UDK 66.017:620.17 ISSN 1580-2949 Professional article/Strokovni članek MTAEC9, 48(4)593(2014) PROGRESSIVE FAILURE ANALYSIS OF COMPOSITE SANDWICH BEAM IN CASE OF QUASISTATIC LOADING NAPREDNA ANALIZA POŠKODB SESTAVLJENEGA KOMPOZITNEGA NOSILCA PRI KVAZISTATIČNEM OBREMENJEVANJU Tomaš Mandys, Tomaš Kroupa, Vladislav Laš University of West Bohemia in Pilsen, NTIS - New Technologies for Information Society, Univerzitni 22, 306 14 Plzen, Czech Republic tmandys@kme.zcu.cz, kroupa@kme.zcu.cz, las@kme.zcu.cz Prejem rokopisa - received: 2013-10-02; sprejem za objavo - accepted for publication: 2013-10-28 This 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. The 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. The material parameters of the outer composite skin were determined using the identification process performed using a combination of optimization method and finite-element simulation. The Low-Density Foam material model was used for the foam core. The 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 Članek obravnava napredno analizo poškodb z uporabo eksplicitne analize sestavljene kompozitne plošče z upoštevanjem nelinearnega modela jedra in skorje. Lastnosti materiala so bile določene iz nateznih in tlačnih preizkusov zunanje kompozitne skorje in penaste sredice. Uporabniško določen model materiala je bil uporabljen za opis nelinearnega ortotropnega elastičnega vedenja kompozitne skorje. Materialni parametri zunanje kompozitne skorje so bili določeni z identifikacijskim procesom, izvršenim z uporabo kombinacije metod optimiranja in simulacije s končnimi elementi. Materialni model pene z nizko gostoto je bil uporabljen za jedro iz pene. Dobljeni podatki za material so bili ocenjeni z uporabo tritočkovnega upogibnega preizkusa sestavljenega nosilca. Ključne besede: sestavljena plošča, tkanina iz steklenih vlaken, jedro iz pene, tritočkovni upogibni preizkus, poškodba, optimizacija 1 INTRODUCTION duct name Aeroglass (material density p = 390 g/m2) and epoxy resin designated as Epicote HGS LR 285. The The principle of sandwich structures is based on a thicknesses of the outer composite skins were 1.2 mm. low-density material (core) placed between two stiffer The core of the sandwich panel was a closed-cell, cross-outer skins. The main purpose of the core is to maintain linked polymer foam Airex C70.55. This foam core is the distance between the outer skins and to transfer the characterized by a low resin absorption. The resultant shear load while the outer skins carry the compressive sandwich panel was cured for 6 h at 50 °C. and tensile load. The outer skins are obviously thinner Tensile and compressive experimental tests were tha^Jhe core^This type of structural arrangement has a performed using a Zwick/Roell Z050 testing machine on much larger bending stiffness than a single solid plate the separated specimens of the laminated composite skin and foam core of the resultant sandwich structure. The made of the same total weight from the same material as a outer skin only. This fact together with other advantages, such as corrosion resistance, product variability foam core was additionally subjected to a three-point and thermal or acoustic insulation, make sandwich struc- bending test too. tures the preferred alternative to conventional materials Three types of specimens of laminated composite in all types of structural applications where the weight skin were used, the chosen material principal direction must be kept to a minimum value. (weft) form angle 0° (Type A), 45° (Type C) and 90° (Type B) with the direction of the loading force. The specimens of the laminated outer skin had the dimensions 135 mm x 15 mm and a thickness 1.2 mm. The The used sandwich composite panel was manufac- dimensions of the specimens of the isotropic foam core tured using a vacuum infusion process and its overall were 150 mm x 15 mm with a thickness 10 mm. The thickness was 12.5 mm. The outer composite skins were loading velocity during the tensile tests was 2.0 mm/min made from three layers of fibre-glass fabric with the pro- in the case of the composite skin and 1.0 mm/min in the 2 EXPERIMENTAL SET-UPS AND SPECIMENS case of the foam core. Four specimens for each angle of composite skin and for the foam core were tested. The three-point bending tests of the foam core were performed on specimens with the same dimensions that were used for the tensile tests. The distance of the supports of the testing device was 100 mm and the diameters of all three supports were 10 mm. The resulting sandwich beam with the dimensions 330 mm x 50 mm and a total thickness 12.5 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. The thicknesses of the composite skins were 1.2 mm. The distance of the supports of the testing device was 250 mm and the supports consisted of rotationally joined cylinders with diameters of 30 mm. The loading velocity of the sandwich beam was 20 mm/min. Three specimens were tested in total. 2.1 Material model o^ the skin A user-defined material model of the composite skin was implemented in Abaqus software using the VUMAT subroutine written in the Fortran code. The non-linear function describing the stress-strain relationship starting from the deformation £« (i = 1, 2) was assumed in the case of the principal material directions 1 and 2 (equations (2) and (4)). The non-linear function with a constant asymptote was considered in the case of the shear in plane 12 1 (equation (8)). The following equations describe the stress-strain relationship of the laminated outer skin: CT1 = C11 • £1 + C12 • £ 2 + C13 • £ 3 for £1 < £01 Al 2 2 o 1 = (C 11 • (£1 •(£ 01 -£i )- A1 •£ 01 • (£01 -£1)) + C12 • £2 +C13 • £3) ^(1-D) for £1 > £01 CT2 = C12 • £1 +C22 • £2 +C23 • £3 for £2 < £02 A1 , , CT 2 = (C 12 • £1 + C 22 • (£ 2 • (£ 22 - £ 2) - A2 • £ 02 • (£ 02 - £ 2))+C 23 • £ 3) ^(1-D) for £2 > £02 CT 3 = (C 13 • £1 +C 23 • £ 2 +C 33 • £ 3) ^(1-D) CT 23 = (G 23 • y 23) • (1-D) CT 13 = (G13 • y 13)• (1-D) G102 • y 12 (1) (2) (3) 1+ 0 G12 y 12 \n 12 (1-D) (4) (5) (6) (7) (8) C= E1 • (1-v23 •V32 ) C12 = E1 •(v21 + V23 • V32) E1 •(V31 -V32 • V21 ) E2 •(1-V31 • V13) C13 = X C 22 = X (9) C = E2 • (V 32 -V 31 • V12) C = E 3 •(1-V12 ^ V 21 ) C 23 x C 33 X A=1-V12 •v 21 - V 23 •V 32 - 2 •V12 •V 23 •V 31 where E1, E2 and E3 are the Young's moduli in the principal directions 1, 2 and 3 and V12, V23, V31 are the Poison's ratios in the planes defined by the principal directions 1, 2 and 3. The shear moduli in planes 23 and 13 are designated as G23 and G13, respectively. The non-linear behavior in shear in plane 12 (8) is described using the initial shear modulus G102, the asymptotic value of the shear stress r1'2 and the shape parameter «12. The parameters A1 and A2 in (2) and (4) describe the straightening of the yarns of the fiber-glass fabric and the loss of stiffness in the directions 1 and 2, respectively. The values of the deformations £01 and £02 indicate the the transitions between the linear and non-linear parts of the stress-strain relationship in the given directions 1 and 2 during the loading. The maximum stress failure criterion was used to predict failure on the composite skin: F 1 F2C = F1C = CT2 f2T= (10) F = — F12 where the subscripts T and C denote the tension and compression, X and Y are the strengths in the principal directions 1 and 2, respectively, and ^l denotes the shear strength. The values of the degradation variable D are dependent on the kind of occurred failure.2 The principle of material degradation is shown in Figure 1 and the degradation parameters are summarized in (11). The degradation parameter after failure initiation was implemented in the case of shear failure (F12 > 1.0 and y 12 1 ^ D = 1.0 F1C > 1 ^ D = 0.6 F2T > 1 ^ D = 1.0 F2C > 1 ^ D = 0.6 F12 >1and y ^ < y F2 ^ D=1- e -(F12)" (11) F12 >1 and y 12 > y 1F2 ^ D=1.0 The constants occurring in equations (1) to (5) are: In the case of shear failure the non-negative material constant m12 is represented by the integer and y1F2 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. The optimization process was CT12 = n 0 D = 0.0 Non-linear/^'''^ /\ Lineaf/^ I / 1 / 1 / 1 / 1 / 1 / 1 F,, >1.0 £) = 1.0 / i Z- Figure 1: The principle of material degradation in the principal direction 1 Slika 1: Na~elo degradacije materiala v glavni smeri 1 handled using Optislang 3.2.0. The 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 Table 1. The parameters E3, G13 and G23 were taken from the literature.4 The strengths of the composite skin were determined directly from the experimental data. Table 1: Material parameters of the composite skin Tabela 1: Parametri materiala kompozitne skorje Optimized values: Constant values: El GPa 16.9 V12 - 0.337 E2 GPa 18.5 V23 - 0.337 g02 GPa 4.96 V31 - 0.28 r 02 MPa 39.66 G13 GPa 4.0 n12 - 0.9 G23 GPa 2.75 A1 - 10.0 E3 GPa 8.0 A2 - 14.0 Y - 0.324 e01 - 0.0008 Pc kg/m3 1554 e02 - 0.005 Xt MPa 325 m12 - 5 Yt MPa 347 Xc MPa 65 Yc MPa 67 Sl MPa 35 at / : arctan isV £ i / Figure 2: Tensile and compressive unaxial stress-strain behavior of foam core Slika 2: Vedenje jedra iz pene pri enoosni natezni in tla~ni obremenitvi 2.2 Material model of the foam core The used material model of the foam core was the Low-Density Foam model from the Abaqus software library.5 This material model is intended for highly compressible elastomeric foams. The material behavior was specified directly via unaxial stress-strain curves for tension and compression (Figure 2). In the case of tension the unaxial stress-strain behavior was described via a curve added in the form: a(e) = 4.35•109 • e3 -8.76•108 • e2 + +6.09 10' • e-1.44•104 (12) The material is fully damaged after reaching the tensile strength RmT. The compressive behavior of the foam core was described as an ideally elastoplastic material 6000 5000 4000 z S 3000 £ 2000 1000 (a) i 1 1 : ! .... --------- ! i 1 _________L________ --------- ..... 7 \________ _i_ t ^ -J- ^—Experiment 1 Simulation 0 0.2 0.4 0.6 0.8 1 Displacement [mm] 1.2 6000 5000 _4000 8 3000 £ 2000 1000 (b) 1000 800 600 400 200 j I 1 i i __________L_________i_________- ----------j.---------.J--------^ _________ J __________ i _________j__________ .j 1 i T ] ^"Experiment 0.2 0.4 0.6 0.8 1 Displacement [mm] 1.2 (C) --------------- --------- ------- J 1 i i Experiment Simulation 2 4 6 Displacement [mm] Figure 3: The resultant force-displacement diagrams of the composite skin types A (top), B (center) and C (bottom) Slika 3: Diagrami sila - raztezek kompozitne skorje A (na vrhu), B (v sredini) in C (spodaj) with the Young's modulus E and the yield limit RmC. The material parameters are summarized in Table 2. Table 2: Material parameters of foam core Tabela 2: Parametri materiala pene v jedru E RmC RmT Pf V eu MPa MPa MPa kg/m3 - - 50 1.2 1.5 60 0.0 0.53 2.3 Numerical simulations and results The simulations were performed as quasi-static explicit analyses in the FEM software Abaqus 6.11 using finite-strain theory. The numerical models of the outer skin and the foam core were meshed using 8-node solid elements (element type C3D8R). Figure 3 shows the resulting force-displacement dependencies from averaged experiments and the numerical simulations for specimens of type A, B and C. The 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 Figure 4. The numerical model of the sandwich beam was created as a fully contact problem of four bodies - sandwich beam and three supports. The friction between the sandwich beam and supports has been neglected. Figure 4: a) The 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 tritockovnem upogibnem preizkusu jedra iz pene Figure 5: a) The 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 tritockovnemu upogibu in b) numericni model obremenjenega sestavljenega nosilca Figure 6: The force-deflection diagram of the three-point bending test of the resulting sandwich beam Slika 6: Diagram sila - upogib pri tritockovnem upogibnem preizkusu nosilca The failure of the upper composite skin occurred in compression in principal direction 2 during loading in place under the center support, both in the case of experiments and the numerical simulation. This situation is shown in Figure 5. The comparison of the force-deflection diagrams for the three-point bending tests of the sandwich beam is shown in Figure 6. 3 CONCLUSION The user-defined material model describing the non-linear orthotropic elastic behaviour, considering the progressive failure analysis, was implemented in the FEM system Abaqus. The material parameters of the composite outer skin of the sandwich panel were identified using the mathematical optimization method. In the case of the foam core the Low-Density Foam material model from FEM software library was used. The obtained material parameters of the composite skin and foam core were verified via a three-point bending test of the resulting sandwich beam. The future work will focus on low-velocity impact events involving sandwich plates. Acknowledgement The work has been supported by the European Regional Development Fund (ERDF), project "NTIS -New Technologies for Information Society", European Centre of Excellence, CZ.1.05/1.1.00/02.0090, the student research project of Ministry of Education of Czech Republic No. SGS-2013-036 and the project of Grant Agency of Czech Republic No. GAČR P101/11/0288. 4 REFERENCES 1 T. Kroupa, V. Las, R. Zemcik, Improved nonlinear stress-strain relation for carbon-epoxy composites and identification of material parameters, Journal of Composite Materials, 45 (2011) 9, 1045-1057 2V. Las, R. Zemcik, Progressive damage of undirectional composite panel, Journal of Composite Materials, 42 (2008) 1, 22-44 3 C. F. Yen, Ballistic Impact modeling of Composite materials, 7th International LSDyna User's Conference, Dearborn, Michigan, 2006 4 R. Zemcik, V. Las, T. Kroupa, H. Purs, Identification of material characteristics of sandwich panels, Bulletin of Applied Mechanics, 26 (2011), 26-30 5 Abaqus 6.11 Documentation, Dassault Systemes Simulia Corp., 2011