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What are the types of internal stress in glass and why they form？

The internal stress of glass includes surface compressive stress and internal tensile stress, which is formed by rapid cooling, enhancing strength and safety.

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What are the types of internal stress in glass and why they form

The interaction force on the unit cross-section inside the material is called internal stress. The internal stress in glass can be divided into three categories: the first category is caused by external force or thermal change, called macro stress, which can be studied by the methods of material mechanics and elastic mechanics; the second category is called micro stress, which is caused by microscopic inhomogeneous areas or phase separation in the glass, such as borosilicate glass; the third category is called unit stress or ultra-micro stress, which is equivalent to the stress caused within the volume range of the unit cell size. The latter two types of internal stress are reflected in the physical properties of glass, such as refractive index, thermal expansion coefficient, density, etc. These internal stresses caused by structural characteristics are not very large for the mechanical strength of glass. We mainly study the macro stress caused by thermal changes in glass, that is, the thermal stress of glass.
The thermal stress of glass can be divided into temporary stress and permanent stress (or residual stress).

Temporary stress

(1) When glass is heated and cooled within the elastic deformation range, a certain temperature difference is generated in its inner layer, since glass is not a good conductor of heat transfer, thus generating a certain thermal stress. This stress exists with a temperature gradient and disappears with the disappearance of the temperature gradient, so it is called temporary stress.
As shown in the figure, when a stress-free glass is heated from room temperature to below Tg temperature, a temperature difference is generated between the inner and outer layers of the glass. The temperature of the outer layer is higher than that of the inner layer, and the outer layer expands more than the inner layer when heated. In this way, the outer layer extends under the obstruction of the inner layer (compression), while the inner layer expands under the expansion of the outer layer (stretching) [Figure (b), Figure (c)]. Therefore, when heated, compressive stress is generated on the surface of the glass, and tensile stress is generated on the inner layer. Moreover, tensile stress is defined as positive, and compressive stress is defined as negative.

If the outer layer is heated to a certain temperature and the entire glass is heated, the outer layer of the glass no longer expands, but the inner layer continues to expand. In this way, the outer layer is subject to tensile stress, while the inner layer is subject to compressive stress. Their magnitude is equal to the stress generated during the heating process but in the opposite direction. Therefore, when the internal and external temperatures are balanced, the stress in the glass disappears [Figure (d)]. Similarly, the stress distribution generated by a piece of stress-free hot glass at the beginning of the cooling process is exactly opposite to that of the heating process, that is, the outer layer is tensile stress and the inner layer is compressive stress [Figure (e) to Figure (h)]. Therefore, the temporary stress in the glass disappears after the temperature is balanced. However, when the temporary stress exceeds the ultimate strength of the glass, the glass will also crack, especially during the cooling process, the cooling rate should be lower than the heating rate during the heating process.

 Permanent stress

When the temperature of the glass is balanced, the stress that still exists in the glass is called permanent stress. As shown in Figure 3-1, when the glass is cooled to a high temperature (> Tg), a temperature difference is generated between the inner and outer layers of the glass. Because the thermal motion energy of the molecules is large in the transition temperature region (η<101¹Pa·s), displacement and deformation can occur between the structural groups inside the glass, which makes the internal stress generated by the temperature difference disappear. We call this process stress relaxation. At this time, although there is a temperature difference between the inner and outer layers of the glass, no stress is generated. However, when cooled at a certain cooling rate at Tg temperature, the glass gradually transforms from a viscous plastic body to an elastic body, and only part of the internal stress P generated by the temperature difference is relaxed. When the temperature is cooled below the strain point, the corresponding internal stress generated in the glass is P-x; when further cooling eliminates the temperature difference between the inner and outer layers of the glass, the change value of the stress at this time is P. That is to say, after the temperature is balanced, the magnitude of the internal stress remaining in the glass is (P-C)-P=-X. This internal stress is called permanent stress or residual stress.

The direct cause of permanent stress in glass is the result of stress relaxation in the annealing temperature zone. The degree of stress relaxation depends on the cooling rate, temperature gradient, viscosity, and product thickness in this zone.
In addition to the permanent stress caused by thermal stress, permanent stress can also be generated in glass due to chemical inhomogeneity. For example, during the glass manufacturing process, due to insufficient melting homogenization, defects such as streaks and stones are generated in the glass. The chemical composition of these defects is different from that of the glass body, and their expansion coefficients are also different. For example, the expansion coefficient of silica bricks or material stones is 60×10-7/℃, while that of general glass is about 90×10-7/℃. Therefore, the stress generated between them cannot be eliminated.

Glass Types and Permissible Permanent Stress Values
Glass Type Permissible Permanent Stress (MPa)
Class I-II Optical Glass 2-6
Class III-IIV Optical Glass 10-20
Flat Glass 20-95
Rolled Glass 20-60
Bottles and Containers Glass 50-400
Hollow Glass 60
Glass Tubing 120
Tempered Glass 1350-2400
Aviation Glass 25
In addition to the above-mentioned cases, permanent stress will be generated when sealing and nesting between glasses with different expansion coefficients or between glass and metal. If the product is not manufactured properly, it often causes uneven heat dissipation and stress concentration. This stress is difficult to eliminate and is also one of the reasons for the explosion of the product.

The existence of permanent stress brings the following disadvantages to the production and use process: excessive permanent stress will cause the glass to explode during processing or use; due to the existence of permanent stress, optical precision instruments will produce double refraction and affect the working accuracy of the instrument; using the instrument at high temperature for a long time will cause the optical parts to deform and affect the imaging quality. Various industrial glass products have their own allowable permanent stress values, see the following table.

The internal stress in glass can be expressed by the optical path difference of light refraction. There are two mutually perpendicular internal stresses (tensile stress, represented by Ox and Oy) on the glass plate, and Oy>Ox, then the propagation speed of light along the x and y axes (represented by Vy and Vx respectively) is also different, Vy>Vx, thus generating an optical path difference △, i.e., refraction phenomenon. The optical path difference is proportional to the thickness d of the sample and the light propagation speed difference Vy-Vx in the glass, and Vy-Vx is proportional to the internal stress difference oy-ox. The calculation of the optical path difference is
△=Bd(oy-ox)
△——optical path difference, nm/cm;
B——stress optical constant;
d——glass thickness, mm.
The optical constants of some industrial glasses are listed in the following table.
Glass Types and B Values
Glass Type B Value
Quartz Glass 3.4
Light Barium Crown Glass 2.8
96% High Silica Glass 3.6
Heavy Barium Crown Glass 2.14
Low Expansion Silicate Glass 3.8
Barium Crown Glass 3.10
Low Tano Borosilicate Glass 4.7
Light Crown Glass 3.50
Lead Glass 2.6
Medium Crown Glass 3.12
Flat Glass 2.8
Heavy Crown Glass 2.67
Calcium Silicate Glass 2.4 – 2.6
Extra Heavy Crown Glass 1.19

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