Experimental Investigation and FE Analysis of Fiber Woven Layered Composites under Dynamic Loading

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1 2th International LS-DYNA Users Conferene Constitutive Modeling(2) xperimental Investigation and F Analysis of Fiber Woven Layered Composites under Dynami Loading Pavel A. Mossakovsky, Fedor K. Antonov, Reaserh Institute of Mehanis of Lomonosov Mosow State University, 992, Mihurinsky Av., Mosow, Russia. Mikhail. Kolotnikov, Lilia A. Kostyreva FSU Gas Turbine ngineering Researh and Prodution Centre "Salut, 58, 6 Budionny Av., Mosow, Russia. Anatoly M. Bragov, Vladimir V. Balandin Reaserh Institute of Mehanis of Lobahevsky State University of Nizhni Novgorod, 6395, 23 Gagarina Av., Nizhni Novgorod, Russia. Abstrat Woven omposites are used in a wide range of industrial appliations suh as development of individual body armor, aviation, astronautis and others. Thus, it is important to learn the mehanial behavior of the omposite and to perform it s adequate modeling under dynami impat loading. The paper is onerned with modeling of woven fabri omposite made of aramid yarns. The experimental investigation inluding stati tests, dynami tests with the Split Hopkinson Bar and ballisti impat tests was performed. The full-sale model with yarn-level detalization was onstruted using obtained experimental data. The method allows getting qualitative results on the small speimens but realisti analysis of real-size models onsisted of billion elements requires huge omputational resoures. So the paper is foused on the development of the alternative homogenized maro-model of the layered omposite. Introdution Adequate simulation of woven omposites onstitutive behavior and failure predition under omplex impat loading is required for a wide range of appliations.. Today, many investigations all over the world are onerned with this problem. Generally, they an be divided into two main groups. One is a miro- or full-sale modeling whih takes into aount a detailed geometrial struture of a omposite []. Suh method requires large omputational resoures but generally simple material models an be used to desribe behavior of individual yarns, forming the omposite. Parameters for suh models, suh as geometry, elasti moduli, failure riterion, et., an be determined from experiments with the yarns [2]. The other method is so alled maro or redued modeling [3]. The method is based on the homogenization of material properties of the omposite and its effetive harateristis. So the omposite is represented as anisotropi solid media with omplex nonlinear mehanial behavior. In this ase it is very diffiult to obtain the unique omposite failure mehanism. Nonlinearity is onerned with the loal damage and internal frition. Thus in most ases multilayered shell elements with several

Constitutive Modeling(2) 2th International LS-DYNA Users Conferene through thikness

In this work, woven omposite is represented as a set of multilayered homogeneous orthotropi

The material was assumed to be linear until failure.

full-sale model. All data below relate to woven fabri made of Rusar aramid fibers. Fig.

Full sale model F model with detailed representation of eah fill and warp yarn was

It is important to take into aount the differene in the geometry of the fill and warp

2 Constitutive Modeling(2) 2th International LS-DYNA Users Conferene through thikness integration points and lassial laminate theory is applied [4]. In this work, woven omposite is represented as a set of multilayered homogeneous orthotropi shells (Fig. ) without internal frition. The material was assumed to be linear until failure. The elasti harateristis were defined from the stati and dynami tests in omparison with full-sale model. All data below relate to woven fabri made of Rusar aramid fibers. Fig. F redued model of a multilayered woven omposite. Full sale model F model with detailed representation of eah fill and warp yarn was onstruted (Fig. 2). It is important to take into aount the differene in the geometry of the fill and warp yarns, sine it affets the initial elasti harateristi of the layer and failure riterion. Fig. 2 Fragment of the F model. ah yarn was assumed to be a transversally anisotropi body with its -axis direted along the yarn and the other axes at its ross setion (Fig. 3). Fig. 3 F model of an individual yarn. Stiffness matrix of the material is a symmetri one. 2

3 2th International LS-DYNA Users Conferene Constitutive Modeling(2) С L a = ab a a a b ba b b b a b G a The yarn is supposed to arry loads only in longitudinal tension, so elasti moduli in transverse diretion are small in omparison with longitudinal. Also aording to the hypothesis of inompressibility of the yarn setion and a form of the first strain tensor invariant θ σ σ G ab G b ( ) + b ( ) + ( ) = a ab a ba b a b, a b we obtain a speial ondition on the Poisson s ratios: ab + a =, ba + b = lasti properties of the yarns are listed in Table. a, GPa b, GPa, GPa σ Table G ab, GPa G b, GPa G a, GPa ba b a Fill Warp Stress-strain urves obtained in the single yarn tensile tests are represented in the Fig. 4 (dotted urve is a simulation). Stress-strain urves for the speimen onsisted of 8 layers plaed in the alternating material diretions are shown in the Fig. 5. Stress, MPa Strain Fig. 4 Stress-strain urve in tensile tests with a single-layer fiber. 3

4 Constitutive Modeling(2) 2th International LS-DYNA Users Conferene xperiment Simulation 9 8 Stress, MPa Stress, MPa,%,% 2,% 3,% 4,% 5,% Strain Strain Fig. 5 Stress-strain urves in tensile tests with 8-layer pakage. It should be noted that in the simulation as well as in the experiments with multilayered speimens, an initial inrease in the speimen thikness was observed, whih an be explained by interation between adjaent layers due to fiber straightening during tension. Also the yarn pull out tests were onduted to identify the parameters of interior frition. The speimens of 3.56 mm and 3.4 mm length for fill and warp yarns pull out respetively were used. The maximum fore values, obtained in experiments were.9 N and.3 N respetively. Fore reeived during simulation is shown in the Fig. 6. Fig. 6 Frition urve obtained in the simulation of the pull out tests. As a result of pull out test the following parameters of the frition model was defined: 4

2th International LS-DYNA Users Conferene Constitutive Modeling(2) τ n vab = τ n vab τ n = min{ µ pn, VC), µ = FD + ( FS FD)exp( vabdc), where v ab is

3 stati and dynami frition oeffiients; VC =.22 MPa oeffiient for visous frition.

performed. xperiments on normal and angular impat were onduted. The virtual model is shown in Fig.

5 2th International LS-DYNA Users Conferene Constitutive Modeling(2) τ n vab = τ n vab τ n = min{ µ pn, VC), µ = FD + ( FS FD)exp( vabdc), where v ab is a relative sliding veloity of the ontat pair; τ n and p n - tangential and normal omponent of the ontat fore; FS =.3 and FD =.3 stati and dynami frition oeffiients; VC =.22 MPa oeffiient for visous frition. Finally, a set of ballisti test inluding different types of speimens with from to layers of fabri with alternating paking of adjaent layers were performed. xperiments on normal and angular impat were onduted. The virtual model is shown in Fig. 7. Fig. 7 Full-sale F model for ballisti angular test with 2-layer pakage. The omparison of full-sale and virtual test on normal impat on 4-layered target is shown in Fig. 8. Fig. 9 illustrates the omparison for angular impat on 2-layered omposite. Fig. 8 Results of a ballisti test with 4-layered omposite. 5

Constitutive Modeling(2) 2th International LS-DYNA Users Conferene Fig. 9 Results of a ballisti angular test with 2-layered omposite.

and fill yarns detailization as shown on Fig. 8-9. However, suh an approah is possible only for small size speimens.

Thus, even with modern failities, the simulation of a real full-sale test like a blade-out test is impossible.

6 Constitutive Modeling(2) 2th International LS-DYNA Users Conferene Fig. 9 Results of a ballisti angular test with 2-layered omposite. Maro model of a woven layered omposite The most realisti desription of the woven omposite behavior under dynami loading is obtained by the full-sale simulation of material with the individual warp and fill yarns detailization as shown on Fig However, suh an approah is possible only for small size speimens. For example, F model of a single-layer of 5 5 mm size onsists of approximately million elements. Thus, even with modern failities, the simulation of a real full-sale test like a blade-out test is impossible. In this study, a omputational model of a single-layer woven omposite proposed is an orthotropi elasti media with material axes a and b direted respetively along the fill and warp diretions (Fig. ). The 8-node shell elements with 3 through thikness integration points were used. Fig. Fragment of a F maro model of a layer. The elasti properties of proposed model were alulated aording to the full-sale model and are listed in Table 2. Table 2 a, GPa b, GPa, GPa G ab, GPa G b, GPa G a, GPa ba b a The failure riterion was defined by *MAT_ADD_ROSION ard with two parameters MXPS = 8 %, SIGP = 7 MPa. Maximum effetive strain at failure orresponds to fiber failure in tension. The seond ondition on prinipal stress was introdued to exlude material failure due to large shear strains. 6

2th International LS-DYNA Users Conferene Constitutive Modeling(2) The

single-layer speimen of 5 5 mm size ontains approximately, elements.

In this paper, it is proposed to simulate multilayer woven pakages with

diretions of the material axes using *INTGRATION SHLL ard.

-3. Fig.. 4-layer omposite. Initial veloity is 266 mps. Fig. 2. 4-layer omposite. Impat veloity is 38 mps.

First, inreasing number of integration points in the shell auses an inrease in

neessity in a new failure riteria and qualitative mismath of full-sale and

Seondary, the F model should inlude 5 to layers to simulate delamination of the

It an be onluded that eah layer in F model should ontain 4 to physial layers

A Simple Global/Loal approah to Modeling Ballisti Impat onto Woven Fabris, th

7 2th International LS-DYNA Users Conferene Constitutive Modeling(2) The parameters of frition model between fiber and the striker are listed in the Table 3. Table 3 FS FD VC. МПа This approah gives a serious savings in omputational resoures: a single-layer speimen of 5 5 mm size ontains approximately, elements. But still, real strutures an onsist of more than ten million elements. In this paper, it is proposed to simulate multilayer woven pakages with multilayer shell elements, whih inlude multiple fabri layers with alternating diretions of the material axes using *INTGRATION SHLL ard. The results of omparison of some ballisti tests and simulation are shown in Fig. -3. Fig.. 4-layer omposite. Initial veloity is 266 mps. Fig layer omposite. Impat veloity is 38 mps. This approah also has some negative aspets. First, inreasing number of integration points in the shell auses an inrease in bending stiffness of the material in the transverse diretion, whih leads to neessity in a new failure riteria and qualitative mismath of full-sale and virtual ballisti tests. Seondary, the F model should inlude 5 to layers to simulate delamination of the omposite and the layers interation. It an be onluded that eah layer in F model should ontain 4 to physial layers optimal. Referenes. Rao, M.P., Keefe, M., Powers, B.M., Bogetti, T.A. A Simple Global/Loal approah to Modeling Ballisti Impat onto Woven Fabris, th International LS-DYNA Users Conferene, p , Simmons, J., rlih, D., and Shokey, D., xpliit FA Modeling of Multilayer Composite Fabri for Gas Turbine ngines Containment Systems, Part 3: Model Development and Simulation of xperiments, FAA report DOT/FAA/AR-4/4, P3, November Tabiei, A. and I. Ivanov, Computational miro-mehanial Model of Flexible Woven Fabri for Finite lement Impat Simulation, IJNM, 53, (6), , (22). 4. "LS-DYNA Theory Manual", Marh, 26. 7

8 Constitutive Modeling(2) 2th International LS-DYNA Users Conferene 8

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