IMPACT PERFORATION OF COMPOSITE SANDWICH PANELS

Transcription

1 6 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS IMPACT PERFORATION OF COMPOSITE SANDWICH PANELS Mihelle S. Hoo Fatt, Duhanth Sirivolu Department of Mehanial Engineering, The Univerit of Akron, Akron OH Keword: Compoite andwih; impat perforation, analtial model. Abtrat Analtial model for the quai-tati and lowveloit perforation of ompoite andwih panel with woven roving E-gla/vinl eter faeheet and Coremat TM were developed. A multi-tage perforation proe involving delamination, debonding, ore hear frature and faeheet frature wa ued to alulate the quai-tati failure load and balliti limit of the panel. The high ore ruhing reitane of the Coremat TM aued the dital faeheet to frature before the inident faeheet during panel perforation. Thi i in ontrat to andwih panel with honeomb and onventional polmeri foam, whereb damage firt our on the inident faeheet. Analtial predition of the quai-tati load-defletion repone and the dnami ontat fore hitor were within 0% of the tet reult. Introdution Compoite andwih panel are ued extenivel in the aeropae, marine, tranportation, and rereational indutrie beaue of their high peifi tiffne and trength, orroion reitane, tailorabilit, and high fatigue life. In man of thee appliation, the ompoite panel ma be ubjeted to loalized projetile impat. Therefore, muh work ha been done in an effort to determine the failure load, balliti limit, perforation energ and damage indued into ompoite andwih panel ubjeted to quai-tati indentation and projetile impat [-3]. While mot of thi reearh ha been experimental, few analtial olution have been propoed beaue of the ompliated interation between the ompoite faeheet and ore during deformation and failure. The objetive of thi paper i to preent analtial model that an be ued to deribe quaitati and impat perforation of an E-gla/vinl eter and Coremat TM andwih panel. The analtial model are derived uing experimental reult from Mine et al. [3]. In Ref. [3], quai-tati and lowveloit impat perforation tet with a hemipherial-ended indenter/projetile were done on two tpe of ompoite andwih panel: a woven roving E-gla/vinl eter kin with Coremat TM ore and an E-gla/epox with an aluminum honeomb ore. Coremat TM i a high denit/high energ aborption rein impregnated non-woven poleter with 50% mirophere and i ommonl ued in the marine indutr []. Although the mehanial propertie of the faeheet in both andwih panel were imilar in thee tet, the Coremat had a muh higher ruhing reitane than the aluminum honeomb. A a reult of thi, failure in the Coremat andwih firt ourred on the bak (dital) faeheet while failure in the aluminum honeomb andwih ourred on the front (inident) faeheet. In earlier work, Lin and Hoo Fatt [5] developed an analtial model to deribe the quai-tati and impat perforation the E- gla/epox with the aluminum honeomb ore. Thi paper i an extenion of earlier work to develop analtial model for the impat perforation of ompoite andwih panel. Problem Formulation Conider the ompoite andwih panel, a hown in Fig.. The faeheet are thin orthotropi membrane of dimenion a x a x h, and the ore i a ruhable polmeri foam of dimenion a x a x H. Thi partiular ore i made of a Coremat, whih ha a ore ruhing reitane that i linear trainhardening [3]. Tpial low-denit foam ore have ontant ore ruhing reitane. The indenter/projetile ha a hemipherial-noe of radiu R and a ma M o. The indenter/projetile i aumed rigid ompared to the andwih panel.

2 Hoo Fatt M. S.,Sirivolu D. Upon loading, the panel experiene imultaneou loal indentation and global deformation. Analtial olution for the loal load-defletion a well a the global load-defletion will be derived uing the priniple of minimum potential energ in the following etion. Experiment [-3] indiate the frature mehanim a well a the loaddiplaement harateriti of andwih panel ubjeted to low-veloit impat are imilar to thoe oberved in quai-tati ae. Three tage mut our for total perforation of the andwih panel: (i) initial failure during whih one of the kin of the panel frature; (ii) penetration of the indenter through ore and urviving faeheet; and (iii) omplete panel perforation inluding fritional reitane between the indenter/projetile and andwih panel. Delamination, debonding, ore hear frature, and tenile frature of inident and dital faeheet our during the perforation proe. The order in whih thee failure mehanim our depend on geometr and material propertie. Simple analtial failure riteria have been propoed for ompoite andwih beam truture [6], but thee annot be diretl applied to the ompoite andwih plate. 3 Stati Perforation Approximate olution for the quai-tati loal indentation and global deformation of a ompoite andwih panel will be derived uing the priniple of minimum potential energ. Loal indentation onit of front faeheet indentation and ore ruhing, while global deformation onit of bending and hearing of the entire panel. Loal indentation and global deformation will be onidered independentl, and the total panel deformation i onidered a the um of the loal indentation and global deformation. When either the top or bottom faeheet fail, both loal and global load-defletion harateriti will hange. Complete andwih panel perforation doe not our until both faeheet and ore have failed. 3. Loal indentation Top faeheet indentation i modeled b onidering a rigid indenter preing into an orthotropi membrane reting on a rigid-plati foundation. The total potential energ of the tem i = U + D W () Fig. Geometr of ompoite andwih panel. where U i the elati train energ of the faeheet, D the work diipated in ruhing the ore, and W the external work done. Under moderatel large defletion, the faeheet repond like an orthotropi membrane. The train energ aoiated with bending i negligible ompared to the membrane energ aoiated with in-plane trething. In addition, inplane deformation, u and v, are negligibl mall ompared to tranvere defletion, w. With thee two aumption, the elati train energ beome w w U = A + A 8 S x () w w + ( A + A66 ) ds x where Aij i the membrane tiffne of the orthotropi faeheet and S i the area. The work diipated in ruhing the Coremat i given b k D = a + wwds (3) S H where a and k are the ore ruhing flow trength and train hardening modulu, repetivel. The exat olution for the tranvere defletion of an axi-mmetrial iotropi plate under enter point loading i ued to deribe the loal indentation of the andwih panel, w:

3 IMPACT PERFORATION OF COMPOSITE SANDWICH PANELS w(r) r = δ () ξ where δ the loal indentation under the indenter, ξ i the length of the deformation zone, and r = x +. The total potential energ then beome δ πa kπ = C + δξ + δ ξ Pδ ξ 6 5H (5) π where C = ( 3A + 3A + A + A66 ).. 60 The total potential energ i a funtion of two unknown parameter, ξ and δ. From the priniple of minimum potential energ, an equilibrium ( δ, ξ) ondition our when = 0. Minimizing δ the potential energ ield the following loadindentation repone: 3 C a k P δ π ξ π δξ = + + (6) ξ 6 5H The load-deformation repone i dependent on ξ P and i minimum when = 0. ξ P = Cδ ( 5πa Hδ + πkδ ) 0CH 3 5 ah k π δ + π δ + 30H Therefore, 0C H ( 5πa Hδ + kπδ ) The firt term in the right-hand ide of Eq. (7) repreent membrane reitane of the faeheet, while the eond term in Eq. (7) i due to the Coremat ruhing reitane. 3. Global panel deformation (7) Again auming in-plane deformation are negligible ompared to the tranvere deformation, one find the following expreion for the elati train energ of the mmetri andwih panel with orthotropi faeheet: aa D α β α D β U= + D 00 x + + x α w w w w β A55 A +α + + x x +β + D α α β β + 66 dxd + + x x (8) where w i again ued to expre tranvere defletion, α and β are hear angle aoiated with the x- and -diretion, repetivel, andwih bending tiffne matrix, and Dij A and i the A 55 are the tranvere hear tiffnee. The uperript i ued to denote the andwih. Finite element anali uing ABAQUS Standard wa ued to deribe the tranvere deformation, w, and the hear rotation with repet to the x- and -axi, α and β, a follow: w and ( x, ) x = (9) a a πx ( x, ) αo in α = (0) a a π x ( x, ) o in β = β () a a where i the global defletion under the indenter and αo and βo are rotation at the enter of the panel. The above funtion atif the boundar ondition that w = 0 and α = β = 0 at the edge. Subtituting derivative of the expreion in Eq. (9)-() into Eq. (8) give the following expreion for the train energ: U = F + Fα o + F3β 0 + F α0 + F5 β0 + F6 α0β0 () 3

4 Hoo Fatt M. S.,Sirivolu D. where 3768 F = ( A + A55 ) π 8 F = a A55 + D + D π 8 F 3 = a A + D + D F = aa π 096 F5 = aa 3 05π 30 F 6 = D 6 + D 66 π ( ) The total potential energ then beome Π = F + Fα o + F3β 0 + F α0 + F5 β0 + F6 α0β0 P (3) Minimizing Π with repet to, α o and β o give a loed-form expreion for the global loaddefletion repone, P = K g () [ ( ) ( ) ] F F + F3 + F6 F + F5 where K g =. ( F + F3 + F6 ) Table give the faeheet and ore material propertie for the andwih panel onidered in thi reearh. Mot of thee material propertie ome from Ref. [3], but ome have been etimated from Ref. [7] and [8]. Thee material propertie were ued to alulate the loal indentation and global deformation under tati indentation with a 5 mm diameter tup. A omparion of the predited loaddefletion harateriti under the tup with tet data i hown from point A-C in Fig.. The total defletion X in Fig. i the diplaement of the indenter. It i the um of loal indentation δ and global deformation, i.e., X = δ +. Neither the front (inident) nor the bak (dital) faeheet were perforated during thi event, and the analtial olution for the load-defletion i within 5% of the tet data. Table. Material propertie of woven roving E- gla/vinl eter and Coremat. E-Gla/ Vinl Eter Firet Coremat Denit (kg/m 3 ) Thikne (mm) E (+) (GPa) E (+) (GPa) E 33 (GPa) ν ν ν ν ν ν G =G (GPa) G 3 =G 3 (GPa) G 3 =G 3 (GPa) σ 3f (-) (MPa) -- a (MPa) -- 0 k (MPa) ILSS (MPa) * G IIC (J/m ) σ f (+) (MPa) σ f (-) (MPa) σ f (+) (MPa) σ f (-) (MPa) τ f (+)=τ f (+) (MPa) 0 -- τ 3f (+)=τ 3f (+) (MPa) -- 5 τ 3f (+)=τ 3f (+) (MPa) -- 5 ε f (+) ε 3f (-) E a (MJ/m 3 ).7 -- * Interlaminar hear trength i aumed equal to E-Gla/vinl eter. Failure Mehanim A mentioned earlier everal failure mehanim ma our during loal indentation and global deformation. Simple failure riteria are derived for eah of thee mehanim below. A multi-tage damage model to omplete perforation will be propoed one the initial failure mehanim i determined.

5 IMPACT PERFORATION OF COMPOSITE SANDWICH PANELS L o a d ( k N ) B C 0 A D E Total defletion, X (mm) Tet Predited Stage III interlaminar hear frature toughne are generall not the ame. The ize of the delamination ma found from equilibrium onideration and auming that the tranvere tre i paraboli through the thikne, 3P τrz = πr z ( H + h) H + h (6) where r and z are the radial and through-thikne oordinate, repetivel. The delamination or debonding radiu i found b evaluating τ rz at the appropriate interlaer and tetting it equal to the interlaminar hear trength of the faeheet or the interlaminar bond trength of between the faeheet and ore. Fig. Variation of quai-tati load with penetrator diplaement.. Delamination/debonding Although not a atatrophi failure mode, delamination between plie and debonding between faeheet and ore will our when the interlaminar hear trength and bond trength are exeeded. Frature mehani an be ued to alulate threhold load for the onet of delamination and debonding. An approximate olution for the delamination threhold load in a quai-iotropi orthotropi plate under tati indentation i given b Olon et al. [9] a P t del where 3GII D = π (5) 3 G II i the Mode II interlaminar frature toughne and D = D D ( η + ) /, η = ( D + D66 )/ DD. Thi formula an be ued to alulate the threhold load for delamination/debonding in the E-gla/vinl eter and Coremat andwih panel b auming Dij = Dij. Under impat load, the threhold dn t delamination load i P del =.3Pdel. Separate load hould be alulated for delamination and debonding beaue value for the Mode II. Core hear failure Conider loal indentation of iolated Coremat (no faeheet) b the hemipherial-noe indenter. The ruhing load under the indenter i given b ρ kw P = π a + rdr (7) H 0 where w = R r + δ R i the loal defletion under the indenter and ρ i the ontat radiu of the indenter with the top faeheet. A imple relation between loal indentation δ and ontat radiu ρ i given b δ = R ρ R (8) Iolated ore hear failure take plae when P = P = πρ Hτ r, where ρ i the ritial ontat radiu at ore hear failure andτ r = τ3 i the tranvere hear trength of Coremat. Integrating Eq. (7), uing Eq. (8) to eliminate δ, and etting P = P give the following impliit olution for ρ : aρ k 3 + R H 3ρ H kρ R ρ = τr H ( R ρ ) 3 (9) 5

6 Hoo Fatt M. S.,Sirivolu D. The orreponding load for iolated ore hear frature an be alulated one ρ i known. The load at whih the Coremat andwih panel undergoe ore hear failure i higher than the ore hear frature load of iolated Coremat ine the andwih alo ha to reit the front faeheet membrane reitane. The ore hear frature load for the Coremat andwih panel i found b requiring the eond term of Eq. (7) be equal to P..3 Front/bak faeheet failure One an ue train energ denit to predit faeheet failure. The train energ denit in an orthotropi faeheet i U o = (Q ε x + Q ε + Q ε x ε + Q 66 γ x ) (0) where ε x, ε, and γ x are in-plane train and Q ij are omponent of the tranformed tiffne matrix. When the train energ denit i larger than the toughne, i.e, the peifi energ aborbed in a uniaxial tenion tet E a, failure an our. In the bak faeheet, the train varie through the andwih panel thikne and are given b α β α β ε x = z, ε = z, and x z. x x γ = + where Eq. (0) and () are ued to evaluate train. Aording to thee expreion, the maximum ompreive and tenile train due to global deformation our in the front and bak faeheet, repetivel. The front faeheet train ma be etimated b the average train method preented in Ref. [5]. Sine the train due to loal indentation in the front faeheet are tenile and oppoite in ign to the ompreive train aued b global bending, the magnitude of the train in the bak faeheet i alwa larger. Failure due to global deformation will therefore firt our in the bak faeheet rather than the front faeheet. Our alulated reult how that the train energ denit in both front and bak faeheet are maximum under the indenter and along the 0 and 90 o diretion. Thi mean rak in the front or bak faeheet will emanate in four diretion orreponding to the 0 and 90 o reinforement diretion of the woven kin. The failure load for delamination, debonding, ore hear frature, and bak faeheet frature are given in Table. The lowet load orrepond to ore hear frature, thereb ignifing that thi take plae before frature of either top or bottom faeheet. Sine the ore i till trapped between faeheet, the loal indentation and global deformation repone remain relativel unhanged. After ore hear frature, the ontat radiu between indenter and top faeheet till inreae with load and the Coremat ruhe with almot the ame harateriti a when there wa no ore hear frature. Debonding and delamination then take plae at 7.6 and 0.7 kn, repetivel. The bak faeheet finall frature at 7. kn. Thi i about 5% higher than the experimental failure load at kn. Approximate energ method are generall le aurate in prediting tree and train than the are defletion. When the bak faeheet fail, new loaddefletion relation mut be derived ine the panel beome weaker and le tiff. A progreive or multi-tage perforation model will be ued to derive thee new load-defletion relation in the next etion. Table. Load and defletion at eah failure mode. Failure Mode Load (kn) Loal Indentation Global Defletion (mm) (mm) Delamination Debonding Core Shear Bak Faeheet. Multi-tage perforation model The following multi-tage perforation model i propoed a illutrated in Figure 3 (a)-(): Stage I Loal indentation and global deformation up to ore hear frature, a depited in Fig. 3 (a). Core hear frature our at roughl 5 degree with repet to the plane of the panel ine thi orrepond to a plane of maximum hear tre. It i eaier for the rak to extend horizontall thereb debonding the ore from the bak faeheet rather than ontinue at the 5 degree angle into the faeheet. The tranvere bond trength i an order of magnitude maller than the tranvere hear trength of the faeheet. 6

7 IMPACT PERFORATION OF COMPOSITE SANDWICH PANELS Stage II Deformation beond ore hear frature and ending with bak faeheet frature, a indiated in Fig. 3 (b). The ore ruhing reitane ued to alulate the loal load-indentation repone remain unhanged ine the faeheet are intat. Eventuall a ro-hair frature develop on the bak faeheet, a i alo hown in Fig. 3(b). Stage II I Deformation up to front faeheet frature (ee Fig. 3 ()). Both global and loal deformation ontinue after the bak faeheet fail. The bak faeheet petal under the indenter and loal indentation beome ofter. A new loaddeformation repone will our in Stage III and will be diued in the next etion. The global panel tiffne i little affeted b the ro-hair frature and i aumed to be roughl the ame prior to bak faeheet frature.. Bak faeheet debonding after ore hear frature Bak faeheet debonding i triggered b ore hear frature at a 5 degree angle. The ize (radiu) of the bak faeheet debond λ an be alulated b auming the tenile trength at the interfae of the E gla/vinleter and Coremat i σ t = 73 [0] and the following equilibrium ondition: σtπ λ πk 3 ( d ) = πa ρ + R ( R ρ ) πkρ H R ρ 3H 3 () where d = ρ + H i the radial ditane to the tart of the debonding region and ρ i the ritial ontat radiu at ore hear frature. The right-hand ide of Eq. () i the fore exerted on the bak faeheet b the Coremat in term of ρ. Sine ρ i related to δ b Eq. (8), one an determine the debond radiu for an load uing the load-indentation relation in Eq. (7). Subtituting geometri and material propertie into Eq. (9) give ρ = 7. 8 mm. Solving Eq. () at the bak faeheet failure load and defletion give λ = 3. 9 mm..5 Loal indentation repone in Stage III andwih panel tiffne i little affeted b the loalized petaling, but the loal indentation reitane i muh redued, epeiall under the indenter. A hown in Fig. 3 (), tranvere hearing rather than ompreion of the Coremat i ourring beneath the indenter. One again the minimum potential energ i ued to predit the loalindentation repone. (a) Core hear frature and bak faeheet debonding. (b) Bak faeheet failure. () Front faeheet failure and perforation. bak bak Fig. 3 Multi-tage perforation proe: (a) ore hear failure and bak faeheet debonding, (b) bak faeheet frature, () front faeheet failure and perforation. The total potential energ during Stage III loal indentation i given b ~ δ G3πH 8D = C + δ + ( δ δ ) Pδ () λ 3λ Loal petaling our immediatel following ro-hair frature in the bak faeheet. The global 7

8 Hoo Fatt M. S.,Sirivolu D. where G3 D ~ = N j= i the ore tranvere hear tiffne, E j + E j 3 3 ( ) z j z j i a beam equivalent bending tiffne, N i the number of plie in the faeheet, and δ i the loal defletion at bak faeheet failure. The firt term of the potential energ i the membrane energ of the front faeheet, the eond term i the ore hearing energ and the lat term i the bending energ of four petal (ee Fig. 3 ()). Minimizing the potential energ ield the following load-indentation repone: P ~ C 3 G3πH 6D δ + δ + λ 6 3λ = ( δ δ ) (3) The predited load-defletion repone in Stage III i indiated b the dahed line in Fig.. Beaue the bak faeheet failure load wa overpredited onl a mall portion of thi graph i atuall ued in the predited repone. The load drop at E orrepond to tenile failure of the front faeheet. 5 Low-Veloit Impat Repone The impat repone of the panel i found from the two degree-of-freedom ma-pringdahpot tem hown in Fig.. The projetile ma i denoted M o, and the effetive ma of the top faeheet and andwih are repreented b m and m, repetivel. Expreion for the f effetive faeheet and andwih mae are derived b auming the loal and global veloitie are ditributed the ame a their deformation. The loal deformation and global deformation are given b δ = X X and = X, repetivel. The loal indentation reitane tiffne K g are found from quai-tati reult and adjuted with the train rate-dependent material propertie of the faeheet and ore. High train material tet how that the tiffne and trength of the E-gla/vinl eter inreae with inreaing train rate []. High train rate tet on polmeri foam indiate that the are fairl rate inenitive []. The Coremat material propertie are therefore aumed to be the ame a in quai-tati tet. In addition to the loal and global tiffne, a linear dahpot i ued to repreent damping of the P l and the global pring Coremat. The damping ontant for the dahpot i alulated from the impat tet reult ine there i no publihed data on Coremat damping propertie. Fig. Two degree-of-freedom model for impat of ompoite andwih panel. The equation of motion for the two-degree-offreedom tem are M + m ) X& + P + ( X& X& ) 0 () ( o f l = and m X& P X& X& ) + K X 0 (5) l ( g = The initial ondition for the two-degree-of-freedom tem are a follow: X (0) = 0, X (0) = 0, X & (0) = V o, and X & (0) = 0, where V o i the initial veloit of the projetile. Equation () and (5) repreent a nonlinear, oupled initial-value problem. An ode olver wa ued in MATLAB to olve for X and X. The ontat fore between the projetile and the impated faeheet i given b F = M o X& (6) Eah failure event ourring during tranient deformation would dereae the kineti energ of the tem. The energ aborbed b delamination/debonding i the produt of the interlaminar hear frature toughne and appropriate area. Thee area ma be etimated from Eq. (5) and the delamination and debonding 8

9 IMPACT PERFORATION OF COMPOSITE SANDWICH PANELS load. The ore hear frature energ i given alo given b the produt of the ore tranvere hear frature toughne and it aoiated frature area. The frature energ due to petaling of the bak and front faeheet are etimated from the tear energ of the E-gla/vinl eter. Expreion for the tear energ aoiated with petaling are taken from Lin and Hoo Fatt [5]. Figure 5 ompare the alulated ontat fore with tet data for panel impated b a 0 kg projetile and exhibiting neither top or bottom faeheet frature. A 0% inreae in the faeheet tiffne and trength i aumed and the damping ontant i etimated at 59.8 N/m. The analtial model i able to predit an average ontat fore to within 0% of the experimental data. In all of thee tet, the maximum global deformation were le than 36.8 mm, whih i about the defletion at whih the bak faeheet would have failed. It i aumed both the tiffne and trength of the faeheet would inreae with inreaing train rate b the ame amount uh that the global defletion at bak faeheet failure remain the ame in the impat tet. Load (kn) Time (m) 7.67m/ 6.6m/.3 m/ Analtial Tet Fig. 5 Contat fore hitor of impat with 0 kg ma projetile at.3, 6.6 and 7.67 m/. Core hear frature, delamination and debonding energ hould be ubtrated from the kineti energ of the tem at the intant the our. The time duration of thee event are intantaneou ompared to the andwih repone time ine thee failure ontituted brittle or untable rak propagation. The energ aoiated with delamination and debonding i ver mall and ha negligible effet on the olution. The ore tranvere hear frature energ ould not be etimated for lak of data on the ore tranvere frature toughne. It i aumed to be negligibl mall, although it wa notied that there wa a load drop in the tet data at about the load ore hear frature would our. With inreaing ma or projetile veloit, damage would our. Figure 6 ompare the alulated and experimental ontat fore for the panel with an impat ma of 0 and 30 kg and an impat veloit of 6.6 m/. Load (kn) kg 0 kg Analtial Tet Time (m) Fig. 6 Contat fore hitor of impat with 0 and 30 kg ma projetile at 6.6 m/. Impat with the 0 kg jut aue frature of the bak faeheet when the ontat fore i at a maximum value. At thi time, the global panel defletion i almot 36.8 mm. The final defletion and veloitie at thi time are ued a initial ondition in a new imulation of the oupled equation of motion with the Stage III loalindentation repone intead of the Stage I/II loalindentation repone. The damping ontant i aumed to inreae to 000 N/m ine damping aoiated with loalized ore hearing i higher than damping aoiated with ore ruhing. The predited olution i ver loe to the tet data in Stage I/II, but the ontat fore in Stage III i about 0% higher than the tet reult. Thi i beaue lo of kineti energ due to tearing of the bak faeheet i not aounted for ine the veloitie at the intant of bak faeheet frature are zero at the peak ontat fore. Impat with the 30 kg ma aue omplete panel perforation. Unlike the 0 kg ma impat, bak faeheet failure take plae at 8. m, about 9

10 Hoo Fatt M. S.,Sirivolu D.. m before the time peak ontat fore would have ourred. The tear energ i ubtrated from the kineti energ of the bak faeheet at thi time and a new reidual veloit of the bak faeheet i alulated. The oupled equation of motion are then olved again uing thi reidual veloit and the orreponding diplaement and projetile veloit a initial ondition, the Stage III loal indentation repone and the damping ontant et to 000 N/m. Immediatel the loal defletion X X, exeed the amount to aue front faeheet failure. Therefore both bak and front faeheet take plae at the ame time. Thi predited reult i imilar to what wa found in the tet. 6 Conluion Analtial model were derived for quai-tati and impat perforation of an E-gla/vinl eter and Coremat andwih panel. The panel deformation wa deompoed into loal indentation and global deformation. An equivalent two degree-of-freedom ma-pring-dahpot tem wa ued to find the dnami repone of the ompoite andwih panel ubjeted to a drop-weight impat b a rigid hemipherial-noe projetile. Equivalent pring reitane were derived from the quai-tati loaddiplaement repone and adjuted dnami material propertie of the faeheet. Several failure mode were onidered, inluding delamination, debonding, ore hear frature, and top and bottom faeheet failure. Analtial predition of the quai-tati loaddefletion repone were within 5% of the tet data. However, the alulated failure load wa about 5% higher than the tet data. Thi tpe of aura i tpial of uing the minimum potential energ to approximate the load-deformation repone of panel. Analtial predition of the dnami repone, in partiular the ontat fore hitor, alo ompared ver well with the tet data. The two degree-of-freedom model wa able to imulate the orret phi of impat perforation. Without failure of either bak or front faeheet, predited ontat fore hitorie were within 0% of tet data. Aknowledgement The author aknowledge finanial upport from Dr. Yapa Rajapake at the Offie of Naval Reearh under grant N The author would like to thank Dr. R. A. W. Mine for providing experimental reult on the tati and lowveloit perforation of the E-gla/vinl eter and Coremat andwih panel. Referene [] Belingardi G., Cavatorta M.P., Duella R. Material haraterization of a ompoite-foam andwih for front truture of a high peed train, Compoite Struture, Vol. 6, No., pp. 3-5, 003. [] Wen H.W., Redd T.Y., Reid S.R., Soden P.D. Indentation, penetration and perforation of ompoite laminate and andwih panel under quai-tati and projetile loading, Ke Engineering Material, Vol. -3, pp , 998. [3] Mine R.A.W., Worrall C.M., Gibon A. G. Low veloit perforation behavior of polmer ompoite andwih panel, International. Journal of Impat Engineering, Vol., No. 0, pp , 998. [] Lantor, B.V. Firet Coremat data heet, Veenendaal, The Netherland, 993. [5] Lin C., Hoo Fatt, M.S. Perforation of andwih panel with honeomb ore b hemipherial-noe projetile, Journal of Sandwih Struture and Material, Vol. 7, No., pp. 3-7, 005. [6] Mine R.A.W., Jone N. Approximate elatiplati anali of the tati and impat behavior of polmer ompoite andwih beam, Compoite, Vol. 6, No., pp , 995. [7] Stevanovi D., Jar P.-Y.B., Kalnaundaram S., Lowe A. On rak-initiation ondition for mode I and mode II delamination teting of ompoite material, Compoite Siene and. Tehnolog. Vol. 60, No. 9, pp , 000. [8] Kolat K., Neer G.., Oze C. The effet of ea water expoure on the interfaial frature of ome andwih tem in marine ue, Compoite Struture, Vol. 78, No., pp. -7, 007. [9] Olon R., Donadon M.V., Falzon B.G. Delamination threhold load for dnami impat on plate, Int J Solid Strut, Vol. 3, No. 0, pp. 3-3, 006. [0] Swaminathan G., Shivakumar K.N., Sharpe M. Material propert haraterization of gla and arbon/vinl eter ompoite. Compoite Siene and Tehnolog, Vol. 66, No. 0, pp , 006. [] Johnon H.E., Loua L.A., Mouring S.E. Current reearh into modelling of hok damage to large ale ompoite panel. J. Mater. Si., Vol., No. 0, pp , 006. [] Ouellet S., Cronin D., Worwik M. Compreive repone of polmeri foam under quai-tati, medium and high train rate ondition, Polmer Teting, Vol. 5, No. 6, pp. 73-7,