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Voxel and Finite Element Analysis Models for Ballistic Impact on Ceramic-polymer Composite Panels
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Procedia Engineering 206 (2017) 182–187
International Conference on Industrial Engineering, ICIE 2017 International Conference on Industrial Engineering, ICIE 2017
Voxel and Finite Element Analysis Models for Ballistic Impact on Voxel and Finite Element Analysis Models for Ballistic Impact on Ceramic-polymer Composite Panels Ceramic-polymer Composite Panels S.B. Sapozhnikov, E.I. Shchurova* S.B. Sapozhnikov, E.I. Shchurova* South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation
Abstract Abstract Protective shields are used to protect the technical devices from the impacts of high-speed objects, for example, the space systems from orbital problem is so important special spacecrafts designedobjects, to cleanfor up example, the trash. the CeramicProtective shields aregarbage. used toThis protect the technical devicesthat from the impacts of are high-speed space polymer composite panels have some advantages. However, the characteristics of such panel components have not been studied systems from orbital garbage. This problem is so important that special spacecrafts are designed to clean up the trash. Ceramicsufficiently yet. Thepanels finite have element is an However, efficient method for the composite improvement. Obviously, polymer composite someanalysis advantages. the characteristics of such characteristics panel components have not been studied such improvement searching forisa an richefficient variety method of composites Each optionimprovement. requires creating a brick sufficiently yet. Thenecessitates finite element analysis for the characteristic. composite characteristics Obviously, elements mesh. Adequate FE models have for to bea developed cones, forEach example) as requires well as for panels.aVoxel such improvement necessitates searching rich varietyforofpenetrators composites(metal characteristic. option creating brick based micro modeling makes it possible a composite structure (metal parametrical Furtherason, it as is easy to transform elements mesh. Adequate FE models havetotodevelop be developed for penetrators cones, model. for example) well for panels. Voxel this FE one. makes Developing a material modela is an important problem of the impact ceramicbasedmodel microtomodeling it possible to develop composite structure parametrical model.simulation. Further on, To it isstudy easy the to transform polymer composite behavior using aa material traditional Johnson-Holmquist andofthe recent Toughened Adhesive Polymer this model to FE one. Developing model is an important model problem themost impact simulation. To study the ceramicmodel is composite suggested. behavior The calculations LS-DYNA give initial adequate results impact modeling and Adhesive thus the suggested polymer using a using traditional Johnson-Holmquist model and thefor most recent Toughened Polymer approaches of geometrical and of FE modeling are rathergive effective model is suggested. The calculations using LS-DYNA initial. adequate results for impact modeling and thus the suggested © 2017 The Authors. Published B.V. approaches geometrical and ofby FEElsevier modeling rather effective. © 2017 Theof Authors. Published by Elsevier Ltd.arecommittee Peer-review under responsibility of Elsevier the scientific of the International Conference on Industrial Engineering. © 2017 The Authors. Published by B.V. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering Keywords: Ceramic-polymer composite; orbital garbage; ballistic impac; voxel. Conference on Industrial Engineering. Peer-review under responsibility of the scientific committee of the FEA; International Keywords: Ceramic-polymer composite; orbital garbage; ballistic impac; FEA; voxel.
1. Introduction 1. Introduction Protective panels are used to defend technical devices from impacts of high-speed objects, for example, space systems from panels orbital are garbage. problem so important special spacecrafts are designed clean up the space trash. Protective used This to defend technical devicesthat from impacts of high-speed objects,tofor example, These aregarbage. suppliedThis withproblem «umbrella» in whichthat garbage should be stuck Ceramic-polymer systemsspacecrafts from orbital so important special spacecrafts arein.designed to clean upcomposite the trash. These spacecrafts are supplied with «umbrella» in which garbage should be stuck in. Ceramic-polymer composite
* Corresponding author. Tel.: +7-351-267-9111; fax: +7-351-267-9111. E-mail address:author. [email protected] * Corresponding Tel.: +7-351-267-9111; fax: +7-351-267-9111.
E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier B.V. Peer-review©under the scientific committee 1877-7058 2017responsibility The Authors. of Published by Elsevier B.V.of the International Conference on Industrial Engineering . Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering .
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.457
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panels have some advanced features: they are hard like ceramics and elastic and viscous like resin. A number of patents and articles which offer to use polymer matrix or fabric and ceramic balls (Fig. 1, a) is known [1-3]. Panel light weight, high impact toughness and the hardness of ceramics are the advantages of such materials [4,5].
Fig.1. (a) US Patent N 3431818 (1969) [1]; (b) SiC foam (20 ppi) infiltrated with thermosetting polyurethane [3].
However, the behavior of the panel made of such material is not sufficiently investigated. FE models given in some scientific researches describe balls as absolute smooth spherical objects [6,7]. Actually they do not have so smooth surfaces (Fig.1, b). Moreover, composite structures containing such balls often have no regular dense balls arrangement (cellular structure). Another actual problem is application of models of materials which form ceramicpolymer composite and of materials of complex structured penetrators. There are many studies of panel piercing, but some of these studies do not offer material models, which consider speed, temperature and damage. Other studies offer models, which are quite different from each other [8]. Problems of panel piercing are often solved using special commercial programs, such as LS-DYNA or ABAQUS. However, to make correct calculations it is necessary to use meshes of brick (8 nodes) finite elements. Automatic generation of such meshes for composite structures with densely located balls is a certain problem still. Also, the parameters which characterize process dynamics and the contact phenomena at the moment of panel piercing are still insufficiently studied [9,10]. Thus, to search the best characteristics of panel components it is necessary to develop various geometrical and physical settlement calculation models. Automated developing of such models is an actual problem. One of modeling methods of geometrical structures, which develops brick finite element meshes automatically is voxel modeling [11-14]. Appropriate analytic dependences for voxel models developing have to be determined. However, it is impossible to solve the problem using voxels typically, developing one regular mesh, as it is necessary to apply small size voxels to model small-sized balls accurately. In this case, the model is high-sized and the resources of modern computers are insufficient. Thus, the modeling based on panel division into two areas is offered. The first area is described by micro model, the second area – by macro model. It is supposed that all physical phenomena at impact on ceramic-polymer composite panel can be studied within a limited area of contact with the penetrator. Exactly here cracks are initiated and the panel failure starts. Further, when cracks are rather strong, the whole panel fails in a similar way. Thus, it is offered to develop a micro model to describe localized panel area in detail, and to develop a macro model to describe the other area of the panel. This is a compromise approach, and in the authors’ opinion, it produces the most realistic results using the resources of modern computers. It is obvious that searching for the best characteristics of panel components using calculations is impossible without an adequate description of a penetrator. Orbital garbage model, for example, can be described as an ordinary multilayer cone. The main features of the proposed research are the most adequate panel micro model with description of a set of ceramic balls regularly arranged within a polymer matrix, and penetrator model almost completely comparable to its design drawing.
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2. Computer models of ceramic-polymer composite panel and of a penetrator For research of panel piercing it is necessary to develop two types of computer models: geometrical and FE models; models of materials. These models are described below. 2.1. Geometrical and finite element models At the start of research, it is necessary to develop composite panel model. Multilayer panel is described as an example. The first layer of the plate attains a thickness of about 3.3 mm and is made of polymer matrix and ceramic balls 1.5 mm in diameter. Balls are located densely in three ranks and are arranged in chessboard order. One composite layer is a 40х40 mm square. This layer is stick down to 0.8 mm thick steel plate. Dynamic analysis of panel piercing can be carried out using LS-DYNA. For this purpose, it is necessary to develop a mesh of brick finite elements. A convenient mesh generation way is initial voxel geometrical modeling and next following transformation of voxel mesh into FE one. For adequate description of a ceramic ball, voxel mesh step has to be rather small to place 10–20 voxels at the distance equal to ball diameter. So, voxel size is taken as 0.1 mm. Thus, there are about five million voxels in the geometric model of composite plate with the sizes of 40х40х3.3 mm. Respectively, number of finite elements is the same. It is difficult to calculate such model because of limited computer resources. Thus, it is suggested to model panel piercing within a limited 10 mm diameter area. The other area of the panel is modeled as homogeneous having average parameters of a ceramic-polymer plate. A voxel model developing has been described in one of the previous author’s publications. This type of modelling requires determination of state parameter for each voxel. State parameter is equal to material number depending on location of the voxel nodal point within the modelled area. Sphere equation has to be used to model a ceramic ball. For example, to compare an abscissa of voxel nodal point with the coordinate of sphere surface it is satisfactory to use the well-known equation: xe Re2 ( ye Be )2 ( ze Ce ) 2 Ae
(1)
where Re , Ae , Be , Ce – radius of sphere and three coordinates of its center in subarea coordinate system, respectively (e=i, j, k). Then it is necessary to determine voxels of all spherical balls within the panel. To do this that is enough to determine coordinates of the sphere centers in the specified coordinate system. For this purpose, first of all, it is necessary to determine steps between ball centers. This calculation is performed in view of balls regular location in chessboard order (Fig.2, a). It is clear that the distance between ball centers depends on ball radius and the specified gap between their surfaces G on condition that the gap is required: S
(4 / 3)(2 Re G ) 2
(2)
The formula is checked using CAD system (Fig. 2, b). Searching for the best panel characteristics it is easy to generate different FE meshes automatically by variation of Re and G parameters and relocation of ball rows for a distance of S/2. Thus, this approach gives the chance to generate parametric model. Based on given formulas and relations published earlier [15] the authors have generated voxel and FE meshes of the described panel (Fig. 2, c). At the next stage of study parametric model and FE mesh for a penetrator have been developed. For research of spacecraft panel piercing it is necessary to develop a model of orbital garbage. Garbage objects have complex structures, as they are spacecraft fragments mostly. Generally, any object may appear as a metallic part. However, it is necessary to accept some certain model for the presented research. A model of the ordinary cone is used. According to data from open publications, orbital garbage may be described as a multilayer cone [16,17]. The total FE calculation model with all boundary conditions, ties, symmetry conditions is given in Fig. 3.
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Fig.2. Location of ceramic balls within the panel: (a) computational scheme, (b) scheme check using 3D model, (c) FE mesh.
Fig.3. Finite element models of all objects of the research.
2.2. Material models To model materials behavior, as known, two models are used: state equation (stress-strain-internal energy relationship) and strength model (material behavior related with stress in excess of yield stress). The presented research has two specific aspects: modeling of high-speed interaction and modeling of considerably different materials: fragile ceramics, elasto-plastic metals and viscous polyethylene. Thus, different models of materials have to be developed. For the problem solution appropriate material models have to be present among the models set of FE program, in particular, in the model set of LS-DYNA. Hence, based on the published data, the following material models have been accepted [18]. Ceramic balls Al2O3 are described using Johnson-Holmquist model. Material characteristics used for this model are as follows [19]: ρ=3700 kg/m3 – density; G=90.16 Gpa – shear modulus; a =0.93 – intact normalized strength parameter; b=0.31 – fractured normalized strength parameter; c=0 – strength parameter (for strain rate dependence); m=0.6 – fractured strength parameter (pressure exponent); n=0.6 – Intact strength parameter (pressure exponent); 0 = 1.0 EPSI – quasi-static threshold strain rate; T=0.2 GPa – maximum tensile pressure strength; Sf max – maximum normalized fractured strength (NA); hel=2.79 GPa – Hugoniot elastic limit; Phel=1.46 GPa – pressure component at the Hugoniot elastic limit; β=1.0 – fraction of elastic energy loss converted to hydrostatic energy; d1=0.005 – parameter for plastic strain to fracture; d2=1.0 – parameter for plastic strain to fracture (exponent); k1=130.95 GPa – first pressure coefficient (equivalent to the bulk modulus); k2 = 0 – second pressure coefficient; k3=0 – third pressure coefficient; Fs – failure criteria: Fs <0 – fail if . (tensile failure); Fs=0 – no failure (default); Fs >0 – fail if the effective plastic strain greater than Fs. The equivalent stress for a ceramic-type material is given by Johnson-Holmquist model equations [19]:
* i* D( i* *f ), i* a ( p* t * ) n (1 c ln(* )), D T / Phel , p* p / Phel p / fp , t *
(3)
S.B. Sapozhnikov et al. //Procedia (2017) 000–000 182–187 S.B. Sapozhnikov, E.I. Shchurova ProcediaEngineering Engineering206 00 (2017)
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where fp d1 ( p* t * ) d2 – is plastic strain per computational cycle and the plastic strain to fracture and *f b( p * ) m (1 c ln( )) S f max represents the damaged material behavior. In undamaged material, the hydrostatic pressure is given by p k1 k2 2 k3 3 , where / 0 1. For the polymer, the Toughened Adhesive Polymer model (MAT_252, LS-DYNA) has been accepted. The main parameters are [20]: ρ=950 kg/m3 – density; = ܧ1.586GPA – Young’s modulus; ߥ = 0.34 – Poisson’s ratio; ߬0=23.17MPa – initial shear yield stress; q=2.825 MPa – isotropic nonlinear hardening modulus; b=10.37 – isotropic exponential decay parameter; H=17.11 MPa – isotropic linear hardening modulus; C=0.1076 – strain rate coefficient, etc. Orbital garbage metallic components are described using quite well known plastic kinematic model.
Fig.4. Equivalent stress and strains within the penetrator, part of panel and ceramic balls.
3. Results and discussion Overall, parametrical geometrical model and FE models of ceramic-polymer panel and of penetrator have been developed. However, in certain cases, calculations are unstable because it is necessary to combine micro- and macro-model (Fig.4). One more difficulty is caused by the model high size. Because of limited computer resources, only a quarter of panel has been described. Thus, the modeling results are not entirely realistic, i.e. some of finite elements are located out of the coordinate planes. 4. Conclusion The accepted approach of developing FE model on the basis of voxel model guarantees complete model parametrization. So, smart modification of ceramic-polymer composite structure is achieved. Micro-modeling using
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Johnson-Holmquist model for ceramics, Toughened Adhesive Polymer model for polyethylene, and plastic kinematic model for multilayer cone metals allow to obtain rather realistic stress-strain state pictures for ceramicpolymer composite. Acknowledgements The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011. References [1] H.A. King, Lightweit protective armor plate, US patent N 3431818, 1969. [2] M.M. Kononenko, A.I. Malkin, T.A. Shumikhin, Device for protection of spacecraft and space stations against impact action of space medium particles, RU patent N 2299839,2007. [3] P. Colombo, F. Zordan, E. Medvedovski, Ceramic-Polymer Composites for Ballistic Protection, Advances in Applied Ceramics. 105(2) (2006) 78–83. DOI: 10.1179/174367606X84440. [4] E. Medvedovski, Ballistic performance of armour ceramics: Influence of design and structure, Part 2, Ceramics International. 36 (2010) 2117–2127. DOI:10.1016/j.ceramint.2010.05.021. [5] V.A. Grigoryan, I.F. Kobyilkin, V.M. Marinin, E.N. Chitsyakov, Materials and protective structures for local and individual reservations, Radiosoft, Moscow, 2008, 406. [6] J. Jovicic, A. Zavaliangos, F. Ko, Numerical modeling of impact behavior of integrated gradient design composite materials, Research Gate. (2015) 1–35. DOI: 10.13140/RG.2.1.2931.9120. [7] J. Jovicic, A. Zavaliangos, F. Ko, Modeling of the ballistic behavior of gradient design composite armors, Composites, Part A. 31 (2000) 773– 784. DOI: http://dx.doi.org/10.1016/S1359-835X(00)00028-2. [8] D. Kreculj, B. Rašuo, Review of impact damages modelling in laminated composite aircraft structures, Technical Gazette. 20(3) (2013) 485495. SSN:1330-3651. [9] D.P. Gonçalvesa, F.C.L. de Meloa, A.N. Kleinb, H.A. Al-Qureshib, Analysis and investigation of ballistic impact on ceramic/metal composite armour, Int. J. of Machine Tools and Manufacture. 44 (2004) 307–316. DOI:10.1016/j.ijmachtools.2003.09.005. [10] P. Chabera, A. Boczkowska, A. Morka, T. Niezgoda, A. Oziębło, A. Witek, Numerical and experimental study of armour system consisted of ceramic and ceramic-elastomer composites, Bulletin of the polish academy of sciences technical sciences. 62(4) (2014) 853–859. DOI: 10.2478/bpasts-2014-0094. [11] S.A. Smitheman, I.A. Jones, A.C. Long, W. Ruijter, A voxel-based homogenization technique for the unit cell thermomechanical analysis of woven composites, The 17st International Conference on Composites (ICCM-17), 2009. [12] G. Erns, M. Vogler, C. Hühne, R. Rolfes, Multiscale Progressive Failure Analysis of Textile Composites, Composites Science and Technology. 70 (2010) 61–72. DOI:10.1016/j.compscitech.2009.09.006. [13] J.D. Hiller, H. Lipson, STL 2.0: a proposal for a universal multi-material additive manufacturing file format, Proceeding of the 20th annual Int. Solid freeform fabrication symposium, Austin, 2009, pp. 266–278. [14] C.I. Shchurova, A methodology to design a 3D graphic editor for micro-modeling of fiber-reinforced composite parts, Advances in Engineering Software. 90 (2015) 76–82. DOI: http://dx.doi.org/10.1016/j.advengsoft.2015.07.001. [15] E.I. Shchurova, Modeling of the Ceramics Structure for the Finite Element Analysis, Procedia Engineering. 150 (2016) 179–184. DOI: http://dx.doi.org/10.1016/j.proeng.2016.06.744. [16] V.N. Dvoryaninov, Combat ferry riflemen. Modern domestic cartridges, chronicles of designers: Monograph in 4 books, Book 4, D'Solo, Klimovsk, 2015, 564 p. [17] M. Andrenucci, P. Pergola, A. Ruggiero, Active removal of space debris. Expanding foam application for active debris removal: Final report, European Space Agency, 2011, 132 p. [18] LS-DYNA_Manual_Volume_II_R8.0_MATERIALS.pdf [19] D.S. Cronin, K. Bui, C. Kaufmann, G. McIntosch, T. Berstad, Implementation and Validation of the Johnson-Holmquist Ceramic Material Model in LS-Dyna, 4-th European LS-DYNA Users conf. Material I. D-I-47–59. [20] A. Matzenmiller, F. Burbulla, Robustness and reliability of methods to simulate adhesive joints with high strength steel sheets at crash conditions: Tech. reporst, Institute of Mechanics Department of Mechanical Engineering University of Kassel, Germany, pp. 245–411.
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Available online at www.sciencedirect.com Procedia Engineering 00 (2017)000–000 Procedia Engineering 00 (2017)000–000
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Procedia Engineering 206 (2017) 182–187
International Conference on Industrial Engineering, ICIE 2017 International Conference on Industrial Engineering, ICIE 2017
Voxel and Finite Element Analysis Models for Ballistic Impact on Voxel and Finite Element Analysis Models for Ballistic Impact on Ceramic-polymer Composite Panels Ceramic-polymer Composite Panels S.B. Sapozhnikov, E.I. Shchurova* S.B. Sapozhnikov, E.I. Shchurova* South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation South Ural State University, 76, Lenin Avenue, Chelyabinsk 454080, The Russian Federation
Abstract Abstract Protective shields are used to protect the technical devices from the impacts of high-speed objects, for example, the space systems from orbital problem is so important special spacecrafts designedobjects, to cleanfor up example, the trash. the CeramicProtective shields aregarbage. used toThis protect the technical devicesthat from the impacts of are high-speed space polymer composite panels have some advantages. However, the characteristics of such panel components have not been studied systems from orbital garbage. This problem is so important that special spacecrafts are designed to clean up the trash. Ceramicsufficiently yet. Thepanels finite have element is an However, efficient method for the composite improvement. Obviously, polymer composite someanalysis advantages. the characteristics of such characteristics panel components have not been studied such improvement searching forisa an richefficient variety method of composites Each optionimprovement. requires creating a brick sufficiently yet. Thenecessitates finite element analysis for the characteristic. composite characteristics Obviously, elements mesh. Adequate FE models have for to bea developed cones, forEach example) as requires well as for panels.aVoxel such improvement necessitates searching rich varietyforofpenetrators composites(metal characteristic. option creating brick based micro modeling makes it possible a composite structure (metal parametrical Furtherason, it as is easy to transform elements mesh. Adequate FE models havetotodevelop be developed for penetrators cones, model. for example) well for panels. Voxel this FE one. makes Developing a material modela is an important problem of the impact ceramicbasedmodel microtomodeling it possible to develop composite structure parametrical model.simulation. Further on, To it isstudy easy the to transform polymer composite behavior using aa material traditional Johnson-Holmquist andofthe recent Toughened Adhesive Polymer this model to FE one. Developing model is an important model problem themost impact simulation. To study the ceramicmodel is composite suggested. behavior The calculations LS-DYNA give initial adequate results impact modeling and Adhesive thus the suggested polymer using a using traditional Johnson-Holmquist model and thefor most recent Toughened Polymer approaches of geometrical and of FE modeling are rathergive effective model is suggested. The calculations using LS-DYNA initial. adequate results for impact modeling and thus the suggested © 2017 The Authors. Published B.V. approaches geometrical and ofby FEElsevier modeling rather effective. © 2017 Theof Authors. Published by Elsevier Ltd.arecommittee Peer-review under responsibility of Elsevier the scientific of the International Conference on Industrial Engineering. © 2017 The Authors. Published by B.V. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering Keywords: Ceramic-polymer composite; orbital garbage; ballistic impac; voxel. Conference on Industrial Engineering. Peer-review under responsibility of the scientific committee of the FEA; International Keywords: Ceramic-polymer composite; orbital garbage; ballistic impac; FEA; voxel.
1. Introduction 1. Introduction Protective panels are used to defend technical devices from impacts of high-speed objects, for example, space systems from panels orbital are garbage. problem so important special spacecrafts are designed clean up the space trash. Protective used This to defend technical devicesthat from impacts of high-speed objects,tofor example, These aregarbage. suppliedThis withproblem «umbrella» in whichthat garbage should be stuck Ceramic-polymer systemsspacecrafts from orbital so important special spacecrafts arein.designed to clean upcomposite the trash. These spacecrafts are supplied with «umbrella» in which garbage should be stuck in. Ceramic-polymer composite
* Corresponding author. Tel.: +7-351-267-9111; fax: +7-351-267-9111. E-mail address:author. [email protected] * Corresponding Tel.: +7-351-267-9111; fax: +7-351-267-9111.
E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier B.V. Peer-review©under the scientific committee 1877-7058 2017responsibility The Authors. of Published by Elsevier B.V.of the International Conference on Industrial Engineering . Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering .
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.457
2
S.B. Sapozhnikov et al. / Procedia Engineering 206 (2017) 182–187 S.B. Sapozhnikov, E.I. Shchurova / Procedia Engineering 00 (2017) 000–000
183
panels have some advanced features: they are hard like ceramics and elastic and viscous like resin. A number of patents and articles which offer to use polymer matrix or fabric and ceramic balls (Fig. 1, a) is known [1-3]. Panel light weight, high impact toughness and the hardness of ceramics are the advantages of such materials [4,5].
Fig.1. (a) US Patent N 3431818 (1969) [1]; (b) SiC foam (20 ppi) infiltrated with thermosetting polyurethane [3].
However, the behavior of the panel made of such material is not sufficiently investigated. FE models given in some scientific researches describe balls as absolute smooth spherical objects [6,7]. Actually they do not have so smooth surfaces (Fig.1, b). Moreover, composite structures containing such balls often have no regular dense balls arrangement (cellular structure). Another actual problem is application of models of materials which form ceramicpolymer composite and of materials of complex structured penetrators. There are many studies of panel piercing, but some of these studies do not offer material models, which consider speed, temperature and damage. Other studies offer models, which are quite different from each other [8]. Problems of panel piercing are often solved using special commercial programs, such as LS-DYNA or ABAQUS. However, to make correct calculations it is necessary to use meshes of brick (8 nodes) finite elements. Automatic generation of such meshes for composite structures with densely located balls is a certain problem still. Also, the parameters which characterize process dynamics and the contact phenomena at the moment of panel piercing are still insufficiently studied [9,10]. Thus, to search the best characteristics of panel components it is necessary to develop various geometrical and physical settlement calculation models. Automated developing of such models is an actual problem. One of modeling methods of geometrical structures, which develops brick finite element meshes automatically is voxel modeling [11-14]. Appropriate analytic dependences for voxel models developing have to be determined. However, it is impossible to solve the problem using voxels typically, developing one regular mesh, as it is necessary to apply small size voxels to model small-sized balls accurately. In this case, the model is high-sized and the resources of modern computers are insufficient. Thus, the modeling based on panel division into two areas is offered. The first area is described by micro model, the second area – by macro model. It is supposed that all physical phenomena at impact on ceramic-polymer composite panel can be studied within a limited area of contact with the penetrator. Exactly here cracks are initiated and the panel failure starts. Further, when cracks are rather strong, the whole panel fails in a similar way. Thus, it is offered to develop a micro model to describe localized panel area in detail, and to develop a macro model to describe the other area of the panel. This is a compromise approach, and in the authors’ opinion, it produces the most realistic results using the resources of modern computers. It is obvious that searching for the best characteristics of panel components using calculations is impossible without an adequate description of a penetrator. Orbital garbage model, for example, can be described as an ordinary multilayer cone. The main features of the proposed research are the most adequate panel micro model with description of a set of ceramic balls regularly arranged within a polymer matrix, and penetrator model almost completely comparable to its design drawing.
S.B. Sapozhnikov et al. / Procedia Engineering 206 (2017) 182–187 S.B. Sapozhnikov, E.I. Shchurova / Procedia Engineering 00 (2017) 000–000
184
3
2. Computer models of ceramic-polymer composite panel and of a penetrator For research of panel piercing it is necessary to develop two types of computer models: geometrical and FE models; models of materials. These models are described below. 2.1. Geometrical and finite element models At the start of research, it is necessary to develop composite panel model. Multilayer panel is described as an example. The first layer of the plate attains a thickness of about 3.3 mm and is made of polymer matrix and ceramic balls 1.5 mm in diameter. Balls are located densely in three ranks and are arranged in chessboard order. One composite layer is a 40х40 mm square. This layer is stick down to 0.8 mm thick steel plate. Dynamic analysis of panel piercing can be carried out using LS-DYNA. For this purpose, it is necessary to develop a mesh of brick finite elements. A convenient mesh generation way is initial voxel geometrical modeling and next following transformation of voxel mesh into FE one. For adequate description of a ceramic ball, voxel mesh step has to be rather small to place 10–20 voxels at the distance equal to ball diameter. So, voxel size is taken as 0.1 mm. Thus, there are about five million voxels in the geometric model of composite plate with the sizes of 40х40х3.3 mm. Respectively, number of finite elements is the same. It is difficult to calculate such model because of limited computer resources. Thus, it is suggested to model panel piercing within a limited 10 mm diameter area. The other area of the panel is modeled as homogeneous having average parameters of a ceramic-polymer plate. A voxel model developing has been described in one of the previous author’s publications. This type of modelling requires determination of state parameter for each voxel. State parameter is equal to material number depending on location of the voxel nodal point within the modelled area. Sphere equation has to be used to model a ceramic ball. For example, to compare an abscissa of voxel nodal point with the coordinate of sphere surface it is satisfactory to use the well-known equation: xe Re2 ( ye Be )2 ( ze Ce ) 2 Ae
(1)
where Re , Ae , Be , Ce – radius of sphere and three coordinates of its center in subarea coordinate system, respectively (e=i, j, k). Then it is necessary to determine voxels of all spherical balls within the panel. To do this that is enough to determine coordinates of the sphere centers in the specified coordinate system. For this purpose, first of all, it is necessary to determine steps between ball centers. This calculation is performed in view of balls regular location in chessboard order (Fig.2, a). It is clear that the distance between ball centers depends on ball radius and the specified gap between their surfaces G on condition that the gap is required: S
(4 / 3)(2 Re G ) 2
(2)
The formula is checked using CAD system (Fig. 2, b). Searching for the best panel characteristics it is easy to generate different FE meshes automatically by variation of Re and G parameters and relocation of ball rows for a distance of S/2. Thus, this approach gives the chance to generate parametric model. Based on given formulas and relations published earlier [15] the authors have generated voxel and FE meshes of the described panel (Fig. 2, c). At the next stage of study parametric model and FE mesh for a penetrator have been developed. For research of spacecraft panel piercing it is necessary to develop a model of orbital garbage. Garbage objects have complex structures, as they are spacecraft fragments mostly. Generally, any object may appear as a metallic part. However, it is necessary to accept some certain model for the presented research. A model of the ordinary cone is used. According to data from open publications, orbital garbage may be described as a multilayer cone [16,17]. The total FE calculation model with all boundary conditions, ties, symmetry conditions is given in Fig. 3.
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Fig.2. Location of ceramic balls within the panel: (a) computational scheme, (b) scheme check using 3D model, (c) FE mesh.
Fig.3. Finite element models of all objects of the research.
2.2. Material models To model materials behavior, as known, two models are used: state equation (stress-strain-internal energy relationship) and strength model (material behavior related with stress in excess of yield stress). The presented research has two specific aspects: modeling of high-speed interaction and modeling of considerably different materials: fragile ceramics, elasto-plastic metals and viscous polyethylene. Thus, different models of materials have to be developed. For the problem solution appropriate material models have to be present among the models set of FE program, in particular, in the model set of LS-DYNA. Hence, based on the published data, the following material models have been accepted [18]. Ceramic balls Al2O3 are described using Johnson-Holmquist model. Material characteristics used for this model are as follows [19]: ρ=3700 kg/m3 – density; G=90.16 Gpa – shear modulus; a =0.93 – intact normalized strength parameter; b=0.31 – fractured normalized strength parameter; c=0 – strength parameter (for strain rate dependence); m=0.6 – fractured strength parameter (pressure exponent); n=0.6 – Intact strength parameter (pressure exponent); 0 = 1.0 EPSI – quasi-static threshold strain rate; T=0.2 GPa – maximum tensile pressure strength; Sf max – maximum normalized fractured strength (NA); hel=2.79 GPa – Hugoniot elastic limit; Phel=1.46 GPa – pressure component at the Hugoniot elastic limit; β=1.0 – fraction of elastic energy loss converted to hydrostatic energy; d1=0.005 – parameter for plastic strain to fracture; d2=1.0 – parameter for plastic strain to fracture (exponent); k1=130.95 GPa – first pressure coefficient (equivalent to the bulk modulus); k2 = 0 – second pressure coefficient; k3=0 – third pressure coefficient; Fs – failure criteria: Fs <0 – fail if . (tensile failure); Fs=0 – no failure (default); Fs >0 – fail if the effective plastic strain greater than Fs. The equivalent stress for a ceramic-type material is given by Johnson-Holmquist model equations [19]:
* i* D( i* *f ), i* a ( p* t * ) n (1 c ln(* )), D T / Phel , p* p / Phel p / fp , t *
(3)
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where fp d1 ( p* t * ) d2 – is plastic strain per computational cycle and the plastic strain to fracture and *f b( p * ) m (1 c ln( )) S f max represents the damaged material behavior. In undamaged material, the hydrostatic pressure is given by p k1 k2 2 k3 3 , where / 0 1. For the polymer, the Toughened Adhesive Polymer model (MAT_252, LS-DYNA) has been accepted. The main parameters are [20]: ρ=950 kg/m3 – density; = ܧ1.586GPA – Young’s modulus; ߥ = 0.34 – Poisson’s ratio; ߬0=23.17MPa – initial shear yield stress; q=2.825 MPa – isotropic nonlinear hardening modulus; b=10.37 – isotropic exponential decay parameter; H=17.11 MPa – isotropic linear hardening modulus; C=0.1076 – strain rate coefficient, etc. Orbital garbage metallic components are described using quite well known plastic kinematic model.
Fig.4. Equivalent stress and strains within the penetrator, part of panel and ceramic balls.
3. Results and discussion Overall, parametrical geometrical model and FE models of ceramic-polymer panel and of penetrator have been developed. However, in certain cases, calculations are unstable because it is necessary to combine micro- and macro-model (Fig.4). One more difficulty is caused by the model high size. Because of limited computer resources, only a quarter of panel has been described. Thus, the modeling results are not entirely realistic, i.e. some of finite elements are located out of the coordinate planes. 4. Conclusion The accepted approach of developing FE model on the basis of voxel model guarantees complete model parametrization. So, smart modification of ceramic-polymer composite structure is achieved. Micro-modeling using
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Johnson-Holmquist model for ceramics, Toughened Adhesive Polymer model for polyethylene, and plastic kinematic model for multilayer cone metals allow to obtain rather realistic stress-strain state pictures for ceramicpolymer composite. Acknowledgements The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011. References [1] H.A. King, Lightweit protective armor plate, US patent N 3431818, 1969. [2] M.M. Kononenko, A.I. Malkin, T.A. Shumikhin, Device for protection of spacecraft and space stations against impact action of space medium particles, RU patent N 2299839,2007. [3] P. Colombo, F. Zordan, E. Medvedovski, Ceramic-Polymer Composites for Ballistic Protection, Advances in Applied Ceramics. 105(2) (2006) 78–83. DOI: 10.1179/174367606X84440. [4] E. Medvedovski, Ballistic performance of armour ceramics: Influence of design and structure, Part 2, Ceramics International. 36 (2010) 2117–2127. DOI:10.1016/j.ceramint.2010.05.021. [5] V.A. Grigoryan, I.F. Kobyilkin, V.M. Marinin, E.N. Chitsyakov, Materials and protective structures for local and individual reservations, Radiosoft, Moscow, 2008, 406. [6] J. Jovicic, A. Zavaliangos, F. Ko, Numerical modeling of impact behavior of integrated gradient design composite materials, Research Gate. (2015) 1–35. DOI: 10.13140/RG.2.1.2931.9120. [7] J. Jovicic, A. Zavaliangos, F. Ko, Modeling of the ballistic behavior of gradient design composite armors, Composites, Part A. 31 (2000) 773– 784. DOI: http://dx.doi.org/10.1016/S1359-835X(00)00028-2. [8] D. Kreculj, B. Rašuo, Review of impact damages modelling in laminated composite aircraft structures, Technical Gazette. 20(3) (2013) 485495. SSN:1330-3651. [9] D.P. Gonçalvesa, F.C.L. de Meloa, A.N. Kleinb, H.A. Al-Qureshib, Analysis and investigation of ballistic impact on ceramic/metal composite armour, Int. J. of Machine Tools and Manufacture. 44 (2004) 307–316. DOI:10.1016/j.ijmachtools.2003.09.005. [10] P. Chabera, A. Boczkowska, A. Morka, T. Niezgoda, A. Oziębło, A. Witek, Numerical and experimental study of armour system consisted of ceramic and ceramic-elastomer composites, Bulletin of the polish academy of sciences technical sciences. 62(4) (2014) 853–859. DOI: 10.2478/bpasts-2014-0094. [11] S.A. Smitheman, I.A. Jones, A.C. Long, W. Ruijter, A voxel-based homogenization technique for the unit cell thermomechanical analysis of woven composites, The 17st International Conference on Composites (ICCM-17), 2009. [12] G. Erns, M. Vogler, C. Hühne, R. Rolfes, Multiscale Progressive Failure Analysis of Textile Composites, Composites Science and Technology. 70 (2010) 61–72. DOI:10.1016/j.compscitech.2009.09.006. [13] J.D. Hiller, H. Lipson, STL 2.0: a proposal for a universal multi-material additive manufacturing file format, Proceeding of the 20th annual Int. Solid freeform fabrication symposium, Austin, 2009, pp. 266–278. [14] C.I. Shchurova, A methodology to design a 3D graphic editor for micro-modeling of fiber-reinforced composite parts, Advances in Engineering Software. 90 (2015) 76–82. DOI: http://dx.doi.org/10.1016/j.advengsoft.2015.07.001. [15] E.I. Shchurova, Modeling of the Ceramics Structure for the Finite Element Analysis, Procedia Engineering. 150 (2016) 179–184. DOI: http://dx.doi.org/10.1016/j.proeng.2016.06.744. [16] V.N. Dvoryaninov, Combat ferry riflemen. Modern domestic cartridges, chronicles of designers: Monograph in 4 books, Book 4, D'Solo, Klimovsk, 2015, 564 p. [17] M. Andrenucci, P. Pergola, A. Ruggiero, Active removal of space debris. Expanding foam application for active debris removal: Final report, European Space Agency, 2011, 132 p. [18] LS-DYNA_Manual_Volume_II_R8.0_MATERIALS.pdf [19] D.S. Cronin, K. Bui, C. Kaufmann, G. McIntosch, T. Berstad, Implementation and Validation of the Johnson-Holmquist Ceramic Material Model in LS-Dyna, 4-th European LS-DYNA Users conf. Material I. D-I-47–59. [20] A. Matzenmiller, F. Burbulla, Robustness and reliability of methods to simulate adhesive joints with high strength steel sheets at crash conditions: Tech. reporst, Institute of Mechanics Department of Mechanical Engineering University of Kassel, Germany, pp. 245–411.