# Hydrostatic stress induced by the boundary conditions and the incompressibility

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## Mechanical behavior of the interlayer

The interlayer meachanical behavior was investigated in both the small strain and large strain regimes. The different devices and techniques used to conduct this study are presented here. Since the mechanical tests were done on a PVB as received and that the PVB in laminated glass is subjected to a heat and pressure treatment during the lamination process, we checked that the behavior in both small strain and large strain deformation are similar before and after lamination temperature and pressure treatment. Results can be found in Appendix A.

### Dynamical Mechanical Analysis (DMA)

Mechanical response of polymers subjected to small oscillatory strain When applying an oscillatory deformation on a viscoelastic sample at a given frequency ! ( = 0 cos(!t)) the response of the material is delayed in time. This delay characterizes the viscoelastic response of the material ( = 0 cos(!t + )). One can then define a complex modulus E. The real part E0, is called the storage modulus and reflects the elastic storage of the energy. The imaginary part E00 is called the lost modulus and accounts for the viscoelastic losses. The ratio between these two moduli is often denoted tan and it is a way to compare the stored versus lost energy during the deformation of the material. The stress is then given by = E.

#### Different models to describe the constitutive behavior of the interlayer

The complex behavior of the interlayer described later in Chapter 3, is difficult to model as it displays simultaneously a viscoelastic behavior, a hyperelastic behavior and a plastic behavior. We choose to use a Generalized Maxwell description for the viscoelastic part [15] through a Prony’s serie. It will model the time and temperature dependence of the material. As the polymer is subjected to large strain, linear elasticity is no longer adapted. The hyperelastic model will also have to take into account of the hardening of the material at really high strains. Thus an Arruda- Boyce model will be used [16]. These different models are described here.

Small strain description: Generalized Maxwell model

In order to model the small strain behavior one can use a generalized Maxwell model and the associated Prony’s serie. In this model (Figure 2.5), the material is described by dashpots to represent elastic relaxation with different characteristic times (i) of the material and the associated elasticity with springs (Ei). The springs and dashpots are associated in series for each characteristic time. All the branches are in parallel. A final spring is associated in parallel with these dissipative branches to represent the long term elasticity (E1).

Delamination experiments on laminated glass

In order to assess the adhesive properties of the interlayer on the glass, some peel experiments were conducted by Raphaelle Kulis [13] during her internship. Special peel samples were prepared. A glass of 5 cm width, 15 cm length and 2mm thickness were used. The interlayer assembled with the glass was 2 cm width, 20 cm length and 0.76mm thickness.
The assembly (Figure 2.6) was made as for a classical laminated glass (cleaning and assembly in clean room) but instead of applying a second glass on top of the interlayer a cloth backing was put above the interlayer. A small part of the bottom glass was also covered with Kapton R to make the peeling initiation easier.

Through crack tensile test

The through crack tensile test is a uniaxial tension test made on a pre-cracked laminated glass (Figure 2.8). The test is conducted on a Zwick Hamsler HC25 hydraulic machine with a 10 kN load cell. The laminated glass sample used for this experiment has a 5 cm width and a 10 cm length. The two glass panes are 2mm thick and the interlayer thickness is most of the time 0.76mm. Just before the TCT experiment, the two glasses are cut in their middle through their width. A first scratch is made on the glass along its width thanks to a diamond cutting wheel.
Then the laminated sample is subjected to very small bending in order to propagate the crack. The sample is then mounted in the tensile rig and a pressure of 8MPa is applied in-between the clamps to avoid any sliding of the sample. Finally the cracked laminated glass is subjected to a uniaxial tension experiment. During the experiment, the upper clamp velocity is controlled and the bottom glass is fixed. The interlayer is delaminating from the glass and stretched. The position of the delamination fronts is measured with a Baumer BM20 camera. The environment is controlled as in 2.3.3.

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1 Introduction
1.1 A brief industrial history of laminated glass
1.2 Impact on laminated glass
1.2.1 Standard tests
1.2.2 Kinematics of impact on laminated glass
1.2.3 Previous works on impact
1.3 Questions
2 Methods
2.1 Laminated glass assembly
2.2 Silanization
2.3 Mechanical behavior of the interlayer
2.3.1 Dynamical Mechanical Analysis (DMA)
2.3.2 Rheology
2.3.3 Uniaxial tension
2.4 Different models to describe the constitutive behavior of the interlayer
2.4.1 Small strain description: Generalized Maxwell model
2.4.2 Hyperelasticity: Arruda-Boyce model
2.5 Delamination experiments on laminated glass
2.5.1 Peel test
2.5.2 Through crack tensile test
2.6 Optical methods
2.6.1 Video acquisition
2.6.2 Digital image correlation
2.6.3 Photoelasticity
2.7 Differential Scanning Calorimetry
2.8 X-ray scattering
3 A complex structure and rheology
3.1 Introduction
3.2 Poly(Vinyl Butyral) interlayer
3.2.1 Chemistry
3.2.2 Hydroxyl groups
3.3 Rheology of the PVB
3.3.1 Small strain viscoelasticity
3.3.2 Large strain uniaxial tension
3.4 Strain induced birefringence
3.4.1 Influence of strain rate and temperature on birefringence
3.4.2 Birefringence during relaxation experiment
3.4.3 Partial conclusion
3.5 Evidence of a second phase
3.5.1 An exothermic signal
3.5.2 Evidence through X-ray scattering
3.5.3 A schematic model of the structure
3.6 A rheological model: two dissipation mechanisms
4 Model delamination experiment
4.1 Introduction
4.2 Description of a typical Through Crack Tensile Test
4.3 Influence of velocity and temperature on delamination: phase diagram
4.3.1 Results
4.3.2 Comparison with previous studies
4.4 Distribution of the deformation of the interlayer in the TCT test
4.4.1 Deformation zone measured by photoelasticity
4.4.2 Fast stretching zone measured in DIC
4.4.3 Dependence of the fast stretching zone length on applied velocity and temperature
4.5 Conclusion
5 Energy dissipation during delamination
5.1 Introduction
5.2 Macroscopic work of fracture
5.3 Impact of the interlayer thickness
5.4 Different zones of dissipation
5.5 Modeling the bulk stretching of the interlayer
5.6 Dissipated energy
5.7 Influence of the temperature and applied velocity on the dissipation mechanism
5.8 Discussion and Conclusion
6 Interface modification – Preliminary results
6.1 Introduction
6.2 Impact of silanization on the interface and on the peel work of fracture
6.3 Impact of an interface modification on the TCT test response
6.3.1 Different steady state delamination regimes
6.3.3 A change in the dissipated energies
6.4 Discussion
6.5 Conclusion
7 Finite element modeling description
7.1 Introduction
7.2 Cohesive zone model for the interfacial rupture
7.3 Model description
7.4 Recovering a steady state delamination
7.4.1 Decohesion processes
7.4.2 Hydrostatic stress induced by the boundary conditions and the incompressibility
7.4.3 Energy flows balance
7.4.4 Far field measurements
7.5 Two zones of dissipation
7.5.1 The fast stretching zone
7.5.2 Near crack process zone
7.6 Near crack work of fracture
7.7 Impact of interlayer relaxation time and work of separation
7.7.1 Work of separation
7.7.2 Viscoelastic relaxation time
7.8 Coupling between the near crack and bulk stretch responses.
7.9 Conclusion
8 Conclusions and perspectives
Résumé en français
Appendices
A Effect of the thermal treatment during laminated glass preparation on the mechanical behavior of the interlayer
B Arruda Boyce Model
Bibliography
Abstract

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