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Laminated glass under impact: from ball drop tests to fracture mechanics
After a brief introduction to laminated glass in section I.1, we review the experimental methods for impact-resistance testing in section I.2, from standard tests to lab-scale setups.
Then, we enter in the details of the literature on laminated glass under impact. First, the problem of glass breakage is addressed in section I.3. However, even if glass breakage matters for impact resistance, we will see that the role of the interlayer is critical for energy dissipation and that most of the energy dissipation occurs in the post-breakage behavior. That is why we present in section I.4 the methods to characterize debonding and stetching of the interlayer between glass fragments, the peel test and the Through Crack Tensile Test.
Finally, some notions of fracture mechanics are developed in section I.5. In partic-ular, we insist on the enhancement of the fracture energy by dissipation mechanisms in the materials, which will be the underlying principle all along this work. We discuss the crack propagation problem in viscoelastic and plastic media, and also the influence of mode-mixity on the fracture resistance of materials.
Safety is a major—if not the most important—issue in every industrial application. Brittleness of glass limits its use in structural applications: nobody would want a transparent flooring or a windshield to break into pieces like a basic annealed soda-lime glass window would do, as depicted in figure I.1. The aftermath of glass breakage is the main issue: glass shards are extremely sharp and can potentially induce severe wounds. In order to answer the market demand for elegant, transparent but also safe materials, glass needs to be strengthened and toughened.
Glass strength can be improved with tempering, by thermal or chemical methods. Tempering results in compressive stresses at the surface of the glass which prevent the propagation of small cracks. Tempered glass is easily recognizable: it breaks into thousands of tiny pieces (figure I.1). Tempered glass is used for lateral windows in cars, glazings for bus stops, and screens for smartphones.
Toughness and resistance to impacts is enhanced with laminated glass. Lamina-tion consists in inserting a polymer interlayer between two glass plies. The interlayer has two roles: holding the shards together when the glass breaks, and dissipating the kinetic energy of the impactor. Laminated glass is easily recognizable: the window breaks in a radial pattern but retains its structural integrity (cf figure I.1). Wind-shields, glass floorings and balustrades, building facades and store windows are made of laminated glass.
Another advantage of laminated glass resides in the post-breakage behavior. With the interlayer, the structure of the glazing is preserved even if the glass plies are cracked. It prevents foreign objects from going through the glazing, such as debris carried by strong winds.
Chemical composition of the polymer was originally celluloid or derivatives[8]. Since the second half of the 20th century, plasticized poly(vinyl butyral)—PVB—has been used in most laminated products. A more detailed description of the interlayers will be provided later in II.1.
Figure I.1 Illustration of the differences between standard (annealed) glass, toughened glass and laminated glass upon breakage.
Source: “Laminated Glass: Assured Protection”, Pioneer Glass (online).
Manufacturing process
Laminates are assembled in the controlled environment of a cleanroom. After piling up one glass ply, the polymer interlayer and another glass ply, air is removed by the use of a calender (“nip-rolling” process) or a vacuum bag. The de-airing step is crucial to avoid the formation of bubbles at the interfaces. Later, the laminate is heated under pressure in an autoclave. During the thermal treatment, the polymer flows and achieves initimate contact with the glass surface: in other words, the interlayer is adhered to the glass. The laminate is then cut to the adequate dimensions, and ready for use.
Laminated glass under impact: from standard tests to lab-scale experiments
Impact tests
Resistance of laminated glass to impacts is assessed and classified by several norms that depend on the application.
Ball drop test
The ball drop test is defined by the European standard EN356 for buildings applica-tions and ECE R43 for automotive applications. This test consists in letting a steel ball fall on a glazing, and merely assess if the ball has gone through the glazing completely.
In EN356, the steel ball (radius 10 cm, weight 4 kg) impacts a 1 m2 specimen 3 times in a row, in a 20-cm wide triangle approximately located at the center of the panel. The temperature of the specimen should be around 23 C. The drop height is 1.5 m for the minimum safety level P1A, and increases up to 9 m—and 9 repeated impacts—for the highest level P5A. The laminate passes the test if the steel ball never goes through the panel entirely. In building applications like EN356, impacts are in the dynamic range with strain rates between 10 and 100 s 1 [4].
For the automotive version ECE R43, the principle is the same with a smaller and lighter impactor, smaller glass specimens (30 30 cm2), and various temperatures.
Pendulum test
The pendulum test is defined by the European standard EN12600 and mimics the im-pact of a human body—affectionately known as the “stepmother test” for the cognoscenti. The test temperature is also 23 C. The pendulum is actually a 50 kg weight, decorated with two rubber tires. This impactor is then pulled up to a certain angle, or equivalent drop height, and then released to let it impact the glass specimen. The glazing has to resist one single impact from this heavy mass to be certified.
More original impactors: axe, pummel, birds and bullets
More original testing methods are used to assess impact performance. For instance, EN356 also defines the “axe” test, designed to determine the resistance to manual attack. The level of protection is defined according to the number of axe strikes required to hack out an opening in the glazing—typically between 30 and 90.
The “pummel” test is similar and evaluates adherence between glass and inter-layer. In this peculiar adhesion test, the laminate is pummeled with a hammer and the mass of glass lost in the process defines a grade: the lower the amount of glass detached, the higher the pummel grade.
Transport applications are worth mentioning for the wide variety of impactors en-countered in impact tests, among which birds—of different sizes, shapes and weights—for plane windshields or stone gravels for windshields of road vehicles. Nonetheless, such complex impactors are irrelevant for the present work—we only evoke them for the curious reader.
Finally, a noteworthy field of application is ballistic protection. For instance, STANAG 4569 defines four types of bullets, depending on their velocity and hardness. Ballistic glass is then evaluated by shooting a few bullets and assess whether the projectile went through, and also whether glass splinters were projected. However, ballistic impacts are out of the scope of this work, as perforation by a bullet is a peculiar phenomenon that involves pulverization of the glass and heating effects.
Proceedings of a dynamic impact on laminated glass
In all these impacts tests, in particular for building applications, we notice a similar course of events. Indeed, we observe that the breakage of a laminated glass piece can be decomposed into 4 critical stages (figure I.2):
1. “Bending” step: the impactor reaches the glass panel, which first bends. For dynamic impacts, elastic waves propagate within the laminate and participate to the shattering of glass plies. The bending properties are the focus for structural applications, for which the deflection under constant or quasi-static loading should be as small as possible.
2. “Shattering” step: the glass plies break into several pieces maintained together by interlayer ligaments. As developed in section I.3, the crack pattern depends on the glass properties, on the thickness of the interlayer and on the velocity of the impactor.
3. “Stretching” step: once the glass plies are broken into pieces, the interlayer undergoes a membrane deformation due to the remaining kinetic energy of the im-pactor. This step actually concentrates most of the energy dissipation, as explained in section I.4.
4. “Tearing” step: in the case of high energy impacts, the interlayer is torn by the impactor and/or the glass shards. As a result, the impactor perforates the interlayer and goes through the laminate. Sharp glass shatters induce cracks within the inter-layer, which results in the tearing of the polymer membrane. This last perforation stage is the focus of the standard tests such as EN356 and EN12600, and a major point of concern for the manufacturing industry.
From the industrial point of view, performance upon impact has usually been assessed considering only the outcome of the last “tearing” step. Nevertheless, perfo-ration of the laminate critically depends on the previous stages of the impact. Indeed, the “shattering” process dictates how many glass fragments are formed, conversely generating a given number of interfaces for adhesive rupture. Then, the “stretching” stage is crucial for energy dissipation:
Interlayer’s key role for energy dissipation
Energy dissipation occurs in the interlayer
A noteworthy experimental setup is the “cannon” setup, developed at Saint-Gobain Re-search Compiègne in the early 2000s by Nourry[9,10] and then Decourcelle[11]. Inspired from the split Hopkinson bar dynamic test, this setup is meant to mimic the ball drop test on 30 30 cm2 specimens. The position of the impactor head was measured in real time, allowing access to the velocity and therefore to the evolution of the kinetic energy over time (figure I.3).
The characteristic value obtained with this setup was the critical energy for per-foration, defined as the initial kinetic energy of the impactor required for complete perforation. As shown by figure I.3, 100% of the initial kinetic energy is dissipated in the case of a non-perforating impact.
Figure I.3 Impactor kinetic energy decrease over time during a ball-drop-like impact, from Nourry’s PhD thesis[9]. The initial impactor energy is close to the critical energy for perforation. Lengths in mm correspond to the arrest distance of the mpactor in the incremental procedure.
Using an incremental procedure, energy dissipation could be decomposed into the contributions of glass breakage and polymer stretching. One of the major conclusion of Nourry’s work is that the breakage of the glass is negligible compared to the energy spent to delaminate and stretch the interlayer bridges between glass shards. Once the glass plies are broken, the interlayer dissipates 70% to 90% of the impactor kinetic energy.
Impact performance depends on the interlayer
The key role of the interlayer appears even more clearly in the experimental results of Novotny & Poot[12] (figure I.4). They investigated the effect of temperature on impact performance for 5 different interlayers with the mean break height (MBH) strategy, a quantitative variation around the “ball drop” test. The MBH procedure consists in dropping a 2-kg steel ball on 30 cm 30 cm glass panes from a variable height. The drop height is increased when the laminate retains the steel ball (“OK” case), and decreased when the impactor perforates through the glass (“NOK” case). After a few trials, the test sequence oscillated between “OK” and “NOK” cases around the so-called mean break heigh. In figure I.4, the MBH value varied from 1 m at the lowest impact resistance up to 8 m at the optimum of performance. These results quantify the strong dependance of impact performance upon the nature of the polymer. In fact, a performance optimum was observed for a temperature correlated to the glass transition temperature Tg , indicated as a range by colored bars in figure I.4.
For instance, the EVA—poly(ethylene – vinyl acetate)—interlayer shows poor im-pact resistance around 20 C—the usual temperature for standard tests in building applications—but outperforms all other interlayers at -20 C. Such significant differ-ence upon temperature will guide our choice of a different interlayer later in this work: EVA appears as a good candidate for a complete change is mechanical response compared to standard PVB.
State of the art on glass breakage: from quasi-static flexion to blast loading
Getting into more details of the four stages of laminated-glass breakage (cf section I.2.2), we will now describe the state-of-the art on glass fracture in section I.3, and then focus on the “stretching” problem in section I.4. In this section, we present sig-nificant results from the literature, from the late 1990s to contemporary publications, about laminated glass fracture—what we called “shattering” step. We rely on the recent review by Vedrtnam & Pawar[13] on plate theories and numerical simulations developed for both quasi-static and impact testing of laminated glass.
Number of cracks?
The shape of radial cracks was rationalized by Vandenberghe et al.[14,15], providing a scaling law for the number of cracks which depends on elastic modulus E, thickness h, density (via the speed of sound waves c) and fracture energy of the material, and the impact velocity V : E h 1=3 V 1=2 c
High-rate laminated glass fracture was investigated by Chen et al., with experiments[16] and numerical simulations[17,18]: they showed that the number of radial and ortho-radial cracks increased at higher impact rates—as derived by Vandenberghe for glass alone—and also when the thickness of the PVB interlayer decreased.
Locus of failure?
Strength of laminated glass was assessed experimentally by Bennison et al.[19], with a three-point flexion test. They focused on the influence of the impactor velocity on the failure of the glass plies, using time-temperature superposition to access fast and slow regimes. When the loading rate increased, they predicted a transition from monolithic to layered response of the laminate. “Monolithic” referred to the behavior of single glass specimen with doubled thickness, “layered” to the behavior of two glass plies stacked upon each other. Such transition implied a change of the preferred locus of failure from the upper glass ply to the lower glass ply (figure I.5). Their predictions were in agreement with earlier numerical simulations of slow-rate impacts by Flocker & Dharani[20,21].
Table of contents :
Introduction
I Laminated glass under impact
I.1 Introduction to laminated glass: an industrial product for safety applications
I.2 Laminated glass under impact: from standard tests to lab-scale experiments
I.2.1 Impact tests
I.2.2 Proceedings of a dynamic impact on laminated glass
I.2.3 Interlayer’s key role for energy dissipation
I.3 State of the art on glass breakage: from quasi-static flexion to blast loading
I.4 Post-breakage behavior: investigating adhesion, stretching and delamination of the interlayer
I.4.1 Debonding characterization: the peel test
I.4.2 State-of-the art of the TCTT
I.5 Fracture mechanics concepts
I.5.1 Fracture energy: the basics
I.5.2 Modeling crack propagation with a cohesive zone model
I.5.3 Cracks in viscoelastic media
I.5.4 Cracks in plastic media
I.5.5 Mode mixity: the influence of loading conditions
I.6 Our Holy Grail: understanding the coupling between energy dissipation
at the interface and in the volume of the interlayer
II Experimental methods
II.1 Polymers used as interlayers in laminated glass
II.1.1 Poly(vinyl butyral)
II.1.2 Poly(ethylene – vinyl acetate)
II.2 Surface modification with silane chemistry
II.2.1 Surface characterization: contact angle measurement with a sessile drop
II.3 Thermal and structural analyses: DSC and X-ray diffusion
II.3.1 Differential Scanning Calorimetry
II.3.2 Wide and Small Angle X-ray Scattering
II.4 Mechanical testing
II.4.1 Small strain mechanical analysis
II.4.2 Large strain tensile testing
II.5 Adhesion characterization
II.5.1 The peel test
II.5.2 The Through Crack Tensile Test
III Adhesion modification with PVB
III.1 Surface treatment protocol with silane mixes
III.2 Control of PVB/glass adhesion by the TEOS content
III.3 Through Crack Tensile Tests with adhesion-modified laminates
III.3.1 The steady-state regime and its limits
III.3.2 Lateral crack initiation at high adhesion for thin interlayers
III.3.3 Loss of symmetry at low adhesion for thick interlayers
III.3.4 Higher work of fracture at higher adhesion: a stretch effect
III.3.5 Adhesion modification affects mostly the interface dissipation
III.4 Comparison with previous experiments: effect of the relative humidity
III.5 A hand-waving model for the coupling between adhesion and macroscopic work of fracture
IV EVA: elasto-plastic interlayer
IV.1 Thermal transitions of EVA: crosslinking, crystallization, glass transition
IV.1.1 Thermal treatment during lamination
IV.1.2 Effect of temperature on the structure
IV.2 Structural characterization: semi-crystalline nature
IV.2.1 Crystalline content and crystallite size from DSC
IV.2.2 Characterization of the crystallinity by X-ray diffraction
IV.3 Crosslinking upon thermal treatment
IV.3.1 Characterization of the curing kinetics: cure law
IV.3.2 Kinetics model
IV.4 Mechanical behavior of cured EVA: elasto-plasticity
IV.4.1 Small strain behavior of EVA
IV.4.2 Large strain behavior of EVA
V Delamination in EVA laminates
V.1 Adhesion between EVA and glass: surface chemistry strikes back
V.1.1 EVA on bare glass: immediate rupture in the TCTT
V.1.2 Modification of the adhesion between EVA and glass: return of the silanes
V.1.3 Surface chemistry and TCTT—from rupture to unstable regimes, and recovery of stable delamination
V.2 Adhesion rupture in the TCTT with EVA at ambient temperature
V.2.1 (No?) effect of interlayer thickness
V.2.2 (No?) effect of velocity
V.3 Recovery of high fracture energy at the glass transition of EVA
V.3.1 Thickness effect at the glass transition: high dissipation in the bulk
V.3.2 A strong rate effect at the glass transition
V.3.3 Plastic at the crack tip, viscoelastic in the bulk?
VI Numerical modeling: steady-state crack
VI.1 Modeling the TCTT: dissipative interlayer and cohesive zone model?
VI.2 Constitutive behaviors in small deformations
VI.2.1 Plasticity in the linear regime: additive decomposition of the strain
VI.2.2 Non-linear viscoelasticity in small strains: creep formulation
VI.3 Steady-state scheme
VI.3.1 Principle of the method: “integrate along streamlines”
VI.3.2 Technical implementation: post-processing of elastic solutions
VI.3.3 Energy release rate and total work of fracture
VI.4 Validation of the model: plane-strain opening crack in a rate-dependent plastic material
VI.4.1 Material properties and plastic zone size
VI.4.2 Stress-based crack propagation criterion
VI.4.3 Effects of plasticity and loading rate
VI.5 Application to steady-state TCTT, with rate-dependent plasticity
VI.5.1 Mixed-mode propagation criterion
VI.5.2 Steady-state fracture energy with a viscoplastic material
VI.5.3 From small-scale yielding to a fully-plastifying interlayer
VI.6 Conclusions and perspectives
VI.6.1 Successful implementation of a steady-state crack with a commercial FEA code
VI.6.2 Perspectives and improvements
VII Conclusion(s) & perspectives
VII.1 Adjusting adhesion for optimal energy dissipation
VII.1.1 Surface chemistry: a toolbox for a quantitative approach to adhesion modification
VII.1.2 Interlayer strength as the limit to delamination
VII.2 A large dissipating volume is needed for optimal performance
VII.2.1 Elasto-plastic interlayer above the glass transition: localized dissipation?
VII.2.2 Dissipation dominated by viscoelasticity at the glass transition
VII.3 Numerical modeling of a steady-state crack
VII.3.1 Steady-state modeling, long story short
VII.3.2 Lower limit in the TCTT phase diagram: bridging viscoelasticity and plasticity
VII.3.3 Perspectives: finite deformations and rate-dependent materials
Appendices
