Stress analysis of laminated glass with different interlayer materials

Transcription

1 Alexandria Engineering Journal (01) 51, Alexandria University Alexandria Engineering Journal Stress analysis of laminated glass wit different interlayer materials Mostafa M. El-Sami a,b, *, Scott Norville b, Yasser E. Ibraim c a Civil Engineering Department, Menoufia University, Egypt b Civil and Environmental Engineering Department, Texas Tec. University, USA c Construction Engineering Department, College of Engineering, Dammam University, Saudi Arabia Received 11 November 010; accepted 1 April 01 Available online 4 August 01 KEYWORDS Finite element; Arcitectural glass; Laminated glass; Experimental Abstract Te use of window glass in building design is becoming increasingly popular. Laminated glass as gained popularity as a suitable and practical alternative to monolitic and insulating glass in many design situations. Laminated glass plate performance is influenced by several factors suc as glass tickness, glass type, temperature, aspect ratio, load duration, and ardness of te interlayer material. A new iger order finite element model (presented by te first two autors) using 9-noded quadrilateral elements was applied to investigate laminated glass plates wit bot different interlayer materials. An experimental load-testing program is described. Two types of interlayer materials, regular polyvinyl butyral and strong formulation of polyvinyl butyral were used. First, simply supported rectangular laminated glass plates wit regular polyvinyl butyral interlayer wit aspect ratios 1 5 under different temperatures were tested. Second, one set of laminated glass plates wit te strong formulation of polyvinyl butyral interlayer was tested under room temperature. Te experimental and teoretical results are compared and discussed. In general, te performance of laminated glass wit regular polyvinyl butyral interlayer is closer to tat of layered glass at iger temperature. Also, laminated glass wit strong formulation of polyvinyl butyral interlayer as a significantly larger load resistance tan similar regular polyvinyl butyral samples. ª 01 Faculty of Engineering, Alexandria University. Production and osting by Elsevier B.V. All rigts reserved. * Corresponding autor at: Civil and Environmental Engineering Department, Texas Tec University, Lubbock, TX , USA. address: mostafa.el-sami@ttu.edu (M.M. El-Sami). Peer review under responsibility of Faculty of Engineering, Alexandria University. Production and osting by Elsevier 1. Introduction Te use of window glass in building design is becoming increasingly popular. Laminated glass (LG) as gained popularity as a suitable and practical alternative to monolitic and insulating glass in many design situations. LG consists of two plates of glass joined by an elastomeric interlayer to form a unit. Te most prevalent interlayer material used in arcitectural glazing is polyvinyl butyral; PVB, wic comes off te production line as an opaque, flexible seet tat becomes clear during te lamination process. Anoter strong ª 01 Faculty of Engineering, Alexandria University. Production and osting by Elsevier B.V. All rigts reserved. ttp://dx.doi.org/ /j.aej

2 6 M.M. El-Sami et al. formulation of polyvinyl butyral, called HG/MD as recently become more popular in LG as an interlayer material. Tere is a growing interest in understanding te effect of temperature on LG and its performance. Te two most important factors affecting LG strengt and beavior are load duration and temperature. Considerable researc as been done on laminated glass plates. Quenett [1] studied LG units subjected to bot bending and impact loads. His researc led to te conclusion tat te beavior of LG is governed by te material properties of te interlayer and its tickness. Hooper [] as sown tat te bending of laminated glass beams is dependent on te tickness and sear modulus of te interlayer. Linden et al. [3] conducted non-destructive tests on monolitic layered and LG lite specimens instrumented wit strain gauges. Tey found tat LG lite strengt and monolitic glass lite strengt appeared to be equivalent at normal temperatures. Linden et al. [4] studied two different plate geometries wit two interlayer ticknesses at room temperature and at 77 C. Tey reported tat LG lite is stronger tan monolitic at room temperature and weaker at 77 C for te same rectangular dimensions and nominal glass tickness. Nagalla et al. [5] advanced teoretical work comparing layered glass to monolitic glass. Tey discovered tat some aspect ratios of layered glass experienced lower principal stresses tan monolitic glass subjected to uniform, transverse loading in certain ranges of loading. Reznik and Minor [6] destructively tested different sizes of LG specimens at room temperature, 49 C, and 170 C. Tey compared te results wit tose from tests on monolitic glass lite specimens aving te same dimensions. Te testing led to very important conclusions; as temperature increases, LG beavior migrates towards te layered glass model. Norville [7] tested two lite specimens wit aspect ratios of 1 and. His results were consistent wit tose of Reznik and Minor [6]. Ber et al. [8] studied LG beams at different temperatures. Tey found tat traditional testing metods wit te glass simply supported on two sides would not adequately account for te effect of aspect ratio on LG beavior. Vallaban et al. [9] developed a matematical model to analyze te LG plate. Experimental tests were conducted to validate te teoretical model. Tey found tat te sear modulus varies as a function of te level of sear strain in te PVB interlayer at room temperature. Norville et al. [10] developed a teoretical, engineering mecanics model tat accounts for te beavior of LG plates. Duser et al. [11] presented a model for stress analysis of laminated plates taking into account te PVB interlayer as viscoelastic material. Recently, Asik and Tezcan [1] publised a matematical model of laminated glass beams, wic is based on nonlinear strain displacement relationsip. Te model was used to investigate te linear and nonlinear beavior of symmetric triplex glass beams in comparison wit LG plate s beavior. Ivanov [13] presented a finite element model for LG beams. On is model, te distribution of strain and stress troug te beam tickness and along its axis was obtained as a result of linear finite element analysis. He developed a matematical model of triples glass beam, consisting of a bending curvature differential equation and a differential equation of PVB-interlayer sear interaction. Te objectives of te tis paper can be summarized as following: 1. Studying te beavior of LG wit PVB under a different range of temperatures. Te effect of aspect ratio is considered.. Comparing te beavior of LG using PVB and HG/MD interlayer materials at room temperature. A iger order finite element metod (FEM) wit nine nodes quadrilateral element was used in te analyses [14,15]. Tis FEM is designed for large deflections and rotation analysis of LG considering te effect of interlayer material under a different range of temperatures. Te results obtained from te experimental study are compared wit te corresponding FEM results and pronounced conclusions are obtained. El-Sami et al. [16] studied te structural beavior of glass plates oter tan rectangular sapes. Tey used a iger-order finite element model to analyze several examples wit trapezoidal, rectangular, triangular, and exagonal saped glass plates (monolitic and LG). Figure 1 Undeformed and deformed geometries wit respect to x and z axes.

3 Stress analysis of laminated glass wit different interlayer materials 63. Matematical model Since te teory of mindlin plate and solution tecniques ave previously been publised in textbooks e.g., Cook et al. [17] and in papers e.g., Vallaban et al. [9] and El-Sami et al. [16], only a brief account of te teory is presented ere. Te effect of interlayer material, on te laminated plate element is considered as sear strains c xz and c yz (Fig 1). Te values of c xz and c yz can be calculated as: c xz ¼ u u þ y t 1þt þ w ;x c yz ¼ v v xð t 1þt þ w ;y Þ were u; u; v; and v are te displacements in te x and y directions, for te upper and lower plates; respectively, w,x and w,y are te first derivatives of deflection wit respect to x and y; respectively and t 1, t, and are te ticknesses of te upper and lower plates and te interlayer; respectively. Te degrees of freedom will be increased by two for eac node. Ten te total number of degrees of freedom will be 63 per element; 7 d.o.f per node. To calculate te stiffness matrix, te relation between te displacements and te strains sould be calculated. Tis relation is called [B] matrix [18]. Tis matrix can be calculated as; c xz ¼½B 1 ŠfUg; ¼ 1 ½N i 0 N i 0 N i;x 0 N i ð t 1þt Þ...Š fug were N i denotes te sape function, and fug T ¼ fu i v i u i v i w i xi yi...g denotes te displacement vector for it node in wic i = 1,,..., 9. Similarly, c yz ¼½B ŠfUg; ¼ 1 0 N t i 0 N i N i;y N 1 þt i 0... fug Ten, B 1 fcg ¼ c xz gamma yz ¼½BŠfUg ¼ fug; Te stiffness matrix for te interlayer can be calculated as: ½K INT Š¼ 1 ZZ ½BŠ T ½D G Š½BŠdxdy ¼ G ZZ INT ½BŠ T ½IŠ½BŠdxdy were [K INT ] denotes te interlayer stiffness matrix, G INT denotes te modulus of rigidity for te interlayer, and [I] denotes te identity matrix. Because LG consists of two plates, tis solution employs two different linear membrane stiffness matrices, two different nonlinear membrane stiffness matrices, and one linear bending stiffness matrix. Te nonlinear stiffness matrix will be modified due to te fact tat tere are two plates. Te total stiffness matrix for plates ½K P Š can be written as: 3 ½K M1 Š 1818 ½0Š ½K L1 Š ½K P Š¼4 ½K M Š 1818 ½K L Š Sym: ½K B þ K r Š 77 were [K M1 ] and [K M ] denote te linear membrane stiffness matrices for te upper and lower plate; respectively. [K L1 ] and ½K L Š denote te nonlinear membrane stiffness matrices. [K B ] denotes te linear bending stiffness matrix and [K r ] B denotes te nonlinear stiffness matrix due to te membrane actions, i.e., te initial stress matrix [18]. ½K P Š ere is calculated in relation to {U}, were {U} is given as; fug T ¼fu 1 v 1 u 9 v 9 u 1 v 1 u 9 v 9 w 1 x1 y1 w 9 x9 y9 g Consequently, te autors must use a special transformation matrix [T] to make te plate stiffness matrix ½K P Š matc wit te displacement vector {U}, ten ½K P Š¼½TŠ t ½K P Š½TŠ Te final stiffness matrix [K] for LG takes te following form: ½KŠ ¼½K p Šþ½K INT Š 3. Experimental procedure Glass Researc and Testing Laboratory (GRTL) staff tested different LG geometries, mainly two groups. Table 1 summarizes te geometries of group A specimens. Te specimens ave a PVB interlayer tickness of 0.76 mm. All te specimens were tested witin a temperature range of 0 60 C. Te specimens of group B ave a HG/MD interlayer tickness of.67 mm. Only one geometry was used as sown in Table. All specimens were tested under a temperature of 35 C. Apecial type of strain gauge rosettes (CEA UR-350) was used. Te strain gauges were temperature compensating and ad an operating range of 75 to +175 C. M-Bond AE 10 epoxy adesive, wit an operating range between 195 and 95 C, bonded te gauges to te glass. Te strain gauges were connected to te LG at te center and at te corner (50 mm from te edge). Te test camber, constructed of a 1.7 mm steel plate wit four 03 mm steel cannels welded onto it to form an open rectangular box, provided four sides support for te specimen. Tis test camber provided support condition corresponding to ASTM E998 [19]. Te steel camber ad four openings connected to te vacuum macine. As te vacuum was applied, te plate was loaded wit negative pressure. Te eating system consists of eating camber, space eaters, eated blowers, and appropriate ductwork to distribute warm air over te surfaces of te test specimen. Four space Table 1 Aspect ratio Geometries of test specimens (group A). Nominal specimen dimension (mm) Table Aspect ratio Geometries of test specimens (group B). Nominal specimen dimension (mm) Design load (kpa) Design load (kpa)

4 64 M.M. El-Sami et al. Figure Experimental setup. (a) Temperature = 0 0 c (b) Temperature = 30 0 c (c) Temperature = 40 0 c (d) Temperature = 50 0 c (e) Temperature = 60 0 c Figure 3 (a) Temperature = 0 C. (b) Temperature = 30 C. (c) Temperature = 40 C. (d) Temperature = 50 C. (e) Temperature = 60 C.

5 Stress analysis of laminated glass wit different interlayer materials 65 eaters were used to warm te air inside te eating box. A eated blower was used to blow te pre-eated air (into te eated box) to te eating camber. To start te proceeding, Te GRTL staff removed te specimen from te crate. Ten, tey measured and record te tickness of te glass specimen at different locations and obtain an average tickness. Te staff mounted te spacemen on te test frame. To control te temperature, GRTL staff mounted te eating camber over te test camber containing te glass specimen. Tey connected te eating box to te camber and te eated blower to te box to start te eating processes. Two small oles wit sliding covers, one located near to te center and anoter near te top of te eating camber, allowed te staff to measure temperature. Te ot air blown on te glass surface allowed te glass to reac te required temperature. Ten, te researcers loaded te specimen to one-alf te design load and te measurements were recorded. Finally tey loaded te specimen to te design load and record te measurements. Tey repeated tis procedure at different temperatures. Once te staff completed te test, tey removed te specimen from te test camber. Fig. sows a sketc for te experimental setup. Figure 4 Deflection at te center of te plates at different temperatures for aspect ratio 1 of group A. 4. Results of experiments versus teory To verify te FEM, some problems ave been solved and compared wit te experimental results of previous researcers suc as Vallaban et al. [9]. Te comparison sowed very good agreement between te teoretical and te experimental results. Fig. 3a e sows te comparison between te FEM maximum principal stresses and te experimental results at te center of te plate at full design load for group A. Te figures are for different aspect ratios, as given in Table 1, at different temperatures; 0, 30, 40, 50 and 60 C; respectively. Te corresponding values of sear modulus were , , , and 44.8 kpa, respectively [0,1]. It sould be noted tat tese values ave been cosen for te corresponding temperatures. Direct sear testing can be used to determine te sear modulus for te interlayer material in LG. Te figures sow very good agreement between te FEM and experimental results. Te average difference percentage between te results were 9.13%, 8.71%, 9.4%, 8.30% and 9.00% for te temperature cases of 0, 30, 40, 50 and 60 C, respectively. Fig. 4 sows te comparison between teoretical deflections at te center of te plates at different temperatures for aspect ratio 1 of group A. It can be seen from tis figure tat te deflection increases as te temperature increases. Tis is a direct result of te caracteristic viscoelastic properties of PVB at ig temperature [0]. Tis is clear in comparing wit te curve of layered plates (see Fig. 4), in wic te autors used modulus of rigidity equal to zero for PVB. For group B, te comparison between te experimental and te teoretical deflections is sown in Fig. 5. It can be seen from Fig. 5 tat tere is a very good agreement between te teoretical and experimental results. Te value of sear modulus for te HG/MD was cosen to be 174 kpa []. Also, Fig. 5 sows te comparison between te LG wit PVB interlayer and HG/MD interlayer; respectively. It is clears from Fig. 5 tat te deflections for LG wit PVB interlayer are iger tan tose of LG wit HG/MD interlayer. Fig. 6 sows te maximum tensile principle stresses for group B for of LG plate Figure 5 Deflections at te center of te plates for group B (aspect ratio = ) (a) LG wit HG/MD interlayer (b) LG wit PVB interlayer Figure 6 Maximum tensile stresses (MPa) for group B.

6 66 M.M. El-Sami et al..5 times tat of PVB. Tis will enance te structural beavior of LG wit HG/MD interlayer rater tan tat wit PVB. Acknowledgement Te experimental part of researc described erein was conducted at te Glass Researc and Testing Laboratory (GRTL) at Texas Tec. University. References Figure 7 type. wit PVB interlayer and HG/MD interlayer; respectively. It can be seen tat using HG/MD interlayer decreases te maximum tensile principal stresses in comparison wit PVB interlayer under te same load conditions. Using te failure prediction metodology, te probability of breakage of a glass ply at te design load is [4]; P B ¼ 1 exp½ BŠ were P B is te probability wic is used to be [3] and B is te risk function, wic can be calculated as; Z Z B ¼ k ½cðx; yþ~r max ðx; yþš m dxdy AREA were m and k denote te Weibull parameters [4], c(x, y) denotes a stress correction factor at location (x, y), and ~r max ðx; yþ is te maximum equivalent principal tensile stress at location (x, y). Te autors noted tat te probability of breakage of te LG wit HG/MD interlayer is smaller tan tat of te LG wit PVB interlayer (see Fig. 7). In oter words, using HG/MD interlayer instead of PVB enances te structural beavior of LG plates. 5. Conclusions Probability of failure of LG wit different interlayer Te objective of tis paper was to investigate te structural beavior of LG wit different interlayer materials. Te factors used in te analysis were analytical results used FEM and experimental test results. Te employed FEM takes into account te effect of te interlayer as a sear strain. Two types of experiments were considered for simply supported rectangular LG plates; one using PVB interlayer material wit aspect ratios of 1,, 3, 4 and 5 under a range of temperature and te oter using HG/MD interlayer at room temperature for aspect ratio. Te agreement between te experimental and FEM results for bot interlayer materials sows te capability of te present FEM to andle te effect of te different kinds of interlayer materials at different temperatures. Te autors observe also tat te effect of te interlayer material on transferred sear between te two glass plates is decreasing as te temperature is increasing for PVB interlayer. In general, LG wit PVB interlayer comes close to te layered case at ig temperature. Also te sear modulus of HG/MD is almost [1] R. Quenett, Te Mecanical Beavior of Laminated Safety Glass under Bending and Impact Stresses, Forgetragen auf dem DVM-Tag, Wurzburg (Germany), Manuskript-Eing., [] J.A. Hooper, On te bending of arcitectural laminated glass, International Journal of Mecanical Sciences (Great Britain) 15 (1973) [3] M.P. Linden, J.E. Minor, R.A. Ber, C.V.G. Vallaban, Evaluation of Laterally Loaded Glass Units by Teory and Experiment, Glass Researc and Testing Laboratory, Texas Tec University, Lubbock, Texas, 1983 (NTIS Accession No. PB ). [4] M.P. Linden, J.E. Minor, R.A. Ber, C.V.G. Vallaban, Evaluation of Laterally Loaded Glass Unites by Teory and Experiment, Supplemental Report No. 1. Glass Researc and Testing Laboratory, Texas Tec University, Lubbock, Texas, 1984 (NTIS Accession No. PB ). [5] S.R. Nagalla, C.V.G. Vallaban, J.E. Minor, H.S. Norville, Stresses in Layered Units and Monolitic Glass Plates, Glass Researc and Testing Laboratory, Texas Tec University, Lubbock, Texas, 1985 (NTIS Accession No. PB / AS). [6] P.L. Reznik, J.E. Minor, Failure Strengts of Laminated Glass Units, Glass Researc and Testing Laboratory, Texas Tec University, Lubbock, Texas, 1986 (NTIS Accession No. PB /AS). [7] H.S. Norville, Breakage Tests of Du Pont Laminated Glass Units, Glass Researc and Testing Laboratory, Texas Tec University, Lubbock, Texas, [8] R.A. Ber, J.E. Minor, H.S. Norville, Structural beavior of arcitectural laminated glass, Journal of Structural Engineering, ASCE 119 (1993) 0. [9] C.V.G. Vallaban, Y.C. Das, M. Magdi, M. Asik, J.R. Bailey, Analysis of laminated glass units, Journal of Structural Engineering, ASCE 119 (5) (1993) [10] H.S. Norville, K.W. King, J.L. Swofford, Beavior and strengt of laminated glass, Journal of Engineering Mecanics, ASCE 14 (1) (1998) [11] A.V. Duser, A. Jagota, S.J. Bennison, Analysis of glass/ polyvinyl butyral laminates subjected to uniform pressure, Journal of Engineering Mecanics, ASCE 15 (4) (1994) [1] M.Z. Asik, S. Tezcan, A matematical model for te beavior of laminated glass beams, Computers and Structures 83 (005) [13] I.V. Ivanov, Analysis, modeling, and optimization of laminated glasses as plane beam, International Journal of Solids and Structures 43 (006) [14] M.M. El-Sami, C.V.G. Vallaban, S.A. Kandil, Comparison of nonlinear Von Karman and Mindlin plate solutions, in: Proceedings of te Texas ASCE Conf., Spring Meeting, Houston, Texas, [15] M.M. El-Sami, H.S. Norville, Finite element modeling of arcitectural laminated glass, IES Journal Part A: Civil and Structural Engineering, Taylor & Francis 4 (1) (011) 8 16.

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