MODELING STRUCTURAL BEHAVIOUR OF PVC FOAM PANELS REINFORCED BY CFRP PINS

Transcription

1 THE 19 TH INTERNATIONAL CONERENCE ON COMPOSITE MATERIALS MODELING STRUCTURAL BEHAVIOUR O PVC OAM PANELS REINORCED BY CRP PINS J. Zhou 1, Z. W. Guan 1,* and W. J. Cantwell 2 1 Shool o Engineering, University o Liverpool, Liverpool, UK, 2 Department o Aerospae Engineering, Khalia University o Siene, Tehnology and Researh, Abu Dhabi, UAE * Corresponding author (zguan@liv.a.uk) Keywords: PVC oam, impat, inite element, CRP pin, damage 1 General Introdution As a result o their superior speii strength and stiness harateristis, exellent atigue properties and impressive orrosion resistane, omposite materials, suh as arbon ibre reinored asti (CRP) are urrently inding widespread use in a wide range o high-perormane engineering strutures. An additional attrative eature o these lightweight materials is their ability to absorb signiiant energy under ertain well-deined loading onditions. Extensive testing has shown that omposites, when produed in a tubular orm and loaded in ompression, are apable o absorbing signiiant energy through a range o ailure mehanisms inluding ibre rature, matrix raking, debonding and delamination [1]. Over the years, this impressive energy-absorbing apability has attrated the interest o many vehile manuaturers, inluding Chrysler and ord. Indeed, Jaob et al [2] alulated that only 600 grams o omposite is required to absorb the energy o a medium-sized ar travelling at 5 mph. igure 1 highlights the extraordinary ailure harateristis assoiated with omposite materials, where a 10 mm diameter CRP tube is being rushed at a low rate o strain. These ailure modes are typial o those observed in larger diameter tubes, with extensive saying, ibre rature and matrix raking being in evidene. igure 2 shows the progress ailure o arbon and glass ibre rods subjeted to ompression. The ailure o both rods is initiated on the top end. The arbon ibre rod under ompression demonstrates more dutile ailure than the glass ibre one. Clearly, the ailure pattern o the rod inluenes its energy absorbing apaity. I bukling ailure an be avoided the energy absorption will be maximized. Thereore, it is neessary to introdue onstraints to omposite tubes or rods. An eetive way to apy suh onstraints is to embed them into PVC oam, so that a progressive rushing o omposite tube or rod an be realised. igure exhibits ailed PVC oam ore with embedded arbon ibre and glass ibre pins. Both arbon and glass ibre rods turn into dust, whih indiate tests with suessul onstraints oered by PVC oam. ig.1. Images o a 10 mm tube during and ollowing rushing. ig. 2. Progressive ailure o arbon and glass ibre reinored rods under ompression. The energy-absorbing apaity o a omposite tube or rod is most requently evaluated by determining its speii energy absorption (SEA) apability in J/kg. SEA values an vary greatly, or exame, rom 20 kj/kg or a pultruded glass ibre/epoxy [2] to values well in exess o 100 kj/kg or arbon

2 Modeling strutural behavior o PVC oam panels reinored by CRP pins ig.. ailure modes o sandwih ores with embedded C (let) and G (right) rods. ibre-based systems []. The preise value depends on a number o parameters, inluding the geometry o the tube, its ibre arhiteture, as well as the mehanial properties o the matrix phase. or exame, Hamada and o-workers [] showed that the energy-absorbing apaity o a 55 mm diameter CRP tube dereased by iteen perent in passing rom a unidiretional 0 o tube to one with its ibres oriented at +/-25 o. A number o researhers have studied the inluene o speimen geometry on the energy-absorbing apability o omposite tubes. Thornton and Edwards [4,5] investigated geometrial eets in the energy-absorbing response o tubes based on irular, square and retangular ross-setions and showed that the ormer outperormed both their square and retangular tubular ounterparts. arley [6] onduted tests on arbon and Kevlar ibre reinored tubes, with y orientations typial o those used in sub-loor beam strutures and showed that the tube diameter to thikness ratio ayed a signiiant role in determining its subsequent strain energy-absorbing apaity. Similar trends have been observed by Ruzanna and Cantwell [7] ollowing tests on irular omposite tubes, igure 4a, with values inreasing by over ity perent as the D/t ratio is redued rom approximately 42 to 6. This evidene suggests that the use o very low values o D/t an lead to greatly enhaned energy absorption in tubular strutures. ollowing these initial tests on small diameter reinorements, individual tubes were embedded in a polymer oam (as shown in igure 4b) and rushed at quasi-stati rates o strain [7]. Composite sandwih strutures are inreasingly inding use in a wide range o lightweight loadbearing engineering strutures. Sandwih strutures, suh as those used in high-perormane aerospae omponents, are typially based on thin omposite (a) (b) ig. 4. (a) The variation o the speii energy absorption o irular CRP tubes with diameter/thikness ratio [7] (b) Photograph o a partially-inserted tube in a polymer oam (note that the tube has not been ully inserted). skins bonded to a low density oam or honeyomb ore. The skins are usually thin, oten rendering these lightweight panels highly suseptible to damage by a hard projetile, suh as that assoiated with runway debris or hail. A number o investigations have oused on the potential hazard resulting rom an unontained turbine engine ailure on outer parts o an airrat [8-10]. In suh sandwih strutures, the skin sheets arry bending loads, whilst the ore resists transverse shear and through-thikness indentation ores. Thereore, to enhane the load arrying apaity it is desirable to maximize the through-thikness stiness and strength o the ore. One approah to ahieve this goal is to add reinoring pins to the ore, with the ends o the pins embedded in woven arbon ibre skin sheets. Cartie and lek [11] undertook the theoretial analysis and revealed that the through-thikness stiness and strength are relatively insensitive to the pin arrangements in pyramidal, tetrahedral and random patterns. This paper presents numerial modeling o ompressive strutural behavior o PVC oam ore panels reinored by CRP pins. Here, the oam was modeled as a rushable oam material with strain hardening, whilst CRP as an orthotropi linear elasti material up to ailure ollowed by damage initiation and evolution using Hashin riteria. Energy absorption o the sandwih panels made with the ores o dierent densities was also investigated. Modeling results were ompared with the experimental results, in terms o load-disaement relationships, deormation and ailure modes. Reasonably good orrelation was obtained.

3 Modeling strutural behavior o PVC oam panels reinored by CRP pins 2 inite element modeling 2.1 PVC oam The ore in the sandwih strutures was modeled as a rushable oam using hardening urves obtained ollowing ompression tests on square sames. It was assumed that the Poisson s ratio o all o the oams was 0.2. Deshpande and lek [12] proposed a phenomenologial yield surae or a losed-ell oam material, given by: q 0 2 m y 1 (1) where y is the uniaxial yield strength (in tension or ompression) o the oam, q is the Von Mises stress, and m is the mean stress. The term desribes the shape o the yield surae, whih is related to the ratios o the initial uniaxial yield stress,, and the hydrostati tensile yield stress, o o p t, to the hydrostati ompressive yield stress, p, respetively. The yield stress in hydrostati ompression, p desribes the development o the size o the yield surae and is given as: vol vol 1 1 pt ( ) ( ) 2 9 vol p ( ) vol ( ) p t (2) where is deined as the asti volumetri strain vol in the volumetri hardening model, and is set equal axial to the ompressive asti strain. The term, p an thereore be deterimed rom a ompression test on the oam. Mehanial properties o the oams investigated are shown in Table 1. Here, it is assumed that the response o a rate-dependent solid obeys the uniaxial low rate deinition, whih is given as: hq (,, ) () in whih the term h is a strain-hardening untion, is deined as the equivalent asti strain, and the parameter is the temperature. The rate-dependent hardening urves an thereore be expressed as:, ) ( ) R( ) (4) ( y in whih and R are deined as the equivalent asti strain-rate and the stress ratio (= / ) y respetively. Table 1. Mehanial properties o the oams investigated. C40 C10 C200 Density ( kg / m ) Poisson's ratio Compressive modulus Compressive strength Compressive rature strain Tensile modulus Tensile strength Shear modulus Shear strength Shear rature strain Damage development in the oams was modelled by adopting a dutile damage riterion along with a shear damage riterion [1,14]. In the urrent loading ondition (ompression dominant), the ormer riterion is the predominant one. There may be some shear damage introdued by possible bukling ailure o C pins when they are not ully restrained by the oam. The apied strains assoiated with the initiation o dutile and shear damage, as well as the strain-rate, need to be established. Here, a linear sotening law was adopted, involving a linear relationship between the sotening stress and the disaement ater the onset o the damage or elasto-asti materials. Damage development was ontrolled by the rature energies in tension and in shear. igures 5 and 6 show loaddisaement traes obtained ollowing Mode I (opening) and Mode II (shear tests) tests on the oams. The ormer was obtained using the single edge noth bending geometry as shown in igure 1a and the latter using a reently-developed shear geometry as shown in igure 6a. An examination o

4 Modeling strutural behavior o PVC oam panels reinored by CRP pins ig. 5 indiates that the rosslinked and PET oams ail in an unstable manner, whereas the linear PVC oam ails in a more dutile ashion involving gross asti deormation in the ell walls. ailure in shear generally ourred in a stable ashion although some load drops were apparent in the rosslinked oams. The toughness properties o the oams were haraterised by determining the work o rature rom the energy under the load-disaement traes and the area o the ratured ligament. The resulting values are presented in Table 2. Here, it is evident that the Mode I rature properties o the linear PVC oams are signiiantly higher than those assoiated with its rosslinked ounterpart. It is also evident that the Mode II work o rature properties o the oams are muh higher than the Mode I values, with the dierene being most pronouned in the rosslinked systems. (a). Crosslinked oams, (b). Linear and PET oams, ig. 5. ore-disaement urves rom the single edge noth bending tests or dierent oam ores. in tension (kj/m 2 ) rature in shear (kj/m 2 ) C C C C C L L PET PET CRP pin Prior to damage initiation, the CRP pins were modeled as an orthotropi elasti material. The elasti modulus values o the ain weave skins were assumed to be equal in the longitudinal and transverse diretions. Damage initiation was modelled using Hashin s ailure riteria [15] whih assumes our damage initiation mehanisms, namely ibre tension, ibre ompression, matrix tension and matrix ompression. Using the longitudinal, transverse and shear eetive stress tensor omponents within the ane o the CRP, the damage initiation riteria an be determined [16] and are expressed as: ibre tension:, 11 0 t XT XL ibre ompression: 2 (5) (a). Crosslinked oams, (b). Linear and PET oams, ig. 6. ore-disaement urves rom the shear tests or dierent oam ores. Table 2. Work o rature values. oam Work o rature Work o X 11 C 2 Matrix tension:, t m YT SL, 11 0 Matrix ompression: m 1 2YT 2ST YC SL Y C (6) (7) (8)

5 Modeling strutural behavior o PVC oam panels reinored by CRP pins where X, X are the tensile and ompressive T C strengths in the longitudinal diretion, Y, T Y are the C tensile and ompressive strengths in the transverse diretion, S, L S are the longitudinal and transverse T shear strengths, and β is a oeiient that speiies the ontribution o the shear stress to the ibre tensile initiation riterion. Here β is set to zero, i.e. it is assumed that there is no shear stress ontribution involved in the initiation o ibre tensile ailure. Table shows the related material parameters that were used. Table. Damage initiation data or the CRP. 2. Mesh generation and boundary/loading onditions ig. 7 shows the mesh generation o a PVC oam panel with embedded CRP pins. Here, the PVC ore and the CRP pins are meshed by 8-noded solid elements with redued integration. The ore size is (in mm) and the diameters o the pins modelled are and 4 mm. The loading atens on both the top and bottom o the panel are meshed using rigid surae elements. The ompressive load is apied to the top aten, with an only degree o reedom in the vertial diretion. The bottom aten is ully ixed. X T X C Y T Y C S L S T The damage elasti matrix, whih relates the stress and strain and ontrols degradation o the material stiness, an be expressed as: (1 d ) / E1 (1 d )(1 dm) v21 / E1 0 1 CD (1 d )(1 dm ) v12 / E2 (1 dm ) / E2 0 D 0 0 (1 ds ) G D (9) In the above equation, G is the shear modulus and D is an overall damage variable, whih is given by: D 1 (1 d )(1 d ) v v (10) m ig. 7. Mesh generation. There are various interaes in the model to be dealt, whih inlude interations between the oam ore and atens, between the CRP pins and atens, between the CRP pins and the oam. It is allowed the atens to ontat the PVC ore ell, i.e. the interior surae o the oam an touh the atens one its external surae ails. where, d, d m, and d s represent the urrent state o ibre, matrix and shear damage, respetively. Damage development is haraterised by the negative slope o the equivalent stress-disaement relation ollowing damage initiation. The rature energies assoiated with tensile ibre ailure ibre ompression ailure G G, t, tensile matrix ailure G and matrix ompressive ailure G are required mt m in order to determine the energy dissipated during the development o damage within the omposite. Results and disussion Here, PVC oam panels with densities o 50 and 200 kg/m are embedded CRP pins in two diameters, i.e. and 4 mm. igure 8 shows load-disaement traes obtained rom numerial modeling and the orresponding experimental results o the ormer 5

6 Modeling strutural behavior o PVC oam panels reinored by CRP pins ig. 8. Comparisons o experimental and numerial load-disaement traes or a C40 oam panel with embedded C pins in diameter o and 4 mm. panel. The test results o a PVC oam panel without any C pin are also shown in the igure to assist better omparison. Clearly, reasonably good orrelation has been obtained between the measurements and the E preditions in terms o the initial stiness, the peak load and damage evolution, espeially or the oam panel embedded with C pins in diameter o mm. 78% inrease on C pin volume indues 150% enhanement on the peak load. The omparison o the load-disaement traes or the oam panel with a density o 200 kg/m and embedded C pins in diameters o and 4 mm are exhibited in igure 9. Again, agreements between the experimental results and the inite element simulations are very good, with well aptured eatures in the initial stiness, the peak load, the damage evolution and the densiiation. The enhanement on the peak load is not as muh as that o the PVC oam panel with a muh lower density as shown in ig. 8. It is antiipated that with urther inreasing on PVC oam ore density the enhanement o the peak load will also be urther redued. ig. 9. Comparison o experimental and numerial load-disaement traes or a C200 oam panel with embedded C pins in diameter o and 4 mm. igure 10 shows the omparison o energy absorptions obtained rom experimental tests and E preditions or C40 and C200 PVC oam panels with embedded C pins in diameters o and 4 mm. In general, orrelation is quite good. The E preditions or the oam panels with a lower density are slightly higher than those o experimental measurements, whilst suh the preditions or the higher density panels are slightly lower. The possible reason is that due to the weak onstraint oered by the oam with the lower density bukling ailure o the pin likely ours, whih was not aptured by the E modelling. In the higher density ase, the strong onstraint rom the oam ores the C pins ailure rushing along their longitudinal axis. However, in the modeling suh rushing auses element penetration with eah other, whih underestimates resistane o the pin to the ompressive load.

7 Modeling strutural behavior o PVC oam panels reinored by CRP pins ig. 10. Comparison o energy absorption o PVC oam panels with embedded CRP pins. More omprehensive omparisons o energy absorptions related to PVC oam panels with dierent densities, with and without C pin embedment are also arried out based on both experimental and numerial work. Here, the diameters o the pin over 2, and 4 mm. igure 11 disays suh the omparison. The energy absorption is enhaned signiiantly with inreasing o diameter o the C pin and density o the oam, as expeted. However, the rate o enhanement on energy absorption in perentage is deelerated with inreasing o oam density. Thereore, there should be an eetive oam density range within the energy absorption enhanement an be maximized. igure 12 shows the deormation and ailure modes o a oam ore panel with embedded CRP pins obtained rom test and E modelling. The ore struture was deormed by 75% rom its original oniguration. The basi eatures o the oam rushing ailure and the pin ailure were aptured. The ailed pin is disayed in igure 1, whih indiates a omete ollapse o all pins embedded in the PVC oam. ig. 11. Energy absorptions obtained rom experimental tests and numerial models. (a) Test, (b) E modelling ig. 12. Deormation and ailure modes o a PVC oam ore panel with embedded CRP pins. Conlusions ig. 1. Collapsed CRP pins. inite element models have been developed to simulate load-disaement traes o PVC oam panels with embedded arbon ibre pins, whih are 7

8 Modeling strutural behavior o PVC oam panels reinored by CRP pins ompared with the orresponding test results. Reasonably good orrelation has been obtained between the experimental results and E preditions, in terms o the initial stiness, the peak load and the damage evolution. Here, three densities o the oam and two sizes o the CRP pin are investigated. In addition, energy absorption eatures o the sandwih ore strutures are aptured. The results show that the embedment o CRP pins inside PVC oam ore is a very eetive way to enhane energy absorption o this novel sandwih struture. However, there is an optimum range o the PVC oam density, within whih the energy absorption an be maximized in perentage sense. Reerenes [1]. G.L. arley and R.M. Jones, J. Comp. Mats, 26, 1992, pp7-50. [2]. G.C. Jaob, J.. ellers, S. Simunovi and J.M. Starbuk, J. Comp. Mats, 6, 2002, pp []. H. Hamada et al, 8th Int. SAMPE Symposium, 8, pp [4]. P.H. Thorton and P.J. Edwards, J. Composite Materials, 16, 1982, pp [5]. P.H. Thornton, J. Composite Materials, 26, 1979, pp [6]. G.L. arley, J. Composite Materials, 1986, 20, pp [7]. A. Ruzanna and W.J. Cantwell, unpublished work. [8]. D.D. Le. Evaluation o lightweight material onepts or airrat turbine engine rotor ailure protetion, ederal Aviation Administration Report No. DOT/AA/AR- 96/110, July [9]. A.A. Shokey, J.H. Giovanola, J.W. Simons, D.C. Erlih, R.W. Klopp and S.R. Skaggs. Advaned armor tehnology: apiation potential or engine ragment barriers or ommerial airrat, ederal Aviation Administration Report No. DOT/AA/AR- 97/5, September [10]. M. Rouse, D.M. Ambur, J. Bodine and B. Dopker. Evaluation o a omposite sandwih uselage side panel with damage and subjeted to internal pressure. NASA Tehnial Memorandum [11]. D. Cartie and N. lek. The eet o pin reinorement upon the through-thkness ompressive strength o oam-ored sandwih panels, Composites Siene and Tehnology, 200, Vol. 16, pp [12]. V.S. Deshpande. and N.A. lek. Multi-axial yield behavior o polymer oams, Ata mater. 2001, Vol. 49, pp [1]. ABAQUS, Theory Manual. Version Pawtuket: Hibbitt, Karlsson & Sorensen, In., [14]. J. Zhou, M.Z. Hassan, Z.W. Guan and W.J. Cantwell. The low veloity impat response o oam-based sandwih panels; Composites Siene and Tehnology, 2012, 72, pp [15]. Z. Hashin and A. Rotem. A atigue ailure riterion or iber reinored materials. Journal o Composite Materials, 197, vol. 7, pp [16]. J. an, Z.W. Guan and W.J. Cantwell. Numerial modelling o peroration ailure in ibre metal laminates subjeted to low veloity impat loading. Composite Strutures, 2011, Vol. 9, pp