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Composites are being increasingly used for industrial applications and combine the advantageous properties of two or more constituents. The urge to reduce material to a minimum and the trend towards lightweight glass structures require further developments in high performance and fully transparent composite structures for the building industry. Novel innovative glass–plastic-composite panels combining a lightweight polymer polymethylmethacrylate (PMMA) interlayer core and cover layers of thin glass are currently under development. The panels exhibit high structural load-bearing performance, are durable and fully transparent with a low self-weight. These properties make the composite panels suitable for slender and lightweight glass constructions and reveal new design possibilities for the building industry. However, the material properties of the modiﬁed PMMA polymer interlayer core for precise design considerations are lacking. Furthermore, the material behaviour of thermoplastic polymers changes over time, ages due to environmental inﬂuences and is temperature-dependent. This signiﬁcantly affects the composite load-bearing behaviour and deﬁnes the limits of application for the composite panels in the building industry. In order to facilitate during the development process and to build a design basis for the composite panels, material model parameters and simulation methods are required. Hence, an extensive test programme was conducted to investigate the material properties of the PMMA interlayer core by means of dynamic mechanical thermal analysis as well as uniaxial tensile and creep tests. The dataset and subsequent implementation into ﬁnite element software allowed for realistic simulations of the glass–plastic-composite panels and an extension of experimental results. Numerical simulations were performed with the commercial ﬁnite element programme ANSYS Workbench 19.3. Additionally, four-point bending tests were performed on composite test specimens with a different build-up and conventional glass panels to validate the material model and ﬁnite element simulations. These investigations and adopted material properties formed the basis for a numerical parametric study to evaluate the inﬂuence of stiffness, the load-bearing and lightweight performance in different build-ups. All the results are evaluated in detail and discussed in comparison with conventional monolithic and laminated glass panels. The dataset and material model parameters can be applied to further developments and design of lightweight glass–plastic-composite panels for structural applications in the building industry. Keywords Glass–plastic-composite · Sandwich structure · Material model · Numerical simulation · Tensile testing · Dynamic mechanical thermal analysis · PMMA · Acrylic glass · Four-point bending · Finite element analysis · Thin glass · Composite material · Transparency 1 Introduction tional materials. In different industries, such as automotive and aerospace, lightweight, strong, stiff and durable com- Composites combine the beneﬁts of two or more materials posite materials are frequently used and developing at a and exhibit improved mechanical properties over conven- high rate. Similarly, the glass industry is searching for novel lightweight glass composites with high structural perfor- Julian Hänig mance to realise slender structures with maximum trans- Julian.email@example.com parency (Nehring and Siebert 2018; Neugebauer et al. 2018; 1 Ribeiro Silveira et al. 2018; Weimar and López 2018). Glass– Institute of Building Construction, Technische Universität plastic-composite panels, called NEEROGLAS , combine Dresden, Dresden, Germany 123 250 J. Hänig, B. Weller Fig. 1 Edge view of a glass–plastic-composite panel with polished edge treatment and corresponding build-up (a) and connection prototypes (b) lightweight polymethylmethacrylate (PMMA), also known as acrylic glass, as plastic interlayer core and thin glass as protective cover layers in a fully bonded transparent sand- wich assembly (see Fig. 1a). A casting manufacturing process bonds the polymer interlayer core to the glass through radi- cal polymerisation without the use of adhesives or interlayer ﬁlms. Covalent bonds at the glass interface result in strong adhesion and shear coupling between the layers. Additional edge processing provides high glossy ﬁnish, like the conven- tional glass edge polishing. The promising material combination and composite load- bearing performance pushes the boundaries for novel innova- Fig. 2 Transmission-wave length diagram of thin glass, PMMA, con- tive lightweight and transparent glass structures. Mechanical ventional laminated glass with a standard PVB, soda-lime glass and milling, drilling and processing of the polymer interlayer core glass–plastic-composite (build-up: 1ANG-6PMMA-1ANG); related visible light transmittance according to (DIN EN 410:2011-04 2011)in enables novel discretely bonded and mechanically integrated brackets connection joints (see Fig. 1b). A high structural performance combined with low self-weight provides novel design possi- bilities. cores and even inﬁlls, such as LEDs, fabrics, metal grids and Glass–plastic-composite panels can be manufactured with solar panels can be integrated in the design. a total interlayer core thickness of up to 20 mm with all types Conventional laminated glass for building industry appli- of cuttable glass—preferably 0.5 mm to 3 mm in thickness cation has been extensively investigated. The mechanical (Neeb 2017). Hence, combinations with annealed (ANG) properties of glass are isotropic linear-elastic and very well and chemically strengthened glass (CSG) are possible. CSG known. The interlayer properties have been also widely stud- would enable higher impact resistance, improved ﬂexural ied in last decades, as described in the review of (Martín et al. strength as well as higher scratch resistance, however, at 2020). A wide range of material investigations and models increased costs compared to ANG (Karlsson et al. 2010). for standard polyvinyl butyral (PVB) (Andreozzi et al. 2014; The light transmittance of glass mainly dependents on the Botz et al. 2019; Sobek et al. 2000), ethylene-vinyl acetate glass composition, supplier and thickness. Figure 2 compares EVA (Hána et al. 2019; Schuster et al. 2018), polyurethane the light transmission in visible light range according to (DIN PU (Scherer et al. 2020), thermoplastic polyurethane TPU EN 410:2011-04 2011) of the novel glass–plastic composite (Kuntsche 2015; Rühl 2017) and stiff PVB interlayers build-up and its individual layers to conventional glass with (Kuntsche 2015) are available for implementation in ana- total thicknesses of 8 mm. The light transmission of the glass– lytical calculations and numerical simulations. plastic composite (containing UV absorbers in PMMA) with The application of the novel glass–plastic-composites, as 1 mm thin glass cover layers is 89.2%, marginally higher a lightweight substitute to conventional glass panels in the than the light transmission of conventional soda-lime glass building industry, requires the knowledge of precise material (88.9%). properties of the PMMA interlayer core and detailed com- Within the polymerisation process of the composite pan- posite load-bearing behaviour. The mechanical properties els, transparency, UV-transmittance, adhesion, and mechani- such as strength, rigidity, ductility, temperature dependency cal parameters of the PMMA interlayer core can be modiﬁed and durability are highly important for the structural design. by adjusting the chemical composition and ﬁllers. Multi- Various parameters, such as loading rate, temperature, envi- coloured panels can be produces with colour-ﬁlled interlayer ronmental inﬂuences and manufacturing greatly affect the molecular characteristics and mechanical properties of ther- 123 Experimental investigations and numerical simulations 251 moplastic polymeric materials. It is particularly important to of glass–plastic-composite panel build-ups. Furthermore, determine the PMMA’s glass transition temperature in order an assessment of glass–plastic-composites in comparison to ensure thermal stability of the PMMA in the tempera- with conventional glass panels in terms of structural per- ture range deﬁned by the ﬁnal application of the composite. formance and lightness is provided. The paper combines Dynamic mechanical thermal analysis and material testing a material study on the PMMA interlayer core and the evaluate the temperature-dependent material properties and glass–plastic-composites with numerical investigations for deﬁne the effective application limits for the material. Fur- detailed investigations and extension of results. All results thermore, the understanding of the inﬂuence of durability and are evaluated and discussed in detail with consideration of the ageing on structural behaviour is a key requirement for the requirements in building applications. Based on the overall application in the building industry, particularly in façades work, the ﬁnal section summarises the results, draws conclu- with exposure to climate changes, high radiation and mois- sions and gives a short outlook for further research on the ture. topic of glass–plastic-composite panels. Commercial PMMA product material properties have been extensively investigated with regards to their yield behaviour (Rühl et al. 2017; Zhang et al. 2016), creep 2 Study approach (Arnold and White 1995; Crissman and McKenna 1987; Fernández et al. 2011), ageing (Martinez-Vega et al. 2002) This paper presents an extensive study following a bottom-up and solvent stress crazing (Andrews and Levy 1974); lami- approach according to Fig. reff3. The experimental test pro- nated PMMA-TPU setups subjected to low velocity impact gram includes material investigations by means of dynamic were investigated in (Rühl 2017) for automotive applica- mechanical thermal analysis (DMTA), uniaxial tensile tests tions. However, material composition variations with the (DIN EN ISO 527-2:2012-06 2012) and uniaxial creep tests addition of modiﬁers, such as adhesive promoters for achiev- (DIN EN ISO 899-1:2018-03 2018) at different tempera- ing the adhesion to the glass surface, and the customised tures, as well as artiﬁcial ageing on dumbbell test specimens polymerisation process for glass–plastic-composite panels (DIN EN ISO 3167:2014-11 2014) of the PMMA inter- affect the material properties of the PMMA (Neeb 2017). layer core. Supplementary four-point bending tests (DIN EN Signiﬁcant changes in performance are expected compared 1288-3:2000-09 2000) on glass–plastic-composite and con- to industrially cast or extruded PMMA products. Further- ventional glass specimens accompany the investigations and more, the exact PMMA interlayer core applied in the here evaluate the structural load-bearing behaviour in comparison explored composite panels has not been investigated regard- with conventional glass panels. Based on the experimen- ing the speciﬁc building application requirements related tal results, suitable material model parameters are derived to loading, temperature and durability. At present, a com- and implemented into FE software. Numerical simulations parative study of the structural load-bearing behaviour and are compared to experimental results to validate the material lightweight aspects of the glass–plastic-composites versus parameter assumptions and evaluate the stress distribution in conventional glass panels has not been performed. In order the composite assembly. A stiffness study examines the inﬂu- to enhance the understanding of the structural behaviour of ence of the PMMA interlayer core Young’s modulus on the glass–plastic-composite panels, the extensive experimental overall bending stiffness and corresponding PMMA stresses. study presented in the ﬁrst part of the paper investigates A subsequent parametric study investigates relevant compos- the temperature and load-dependent mechanical properties ite build-ups in four-point bending simulations and evaluates and the durability of the reference PMMA interlayer core the structural performance and lightweight characteristics in material. Additional four-point bending tests examine the comparison with conventional glass panels. composite load-bearing behaviour in comparison with con- The following paragraphs introduce the individual steps ventional glass panels. This gives a broad experimental basis of the study approach shown in Fig. 3: for the evaluation of the composite material behaviour for Dynamic mechanical thermal analysis (DMTA) the application in the building industry. The DMTA examines the thermodynamic and viscoelastic To reduce extensive testing and prototyping, calculation behaviour and glass transition of the PMMA interlayer core. methods or computational models are essential for the devel- A deﬁned temperature-frequency program in a three-point opment, structural optimisation and design. Therefore, in bending ﬂexural oscillation mode determines the viscoelastic the second part of the paper numerical simulations and ◦ ◦ properties. The temperatures range from –40 Cto +140 C the use of suitable material models based on the exper- (1 K/min heating rate) in multi-frequency stress sweeps (0.5, imental dataset provide further insights on the structural 1, 5 and 10 Hz). behaviour. Parametric studies investigate the inﬂuence of the PMMA interlayer core Young’s modulus on the composite Uniaxial tensile tests The uniaxial quasi-static tensile tests stiffness and load-bearing behaviour across a wide range (DIN EN ISO 527-2:2012-06 2012) evaluate the in-plane 123 252 J. Hänig, B. Weller Fig. 3 Study approach through the experimental and numerical investigations stress-strain behaviour, stiffness and failure characteristics Uniaxial creep tests The uniaxial tensile creep tests accord- of the PMMA interlayer core on mechanically processed ing to (DIN EN ISO 899-1:2018-03 2018) reveal the vis- dumbbell test specimens Type 1B (DIN EN ISO 3167:2014- coelastic creep behaviour of the PMMA interlayer core over 11 2014). The initial mechanical properties are examined 1000 hours. Tests were performed at room (+23 C) and ◦ ◦ at temperatures of –20, +23 and +60 C at a strain-rate elevated temperature (+60 C) according to relevant temper- of 1 mm/min. Furthermore, the load-dependent behaviour atures for laminated glass following (DIN EN 16613:2020-01 is evaluated at standard (1 mm/min) and high loading rate 2020). Five different stress levels ranging from 5% to 65% (100 mm/min) at +23 C. Artiﬁcial ageing scenarios examine of short-term initial strength were applied. the material’s durability and resistance to potential envi- Composite load-bearing tests The composite four-point ronmental inﬂuences. A comparison of residual material bending tests were conducted according to (DIN EN 12337- properties with the initial properties demonstrates the age- 1:2000-11 2000) to describe the load-bearing behaviour in ing effects on the material behaviour. Four different ageing bending. As numerous test specimens are required for sta- scenarios are examined: tistical strength evaluation, this paper addresses the intact load-bearing behaviour in non-destructive tests. Two test • cleaning: immersion in façade cleaning agent at a tem- ◦ series of glass–plastic-composite panels of a total thick- perature of +45 C for 500 hours according to (DIN EN ness of 8 mm are examined and compared to conventional ISO 175:2011-03 2011; ETAG 002-1 2012). monolithic and laminated glass of equivalent thickness. The • water: immersion in demineralised water at a tempera- ◦ composite build-ups consist of thin glass faces of 1 and 2 mm ture of +45 C for 500 hours according to (ETAG 002-1 ANG with a corresponding PMMA core of 6 and 4 mm thick- 2012). ◦ ness. • SUN: combined exposure to high temperature (+65 C), UV radiation (550 W/m ) and demineralised water at Material model parameters and ﬁnite element implemen- +45 C for 500 hours (250 cycles) according to (DIN EN tation Based on the material examination dataset, linear ISO 4892-2:2013-06 2013; DIN EN ISO 11431:2003-01 material model parameters with a focus on the temperature- 2003). dependent short-term material behaviour of the PMMA inter- • climate: cyclic climate change test according to (DIN EN layer core are derived and implemented into FE software. ISO 9142:2004-05 2004); modiﬁed cycle D3: tempera- Experimental test results serve to validate the uniaxial tensile ◦ ◦ tures ranging from –20 Cto +80 C at a high relative simulations and the implemented material model parameters humidity of up to 95% for 504 hours (21 cycles). within the linear elastic range. Subsequent numerical simula- tions of four-point bending allow for extended stress analysis 123 Experimental investigations and numerical simulations 253 Table 1 Summary of material properties applied in the research according to technical data sheets and standards Material Methyl methacrylate Thin glass (Float) Conventional glass Supplier Evonik Industries AG Pilkington (NSG Group) Thiele AG Product MMA with 10 ppm ANG Lahti MICROFLOAT FTG: TG-ESG® MEHQ polymerisation LG: TG-Protect® to PMMA from ANG Density [kg/m ] 1190 2490 2500 −1 −6 −6 −6 Coefﬁcient of thermal expansion [K]70 × 10 9 × 10 9 × 10 Young’s modulus [N/mm ] – 73 000 70 000 Poisson’s ratio [–] – 0.224 0.23 in the PMMA interlayer core and over the whole panel as commercial monomer methyl methacrylate (Evonik Indus- well as an extrapolation of load-bearing behaviour to differ- tries AG: MMA with 10 ppm Hydroquinone monomethyl ent build-ups and increased load levels. ether MEHQ stabilizer) with UV absorbers was used in the study. To achieve the highest dimensional accuracy, all test Parametric study The stiffness study, performed on the specimens were cut out of homogeneous sheet material by basis of the four-point bending simulations, evaluates how waterjet processing. The processing quality may affect the the Young’s modulus of the PMMA interlayer core affects ultimate strength due to quality differences compared to the overall composite bending stiffness and the expected in-shape cast or polished specimens. Such inﬂuences were stress distribution through the centre cross-section. It also accepted within the study and considered in the evaluation. assesses the temperature dependency and reviews the lim- Composite test specimens were manufactured in panel sizes its of the implemented linear material model parameters. 2 of 2.1 × 1.3m and afterwards cut in size via waterjet The subsequent parametric study extends the investigation processing. The composite specimens underwent additional of the composite load-bearing behaviour to a wide collec- chamfering (1 mm) and polishing in a vertical glass edge- tion of glass–plastic-composites and laminated glass panels grinding machine. Glass supplier of the thin glass faces was in build-ups ranging from 6 to 15 mm in total thickness. Pilkington (Pilkington Group Limited 2002). Conventional The composite stiffness, expressed as Young’s modulus of fully tempered glass (FTG) and laminated glass (LG) speci- an equivalent homogeneous material, is individually eval- mens used as a reference came from a standard glass supplier. uated by the centre panel deﬂection and the application of For conventional glass, material properties according to (DIN Euler-Bernoulli beam theory. Following from this, the spe- EN 572-1:2016-06 2016; DIN 18008-1:2020-05 2019)were ciﬁc stiffness (Gooch 2011) or speciﬁc modulus, deﬁned as considered. Table 1 summarises the material properties. Young‘s modulus per unit mass density, is determined for the analysed build-ups. The speciﬁc stiffness quantiﬁes the 3.2 Dynamic mechanical thermal analysis potential of the composites and permits the evaluation of the lightweight performance of glass–plastic-composite pan- 3.2.1 Test method els in comparison with conventional glass panels and other composite materials. It further provides a ﬁrst rough design The mechanical properties of viscoelastic polymers, such as of the composite panels as substitution for monolithic glass thermoplastic PMMA, are highly dependent on temperature, by means of the equivalent glass thickness approach. time and loading (Grellmann and Seidler 2013; Schwarzl 1990). The DMTA is a method for determining the thermo- dynamic and viscoelastic properties of polymers by applying 3 Experimental investigation a sinusoidal force to the material test sample and measuring the responding sinusoidal deformation (DIN EN ISO 6721- 3.1 Materials 1:2019-09 2019; Grellmann and Seidler 2013). Viscoelastic material behaviour causes a shift between the applied force Dumbbell test specimens for the PMMA interlayer core (stress) and the corresponding deformation (strain). The devi- material investigations were manufactured by the repre- ation is referred to as the phase shift δ. Applying the Fourier sentative radical polymerisation cast process for glass– Transformation results in storage modulus E (refers to elas- plastic-composite panels in the reference composition. The tic materials stiffness) and loss modulus E (released energy 123 254 J. Hänig, B. Weller modulus E ) with increasing temperature, which is typ- ical for thermoplastic polymers. Deviations are speciﬁed by error indicators. Slight differences in thermomechan- ical behaviour at altering frequencies indicate marginal frequency-dependent behaviour. The storage modulus sig- niﬁcantly decreases at appx. +100 C and characterizes the relaxation transition (glass transition). Beta-relaxations due to local mobility of side groups are observed in the region between 25 to 30 C and conﬁrm the ﬁndings in (Ionita et al. 2015; Menard and Menard 2020). The glass transition is determined as a temperature range between the onset of the storage modulus curve (start of soft- Fig. 4 DMTA test setup (Netzsch 2009) ening) and the maximum of the loss modulus curve (end of glass transition) according to (ASTM D4065-20 2020; ASTM E1640-18 2018). It ranges from T =+97.0 C g,onset (0.5 Hz) to T =+135.3 C (10 Hz). The softening g,peak starts 17 K above the application temperature range of the building industry. The PMMA exhibits a storage modulus 2 ◦ > 2000 N/mm until +80 C. Low energy dissipation (loss factor tan δ< 0.12) indicates mainly elastic behaviour. The DMTA results ﬁt with the information from literature on conventional PMMA investigations (Menges et al. 2011). The characteristics of the glass transition area itself and the entropy elastic state do not play a signiﬁcant role for the design and are not further studied within this paper. In sum- mary, the DMTA veriﬁes high elastic stiffness and no phase Fig. 5 Thermograms of the multi-frequency DMTA measurements on change of the PMMA at the building application relevant PMMA with remarks of the building industry application range as well temperatures. This leads to desirable material properties of as examined glass transition the PMMA interlayer core for the application in composite panels for the building industry. as heat). The loss factor tan δdeﬁnes the ratio between E and E and describes the viscoelastic damping. The DMTA sen- sitively detects state changes of polymers that can be directly associated with the change in the physical modules. Figure 4 3.3 Uniaxial tensile tests shows the DMTA test setup and its individual components. 3.3.1 Test method 3.2.2 Analysis The uniaxial tensile test setup and specimen preparation are The presented analysis focuses on the determination of the shown in Fig. 6. A test rig Instron UPM 5881 in combination storage modulus E and loss factor tan δ that both deﬁne with an optical extensometer measures contactless nominal the corresponding glass transition range (transition between (engineering) axial and transversal strains using high contrast glassy energy elastic to rubbery entropy elastic state). Three measuring points (white marks on black painted specimens). test samples with the dimensions of 30 x 6 x1.2 mm were The test setup was equipped with an environmental test tested in three-point bending mode (20 mm free bending chamber and feedback temperature control. The standard length) that is recommended for materials with high stor- loading-rate was set to 1 mm/min for the evaluation of ten- age modulus (Netzsch 2009). The displacement-controlled sile properties according to (DIN EN ISO 527-2:2012-06 bending amplitude amounted to 30 μm. Figure 5 shows the 2012). Additional polymer strain gauges precisely evaluate thermograms presenting storage modulus E and the loss fac- the Poisson’s ratio in the centre of the specimen (backside) tor tan δ curves of the PMMA (mean values of three samples) from transversal to axial strains at +23 C. Within each test for altering frequencies in the temperature range from –20 to series, minimum ﬁve test specimens were examined and their +140 C. nominal stress ε-nominal strain σ behaviour, tensile Young’s The thermomechanical behaviour of the PMMA inter- modulus E , ultimate strength σ and elongation at break ε t u u layer core manifests continuous decrease in stiffness (storage characterised. 123 Experimental investigations and numerical simulations 255 Fig. 6 Tensile test setup (a), dimensions of test specimen type 1B in mm according to (DIN EN ISO 527-2:2012-06 2012) with positioning of polymer strain gauges as well as extensometer points (b)and black painted test specimen before and after testing (c) and high temperatures (+60 C) are considered. Figures 8 and 9 compare the stress-strain behaviour at different tem- peratures at standard (1 mm/min) and at high (100 mm/min at +23 C) loading strain-rates. The effects of temperature are clearly visible by an increased strength and brittleness at low temperatures, whereas the PMMA softens at high temperatures, lead- ing to increased elongation at break and decreased tensile strength. The high loading strain-rate results in higher ulti- mate strength with lower elongation at break. Figure 9 summarises and compares the results of short-term tensile testing. The inﬂuence of temperature on the stiffness decrease is approximately linear across the considered range of –20 C Fig. 7 Nominal stress-nominal strain diagram and evaluation of ◦ ◦ and +23 Cto +60 C, matching the ﬁndings in the DMTA. Young’s modulus of PMMA interlayer core at a temperature of +23 C and a loading strain-rate of 1 mm/min 3.3.4 Ageing inﬂuences 3.3.2 Reference material behaviour Figure 10 presents the inﬂuences of the accelerated ageing scenarios according to the test program. The immersion in Figure 7 shows the reference engineering stress-strain dia- cleaning agents and water only slightly inﬂuences the mate- gram as mean value regression curve (bold black) and the rial behaviour and properties (Young’s modulus, strength and individual test results (grey) at a strain-rate v = 1 mm/min ◦ elongation at break). No differences in the optical appearance at laboratory conditions +23 C/50% RH (DIN EN ISO were observed after these ageing scenarios. The SUN age- 291:2008-08 2008). The chart illustrates ideal linear stress- ing scenario as combined UV, high temperature and water strain behaviour of the PMMA until approximately 0.8% exposure embrittles the material, which stiffens it (+13%), strain (deviation from linear behaviour: 2%). Within the ideal but signiﬁcantly lowers the strength (–29%) and elongation linear elastic range, the tensile Young’s modulus E = σ/ε at break (–57%) compared to the initial properties. Slight is derived using the gradient (dashed line). After approx- material yellowing was observed. The material strength does imately 0.8% axial strain, the material behaves viscoelastic not fall below 30 N/mm . The climate ageing scenario very until brittle failure. No yield point indicates an onset of plastic slightly inﬂuenced the mechanical properties, with no effects deformation. The PMMA exhibits stiff but brittle behaviour on the optical appearance. and fails on average at strains of 2.92% at a strength of 2 ◦ 46.2 N/mm . The Poisson’s ratio at +23 C at a strain-rate of 1 mm/min is evaluated to 0.37, between 0.3 to 1.5% strain. 3.3.5 Summary and discussion 3.3.3 Temperature and loading strainrate dependency The mechanical material properties are summarised in Table 2. The average X of each test series serves as a com- mean Composite panels in the building industry are exposed to parative value of the Young’s modulus, tensile strength and different loadings as well as environmental conditions. The elongation at break to the unaged initial properties (+23 C| requirements can be associated to those of conventional lam- 1 mm/min). inated glass (DIN EN 16613:2020-01 2020;DIN EN ISO The experimental tests on dumbbell specimens of the 12543-2:2011-12 2011). Hence, the limits of low (–20 C) PMMA interlayer core reveal mainly linear behaviour under 123 256 J. Hänig, B. Weller Fig. 8 Nominal stress-nominal strain diagram of PMMA interlayer core—extract (a)and full scale (b); labelling of test series: temperature | loading rate in mm/min; dashed lines indicate the Young’s modulus Fig. 9 Young’s modulus E (a), tensile strength σ and elongation at break ε (b) depending on temperature and loading rate; labelling of test series: temperature | loading rate in mm/min Fig. 10 Young’s modulus modulus E (a), tensile strength σ and elongation at break ε u u (b) depending on ageing scenario (+23 C | 1 mm/min) Table 2 Short-term mechanical properties of PMMA interlayer core: mean value | standard deviation (ratio: property/initial property); labelling of test series: temperature | loading rate in mm/min 2 2 Test condition Test series Young’s Modulus E (N/mm ) Tensile strength σ (N/mm ) Elongation at break ε (%) t u u Initial +23 C | 1 unaged 2337 | 190 (100%) 46.2 | 1.5 (100%) 2.92 | 0.35 (100%) Temperature –20 C | 1 unaged 2790 | 336 (119%) 52.9 | 6.9 (115%) 2.13 | 0.18 (73%) +60 C | 1 unaged 1545 | 96 (66%) 30.6 | 0.9 (66%) 3.15 | 0.25 (108%) High loading rate +23 C | 100 unaged 2609 | 75 (112%) 56.8 | 2.0 (123%) 2.63 | 0.08 (90%) Ageing +23 C | 1 cleaning 2278 | 43 (97%) 41.9 | 2.6 (91%) 2.32 | 0.28 (80%) +23 C | 1 water 2200 | 47 (94%) 39.7 | 2.1 (86%) 2.25 | 0.30 (77%) +23 C | 1 SUN 2651 | 50 (113%) 32.6 | 2.4 (71%) 1.27 | 0.11 (43%) +23 C | 1 climate 2303 | 39 (99%) 43.7 | 1.3 (95%) 2.57 | 0.19 (88%) 123 Experimental investigations and numerical simulations 257 quasi-static loads with small strains until brittle failure. The 3.4 Uniaxial creep tests polymer chains of the thermoplastic polymer get more entan- gled as they soften at higher temperatures. This results in 3.4.1 Test method reduced stiffness and lower strength with higher elongation at break. At lower temperatures and higher loading strain- The Creep modulus is of central importance in the design rates, the polymer exhibits stiffer, stronger but more brittle of plastic materials under long-term loading. Uniaxial creep behaviour. tests on dumbbell specimens examine the inﬂuences of load The reference unaged material strength at +23 C| duration on the mechanical material properties of the PMMA 2 2 1 mm/min amounts to 46.2 N/mm with an elongation at interlayer core. Stress levels of 3, 5, 10, 20 and 30 N/mm ◦ 2 ◦ break of 2.9%. The Young’s modulus amounts to at +23 C and 3, 5, 10, 15 and 20 N/mm at +60 C reveal 2337 N/mm . Industrially cast or extruded PMMA pan- stress-dependent viscoelastic material behaviour. Two test els (e.g. PLEXIGLAS®7N) exhibit higher tensile Young’s specimens per series were examined in a creep test rig (see 2 2 modulus (3200 N/mm ) and strength (73 N/mm ) with an Fig. 11). Lowering the weights in a pneumatic system started ultimate strain of 3.5%. These alterations can be assigned the loading shock-free. The initial strain is considered at a to the industrial manufacturing process and the inﬂuence measurement time of t = 10 s. This eliminates material and of additional processing. The waterjet inlet and outlet cause measurement inﬂuences of load introduction. In order to cor- defects at the specimen edges that may reduce the strength rect the non-uniform load introduction and to unify the test compared to the edge processed/ polished or in form cast results, the initial strains are derived using the initial Young’s specimens. No additional tests were performed to investigate modulus from the short-term test results at the corresponding these inﬂuences. temperature (compare equation 1). Hence, the initial strain, at The PMMA interlayer core softens at elevated temper- 10 s after the load introduction, corresponds with the elastic atures with lower strength at increased strains. However, component of the material. even at +60 C, the PMMA exhibits a Young’s modulus of 1545 N/mm . Compared to conventional interlayers for ε (t ) = ε (t ) − ε (t = 10 s) corrected measured measured laminated glass, the stiffness is several times higher, even +ε (1) 0,short −term for the stiff PVB or ionoplast interlayers (Kuntsche 2015). Inﬂuences of ageing on the PMMA leads to negligible effects Optical extensometer contactlessly measured the axial strains on the load-bearing behaviour, apart from the SUN ageing over a time period of 1000 h with (at least) the measurement that embrittled the material leading to slightly higher stiff- frequencies deﬁned in (DIN EN ISO 899-1:2018-03 2018). ness and reduced strength. The results demonstrate the high durability of the PMMA interlayer core. In the ﬁnal applica- 3.4.2 Creep behaviour tion, the glass cover layers additionally protect the PMMA core surfaces from ageing, which further improves the dura- The strain–time diagrams in Figs. 12 and 13 present the tem- bility in the composite assembly. However, it should be noted perature and stress-dependent creep behaviour. The dashed that PMMA is highly susceptible to stress corrosion crack- lines indicate the mean values, whereas the solid lines ing (Andrews and Levy 1974). Cleaning agents with high approximate the strain behaviour over time using power solvent content, such as acetone or isopropyl alcohol, can law function according to equation 2 (Findley 1976). The lead to visible stress corrosion cracking resulting in reduced strength and premature failure. The contact and exposure to such cleaning agents must be explicitly excluded in applica- tion and maintenance. In summary, the experiments on dumbbell test specimens provide an extensive dataset. This allows for the development of a material parameter set for the FE simulations and reliable predictions of the material behaviour of the PMMA and the structural load-bearing behaviour of glass–plastic composite panels in different build-ups. Fig. 11 Coesﬁeld creep test rig: ten specimens with applied measure- ment marks for contactless measurement of axial strain 123 258 J. Hänig, B. Weller Fig. 12 Nominal axial strain ε (a) and derived Creep modulus E (b)over time (logarithmic scale) at different stress levels (+23 C) Fig. 13 Nominal axial strain ε (a) and derived Creep modulus E (b) over time (logarithmic scale) at different stress levels (+60 C); rhombus marks failure Table 3 Creep modulus for the evaluated stress levels at different temperatures for individual time steps 2 2 2 Stress level σ (N/mm ) Creep modulus after 1 h: E (N/mm ) Creep modulus after 1000 h: E (N/mm ) c,1h c,1000h ◦ ◦ ◦ ◦ +23 C +60 C +23 C +60 C 3 2324 1185 2252 658 5 2297 1196 2209 587 10 2288 1140 1991 492 15 – 1004 – 280 20 2115 727 1609 Failure 30 1810 – 1045 – derived Creep modulus E is given in the corresponding marises the results at different stress levels for the time steps Creep modulus–time diagrams. of 1 h and 1000 h. The creep coefﬁcient c , following equation 3, speciﬁes the creep behaviour and respectively the temporal decrease ε (t ) = ε + m · t (2) of material stiffness by relating the end value of Young’s modulus E to a reference value E or E . c,1000 h c,initial c,1h m, n material constants from regression optimisation. Since the temperature and applied load level affect the creep The viscoelastic strain component increases with progres- rate, different operating temperatures of polymers must be sive load duration and grows at elevated temperatures and considered in the design stage. levels (Grellmann and Seidler 2013). Linear viscoelasticity of the PMMA leads to a linear correlation between stress and E (t ) c end strain, independent of the load duration (Schwarzl 1990). At c = (3) higher load durations and higher stress levels σ> 10 N/mm E (t ) c ref the PMMA interlayer core exhibits increasingly nonlinear- viscoelastic behaviour. (Zhao et al. 2008) speciﬁes a critical Table 4 summarises the evaluated creep coefﬁcients for all stress limit of 18 N/mm for the transition of linear- to the tested conﬁgurations by using the initial Young’s modulus nonlinear-viscoelastic creep at room temperature for a com- and the Young’s modulus after 1 h. mercial PMMA with a glass transition temperature of about To classify the results, the stresses in the PMMA inter- 105 C. The increasing nonlinear-viscoelastic effects are layer core in the composite assembly were roughly calculated enhanced by elevated temperatures and disproportionately under bending loads. The precise interlayer core stresses will increase with load duration (Schwarzl 1990). Table 3 sum- be presented in section 3.4. The stress levels in the compos- 123 Experimental investigations and numerical simulations 259 Table 4 Creep coefﬁcients of PMMA interlayer core at investigated temperatures and stress levels Ec,1000h Ec,1000h 2 2 2 Stress level σ (N/mm ) Creep coefﬁcient c = (N/mm ) Creep coefﬁcient c = (N/mm ) c c E E c,initial c,1h ◦ ◦ ◦ ◦ +23 C +60 C +23 C +60 C 3 0.96 0.47 0.97 0.56 5 0.96 0.41 0.96 0.49 10 0.86 0.34 0.87 0.43 15 – 0.28 – 0.28 20 0.71 Failure 0.76 Failure 30 0.49 – 0.58 – ite assembly under bending loads are expected not to exceed Axial strain gauges on the glass surfaces (centre top and bot- 5N/mm , as the glass stresses would lead to an early failure. tom) and vertical displacement sensors in the centre, centre Therefore, at the stress levels up to 5 N/mm at room temper- edge and below one bending roller (see Fig. 14) recorded ature, the creep coefﬁcient amounts to 0.96. This indicates the strains in x direction and deﬂections in z direction. Two minimal creep tendency and nearly constant stiffness for the series, 1ANG-6PMMA-1ANG and 2ANG-6PMMA-2ANG, expected loading on glass–plastic-composite panels in use. were tested. Monolithic 8 mm (FTG) thick glass and lam- At elevated temperatures and higher stress levels, a more sig- inated glass composed of two layers of 4 mm ANG with niﬁcant creep inﬂuence on the PMMA is to be expected and a standard PVB interlayer with a thickness of 0.76 mm must be considered in the design of glass–plastic-composite (LG 44.2 - PVB) were tested to compare the load-bearing panels. behaviour to conventional glass panels. To get a more widespread dataset, further test series at a lower temperature limit for laminated glass (–20 C) and 3.5.2 Composite load-bearing behaviour additional stress levels could be carried out. However, at lower temperatures the PMMA behaves stiffer and creeps Figure 15 shows the load-bearing behaviour of the test series less, leading to beneﬁcial material properties for the design of (mean regression curve) in a force-deﬂection and force-stress glass–plastic-composite panels. The conducted experimental (strain gauge SG1) diagram. To evaluate the speciﬁc glass investigations cover the important design-relevant tempera- stresses from measured strains, Young’s moduli according tures and stress levels sufﬁciently for building applications. to the thin glass manufacturer’s technical data sheet and the Based on the experimental dataset, material models for ana- standards for conventional glass are applied (see Table 1). lytical or numerical simulations can be developed in further The composite panels exhibit linear load-bearing studies, however, as this exceeds the scope of this paper. Pre- behaviour (coefﬁcient of determination R > 0.999). No dictive models for creep behaviour of commercially available creep effects of the interlayer material are observed in the thermoplastic PMMA are mainly established on exponential short-term tests. This proves the persistent short-term stiff- functions (Arnold and White 1995) also taking into account ness of the PMMA interlayer core and complete connection creep rupture (Crissman and McKenna 1987), generalized between the layers. The glass cover layer thicknesses sig- Maxwell models, as developed in (Rühl et al. 2017), or gen- niﬁcantly inﬂuence the load-bearing behaviour (deﬂection eralized Maxwell models as a generation of Prony-Series and stress response) according to the overall composite (Fernández et al. 2011). panel stiffness. Laminated glass with standard PVB inter- layer exhibits signiﬁcant initial shear coupling. However, 3.5 Composite load-bearing tests standard PVB softens already at room temperature leading to time-dependent creep. This lowers the coupling effect of the 3.5.1 Test method glass panes during the experiments and results in nonlinear deﬂection and glass stress increase (see Fig. 15). The initially Four-point bending tests according to (DIN EN 1288-3:2000- very high stiffness up to a force level of around 70 N can be 09 2000) examine the load-bearing behaviour and calculate assigned to the sensitivity of the test machinery—the faster the linear composite stiffness and glass stress response. Min- load application speed at the start of testing until the machine imum ﬁve test specimens per series were loaded up to a had adjusted. force level of 400 N (load application speed of 400 N/min) at For a comparison of the bending stiffness, the corre- +23 C. A detailed description and evaluation of composite sponding Young’s moduli of the specimens (E ) were composite load-bearing tests are presented in (Hána and Weller 2019b). derived from the maximum centre deﬂection by the appli- 123 260 J. Hänig, B. Weller Fig. 14 Schematic four-point bending test setup with dimensions of the test specimens (mm) and measurements (a)and image of test rig (b) Fig. 15 Force-deﬂection (a)and force-stress (b)charts (regression curves) from four-point bending tests cation of the Euler–Bernoulli beam theory as conducted in tional glass panels. Wide ranging analytical sandwich beam (Hána and Weller 2019b). It assumes the elastic modulus in theories can also be applied to calculate the deformation accordance with Hooke’s Law and that the plane sections and stresses in composite structures (Altenbach et al. 2004; of the composite remain plane and normal to the axis of the Stamm and Witte 1974;Wölfel 1987). One is referred to beam. This can be assumed for materials with high shear stiff- (Hána and Weller 2019b) for the application of sandwich ness, as used in glass–plastic-composite panels, and full shear beam theory (Wölfel 1987) assumptions on glass–plastic connection due to the permanent chemical bond between the composite panels. It was shown that an approximation is pos- glass and PMMA interface. The ﬂexural rigidity and Young’s sible, however, only to a limited degree of precision. For a modulus of the composite in bending can be analytically more detailed analysis, FE simulations using the material derived from the centre deﬂection and used to describe the dataset are used to extrapolate the load-bearing behaviour stiffness of an equivalent homogeneous material. The mono- to varying build-ups. This also allows for the observation lithic glass as a reference represents the limit for full coupling of detailed glass and PMMA interlayer core stresses over the and corresponding glass bending stiffness as derived Young’s full panel, even at higher load levels, and a direct comparison modulus. The evaluated results for the tested build-ups are of various composite build-ups to conventional glass panels. summarised in Table 5. The monolithic glass Young’s modulus matching the ref- erence value of 70 000 N/mm (deviation +1.6%) validates the test method. LG 44.2—PVB exhibits a stiffness of 41 818 4 Numerical simulations and parametric study N/mm (60% of monolithic glass) due to only partial shear coupling at +23 C. The stiffness of the glass–plastic- composite panels is sensitive to the interlayer core-to-cover This section describes the implementation of the temperature- dependent material parameters (–20, +23 and +60 C) in layer ratio. In summary, the weight can be highly reduced by 39% or by 26%, still offering composite Young’s moduli the commercial FE software ANSYS Workbench 19.3 and of 61% and 93% for the assembly with 1 mm or 2 mm thin subsequent numerical simulations of the uniaxial tensile tests and four-point bending tests. The focus is set on the glass cover layers. The tensile glass stresses σ in the x ,SG1 composites are, however, larger compared to those in mono- short-term time independent linear material behaviour as the lithic glass as the glass is acting with a higher load fraction stresses in the interlayer are expected not to exceed the linear elastic limit in the composite load-bearing behaviour. This due to the glass-to-PMMA Young’s modulus ratio and the corresponding layer thicknesses. assumption is veriﬁed in the following parts of this paper. This evaluation forms the basis for comparison of the Post-processing of the simulation results examines the load- bearing behaviour and the detailed stress distributions in the individual composite build-ups and corresponding conven- panel cross section. The conducted experimental uniaxial 123 Experimental investigations and numerical simulations 261 Table 5 Evaluated results from composite tests (force level F = 400N) Build-up 1ANG-6PMMA- 2ANG-4PMMA- LG 44.2—standard monolithic glass 1ANG 2ANG PVB (ANG) 8mmFTG Amount of test specimen 5 8 5 5 Precise thickness measurement (mm) 0.99-5.80-1.02 1.89-3.60-1.89 8.47 (total) 7.80 Young’s modulus E (N/mm ) 43 593 (61%) 64 864 (93%) 41 818 (60%) 71 125 (100%: 70 000) composite Weight reduction to glass −39% −26% – – Stress σ (N/mm ) 33.27 (+82%) 24.66 (+35%) 20.95 (+15%) 18.28 (reference) x ,SG1 quasi-static tensile test are compared to the numerical imple- Fig. 16a compares the numerical simulations with the exper- mentation of the linear material parameters and checked for iments at temperatures of –20, +23 and +60 C. deviations within the linear elastic range. The experimental The isotropic linear model overestimates the stiffness at composite tests results validate the four-point bending FE increasing strains and increasingly deviates from the test model. The inﬂuence of the PMMA interlayer core stiffness results. The divergences for the overestimation of stiffness on the bending stiffness, i.e. the composite Young’s modu- compared to the experiments are marked by error bars for 5 lus, and PMMA interlayer core stresses are brieﬂy analysed. and 10% divergence. Up to stresses of 15.9 (–20 C), 24.7 ◦ 2 ◦ The following parametric study extends the composite load- (+23 C) and 15.0N/mm (+60 C) the linear stress-strain bearing behaviour analysis to other build-ups and examines behaviour matches the load-bearing behaviour with devia- the resulting performance in comparison with conventional tions of less than 5%. The corresponding strains are marked glass panels. by dashed lines in Fig. 16a. The deviations in the linear elastic range provoke minimal errors across the following simula- 4.1 Material parameters tion; as only low PMMA interlayer core stresses are expected in the composite bending mode, linear elastic material param- Isotropic linear elastic material behaviour by the deﬁnition eter assumptions permit sufﬁciently correct evaluation of the of Young’s modulus and Poisson’s ratio is implemented. composite material load-bearing behaviour in the FE analy- The isotropic deﬁnition similarly considers tension, shear sis. and compression stress states. The material parameters are assumed temperature-dependent according to experimen- 4.3 Four-point bending simulations tally evaluated properties (see table 6). Since the Poisson’s ratio of the thermoplastic PMMA changes insigniﬁcantly An FE model for the simulation of the composite load- ◦ ◦ across the temperature range from –20 Cto +60 Cupto bearing behaviour is developed following the four-point strains of around 2% and the evaluation for every temperature bending test setup. The material parameters for glass accord- and loading strain-rate is very complex as well as suscepti- ing to Table 1 assume linear isotropic elasticity. The user ble to measurement errors, the examined Poisson’s ratio of deﬁned material parameters implement the linear isotropic 0.37 at +23 C | 1 mm is generally applied. Only minor elastic properties of the PMMA interlayer core according deviations are expected compared to a more speciﬁc imple- to Table 6. Prony series coefﬁcients from (Andreozzi et al. mentation of the Poisson’s ratio. No failure mechanisms of 2014) describe the complex viscoelastic material behaviour the polymer PMMA are considered within the simulations for a standard PVB interlayer in laminated glass. All solid as signiﬁcantly higher glass tensile stresses are expected to bodies of the composite are bonded assuming full force trans- be decisive in the ultimate design. mission at the interfaces between the individual layers. Based on the preliminary convergence study with reﬁned meshing 4.2 Uniaxial tensile simulations and multiple segmentations over the thickness, the appropri- ate mesh size is set to 5 mm. Mid-size nodes in Solid186 FE simulations of the uniaxial tensile test inspect the mate- elements with full integration of quadratic elements serve rial parameter assumptions and FE model settings. Dumbbell for proper identiﬁcation of stress distributions. Table 7 intro- specimens with ﬁxed support conditions and force applied duces the simulation properties. on the opposite side are modelled. Higher order 3D 20- Figure 17 shows the FE model and detailed build-up with node solid elements (SOLID186) with full integration of the mesh sizing. The implemented layer thicknesses come from quadratic elements are used. A displacement-controlled load- the mean values of measurements within the experimental ing in –x direction simulates the behaviour considering large test series. Symmetry conditions in x-z and y-z plane deﬁne deﬂections. The resulting axial stress-axial strain diagram in the quarter symmetry. For accurate simulations, the bearing 123 262 J. Hänig, B. Weller Table 6 Isotropic elastic ◦ ◦ ◦ Isotropic elasticity −20 C +23 C +60 C material parameters for the PMMA interlayer core resulting Young’s modulus E [N/mm ] 2790 2337 1545 from the experimental test Poisson’s ratio μ [–] 0.37 0.37 0.37 results Fig. 16 Nominal stress-nominal strain diagram: comparison of experiments and numerical simulations of the uniaxial quasi-static tensile tests at different temperatures with marked divergences and assessed linear elastic range (a) and FE model with deﬁned mesh, support/ load conditions and corresponding axial stress distribution in x direction (b) Table 7 Introduction of simulation properties Properties Glass (conventional) Thin glass PMMA Standard PVB Material model Linear isotropic elastic Linear isotropic elastic Linear isotropic elastic Viscoelastic 2 2 2 ◦ 2 ◦ Elasticity E = 70 000 N/mm E = 73 000 N/mm E = 2337 N/mm (+23 C)E = 2790 N/mm (–20 C) Prony shear relaxation 2 ◦ E = 1545 N/mm (+60 C) (Andreozzi et al. 2014) 3 3 3 3 Density ρ 2500 kg/m 2490 kg/m 1190 kg/m ∼ 1100 kg/m Poisson’s ratio μ 0.23 0.224 0.37 0.49 Mesh size 5 mm (Solid 186 Elements with full integration of quadratic elements) and bending rollers are simulated as structural steel with a ment points corresponding with the experiments are used to nonlinear contact approach as proposed in (Müller-Braun and validate the FE model. Schneider 2017). The bending roller and support roller are Table 8 presents the measured and simulated deﬂections deﬁned with frictionless contact surfaces to the glass surface and stresses at the force level of 400 N. For the monolithic (target). Augmented Lagrange formulation with the detec- glass, the deﬂections and stresses in the centre are further ana- tion method of nodal point normal to target surface is used. lytically calculated according to the Euler-Bernoulli beam The pinball radius for ﬁnding the contact to the target was theory. The relative deviations evaluate the agreement of the set to 5 mm. Stepwise load-introduction (10 steps with mini- numerical calculations with the measured/ analytical values. mum 10 substeps) considers structurally nonlinear behaviour The comparison shows a generally good match between that affects the contact status of the rollers to the glass during the numerical simulations and experimental measurements bending. Force-controlled loading is applied on the bending as well as analytical calculations. The exceptionally high roller in +z direction. The bending roller is ﬁxed for move- deviations observed for the monolithic glass test series are ments in x and y direction, whereas the support roller is fully assigned to misapplication of the strain gauge series that was ﬁxed at the bottom. Stresses and deﬂections at the measure- found at the end of the tests. A further repetition of the test series was not possible. However, the analytical beam the- Fig. 17 Quarter FE model of four-point bending simulations (a) and detailed build-up with mesh sizing and evaluated stresses and deﬂections (b) 123 Experimental investigations and numerical simulations 263 Table 8 Comparison of experimental, analytical (Euler-Bernoulli beam theory) and numerical results (ANSYS) at force level of F = 400 N Detailed build-up (mm) (mean values) Temperature Deﬂections (mm) Glass stresses (N/mm ) T =+23 C w w w σ σ centre edge bendingroller x ,SG1 x ,SG2 7.80 FTG Test | Analytical 7.36 | 7.89 7.64 7.00 18.28 | 21.92 N/A | -21.92 ANSYS 7.71 7.86 7.32 21.50 − 21.89 Deviation +4.7% | -2.3% +2.9% +4.7% +17.6% | -1.9% N/A | -0.1% 0.99 ANG 5.80 PMMA 1.02 ANG Test 12.19 12.49 11.63 33.27 −34.76 ANSYS 12.74 13.00 12.11 34.89 − 36.66 Deviation +4.5% +4.1% +4.1% +4.9% +5.5% 1.89 ANG 3.60 PMMA 1.89 ANG Test 9.72 9.92 9.23 24.66 − 26.51 ANSYS 10.28 10.48 9.77 26.92 −27.65 Deviation +5.7% +5.7% +5.9% +9.2% +4.3% 3.86 ANG 0.76 standard PVB 3.86 ANG Test 10.10 10.22 9.52 20.95 N/A ANSYS 10.90 11.01 10.32 24.00 −24.27 Deviation +7.9% +7.7% +8.4% +14.6% N/A 264 J. Hänig, B. Weller Fig. 18 Stress distribution σ over centre cross section; force level F = 400 N (scaling PMMA interlayer core: 4x) x ,centre ory allows for veriﬁcation of the numerical simulations with Nonlinear stress-strain behaviour of the PMMA at increas- deﬂection and stress deviation of -2.3% for w ,1.9%for ing strains does not become relevant in the investigated range centre σ and -0,1% for σ . The exceptionally high devi- of the examined composite build-ups and loading conditions, x ,SG1 x ,SG2 ations of deﬂection and stresses in laminated glass can be as the linear elastic range is not exceeded. Only at larger assigned to the faster load application speed up to 70 N at stresses and strains of the interlayer core, the linear isotropic the start of testing until the machine had adjusted. This led to elasticity increasingly deviates from the actual stress-strain initially higher PVB short-term stiffness resulting in lower behaviour and causes errors by overestimating the stiffness. deﬂections and glass stresses than calculated in the numeri- Furthermore, beyond the linear elastic range, stresses in the cal simulations applying the Prony shear relaxation material PMMA interlayer core are redistributed in viscoelastic and model. In all cases, the FE model slightly overestimates the plastic range of the polymer and lead to propagated nonlin- stresses and deformations for glass–plastic-composite pan- ear stress distributions and an upwards shift of the neutral els, leading to conservative simulations. In conclusion, the axis due to the separate tension and compression behaviour composite FE model is suitable for numerical predictions that (Schwarzl 1990). can be applied to alternative scenarios in varying geometries, panel compositions and support conditions. 4.4 Influence of stiffness Evaluated stress distributions through the panel thick- ness (see Fig. 18) based on the FE simulations assess the In order to evaluate the inﬂuence of the PMMA interlayer PMMA interlayer core stresses. Monolithic glass with a typ- core Young’s modulus on the overall bending stiffness of the ical monolithic stress distribution and laminated glass with composite with corresponding stresses, numerical four-point partial shear coupling serve as references for the conventional bending simulations are carried out with a parameterisation glass structures. Even laminated glass with standard PVB of the PMMA Young’s modulus for –20, +23 and +60 C exhibits shear coupling between the glass panes that, how- (see Table 6) and extended to properties varying from 500 ever, signiﬁcantly lowers over time due to time-dependent to 10 000 N/mm . The simulations are performed with an creep inﬂuences. The stresses in the interlayer are negligibly extended force level of 2000 N. Figure 19 describes the com- small and not evaluated in detail. posite Young’s modulus (ﬁrst y axis) for composite build-ups The monolithic glass shows slight differences in compres- of 8 mm total thickness with 1 and 2 mm glass cover layers sion and tension values. These derive from the additional (1-6-1 and 2-4-2) calculated from centre deﬂection by the normal stresses generated by the shortening of the bear- application of the Euler–Bernoulli beam theory. The cen- ing at increased panel deﬂections and the large deﬂection tre glass tensile stresses amount to 170 N/mm (1-6-1) and consideration in the FE simulations (Baratta et al. 1987; 115 N/mm (2-4-2). The derived composite Young’s mod- Grellmann and Seidler 2013). The laminated glass shows ulus shows an insigniﬁcant change of less than 1% at –20 ◦ ◦ a stress distribution for partial shear interaction with tension and +60 C compared to the reference case at +23 C. This and compression in each glass layer. shows an insigniﬁcant change in the load-bearing behaviour The stress evaluation in the glass–plastic-composite pan- due to temperature-dependent PMMA Young’s modulus for els show pure compression in the top and pure tension in the the building industry relevant temperatures. Even a very low bottom glass cover layers. The neutral axis is situated about interlayer Young’s modulus of 500 N/mm or a very high the centre of the cross section within the polymer interlayer Young’s modulus of 10 000 N/mm inﬂuences the derived core. The experimental mean tensile strength of the PMMA composite Young’s modulus by a limited degree of –3.4% to interlayer core is utilised to only 1.9% for 1AN 6PMMA - +8.6% for 1-6-1 and –1.8% to +2.0% for 2-4-2. The nor- 1AN and 1.1% for 2AN 4PMMA - 2AN. The low stress mal tensile stresses in x direction of the PMMA interlayer levels in the interlayer core (< 1N/mm ) in tension guaran- core were assessed in the stiffness analysis in Fig. 19 on the tee minimal creep at a temperature of +23 C. The strength second y axis. The stresses linearly increase with increased utilisation of the PMMA is less than 2%, whereas the glass PMMA interlayer core stiffness related to Hooke’s Law. The stresses are by a multiple larger and utilised up to 78%. stress-PMMA Young’s modulus slope is highly dependent on the glass-to-cover layer ratio of the composite build-up. 123 Experimental investigations and numerical simulations 265 However, it demonstrates that in the range of the building To classify the results, the decisive tensile stresses of industry relevant temperatures (–20 to +60 C), the PMMA PMMA and glass are evaluated and compared to the char- stress-strain behaviour remains linear elastic (see Sect. 4.2). acteristic material strength. Table 10 presents the decisive During the following parametric study, it was continuously tensile stresses (force level F = 2000 N) at the centre-span checked whether the stress-strain behaviour of the PMMA is cross section and evaluates the individual strength utilisation. still in the linear elastic range. Otherwise, the results could The PMMA interlayer core tensile stresses do not exceed signiﬁcantly deviate from reality and hence, the application 6.37 N/mm and remain in linear elastic range with a 14% of a nonlinear material model would be required to correctly utilisation of PMMA tensile strength, whereas the glass represent the nonlinear PMMA material behaviour. strength of ANG is exceeded in all of the cases at the force level of 2000 N. To compare the composite bending stiffness to conven- 4.5 Parametric study tional glass stiffness, the composite Young’s modulus as extensional stiffness of an equivalent homogeneous plate The following parametric study deploys the PMMA mate- was derived according to Sect. 3.5. Based on the composite rial parameters and four-point bending FE model to evaluate Young’s modulus, an equivalent glass thicknesses d equ,glass the load-bearing behaviour in different glass and composite is calculated for the individual build-ups according to equa- build-ups at a temperature of +23 C. The objective is to com- tion 4. This provides a quick comparison to the conventional pare the bending stiffness, examined as composite Young’s monolithic glass. modulus, as well as maximum stresses in the individual lay- ers and ﬁnally rate the load-bearing performance in relation E · d composite 3 composite to lightness by using the unit mass density and derived corre- d = (4) equ,glass glass sponding speciﬁc stiffness of the build-ups. All calculations were performed up to a force level of 2000 N with a load application speed of 400 N per min. Figure 21a describes the evaluated composite Young’s mod- Glass–plastic-composite panel build-up parameters are uli for the glass–plastic-composites that quantiﬁes the ﬂexu- deﬁned ranging from 6 to 15 mm nominal total thickness ral stiffness according to the individual nominal build-up. following conventional standardised thicknesses for glass The equivalent glass thickness is described in the bot- (DIN EN 572-1:2016-06 2016). The material assumptions tom of the bars in Fig. 21a. Figure 21b describes the and simulation properties are described in Sect. 4.3. Sym- nominal weight by unit mass density-to-glass density ratio metric laminated glass with standard PVB and monolithic (ρ /ρ ) that is determined by applying the indi- composite glass glass serve as a reference. All parameters are summarised in vidual material densities for each layer (see Table 1). The Table 9. speciﬁc unit mass density is provided in the bottom of the Figure 20 presents the evaluated results for the different bars for each build-up. build-ups of glass–plastic-composites in force-deﬂection and The composite Young’s modulus for panels with 1 mm force-stress charts with monolithic glass as a reference. The thin glass cover layers decreases from 47 878 N/mm at lower the polymer-to-glass ratio, the closer the charts fol- 6mmto27460 N/mm at 15 mm total thickness, however, low the monolithic glass-like behaviour. The characteristic resulting in reduced weight from 65 to 54% of conven- strength of ANG f = 45 N/mm according to (DIN tional glass mass density, respectively. The composites with k,ANG EN 572-1:2016-06 2016) are exceeded for all the evalu- 2 mm thin glass cover layers behave signiﬁcantly stiffer. ated glass–plastic-composite structures at 2000 N. Hence, the Hence, the Young’s modulus amounts to nearly monolithic force-stress charts deﬁne the maximum characteristic capac- glass stiffness (69 783 N/mm ) at 6 mm, that reduces to ity for the evaluated composite build-up. Improvements of 45 662 N/mm at 15 mm total thickness. The unit mass the maximum capacity could be achieved by the application density is still reduced ranging from 82 to 62% of the conven- of CSG with a characteristic strength f = 150 N/mm tional glass density. The equivalent composite stiffness of the k,CSG according to (DIN EN 12337-1:2000-11 2000). These stan- LSG slightly decreases at higher nominal total glass thick- dard speciﬁcations represent an essential reference support ness due to the lower shear coupling effects at increased glass for CSG strength even if, till now, the strength value remains to interlayer ratio, whereas the unit mass density of the LSG quite general and is signiﬁcantly dependent on the glass linearly increases to a very low degree with increased glass- composition and glass strengthening process parameters to-interlayer ratio. This evaluation shows a high dependence (Mognato et al. 2016). The limits are similarly provided in the of the composite Young’s modulus on the glass-to-interlayer force-stress charts and indicate the maximum load-bearing core ratio. However, the composite unit mass density needs capacity with CSG cover layers. Signiﬁcantly higher capac- to be taken into consideration in equal shares for effective ities are reached. weight reduction. In summary, this leads to a quick overview 123 266 J. Hänig, B. Weller Fig. 19 Composite Young’s modulus/ tensile stress-Young’s modulus PMMA charts for glass–plastic-composites in four-point bending based on FE simulations at a force level of F = 2000 N Table 9 Introduction of parameter sets for the investigated build-ups FE parameters Glass LG (symmetric) Glass–plastic-composite (PMMA interlayer core) Monolithic 0.76 mm standard PVB 1 mm thin glass 2 mm thin glass Build-up [mm] 6 33.2 1-4-1 2-2-2 8 44.2 1-6-1 2-4-2 10 55.2 1-8-1 2-6-2 12 66.2 1-10 1 2-8-2 15 N/A 1-13-1 2-11-2 Fig. 20 Force-deﬂection (a)and force-stress charts (b)for glass–plastic-composites and monolithic glass as reference up to 60 mm deﬂection and 160 N/mm maximum tensile stress Fig. 21 Evaluation of composite Young’s modulus (a) and composite unit mass density/glass density (b)forthe analysed build-ups within the parametric study 123 Experimental investigations and numerical simulations 267 Fig. 22 Evaluation of speciﬁc stiffness for the analysed build-ups within the parametric study Table 10 Normal tensile stresses and strength utilisation of glass and PMMA at a force level of 2000 N for glas–plastic-composite panels with 1mmand2mmthinglass coverlayers x,PMMA,centre Glass tensile stress σ PMMA tensile stress σ x ,Glass,centre x ,PMM A,centre 2 2 [N/mm][N/mm ] 1mmglass σ /f σ /f 2mmglass σ /f σ /f 1mmglass σ /σ 2mmglass σ /σ k,AN k,CSG k,AN k,CSG u,mean u,mean x,Glass,centre Build-up [mm] 6 279.91 6.22 1.87 195.17 4.34 1.30 6.37 0.14 2.07 0.04 8 170.83 3.80 1.14 114.58 2.55 0.7 4.40 0.10 1.91 0.04 10 127.27 2.83 0.85 81.56 1.81 0.54 3.51 0.08 1.67 0.04 12 101.73 2.26 0.68 63.56 1.41 0.42 2.94 0.06 1.46 0.03 15 78.34 1.74 0.52 47.13 1.05 0.31 2.36 0.05 1.20 0.03 of the composite Young’s modulus and weight reduction in icantly improved for all thicknesses due to the high stiffness comparison with the monolithic glass and provides a ﬁrst of the PMMA interlayer core, complete coupling between the rough design tool for composite panels as substitution for layers and the resulting composite load-bearing behaviour. conventional glass using the equivalent glass thickness. Figure 22 presents the detailed evaluation of the spe- 4.6 Discussion ciﬁc stiffness ϕ in bending for the analysed build-ups. This quantiﬁes the lightweight performance as composite Young’s For characterising the mechanical behaviour of the PMMA modulus per unit mass density and allows for comparison of interlayer core in the FE software, linear isotropic material glass–plastic-composite panels to conventional glass panels parameters were derived from the experimental study. This and any other materials. allowed for the simulation of the PMMA material behaviour Conventional monolithic glass offers a speciﬁc stiff- time independently within the linear elastic range. The mate- 6 2 2 ness of 29 × 10 m /s , whereas laminated glass with a rial parameter implementation was validated within the linear standard PVB interlayer reaches around 15 to 13 × 10 elastic range and limited by a maximum allowable deviation 2 2 m /s depending on the overall thickness. The partial shear of 5%. Four-point bending simulations of the composite and coupling effects in the standard PVB laminates cause rela- conventional glass panels were conducted to evaluate the gen- tively low bending stiffness at still high unit mass density. eral load-bearing behaviour and stress distributions over the Glass–plastic-composite panels exhibit speciﬁc stiffness in centre panel cross sections. The model itself was validated relation to the interlayer core-to-cover layer ratio. Glass– and veriﬁed by the experiments and the linear beam theory plastic-composites with 2 mm glass cover layers provide calculations. All the following evaluations were based on the highest speciﬁc stiffness in the evaluated range of thick- the numerical simulation results. Further possibility is the nesses, whereas 1 mm glass cover layers lead to just slightly application of general analytical beam theory for sandwich higher speciﬁc stiffness than monolithic glass up to 8 mm structures (Stamm and Witte 1974; Zenkert 1997). However, total thickness. This is decreasing at thicker build-ups due such approaches are limited by support conditions and load to a signiﬁcant decrease in bending stiffness that is not cases when designing with glass–plastic-composite panels. counterbalanced by weight reduction. However, compared to The stiffness analysis has revealed the PMMA Young’s conventional laminated glass, the speciﬁc stiffness is signif- modulus inﬂuences on the novel glass–plastic-composite 123 268 J. Hänig, B. Weller panels for two composite build-ups (1-6-1 and 2-4-2). This state even the CSG tensile strength is regularly exceeded. analysis speciﬁcally addressed the composite Young’s modu- Accompanying composite bending strength tests prove this lus and interlayer core stresses in the glass–plastic-composite statement. Exceeded glass stresses lead to initial glass crack- panels. It has demonstrated a linear elastic stress-strain ing and causing PMMA fracture right after. The results behaviour of the PMMA and a limited inﬂuence of the com- will be presented in a following publication. The paramet- posite Young’s modulus within the relevant temperatures in ric study has pointed out the lightweight performances of the building industry applications. One should bear in mind glass–plastic-composite panels by evaluating the composite that this analysis has not considered the inﬂuence of creep on Young’s modulus, the equivalent glass thickness, and the unit the polymer and all the relevant build-ups in detail, but it has mass density as well as the resulting speciﬁc stiffness. Pre- shown a limited inﬂuence on the composite Young’s modu- sented diagrams quantify the signiﬁcant weight reduction at lus and load-bearing behaviour. This statement is supported still high Young’s moduli over conventional glass panels and by the examined Young’s moduli at the building industry rel- thereby demonstrates the potential of glass–plastic compos- evant temperatures in the uniaxial quasi-static tensile tests ites for applications in novel lightweight all-glass systems for and time-dependent Creep moduli at relevant stress states the building industry. The use of stiff interlayers such as stiff in the uniaxial creep tests. In summary, this stiffness analy- PVB in laminated glass would considerably increase the spe- sis proves a predictable and reliable structural behaviour of ciﬁc stiffness of laminated glass leading to nearly full shear glass–plastic-composite panels within the addressed require- coupling effects in short-term loadings (Hána et al. 2019a). ments of the building industry. Further creep investigations This behaviour is adequately represented by the limit of the by means of a suitable creep model and FE analysis could full shear coupling as monolithic glass. However, at higher provide exact information on the load-bearing behaviour over temperatures and under long-term loading even stiff interlay- time but would exceed the scope of this paper. ers soften and are susceptible to creep lowering the speciﬁc Subsequent composite investigations have demonstrated stiffness signiﬁcantly. Only very stiff ionoplast interlayers the sufﬁciency of linear isotropic material parameter assump- offer high long-term performance with minimal creep, even tions of the PMMA for the composite simulations as the at elevated temperatures. (Hána et al. 2019a) compared the interlayer core stresses and strains never exceeded the lin- long-term performance of glass–plastic-composite panels to ear elastic range. No extension to the nonlinear material conventional laminated glass with standard and stiff PVB models is required for bending applications in the building at room temperature. The examined long-term behaviour industry. Nevertheless, the linear models overestimate the showed a clear preference of glass–plastic-composite panels PMMA interlayer core stiffness at increased strains leading over conventional laminated glass in terms of long-term sta- to uncertain simulation results. For simulations of altering bility. One should bear in mind that the speciﬁc stiffness is not applications, where high interlayer core stains are expected, considering material strength, which often becomes decisive an extension to nonlinear models is recommended. Conse- for connection joints and point ﬁxings due to stress concen- quently, it needs to be continuously checked whether the trations. Especially, the improved strength of tempered glass linear material parameters are still effective, or a nonlinear reveals signiﬁcant advantages in strength over glass–plastic- material model is required to properly simulate the mate- composites with cover layers of ANG. rial behaviour at increased strains. Plasticity material models While the choice of specimen in other thin glass research such as multilinear isotropic hardening (MISO) or hyperelas- activities focuses on the use of chemically strengthened glass, tic material models such as Neo-Hookean or Mooney-Rivlin this publication referred mainly to annealed glass cover lay- would suit for describing the material behaviour at increased ers. The question arises: What is the most suitable cover layer strains exceeding the linear elastic range of the PMMA glass type for glass–plastic-composites, also with respect to Further experimental testing is required for full reliable cali- availability and composite strength? The manufacturing and bration of nonlinear material model parameters as researched subsequent composite processing as well as the availability in (Arriaga et al. 2007; Bergström 2015; Rühl 2017;Van of thin glass in architectural dimensions causes the current Lancker et al. 2020). Extended creep material formula- main limitation. Moreover, to shape the panels, cuttable glass tions (e.g. Prony shear relaxation models or viscoplasticity is required. Annealed glass cover layers allow for cutting material formulations) reliably describe time-dependency. and edge treatment, as for conventional glass. The cutting However, this is primarily necessary at high stress levels or of chemically strengthened glass to size is highly dependent elevated temperatures. on the strengthening parameters. Furthermore, cut edges and From the evaluation of decisive tensile stresses in the para- the interference with the initial compressive stress state will metric study it can be concluded that glass strength is decisive result in reduced edge strength (Karlsson et al. 2010; Mog- for the design of glass–plastic-composite panels, whereas nato et al. 2016). Studies with varying types of glass and the PMMA material strength is never exceeded. Maximum optimisation of the cutting processes offer further develop- 14% utilisation of the PMMA strength was observed. At this 123 Experimental investigations and numerical simulations 269 ment potential for realizing remarkably increased strength of chemically strengthened glass becomes decisive and limits glass–plastic-composite panels. the design of the composites. Limitations to the application of the glass-plastic compos- The stiffness analysis has revealed little inﬂuence of alter- ite panels arise from the general brittle failure characteristics. ing the interlayer core Young’s modulus in the range from It is important to discuss the brittle failure of the PMMA 500 to 10 000 N/mm on the composite panel stiffness. In interlayer core that does not provide residual capacity in conclusion, insigniﬁcant change in load-bearing behaviour glass–plastic-composite assembly compared to a conven- due to time- and temperature-dependent PMMA Young’s tional laminated safety glass. To overcome the shortcomings modulus at the building industry relevant temperatures and and achieve desired ductility as well as safe failure in the loading is to be expected. The parametric study extended context of post-fracture performance, further developments the composite load-bearing performances to a wide range of and investigations are necessary. Solutions may include the composite build-ups and compared it to conventional glass modiﬁcation of the PMMA interlayer core with nanoparticles panels. Derived speciﬁc stiffness as Young’s modulus with leading to enhanced ductility even after glass breakage or pro- respect to unit mass density quantiﬁed the lightweight per- cessing into laminated structures. These approaches counter formances of the composites. The glass–plastic-composite the brittle failure of the PMMA and lead to desired safe fail- panels with 2 mm cover layers provide a higher speciﬁc ure and residual capacities required for the structural glass stiffness than the monolithic glass for the evaluated total applications. However, lamination results in higher costs and thicknesses ranging from 6 mm to 15 mm. The composite leads to shear coupling considerations of the conventional panels with 1 mm cover layers show higher weight reduction laminated glass. This would moderate the actual compos- at, however, lower speciﬁc stiffness than monolithic glass ite load-bearing performance but allow for a wider range of at thicknesses larger than 8 mm. All the observed compos- applications where safe failure is required. ite build-ups exhibit signiﬁcantly higher speciﬁc stiffness in comparison with conventional laminated glass with a stan- dard PVB interlayer. All in all, the glass–plastic-composite 5 Summary, conclusions and outlook panels demonstrate adequate mechanical performance for structural applications by showing signiﬁcantly reduced self- This research comprised the extended experimental mate- weight compared to conventional glass. rial investigations on PMMA and glass–plastic-composite Glass–plastic-composite panels are rather novel structures panels as well as the subsequent numerical simulations and that provide new application opportunities in the building investigations of the stiffness and the parametric study. The industry. In particular, the trend towards maximum trans- experimental investigations addressed the lacking mechan- parency at low self-weight requires novel solutions, design ical properties of the modiﬁed PMMA interlayer core for ideas and lightweight products. To achieve such full trans- glass–plastic-composites in DMTA, uniaxial quasi-static ten- parency in all-glass systems, novel connection types that sile and uniaxial creep tests as well as durability tests are directly implemented in the interlayer core are currently according to the building industry requirements. The inves- under development. The use of the presented material dataset tigations have demonstrated sufﬁcient stiffness, strength as in combination with numerical simulations allow for the well as durability of the used PMMA under quasi-static loads development of discreet and optimised inserted connection with small strains until brittle failure. This examination led joints for glass–plastic-composite panels. Current research to a comprehensive PMMA material dataset suitable for the also focuses on the strength of glass–plastic-composite pan- design of glass–plastic-composite panels that is now open els with chemically strengthened thin glass cover layers for use in variety of potential applications. Furthermore, the and the need for improved ductility and safe post-fracture four-point bending tests have shown the linear load-bearing behaviour for fail-safe application. This gives conﬁdence for behaviour, high stiffness and adhesion to glass leading to novel spectacular and technically feasible lightweight appli- full force transfer between the layers of the glass–plastic- cations in architectural all-glass design. composite panels. Acknowledgements The investigations were conducted as part of a The material dataset was implemented into an FE software research Project supported by the German Federal Ministry of Eco- by using the linear isotropic material parameters. Experimen- nomic Affairs and Energy. The authors would like to thank the project tal tensile tests have validated the material model parameters partner KRD Coatings GmbH for the close collaboration and the to a conﬁdent degree. The PMMA tensile stresses in com- technical support with respect to the production of all needed test specimens. Furthermore, the technical assistance and support of all posite assembly do not exceed the linear elastic limit. In Friedrich-Siemens-Laboratory members that contributed to preparing conclusion the material model parameters are suitable for and conducting the tests is gratefully acknowledged. the investigation and design of glass–plastic composite for building industry relevant applications in bending. As the Funding Open Access funding enabled and organized by Projekt DEAL. PMMA strength is not critical, the glass strength, even of 123 270 J. Hänig, B. 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Glass Structures & Engineering – Springer Journals
Published: May 23, 2021
Keywords: Glass–plastic-composite; Sandwich structure; Material model; Numerical simulation; Tensile testing; Dynamic mechanical thermal analysis; PMMA; Acrylic glass; Four-point bending; Finite element analysis; Thin glass; Composite material; Transparency
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