Different models to describe the constitutive behavior of the interlayer 

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Hydroxyl groups

This polymer contains a certain amount of hydroxyl (OH) groups that are available for bonding to the glass but also for forming inter-chain bonds. Polarized hydrogen atoms are linked to a more electronegative atom such as oxygen. In the case of PVB it can be an hydrogen on the vinylalcohol group, the silanol group at the glass surface or any other OH group. Hydrogen bonds form between this polarized hydrogen and an electronegative atom which can be here the acetate group. This interaction has a strength around 10 kJ mol−1 which has to be compared to the covalent bond which has an energy > 100 kJ mol−1 and the Van derWaals interaction which has an energy around 1 kJ mol−1. However, a large number of this relatively weak hydrogen bonds can form strong links. The number of hydroxyl groups and acetate groups are thus very important for the rheology and mechanical behavior of the polymer but also for the adhesion strength. The PVB reference which has been used during this work presents an amount of OH groups around 17-18wt% or 40mol%. By changing the hydroxyl group content, both adhesion on glass and bulk materials properties are impacted. In previous works made in Saint-Gobain ([19] and [18]), a relationship between interlayer chemistry (and chemical structure) and its mechanical behavior has been studied. In particular it has been shown that the amount of hydroxyl bond has a strong influence on the mechanical behavior of the interlayer. For example Klock ([19]) has shown that the Young modulus of the PVB is strongly affected by the amount of hydroxyl groups (Figure 3.3). In this figure, the amount of hydroxyl groups varies between 40 mol% and 85 mol% and the young modulus increases from 1MPa to 1GPa. The plasticizer amount is fixed at 26 mol%. The polymer is going through the glass transition towards the glassy plateau as the amount of hydroxyl groups increases at constant temperature and constant plasticizer content. The hydroxyl group content is also changing adhesion properties. In Figure 3.4, the peeling energy is measured during a 90 peel test at 10mmmin−1, at room temperature and shows this large increase.

Rheology of the PVB

In order to study the mechanical behavior of the PVB interlayer, in both linear (small strain) and non-linear (large strain) regimes, rheology experiments (namely DMA and parallel plate rheometer) and uniaxial tension tests were conducted. Hooper made similar mechanical tests on the same PVB interlayer [20]. Others, used different PVB but provided complementary insight such as dynamic loading experiments at large strain [21] or large strain cyclic experiments [22]. In the next sections we present our own results which confirm the literature and also provide a new insight in the relationship between the mechanical behavior, the chemical structure and the energy dissipation in the PVB.

Small strain viscoelasticity

In order to investigate the small strain behavior of the interlayer and to get a proper description of the time dependence of its linear behavior, DMA and parallel plate rheology experiments were conducted. The DMA experiments measured the time and temperature dependence of the young modulus in a range of temperature from −40 C to 60 C. The rheometer experiments give the dependence on time and temperature of the shear modulus in the range of temperature from 40 C to 160 C. We also checked that the autoclaving process and the delamination from glass after the autoclave did not affect the interlayer behavior. Thus, the mechanical behavior of the interlayer can be measured on the PVB film as received (Appendix A).
DMA experiments were conducted first at a frequency of 1 Hz with a strain amplitude of 0.01%. Temperature increases from −40 C to 80 C at a heating speed of 3 Cmin−1. The glass transition temperature of the plasticized PVB is around 30 C (Figure 3.5). To compare with other experiment it is important to note that the measured glass transition varies with the heating speed. The polymer displays a glassy behavior for temperatures lower than 20 C. No clear value for the glassy storage modulus can be measured there, as it keeps increasing from 0.3GPa to 1GPa as the temperature decreases from 10 C to −40 C. On this plateau, the dissipation ratio is low as the loss modulus represents only 10% of the storage modulus. At temperatures higher than 50 C, the polymer exhibits a rubbery behavior. The storage modulus drops to values ranging from 0.8MPa to 1MPa. Again, the dissipation ratio is low in this regime, where the loss modulus represents only 10% to 20% of the storage modulus. However, during the glass transition, the dissipation ratio is maximal (tan() is higher than 1). There seems, as well, to be a slight increase of the dissipation at 70 C but as the DMA reaches its limits, the result has to be taken with caution.
As we are interested in the time dependence of the PVB behavior, the same DMA experiment is made at different temperatures from −40 C to 60 C but for different oscillation frequencies. Each 5 C, 5 frequencies per decades from 0.1 Hz to 10 Hz are tested (Figure 3.6(a)). Thanks to the time/temperature equivalence principle, a master curve can be obtained by shifting the different curves. A reference temperature of 20 C was used to build the curve.

Influence of strain rate and temperature on birefringence

Some photoelastic experiments (see 2.6.3) were performed on the PVB interlayer during uniaxial tension at controlled strain rate and temperature. The experiments were performed with a red filtered light. A typical intensity signal observed during this experiment at 20 C and 1 s−1 is plotted in Figure 3.18. The intensity is a mean value, measured on a square of approximately 10px in the middle of the stretched sample (red square on the frames in Figure 3.18(b)). The intensity oscillates between bright and dark birefringence fringes. When the intensity is maximal the delay introduced by the material in the light propagation results in a polarized wave which is in the same direction as the polarizer (after the quarter wave length plate). The fringe order N is the number of time the received light gets to maximal intensity.
The initial intensity being maximal, it corresponds to a fringe order of N = 0. In this experiment, the interlayer is stretched up to 100% strain and there are 6 fringes the last one being of N = 5th order. The fringe order also depends on time and temperature (Figure 3.19 and 3.20). At 20 C, three different strain rates were tested 0.01 s−1, 0.1 s−1 and 1 s−1 in a uniaxial tension test up to 200%. The result is that the faster the strain the higher the fringe order. Similarly, at 0.1 s−1 three temperatures were tested 20 C, 50 C and 70 C in a uniaxial tension test up to 200%. We find that the lower the temperature, Moreover, the birefringence is not directly proportional to strain. Considering the Gaussian network as described by Treloar [17], the fringe order is supposed to be proportional to the difference of principal stresses (Equation 2.6.3). However, the non linearities introduced by this simple theory of the polymer network are not sufficient to describe the fringes observed here. Indeed, the same results as in Figure 3.19 are plotted in Figure 3.21, as a function of the Gaussian theory principal stress difference (for an incompressible material in uniaxial tension) and with a corrected value of the interlayer thickness and the relationship diverges from the simple proportionality (that would have been expected) especially at larger strains.
It is also interesting to notice that, after a uniaxial tension test on the interlayer up to 200% deformation, there is no permanent deformation when the sample is removed from the clamps at 20 C whereas at 50 C and 70 C, the remnant deformation described earlier is clearly visible (Figure 3.22).

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Birefringence during relaxation experiment

An interesting result arises from a photoelastic measurement during a relaxation test on the PVB interlayer. The interlayer is stretched at 20 C at 0.1 s−1 up to 200%. The polymer is then maintained at this level of deformation during 1000 s. In figure 3.23, during the loading phase, the usual fringe pattern with 8 fringes (up to fringe order N = 7) is observed. However, during, the relaxation phase, one can see that while the stress relaxes from 180MPa to 25MPa in 1000 s (with a very fast decrease down to 80MPa in the first 10 s), the birefringence signal only varies from half a fringe. The photoelastic signal seems to be quenched by the constant strain imposed on the material.

Table of contents :

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 Opticalmethods
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
6.3.2 Steady state delamination for the lower adhesion
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 fieldmeasurements
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 BoyceModel
Bibliography 

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