The mechanical response of CFRP-Al/HC (carbon fibre-reinforced/epoxy composite face sheets with Al honeycomb core) sandwich panels to hyper-velocity impact (up to 1 km/s) is studied using a finite-element model developed in ABAQUS/Explicit. The intraply damage of CFRP face sheets is analysed by mean of a user-defined material model (VUMAT) employing a combination of Hashin and Puck criteria, delamination modelled using cohesive-zone elements. The damaged Al/HC core is assessed on the basis of a Johnson Cook dynamic failure model while its hydrodynamic response is captured using the Mie-Gruneisen equation of state. The results obtained with the developed finite-element model showed a reasonable correlation to experimental damage patterns. The surface peeling of both face sheets was evident, with a significant delamination around the impact location accompanied by crushing HC core

Vadim Silberschmidt (1248129)

Vaibhav A. Phadnis (7201589)

EPJ Web of Conferences

English

Vaibhav A. Phadnis

Vadim V. Silberschmidt

EDP Sciences OAI-PMH repository (1.2.0)

Finite element analysis of hypervelocity impact behaviour of CFRP-Al/HC sandwich panel

Loughborough University Institutional Repository

EPJ Web of Conferences 94, 04051 (2015)DOI: 10.1051/epjconf/20159404051c© Owned by the authors, published by EDP Sciences, 2015Finite element analysis of hypervelocity impact behaviour of CFRP-Al/HCsandwich panelVaibhav A. Phadnis1 and Vadim V. Silberschmidt2,a1 AMRC with Boeing, The University of Sheffield, UK2 Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, UKAbstract. The mechanical response of CFRP-Al/HC (carbon fibre-reinforced/epoxy composite face sheets with Al honeycombcore) sandwich panels to hyper-velocity impact (up to 1 km/s) is studied using a finite-element model developed inABAQUS/Explicit. The intraply damage of CFRP face sheets is analysed by mean of a user-defined material model (VUMAT)employing a combination of Hashin and Puck criteria, delamination modelled using cohesive-zone elements. The damagedAl/HC core is assessed on the basis of a Johnson Cook dynamic failure model while its hydrodynamic response is capturedusing the Mie-Gruneisen equation of state. The results obtained with the developed finite-element model showed a reasonablecorrelation to experimental damage patterns. The surface peeling of both face sheets was evident, with a significant delaminationaround the impact location accompanied by crushing HC core.1. IntroductionAdvanced composite materials such as CFRP/Al-HC(carbon fibre-reinforced plastic face-sheets/aluminiumhoneycomb core) sandwich panels typically find theirapplication in satellite structures due to their excellentmechanical properties such as high specific strength,stiffness and ability to provide tailored properties. Inthe absence of proper shielding, these structures can beoften exposed to impacts by space debris. Many satellitesalready employ honeycomb sandwich panels with CFRPface-sheets covered by multi-layer thermal insulation asexternal walls [1]. Furthermore, FRPs are often usedin the construction of spacecraft components such asantenna struts, low distortion frames and lightweightrobotic arms [2–5].Still, many concerns remain about the possibility ofemploying polymer-matrix composites as the primarysatellite structure for long-duration missions because ofsevere environmental conditions encountered in space.One of the major problems is related to the vulnerabilityto impact damage from meteoroids and man-made spacedebris that populate the near-Earth orbital environment.Such particles travel at speeds of several km/s, thuspresenting a serious hazard for existing satellites. Previousresearchers found that damage due to high velocity impacts(HVIs) on composite materials consists of an impactcrater, surface peeling of the outer laminae on both thefront and rear side of the plate and a significant internaldelamination around the impact point, that can lead tosevere degradation of the material’s mechanical strength.Moreover, if a hypervelocity particle has enough energyto fully perforate the impacted plate, a debris cloudemerging from the rear face of the target can significantlya Corresponding author: v.silberschmidt@lboro.ac.ukdamage adjacent structures and internal components of thespacecraft.This study focuses on the development of a finiteelement (FE) model to simulate a HVI behaviour (withvelocities up to 1 km/s) of a CFRP-Al/HC sandwich panelusing general-purpose FE software Abaqus/Explicit [6]. Auser-defined material model (VUMAT) developed to studydamage of CFRP face sheets employing combined Hashinand Puck criteria was used, while the interply damagewas modelled by means of cohesive-zone elements. Ahydrodynamic response of Al/HC was captured usinga Mie-Gruneisen equation of state and its damage wasmodelled using a Johnson Cook dynamic failure model.The developed FE model was validated with experimentaldata from Wicklein et al. [7] and showed a reasonablecorrelation between damage patterns experimentally andnumerically.2. Finite-element modelA quarter of the full geometry of the sandwich plate wasmodelled owing to its symmetry about relevant planes;this resulted in significantly reduced computational efforts.A steel projectile of 3 mm diameter was impacted onthe sandwich structure with an impact velocity rangingfrom 700 m/s to 1 km/s. The general contact algorithmin ABAQUS/explicit[6] was used to simulate contactconditions between the projectile and the composite face-sheets and Al/HC, and between the layers of CFRPlaminate by defining appropriate contact-pair properties.The setup of FE model is shown in Fig. 1.The elastic response of CFRP laminate was accountedfor; it is discussed in Sect. 2.1. An element-deletionapproach was used to model a material-erosion processbased on initiation and evolution of damage in the meshedelements. Criteria for damage initiation and evolution arediscussed in Sect. 2.2.This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,and reproduction in any medium, provided the original work is properly cited.EPJ Web of ConferencesFigure 1. Setup of FE model.2.1. Response of UD composite laminateAn elastic stress-strain relationship for a UD compositeply was introduced assuming the orthotropic damagedelasticity response. Its constitutive behaviour beforedamage is expressed using a generalised Hooke’s law inthe tensorial form:{σ } = C {}. (1)The effect of strain-rate on elastic moduli and strength wasdefined in order to accurately account for a high strain-rateresponse of the laminated composite material. It shouldbe noted that for carbon/epoxy-like systems, where carbonfibres are brittle and show no strain-rate dependence, thestrain-hardening at higher loading rates is entirely due toepoxy matrix; while in glass/epoxy like systems both glassfibres and epoxy matrix may contribute towards this.The strain-rate effects in the elastic and shear moduliare defined by the following expressions:E(˙) = E(˙0) +[me · log(˙˙0)+ 1](2)G(γ˙ ) = G(γ˙0) +[ms · log(γ˙γ˙0)+ 1],where E(˙) and G(γ˙ ) are elastic and shear moduli for agiven strain rate, E(˙0) and G(γ˙0) are elastic and shearmoduli at the reference strain rate ˙0 and γ˙0, respectively,in three directions and three planes of a 3D co-ordinatesystem. me and ms are the material parameters obtainedby fitting a curve to the experimentally obtained data. Theeffects of strain rate on ply strength are discussed in thefollowing sections where initiation of different damagemodes is considered.2.1.1. Damage initiationModelling of composites and their damage at a laminatelevel typically requires input of several parameters,including homogenised ply properties, interply strengthand information about the laminate lay-up. Here, a layer-by-layer modelling strategy was adopted to capture failurein each ply. This offers several advantages. Firstly, full3D stress states can be analysed. Typically, FE modelsof composite deformation involve the use of 2D shellelements to simulate composite plies, which do not allowfor accurate representation of stress through the compositethickness.Secondly, intraply and interply damage can be intro-duced discretely along with phenomenological models thataccount for complex interaction between them. Here, amaterial model offering a combination of Hashin’s [7]and Puck’s failure criteria [8] was used to implement theadvantages of both. The Hashin’s criteria were employedto estimate damage in carbon fibres while damage inepoxy matrix was modelled using the Puck’s criteria. Theempirical forms of these criteria are discussed below.(a) Fibre damage– in tension.Here, tensile failure of fibres is defined as a function oftensile strength of lamina along the fibre direction as well04051-p.2DYMAT 2015as shear strength in transverse directions (in and out-ofplane). The empirical relation is expressed in the followingform:(σ11X1t)2+(σ12S12)2+(σ13S13)2≥ 1, d f t = 1 (3)where X1t is the tensile strength of a composite in fibredirection, while S12 and S13 are its shear strengths in1–2 and 1–3 planes, respectively. d f t is a scalar damagevariable indicating fibre damage in tension such that0 ≤ d f t ≤ 1, 0 represents no damage, while 1 indicatesfully-damaged state; this nomenclature applies to alldamage modes discussed below. Here, X1t is assumedequal to its quasi-static magnitude since fibres shownegligible or no strain-rate dependence at high loadingrates.– in compression.Longitudinal compressive failure of composites is drivenby shear mechanisms in an intricate way. A first crack maybe started by shear fracture of fibres followed by rotationand in-plane shearing of the matrix at the crack tip, whichin turn promotes kink-band development. The empiricalrelation for this damage mode is expressed in the followingform(σ11K (˙)Xqs1c)+(σ12K (γ˙ )Xqs12)+(σ13K (γ˙ )Xqs13)≥ 1, d f c = 1.(4)The scaling parameter K is defined as:K =Sdyn12 (γ˙12)Sqs12=Sdyn13 (γ˙13)Sqs13· (5)Here, Sdyn12 (γ˙ ) and Sdyn13 (γ˙ ) are in-plane and out-of-planeshear strengths of a ply in dynamic loading condition at agiven strain rate and Sqs12 and Sqs23 are its shear strengths inquasi-static loading condition.(b) Matrix damage.The phenomenological matrix-failure criteria for 3DQS failure analysis of UD composites were previouslyformulated by Puck and Schu¨rmann [8]. These criteriaforms a basis of the criterion presented here. Theapplicability of the originally proposed tensile andcompressive failure criteria for quasi-static loadingconditions was extended to the model material’s responseunder dynamic loading.The polymer matrix material in a CFRP compositedemonstrates strain-rate sensitivity at high strain rates(∼ 103/s) which are typical for high-velocity impactevents. This effect becomes significant, particularly intransverse directions, where the polymer matrix is aprimary load bearing. An approach, similar to thatemployed in modeling compressive failure of fibres wasadopted here to account for strain-rate sensitivity. Thefollowing criteria were proposed to model failure in theFigure 2. Concept of equivalent stress vs. equivalent displace-ment in evolution of damage variable.matrix material in compression and tension:(σ22K (˙)Xqs2t)2+(σ12K (γ˙ )Sqs12)2+(σ23K (γ˙ )Sqs23)2≥ 1;σ22 + σ33 > 0, dmt = 1 . . . (tensile failure), (6)σ22 + σ33 < 0, dmc = 1 . . . (compressive failure).2.1.2. Damage evolutionTo alleviate mesh dependency during strain softening,a characteristic length (Lc) of a finite element wasintroduced into the formulation so that the constitutive lawwas expressed as a stress-displacement relation as shownin Fig. 2. The positive slope of the stress-displacementcurve prior to damage initiation corresponds to a linear-elastic material behaviour; while the negative slope afterdamage initiation is achieved by evolution of damageparameter d as following:di = f ieq(eq − 0eq)eq(f ieq − 0eq) · (7)where 0eq is the strain at damage initiation, and  feq isthe strain at which the material is completely damaged.i = ft , fc, mt , mc corresponds to damage variables asso-ciated with failure modes of fibre and matrix material intension (t) and compression (c). The strain at failure wasexpressed as, feq =2G fσfeq .Lc, (8)where G f is the fracture energy, and Lc representscharacteristic element length (for a typical hexahedralmesh, it represents the shortest distance betweendiagonally opposite nodes of a smallest element). Theelastic and strength properties for CFRP compositelaminates were taken from [7] and [11]. The mechanicaland shock-related properties for Al-HC core were obtainedfrom the manufacturer’s catalogue, and the Abaqustechnical brief [10], respectively, owing to identicalmaterial system. These are listed in Table 1.04051-p.3EPJ Web of ConferencesTable 1. Material properties for Al 6061-T6 core.For Mie-Gru¨neisen EOS modelReference density (kg/m3) 2700Gru¨neisen coefficient 1.97Wave speed (m/s) 5240Parameter, s 1.40Reference temperature (K) 293.2Specific heat (J/kg K) 885For Johnson Cook plasticity and failure modelA 324.1B 113.8n 0.42θmelt (K ) 925θtransi tion (K ) 293.2m 1.34c 0.002˙0 (1/s) 12.1.3. Element deletionAn element-deletion approach [11] used to remove thefailed elements from the mesh was based on the magnitudeof damage variables, di = ft , fc, mt , mc as calculatedusing Eq. (7) applied to discrete damage modes in thecomposite laminate. The element was removed when themagnitude of any of the damage variables associated withthe fibre failure reached dmax (= 1), at an integration pointof the element. When this condition was satisfied, theelement was removed from the mesh, and it offered nosubsequent resistance to deformation.2.2. Response of Al honeycombA hydrodynamic response of Al honeycomb wasaccounted for using the Mie-Gruneisen equation of state,while its deviatoric response was modelled using the linearelastic and Johnson-Cook plasticity model available inABAQUS/Explicit. An identical element deletion strategywas used to remove excessively deformed elements fromthe simulation as discussed in Sect. 2.1.3.3. Results and discussionDelamination patterns at the entry and exit sides of CFRPface sheets were studied using the developed FE model.The extent of delamination between adjacent plies after theprojectile perforated the CFRP/Al-HC structure is shownin Figs. 3 and 4. It should be noted that though the FEmodel was quarter-symmetric, full delamination planeswere obtained during the post-processing offering betterobservation of these results. The ply-level damage was alsostudied: here fibre damage/spallation was the dominantmode of damage. The fibre damage on the front and backfaces of entry and exit side face sheets is shown in Figs. 5aand b. Shear-driven crushing of Al core directly below thepoint of impact was also evident from simulations. ThisFigure 3. Entry-side delamination of CFRP face sheet between0◦ and 45◦(a), −45◦ and 45◦(b), 45◦ and 0◦(c), 45◦ and −45◦(d) plies. vi = 1 km/s, projectile radius 3 mm.Figure 4. Exit-side delamination of CFRP face sheet between0◦ and 45◦(a), −45◦ and 45◦(b), 45◦ and 0◦(c), 45◦ and −45◦(d)plies. vi = 1 km/s, projectile radius 3 mm.Figure 5. Fibre damage on surface of CFRP sheets at entry(a)and exit(b) sides. vi = 1 km/s, projectile radius 3 mm.04051-p.4DYMAT 2015Figure 6. Damage of Al-HC core:comparison of experiment andFE analysis. vi = 1 km/s, projectile radius 3 mm.Figure 7. Cut view of final state of studied composite laminateshowing surface peel up of CFRP face sheets. vi = 1 km/s,projectile radius 3 mm.was compared with the experimental results of [7] andshown in Fig. 6 (X–Z plane of simulation corresponds to2–3 plane of experimental results). The cut-view showingfinal configuration of CFRP/Al-HC composites structure ispresented in Fig. 7.4. ConclusionsIn this work, the hypervelocity (vi = 1 km/s, projectileradius 3 mm) impact response of the CFRP/Al-HCcomposite structure was studied using a developed 3Dfinite-element model. Damage to CFRP face sheets wasobserved in terms of dynamic spall and surface peeling,while Al-HC core failed due to core cracking driven byshear. The simulation results offer a reasonable agreementwith experimental observations.References[1] Riedel, W., Harwick, W., White, D.M. & Clegg,R.A. (2003) ADAMMO – advanced material damagemodels for numerical simulation codes. ESA CR(P)4397, EMI report I 75/03, Freiburg.[2] Riedel, W., Nahme, H., White, D.M. & Clegg R.A.(2006) Hypervelocity impact damage prediction incomposites: part II – experimental investigations andsimulations. Int. J. Impact Engng 33, 670–80.[3] Hiermaier. S., Riedel, W., Hayhurst, C., Clegg, R.A.& Wentzel, C. (1999) AMMHIS – advanced materialmodels for hypervelocity impact simulations. Finalreport, EMI report E 43/98, ESA CR(P) 4305,Freiburg.[4] White, D.M., Wicklein, M., Clegg, R.A. & Nahme,H. (2008) Multi-layer insulation material modelssuitable for hypervelocity impact simulations. Int. J.Impact Engng 35(12), 1853-1860.[5] White, D.M., Taylor, E.A. & Clegg, R.A. (2003)Numerical simulation and experimental characteriza-tion of direct hypervelocity impact on a spacecrafthybrid carbon fibre/Kevlar composite structure. Int.J. Impact Eng 29(1–6), 779–90.[6] ABAQUS 6.10. Theory manual (2010) DassaultSystem.[7] Wicklein, M., Ryan, S., White, D.M. & Clegg,R.A. (2008) Hypervelocity impact on CFRP: Testing,material modelling, and numerical simulation. Int. J.Impact Engng 35: 1861–1869.[8] Hashin, Z. (1980) Failure criteria for unidirectionalfibre composites. J. Appl. Mech. 47: 321–329.[9] Puck, A. & Schu¨rmann, H. (1998) Failure analysisof FRP laminates by means of physically basedphenomenological models. Comp. Sci. Technol.58(7): 1045–1067.[10] Simulia Abaqus technical brief (2012) Simulation ofthe ballistic performance of aluminium plates withAbaqus/Explicit, USA.[11] Phadnis, V.A., Makhdum, F., Roy, A. & Sil-berschmidt, V.V. (2013) Drilling in carbon/epoxycomposites: Experimental investigations and finiteelement implementation. Comp. Pt A 47: 41–51.04051-p.5

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Finite element analysis of hypervelocity impact behaviour of CFRP-Al/HC sandwich panel

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