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Structural analysis of failure behavior of laminated glass
Composites Part B 125 (2017) 89e99
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Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Structural analysis of failure behavior of laminated glass Giulio Castori, Emanuela Speranzini* Department of Engineering, University of Perugia, Via Duranti 93, 06125 Perugia, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 December 2016 Received in revised form 12 April 2017 Accepted 21 May 2017 Available online 23 May 2017
The use of laminated glass is increasing since it is able to guarantee robustness requirements so by improving the post-breaking characteristics of the glass. Due to the brittle nature of glass the reason for employing such composite materials are related to their ability to avoid cracks propagation, retain the glass fragments and present a post-cracking phase. Since the behavior of laminated glass depends on the constituent materials and especially on the type of interlayer, this research deals with the structural behavior of laminated glass plates made with different types of interlayer materials: PVB, SGP, EVA and XLAB. Twenty-four specimens were constructed with two annealed glass plies and transparent interlayer and were subjected to four point bending tests with the aim to study their structural behavior in both elastic and post-breaking phases. Laboratory outcomes highlight the enhanced initial-breakage strength of the XLAB plates, as well as the influence of the laminate type on the post-failure safety, since the use of thicker (double or triple ply) and/or stiffer (such as SGP and XLAB) interlayers seemed not to improve the residual load-carrying capacity. Finally, a 3-dimensional FE model is also presented for reproducing the structural behavior of the glass plates. The ability of the numerical model to reproduce experimental results for the loadedeflection curves is validated promoting a deeper understanding and knowledge of the capabilities of the different types of interlayers in the context of the laminated glass design. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Glasses Layered structures Strength Mechanical testing FEM analysis
1. Introduction Structural robustness is an essential requirement in glass structures design, since glass breaks suddenly (even if stresses are low) due to inclusions within glass, to the presence of microdefects or to scratches caused by the finishing and cutting process as investigated by Speranzini et al. in Ref. [1]. Robustness is a property that makes constructions not suffer disproportionate failure, including progressive collapse [2]. It can be obtained by eliminating or reducing risks to which structures can be subjected, or by designing structural solutions with low sensitivity to risks [3,4]. Thus structural glass design is based on the new “fail-safe” design philosophy, which is aimed at ensuring safe breakage and avoiding collapse [5]. These objectives can be achieved by structural robustness concepts using structural redundancy, which is the structure's capacity to distribute internal stresses [4,6], so that the failure of its parts does not cause the collapse of the entire structure. Redundancy can be introduced in different ways, which are: section redundancy, structural element redundancy and structural
* Corresponding author. E-mail address: [email protected] (E. Speranzini). http://dx.doi.org/10.1016/j.compositesb.2017.05.062 1359-8368/© 2017 Elsevier Ltd. All rights reserved.
system redundancy. Section redundancy is a feature of laminated glass that avoids cracks propagation and, for this reason, provides structural advantages over a monolithic section especially in the post-breaking phase. Indeed laminated glass is a multilayer made of two or more glass sheets bonded together by a transparent or colored interlayer. The glass sheets can be of the same or different types, or of different thicknesses, and, in these cases, they are called hybrid [7,8]. The function of the interlayer is to distribute impact forces across a greater area of the glass sheets (so that the impact strength of the glass increases), retain the glass fragments, limit the size of cracks, offer residual resistance and reduce the risk of cutting or deep injuries, in the case of breakage [9,10]. Moreover, the interlayer is capable of undergoing plastic deformation during impact [11] and under static loads after impact [12], decreasing the impact energy and absorbing energy as well as reducing the penetration effect by impacting objects [13,14]. Scientific community researchers have made many efforts to acquire new knowledges and develop glass lamination technology. Some studies were aimed at the experimental investigation of: the bending behavior of the laminated glass with different interlayers [15], the mechanical behavior of progressively damaged laminated glass [16], the temperature effect on the structural response of glass/SGP laminates [17], the influence of weathering on the
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mechanical and physical properties of the PVB interlayer [18] as well as the long term response of laminated glass [19,20,21]. Other studies were aimed at: the analysis of curved laminated glass [22,23], the creation of mathematical model for laminated plates with a viscoelastic interlayer [24,25] and the use of discrete element modeling to simulate their nonlinear behavior after the cracking [26,27]. Due to its ability to retain fragments, laminated glass is also used in hybrid glass beams coupled with tensile resistant materials to provide a residual load-bearing capacity [28,29]. Furthermore, adhesion phenomena were studied [4] and more specifically the coupling that the interlayer is able to establish between the glass plies was evaluated [19]. This study deals with the structural behavior of glass plates laminated with different types of interlayer: PVB, polyvinyl butyral; SGP, SentryGlas plus; EVA, ethylene vinyl acetate; XLAB, a plastic film between two plies of ethylene vinyl acetate. The glass plates were constructed with two glass sheets having dimensions of 1100 360 4 mm, and were laminated with different numbers of interlayer plies. Then, they were tested with a four point bending test using the same load rate with an electronic hydraulic testing machine, in displacement control conditions. The main goal of this experimental campaign was to study the bending behavior of these different types of laminates, analyzing both the elastic and the postcritical phase. Furthermore, a finite element analysis able to model the behavior of the laminated glass plates in the post-breaking phase (considering the cracked section) was performed, at the aim to supply a numerical model useful to the structural design.
2. Laminated glass Two distinct phases can be discerned in laminated glass behavior: the elastic phase and the post-breaking phase [29e31]. In the former, the glass sheets are not cracked and the stress distribution of each sheet depends on the mechanical characteristics of the interlayer and its ability to transfer the tangential stresses from one layer to another [4]. The elastic phase ends when the glass tensile strength limit is reached or high tensile stresses coincide with randomly distributed surface flaws [1]. In the post-breaking phase, the load can be carried by the uncracked glass plies while the interlayer retains the fragments. When glass sheets are overloaded and are not able to transfer the tensile stress, the interlayer is essential to equilibrium permitting the formation of a resistant couple together with the compression force generated by the direct contact between the pieces [4,27,29]. Furthermore, the high load and the increasing of the load duration can result the loss of the fragments in compression, so that the bending stiffness decreases and the laminate deflection can reach high values depending on the interlayer viscoplastic behavior. The collapse of the laminate occurs due to the reaching of the interlayer tensile strength limit or to the cuts caused by the glass fragments.
Fig. 1. Method of test by coaxial double rings (CDR).
3. Materials characterization 3.1. Glass All glass plates were built using soda-lime-silicate float glass, conforming to the European standard as well as to [32]. All glass was provided by the same commercial supplier and was treated during manufacture to reduce the residual stress in the specimens (annealing). Furthermore, since in float glass the air side and the tin side present a different-in-type defectiveness and, consequently, have different strengths, in order to rule out any source of uncertainty, each plate was laid so that the surface that had been in contact with the air during the float process dictated the tensile strength (air surface downward, since it showed higher strength but a greater dispersion of results as compared to the surface in contact with the tin). To characterize the mechanical properties of the glass plates [33], ruling out any possible source of uncertainty, coaxial double ring tests were performed in accordance with EN 1288e5 (Fig. 1). Accordingly, the mean bending strength of fifteen 100 mm square specimens (4 mm thick) was found to be equal to 162 N/mm2, while the coefficients of variation was 0.10.
3.2. Interlayer As concerns the interlayer, four different chemical components were used to assemble the specimens (Table 1): 1. Polyvinyl Butyral (PVB) ¼ Made of polyvinyl alcohol by reaction with butyraldehyde, PVB thermoplastic sheet are tough, resilient safety interlayers used in laminated architectural and automotive glass; 2. SentryGlas Plus (SGP) ¼ It is a semi crystalline thermoplastic interlayer;
Table 1 Characteristics of the interlayer materials. Interlayer material
Features
PVB
The most important properties are the high transparency, tensile strength, elongation at break, post- breaking strength, good adhesion to glass and high stability against ultraviolet radiation and temperature. Because of its high strength, clarity, durability, and easy application, it is widely used in civil applications. It gives good ballistic protection, thinner constructions than are now possible with more conventional laminated glass, energy efficiency and safety. It plays an important role in laminated glass - due to the high impact strength, penetration resistance and high transparency. It is also used in decorative art glass, because the manufacture of colored films are possible, and in the production of photovoltaic modules as an encapsulation material for silicon cells, because it ensures better stability against temperature. This new interlayer is significantly stiffer, tougher and chemically more robust than traditional PVBs and provides enhanced structural performance in many applications.
SGP EVA
XLAB
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The series differed from one another by the type (i.e. PVB, SGP, EVA or XLAB) and the number of plies (i.e. one, two or three) of the plastic interlayer. All the specimens had the same geometry: the length of each glass plate was 1100 mm and the width 360 mm. The cross-section of each plate consisted of two glass sheets, whose thickness was 4 mm, and the interlayer. More specifically, seven plates (series PVB) were assembled with one or two plies of PVB interlayer for an overall thickness of 8.76 mm and 9.52 mm, respectively. Thirteen plates (series SGP and series EVA) were built with two plies of SentryGlas (eight specimens) or EVA (five specimens) interlayer, respectively, for an overall thickness of 9.52 mm, whereas the remaining four plates (series XLAB) consist of a single ply of plastic film and two plies of EVA interlayer for an overall thickness of 9.90 mm.
Table 2 Overview of mean mechanical properties of the interlayer at room temperature. Property
PVBa
SGPb
EVAc
PETd
Thickness (mm) Weight density (kg/m3) Tensile strength (N/mm2) Elastic Modulus (N/mm2) Shear Modulus (N/mm2) Ultimate strain (%)
0.760 1070 20.0 24 8 300
0.760 950 34.5 612 211 400
0.760 970 26.0 18 7 350
0.760 1270 53.0 2200 e 200
a b c d
As As As As
reported reported reported reported
by by by by
Ref. Ref. Ref. Ref.
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[34]. [35]. [36]. [37].
3. Ethylene Vinyl Acetate (EVA) ¼ It is the copolymer of Vinyl Acetate and Ethylene. The weight percent ethylene usually varies from 60% to 90%, with the remainder being vinyl acetate. EVA interlayer film owns high-performance safety function properties, long-time and reliable weather resistance because it is less sensitive of moisture; 4. Polyethylene terephthalate þ Ethylene Vinyl Acetate (XLAB) ¼ It is a new interlayer, made of a single ply of PET (Polyethylene terephthalate) interlayer between two plies of EVA (Ethylene Vinyl Acetate) interlayer, which provides a better post-breaking behavior and residual strength than traditional stiff interlayers.
4.2. Test setup Displacement control tests were performed on specimens, under a four point bending configuration in accordance with EN 1288e3 [38], to investigate the residual strength in the post-peak behavior of the plates with the float glass sheets completely cracked. Details of the layout of the tests are shown in Fig. 2. Metal rollers with a diameter of 50 mm were used both to load and to support the specimens along their entire width. The span between supports was 1000 mm, while the distance between the loads was 200 mm. To avoid unequal load transfer to the glass layers, particular care was taken to ensure precise contact at both the support and loading points. More specifically, any stress concentration was compensated with rubber pads, 12 mm thick, interposed between the supports and plate, whereas neoprene was inserted between the glass surfaces and load rollers. All plates were equipped, at mid span, with two inductive LVDT (Linear Variable Differential Transformer) transducers and strain gages to monitor displacement and strains, respectively. The load was generated through a hydraulic actuator, equipped with a load cell, at a fixed displacement rate of 3.0 mm/min. Afterwards, in the post-breaking phase, the displacement rate was increased to 6 mm/min to limit the test time All experimental results were automatically recorded during the entire test using a data acquisition system. Lastly, a sequence of digital photographs was taken on both side of the plate to allow crack formation to be monitored.
In this experimental campaign, the mechanical properties of each interlayer are required in order to estimate the remaining load-carrying capacity of the specimens when the laminated glass completely loses its ability to transfer tensile stresses after the cracking of the annealed glass plies. However, since characterization tests of the interlayers were not performed as a part of this research, the manufacturer's technical information (see Table 2) was used to specify the properties of the interlayer sheets. 4. Experimental program 4.1. Test specimens Four series of four point bending tests, with a total of twentyfour specimens, were conducted on float glass plates manufactured for this experimental program (Table 3). Table 3 Test samples. Series
No of specimens
Interlayer
No of plies
Dimensionsa
PVB
3
Polyvinyl butyral
1
1100 360 8.76
4
SGP
EVA
XLAB
a
8
5
4
2
SentryGlas plus
Ethylene vinyl acetate
Polyethylene terephthalate & Ethylene vinyl acetate
[Length Width Thickness] dimensions in mm.
2
2
3
1100 360 9.52
1100 360 9.52
1100 360 9.52
1100 360 9.90
Geometry 4.00
GLASS SHEET
0.76
PVB INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
1.52
PVB INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
1.52
SGP INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
1.52
EVA INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
0.40 1.10 0.40
EVA INTERLAYER PET INTERLAYER EVA INTERLAYER
4.00
GLASS SHEET
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Fig. 2. Test setup.
5. Test results The results of the bending tests carried out on the plates are grouped in following according to the types of the interlayer materials. An analysis of the following parameters was performed for all the specimens in order to evaluate the influence of the interlayer on the behavior of the glass plate: 1. The values of Fbreak and Dbreak, which represent the load capacity and the corresponding deflection at the elastic limit when the initial glass failure occurs (initial glass breakage); 2. The values of Fresidual and Dresidual, which represent the maximum values of the load capacity and the corresponding deflection determined in the post-breaking phase;
3. The value of the normalized load (Fresidueal/Fbreak), which represents the ratio between the maximum post-breaking load and the initial failure load. Table 4 presents the mean values of these parameters for each plate series. All plates are identified by a three-index code, in which the first designates the types of interlayer materials (PVB, SGP, EVA, XLAB); the second index indicates the number of interlayer plies (SP, single ply; DP, double ply; TP, triple ply); lastly, the third index designates the identification number of the sample. 5.1. PVB plates As shown in Fig. 3, the PVB.SP and PVB.DP series exhibit a similar pattern of collapse. In both cases, the uncracked behavior of the
Table 4 Mean values of the results of experimental tests. Plate series
Fbreak [N]
Dbreak [mm]
PVB.SP
927 ± 172 (0.19) 1104 ± 165 (0.15) 1174 ± 258 (0.22) 935 ± 144 (0.15) 1557 ± 350 (0.22)
16.373 (0.12) 17.996 (0.26) 13.834 (0.23) 14.129 (0.15) 19.170 (0.23)
PVB.DP SGP.DP EVA.DP XLAB.TP
± 2.017 ± 4.738 ± 3.208 ± 2.164 ± 4.405
Fresidual [N]
Dresidual [mm]
Fresidual/Fbreak []
516 ± (0.27) 141 ± (0.55) 362 ± (0.46) 265 ± (0.10) 336 ± (0.30)
36.003 ± 7.780 (0.22) 27.242 ± 0.152 (0.01) 65.832 ± 32.568 (0.49) 26.273 ± 5.523 (0.21) 37.153 ± 5.623 (0.15)
0.58
141 77 167 26 102
The number in parentheses is the value of the coefficient of variation.
Fig. 3. Typical crack pattern in the specimens with PVB interlayer.
0.13 0.34 0.31 0.23
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Fig. 4. Load-displacement curves for the specimens with PVB interlayer.
plates, which was dictated by the longitudinal shear stresses at the interface between the glass and the interlayer, ended after the first cracking, which obviously occurred in the bottom glass sheet (in the zone of maximal bending moments at the lower surface). Afterwards, the cracks started to propagate toward the initially uncracked upper part of the plate and, therefore, the further increase in deflection was not resisted by the behavior of the composite laminate, but was resisted by the monolithic behavior of the upper glass sheet. Under such conditions, the remaining part near the top surface ensured the load-carrying capacity of the plate in the postbreaking phase as long as the interlayer contributed to holding the cracked glass fragments together, then the bearing capacity decreased suddenly and the plates collapsed due to the excessive cracking of the glass. The load-displacement curves showed an elastic-linear phase followed by the post-glass fracture phase, which was characterized by a sudden load drop followed by a slight recovery (Fig. 4). This load drop was very high and it was directly related to the number of interlayer plies. The mean value of the ratio between the maximum post-breaking load and the initial failure load (Fresidueal/Fbreak) was in fact considerably smaller when the amount of PVB was doubled (0.13 rather than 0.58). This is because high initial failure load values signify low post-breaking load values (low elastic limit loads result in the formation of larger fragments, which are easily retained by interlayer and contribute to the post-breaking capacity). In confirmation of that, the use of two plies of PVB interlayer
exhibited a greater load-carrying capacity in the elastic phase (1104 N rather than 927 N), but a strong reduction in the postbreaking load (141 N rather than 516 N). 5.2. SGP plates Unlike the PVB plates, in the glass/SGP laminates the crack initiation points were randomly distributed (occasionally even outside the central loading zone). Subsequently, several localized fan shape cracks developed mainly in transversal direction, resulting in a cracked zone of limited length (the glass was cracked in about 30% of the length of the specimen immediately before the collapse, Fig. 5). In this case, the significantly improved mechanical properties of the interlayer made it possible to hold the glass fragments in place, thus enabling compressive forces to be transmitted through the cracked glass and providing some further postbreaking resistance (with a greater deformability). This response was also confirmed by the values of the post-breaking capacity: ranging between 200 and 600 N for the SGP.DP series and negligible for the specimens laminated with two plies of PVB interlayer. The flexural behavior of the plates laminated with the SGP interlayer was still characterized by an elastic phase until the first cracking, followed by a sudden load drop and a subsequent increase of the load until the collapse (Fig. 6). As a general remark, it can be noted how the use of two plies of SGP interlayer had no influence on the post-cracking response of the plates; as in the previous
Fig. 5. Typical crack pattern in the specimens with SGP interlayer.
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Fig. 6. Load-displacement curves for the specimens with SGP interlayer.
Fig. 7. Typical crack pattern in the specimens with EVA interlayer.
series (PVB.DP plates), there was no generating of additional load bearing capacity by the SGP interlayer. Thus residual loads (362 N) remained less than the initial failure loads (1174 N), with a mean value of the ratio Fresidueal/Fbreak equal to 0.34. 5.3. EVA plates Each glass/EVA laminate showed a resisting system composed of the interlayer and the glass fragments at both its sides (broken laminate glass composite behavior). As observed after mechanical testing, in the majority of the cases the fracture of the bottom glass sheet was immediately followed by the fracture of the remaining sheet in the same section. Because of this chain reaction, once the first crack appeared, the load was transferred to the upper layer, which, consequently, became overloaded and failed to support the applied load. Furthermore, it should be noted how the glass fragments were not always observed in the central loading zone, but occasionally even in the area where high stress concentration factors occurred because tensile stresses coincided with randomly distributed surface flaws, which were the result of mechanical edge treatments (polishing in this case, Fig. 7). As illustrated in Fig. 8, the load-displacement curves obtained
for the glass plates laminated with the EVA interlayer showed a bilinear behavior (i.e. the post-cracking part is also described by a straight line). More specifically, the overall shape of the response showed a first linear upward trend up to the initial failure load (935 N). From then on, with the exception of specimens EVA.DB.02 and EVA.DB.05 that did not show any post-breaking phase1, the further increase in deflection was not resisted by the behavior of the composite laminate but was resisted by the monolithic behavior of the upper portion of the glass. Hence, the experimental response showed a linear post-peak branch up to the collapse, reaching post-breaking load values (265 N) 70% lower than the initial failure load (Fresidueal/Fbreak equal to 0.31). 5.4. XLAB plates As in the previous series, the first crack (characterized by a typical bending V shape) occurred at the bottom surface of the plate, between the load points, and it propagated internally to the
1 Due to the presence of undesirable variables (such as handwork) that may have arisen from the construction of the specimens, this fact may be attributed to the notable variations in results typical of tests on glass.
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Fig. 8. Load-displacement curves for the specimens with EVA interlayer.
lower surface up to the opposite face splitting in several cracks. After glass breakage, a sudden load drop was recorded and further cracks started to occur through both layers of the glass plates (i.e. overlapping over the two glass sheets). At this stage, the generation and transfer of the tensile bending stresses were governed by longitudinal shear forces, which were provided by the bond between interlayer and glass (bridging behavior). Subsequently, the load increased again until both glass plies were broken in the same cross-section and a considerable elongation of the interlayer (as in the case of the SGP.DP series) leaded to a complete collapse of the specimens (Fig. 9). Again, as depicted in Fig. 10, the load-displacement curves obtained for the glass plates laminated with XLAB interlayer showed a bilinear behavior. The overall shape of response initially showed a linear elastic branch, after which the loss of load-carrying capacity occurred due to the initial cracking. Then there was a subsequent recovery until the collapse, which occurred when typical V-shape cracks affected the entire zone between the two points of application of the load. The second branch shows a lower stiffness than that of the linear elastic phase and, above all, a poor value of the ratio Fresidueal/Fbreak (0.23), which give indications of a low safety level since the residual loads (336 N) were considerably lower than the elastic limit loads (1557 N).
5.5. Analysis of the results The main goal of this experimental investigation was to acquire basic insights into the elastic and post-breaking behavior of laminated glass plates with different types of interlayers. The analysis of the test results is done by discussing the effects of interlayer material properties. Remarks are also given on the influence of different interlayer thicknesses (single, double or triple ply). According to this, the following can be highlighted: 1. The type of interlayer seemed to have a significant influence on both initial- and post-breaking strength, particularly when comparing specimens with an equivalent interlayer thickness (PVB.DP, SGP.DP and EVA.DP series). Due to the improved mechanical properties of the interlayer, the SGP plates exhibited a greater load-carrying capacity in the elastic phase (approximately 10% and 25% more than that corresponding to the EVA and PVB plates). A similar trend was observed in terms of residual load-carrying capacity. By making it possible to hold the glass fragments in place and thus enabling compressive forces to be transmitted through the cracked glass, the use of the SGP interlayer provided further post-breaking resistance (with a greater deformability). The residual loads that could be applied to the specimens with the completely cracked glass sheets,
Fig. 9. Typical crack pattern in the specimens with XLAB interlayer.
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Fig. 10. Load-displacement curves for the specimens with XLAB interlayer.
were, in fact, approximately 150% and 40% larger than those recorded for PVB.DP and EVA.DP specimens, respectively. 2. Regardless the amount of interlayer, the initial-breakage strength provided by the glass/XLAB laminates was approximately 30% and 65% greater than that achieved in the SGP.DP and EVA.DP series. Similarly, a strong reduction was observed when a single or double ply PVB interlayer was used, as the initial failure loads were 40% and 30% smaller, respectively. The trend was inverted in terms of residual loads. Compared to PVB.SP specimens, the use of thicker (double or triple ply) and/ or stiffer (such as SGP and XLAB) interlayers seemed not to improve the post-failure safety, as confirmed also by the residual load-carrying capacity of the plates, equal to 58% of the load at the elastic limit for the PVB.SP series and ranging between 13% and 34% for the other specimens. 3. Significant information was also provided by the analysis of LVDT readings at the mid-span of the plate. By comparing the load-displacement curves, a significant difference in postbreaking behavior can be observed between the PVB, SGP, EVA and XLAB plates. The EVA plates demonstrated the lowest ductility and thus the lowest post-breaking curve, whereas this was increased for the PVB and XLAB plates and increased even further for the SGP plates. 6. Numerical analysis
elements across each glass ply and two (6 6 0.76 mm3) elements across the interlayer. This allows the more critical details to be captured avoiding, at the same time, distorted meshes (the finite elements width-to-height ratio was lower than 10) and, consequently, shear lock effect. Fig. 11 shows the complete FE model: it consists of 88,320 elements and 101,565 nodes, with 304,695 degrees of freedom. A tension cut-off type material model (with a Poisson's ratio of 0.22 and Young's modulus of 70000 N/mm2) was assumed for glass. This material model initially used for concrete, accounts for both crushing and cracking failure modes by means of a smeared model. More specifically, the brittle behavior of glass was defined here by means of only two material parameters: uniaxial compressive strength (fc ¼ 1000 N/mm2) and uniaxial tensile strength (ft ¼ 45 N/ mm2). Conversely, the interlayer materials were modeled with a linear elastic material law without damage (data on the material properties were taken from manufacturer's technical information, see Table 1). Lastly, to increase the reliability of the proposed FE model, unilateral contact interfaces were used to simulate of the contacts between the glass plate and the bearing supports and load plates, respectively. The joint modeling requires the use of flexible-flexible contact elements (contact pair type Target 170/Contact 174 in ANSYS). In detail, in this application, a unilateral contact law was applied in the tangential direction, assuming that sliding may e or may not e occur by using the Coulomb friction law.
6.1. FE modeling 6.2. Analysis of the results The experimental tests were simulated numerically using elastic constitutive models within a commercially available finite element (FE) software package [39]. Nonlinear analyses were performed on a complete 3d finite element model of the specimens built with two plies of interlayers (PVB.DP, SGP.DP and EVA.DP series). To this end, the geometry of the glass plates was first defined with CAD drawings; next, the volumes were imported and discretized using isoparametric brick elements (Solid 65), which are defined by eight nodes with three degrees of freedom each and isotropic material properties. The FEM mesh was refined in order to have eight elements across the specimen thickness: three (6 6 1.33 mm3)
In order to simulate the mechanical response of the specimens, a FE analysis was performed, in which the test specimens were subjected to both self-weight and a vertical load pressure under different load stages. The results of the FE analysis are summarized in Fig. 12, showing an example of the distribution of the maximum tensile stress and the corresponding deflection of PVB.DP plates when the initial glass failure occurs (initial glass breakage). To show the accuracy and reliability of the proposed FE model, the predictions of the load-carrying capacity and the deflection over the middle section are compared with experimental results in
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Fig. 11. FE model: mesh discretization.
Fig. 12. Distribution of the maximum tensile stress (soffit view) and the corresponding deflection (lateral view) at the elastic limit in the case of glass plates with PVB interlayer.
Fig. 13. This comparison shows good agreement between experimental data and theoretical predictions for the initial-breakage strength and a slight overestimate by the numerical models for the residual load-bearing capacity (a single exception was in the case of the SGP.DP series, where a lower post-breaking load was numerically observed). A similar trend was observed in terms of deflection over the middle section: while the FE model properly simulated the experimental deflection at the elastic limit, the agreement between
numerical predictions and experimental findings was less satisfactory in the case of the post-peak deflection.
7. Conclusions In this research, the structural behavior of laminated glass plates is assessed by means of experimental and numerical investigations. Twenty-four specimens were constructed with two annealed glass sheets and transparent interlayer. The specimen series differed
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safety since the residual loads (336 N) were considerably lower than the elastic limit loads (1557 N); - PVB.SP and PVB.DP series showed a similar behavior in the elastic phase with slightly lower initial failure load values for the single ply specimen (1104 N rather than 927 N). On the contrary, after initial cracking, the residual load-carrying capacity was considerably smaller when the amount of PVB interlayer was doubled (141 N rather than 516 N); - The analysis of the deflections, recorded at the mid-span of the specimen, showed significant differences in the post-breaking phase depending on the laminate type. The greatest deflections were measured for SGP plates (more than 65 mm), followed by XLAB and PVB plates (ranging between 30 and 40 mm). The lowest deflections were recorded in EVA specimens, which achieved the ultimate load for a deflections 2.5 times lower than the one corresponding to the SGP specimens; - Initial prediction from the FE analysis exhibited good agreement with experimental findings for both the initial-breakage strength (the obtained values differ by less than 20%) and deflection at the elastic limit (the error of the model varied from 12% to 30%). Conversely, the agreement between numerical predictions and experimental findings was less satisfactory in the case of the post-breaking phase (the maximum deviations between the calculated and measured values was found to be more than 40%). Acknowledgements The authors acknowledge Vetromontaggi srl (Perugia - Italy) for providing the PVB, SGP and EVA laminated glass specimens and Laborvetro di Antonello Marano (Campobasso - Italy) for providing the XLAB laminated glass specimen. Particular gratitude is also expressed to Eng. Alessio Molinari of the LASTRU Laboratory in Terni for his assistance during the experimental tests. References
Fig. 13. Comparison between experimental and numerical load-displacement curves: a) PVB.DP series; b) SGP.DP series; c) EVA.DP series.
from one another by interlayer type (i.e. PVB, SGP, EVA, XLAB) and number of plies (i.e. one, two or three). These were subjected to four point bending tests using the same load rate with an electronic hydraulic testing machine, in displacement control conditions. The investigation confirms that the type of interlayer influences the elastic and post breakage phases of laminated glass. The following results are worthy of consideration: - The glass/SGP laminates showed a greater load-carrying capacity in the elastic phase (approximately 10 and 25% more than that corresponding to the EVA and PVB laminated plates). As for the post-breaking phase, the trend was similar: SGP interlayer provided further post-breaking resistance with a greater deformability and the residual loads were approximately 150% and 40% higher than those recorded for PVB.DP and EVA.DP specimens, respectively; - Although the XLAB-glass laminates provided the highest initialbreakage strength values (30% larger than the value obtained on SGP specimens), they did not seem able to improve post-failure
[1] Speranzini E, Agnetti S. The technique of digital image correlation to identify defects in glass structures. Struct Cont Health Monit 2014;21:1015e29. [2] Biondini F, Frangopol DM, Restelli S. On structural robustness, redundancy and static indeterminacy. In: Proceedings of ASCE structures congress. Vancouver; April, 2008. [3] Foraboschi P. Predictive multiscale model of delayed debonding for concrete members with adhesively bonded external reinforcement. Compos Mech Comput Appl 2012;3(4):307e29. [4] Speranzini E, Agnetti S, Corradi M. Experimental analysis of adhesion phenomena in fibre-reinforced glass structures. Compos Part B Eng 2016;101: 155e66. [5] Haldimann M, Luible A, Overend M. Structural use of glass. 2008. IABSE-AIPCIVBH. [6] Speranzini E, Agnetti S. Flexural performance of hybrid beams made of glass and pultruded GFRP. Constr Build Mater 2015;94:249e62. [7] Overend M, Butchart C, Lambert H, Prassas M. The mechanical performance of laminated hybrid-glass units. Compos Struct 2014;110:163e73. [8] Foraboschi P. Hybrid laminated-glass plate: design and assessment. Compos Struct 2013;106:250e63. [9] Larcher M, Solomos G, Casadei F, Gebbeken N. Experimental and numerical investigations of laminated glass subjected to blast loading. Int J Impact Eng 2012;39(1):42e50. la Hashin for cracked [10] Galuppi L, Royer-Carfagni G. A homogenized analysis a laminates under equi-biaxial stress. Applications to laminated glass. Compos Part B Eng 2017;111:332e48. [11] Kaiser N, Behr R, Minor J, Dharani L, Ji F, Kremer P. Impact resistance of laminated glass using “sacrificial ply” design concept. J Archit Eng 2000;6(1): 24e34. [12] Jun X, Yibing L, Bohan L, Mengyi Z, Dongyun G. Experimental study on mechanical behavior of PVB laminated glass under quasi-static and dynamic loadings. Comp Part B Eng 2011;42(2):302e8. [13] Jelagin D, Larsson PL. On indentation and initiation of fracture in glass. Int J Solids Struct 2008;45(10):2993e3008. [14] Koike A, Akiba S, Sakagami T, Hayashi K, Ito S. Difference of cracking behavior due to Vickers indentation between physically and chemically tempered glasses. J Non-Cryst Solids 2012;358(24):3438e44.
G. Castori, E. Speranzini / Composites Part B 125 (2017) 89e99 [15] Serafinavicius T, Kevedaras AK, Sauciuvenas G. Bending behavior of structural glass laminated with different interlayers. Mech Compos Mater 2013;49(4): 437e46. [16] Biolzi L, Orlando M, Piscitelli LR, Spinelli P. Static and dynamic response of progressively damaged ionoplast laminated glass beams. Compos Struct 2016;157:337e47. [17] Louter C, Belis J, Bos F, Callewaert D, Veer F. Experimental investigation of the temperature effect on the structural response of SG-laminated reinforced glass plates. Eng Struc 2010;32(6):1590e9. [18] Andreozzi L, Briccoli Bati S, Fagone M, Giovanna R, Zulli F. Weathering action on thermo-viscoelastic properties of polymer interlayers for laminated glass. Constr Build Mater 2015;98:757e66. [19] Briccoli Bati S, Ranocchiai G, Reale C, Rovero L. Time-dependent behavior of laminated glass. J Mater Civ Eng 2010;22(4):389e96. [20] Foraboschi P. Layered plate with discontinuous connection: exact mathematical model. Compos Part B Eng 2013;47:365e78. [21] Biolzi L, Cagnacci E, Orlando M, Piscitelli L, Rosati G. Long term response of glassePVB double-lap joints. Compos B Eng 2014;63:41e9. [22] Galuppi L, Royer-Carfagni G. Shear coupling effects of the core in curved sandwich beams. Compos Part B Eng 2015;76:320e31. la Newmark for curved [23] Galuppi L, Royer-Carfagni G. Analytical approach a laminated glass. Compos Part B Eng 2015;76:65e78. [24] Galuppi L, Royer-Carfagni G. Laminated plates with viscoelastic interlayer. Int J Solids Struct 2012;49(18):2637e45. [25] Galuppi L, Royer-Carfagni G. Enhanced Effective Thickness of multi-layered laminated glass. Compos Part B Eng 2014;64:202e13. [26] Foraboschi P. Three-layered sandwich plate: exact mathematical model. Compos Part B Eng 2013;45(1):1601e12.
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[27] Baraldi D, Cecchi A, Foraboschi P. Broken tempered laminated glass: nonlinear discrete element modelling. Compos Struct 2016;140:278e95. [28] Speranzini E, Agnetti S. Strengthening of glass beams with steel reinforced polymer (SRP). Compos Part B Eng 2014;67:280e9. [29] Speranzini E, Agnetti S. Post-cracking behavior of reinforced glass beams. In: proceedings of COST Action TU0905. In: Mid-term conference on structural glass. Pore c; April, 2013. [30] Kott A, Vogel T. Safety of laminated glass structures after initial failure. Struct Eng Int 2004;14(2):134e8. [31] Kott A, Vogel T. Controlling the post-breakage behavior of laminated safety glass. In: Proceedings of international symposium on the application of architectural glass (ISAAG). Munich; November, 2004. [32] Italian National Research Council (CNR), Guide for the Design, Construction, and Control of Buildings with Glass Structural Elements. CNR-DT 210/2013 (in Italian). [33] Castori G, Speranzini E. Experimental and numerical investigation of the bending strength of glass. In: Proceedings of challenging glass 5 conference. Ghent; June, 2016. [34] Kuraray. Trosifol® BG R15. Technical sheet. Jul. 15, 2016. http://www.trosifol. de/en/produkte/architecture/trosifol-bg-r1015. [35] Kuraray. SentryGlas® ionoplast interlayer. Technical sheet. Jul. 15, 2016. http://glasslaminatingsolutions.kuraray.com/technicalinformation/#c377. [36] Bridgestone. High performance film “EVA SAFE”. Technical sheet. Jul. 15, 2016. http://www.bridgestone.com/products/diversified/evasafe/index.html. [37] Laborvetro. X-LAB. Technical sheet. Jul. 15, 2016. http://www.laborvetro.it. [38] EN 1288-3. Glass in building e determination of the bending strength of glass e Part 3: Test with specimens supported at two points (four point bending). [39] ANSYS Inc. AUTODYN user manual. 2013.
Contents lists available at ScienceDirect
Composites Part B journal homepage: www.elsevier.com/locate/compositesb
Structural analysis of failure behavior of laminated glass Giulio Castori, Emanuela Speranzini* Department of Engineering, University of Perugia, Via Duranti 93, 06125 Perugia, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 December 2016 Received in revised form 12 April 2017 Accepted 21 May 2017 Available online 23 May 2017
The use of laminated glass is increasing since it is able to guarantee robustness requirements so by improving the post-breaking characteristics of the glass. Due to the brittle nature of glass the reason for employing such composite materials are related to their ability to avoid cracks propagation, retain the glass fragments and present a post-cracking phase. Since the behavior of laminated glass depends on the constituent materials and especially on the type of interlayer, this research deals with the structural behavior of laminated glass plates made with different types of interlayer materials: PVB, SGP, EVA and XLAB. Twenty-four specimens were constructed with two annealed glass plies and transparent interlayer and were subjected to four point bending tests with the aim to study their structural behavior in both elastic and post-breaking phases. Laboratory outcomes highlight the enhanced initial-breakage strength of the XLAB plates, as well as the influence of the laminate type on the post-failure safety, since the use of thicker (double or triple ply) and/or stiffer (such as SGP and XLAB) interlayers seemed not to improve the residual load-carrying capacity. Finally, a 3-dimensional FE model is also presented for reproducing the structural behavior of the glass plates. The ability of the numerical model to reproduce experimental results for the loadedeflection curves is validated promoting a deeper understanding and knowledge of the capabilities of the different types of interlayers in the context of the laminated glass design. © 2017 Elsevier Ltd. All rights reserved.
Keywords: Glasses Layered structures Strength Mechanical testing FEM analysis
1. Introduction Structural robustness is an essential requirement in glass structures design, since glass breaks suddenly (even if stresses are low) due to inclusions within glass, to the presence of microdefects or to scratches caused by the finishing and cutting process as investigated by Speranzini et al. in Ref. [1]. Robustness is a property that makes constructions not suffer disproportionate failure, including progressive collapse [2]. It can be obtained by eliminating or reducing risks to which structures can be subjected, or by designing structural solutions with low sensitivity to risks [3,4]. Thus structural glass design is based on the new “fail-safe” design philosophy, which is aimed at ensuring safe breakage and avoiding collapse [5]. These objectives can be achieved by structural robustness concepts using structural redundancy, which is the structure's capacity to distribute internal stresses [4,6], so that the failure of its parts does not cause the collapse of the entire structure. Redundancy can be introduced in different ways, which are: section redundancy, structural element redundancy and structural
* Corresponding author. E-mail address: [email protected] (E. Speranzini). http://dx.doi.org/10.1016/j.compositesb.2017.05.062 1359-8368/© 2017 Elsevier Ltd. All rights reserved.
system redundancy. Section redundancy is a feature of laminated glass that avoids cracks propagation and, for this reason, provides structural advantages over a monolithic section especially in the post-breaking phase. Indeed laminated glass is a multilayer made of two or more glass sheets bonded together by a transparent or colored interlayer. The glass sheets can be of the same or different types, or of different thicknesses, and, in these cases, they are called hybrid [7,8]. The function of the interlayer is to distribute impact forces across a greater area of the glass sheets (so that the impact strength of the glass increases), retain the glass fragments, limit the size of cracks, offer residual resistance and reduce the risk of cutting or deep injuries, in the case of breakage [9,10]. Moreover, the interlayer is capable of undergoing plastic deformation during impact [11] and under static loads after impact [12], decreasing the impact energy and absorbing energy as well as reducing the penetration effect by impacting objects [13,14]. Scientific community researchers have made many efforts to acquire new knowledges and develop glass lamination technology. Some studies were aimed at the experimental investigation of: the bending behavior of the laminated glass with different interlayers [15], the mechanical behavior of progressively damaged laminated glass [16], the temperature effect on the structural response of glass/SGP laminates [17], the influence of weathering on the
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mechanical and physical properties of the PVB interlayer [18] as well as the long term response of laminated glass [19,20,21]. Other studies were aimed at: the analysis of curved laminated glass [22,23], the creation of mathematical model for laminated plates with a viscoelastic interlayer [24,25] and the use of discrete element modeling to simulate their nonlinear behavior after the cracking [26,27]. Due to its ability to retain fragments, laminated glass is also used in hybrid glass beams coupled with tensile resistant materials to provide a residual load-bearing capacity [28,29]. Furthermore, adhesion phenomena were studied [4] and more specifically the coupling that the interlayer is able to establish between the glass plies was evaluated [19]. This study deals with the structural behavior of glass plates laminated with different types of interlayer: PVB, polyvinyl butyral; SGP, SentryGlas plus; EVA, ethylene vinyl acetate; XLAB, a plastic film between two plies of ethylene vinyl acetate. The glass plates were constructed with two glass sheets having dimensions of 1100 360 4 mm, and were laminated with different numbers of interlayer plies. Then, they were tested with a four point bending test using the same load rate with an electronic hydraulic testing machine, in displacement control conditions. The main goal of this experimental campaign was to study the bending behavior of these different types of laminates, analyzing both the elastic and the postcritical phase. Furthermore, a finite element analysis able to model the behavior of the laminated glass plates in the post-breaking phase (considering the cracked section) was performed, at the aim to supply a numerical model useful to the structural design.
2. Laminated glass Two distinct phases can be discerned in laminated glass behavior: the elastic phase and the post-breaking phase [29e31]. In the former, the glass sheets are not cracked and the stress distribution of each sheet depends on the mechanical characteristics of the interlayer and its ability to transfer the tangential stresses from one layer to another [4]. The elastic phase ends when the glass tensile strength limit is reached or high tensile stresses coincide with randomly distributed surface flaws [1]. In the post-breaking phase, the load can be carried by the uncracked glass plies while the interlayer retains the fragments. When glass sheets are overloaded and are not able to transfer the tensile stress, the interlayer is essential to equilibrium permitting the formation of a resistant couple together with the compression force generated by the direct contact between the pieces [4,27,29]. Furthermore, the high load and the increasing of the load duration can result the loss of the fragments in compression, so that the bending stiffness decreases and the laminate deflection can reach high values depending on the interlayer viscoplastic behavior. The collapse of the laminate occurs due to the reaching of the interlayer tensile strength limit or to the cuts caused by the glass fragments.
Fig. 1. Method of test by coaxial double rings (CDR).
3. Materials characterization 3.1. Glass All glass plates were built using soda-lime-silicate float glass, conforming to the European standard as well as to [32]. All glass was provided by the same commercial supplier and was treated during manufacture to reduce the residual stress in the specimens (annealing). Furthermore, since in float glass the air side and the tin side present a different-in-type defectiveness and, consequently, have different strengths, in order to rule out any source of uncertainty, each plate was laid so that the surface that had been in contact with the air during the float process dictated the tensile strength (air surface downward, since it showed higher strength but a greater dispersion of results as compared to the surface in contact with the tin). To characterize the mechanical properties of the glass plates [33], ruling out any possible source of uncertainty, coaxial double ring tests were performed in accordance with EN 1288e5 (Fig. 1). Accordingly, the mean bending strength of fifteen 100 mm square specimens (4 mm thick) was found to be equal to 162 N/mm2, while the coefficients of variation was 0.10.
3.2. Interlayer As concerns the interlayer, four different chemical components were used to assemble the specimens (Table 1): 1. Polyvinyl Butyral (PVB) ¼ Made of polyvinyl alcohol by reaction with butyraldehyde, PVB thermoplastic sheet are tough, resilient safety interlayers used in laminated architectural and automotive glass; 2. SentryGlas Plus (SGP) ¼ It is a semi crystalline thermoplastic interlayer;
Table 1 Characteristics of the interlayer materials. Interlayer material
Features
PVB
The most important properties are the high transparency, tensile strength, elongation at break, post- breaking strength, good adhesion to glass and high stability against ultraviolet radiation and temperature. Because of its high strength, clarity, durability, and easy application, it is widely used in civil applications. It gives good ballistic protection, thinner constructions than are now possible with more conventional laminated glass, energy efficiency and safety. It plays an important role in laminated glass - due to the high impact strength, penetration resistance and high transparency. It is also used in decorative art glass, because the manufacture of colored films are possible, and in the production of photovoltaic modules as an encapsulation material for silicon cells, because it ensures better stability against temperature. This new interlayer is significantly stiffer, tougher and chemically more robust than traditional PVBs and provides enhanced structural performance in many applications.
SGP EVA
XLAB
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The series differed from one another by the type (i.e. PVB, SGP, EVA or XLAB) and the number of plies (i.e. one, two or three) of the plastic interlayer. All the specimens had the same geometry: the length of each glass plate was 1100 mm and the width 360 mm. The cross-section of each plate consisted of two glass sheets, whose thickness was 4 mm, and the interlayer. More specifically, seven plates (series PVB) were assembled with one or two plies of PVB interlayer for an overall thickness of 8.76 mm and 9.52 mm, respectively. Thirteen plates (series SGP and series EVA) were built with two plies of SentryGlas (eight specimens) or EVA (five specimens) interlayer, respectively, for an overall thickness of 9.52 mm, whereas the remaining four plates (series XLAB) consist of a single ply of plastic film and two plies of EVA interlayer for an overall thickness of 9.90 mm.
Table 2 Overview of mean mechanical properties of the interlayer at room temperature. Property
PVBa
SGPb
EVAc
PETd
Thickness (mm) Weight density (kg/m3) Tensile strength (N/mm2) Elastic Modulus (N/mm2) Shear Modulus (N/mm2) Ultimate strain (%)
0.760 1070 20.0 24 8 300
0.760 950 34.5 612 211 400
0.760 970 26.0 18 7 350
0.760 1270 53.0 2200 e 200
a b c d
As As As As
reported reported reported reported
by by by by
Ref. Ref. Ref. Ref.
91
[34]. [35]. [36]. [37].
3. Ethylene Vinyl Acetate (EVA) ¼ It is the copolymer of Vinyl Acetate and Ethylene. The weight percent ethylene usually varies from 60% to 90%, with the remainder being vinyl acetate. EVA interlayer film owns high-performance safety function properties, long-time and reliable weather resistance because it is less sensitive of moisture; 4. Polyethylene terephthalate þ Ethylene Vinyl Acetate (XLAB) ¼ It is a new interlayer, made of a single ply of PET (Polyethylene terephthalate) interlayer between two plies of EVA (Ethylene Vinyl Acetate) interlayer, which provides a better post-breaking behavior and residual strength than traditional stiff interlayers.
4.2. Test setup Displacement control tests were performed on specimens, under a four point bending configuration in accordance with EN 1288e3 [38], to investigate the residual strength in the post-peak behavior of the plates with the float glass sheets completely cracked. Details of the layout of the tests are shown in Fig. 2. Metal rollers with a diameter of 50 mm were used both to load and to support the specimens along their entire width. The span between supports was 1000 mm, while the distance between the loads was 200 mm. To avoid unequal load transfer to the glass layers, particular care was taken to ensure precise contact at both the support and loading points. More specifically, any stress concentration was compensated with rubber pads, 12 mm thick, interposed between the supports and plate, whereas neoprene was inserted between the glass surfaces and load rollers. All plates were equipped, at mid span, with two inductive LVDT (Linear Variable Differential Transformer) transducers and strain gages to monitor displacement and strains, respectively. The load was generated through a hydraulic actuator, equipped with a load cell, at a fixed displacement rate of 3.0 mm/min. Afterwards, in the post-breaking phase, the displacement rate was increased to 6 mm/min to limit the test time All experimental results were automatically recorded during the entire test using a data acquisition system. Lastly, a sequence of digital photographs was taken on both side of the plate to allow crack formation to be monitored.
In this experimental campaign, the mechanical properties of each interlayer are required in order to estimate the remaining load-carrying capacity of the specimens when the laminated glass completely loses its ability to transfer tensile stresses after the cracking of the annealed glass plies. However, since characterization tests of the interlayers were not performed as a part of this research, the manufacturer's technical information (see Table 2) was used to specify the properties of the interlayer sheets. 4. Experimental program 4.1. Test specimens Four series of four point bending tests, with a total of twentyfour specimens, were conducted on float glass plates manufactured for this experimental program (Table 3). Table 3 Test samples. Series
No of specimens
Interlayer
No of plies
Dimensionsa
PVB
3
Polyvinyl butyral
1
1100 360 8.76
4
SGP
EVA
XLAB
a
8
5
4
2
SentryGlas plus
Ethylene vinyl acetate
Polyethylene terephthalate & Ethylene vinyl acetate
[Length Width Thickness] dimensions in mm.
2
2
3
1100 360 9.52
1100 360 9.52
1100 360 9.52
1100 360 9.90
Geometry 4.00
GLASS SHEET
0.76
PVB INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
1.52
PVB INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
1.52
SGP INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
1.52
EVA INTERLAYER
4.00
GLASS SHEET
4.00
GLASS SHEET
0.40 1.10 0.40
EVA INTERLAYER PET INTERLAYER EVA INTERLAYER
4.00
GLASS SHEET
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Fig. 2. Test setup.
5. Test results The results of the bending tests carried out on the plates are grouped in following according to the types of the interlayer materials. An analysis of the following parameters was performed for all the specimens in order to evaluate the influence of the interlayer on the behavior of the glass plate: 1. The values of Fbreak and Dbreak, which represent the load capacity and the corresponding deflection at the elastic limit when the initial glass failure occurs (initial glass breakage); 2. The values of Fresidual and Dresidual, which represent the maximum values of the load capacity and the corresponding deflection determined in the post-breaking phase;
3. The value of the normalized load (Fresidueal/Fbreak), which represents the ratio between the maximum post-breaking load and the initial failure load. Table 4 presents the mean values of these parameters for each plate series. All plates are identified by a three-index code, in which the first designates the types of interlayer materials (PVB, SGP, EVA, XLAB); the second index indicates the number of interlayer plies (SP, single ply; DP, double ply; TP, triple ply); lastly, the third index designates the identification number of the sample. 5.1. PVB plates As shown in Fig. 3, the PVB.SP and PVB.DP series exhibit a similar pattern of collapse. In both cases, the uncracked behavior of the
Table 4 Mean values of the results of experimental tests. Plate series
Fbreak [N]
Dbreak [mm]
PVB.SP
927 ± 172 (0.19) 1104 ± 165 (0.15) 1174 ± 258 (0.22) 935 ± 144 (0.15) 1557 ± 350 (0.22)
16.373 (0.12) 17.996 (0.26) 13.834 (0.23) 14.129 (0.15) 19.170 (0.23)
PVB.DP SGP.DP EVA.DP XLAB.TP
± 2.017 ± 4.738 ± 3.208 ± 2.164 ± 4.405
Fresidual [N]
Dresidual [mm]
Fresidual/Fbreak []
516 ± (0.27) 141 ± (0.55) 362 ± (0.46) 265 ± (0.10) 336 ± (0.30)
36.003 ± 7.780 (0.22) 27.242 ± 0.152 (0.01) 65.832 ± 32.568 (0.49) 26.273 ± 5.523 (0.21) 37.153 ± 5.623 (0.15)
0.58
141 77 167 26 102
The number in parentheses is the value of the coefficient of variation.
Fig. 3. Typical crack pattern in the specimens with PVB interlayer.
0.13 0.34 0.31 0.23
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Fig. 4. Load-displacement curves for the specimens with PVB interlayer.
plates, which was dictated by the longitudinal shear stresses at the interface between the glass and the interlayer, ended after the first cracking, which obviously occurred in the bottom glass sheet (in the zone of maximal bending moments at the lower surface). Afterwards, the cracks started to propagate toward the initially uncracked upper part of the plate and, therefore, the further increase in deflection was not resisted by the behavior of the composite laminate, but was resisted by the monolithic behavior of the upper glass sheet. Under such conditions, the remaining part near the top surface ensured the load-carrying capacity of the plate in the postbreaking phase as long as the interlayer contributed to holding the cracked glass fragments together, then the bearing capacity decreased suddenly and the plates collapsed due to the excessive cracking of the glass. The load-displacement curves showed an elastic-linear phase followed by the post-glass fracture phase, which was characterized by a sudden load drop followed by a slight recovery (Fig. 4). This load drop was very high and it was directly related to the number of interlayer plies. The mean value of the ratio between the maximum post-breaking load and the initial failure load (Fresidueal/Fbreak) was in fact considerably smaller when the amount of PVB was doubled (0.13 rather than 0.58). This is because high initial failure load values signify low post-breaking load values (low elastic limit loads result in the formation of larger fragments, which are easily retained by interlayer and contribute to the post-breaking capacity). In confirmation of that, the use of two plies of PVB interlayer
exhibited a greater load-carrying capacity in the elastic phase (1104 N rather than 927 N), but a strong reduction in the postbreaking load (141 N rather than 516 N). 5.2. SGP plates Unlike the PVB plates, in the glass/SGP laminates the crack initiation points were randomly distributed (occasionally even outside the central loading zone). Subsequently, several localized fan shape cracks developed mainly in transversal direction, resulting in a cracked zone of limited length (the glass was cracked in about 30% of the length of the specimen immediately before the collapse, Fig. 5). In this case, the significantly improved mechanical properties of the interlayer made it possible to hold the glass fragments in place, thus enabling compressive forces to be transmitted through the cracked glass and providing some further postbreaking resistance (with a greater deformability). This response was also confirmed by the values of the post-breaking capacity: ranging between 200 and 600 N for the SGP.DP series and negligible for the specimens laminated with two plies of PVB interlayer. The flexural behavior of the plates laminated with the SGP interlayer was still characterized by an elastic phase until the first cracking, followed by a sudden load drop and a subsequent increase of the load until the collapse (Fig. 6). As a general remark, it can be noted how the use of two plies of SGP interlayer had no influence on the post-cracking response of the plates; as in the previous
Fig. 5. Typical crack pattern in the specimens with SGP interlayer.
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Fig. 6. Load-displacement curves for the specimens with SGP interlayer.
Fig. 7. Typical crack pattern in the specimens with EVA interlayer.
series (PVB.DP plates), there was no generating of additional load bearing capacity by the SGP interlayer. Thus residual loads (362 N) remained less than the initial failure loads (1174 N), with a mean value of the ratio Fresidueal/Fbreak equal to 0.34. 5.3. EVA plates Each glass/EVA laminate showed a resisting system composed of the interlayer and the glass fragments at both its sides (broken laminate glass composite behavior). As observed after mechanical testing, in the majority of the cases the fracture of the bottom glass sheet was immediately followed by the fracture of the remaining sheet in the same section. Because of this chain reaction, once the first crack appeared, the load was transferred to the upper layer, which, consequently, became overloaded and failed to support the applied load. Furthermore, it should be noted how the glass fragments were not always observed in the central loading zone, but occasionally even in the area where high stress concentration factors occurred because tensile stresses coincided with randomly distributed surface flaws, which were the result of mechanical edge treatments (polishing in this case, Fig. 7). As illustrated in Fig. 8, the load-displacement curves obtained
for the glass plates laminated with the EVA interlayer showed a bilinear behavior (i.e. the post-cracking part is also described by a straight line). More specifically, the overall shape of the response showed a first linear upward trend up to the initial failure load (935 N). From then on, with the exception of specimens EVA.DB.02 and EVA.DB.05 that did not show any post-breaking phase1, the further increase in deflection was not resisted by the behavior of the composite laminate but was resisted by the monolithic behavior of the upper portion of the glass. Hence, the experimental response showed a linear post-peak branch up to the collapse, reaching post-breaking load values (265 N) 70% lower than the initial failure load (Fresidueal/Fbreak equal to 0.31). 5.4. XLAB plates As in the previous series, the first crack (characterized by a typical bending V shape) occurred at the bottom surface of the plate, between the load points, and it propagated internally to the
1 Due to the presence of undesirable variables (such as handwork) that may have arisen from the construction of the specimens, this fact may be attributed to the notable variations in results typical of tests on glass.
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Fig. 8. Load-displacement curves for the specimens with EVA interlayer.
lower surface up to the opposite face splitting in several cracks. After glass breakage, a sudden load drop was recorded and further cracks started to occur through both layers of the glass plates (i.e. overlapping over the two glass sheets). At this stage, the generation and transfer of the tensile bending stresses were governed by longitudinal shear forces, which were provided by the bond between interlayer and glass (bridging behavior). Subsequently, the load increased again until both glass plies were broken in the same cross-section and a considerable elongation of the interlayer (as in the case of the SGP.DP series) leaded to a complete collapse of the specimens (Fig. 9). Again, as depicted in Fig. 10, the load-displacement curves obtained for the glass plates laminated with XLAB interlayer showed a bilinear behavior. The overall shape of response initially showed a linear elastic branch, after which the loss of load-carrying capacity occurred due to the initial cracking. Then there was a subsequent recovery until the collapse, which occurred when typical V-shape cracks affected the entire zone between the two points of application of the load. The second branch shows a lower stiffness than that of the linear elastic phase and, above all, a poor value of the ratio Fresidueal/Fbreak (0.23), which give indications of a low safety level since the residual loads (336 N) were considerably lower than the elastic limit loads (1557 N).
5.5. Analysis of the results The main goal of this experimental investigation was to acquire basic insights into the elastic and post-breaking behavior of laminated glass plates with different types of interlayers. The analysis of the test results is done by discussing the effects of interlayer material properties. Remarks are also given on the influence of different interlayer thicknesses (single, double or triple ply). According to this, the following can be highlighted: 1. The type of interlayer seemed to have a significant influence on both initial- and post-breaking strength, particularly when comparing specimens with an equivalent interlayer thickness (PVB.DP, SGP.DP and EVA.DP series). Due to the improved mechanical properties of the interlayer, the SGP plates exhibited a greater load-carrying capacity in the elastic phase (approximately 10% and 25% more than that corresponding to the EVA and PVB plates). A similar trend was observed in terms of residual load-carrying capacity. By making it possible to hold the glass fragments in place and thus enabling compressive forces to be transmitted through the cracked glass, the use of the SGP interlayer provided further post-breaking resistance (with a greater deformability). The residual loads that could be applied to the specimens with the completely cracked glass sheets,
Fig. 9. Typical crack pattern in the specimens with XLAB interlayer.
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Fig. 10. Load-displacement curves for the specimens with XLAB interlayer.
were, in fact, approximately 150% and 40% larger than those recorded for PVB.DP and EVA.DP specimens, respectively. 2. Regardless the amount of interlayer, the initial-breakage strength provided by the glass/XLAB laminates was approximately 30% and 65% greater than that achieved in the SGP.DP and EVA.DP series. Similarly, a strong reduction was observed when a single or double ply PVB interlayer was used, as the initial failure loads were 40% and 30% smaller, respectively. The trend was inverted in terms of residual loads. Compared to PVB.SP specimens, the use of thicker (double or triple ply) and/ or stiffer (such as SGP and XLAB) interlayers seemed not to improve the post-failure safety, as confirmed also by the residual load-carrying capacity of the plates, equal to 58% of the load at the elastic limit for the PVB.SP series and ranging between 13% and 34% for the other specimens. 3. Significant information was also provided by the analysis of LVDT readings at the mid-span of the plate. By comparing the load-displacement curves, a significant difference in postbreaking behavior can be observed between the PVB, SGP, EVA and XLAB plates. The EVA plates demonstrated the lowest ductility and thus the lowest post-breaking curve, whereas this was increased for the PVB and XLAB plates and increased even further for the SGP plates. 6. Numerical analysis
elements across each glass ply and two (6 6 0.76 mm3) elements across the interlayer. This allows the more critical details to be captured avoiding, at the same time, distorted meshes (the finite elements width-to-height ratio was lower than 10) and, consequently, shear lock effect. Fig. 11 shows the complete FE model: it consists of 88,320 elements and 101,565 nodes, with 304,695 degrees of freedom. A tension cut-off type material model (with a Poisson's ratio of 0.22 and Young's modulus of 70000 N/mm2) was assumed for glass. This material model initially used for concrete, accounts for both crushing and cracking failure modes by means of a smeared model. More specifically, the brittle behavior of glass was defined here by means of only two material parameters: uniaxial compressive strength (fc ¼ 1000 N/mm2) and uniaxial tensile strength (ft ¼ 45 N/ mm2). Conversely, the interlayer materials were modeled with a linear elastic material law without damage (data on the material properties were taken from manufacturer's technical information, see Table 1). Lastly, to increase the reliability of the proposed FE model, unilateral contact interfaces were used to simulate of the contacts between the glass plate and the bearing supports and load plates, respectively. The joint modeling requires the use of flexible-flexible contact elements (contact pair type Target 170/Contact 174 in ANSYS). In detail, in this application, a unilateral contact law was applied in the tangential direction, assuming that sliding may e or may not e occur by using the Coulomb friction law.
6.1. FE modeling 6.2. Analysis of the results The experimental tests were simulated numerically using elastic constitutive models within a commercially available finite element (FE) software package [39]. Nonlinear analyses were performed on a complete 3d finite element model of the specimens built with two plies of interlayers (PVB.DP, SGP.DP and EVA.DP series). To this end, the geometry of the glass plates was first defined with CAD drawings; next, the volumes were imported and discretized using isoparametric brick elements (Solid 65), which are defined by eight nodes with three degrees of freedom each and isotropic material properties. The FEM mesh was refined in order to have eight elements across the specimen thickness: three (6 6 1.33 mm3)
In order to simulate the mechanical response of the specimens, a FE analysis was performed, in which the test specimens were subjected to both self-weight and a vertical load pressure under different load stages. The results of the FE analysis are summarized in Fig. 12, showing an example of the distribution of the maximum tensile stress and the corresponding deflection of PVB.DP plates when the initial glass failure occurs (initial glass breakage). To show the accuracy and reliability of the proposed FE model, the predictions of the load-carrying capacity and the deflection over the middle section are compared with experimental results in
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Fig. 11. FE model: mesh discretization.
Fig. 12. Distribution of the maximum tensile stress (soffit view) and the corresponding deflection (lateral view) at the elastic limit in the case of glass plates with PVB interlayer.
Fig. 13. This comparison shows good agreement between experimental data and theoretical predictions for the initial-breakage strength and a slight overestimate by the numerical models for the residual load-bearing capacity (a single exception was in the case of the SGP.DP series, where a lower post-breaking load was numerically observed). A similar trend was observed in terms of deflection over the middle section: while the FE model properly simulated the experimental deflection at the elastic limit, the agreement between
numerical predictions and experimental findings was less satisfactory in the case of the post-peak deflection.
7. Conclusions In this research, the structural behavior of laminated glass plates is assessed by means of experimental and numerical investigations. Twenty-four specimens were constructed with two annealed glass sheets and transparent interlayer. The specimen series differed
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safety since the residual loads (336 N) were considerably lower than the elastic limit loads (1557 N); - PVB.SP and PVB.DP series showed a similar behavior in the elastic phase with slightly lower initial failure load values for the single ply specimen (1104 N rather than 927 N). On the contrary, after initial cracking, the residual load-carrying capacity was considerably smaller when the amount of PVB interlayer was doubled (141 N rather than 516 N); - The analysis of the deflections, recorded at the mid-span of the specimen, showed significant differences in the post-breaking phase depending on the laminate type. The greatest deflections were measured for SGP plates (more than 65 mm), followed by XLAB and PVB plates (ranging between 30 and 40 mm). The lowest deflections were recorded in EVA specimens, which achieved the ultimate load for a deflections 2.5 times lower than the one corresponding to the SGP specimens; - Initial prediction from the FE analysis exhibited good agreement with experimental findings for both the initial-breakage strength (the obtained values differ by less than 20%) and deflection at the elastic limit (the error of the model varied from 12% to 30%). Conversely, the agreement between numerical predictions and experimental findings was less satisfactory in the case of the post-breaking phase (the maximum deviations between the calculated and measured values was found to be more than 40%). Acknowledgements The authors acknowledge Vetromontaggi srl (Perugia - Italy) for providing the PVB, SGP and EVA laminated glass specimens and Laborvetro di Antonello Marano (Campobasso - Italy) for providing the XLAB laminated glass specimen. Particular gratitude is also expressed to Eng. Alessio Molinari of the LASTRU Laboratory in Terni for his assistance during the experimental tests. References
Fig. 13. Comparison between experimental and numerical load-displacement curves: a) PVB.DP series; b) SGP.DP series; c) EVA.DP series.
from one another by interlayer type (i.e. PVB, SGP, EVA, XLAB) and number of plies (i.e. one, two or three). These were subjected to four point bending tests using the same load rate with an electronic hydraulic testing machine, in displacement control conditions. The investigation confirms that the type of interlayer influences the elastic and post breakage phases of laminated glass. The following results are worthy of consideration: - The glass/SGP laminates showed a greater load-carrying capacity in the elastic phase (approximately 10 and 25% more than that corresponding to the EVA and PVB laminated plates). As for the post-breaking phase, the trend was similar: SGP interlayer provided further post-breaking resistance with a greater deformability and the residual loads were approximately 150% and 40% higher than those recorded for PVB.DP and EVA.DP specimens, respectively; - Although the XLAB-glass laminates provided the highest initialbreakage strength values (30% larger than the value obtained on SGP specimens), they did not seem able to improve post-failure
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