Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 8
Issue 4
Civil Engineering
Available Online: http://www.ejpau.media.pl/volume8/issue4/art-34.html


Jakub Marcinowski
Institute of Structural Engineering, University of Zielona Gora, Poland



A photoelastic method was proposed to examine quality of tempered float glass used in the building facade of the ten-store office building. It turned out that strong disturbances in distribution of residual stresses were present in examined glass, facade panels. It can be concluded that these disturbances were the cause of spontaneous breakages of glass panels, which took place in some circumstances. The proposed inspection procedure is cheap and very effective.

Key words: tempered, float glass, residual stresses, detection of heterogeneities, photoelasticity.


Nearly 90 % of the glass produced contemporary in the world is the float one. Brilliant, glass facades of modern buildings are made of this kind of glass. The float process was invented by Sir Alastair Pilkington in 1952. The float glass is obtained in fully automated production line nearly half kilometer long. The main idea of the float technology lies in pouring continuously of molten glass, at approximately 1000ºC, from a furnace onto a shallow bath of molten tin. It floats on the tin, spreads out and forms a level surface. Thickness is controlled by the speed at which solidifying glass ribbon is drawn off from the bath. The glass obtained by this method is almost ideal optically. Both surfaces of the glass plate are smooth and parallel. At 600°C it creates a solid ribbon, which can be coated in the next stage of the production process. The consecutive stage is a slow annealing. It is the stage in which residual stresses generated during solidification are reduced.

There is other technological process, which makes the glass stronger twice or more. It is tempering. The glass is heated up to approximately 650 degrees Centigrade and then a sustained blast of cooling air is applied to the surfaces. As a result of a quenching the external layers of a glass plate solidify earlier than internal. Stresses are generated during this process and stress distribution across the glass plate is shown in Fig. 1. This state of residual stresses makes the glass stronger and safer providing that the glass is free from flaws and residual stresses are homogenous in the whole glass panel.

Fig. 1. Stress distribution due to tempering

There are excellent flaw inspection techniques in every plant. The float line is equipped with a flaw detector. It is sometimes the high-tech (laser), computer controlled equipment. Automatically driven cutters cut portion of ribbon with flaws. The inspection is so excellent that it is nearly impossible that any flaw may appear in final product. Typical flaws as inclusions, bubbles, sand grains which refused to melt, surface ripples caused by a tremor in the tin, are easy to detect even by the unaided eye. Heterogeneities in distribution of residual stresses can be detected only by sophisticated, optical apparatus. Such disturbances of residual stresses can cause spontaneous breakage of glass during extremely high or extremely low temperatures accompanying by a wind pressure. In such conditions failures shown in Fig. 2 have happened. After excluding mechanical reasons of these failures the examination were focused on the glass. A photoelastic method was chosen as a tool to visual flaws, which are invisible for the unaided eye.

Fig. 2. Spontaneous breakages in glass facade

The photoelastic method is applicable to transparent materials and in such cases it is particularly efficient. In the paper of Liang et al. [1] the residual stress distribution in a synthetic diamond substrate was analysed by this method. The residual stresses induced by using self-drilling screws on polycarbonate plates were investigated in the work of Wang & Shih [2].

The presented paper deals with the detailed description of a procedure leading to detection of disturbances in distribution of residual stresses being result of tempering process of a float glass. The proposed procedure of inspection based on photoelastic principles was successfully adopted to window panels, from which the facade of ten-store office building was made.


The phenomenon of the temporary double defraction was discovered by Brewster in 1814 r. The materials which exhibit this phenomenon are called birefringent materials (comp. [3] and [4]). The main idea of this phenomenon was explained in the Fig. 3. When a ray of a plane polarized light passes through a photoelastic material (most of transparent isotropic materials) it gets resolved along the two principal stress directions and each of these components experience different velocities. After transition through the material these components experience a linear relative retardation d. The magnitude of the retardation at given point of material is given by a formula (comp. [3] and [4])


where: C – the stress optic coefficient dependent on material, t – thickness of the specimen, s1, s2 – principal stresses at given point.

Fig. 3. Temporary double defraction

These two rays (A2 and A3 in Fig. 3) of light passes then through the other polariser and the resulting ray of light amplitude can be expressed as follows


where: A – the initial amplitude of light ray, j – the angle between the first principal direction and axis a-b of polariser P, d – the linear relative retardation, l – the light wavelength. This result refers to the case when axes of both polarisers are mutually perpendicular.

Intensity of the transmitted light is proportional to the square of amplitude A4. The most distinctive domains of a picture are dark fringers, along which the amplitude must vanish. It will happen when


This family of fringers is called isochromatics (comp. [3] and [4]). The case sin 2φ = 0 corresponds to isochlinics. It is possible to eliminate isochlinics from the obtained picture of fringes. It is enough to add two additional filters called quarter plates (comp. [3] and [4]). In such a case only isochronics will be visible in the picture of fringes.

It follows from the eqn. (3) that along dark fringers the following condition must be fulfilled


where m = 0, 1, 2, ... .

It means that along fringers linear relative retardation is integer number of wavelengths. Comparing eqns. (1) and (4) one obtains

where – is called the photoelastic model constant. The last relation in eqn. (5) is called the stress-optic law and is known as Neumann-Maxwell law.

It is worthy to mention that this derivation is valid for thin specimens being in plane stress state. As far as stress-strain relations are concerned, only for the linearly elastic material behaviour the above relations hold true.

There are many methods of identification of the constant K for a given photoelastic material (comp. [4], [5] and [6]). Knowing it and knowing integer m for a given fringe (it is comparatively easy to identification in a given case) one can determine the stress distribution within the model of arbitrary shape. The procedure is particularly easy for thin models and a plane stress state case (comp. Fig. 4).

Fig. 4. Fringes (iscochronics) in t-like cantilever

Experimental stress analysis is possible for models under external loading but also for models within which residual stresses are frozen. In Fig. 5 visualization of residual stresses within plastic school accessories are shown. It is the result of an injection moulding.

Fig. 5. Fringes (isochronics) in plastic school accessories


The procedure of detection of heterogeneities in distribution of residual stresses within the glass plates by means of photoelasticity depends on a glass property. If the light can pass through the glass the procedure is obvious and inspection can be done according to the scheme shown in Fig. 3. Because the light passes through layers of different stress states (it is not plane stress state, comp. Fig. 1), the final picture will be gray, without distinctive fringes. Such a picture will be the proof that the distribution of stresses is heterogeneous within the whole glass plate, excluding corners. If there are stains, smudges, spots of different colors or different intensity, it means that disturbances in distribution of residual stresses are present.

Very often glass panels are unilaterally coated to obtain profound changes in optical properties. It is kind of a mirror and of course the light cannot pass through such window panel. The inspection procedure in this case should be different. The scheme of a test rig for such a case is shown in Fig. 6. The qualitative analysis of the picture obtained in such an analysis is the same as before.

Fig. 6. Scheme of inspection of a coated glass panels


Two families of window panels made of tempered, coated float glass were examined: the first – window panels of good quality (there were never any sudden breakages in windows made of this glass), the second – defective window panels (those which spontaneously break in some circumstances). Tests were performed in linear and circular polariscope according to the scheme shown in Fig. 6. First tests were performed in laboratory (comp. Fig. 7). Panels of the first family have delivered pictures like the one shown in Fig. 8. Panels of the other family have generated pictures the example of which is shown in Fig. 9. The obtained pictures were the first proof that residual stress distributions in panels of the second family were heterogeneous. The disturbances compared to the glass of the first family seem to be significant.

Fig. 7. Inspection of window panel in laboratory

Fig. 8. Picture delivered by flawless tempered panels

Fig. 9. Picture delivered by panels with heterogeneities

The examination procedure was expanded to the window panels installed in the office building. Two polarisers were dismounted from the polariscope. The arrangement of both polarisers and the position of the light source are shown in Fig. 10. Some pictures registered during these examinations are shown in Figs. 11 and 12. They have confirmed that all window panels used in this building manifest significant heterogeneities in distribution of residual stresses and probably this is the reason of sudden breakages, which still happen in the glass, front elevation of this building.

Fig. 10. Inspection of window panels on glass facade

Fig. 11. Picture delivered by panels on glass facade

Fig. 12. Picture delivered by panels on glass facade


The comparatively simple and cheap method of flaw detection was presented in the paper. The proposed method of inspection is based on stress-optic law and requires two polarisers and the light source. It makes possible to register invisible for unaided eye, heterogeneities in distribution of residual stresses due to tempering process. The method was adopted to inspection of window panels installed in tall office building. Sudden breakages have happened in this building in very low and very high temperatures and reason for theses failures were looked for. It was revealed that pictures obtained in the analyzer differ significantly from pictures registered for window panels of good quality, flawless panels. The whole procedure may be easy adopted to glass panels during the manufacturing process or later during inspection accompanying the purchasing procedure. This inspection method does not require expensive apparatus and turned out to be effective also in a case of inspection of the existing glass facade of the tall office building.


  1. Liang H., Chin K. K., Kohn E., Vescan A., 1996, Measurement of stress in a synthetic diamond substrate using photoelastic method, Diamond and related Materials, Vol. 5, Iss. 6-8, pp. 664-668.

  2. Wang W., Shih H., 2002, Hybrid investigation on residual stresses induced by self-drilling screw op polycarbonate plates. Optics and Lasers in Engineering, Vol. 38, Iss. 1-2, pp. 97-113.

  3. Kuske A., Robertson G., 1974, Photoelastic Stress Analysis, Wiley, London.

  4. Durelli A. J., Riley W. F., 1965. Introduction to Photomechanics. New York, Prentice-Hall Inc. /Englewood Cliffs.

  5. Marcinowski J., Wójcik. S., 2001. Wytrzymałosc materiałów w badaniach doświadczalnych. Dolnośląskie Wydawnictwo Edukacyjne, Wrocław, [in Polish].

  6. Będzinski R., Chomiak Ł., Dudek K., 1975. Pomiary naprężeń metoda elastooptyczną. Wydawnictwa Politechniki Wrocławskiej, Wrocław [in Polish].

Jakub Marcinowski
Institute of Structural Engineering,
University of Zielona Gora, Poland
Prof. Szafrana Street 2, 65-516 Zielona Gora, Poland
phone: (+4868)3282527
email: j.marcinowski@ib.uz.zgora.pl

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