Modern Applied Science

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1 Vol., No. 4 November 7 Performace Aalysis o Equivalet Elasticity of D 4-directioal Braided omposites Dog he, Li he, Yig Su Key Laboratory of Advaced Textile omposite Material of Miistry of Educatio Istitute of omposite Material Tiaji Polytechic Uiversity, Tiaji 6, hia chedog@6.com The research is supported by Program for New etury Excellet Talets (No. NET-5-54) ad Program for Tiaji Applicatio Basic Research Pla (No. 5YFJMJ4). Abstract Based o the small parameter asymptotic homogeizatio theory, this article adopts the techology of digitized cell-based fiite elemet method (DB-FEM) to establish the digital cell-based mechaics aalysis model of three-dimesioal 4-directioal braided composite material, aalyzes ad calculates the equivalet elasticity performace of D braided composite material usig homogeizatio method, ad the results show a good agreemet with the experimetal data. Keywords: Three-dimesioal braided composite material, Homogeizatio, Microstructure, Digital model, Fiite elemet method Three-dimesioal braided composite material are the egieerig structure composite material which are developig very fast for recet years. These materials have may advatages such as good itegrated performace, reasoable mechaical structure ad good abilities to resist damage limits ad crackle extesio, which offer wider prospects of applicatios o mai load-bearig structure for D braided composite material (Yag, 99, p.87-9). The mechaical performaces of D braided composite material deped o ot oly performaces of various part materials, but also their microstructures. The yar spaces i D braided structure preset multi-directioal distributio ad form seasoal yar structure by complectig each other, ad just because of the complexity of this microstructure, it becomes very difficult to make the mechaical performace aalysis for D braided composite material. Based o the fiite elemet method of the digital cell-based model, this article establishes the umerical computatio method of homogeizatio for D 4-directioal braided composite material, aalyzes ad calculates the equivalet elasticity costats of these materials, ad makes the comparative research with the test results.. ell-based model of D 4-directioal braided composite material D 4-directioal braided composite material are superposed by sigle seasoal microstructure uit cells (he, 999, p.9-44). The iterior uit cell model is see i Figure. The iterior uit cell model of D 4-directioal braided composite material presets cube shape. If takig braid directio as axis x, so width directio of uit cell is axis y ad thickess directio is axis z. The icluded agle betwee braid yar ad braid axis directio x is the iterior braid agle γ, ad the icluded agle betwee projectio of braid yar o workpiece cross sectio (y-z sectio) ad thickess directio (axis z) is θ which is the iterior tropism agle of iterior yar. Supposed that the cross sectio of braid yar is ellipse which log axis ad short axis respectively are a ad b, the sectio shape alog axis directio of braid yar is ot chageable, the braidig process is stable ad eve to esure the equality ad cosistecy of braid structure, all braid yars have same geometry characters, braid yars have eough tesios to make braid yars produce beds oly o the surface of the preforms, we ca describe the relatios betwee geometry structure of uit cell ad geometry shape of braid yar as follows. Width of iterior uit cell: Thickess of iterior uit cell: 4b W i = () cosϕ 4b T i = () siθ 4

2 Relatio betwee iterior braid agle γ ad braid agle α: Braided pitch legth of iterior uit cell h:. Fiber volume cotet tgγ = tgα () siθ 8b h = (4) tgγ si θ The fiber volume cotet is oe of mai performace idexes for D braid composite material, which is higher ad the performaces of composite material are better. The fiber volume cotet lies o two aspects, oe aspect is the iterspace amog iterior braid yars of D braid composite material, the other oe is the iterspace amog iterior fibers of braid yars, that is the yar fillig factor. The fiber volume cotet V f ca be calculated by the followig formula. V f = volume of fibers / volume of uit cell = 8A secγ ε (5) h tg γ si θ Where, A is the cross sectio acreage of yar, h is the braided pitch legth, θ = 45 ad ε is the yar fillig factor.. Tighteig status I the braid shapig process, because of the fuctio of yar tesio ad tighteig workig procedure after every machie cycle, cotermious braided yars i preform cotact each other ad are i tighteig estate. The complectig estate of iterior yars of D 4-directioal braid composite material is see i Figure. Defie the shape chage factor of yars cross sectio k=a/b, accordig to the tighteig estate of yars, the relatio betwee shape chage factor of yars cross sectio ad various tropism agle of yars ca be described as follows. o Wheθ 45, k = cosγ (csc θ + ctgθ )(csc θ ctgθ ) (6) o Wheθ < 45, k = cosγ (csc θ ctgθ )(cscθ + ctgθ ) (7). Yar surface equatio Supposed the positio of oe braided yar i D 4-directioal composite material i the whole coordiate system (x, y, z) is see i Figure, defie the local coordiate system of yars as ( x, y, z ), axis y ad axis z as the cross sectio of braided yar. Through the trasform from the local coordiates to the whole coordiates, cosiderig the origi of local coordiates is located at the poit ( x, y, z ) i the whole coordiate system, the yar surface equatio ca be obtaied as follows. ((( y y)siθ + ( z z ) cosθ )cosγ ( x x )si γ ) a (( z z )siθ ( y y) cosθ ) + = b The iterior of D 4-directioal braid composite material has 4 directioal braid yars, ad the tropism agles respectively are ( γ, θ ), ( γ, θ ), ( γ, θ ), ad ( γ, θ ). Takig these agles i the equatio (8), four surface equatios of tropism braid yar ca be obtaied. Levelly move various yars to the correspodig positios of uit cell, we ca obtai the iterior uit cell etity model of D 4-directioal braid composite material, which is see i Figure 4.. ell-based digitalizatio of D braided composite material Based o the iterior uit cell etity model of D 4-directioal braid composite material, this article adopts D rasterizig techology to digitalize the uit cell etity model (Wag, ), that is to say, whe the resolutio ratio is, the uit cell of D 4-directioal braid composite material is dispersed as the form of space elemet. Four kids of glue braid yars ad oe kid of substrate material are represeted as to 4, where, represets the substrate material ad to 4 respectively represet four kids of tropism glue braid yar. I the scaig process, first the attribute values of all space elemets are edowed as, that is represets the space elemet material, the accordig to the relatios betwee the positio of space elemet poit ad the braid yar surface equatio, the attribute value of every space elemet is quatified, ad if the space elemet poit is located i the iterior of oe yar surface equatio, so this space elemet poit is activated ad edowed the correspodig material attribute. Whe the digitalizatio of uit cell of D 4-directioal braid composite material is completed, the correspodig data collectio of space elemet is formed, ad the distributio of compoet material i uit cell is detailedly recorded, ad the digital uit cell model obtaied is see i Figure 5.. Numerical computatio of equivalet performace Based o the fiite elemet method of the digital cell-based model (Guedes, 99, p.4-98 & he, 999, p.8-9 & Peg,, P & Wag, & Ma, 6 & he, 7, p.-5), this article aalyzes the (8) 44

3 equivalet elasticity modulus, ad compares it with the test results. Ad the workpiece is made by the D 4-directioal braid techology ad pitch trasfer mould techics (RTM), where, the stregtheed fiber is fiberglass of 44Tex, the substrate material adopts the epoxy resi of TDE-86#, the braid techical parameters are see i Table, ad the compoet material performaces are preseted i Table.. Glue braid yar Whe braid yars i the D composite material ifiltrate the substrate material, it ca be cosidered as the uilateralism fiber stregtheed composite material, which fiber volume cotet is the fillig factor of yar ad is called glue braid yar. The stress-chage relatio of glue braid yar i the material priciple axis directio ca be represeted as the followig equatio. σ σ σ σ σ σ = symmetry ε ε ε ε ε 66 ε Where, σ σ, σ = σ, σ = σ, σ = γ, σ = γ σ = γ = xx yy zz 4 yz 5 xz, 6 ε = ε, ε = ε, ε = ε, ε = τ, ε = τ, ε = τ xx yy zz 4 yz 5 xz 6 xy, ad [] = rigidity matrix of uilateralism fiber stregtheed material xy For the glue braid yar with four kids of tropism i D 4-directioal composite material, the material priciple axis directio is ot cosistet with the whole coordiate of the composite material, which eeds be uiformed ito the whole coordiate system. Rotatig axis formula of material rigidity is [ ( θ )] T γ, θ )] = [ T ( γ, θ )][ ][ T ( γ, () Where, [ ( γ, θ) ] is the rigidity matrix i the material priciple axis,[ T ( γ, θ) ] is the stress coversatio matrix, ad the the fiber volume cotet superscript V T represets the traspose of the matrix. f is 55%, if the iterior braidig agle γ chages, we will obtai Figure 7 which presets the values of effective Ad elasticity [ T ( γ, θperformace )] has the followig forecast form. composite material chage with the iterior braidig agle γ. Form l l l [ T ( γ, θ )] = ll ll ll m m m m m m m m m m m + m m m m + m m + m l l + l Where, l = cosγ, l = si γ siθ, l = si γ cosθ m = si γ, m = cosγ siθ, m = cosγ siθ, ad =, = cosθ, siθ. =. Numerical computatio l l l + l l + l l m lm l m lm + lm l + m lm lm + lm This article adopts the developmet software of Visual ++ to implemet the umerical computatio. First takig the fiber fillig factor obtaied by computatio as the fiber volume cotet, the homogeizatio equivalet elasticity modulus is calculated, the iput the above results as the material performaces, calculate the homogeizatio equivalet modulus of D 4-directioal braid composite material. The iput parameters iclude elasticity costats of substrate material ad glue braid yar, diameter ad braidig agle of braid yar, fiber volume cotet ad cavalcade lie yar coefficiets. The comparative results betwee the theory values ad test values of portrait elasticity modulus E are see i Figure 6, ad the computatio results show a good agreemet with the test data, which idicates that this method is feasible. 4. Iflueces of braid techical parameters 4. Braidig agle The factors which ifluece the mechaical performaces of braid structure composite materials maily iclude the iterior braidig agle γ ad fiber volume cotet V f. Keepig the performaces of compoet material ad supposed (9) () 45

4 Figure 7, we ca see that with the icrease of the iterior braidig agle γ, the extesio modulus E sharply decrease, E ad E gradually icrease, ad the trasverse extesio modulus E ad E are much smaller tha the portrait extesio modulus E ad the chagig curret is reverse with the portrait, ad with the icrease of the iterior braidig agle γ, the clippig modulus G gradually icrease, the icreasig curret of G ad G is from fast to slow, ad whe γ = 4, the portrait clippig modulus G ad G achieve maximal, ad the Poisso s ratio v ad v is from icrease to decrease with the icrease of the iterior braidig agle, ad whe γ < 5, v ad v icrease with the icrease of γ, the decrease with the icrease of γ, ad the Poisso s ratio v is from decrease to icrease with the icrease of γ, ad whe γ <, v decreases with the icrease of γ ad achieves miimal whe γ =, ad whe γ >, v icreases with the icrease of γ. I a word, the iterior braidig agle γ observably iflueces the extesio modulus E. 4. Fiber volume cotet Keepig the performaces of compoet material ad supposed the iterior braidig agle γ is %, if the fiber volume cotet V f chages, we will obtai Figure 8 which presets the values of effective elasticity performace forecast composite material chage with the fiber volume cotet V f. Form Figure 8, we ca see that all extesio modulus ad clippig modulus icrease with the icrease of the fiber volume cotet V f, but the chage of Poisso s ratio is relative complicated, with the icrease of the fiber volume cotet V f, Poisso s ratio v gradually decrease, but v ad v is from the icrease to decrease, whe the fiber volume cotet V f achieves about 45%, they get the maximal values, ad whe V f < 45%, v ad v icrease with the icrease of V f, ad whe V f > 45%, v ad v decrease with the icrease of V f. Ayway, the Poisso s ratio v ad v are maily cotrolled by the iterior braidig agle γ ad the fiber volume cotet V f has few iflueces to them. 5. oclusios Based o the small parameter asymptotic homogeizatio theory, this article adopts the techology of D graph digital processig to establish the digital cell-based mechaics aalysis model of D 4-directioal braided composite material, aalyzes ad calculates the equivalet elasticity performace of D braided composite material usig homogeizatio method, ad the results show a good agreemet with the experimetal data. Therefore the forecast method of the elasticity performace of D 4-directioal braided composite material is established, ad this article offers a effective aalysis method for the techical parameter choosig, performace desig ad structure optimizig of this type of material i the developig process, promotes the further applicatio of D composite material i the area of aviatio ad spaceflight, ad establishes the bases for further aalyzig the damage, itesio ad o-liearity activity of this type of material. Figure. Schematic Illustratio of the Spatial Traces of Iterior Yars Refereces he, Li, Tao X M & hoy L. (999). O the microstructure of three-dimesioal braided performs. omposites Sciece ad Techology. 59(). p heli, X M. Tao &. L. hoy. (999). Mechaical aalysis of -D braided composite by the fiite multiphase elemet method. omposite Sciece ad Techology. No.59. p.8-9. he, Li, Zha, Lili & Su, Yig. (7). Numerical simulatio of costitutive relatio of D braid composite material based o cell-based digital model. Joural of Tiaji Polytechic Uiversity. 6 (). p.-5. Guedes Jose Mirada & Kikuchi Noboru. (99). Preprocessig ad postprocessig for materials based o the homogeizatio method with adaptive fiite elemet methods. omputer Methods i Applied Mechaics ad Egieerig. No.8. p Ma, Zhejie. (6). Two-scale aalysis of D 4-directioal braid composites elasticity performace. Master Paper of Tiaji Polytechic Uiversity. 46

5 Peg, Xiaoqi & ao, Jia. (). A dual homogeizatio ad fiite elemet approach for material characterizatio of textile composites. omposites Egieerig (Part B). (). (). P Wag, Maocheg. (). Fiite Elemet Method. Beijig: Tsighua Uiversity Press. Wag, Yaoa, Li, Shutao & Mao, Jiaxu. (). omputer Image Processig ad Idetificatio Techology. Beijig: hia Higher Educatio Press. Yag, Gui & og, Lizhe. (99). Itegrated kitted techology ad characteristics of composite material. Acta Materiae omposite Siica. 9 (). p Figure. The ross Sectio Photograph of Preform Figure. The Directios of Braided Yar Figure 4. Iterior Uit ell Model of D 4-directioal Braided omposites Figure 5. The Digitized ell Model of D Four-directioal omposites Figure 6. Predictio ad Test Results of E 47

6 Figure 7. Elastic ostats Variatio with Braidig Agle Figure 8. Elastic ostats Variatio with Fiber Volume otet 48

7 Table. Techical parameters of the specimes No. Materials Fiber Size (mm mm mm) Mai body yar Braid agle (Deg.) Fiber volume cotet (%) GT45 Glass 44Tex GT445 Glass 44Tex GT55 Glass 44Tex GT455 Glass 44Tex Table. Mechaical property parameters of compoets properties Extesio modulus (GPa) Poisso s ratio Desity (g/cm ) Glass fiber Epoxy resi