Digital Photoelasticity of Glass a Comprehensive Review

Opticss and Laser Optic Laserss in Engine Engineering ering 87 (201 (2016) 6) 59 –74

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Digital photoelasticity of glass: A comprehensive review Ramesh Kn, Vivek Ramakrishnan Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, India

a r t i c l e

i n f o

 Article history: Received 10 January 2016 Received Received in revised revised form 13 March 2016 Accepted 15 March 2016 Available online 31 March 2016 Keywords: Digital photoelasticity Tempered glass Float glass Residual stress Scattered light

a b s t r a c t

The recent advances in digital photoelasticity have made it possible to use it conveniently for the stress analysis of articles and components made of glass. Depending on the application, the retardation levels to be measured range from a few nanometres to several thousand nanometres, which necessitates different techniques and associated equipments. This paper reviews the recent advances in the photoelasticity of  glass with a focus on the techniques/methods developed in the last decade. A brief introduction to the residual stress in glass is provided initially to bring out its tensorial nature. The subsequent sections are organised thematically rather than chronologically, for better readability and easy access of information. &  2016 Elsevier Ltd. All rights reserved.

1. Introduct Introduction ion

Glass is one of the oldest man made materials and history of  glass making can be traced back to third century B.C. Over the last decade, there has been an explosion in the use of glass ranging from structural structural applicatio applications ns to bio-medica bio-medicall engineerin engineering. g. One of  the main concerns in the applicability of glass is its brittle nature and failure under tensile stress. Over the years, researchers have understood that the structural behaviour of glass can be regulated to a large extent by controlling the residual stress in them  [1 –4] 4].. Residual Residual stresses stresses are introduced introduced in glass articles during manufacturing facturing when they are cooled from the glass transition transition temperature to the room temperature. The residual stresses affect the bending bending strength strength and fragmentati fragmentation on propertie propertiess of glass. glass. Hence, Hence, their their measur measureme ement nt and contro controll are are very very import important ant in glass glass industries. Photoelasticity is based on the phenomenon of stress/straininduced birefringence and basically provides principal stress difference and their orientations. This technique has been in use for stress measurement in glass since it exhibits stress-induced birefringence. fringence. Though birefringen birefringence ce in glass was �rst observed by Arago [5]   in 1811 811, it was Seebeck [6] who �rst performe performed d systematic studies on the birefringence in glass specimens of different shapes with different thermal treatments. Initial signi�cant contributions were made by Brewster  [7  [7,,8] 8],, who independently performed thorough investigation on the photoelastic effect in glass. The roles of Arago Arago,, Seebec Seebeck k and Brewst Brewster er on the discover discovery y of  n

Corresponding author. E-mail address:  [email protected]  (Ramesh K.).

http://dx.doi.org/10.1016/j.optlaseng.2016.03.017 0143-8166/&  2016 Elsevier Ltd. All rights reserved.

photoelastic effect in glass is detailed in Ref.  [9]  [9].. Over the years, a number number of photoelas photoelasticit ticity y based measurement measurement techniqu techniques es and commercial equipments have been developed for residual stress measurements and on-line quality inspection of glass. One of the earliest monographs [1]   on the topic appeared appeared in 1993, 993, which which gives an exhaustive discussion on the various techniques adopted till then. In 1999, Mckenzie and Hand [10] Hand  [10] surveyed  surveyed the available optical methods for glass stress analysis, which is relevant for the users of  photoelastic analysis in glass industries. The use of digital computers for photoelastic analysis was still in its infancy during that period. The advent of affordable high quality digital image acquisition sition and proce processi ssing ng syste systems ms led to the emerge emergence nce of digita digitall photoelasticity [1 [11 1–14] 14].. The recent reviews [15 [15,,16] 16]   focussed focussed on speci �c issues in the use of 2D transmission photoelasticity for retardation measurements in glass. In 2008, Aben et al.  [17]  [17] have  have brie�y reviewed the use of modern photoelastic technology for the residual stress measurement in glass articles. The last decade has seen rapid advancements in glass stress analysis using photoelasticity. A range of photoelastic techniques are available that can be used for either quick approximate estimation mation or to carry carry out out detaile detailed d studie studiess in cases cases that that demand demand accuracy of the evaluated parameters. A comprehensive review of  the techniques/methods will enable users to make an informed choice and may also aid them to develop newer techniques leading to the advanc advanceme ements nts in the topic. topic. The review review is organi organised sed thematically rather than chronologically, to facilitate easy access of  information to the user. Glass literature is aplenty with domain speci �c termin terminolo ologie gies, s, which which usually usually deters deters a generi genericc stress stress

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analyst. A brief introduction to the residual stress in glass is provided initially to bring out its tensorial nature.

2. Residual stress in glass

Usually, the residual stresses are introduced in glass plates either by thermal or chemical means. The thermal residual stresses are created during their manufacturing process when they are cooled from the glass transition temperature to the room temperature. These residual stresses affect the structural as well as the optical properties of glass. Usually for structural applications, presence of compressive residual stresses on the surface of glass is bene�cial as it improves the strength and fragmentation characteristics. Whereas, for optical applications, this is detrimental as it alters the refractive index. Hence, the measurement of residual stresses in glass articles is important. For structural applications, the minimum residual stress requirements are prescribed by ASTM [18,19]. The residual stress in glass vary from 0 to 1 MPa in moulded glass lens, 70–120 MPa in thermally tempered glass plates to as high as 1000 MPa in chemically tempered glass plates. Generally, the problems involving stress analysis of glass can be classi�ed into three –  � at glass, axi-symmetric and generic threedimensional problems. The glass literature generally labels the residual stresses in a manner that could be understood in a processing unit as thickness, membrane and edge stresses. Stress is a tensor of Rank 2 and it is desirable that these stresses are also identi �ed as suitable tensorial components. The subsequent sections provide an overview of the nature of residual stress in various glass articles.  2.1. Flat glass

Thermal residual stresses in plate glass are generally divided into two –   thickness and membrane stresses [1,2]. The thickness stresses are the stresses induced due to the thermal gradients across the thickness of the glass plates. Membrane stresses are introduced due to the thermal gradients along the surface of the plate. Membrane stresses near the edge of the glass plate is termed as edge stress. In glass literature [1,20], one would also  � nd a term surface stress which denotes the combined effect of the thickness and membrane stresses on the glass surface. Nomenclature of 

residual stress as thickness, membrane and edge stress is convenient as the reason for their formation can be identi �ed and controlled separately. Further, in measurement, the optical methods lend themselves to measure these separately. Fig. 1 illustrates the nature of residual stresses in a heat treated glass plate in typical blocks taken at selected locations. For a block at A  which is taken away from the edges, the variation of thickness stress components on  x  and  y  planes are shown. Tensorially these are σ  y and σ  x   components for the coordinate system shown in Fig. 1. Variation of  σ  x and σ  y  across the thickness of the plate is parabolic in nature with compression near the surface and tension in the central region. The maximum tensile stress is usually half  the magnitude of the surface compressive stress   [21]. The compressive stress near the surface increases the bending strength of  glass, whereas the tension in the mid-plane affects its fragmentation properties. The magnitude of thickness stress is found to depend on the cooling process  [22 –24] and the dimensions of the glass plate [25]. It is reported that the stress state is hydrostatic (σ  x E σ  y) at zones away from the edges and cut-outs  [1,2]. Membrane stresses are created due to the non-uniformity in cooling across the surface of the glass plate. They are constant throughout the thickness of the plate  [1]. Among the membrane stresses, the stresses near the edge are of interest to the glass manufacturers [21]. Block  B  (Fig.1) is taken along the edge parallel to the y-direction and the edge stress component for a typical section in the – x  plane are illustrated. Tensorially it is σ  y  and is compressive in nature. Similarly, block  C  (Fig. 1) is taken along the edge parallel to the x-direction and σ  x   is the edge stress for a typical section in the y-plane. The σ  z    component is usually neglected owing to the small thickness. Edge stresses are created since the edges of the glass plate act as additional cooling surfaces and cool down faster compared to the central region. They are generally compressive in nature and are bene�cial to arrest crack growth and improves the glass strength. Recently, Aben et al. [26,27]   reported a correlation between edge stress and surface stress in tempered glass plates. This allows one to determine one type of stress when the other is known.  2.1.1. Visualisation and measurement using photoelasticity In photoelastic measurements, only those stress components in a plane perpendicular to the light path contribute to photoelastic

Fig.1.  Schematic illustration of the nature of residual stress in a heat treated glass plate. A rectangular block A  is considered at the zone away from the edges to illustrate the nature and variation of thickness stress. Blocks  B  and  C  located at the edges illustrate the nature of edge stresses.

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Fig. 2.  Generic optical arrangement in a circular polariscope. Illustration of the typical viewing directions for measuring different types of stress (a) Thickness stress (light direction along the  x -axis) (b) Dark  � eld isochromatic fringe patterns corresponding to thickness stress in a  � oat glass slice. (c) Membrane stress (light direction along the  z axis). (d) Dark  � eld isochromatic fringe patterns corresponding to edge stress in a tempered glass plate.

Fig. 3.  Schematic illustration of the nature of residual stress in chemically strengthened glass (a) Chemically strengthened glass bar (b) Nature of residual stresses on a section of the bar (c) Dark �eld isochromatics corresponding to the bar shown in Fig. 3(a) when it is viewed such that light passes through  y -direction. The surfaces in the  x- z  plane are ground and polished to a depth of 1 mm to remove the strengthened layers. (d) Magni�ed view of the isochromatic fringes near the edge (courtesy: Ref. [30]).

effect. Fig. 2  shows the optical arrangement in a circular polariscope with two different orientations of the glass plate. The thickness stress component of  σ  y  is directly measurable by placing the glass plate such that the light passes through the width ( x– direction) of the glass (Fig. 2(a)).  Fig. 2(b) shows dark �eld isochromatics corresponding to the thickness stresses in a commercial  � oat glass slice. They appear as straight fringes with increasing gradient towards the edges. When this �oat glass slice is rotated and observed such that light passes through the z -direction, no perceivable fringes are observed since the integrated retardation is close to zero owing to the parabolic variation of the residual stress components σ  x  and  σ  y. Membrane stresses in tempered/heat strengthened glass plates can be viewed by placing the glass such that the light passes through the glass thickness ( z  –  direction) as shown in  Fig. 2(c). Fig. 2(d) shows the dark �eld isochromatic fringes near the edge of  a tempered glass plate. It can be clearly seen that the edge of the glass plate is highly stressed compared to the other regions. The fringe pattern represents integrated effect of  |σ  x-σ  y|   and at the edge of the plate, it corresponds to  σ  y. The fringe order decreases sharply with distance from the edge.

The optical information obtained using the polariscope is related to the stress values by the stress-optic law given by  [11],

σ 1  σ 2  ¼

NF σ  h

ð1Þ

where, (σ 1  σ 2 ) is the principal stress difference, N   is the fringe order, F σ  is the material stress fringe value and h  is the effective length of the light path. Hence, if one knows the fringe order and the material stress fringe value, principal stress difference can be obtained. Determination of material stress fringe value is called photoelastic calibration which is discussed in  Section 3.  2.1.2. Chemically-strengthened glass In chemically tempered glass, residual stresses are introduced by ion-exchange process where the original glasses are immersed in a molten alkali salt at temperatures below the glass transition. The alkali ions close to the surface of the glass are exchanged with those from the molten salt during the thermally activated interdiffusion process. If the ionic radius of the penetrating ions is larger than the ions leaving, then the surface of the glass is sub jected to compression [1,28–31]. Here, a zone of very high

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compressive stresses is created at the surface of the glass with a depth of less than 1 mm. Fig. 3(a)-(b) shows the schematic illustration of the nature of  residual stresses in a chemically tempered glass bar. The compressive stresses close to the edge AB in terms of stress components is only  σ  x. Fig. 3(c) shows the dark  � eld isochromatics [30] corresponding to the bar shown in Fig. 3(a) when it is viewed such that light passes through y-direction. The viewing surfaces ( x– z  plane) are ground and polished to a depth of 1 mm to remove the strengthened layers before observation.  Fig. 3(d) shows the magni�ed view of the isochromatics near the edge and it can be seen that the fringe gradient is very high close to the edge. The use of  chemically strengthened glasses are increasing due to their advantages like high surface compression, unaffected optical quality and ability of the tempering process to strengthen thin glasses of any complicated shapes.  2.2. Axi-symmetric glass articles

Z  



σ  x  σ  y dz  and  δ   sin 2θ  ¼ 2C 

3. Stress-optic coef �cient of glass  3.1. Measurement of glass stress-optic coef  �cient  ‘ C’  

Similar to the glass plates, residual stresses are also introduced in axi-symmetric glass articles like tumblers, glass cooking ware and bulbs during their manufacturing process. In articles such as tumblers, residual stresses of the order of 90 MPa are introduced for improving their strength and resistance  [32]. Though the nature of the stresses introduced is similar to the glass plates, their quanti�cation becomes quite complex and concepts of tensorial tomography are needed to interpret them. In a general three dimensional photoelastic model, the principal stress difference as well as the principal stress orientations vary along the light path. If the principal stress directions remain constant or when the birefringence is weak, the optical information can be linked to the stress distribution by integral Wertheim law [1,32], which is given by,

δ  cos 2θ  ¼ C 

tumbler. Dark �eld integrated fringe pattern in a convex lens obtained using a plane polariscope is shown in  Fig. 4(b). To record these patterns, the glass articles are immersed in a bath of  immersion liquid which has the same refractive index as that of  the glass sample. The residual stresses in the glass tumbler are intentionally introduced to improve its strength. Quanti �cation of  stresses in axi-symmetric articles is dealt in Section 4.4.1. Residual stresses in the lens affect its optical properties especially the refractive index [33]. These stresses need to be relieved by careful control of the annealing process. However, optimisation of the total time period is also gaining importance in precision moulding of glass lens. Use of birefringence measurement for improved numerical modelling is discussed in  Section 5.

Z 

τ  xy dz 

ð2Þ

where light propagates in the z -direction, C   is the stress-optic coef �cient (C ¼ λ/F σ ), σ  x, σ  y and τ  xy   are the components of the stress tensor and  λ  is the wavelength of light. Eq. (2) is valid if  δ  is less than approximately ¼   of the wavelength and the angle of  rotation of the principal stress directions is less than π/6. In the case of axial symmetry,  δ   should be less than ¾  of the wavelength [1]. This equation �nds use in several techniques for glass stress measurement. Fig. 4(a) shows the magni�ed view of dark �eld integrated photoelastic fringe patterns in a section of the wall of a glass

Unlike in conventional photoelasticity where material stress fringe value (F σ , N/mm/fringe) is widely used for quantifying the photoelastic behaviour; in glass literature [1,34–45] one �nds the use of photoelastic constant  C   (TPa  1). For most glasses, the value of  C  lies in the range of 2 –4 TPa  1 [1] whereas for commonly used photoelastic materials like epoxy it is in the order of 50 TPa  1. Hence, the birefringence in glass is weak and its accurate determination poses a challenge. Early methods for the determination of photoelastic constant (usually called photoelastic calibration) are detailed in Ref  [1]. Calibration is performed on simple specimens with known stress state. The standard test method for measuring the stress-optic coef �cient of glass using conventional photoelasticity is detailed in Ref.   [34]. The specimens used in general are glass �bre under tension [34,35], four point bending [34,36–38], concentrated force at a point [1,39], uni-axial tension/compression [40–44] and cylinder/disc under diametral compression [45,46]. Considering the easiness of specimen preparation and accuracy of loading, the use of beam under four point bending is preferable.  Table 1  lists the various approaches used for the calibration of glass. Early methods involved the use of compensators for point by point retardation measurements  [34,38,40–43]. Recently, Ramesh et al.   [36]  have explored the use of recent advances in digital photoelasticity for the photoelastic calibration of glass. They used a beam specimen and recommended the use of phase shifting for accurate estimation of  C   and carrier fringe method for quick

Fig. 4.   Dark  � eld isochromatics: (a) Section of a glass tumbler recorded in monochromatic light and (b) convex lens recorded in a plane polariscope under white light.

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 Table 1 Methods for photoelastic calibration of glass reported in literature.

Fig. 5.  (a) Dark  � eld isochromatics in glass beam free of residual stress under no-load. Composite fringes obtained by the superposition of glass and the carrier under (b) noload (c) loaded condition. (d) Dark  � eld isochromatics in a commercially  � oat lass beam under no-load. Composite fringes obtained by the superposition of glass and the carrier under: (e) no-load (f) loaded condition.

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calibration applications. In both approaches, the emphasis was on the use of whole  � eld data for accurate measurement. Usual methods for calibration demand glass samples free of any residual stresses. If the sample has residual stress, it has to be removed by a carefully controlled annealing cycle which is timeconsuming in an industrial scenario. Further, it is also reported [48] that the photoelastic constant value of glass depends even on the thermal history. Fontana [48] found that the stress optic coef �cient of annealed soda lime glass is lower than that of un-annealed glass. Hence, it is desirable to develop methods that can be used to calibrate glass with residual stress. In 2010, Nielsen et al.  [49,50] used a scattered light polariscope, SCALP, to calibrate tempered glass plate by measuring the surface stress change on loading. Vivek and Ramesh [37] improved the method of carrier fringes in Ref. [36] to calibrate  � oat glass with residual stress. It would be of interest to see how the fringe patterns differ in a specimen with residual stress compared to a stress free specimen.   Fig. 5(a)– (c) shows the photoelastic fringe pattern in the glass and the composite fringes obtained by the superposition of glass and carrier. When the glass beam is loaded, the composite fringes rotate (Fig. 5(c)). This deviation from the vertical is used for the determination of retardation. Fig. 5(d)–(f) shows the photoelastic fringe pattern in a �oat glass with residual stress and the composite fringes obtained by the superposition of glass and carrier. The deviation of the composite fringes shown in  Fig. 5(f) with respect to the ones shown in  Fig. 5(e) is used to determine the photoelastic constant. Mathematical details used for the estimation can be found in Refs.  [36,37].

to choose the composition of oxide glass so as to minimise  C . Using this correlation, Guignard and Zwanziger   [56]   have found that barium tellurite glasses also exhibit zero stress-optic behaviour. Recently, Galbraith and Zwanziger [57] proposed a new composition of barium and lead phosphates to develop glass whose stressoptic response is non-dispersive over the optical range. Their results suggest that with appropriate glass compositions, the stress optic response can be controlled over a range of wavelengths. For optical glasses with very low photoelastic constant ( o 0.1 TPa  1), Tarkes and Ramesh  [39] proposed the use of concentrated force acting on an edge of glass in conjunction with phase shifting for photoelastic calibration.

 3.2. In �uence of glass composition on stress-optic coef  �cient C 

4.1.1. Compensation techniques Compensation techniques may either involve an additional birefringent plate (called compensator or tint plates) to augment the total retardation or use the optical elements in the polariscope itself. External compensators are designed such that their effective thickness can be varied thereby varying the retardation. The commonly used compensators are wedge, polythene square, Babinet-soleil compensators, standard strain discs and Berek compensators [10]. Compensators have been used conventionally for qualitative analysis of residual stress in glass or to determine the retardation at a point. Standard strain discs and tint plates can be used to assess the retardation in the glass by comparing colours using a standard chart. Birefringent wedges, polyurethane square and tint plate can also be used for determination of the sign of  stress near the edge of the glass plate.

The value of the photoelastic constant depends on the composition of glass. The in�uence of the composition on its photoelastic constant was �rst studied by Pockels  [51] who studied the effect of lead oxide content in �int glass. They concluded that as the percentage of lead oxide increases, the photoelastic constant decreases. It was found that as the percentage content of PbO reaches about 75%, the photoelastic constant approaches zero (C ¼ 0) and beyond this it behaves like a negative crystal ( C o 0). The in�uence of additives on the properties of silica, borate and phosphate based glasses have been extensively discussed in the glass literature [1,42–45,52–54]   but the studies on �uoride and chalcogenide glasses [40,41]  are few. Photoelastic behaviour of  borosilicate glasses was studied by Filon  [52], who found that C  increase with the addition of boric oxide whereas it decreases with increase in the percentage of potassium oxide. It is reported that common oxide glass formers (SiO2, B2O3  and P2O5) have positive values of  C   and the addition of alkali and alkaline earth oxides lowers it to some extent [1]. But the addition of oxides such as PbO, Bi 2O3  and Tl 2O can lower it to zero or even negative. Balmforth and Holland [53] found that replacing soda by lime resulted in small but signi�cant increase in the stress-optical coef �cient. Matusita et al.   [54]  studied the photoelastic constants of borate glasses and found that Boron trioxide B 2O3  glass has a very high stress-optical coef �cient of 11 TPa1 and lead oxide-boron trioxide PbO-B2O3  glass has a stress –optical coef �cient of zero. Recently, there is considerable focus on developing zero stressoptic glasses which, as the name implies, exhibit zero birefringence even in the presence of applied stress. Applications of such glasses include optical instrumentation and projection systems. Owing to environmental regulations, the conventional use of lead has now decreased and there have been studies to understand and develop alternate materials to form zero stress-optic glasses. Guignard et al. [42,55]  discovered a correlation between stressinduced birefringence and the ratio of metal oxygen bond metallicity to the metal coordination number. This provides a criterion

4. Methods for photoelastic parameter evaluation in glass

The range of birefringence levels that one encounters in glass applications is wide. Retardations may vary from 0.01 fringe order in optical lens, close to 2 fringes in thermally tempered glass plates to more than 15 fringes in chemically tempered glass. Hence, the methods adopted for retardation measurement is dependent on the problem at hand. In order to make reliable measurements in cases where the retardation is low, various methods of augmenting the basic information are usually employed. With modern developments in phase shifting, it is also possible to measure very low retardations directly, provided high quality optical elements are used. 4.1. Transmission photoelasticity

4.1.2. Carrier fringe method The use of carrier fringes in photoelasticity was  � rst introduced by Rupeng [58]. They are usually used to amplify the retardation in the model when it is low for measurement and this aspect has been used for analysing glass as it is weakly birefringent. Usually used carrier specimens are beam under four point bending, Cshaped specimen under tension or a tensile specimen subjected to eccentric loading. Early methods used carrier fringes as compensators for point by point measurement as discussed in   Section 4.1.1. Recently, Ajovalasit et al. [59] have shown that the method of  carrier fringes could be used for automated measurements of  residual retardation near the edge of a tempered glass plate. Retardation measurement is based on the principle that the intensity of light depends only on the retardation when the carrier and glass plate are oriented in such a way that their principal stress directions are perpendicular/parallel to each other. The novelty in their work is that the measurement of retardation is simpli�ed into the measurement of spatial deviation of the composite fringe pattern with respect to the reference carrier fringes. Naveen et al. [60] made observations that retardation obtained from this method is dependent on the carrier fringe density and

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Fig. 6.  Composite fringe obtained by the superposition of the glass and the carrier. (a) Edge Stress in tempered glass (b) Magni �ed image showing the deviation of composite fringes (c) Thickness stress in  � oat glass (d) Magni�ed image showing the deviation of composite fringes. Skeletons of the composite fringes are also shown in (b) and (d).

suggested the use of a high density carrier.   Fig. 6(a) shows the composite fringes obtained by the superposition of the tempered glass and the carrier. If the principal stresses in the carrier and the glass plate are mutually perpendicular to each other, the retardation in the glass can be given by, N  g ð xÞ ¼

j y  yi j

 p

ð3Þ

ei  ¼

where, p  is the pitch of the carrier, ( y  yi ) gives the deviation in the carrier (Fig. 6(b)). Retardation measurement using carrier fringes involves the identi�cation of the composite fringe corresponding to the reference carrier fringe. This can be dif �cult at higher carrier fringe density using monochromatic light. Vivek and Ramesh  [61] have devised a method for fringe identi�cation under such circumstances based on the fact the fringe orders are less than 0.5 away from the edge. This will aid automated edge stress measurement. Measurement of  thickness stresses in commercial  � oat glass has also been achieved using the carrier fringe method  [62]. Fig. 6(c) shows the composite fringes obtained by the superposition of a slice of  � oat glass and the carrier. It is interesting to note that after the superposition of the glass and the carrier, the composite fringe pattern is parabolic and resembles the stress variation in glass. Hence, it is possible for one to use this qualitatively for residual stress visualisation as well as for quick estimation [1,62]. However, this method could be used only when the residual retardation in the model is constant in the direction perpendicular to the carrier fringes. A technique for identi�cation of the composite fringe and the corresponding carrier fringes for thickness stress measurement was also developed for cases where identi�cation of corresponding fringes is dif �cult [62]. 4.1.3. Three fringe photoelasticity(TFP)/RGB photoelasticity TFP/RGB Photoelasticity [63–65]   involves the use of a single colour image recorded using white light for fringe order estimation. This technique is useful especially in situations where multiple acquisitions are dif �cult. Fringe order at any point on the photoelastic model is obtained by comparing the colour components at that point with those in a calibration table. The most direct method is to calculate the least squares error term ( ei) for each row  i  in the calibration table using the colour difference formula and identify the fringe order corresponding to the minimum value of  ei using the following colour difference equation [63], ei  ¼

q  ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi

ðR  Ri Þ2 þð G  Gi Þ2 þð B  Bi Þ2

where R, G and B   represent the red, green and blue colour components. The use of Eq.  (4) leads to false estimation of fringe order at some locations due to the repetition of colours and hence, the spatial continuity of  N   is lost. This can be eliminated by incorporating fringe order continuity using modi�ed window search method given by [66,67].

ð4Þ

q  ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi

ðR  Ri Þ2 þð G  Gi Þ2 þð B  Bi Þ2 ; N A N  p  ΔN  N  p þ ΔN 



;



ð5Þ

where, ΔN   is 0.4. The average value of the fringe orders of all the neighbouring resolved pixels is used as  N  p  in Eq. (5). Re�ning process is started from points that are correctly resolved during the least squares stage itself and are usually called seed points. Although TFP is now extended to higher fringe orders [66,68], as the retardation levels are low in glass, resolving three fringe orders itself is suf �cient. Ajovalavit et al.   [69]   have demonstrated the use of TFP/RGB photoelasticity for membrane stress measurement in tempered glass plate. They proposed the use of another glass plate with higher retardation for colour code generation (called self-cal). This approach however, requires phase shifting for measuring the retardation in the glass specimen used for calibration. They also concluded that for commonly used glasses that exhibit normal dispersion of birefringence, colour code generated using a polycarbonate specimen in conjunction with colour adaptation  [70,71] gives good results for fringe orders less than 3. The accuracy of fringe order results can be improved by the use of a tint plate superimposed with the glass [72]. Tint plate used is a tensile plate having a uniform retardation of 1 fringe order. The accuracy is enhanced in zones where the retardation in the glass is less than 0.5 fringe orders. However, the method is dependent on the alignment of the principal stress directions in the glass and the tint plate. To retain the advantage of the tint plate method, this misalignment should not be greater than 15°. 4.1.4. Phase-shifting techniques Phase shifting is a technique in which speci �c phase shifts are introduced by rotating the optical elements of the polariscope, which results in the modulation in the phase information over the domain. This is captured as intensity variation in the digitally acquired images. Among the various phase shifting techniques, the ten-step phase shifting has demonstrated its capability to obtain photoelastic parameters of high accuracy for a variety of problems [73,74]. The ten-step phase shifting method intelligently combines

Ramesh K., V. Ramakrishnan / Optics and Lasers in Engineering 87 (2016) 59 –74

66

a four-step plane polariscope approach for isoclinic data evaluation and a six-step circular polariscope based method for isochromatics data evaluation.   Table 2   shows the optical arrangements of the ten-step phase shifting technique and the corresponding intensity equations. These optical arrangements are carefully selected to minimise the in�uence of quarter-wave plate mismatch error. In Table 2,  α  and  β  refer to the orientation of the polarizer and analyser,  ξ  and  η  refer to the orientation of the slow axis of the  � rst and second quarter wave plates respectively.  I a and I b represents the amplitude of light and background light intensity respectively. Phase retardation and the principal stress direction in the model are represented as  δ  and  θ . The isoclinic angle and the retardation are given by [73],

θ c  ¼  tan   1

I  I  

δ c  ¼  tan   1

 I 

4  2

ð6Þ

I 3  I 1

ð 9  I 7 Þ sin 2θ c þð I 8  I 10 Þ cos 2θ c ðI 5  I 6 Þ



ð7Þ

 Table 2 Optical arrangement for ten-step PST and corresponding intensity equations. α 

ξ

η

β 

Intensity equation

1

π /2

–

–

0

2

5π  / 8

–

–

π /8

3

3π /4

–

–

π /4

4

7π  / 8

–

–

3π /8

5

π /2

3π /4

π /4

π /2

6

π /2

3π /4

π /4

0

7

π /2

3π /4

0

0

8

π /2

3π /4

π /4

π /4

9

π /2

π /4

0

0

10

π /2

π /4

3π /4

π /4

2 δ  2 2 sin 2θ  2 I 2  ¼ I b þ I 2a sin 2δ ½ 1    sin 4θ  I 3  ¼ I b þ I a sin 2 2δ  cos 2 2θ  2 I 4  ¼ I b þ I 2a sin 2δ ½ 1 þ   sin 4θ  I 5  ¼ I b þ I 2a ð1 þ cos δ Þ I 6  ¼ I b þ I 2a ð1  cos δ Þ I 7  ¼ I b þ I 2a ð1    sin 2θ  sin δ Þ I 8  ¼ I b þ I 2a ð1 þ   cos 2 θ  sin δ Þ I 9  ¼ I b þ I 2a ð1 þ   sin 2θ  sin δ Þ I 10  ¼ I b þ I 2a ð1    cos 2 θ  sin δ Þ

Step

I 1  ¼ I b þ I a sin

One of the key aspects of the ten-step method is to use unwrapped theta values in the calculation of the fractional retardation i.e., theta values obtained from Eq.  (6)  is unwrapped using suitable unwrapping methodology and this unwrapped theta is used to calculate the fractional retardation using Eq. (7). Several other phase shifting methods reported are a subset of this. For instance, the last six arrangements in  Table 2   correspond to the six-step phase shifting technique [75,76]. Aben et. al.   [77]  have proposed a method to determine the direction of  �rst principal stress uniquely using six-step phase shifting provided the retardations are less than half the wavelength. Four step methods  [78 –81] were also proposed by researchers to evaluate the photoelastic parameters. Since, the orientation of  principal stresses near the boundary of glass plate is known, Ajovalasit et al. [82] used Tardy's and Senarmont's phase shifting with three images, for automated measurement of edge residual stress in tempered glass plates. Tardy's method correspond to the steps 5, 6 and 8 of the ten-step method shown in  Table 2. Senarmont phase shifting employs a slightly different optical arrangement as it does not use the �rst quarterwave plate. They have reported that if the quarter wave plate error is zero, Tardy's phase shifting method is more precise than Senarmont phase shifting. Fig. 7(a)–(j) shows the ten phase shifted images of a tempered glass plate. Fig. 7(k) shows the isochromatics results obtained by post processing these images using Eqs. (6) and (7). The fringe order steadily increases towards the edge and the maximum value being 1.3. Since the edge of the tempered glass plate is chamfered, the fringe order at the edge can be obtained by appropriate extrapolation techniques [18]. Fig. 7(l) shows the isoclinic values in the glass plate as a binary representation in steps of 10°. A Grey �eld polariscope (GFP) has been developed for automated measurement of retardation using photoelasticity  [83 –85]. The  � rst version of GFP is essentially a circular polariscope without the second quarter wave plate. The analyser is rotated continuously and a large number of images (  8) are captured. By post

Fig. 7. (a)–(j) Ten-step phase shifted images of a tempered glass plate corresponding to the arrangements in   Table 2  (k) whole (l) binary representation of isoclinics in steps of 10 °.

�eld

isochromatic fringe order results

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processing the captured images, both retardation as well as the isoclinic parameter are evaluated. The use of grey  � eld polariscope for the measurement of residual stress in glass has been demonstrated in Ref. [83,84]. Fig. 8 shows the image of a toughened glass plate depicting the fringe patterns, obtained using GFP. The sensitivity of GFP is claimed to be 7 0.002 fringes. However, the need for multiple images makes it unsuited for dynamic applications. In 2004, Lesniak et al.   [86]   developed a novel polariscope, christened as poleidoscope, by combining a polariscope and a kaleidoscope. It consists of an objective lens produced by sectioning conventional convex lens into quadrants followed by different sets of optical elements for each quadrant. This enables simultaneous acquisition of four phase shifted images for

Fig. 8.   Toughened glass image obtained using GFP (Courtesy: Ref.  [83]).

67

photoelastic parameter evaluation. Simultaneous acquisition of  images makes it suitable for real time stress inspection in glass industries [83]. These four steps are equivalent to steps 6, 7, 9 and 10 of the ten-step method with a difference that it uses circularly polarised light of single handedness only. Hence, the accuracy of  this four step phase shifting method is sensitive to the quarter wave plate errors [76] and demands use of high quality elements. 4.2. Scattered light photoelastic method

Scattered light photoelasticity [87–89]   is used for threedimensional stress analysis of a model by optical slicing. The intensity of the scattered light is generally weak and is directly proportional to the square of the amplitude obtained by projecting the light ellipse in a plane perpendicular to the direction of observation. In the scattered light photoelastic technique, the primary beam may be unpolarised, plane polarised or elliptically polarised  [1]. The �rst successful attempt to use scattered light photoelasticity for stress measurement in glass was by Bateson et al.  [90] who used a He –Ne laser light of 633 nm wavelength. The extreme parallelism and coherence of the laser light beam improved the de�nition of the fringes and in turn the accuracy of measurement, compared to conventional light sources. Bradshaw [91] proposed a method for determining stress pro �les in thin specimens of chemically tempered glass by progressively etching the surface compressive layer and measuring the change in the magnitude of the centre tensile stress using scattered light technique. Several authors have also developed scattered light polariscopes for stress measurement in �at glass [92–94]. However, all these methods/ equipments developed were bulky and were suitable only for laboratory measurements.

Fig. 9.   (a) Three dimensional illustration of the scattered light polariscope. Faint red lines in the monitor depicts the tracked light path. (b), (c) Schematic optical arrangement of the portable scattered light polariscope. (adapted from  [96]).

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A major stride in the industrial applicability of scattered light photoelasticity for glass stress measurements was brought about by Aben et al. [17,95]. They developed a portable scattered light polariscope for measuring the stress pro �le across the thickness of  glass specimens. Optical measurement scheme of the portable scattered light polariscope (SCALP) is shown in  Fig. 9(a). A laser beam is passed through the glass panel being tested, at an angle  α  (Fig. 9(b)). The intensity of the scattered light along the laser beam is recorded with a CCD camera. The camera is placed in such a way that the direction of observation is perpendicular to the plane of  incidence (Fig. 9). The software module incorporates a light path detection algorithm to track the laser beam inside the glass. The use of oblique light incidence can lead to the refraction of light from the glass surface. This is eliminated by the use of suitable contact liquid and a compact glass prism, which is elegantly designed to eliminate refraction of incident as well as the scattered light beams. All these components are embedded in the polariscope in a compact manner which makes is portable and can even be used as a handy probe for stress measurement in glass. The retardation in the laser beam as it passes through the glass plate, assuming plane stress condition, is governed by the integral Wertheim law (Eq.  (2)) [96,97]. If the residual stress state is isotropic (σ  x ¼ σ y) then a single measurement is suf �cient and the residual stress is given by  [96],

σ ðh0 Þ ¼

δ 0h C sin 2 α 

ð8Þ

where, h0 is the length of the light path, C   is the stress-optic coef �cient of glass, δ   is the optical retardation in ‘nm’ and 0 δ 0h ¼  dδ dhðh0 Þ. If  σ x a σ y, one needs to make two orthogonal measurements at each point. Then, the individual stress components can be computed by [96],

σ  x  ¼

δ 02 þ δ 01 cos 2 α  δ 01 þ δ 02 cos 2 α  σ  and  ¼  y C ð1  cos 4 α Þ C ð1  cos 4 α Þ

ð9Þ

where δ 1  and  δ 2  are the optical retardations measured by placing 0 0 0 1 ðh Þ 2 ðh Þ  δ 02 ¼  dδ dh SCALP along  x  and  y  axes.  δ 1  ¼  dδ dh 0 0 . The scattered light polariscope gives accurate results for �oat glass whose refractive index is close to 1.5. For glass samples of  higher refractive indices, improved light path detection algorithms are used owing to the refraction of the light beam. Scattered light polariscope is now being widely used for testing and research. Nielsen et al.   [49] have used it to characterise the stress state in commercially toughened glass. They have found that the residual stress in tempered glass is highly non-uniform, with a variation in the surface stress as high as 35 MPa in 19 mm glass specimens. Soulie et. al  [97] have studied the nature of residual stresses in tempered glass discs of thickness 4.9 mm used in optical industry. Chen et al. [23] and Anton et al. [98] have studied the in�uence of process parameters on the isotropy in tempered glass and stress inhomogeneity respectively. In 2014, Zaccaria and Overend  [99]  have studied the mechanical performance of chemically and thermally treated (bi-treated) glass. Vivek and Ramesh [100]   studied the in �uence of thermal cycling on the residual stress generated in rectangular glass specimens. Recently, Castellini et al. [101] have explored the use of laser sheet scattered light method for on-line monitoring of throughthe-thickness residual stress in tempered glass. This method is non-contact and does not require a glass prism and contact liquid since the laser sheet is introduced through the edge of the glass plate. However, this method cannot be applied in cases where the edges are not optically transparent due to prior machining. In 2015, Hodemann et al [102] have introduced a micron-scale confocal scattered light photoelastic method for the measurement of  stress pro �le in chemically strengthened glass panels. This method ;

Fig. 10.   Optical arrangement in a grazing angle surface polariscope (GASP) (Courtesy: Ref. [105]).

gives a very high spatial resolution, however, it requires lapping and polishing of one edge of the glass plate. 4.3. Surface guided wave methods

Guided wave photoelastic methods have been developed for the measurement of stress at the surface of glass. There are different methods to measure surface stresses in homogeneous glasses and strati�ed glasses. Differential refractometry is used to determine the surface stress in homogeneous glasses and initial developments were proposed by Guillemet and Acloque   [103]   and Kishii   [104]. For strati�ed glasses, surface wave guided methods (also called Mirage methods) were proposed. Here polarised light is guided through the surface of the glass using prism of high refractive index. The gradient of the refractive index causes the resurgence of the rays out of the panel. Polarisation of the output light depends on the distance travelled and the stress on the glass surface. An apparatus based on this method is called Epibiascope  [103]. The commercially available grazing angle surface polariscope (GASP) also works on a similar principle [21,105]. The set-up is designed such that light is incident on the prism at the critical angle, which on entering the glass plate, travels through its surface (Fig. 10). A Babinet compensator is placed near the eye piece of the polariscope. The tilt in the fringes (similar to the one in  Fig. 5(c)) can be linked to the surface stress values through a chart provided by the manufacturer. However, this cannot be used for chemically strengthened or patterned glass. 4.4. Integrated photoelasticity

Integrated photoelasticity is used for the measurement of  stresses in glass articles of complicated shapes having complex stress distributions [1,17,106–119]. The model is immersed in an immersion liquid and polarised beam of light is passed through it. The use of integrated fringe pattern to determine the stresses in three-dimensional specimens was �rst proposed by Neumann [106]. Integrated photoelasticity is tensor �eld tomography in which the unknown quantity at each point is a tensor of rank two, thus making the problem much more complicated. The propagation of polarised light through a three dimensional inhomogeneous birefringent medium is a function of the stress distribution between the point of entrance and the point of exit. In generic cases, both principal stress differences and their orientations can vary in a general way which makes the problem complex. In integrated photoleasticity, one experimentally measures three parameters along the light path labelled as  θ ,  δ  and  γ . These are termed as characteristic parameters which represent the parameters of an optically equivalent model consisting of a retarder (θ ,  δ ) and a rotator ( γ )[107]. The quantities that represent the stress �eld in the model are then obtained from these characteristic parameters, from multiple measurements along different light paths, by using the concept of inverse Radon transform  [108,109].

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Fig. 11.  (a) Illustration of the formation of integrated fringe pattern in an axi-symmetric tempered glass tumbler, (b) dark � eld isochromatics and (c) axial stress  σ  z  obtained by the method elaborated in Section 4.4.1.

4.4.1. Axi-symmetric stress distribution If the problem is axi-symmetric, then the tensor �eld tomography can be reduced to scalar  � eld tomography for determining a single component of the stress tensor �eld. The axi-symmetric 3D specimen is investigated in an immersion bath and measurements of the isoclinics  θ  and optical retardation  δ  are to be performed in two parallel sections along the axis of the axisymmetric specimen at a small distance Δ z    apart   [111]. By applying Integral Wertheim law for the two parallel sections and by using equations of equilibrium the axial stress (along z-direction) is obtained as [109],

Z   A

C 

σ  z dy0 ¼

1 C ð Δ z Þ

Z  l

B

V 02 dx0 

Z  l

B



V 2 dx0 

V 1 C 

ð10Þ

where V 2  and V 02  represent the variables  δ cos2θ   for the main and the auxiliary sections respectively and V 1  represent δ sin2θ   in Eq. (2). A and C  represents the points of entrance and exit of a light beam in any direction y0 .  l  and  B  represent the radial distance of the light beam and the edge of the specimen from the  z -axis along  x 0 . The component of stress  σ  z  and its distribution can be determined by Radon–inversion techniques [114,115]. Similarly, if the specimen can be rotated during measurements around different axes, distribution of all the normal stresses ( σ  x  and  σ  y) can be determined. If a specimen of any arbitrary cross-section is of prismatic form and has no stress gradient in the direction of its axis  z , then in Eq. (10) one has V 2  ¼ V 02  ¼ 0 and the distribution of  σ  z  can be determined on the basis of photoelastic measurements in a single section. In addition, knowledge that the stress distribution is parabolic is used advantageously in devising the algorithm.  Fig. 11 (a) shows the formation of integrated fringe pattern in a tempered glass tumbler. As light travels through the tumbler, it accumulates retardations, which are recorded as fringe patterns for a small section in the  z -direction as shown in Fig. 11(b). The axial stresses determined using appropriate algorithms [17,109]   is shown in Fig. 11(c). The value of compressive stress on the surface is 100 MPa. These stress measurements are sensitive to the immersion �uid used and to limit the error in surface stress measurements below 5%, one has to use immersion �uids of precision of  about 0.001 in matching the refractive index  [116]. Integrated

photoelasticity have been used for the measurement of residual stress in glass articles like glass tumblers, bottles, CRT glass bulbs and high pressure lamps  [17,110,116,117]. In some problems, the linear approximation of the photoelastic tomography is not valid. An example being the residual stress measurement in glass articles of complicated shapes. Aben and Errapart  [118] have proposed a non-linear method of photoelastic tomography using differential evolution algorithm for measurement under such circumstances. In cases, where the stress distributions are non-axisymmetric residual stress measurement can be carried out using a combination of integrated photoelasticity, scattered light method and surface stress measurement   [119]. Aben et al.   [109]   illustrated that a tomographic method can be elaborated for the measurement of  three-dimensional stress  � eld in glass of any arbitrary shape, based on the linearised solution of equations of integrated photoelasticity. 4.4.2. Peculiarities in inhomogeneous birefringent models Aben et al. [120,121] reported the presence of peculiarities in the integrated fringe pattern in inhomogeneous birefringent models. The appearance of these peculiarities (called interference blots) can be attributed to the rotation of the principal birefringence axes. Because of this, the optical retardation cannot take all the values between 0 and π , which causes blurring or even complete disappearance of fringes, making their ordering ambiguous. These interference blots can be seen in the integrated fringe pattern near the wall-to-bottom region of a tempered glass tumbler  [121]. 4.5. Other photoelastic methods

Apart from the conventional transmission arrangements, there have also been attempts to explore other techniques for glass stress measurements. Tomlinson et al.  [122] have used a range of  photoelastic methods including re�ection photoelasticity and magneto-photoelasticity to study the spontaneous fracture of  automotive glass. The stress distribution in the automotive glass under load was measured using a birefringent coating in con junction with a grey  � eld polariscope.

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Ramesh K., V. Ramakrishnan / Optics and Lasers in Engineering 87 (2016) 59 –74

The use of magneto-photoelasticity to evaluate the stressdistribution along the light path in three-dimensional models was �rst proposed by Aben   [123]. The conventional transmission arrangement along with a magnetic �eld in the direction of light propagation yields information about the stress distribution along the light path. This technique is useful especially in cases where the integrated retardation is zero or close to zero eventhough the stresses are non-zero. In 1998, Clarke et al.  [124] adapted magnetophotoelastic technique for measuring the residual stress in toughened glass plates. Tomlinson et. al.   [125,126]   have developed a pulsed magneto-polariscope, which is capable of data acquisition in continuously varying magnetic �elds. They used this set-up to determine unique set of three characteristic parameters for each �eld strength in thermally toughened glass discs  [127]. This approach is particularly useful to characterize the stress distribution in regions where parabolic assumption of the thickness stress is insuf �cient. Recently, Sung et al.   [128]   have proposed a method called Transmissivity Extremities Theory of Photoelasticity (TEToP) by integrating white light photoelasticity and spectrometry. In this method, initially, a systematic relationship of transmissivity with stress and wavelength is established and then a stress quantifying formula is derived. The use of TEToP to measure stress in low

birefringence materials is demonstrated by performing experiments on a thin glass substrate used for liquid crystal display.

5. Birefringence measurement for optical glass moulding 

Conventionally photoelasticity has been used to validate the results obtained from numerical simulation of the manufacturing processes of glass articles especially the tempering of glass [22,129–131]. Owing to the increase in demand of optical lens, there has been considerable focus recently on the studies on optical glass moulding. Chen et al.   [132]   have validated the numerical simulation of glass moulding process by measuring the birefringence in thin slices from the moulded lenses. Similarly, Yi et al. [133] have compared the integrated birefringence values in a moulded glass lens. In 2014, Tao et al.  [134] have used the whole �eld measurement capability of digital photoelasticity to validate the numerical simulation of aspherical moulding of lens. Ramesh and Tarkes  [135]  customised the commercially available glass polariscope (AP-07) for residual stress measurement in glass lens. The optical arrangement of the modi�ed set-up is shown in Fig. 12(a), which facilitates easy placement of lens in an immersion bath.   Fig. 12(b) and (c) shows the integrated

Fig.12.  (a) Schematic arrangement of the customized set-up for residual stress analysis in lens by modifying automatic polariscope AP- 07. Integrated retardation in optical lens made using (b) Isothermal glass moulding (c) Non-isothermal glass moulding process. (d) –   (f) Numerically simulated birefringence values for different heat transfer parameters for a  � ow rate of 50 L/min in glass disks. (g) Experimentally measured retardation. (Courtesy: Ref. [136]).

Ramesh K., V. Ramakrishnan / Optics and Lasers in Engineering 87 (2016) 59 –74

retardation in optical lens manufactured by isothermal and nonisothermal glass moulding processes respectively measured using the set-up in Fig. 12(a). It is interesting to note that the retardation distribution is axi-symmetric in the former whereas it is non axisymmetric in the latter. This is a very useful information to select appropriate numerical model for simulation. Modelling of isothermal process is simple as axi-symmetric model can be used. Recently, Tarkes Dora et al.   [136]  have proposed digital photoelasticity assisted numerical simulation approach for determining process parameters required for numerical simulation of precision glass moulding. Heat transfer mechanism in such problems is complex and it is dif �cult to determine the equivalent heat transfer coef �cients, which is essential for numerical simulation. Hitherto, these values are usually assumed. The novelty in their work is that, they used integrated birefringence measured using digital photoelasticity to arrive at the thermal boundary condition values. In numerical simulation, the equivalent heat transfer coef �cient is varied (Fig. 12(d)–(f)) till the integrated retardation matches with experimental values (Fig. 12(g)). It can be seen that the numerical and experimental results match closely using the heat transfer coef �cient of  h eqv ¼ 18 W/(m2K).

6. Conclusions and future directions

Digital photoelasticity has now matured for evaluating photoelastic parameters over the entire model domain with a considerable level of accuracy. Various methods used for the retardation measurement in glass have been surveyed in this paper with a focus on the work done in the last decade. Since the range of retardations to be measured in glass is wide, several techniques have been adopted, depending on the problem. Early methods involving point to point methods are now being replaced by digital photoelastic methods. The accuracy of the stress measurement using photoelasticity depends on the accuracy of the measured photoelastic constant. This is now enhanced by the use of recent advances in digital photoelasticity. Among the various transmission photoelastic techniques, the use of phase shifting technique (PST), where it is applicable serves as a benchmark technique as it gives accurate results. Single acquisition based techniques using carrier fringes and white light based TFP/RGB photoelasticity have also been used. A major stride in the use of scattered light photoelasticity was brought about by the development of compact scattered light polariscope which is now

71

used for testing and research. Surface guided waves have also been used for the determination of surface stress in  � at glass. Simpli�cation of the complicated problem of tensorial �eld tomography to scalar  � eld tomography has made the use of integrated photoelasticity convenient for stress measurement in axisymmetric glassware. Several researchers have also explored the use of magneto-photoelasticity and hybrid method like TEToP for stress measurement in glass. Over the years several commercial equipments have been made for glass stress measurement using digital photoelasticity. A summary of these is given in  Appendix A. With the recent advances in digital photoelasticity, it is expected that more challenging problems in glass will be solved in the years to come. Development of zero stress-optic glasses is important for optical applications. Birefringence measurements in precision lens moulding can have a greater impact on the development of better models for numerical simulation. The problem of nickel sulphide (NiS) inclusions has been there for a long time. Optical techniques like photoelasticity can be used for monitoring the delayed phase transformation in NiS inclusions, thus eliminating the chances of  catastrophic failure. The use of bolted glass connections have also been increasing for façade applications. Digital photoelasticity has the potential to enhance the understanding of structural behaviour of glass especially near the bolted joints and holes which will de�nitely pave the way for ef �cient concepts and designs.

 Appendix A   A.1 Commercial equipments for glass stress measurement 

Equipments for the measurement of the stresses in glass have been developed right from the 1950s. With time, several equipments have been developed for laboratory measurements as well as for on-line monitoring of stress in glass [137–140]. Most of primitive devices have now been replaced by modern equipments that used advanced hardware and processing softwares. Table A.1 shows a list of prominent modern devices, their manufacturers and suitability. A polariscope called  Grazing Angle Surface Polariscope (GASP)  has been developed by Strainoptics Inc.   [105]   for measuring the surface stresses in the glass plate (Fig. 10). The use of GASP is restricted to �at or almost  � at (radius of curvature 4 200 mm) surfaces. The use of the commercially available   Grey Field Polariscope  (GFP) for stress measurement in glass is discussed in  Section 4.1.4.

 Table A.1 Commercial equipments for glass stress inspection/measurement.

SI

Equipment

Manufacturer

Methodology

Suitability

AP-07 SCALP Edge stress metre Edge Master Lam maste r GFP GES/PES Edge stress metre DIAS 1600 GASP Stress scanner Strainviewer CSG 100 polarising microscope 13. Surface stress metre

GlasStress Ltd GlasStress Ltd Sharples Stressphotonics Str essph ot onics Stressphotonics Strainoptics Strainoptics Strainoptics Strainoptics Strainoptics Strainoptics

Phase shifting Scattered light method Senarmont compensation Phase shifting - poleidoscope Phase sh if ting - poleidoscope Phase shifting - poleidoscope Spectral content analysis

Luceo

Refractometry

14. Straineye

Luceo

15. St rainm atic

Ilis g mbh .

Rotating analyser/Senarmont/sensitive colour methods Sen ar mont phase shif tin g

Stress in panels/axi-symmetric articles [17,26,27,32,36,117,136,142] Thickness stress pro�le in  � at glass [17,23,26,27,49,95–100,141] Edge Stress in � at glass   [143] Edge stress in � at glass   [144] Th ickness str ess in glass slice   [145] Real time laboratory systems [83–85,122,146] Edge stress in � at glass   [147] Thickness stress in glass slice   [147] Laboratory Surface stress measurement [17,21,105,147] Real time monitoring of membrane stress   [147] Qualitative Stress inspection   [147] Visualise fringe pattern in chemically [147] tempered glass Surface stress in thermally/chemically [148] tempered glass Qualitative Stress inspection   [148]

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

–

Refractometry – – –

Inte grated birefr in gence in glass pane ls/ articles

Refs.

[149]

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Recently, a portable   scattered light polariscope SCALP   and its variants have been developed by GlasStress Ltd which can be used to measure the stresses along the entire thickness of the glass plate [141]. The working principle of SCALP is discussed in  Section 4.2. Several automated polariscopes have also been developed which works on the phase shifting method. One such polariscope is the Automated Polarisope AP-07   [142]   supplied by GlasStress Ltd, which works based on six-step phase shifting method (steps 5–10 of  Table 2). It can be employed to  � nd the residual stresses in �at glass, as well as axi-symmetric specimens. A new nondestructive gradient scattered light method has been recently proposed by Hodemann et al.  [150] for micron-scale stress pro �le measurement in chemically strengthened glass.

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