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Research project: Characterisation and modelling residual stress in glass and its effect on structural design

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Residual stress in glass Owing to the differential cooling takes place during the manufacturing of float (annealed) glass and the tempering process of tempered (toughened) glass, a compressive prestress is developed in the surface region of the glass sheets. The surface pre-compression is balanced by an associated subsurface tensile stresses field. The characteristic strength values of annealed glass and tempered glass are about 45 MPa and 120 MPa respectively. The evolution of stress, the failure load and the form of failure depend on the type of glass and the residual stress in it. For example, Fig. 1 shows the difference between the typical failure behaviour of annealed glass and tempered glass. Despite the significance of the residual stress on the load response and the failure behaviour, the current glass structural design guidelines do not take into account the effect of residual stress explicitly. There is a need for a validated modelling technique that can incorporate the effect of residual stress in glass structural designs.

Broken glass
Fig.1 (a)
Tempered glass
Fig.1 (b)

Fig. 1 Failure behaviour depends on glass type. Typical failure of (a) annealed glass (b) tempered glass


Modelling residual stress

We use the contour method , which is used in aerospace industry for modelling residual stresses in structural components, to model the residual stresses in float glass. The use of the contour method for modelling residual stress in glass is “an ambitious and novel application”. Our research is the first application of the contour method to glass, or to any nonconductive material for that matter. It is also the first use of waterjet cutting for the contour method studies.

Fig. 2a shows the residual stress distribution in a 10 mm thick float glass specimen, as determined by the model. The results show a parabolic stress depth profile, with compression at the surface (6 MPa) and the peak tension (4 MPa) at the mid-thickness. The depth of the compression zones at each side is ~2 mm (~ 20% of the specimen thickness) and is balanced by a mid-depth tension zone of 6 mm (~60% of the thickness). As it can be seen in Fig. 2b, the predicted parabolic residual stress distribution is consistent with the stresses measured using a Scattered-Light-Polariscope (SCALP). Full details of the developed model and the validation using the experimental data obtained from SCALP can be found in our publications (listed below).

The model developed in the study was also extended to devise the residual stresses in tempered glass. Due to the rapid cooling used in the tempering process, the magnitude of the surface compression developed in tempered glass is significantly higher than that in float glass. Fig. 2c shows the typical parabolic shape of the residual stress depth profile exists in a 4 mm thick fully-toughened glass specimen. The figure shows that the predictions from the model agree with the stress data measured using the polariscope.



Fig.2 (a)
Fig.2 (b)
Fig.2 (c)

Fig. 2 (a) Residual stress (xx) distribution (10 mm thick float glass). Comparison between the predicted xx distribution and that determined using SCALP results (b) 10 mm thick float glass, (c) 4 mm thick tempered glass


Applications of research findings

Our model was used to investigate the interaction between complex geometries and the residual stress distribution. For example, Fig. 3a shows the predicted residual stress distribution around a central hole in a 10 mm thick tempered glass piece (only a quarter of the specimen is modelled due to symmetry). As can be seen from the figure, the stress distribution is not uniform in the vicinity of the hole. The knowledge of the exact stress distribution is important in the analysis of glass structures as point fixings are often used. The joints are usually weaker than the structural member, and hence, the joints often determine the strength of the structural member.

The model was also used to evaluate the stress evolution in the vicinity of the hole during subsequent applied loads. For example, Fig. 3b shows the stress depth profile along the edge of the hole when the specimen was loaded by uniaxial loads equivalent to 20 and 30 MPa applied remote stresses respectively. The results suggest that change in stress is not always proportional to the magnitude of the applied load. This indicates a complex interaction between the residual stress and geometry; the simple elastic analyses adopted in the current design guidelines may not be able to predict the actual behaviour of complex glass geometries.



Fig.3 (a)
Fig.3 (b)

Fig. 3 (a) Residual stress (xx) distribution in the vicinity of a central hole in a 10 mm thick tempered glass specimen (b) Residual stress (xx) depth profile along Path A (Fig. 3a) at different applied load levels (remote stress 20 MPa and 30 MPa respectively)



Benefits to structural engineering


  • An experimentally validated numerical tool to incorporate the effect of residual stress in structural glass designs
  • Accurate analysis of the load response and the failure behaviour of practical glass structures
  • Finite Element Analysis based design approach for glass structures



Funding sources


  1. The Institution of Structural Engineers
  2. University of Southampton



Relevant publications

Achintha, M and Balan (2015) An experimentally validated contour method/eigenstrains hybrid model to incorporate residual stresses in glass structural designs. The Journal of Strain Analysis for Engineering Design 50(8): 614–627 doi: 10.1177/0309324715601914.

Balan, B and Achintha, M (2015) Assessment of stresses in float and tempered glass using Eigenstrains. Experimental Mechanics 55(7): 1301–1315 doi: 10.1007/s11340-015-0036-y.

Achintha, M and Balan, B (2015). A combined experimental and numerical approach to the investigation of the influence of geometry on residual stresses in structural glass. 12th Int. Conf. on the Mechanical Behaviour of Materials, Karlsruhe, Germany 10-14 May.

Balan, B and Achintha, M (2014). Hybrid contour method/eigenstrain model for predicting residual stress in glass. 5th Int. Conf. on Computational Methods, Cambridge, UK, 28-30 July 2014. ScienTech Publisher. (Invited keynote)

Balan, B and Achintha, M (2014). Characterisation of residual stress in glass. 8th Int. Conf. on Advanced Computational Engineering and Experiment, Paris, France, 30 June-3 July.



Further information

Please contact Dr Mithila Achintha (E-mail: or 02380 59 2924)






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