PROGRESSIVE FAILURE ANALYSIS OF COMPOSITE SANDWICH BEAM IN CASE OF QUASISTATIC LOADING

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1 UDK 66.7:6.7 ISSN Professional article/strokovni ~lanek MAE9, 48(4)593(4). MANDYS et al.: PROGRESSIVE AILURE ANALYSIS O OMPOSIE SANDWIH BEAM... PROGRESSIVE AILURE ANALYSIS O OMPOSIE SANDWIH BEAM IN ASE O QUASISAI LOADING NAPREDNA ANALIZA PO[KODB SESAVLJENEGA KOMPOZINEGA NOSILA PRI KVAZISAI^NEM OBREMENJEVANJU omá{ Mandys, omá{ Kroupa, Vladislav La{ University of West Bohemia in Pilsen, NIS - New echnologies for Information Society, Univerzitní, 36 4 Plzeò, zech Republic tmandys@kme.zcu.cz, kroupa@kme.zcu.cz, las@kme.zcu.cz Prejem rokopisa received: 3--; sprejem za objavo accepted for publication: 3--8 his paper is focused on a progressive failure analysis of a sandwich composite panel considering a non-linear model of core and skins using explicit analysis. he material properties were determined from tensile and compressive tests of the outer composite skin and the foam core. A user-defined material model was used to describe the non-linear orthotropic elastic behaviour of the composite skin. he material parameters of the outer composite skin were determined using the identification process performed using a combination of optimization method and finite-element simulation. he Low-Density oam material model was used for the foam core. he obtained material data were validated using a three-point bending test of a sandwich beam. Keywords: sandwich panel, fiber-glass fabric, foam core, three point bending test, damage, optimization ^lanek obravnava napredno analizo po{kodb z uporabo eksplicitne analize sestavljene kompozitne plo{~e z upo{tevanjem nelinearnega modela jedra in skorje. Lastnosti materiala so bile dolo~ene iz nateznih in tla~nih preizkusov zunanje kompozitne skorje in penaste sredice. Uporabni{ko dolo~en model materiala je bil uporabljen za opis nelinearnega ortotropnega elasti~nega vedenja kompozitne skorje. Materialni parametri zunanje kompozitne skorje so bili dolo~eni z identifikacijskim procesom, izvr{enim z uporabo kombinacije metod optimiranja in simulacije s kon~nimi elementi. Materialni model pene z nizko gostoto je bil uporabljen za jedro iz pene. Dobljeni podatki za material so bili ocenjeni z uporabo trito~kovnega upogibnega preizkusa sestavljenega nosilca. Klju~ne besede: sestavljena plo{~a, tkanina iz steklenih vlaken, jedro iz pene, trito~kovni upogibni preizkus, po{kodba, optimizacija INRODUION he principle of sandwich structures is based on a low-density material (core) placed between two stiffer outer skins. he main purpose of the core is to maintain the distance between the outer skins and to transfer the shear load while the outer skins carry the compressive and tensile load. he outer skins are obviously thinner than the core. his type of structural arrangement has a much larger bending stiffness than a single solid plate made of the same total weight from the same material as a outer skin only. his fact together with other advantages, such as corrosion resistance, product variability and thermal or acoustic insulation, make sandwich structures the preferred alternative to conventional materials in all types of structural applications where the weight must be kept to a minimum value. EXPERIMENAL SE-UPS AND SPEIMENS he used sandwich composite panel was manufactured using a vacuum infusion process and its overall thickness was.5 mm. he outer composite skins were made from three layers of fibre-glass fabric with the product name Aeroglass (material density 39 g/m ) and epoxy resin designated as Epicote HGS LR 85. he thicknesses of the outer composite skins were. mm. he core of the sandwich panel was a closed-cell, crosslinked polymer foam Airex his foam core is characterized by a low resin absorption. he resultant sandwich panel was cured for 6hat5. ensile and compressive experimental tests were performed using a Zwick/Roell Z5 testing machine on the separated specimens of the laminated composite skin and foam core of the resultant sandwich structure. he foam core was additionally subjected to a three-point bending test too. hree types of specimens of laminated composite skin were used, the chosen material principal direction (weft) form angle (ype A), 45 (ype ) and 9 (ype B) with the direction of the loading force. he specimens of the laminated outer skin had the dimensions 35 mm 5 mm and a thickness. mm. he dimensions of the specimens of the isotropic foam core were 5 mm 5 mm with a thickness mm. he loading velocity during the tensile tests was. mm/min in the case of the composite skin and. mm/min in the Materiali in tehnologije / Materials and technology 48 (4) 4,

2 . MANDYS et al.: PROGRESSIVE AILURE ANALYSIS O OMPOSIE SANDWIH BEAM... case of the foam core. our specimens for each angle of composite skin and for the foam core were tested. he three-point bending tests of the foam core were performed on specimens with the same dimensions that were used for the tensile tests. he distance of the supports of the testing device was mm and the diameters of all three supports were mm. he resulting sandwich beam with the dimensions 33 mm 5 mm and a total thickness.5 mm was subjected to a three-point bending test in order to validate the material data obtained independently for the composite skin and the foam core. he thicknesses of the composite skins were. mm. he distance of the supports of the testing device was 5 mm and the supports consisted of rotationally joined cylinders with diameters of 3 mm. he loading velocity of the sandwich beam was mm/min. hree specimens were tested in total.. Material model of the skin A user-defined material model of the composite skin was implemented in Abaqus software using the VUMA subroutine written in the ortran code. he non-linear function describing the stress-strain relationship starting from the deformation i (i, ) was assumed in the case of the principal material directions and (equations () and (4)). he non-linear function with a constant asymptote was considered in the case of the shear in plane (equation (8)). he following equations describe the stress-strain relationship of the laminated outer skin: + + for < () 3 3 A ( ( + ( ) A ( )) )( D) for () + + for < (3) 3 3 A ( + ( + ( ) A ( )) )( D) for (4) ( + + ) ( D ) (5) ( G ) ( D ) (6) ( G3 3 ) ( D ) (7) G + G n n ( D ) (8) he constants occurring in equations () to (5) are: E ( v3 v3) E ( v + v3 v3) E ( v3 v3 v) E ( v3 v3) 3 (9) E ( v3 v3 v) E3 ( v v) 3 33 v v v v v v where E, E and E 3 are the Young s moduli in the principal directions, and 3 and, 3, 3 are the Poison s ratios in the planes defined by the principal directions, and 3. he shear moduli in planes 3 and 3 are designated as G 3 and G 3, respectively. he non-linear behavior in shear in plane (8) is described using the initial shear modulus G, the asymptotic value of the shear stress and the shape parameter n. he parameters A and A in () and (4) describe the straightening of the yarns of the fiber-glass fabric and the loss of stiffness in the directions and, respectively. he values of the deformations and indicate the the transitions between the linear and non-linear parts of the stress-strain relationship in the given directions and during the loading. he maximum stress failure criterion was used to predict failure on the composite skin: v 3 X X Y Y S L () where the subscripts and denote the tension and compression, X and Y are the strengths in the principal directions and, respectively, and S L denotes the shear strength. he values of the degradation variable D are dependent on the kind of occurred failure. he principle of material degradation is shown in igure and the degradation parameters are summarized in (). he degradation parameter after failure initiation was implemented in the case of shear failure (. and ) from. 3 Due to the non-linear behavior of the composite skin the degradation parameters are assumed in the form: D. D 6. D. D 6. () m ( ) m and < D e and D. In the case of shear failure the non-negative material constant m is represented by the integer and is the ultimate deformation when the material is fully damaged. Mathematical optimization was used to identify the material parameters on data from the performed tensile tests of composite skin. he optimization process was 594 Materiali in tehnologije / Materials and technology 48 (4) 4,

3 . MANDYS et al.: PROGRESSIVE AILURE ANALYSIS O OMPOSIE SANDWIH BEAM... igure : he principle of material degradation in the principal direction Slika : Na~elo degradacije materiala v glavni smeri. Material model of the foam core he used material model of the foam core was the Low-Density oam model from the Abaqus software library. 5 his material model is intended for highly compressible elastomeric foams. he material behavior was specified directly via unaxial stress-strain curves for tension and compression (igure ). In the case of tension the unaxial stress-strain behavior was described via a curve added in the form: () () he material is fully damaged after reaching the tensile strength R m. he compressive behavior of the foam core was described as an ideally elastoplastic material handled using Optislang 3... he material parameters that do not have a significant influence on the results were kept constant during the optimization process. All the material parameters are summarized in able. he parameters E 3, G 3 and G 3 were taken from the literature. 4 he strengths of the composite skin were determined directly from the experimental data. able : Material parameters of the composite skin abela : Parametri materiala kompozitne skorje Optimized values: onstant values: E GPa 6.9 v.337 E GPa 8.5 v G GPa 4.96 v 3.8 MPa G 3 GPa 4. n.9 G 3 GPa.75 A. E 3 GPa 8. A kg/m X MPa 35 m 5 Y MPa 347 X MPa 65 Y MPa 67 S L MPa 35 igure : ensile and compressive unaxial stress-strain behavior of foam core Slika : Vedenje jedra iz pene pri enoosni natezni in tla~ni obremenitvi igure 3: he resultant force-displacement diagrams of the composite skin types A (top), B (center) and (bottom) Slika 3: Diagrami sila raztezek kompozitne skorje A (na vrhu), B (v sredini) in (spodaj) Materiali in tehnologije / Materials and technology 48 (4) 4,

4 . MANDYS et al.: PROGRESSIVE AILURE ANALYSIS O OMPOSIE SANDWIH BEAM... with the Young s modulus E and the yield limit R m. he material parameters are summarized in able. able : Material parameters of foam core abela : Parametri materiala pene v jedru E R m R m f U MPa MPa MPa kg/m Numerical simulations and results he simulations were performed as quasi-static explicit analyses in the EM software Abaqus 6. using finite-strain theory. he numerical models of the outer skin and the foam core were meshed using 8-node solid elements (element type 3D8R). igure 3 shows the resulting force-displacement dependencies from averaged experiments and the numerical simulations for specimens of type A, B and. he resulting force-displacement diagrams of the tensile test and the force-deflection diagram of three-point bending test of the foam core is shown in igure 4. he numerical model of the sandwich beam was created as a fully contact problem of four bodies sandwich beam and three supports. he friction between the sandwich beam and supports has been neglected. igure 5: a) he resulting sandwich beam subjected to a three-point bending test and b) the numerical model of loaded sandwich beam Slika 5: a) Sestavljen nosilec, izpostavljen trito~kovnemu upogibu in b) numeri~ni model obremenjenega sestavljenega nosilca igure 6: he force-deflection diagram of the three-point bending test of the resulting sandwich beam Slika 6: Diagram sila upogib pri trito~kovnem upogibnem preizkusu nosilca he failure of the upper composite skin occurred in compression in principal direction during loading in place under the center support, both in the case of experiments and the numerical simulation. his situation is shown in igure 5. he comparison of the forcedeflection diagrams for the three-point bending tests of the sandwich beam is shown in igure 6. 3 ONLUSION igure 4: a) he resulting force-displacement diagrams of the tensile test and b) the force-deflection diagram of the three-point bending test of the foam core Slika 4: a) Diagrami sila raztezek pri nateznem preizkusu in b) diagram sila uklon pri trito~kovnem upogibnem preizkusu jedra iz pene he user-defined material model describing the non-linear orthotropic elastic behaviour, considering the progressive failure analysis, was implemented in the EM system Abaqus. he material parameters of the composite outer skin of the sandwich panel were 596 Materiali in tehnologije / Materials and technology 48 (4) 4,

5 . MANDYS et al.: PROGRESSIVE AILURE ANALYSIS O OMPOSIE SANDWIH BEAM... identified using the mathematical optimization method. In the case of the foam core the Low-Density oam material model from EM software library was used. he obtained material parameters of the composite skin and foam core were verified via a three-point bending test of the resulting sandwich beam. he future work will focus on low-velocity impact events involving sandwich plates. Acknowledgement he work has been supported by the European Regional Development und (ERD), project "NIS New echnologies for Information Society", European entre of Excellence, Z..5/../.9, the student research project of Ministry of Education of zech Republic No. SGS-3-36 and the project of Grant Agency of zech Republic No. GA^R P//88. 4 REERENES. Kroupa, V. La{, R. Zem~ík, Improved nonlinear stress-strain relation for carbon-epoxy composites and identification of material parameters, Journal of omposite Materials, 45 () 9, V. La{, R. Zem~ík, Progressive damage of undirectional composite panel, Journal of omposite Materials, 4 (8), Yen, Ballistic Impact modeling of omposite materials, 7th International LSDyna User s onference, Dearborn, Michigan, 6 4 R. Zem~ík, V. La{,. Kroupa, H. Pur{, Identification of material characteristics of sandwich panels, Bulletin of Applied Mechanics, 6 (), Abaqus 6. Documentation, Dassault Systèmes Simulia orp., Materiali in tehnologije / Materials and technology 48 (4) 4,