F98-D4 Page ULTRA-THICK CROSS SECTION FIBER REINFORCED COMPOSITES Project Code: F98-D4 Ivestigators: Yog K. Kim, Leader, Armad F. Lewis, Alex Fowler, UMass Dartmouth Graduate Studet: Joatha Reuss PROJECT OBJECTIVE The overall objective of this study is a fudametal examiatio of the basic fiber ad resi material parameters that are importat i the maufacture of thick cross-sectio composites. Advaced fabricatio methods will be used such as i-situ cosolidatio, o-autoclavig curig, ad advaced fiber placemet process for thermoset composites. The thickess rage of iterest is from.9 cm (.75 iches) to 7.6 cm (3. iches) i thickess, which would be adaptable to marie vessels ad other load bearig egieerig structures. INTRODUCTION Limitatios exist i the field of fiber reiforced Orgaic Polymer Egieerig Composite (OPEC) materials with referece to the process fabricatio of composite shapes havig a thick cross sectio (ca. greater tha -3 cm). Problems arise from the exotherm that occurs durig the cure of the composite. This ca lead to ueve curig, ueve mass shrikage ad improper cosolidatio of the fiber/resi composite media. This results i composite material structures of uacceptable egieerig quality. Furthermore, if the reactio exotherm is too high, thermal degradatio of the matrix material ca occur resultig i potetially hazardous processig coditios. Complex textile structures such as two ad three dimesioal wove fabrics ad braided structures offer the potetial to produce et shape preforms cotiuously, as well as provide a product form with improved damage tolerace ad impact resistace at low cost. [Mohamed ad El-Shiekh 994] Combied with resi trasfer moldig (RTM), these techologies also offer a cost reductio potetial for Orgaic Polymer Egieerig Composites (OPEC) for marie applicatios (e.g. ship hulls, submersible structural members) ad costructio egieerig structures. The proposed study will ehace competitiveess of high-tech textile preform maufacturig sectors by providig quality ad cost-effective fiber reiforcemet materials to these relevat idustries. Furthermore, the uses ad markets for polyaramid, glass ad carbo fiber would be greatly impacted if techiques could be developed for fabricatig OPEC materials of thick cross sectio. This year, the focus of ivestigatio is the heat trasfer i bulk fiber/resi masses durig the curig process.
F98-D4 Page THERMO-CHEMICAL MODEL OF CURING PROCESS Goverig Equatios The followig assumptios are made at this time: All material properties (specific heat, desity, thermal coductivity) are costat durig the curig process. This assumptio will be relaxed to accommodate more realistic measured properties i experimetal study phase. Temperature ad degree of cure are fuctios oly of time ad directio ormal to the part surface. The composite is a ifiite medium ad ca therefore be assumed to be oe dimesioal. Deformatio of the material is egligible. There is o covectio heat trasfer. Iitially, the heat trasfer durig the process was described by the followig heat coductio equatio [Beja 99] without takig the degree of cure ito accout. ρc T t T = k + q& () x The variables T, ρ, C, k, ad q are temperature distributio i thickess directio X, the desity, specific heat, thermal coductivity, ad rate of volumetric heat geeratio, respectively. I order to give the model superior flexibility the ext step was to replace the curret variables with dimesioless quatities. The ew dimesioless equatio reads as follows: C K θ θ = τ X + Q () Where the dimesioless variables are defied as, C C = ρ ρrefc p pref (3) θ = T T Tmold T (4) τ α = t L (5)
F98-D4 Page 3 K = k (6) kref & Q = ql T k ( Tmold ) ref (7) where, T, L, ad α are the ambiet temperature, the slab thickess, ad thermal diffusivity of the material, respectively. The dimesioless C ad K terms ca obviously be set to by assumig the referece values are equivalet to the curret values. The other dimesioless quatities are also show here ad their values ca be calculated by usig reported values for glass/polyester (see Table ). Other specific reiforcemet/matrix resi cases for give experimetal setup, these parameters are to be calculated with measured values. Table. Material properties ad Processig parameters for glass/polyester umerical results. [Kim 995] Property/Parameter Variable (Uits) Value R / 98 Heat of Reactio (Resi) H ( kj kg) Resi Mass Fractio γ.6 Desity ( 3 ρ kg / m ) 89. * 3 Thermal Coductivity k( kw / m C) 63. * 4 Cp kj / kg C.6 Specific Heat ( ) Frequecy Factor Z( s ) E( J / mol) 674. * 5 Kietic Expoets, m.476,.54 Ambiet Temperature T ( C) 5 Mold Temperature Tmold ( C) 6 The ext step i the thermo-chemical model is to vary the rate of heat geeratio as a fuctio of cure. The heat geeratio (equatio 8) ca ow be writte as a fuctio of the heat of reactio HR, the resi mass fractio γ, ad the cure rate c as a fuctio of time. The cure rate is calculated i equatio 9, where Z is a frequecy factor, E is the activatio eergy, ad R is the uiversal gas costat. [Kim 995] &q = ργh c R t (8)
F98-D4 Page 4 c t E = Zexp RT ( c) m c (9) Oce agai it was ecessary to form o-dimesioal quatities which could the be icorporated ito the previous o-dimesioal equatio. The ew dimesioless quatities are described fully i equatios - 5. Their values ca also be calculated from Table for glass/polyester composites. [Kim 995] Q = H c τ () H = γh Cp T R ( mold T) () c τ E = Z exp θ + R ( c) m c () Z = Z L α (3) E = E T R ( Tmold ) (4) R = T ( Tmold T) (5) Numerical Results Procedure A fiite differece method usig Trapezoidal Rule was used to itegrate the goverig equatio (). The TR method is secod order accurate i time ad space as well as beig ucoditioally stable. The TR method calculatesθ at time step + ad spatial step i for all i ad by usig both kow ad ukowθ as show i equatio 6. This is doe by placig the ukowθ's ad their coefficiets ito matrix form, settig it equal to the kow θ's, ad solvig it. The matrix formed is a tri-diagoal matrix ad a tri-diagoal matrix solver ca be used, which greatly icreases the speed of the program.
F98-D4 Page 5 + k τ + + + k τ θi = θi + ( θ i+ θi + θi ) + ( θ i+ θ i + θ i ) + Q τ (6) X X The oliear equatio for calculatig the degree of cure (Eq. ) was solved usig a Forward Euler approach. It is oly first order accurate i time ad space, but it is stable for small time steps. The Forward Euler method simply uses the previous time step values at ay give spatial step ad therefore does t require a matrix solver. I order to fid the degree of cure at spatial step i ad time step + you simply implemet + E ci = ci + τ Z exp θ R i ( ci ) ( c i ) m (7) Numerical Results Although the umerical model is a prelimiary oe with limited coditios imposed by the assumptios, we have produced several graphs i order to test its accuracy ad validity. As stated i previous sectios, the dimesioless parameters were calculated usig data preseted i Table. First, a graph of the degree of cure ad θ ceter vs. τ is show i Figure. This model predicts that the cure occurs completely i a very short period of time, which is clearly oly true for ideal situatios. More accurate cure models will be icorporated at a later time. A thermal spike the occurs as a result of the sudde curig. The secod graph show i Figure is of θ max vs. τ. θ max is the maximum temperature withi the composite thickess at ay give time iterval. The thermal spike is idetical to that show i the θ ceter graph, however, it starts at because it is our set boudary coditio. It heats up quickly as would be expected from this type of idealized curig process. It the cools approximately 73 degrees i 4+ miutes, which also appears to be reasoable cosiderig the idealized model we are usig for a ich bulk thickess. The third ad fial graph show i Figure 3 is of θ max vs. Z. Z is the oly dimesioless variable that is directly affected by the thickess ad is therefore used as a dimesioless thickess. The results as Z gets larger become less ad less accurate. This is because the portio of the code cotaiig the Z is highly sesitive to the time step. It is therefore ecessary to reduce the size of the time step as the Z gets larger, which results i much larger data processig times. I view of this accuracy problem further refiemets i the model ad/or the umerical algorithm are eeded.
F98-D4 Page 6 Figure : Thetaceter & Cure vs. Tau Thetaceter & Cure.8.6.4..8.6.4..5..5..5.3.35.4 Tau thetaceter cure Figure : Thetamax vs. Tau Thetamax.8.6.4..8.6.4..5..5..5.3.35.4 Tau
F98-D4 Page 7 Figure 3 Thetamax vs. Z.5 Thetamax.5.5.E+.E+5.E+5 3.E+5 4.E+5 5.E+5 6.E+5 7.E+5 Z CONCLUSION There are several improvemets that eed to be made to the curret umerical model. First, a fluid flow model eeds to be icorporated ito the curret thermo-chemical model i order to model the resi flow resultig from the dowward pressure applied by the hydraulic press plates. Although variatios i thermal coductivity of the material durig the cure have bee show to be uimportat i certai composites [Twardowski 993], we ited to explore whether or ot they are ever sigificat i thick composites. A experimetal apparatus cosistig of a heated copper plates withi a Lexa holder has bee fabricated to measure the thermal coductivity of liquid thermoset matrix resis at differet curig stages. Oce the revised model is completed, various techiques of lowerig the maximum temperature of curig ca be umerically tested ad the checked experimetally. The plaed research activities for this year ad beyod are: Modificatio of model to iclude possible variatios i thermal properties, resi flow durig cosolidatio, ad aisotropic coductivity due to fiber arragemet. Experimetal verificatio of the improved model. Use of the model ad experimetal results to develop testig ad aalytical techiques for uderstadig the behavior of the thick wall composites as a fuctio of curig method ad reiforcemet structure. To develop a processig sciece ad techology basis for the maufacture of these materials ad to develop a uderstadig of the iteractio betwee processig ad performace.
F98-D4 Page 8 REFERENCES Beja, Adria. Heat Trasfer, Joh Wiley ad Sos, New York, 99. Kim, Cheol., The Cotiuous Curig Process for Thermoset Polymer Composites. Part : Modelig ad Demostratio, Joural of Composite Materials, vol. 9(9): pp3-53 (995) Mohamed, M, Aly EI-Shkieh et al, NTC Project Code S9-: Textile Structures for Composite Natioal Textile Ceter Aual Report, September 994 Twardowski, T.E, Curig i Thick Composite Lamiates: Experimet ad Simulatio, Joural of Composite Materials, 7(3): 6-5 (993)