. Moscow, 1964.

6. P. Z. Rumshinskii. Mathematical Processing of Experimental Results. Moscow, 1971.

7. Ya. B. Fridman. Mechanical Properties of Metals. Moscow, Oborongiz, 1952.