UDK 669.018.9:620.1/.2 ISSN 1580-2949 Original scientific article/Izvirni znanstveni članek MTAEC9, 45(6)567(2011) IDENTIFICATION AND VERIFICATION OF THE COMPOSITE MATERIAL PARAMETERS FOR THE LADEVEZE DAMAGE MODEL IDENTIFIKACIJA IN VERIFIKACIJA PARAMETROV KOMPOZITNEGA MATERIALA ZA MODEL LADEVEZE Vaclav Kleisner, Robert Zemcik, Tomaš Kroupa University of West Bohemia in Pilsen, Department of Mechanics, Univerzitni 22, 306 14, Plzen, Czech Republic kleisner@kme.zcu.cz Prejem rokopisa - received:2011-02-01 ; sprejem za objavo - accepted for publication: 2011-04-14 In this investigation we examine the properties of a layered composite material and verify the Ladeveze material model implemented in PAM-CRASH software. The complex material model incorporates plasticity, failure and damage mechanisms and is suitable for dynamic phenomena, such as crash tests. The experimental tests were performed on appropriate laminated specimens made from unidirectional, pre-impregnated, composite fiber (prepregs) - coupons with axially oriented fibers, coupons with fibers at 45°, and ±45° cross-ply laminates. The tests included simple tensile tests to fracture and cyclic tensile tests. Numerical models were created for the finite-element analysis using shell elements. A mathematical optimization was then used to minimize the error between the experimental and numerical results in terms of load-displacement curves for all the tested configurations by varying the material characteristics. Keywords: composite, identification, carbon, fiber, epoxy, plasticity, experiment, finite-element analysis Identifikacija lastnosti plastastega kompozitnega materiala in verifikacja modela Ladeveze za material s PAM-CRASH-sofverom. Kompleksen model materiala vključuje plastičnost, prelom in mehanizem poškodbe ter je primeren za dinamične fenomene kot preizkus trka. Preizkusi so bili izvršeni na primernih laminatnih vzorcih, izdelanih iz enosmernih predimpregniranih kompozitnih vlaken (prepreg) - kuponov z osno orientiranimi vlakni, kuponov z vlakni pod kotom 45° in križnimi laminati ±45°. Preizkusi so obsegali enostavne raztržne in ciklične natezne preizkuse. Pripravljeni so bili numerični modeli za analizo po metodi končnih elementov z uporabo lupinastih elementov. Matematična optimizacija je bila nato uporabljena za zmanjšanje napak med eksperimentalnimi in numeričnimi rezultati s krivuljami obremenitev - pomik za vse preizkušene konfiguracije s spremembami karakteristik materiala. Ključne besede: kompozit, identifikacija, ogljikova vlakna, epoksi, plastičnost, preizkusi, končna elementna analiza 1 INTRODUCTION bility. Many material models have been proposed so far, but none of them is perfect or universal 6. The basic Composite materials are modern materials with failure criteria, such as the maximum stress, maximum advantageous strength- and stiffness-to-mass ratios com- strain and others, are not interactive criteria. This means pared to classical materials, such as steel or aluminum 1,2. that there is no relation between the stress components in Namely, the carbon-fiber-reinforced plastic composites different directions. In this respect, the so-called inte- consisting of continuous carbon fibers and a matrix can ractive criteria, such as Tsai-Wu 1, are more suitable for have similar or better strength than steel structures and crash simulations. On the other hand, the disadvantage is they can have similar or less weight than aluminum that we cannot distinguish between the matrix and fiber structures. As their properties are highly oriented failure, which is important in an impact simulation. The (generally anisotropic), the greatest strength is achieved most recent failure criteria (the so-called direct mode in the direction of the fibers. This can be utilized criteria), such as Puck 8 or LaRC 3, use the advantages of especially in the case of the design of components with both types 9. excessive loading in a specific direction. The Ladeveze material model 5 in the PAM-CRASH Composite materials are increasingly used in the software 7 is implemented only for a multi-layered, thin aerospace and automotive industries for the reason mentioned above. Numerical simulations help to design shell element and transient analysis (i.e., the explicit the desired components or complex structures, including code). It includes the following modes of failure of a the possibility to optimize the fiber orientations or composite material: debonding, micro-cracking, delami- lay-ups. Nevertheless, it is important to know the correct nation, and fiber breaking. The Ladeveze damage model material parameters and to use the appropriate material also includes inelastic material deformations caused by model. This material data must be obtained from the matrix-dominated loading. The plasticity of the experimental measurements. An integral part of any matrix cannot be neglected in general and the effect is material model is the failure/damage prediction possi- best seen, for example, in the case of cyclic loading. 2 MATERIAL AND DAMAGE MODELS The constitutive relationship for materials with a linear response is usually written in the form of the extended Hooke's law 1. The constitutive relationship of the Ladeveze material model can be written with similar formulae, except that elastic constants are herein modified by additional damage parameters or functions The crucial relations are summarized in Table 1. The superscript 0 denotes the initial values (damage free) of the material constants. The quantities dii, d22 and d22 represent the fiber damage in tension, matrix damage, and fiber-matrix debonding damage, respectively. The effect of d12 is shown in the relation of the actual (G12) and initial (G0i2) values of the shear moduli. The shear damage function Y12 is derived from the strain energy Ed for an anisotropic material, where Yc and Yo are the critical shear damage limit and the initial shear damage threshold, respectively. The parameter YR represents the shear failure. Another important improvement to the composite material model is obtained by the inclusion of the matrix plasticity behavior. This is incorporated by changing the yield stress during the cyclic loading. The yield stress is given by R(eP), which is a function of the initial yield stress Roo, the plastic deformation eP and the hardening coefficients ß, m. This represents a power-law approximation of the experimental curve. The fiber tensile damage (longitudinal damage) is characterized by the initial (e'li) and ultimate (£"ii) fiber tensile damage strains. 3 EXPERIMENT AND SIMULATIONS In this study, laminated composite coupons made of HexPly 913C prepregs with Tenax HTS 5631 carbon fibers are tested (see Figures 1-3). The material Figure 1: Fractured [OJs specimen Slika 1: Prelomljen vzorec [0]s Figure 2: Fractured [±45]2S specimen. The position and orientation of the cracks is emphasized Slika 2: Prelomljen vzorec [+45]2s. Poudarjena sta položaj in orientacija razpok Figure 3: Fractured [45]8 specimen Slika 3: Prelomljen vzorec [45]§ characteristics needed for the numerical models are obtained from the experimental data. The detailed description of the measurement can be found in 7. It consists of three types of tests: • simple tensile test on [0]« laminates, • simple tensile test with load/unload cycles on [±45]2s laminates, • simple tensile test on [45]« laminates. Simple [0] tensile test The tensile test was conducted on UD composite coupons with the [0]8 fiber composition (see Figure 1). The coupons were loaded by displacement (speed 1 mm/min) until rupture. The force-displacement curve was measured, see Figure 4. The initial Young's modulus E0ii, the initial fiber failure value e'li and the critical fiber failure value £"ii were assessed from the data obtained using Hooke's law. The averaged experimental results were used directly in the material model within the corresponding numerical simulation. The results of the simulation are in a good Tabela 1: Relacije modela Ladeveze za lupinaste elemente4'5 Table 1: Ladeveze model relations for shell elements 4,5 Figure 4: Load-displacement curves from the [0]8 test Slika 4: Krivulji obremenitev - pomik za preizkus [0]8 Figure 5: Load-displacement curves from the [45] 8 test Slika 5: Krivulji obremenitev - pomik za preizkus [45]8 Tabela 2: Identificirane karakteristike materiala Table 2: Identified material characteristics Figure 6: Load-displacement curves from [±45]2S test Slika 6: Krivulji obremenitev - pomik za preizkus [±45]2S agreement with the experimental data (see Figure 4). The constants £'ii and £"ii have similar values as the whole cross-section ruptured at the same time. ^^clic [±45]2s tension test The composite coupons (Figure 2) were loaded by a cyclic loading - 6 cycles (load/unload) with increasing Parameter Elastic properties Young's modulus in fiber direction Young's modulus in transverse direction Shear modulus in plane 12 Shear modulus in plane 23 Poisson's ratio Failure properties Initial fiber failure Critical fiber failure Shear failure Damage properties Critical shear damage Initial shear damage Plastic properties Yield stress Hardening parameter ß Hardening parameter a Symbol ^22 '^12 r