An Investigation of Stimulating the Autoclave Curing Process of Resin Matrix/Fiber Reinforced Compos

Vol.9 No.2HIGH TECHNOLOGY LETTERSJun.2003An Investigation of Stimulating the Autoclave Curing Process of ResinMatrix/Fiber Reinforced Composite Material ,I : Process model°Wang Zhengping(王正平), Li Chensha* ,Jiao Caishan ,Liu Ying'Zhang Baoyou** * , W ang HongJie, Cao Maosheng( Chemistry Engineering Department , Harbin Engineering University , Harbin , 150001 ,P. R China )( * New Material Division , Institute of Nuclear Energy Technology ,Tsinghua University , Beiing102201 ,P. R China)( ** Harbin University of Commerce , Harbin , 150076 ,P. R China)( *** Center for Analysis and Measurement , Harbin Institute of Technology , Harbin , 150001 ,P. R China)( *** Aerospace Arts and Crafts Institution , China , 100024 ,P. R China)( *** Department of Material Science and Engineering Harbin Engineering University , Harbin , 150001 ,P. R China )AbstractA mathematical model is made which describes the curing process of composites constructedfrom continuous fiber- reinforced，thermosetting resin matrix prepreg materials , and the consoli-dation of the composite is developed. The model provides the variation of temperature distribu-tion，the cure reaction process in the resin , the resin flow and fibers stress inside the compositeand the void variation and the residual stress distribution. It can be used to ilustrate the mecha-nism of curing process and optimize the cure cycle of composite material in order to ensure thequality of a product.Key words composite laminate , cure process , computer code , solution method0 Introductionhere. Factors influencing product quality are verycomplicated. There is no efficient method to knowAdvanced composite materials are being incorpo-the internal state of the prepreg during the cure pro-rated in increasing amounts in combat , launch vehi-cess. This explains why the traditional process tech-cles , space platforms and other primary and secondaryniques are empirical. Once the raw material , additivestructures in aircraft. Parts and structures construct-and the process condition vary , the empirical tech-ed from continuous fiber reinforced thermosettingnique becomes useless. It will result in a great de-resin composites are manufactured by arranging thecrease of the quality.uncured fiber- resin mixture( prepreg ) into the desiredThe shortcomings of empirical approaches couldshape and then curing the material inside the auto-be overcome by use of analytical models. In this pa-clave1 2. The curing process is accomplished by ex-per , a model applicable to the curing process haveposing the material to elevated temperatures and pres-been proposed ，which relates the cure cycle to thesures for a predetermined length of time. The elevat-thermal , chemical , physical and mechanical processesed temperatures applied during the curing provide theoccurring in continuous fiber- reinforced compositesheat required for initiating and maintaining the chem-during cure , and which then can be used to establishcal reactions in the resin that cause the desiredthe most appropriate cure cycle in application.changes in the molecular structure. The applied pres-1 Modelsure provides the force needed to squeeze excess resinout of the material , to consolidate individual plies ,We consider a fiber- reinforced resin matrix com-and to compress vapor bubbles.posite constructed from unidirectional continuous fiberHowever , there are still some drawbacks thatprepreg' ' tape. Configuration of the curing system inlimit the application of composite materials ,in whichautoclaves is shown in Fig. 1. An absorbent materialthe greatest problem is instability of product quality ,(re中国煤化工s placed on one side ofresulted from the diversity of the cure process.the-bleeder system isTherefore，quality control becomes indispensableplaceMYHCN M H Gsheet of Teflon gasket .①Supported by the 863 Project of Chin( Grant No. 2002AA305509 )Received on Now. 14 2002一31一Vol.9 No.2HIGH TECHNOLOGY LETTERSJun.2003cloth is placed between the composite and the toolbag”) is placed around the entire assembly and vacu-plate ,and a sheet of porous Teflon release membraneum is applied during the cure. Sealing filler ( calledis placed between the composite and the bleeder to“dams" ) is also mounted around the prepreg to stickprevent sticking. An air breather is added on thethe vacuum bag and prevent lateral motion of the cur-bleeder in favor of vacuum pumping when curing ising system.done in autoclave. Finally ,a plastic sheet ( vacuumvacuum bagsenling fllersealing illerair breatherporous- bleedermembrane" prepreggasketclothmetal plateFig.1 The curing system inside the autoclaveInitially , the resin is uncured. Starting at time tresin , and the resin viscosity inside the composite de-=0 , the composite system is exposed to an autoclavepend on the rates at which heat is transmitted fromtemperature process Ta which may vary with time inthe environment into the material and heat is generat-a favorable manner. At some time tp( tp≥0 ),aed by cure reaction. For the coordinate system of aknown pressure Pa is applied to the system. The ele-flat prepreg laminate made of continuous fibers ，asvated temperatures and pressures to which the materi-shown in Fig. 2. According to the law of conservational is subjected are referred to as the cure temperatureof energy，the energy equation may be expressedand the cure pressure. The magnitudes and durationsa[12] :of the temperatures and pressures applied during thecuring process ( denoted at the cure cycle ) significant-ρc=n二最的一力最的一)+ly affect the performance of the finished product.(1 )最(《聚) oHV,The model providing the information of cure pro-cess is developed below in four parts( called four sub-processes or four submodels ) which describe( a) thebxheat generated by cure reaction , heat transfer amongthe layers or between the autoclave air and the curingsystem , the variation of viscosity of resin matrix ;( b)compression of laminate , resin flow , fiber deforma-tion and pressure varying in every ply ;(c ) the sizeavariation of voids in every ply ;( d ) residual stressformed in the composite material. The relationshipsbetween the process variables and the behavior of thecomposite can best be established via analytical mod-el. Details of the models are presented subsequently.Note however that the four sub processes occur con-中国煤化工currently .MYHC N M H Gm of prepreg laminate2 Thermal and Chemical ProcessWhere ρ and c are the density and specific heatof the composite ,pr is the density of resin，Vr is the .The temperature distribution , the degree of the一32--Vol.9 No.2HIGH TECHNOLOGY LETTERSJun.2003volume fraction of resin , the sum of V, and the vol-Th = Ti(t)=ht≥0 (8)ume fractionof fiber Vf is 1 ,k。 is the thermal con-Tu= T6(t )=o)ductivity in the direction perpendicular to the plane ofthe composite , kx is the thermal conductivity in the|pcdz =hg( T(t)- Th)-direction parallel to the fiber in plane ,k, is the ther-日Tmal conductivity in the direction perpendicular to the(k.).。+]。o,HiV,dz (9)fiber in plane ,t is time and T is the temperature. HWhere Th and Tu are temperatures on the topis the rate of heat generated by chemical reactions in( z=h ) and bottom surfaces( z=0 )of the compos-unit mass of resin matrix , and is defined in the fol-ite , respectively. hg is heat transfer coefficient of airlowing manner.convection in autoclave , T.( l )is autoclave tempera-H =( daldt )Hu(2)ture process.Hu is the total heat of reaction in unit mass ofresin matrix during cure ,( da/dt )is the reaction or3 Resin Flow and Fiber Deformation Processcure rate. The degree of cure of the resin" a" is theratio of the number of consumed function groups toAt some time tp tp≥0 ), pressure is applied tothe initial number of function groups , its apparentthe composite- bleeder system. As a result of thisvalue is defined as the ratio of evolved heat of reactionpressure, resin flows from the composite into theto the total heat of reaction Hu. For an uncured ma-bleeders.terial a =0 , and for a completely cured material , a. The uncured composite can be modeled as aapproaches unity. The cure rate( daldt ) is deter-porous , nonlinear elastic medium that is filled with amined by temperature and cure degree1 .viscous resin. When pressure is applied to a flat lami-daldt= f(Ta)(3)nate of this type ,it must be shared by both the resinIf diffusion of chemical species is neglected , theand the fiber structure. Initially however , the applieddegree of cure at each point inside the material can bepressure is carried solely by the resin ( zero deforma-calculated in the following waytion). The pressure gradient will cause resin to flowout because there is a lower pressure at the boundaryf"da(4)Jo\ dtof the composite. This loss in resin will allow theIf the resin viscosity is assumed to be independent ofcomposite to compact , thereby compressing the fibershear rate ，then the relationship between viscosity ,network. As a result of this ,part of the applied loadtemperature , and degree of cure can be represented inis now carried by the fibers ，and concurrently thethe fornf1]resin pressure is reduced. The final fiber volume frac-μ=g(Ta)(5)tion of the composite is determined by the deforma-The micro temperature field in the autoclave is as-tion characteristics of the fiber structure 31.sumed consistent ，then the temperature in the sameAs the coordinate system of prepreg laminatelayer of composite is consistent , expression( 1 ) canshown in Fig.2 , we assume that the permeabilities ofbe simplified as follows :fiber bundles S,( in x direction )and S( in y direc-ρc=2(k.+一)+ p,HV,(6)tion )depend onlyon Vf ,and Vj= V(z ). The ex-pression about pressure distribution and resin flow canBefore cure( t<0 ),degree of cure is 0，the tempera-be derived as follows according to three aspects ofture in autoclave and curing system is room tempera-force balance，continuity of resin and fiber , and resinture To. Initial conditions are :flow3].T(z)= ToS.r 2P,Sge 2P，. 1 a0≤x≤h ;t<0 (7)aj=0Vjax2tV,ay2fV学zWhere j denotes the number of every ply , T( z )andaP,g( 1- Vraj are temperature and degree of cure of every ply ,h( VjSx之)=H引v,)( 10)is the thickness of composite laminate.The中国煤化工(ls S;i and the load ofStarting cure process( t≥0 ), the temperaturesfiber;4]:of top and bottom of composite laminate are influ-:YHCNMHG,yenced by autoclave temperature Ta，the temperatureSi-4ki B( 11)of metal plate and thermal transmission. Boundary( V:/Vo- 1)conditions are :σ =As( 1/V;- 1/V。y(12)Vol.9 No.2HIGH TECHNOLOGY LETTERSJun.2003Where in Equations(9 X 10X11 ), P, is thean individual ply ,h is the thickness of the compositepressure in resin , rf is the fiber radius ,and k;; is thelaminate.so called"' Kozeny" constant which is determined byWhen the degree of cure arrives at the gel point ,the parameters of prepreg and the porous ratio of fiberthe compression of laminate ends due to resin losingbundle4] V。 is the original fiber volume fraction ,fluidity.Va is the available fiber volume fraction , and A, isthe' Spring constant" which is determined by the e-4 Voids Growth Processlastic performance of fibers and the geometry struc-ture of prepreg4. Fibers which are misaligned andVoid nuclei may be formed either by mechanicalcrossed over will result in a lower available fiber vol-means( e. g. air or gas bubble entrapment , brokenume fraction. σ is apparent stress of fibers σ= PfVf，fibers ) or by homogeneous or heterogeneous nucle-Pf is the pressure carried by fibers. These equationsatiortsI Once a void is established , its size mayhas the characteristics that at Vj= V。σ=0 ,and aschange due to :( a) changes in vapor mass inside theVr→Va σ→∞.void caused by vapor transfer through the void-Resin flow in the plane of the composite can beprepreg interface ,( b ) changes in pressure inside theneglected for the reason that ( a ) restraints of thevoid due to changes in temperature and pressure infibers ,( b ) both the width and the length of the com-ambient resin matrix. The components inside the voidposite are large compared to the thickness , and( c )bubbles are major air and vapors. A void of equilibri-restraints are placed around the sides of the compos-um state obeys the equation as follows :ite. This situation is generally encountered in prac-P。=P,+48/d( 18)tice. Thus only resin flow normal to the plane is tak-δ is the surface tension between the resin anden into account , Equation( 9 ) can be simplified as :the void. P。is the total pressure inside the void andaVr_1Vroσ +is the sum of the partial pressures of the air and thedtdifferent types of vapors present in the void. d is theX VpS2 )AV;diameter of void , P, is pressure in resin surroundingJσ/a Vf(恶门. (13)the void.The equilibrium state can be broken due to pres-Here σ+ P,=Pa ,Pa is the applied pressure.Resin cannot flow out from the bottom of com-sure or temperature in resin matrix varying. For ex-posite laminate due to the restraint of metal plate.ample ,if the pressure in resin matrix is depressedThe first ply on top of the laminate is compacted invoid will expand due to P。> Pr +48/d , and the par-stantly under autoclave pressure due to its contacttial pressure of vapor inside the void is also depressedwith the bleeder. For the reason that the permeabilityresulting in moistures diffusing from the resin into theof bleeder is much larger than that of prepregs 11 , thevoid. Finally , new equilibrium state is arrived at thepressure gradient in the resin that has entered thebigger diameter of void. If ambient temperaturebleeder can be neglected comparatively to that in thevaries, the saturated vapor pressure will vary , alsoresin of prepreg layers.I hus the pressure in resinmatrix on top of the composite is approximately equalvoid or reverse. Moreover , the variation of tempera-ture leads to the pressure inside the void being varied ,to the pressure in the pores of bleeder , P,.then leads to expansion or shrinkage of void and theInitial conditions are :Vj=Vo，t tp)( 15)d.xWhere D is diffusion cofficient ,dc1dx is con-If the volume variation of resin during cure cyclecentration gradient , M is diffusion rate per unit area.is neglected , the thickness of laminate and every layer，An eauation about the diffusion of moistures incan be expressed as follows :the中国煤化工is derived as fllws ac-l(j)= Volo/V{j )(16)cordMYHC N M H Gthe law of mass conser-h =2(j)( 17)vatiortj=1dc= D["2?c1( 20)Here n is the total number of piles,l( j )is thedt =. ar2rJr」thickness of No j layer , lo is the initial thickness ofHere c is the water vapor concentration , dcIdt一.34一Vol.9 No. 2HIGH TECHNOLOGY LETTERSJun.2003and 3c/ 3r are change rate of concentration and con-d;/2c=c;(22)centration gradient at a radial coordinate r respective-{之心ly ,with r=0 at the center of the void.Boundary conditions of Equation( 19 )are as follows :Initially( t <0 ) the vapor is taken to be dis-c=cmr=d/2,t≥0(23)tributed uniformly in the prepreg at the known con-.c=c;r→∞t≥0centration C;. At times t≥0 the vapor concentrationd; is the initial diameter of void ,d is the void diame-at the void-prepreg interface" cm” is saturated withterattimet.the partial pressure of vapor inside the void and theThe mass of vapor transported in time t throughtransfer of vapor at the void-prepreg interface is inthe surface of the void is :dynamic equilibrium for the reason that the diffusionresistance in resin is much larger than that at them=m20(导)dt(24)void-prepreg interface. Cm should be determined byFor a void of known location and initial size ,thetemperature and the partial pressure of vapor insideinitial mass of water vapor and air in the void is .the void. For an ideal mixture system , Raoult's lawknown , its size and the pressure inside it at any timeor Henry 's law should be obeyed , but the mixture ofcan be predicted.resin and moisture is a real mixture system , the ex-pression about Cm is modified as follows :5 Residual Stress FormationCm = m中”.(21)Where φ is relative humidity inside the void , theResidual stress is due to the interaction of theconstant m and n are different in the different resinplies with different orientations after curing67] ,it istype.showed in Fig.3. The free strain of No k ply withoutInitial conditions of Equation( 20 ) are as fol-restraint caused by temperature difference is :lows :initial statewithout stresseN(O)ultinate stateextemperaturewi thout restraintdifference 0Tk(90) e R(O)real ul timateσ, R(0statedifference OTFig.3 The formation of residual stress lead by temperature difference\( k)\the layer is as follows :N( k)(k)lOT(25 )(eM(k),{ak; } is thermal expansion coefficients matrix in中国煤化工off- axis coordinate systems,OT= Tmx-To , Tmex isMHCNMHGrhe(26 )the maximum temperature in No k layer during cur-ing process.(x-eN(r)The real strain due to the mutual restraint be-For the in-plane situation , the residual stress matrixtween the layers is { }, thus the residual strain ofofNoklayeris:一，35一Vol.9 No. 2HIGH TECHNOLOGY LETTERSJun.2003Rk)Q) Q台Q化》eR1R(k)Q名)Q22) Q26∈R }(27)r的,σxQ1g) Q2g) Qf)Qj is modules matrix in off-axis coordinate sys-tems. The residual stress matrix of No k layer in on-axis coordinate systems is expressed as :r。Rk)2mnR( h)ln2-mnmnm2-nR(k),(28)Where m=cosθ m = sinθ ,θ is the layup angle of Nok layer.Above equations comprise the equations neededfor calculating the residual stresses in each ply. Thspecific formula derivation process about residualstress , the conversions between the expansion coeffi-cients in off-axis coordinate system and the expansioncoefficients in on-axis coordinate systems , the conver-sions between module matrices in off-axis coordinatesystem , on-axis coordinate system and the engineer-ing constant of composite , such as Young's moduleand Poisson's ratio etc , are referred to in Reference[6]References[1] Ciriscioli P R , Springer G S. Smart Autoclave Cure ofComposites, Lancaster , PA : Technomic Publishing Co ,Inc , 1990[2] Telikicherla M K ,Li X ,Altan M C, et al. NumericalStudy of Conjugate Heat Transfer in Autoclave Curing ofThermosetting Composites , Thermal Processing of Materi-als :Thermo-Mechanics，Controls，and Composites ，HeatTransfer Division. ASME. New York , ( Publication )HTD, 1994 ,289 213-221[3]Gutowski T G , Morigaki T ,Cai Z. Journal of CompoiteMaterials , 198721( 9):172[4 ]Gutowski T G ,CaiZ , Bauer S. et al. Journal of Compos-ite Materials , 1987 ,21( 7): 650[5]Lay B, Brunet M , Boivin M. Journal of Materials Pro-cessing Technology , 1998 77 3 ):254[6] Jones R M. Mechanics of Composite Materials , 2nd ed ,Taylor & Francis. Philadelphia , PA :c1999[7 ]Beaumont P W R ,Cowley K D. Composites Science andTechnology ,1997 ,5X 11):1445Wang Zhengping, born in 1958 , Professor ofChemistry Engineering Department ，Harbin engi-中国煤化工neering university. Research area : Technology pro-MHCNMHG.cess of chemistry engineering and materials.一36一