Numerical prediction of temperature distribution in thermoset composites during laser curing process

ISSN 1009 - 3095 Joumal of Zhejiang University SCIENCE V.3 No.2 P. 162 - 165 Apr. - June , 2002http ://www. periodicals. com. cn ; http ://www. zju. edu. cn/English162http :// www. zjupress. com ; http ://lib. zju. edu. cn/ eindex. htm ; jzu_ s@ mail.hz. zj. cnNumerical prediction of temperature distribution in thermosetcomposites during laser curing processW∪Cun-zhen( 吴存真), SUN Zhi-jiar(孙志坚), XU Jian-feng 徐剑锋), QIN Yue-hu(秦悦慧)( Department of Energy Engineering , Zhejiang University , Hangzhou 310027，China )Received June 26 2001 ; revision accepted Oct. 15 2001Abstract : The temperature distribution in the advanced thermoset composite during the laser curingprocess was predicted with the use of the l wo-dimensional thermo-chemical model presented in this pa-per which also gives the governing equations based on the thermal history of the curing process. The fi-nite-difference method was used to get the temperature distribution. This paper also deals with the ef-fect of some factors( such as the w inding velocity , the tape thickness and the laser heat source ) on thetemperature ditribution.Key words: Thermoset composites ，On-line curing ，Temperature distribution ，Degree of curing ，Laser heat sourceDocument code : ACLC number : TK214INTRODUCTIONsults for a glass/ polyester composite were ob-tained by Kim et al.( 1995 ). However , theirLarge thermoset filament- wound or fiber-analyses were based on the steady state andtape- w ound composite structures are widely there was no open report on the on-line laserused to form rigid ，lightweight aerospacecuring process.components，underground pressure vessels ,A two-dimensional thermo- chemical mod-and tubing. In manufacturing such struc-el for the on-line laser curing of thermosettures , the fiber is firstly wound and thencomposite is presented in this paper. A mov-batch-cured in an oven or autoclave in the tra- ing laser heat source and moving boundary areditional method. During the curing process ，adopted in the analysis. Temperature withinthe resin network grows into longer chains the composite during processing is predictedwith branches and cross-lin kings .numerically and the effects of process parame-In the on-line laser curing method ,a laserters on the temperature distribution are ana-heat source is directed incident to the local lyzed .area of the w ound structures to initiate resincuring during the winding process. This ANALYSISmethod offers the possibility of a more uni-form degree of cure and hence less severeresidual stresses distribution in the finishedIn the analysis ,a rectangular，transverse-strueture. Moreover , this process is expected ly isotropic tape of width wply and thicknessto have greater energy ffciency , higher pro- 'ly is considered and shown in Fig.1. Theductivity , be less size restricted and use less tape is wound circumferentially at a constantfloor space compared with the standard batch- 90° winding angle( hoop winding ) at a feedoven curing. Studies related to this on-linerate中国煤化工mandrel of diame-curing are limited. A thermo-chemical modelerHCNMHG velocity 2U/D.was developed by Chern et al. ( 1995 ). A Due to me accreton oI ply layers during thethermo-chemical model of self-sustaining cur- winding ，this condition is not strictly satisfieding process w as developed and numerical re- for long time winding ; but for a practicalProje万方熬据, the cooperation programme of Nebraska University( U.S. A. ) and Zhejiang Universits( China ).Numerical prediction of temperature distribution in themoset composites163Laser heatposite is wound onto the mandrel ply by plysourceand the laser heat source movies with velocityrelative to the mandrel ，so the computationIncoming tape with velocity u| xMandrsldomain and the boundary condition changewith time.1. Energy equationU nder these assumptions , the governingequations are as follows.For the thermoset composites , the ener-gy equation is :Computationaldomain thickness HJTaT2Tρ.CeJt+ ρ.C.UdQFig.1 Physical geometry+ρe dt( 1)where ρ is mass density，C is specific heat，winding situation ，it is satisfied providedU is tape speed，h is thermal conductivity.2H/D≤1. A cylindrical-coordinate system Subscript represents thermoset composite, l( R ,θ，z )having its z-axis coincident withrepresents along fiber axis direction. The twothe mandrel' s axis is used to describe the terms on the left-hand side of Eq.( 1 )are themandrel and the composite geometry. Forunsteady term and the energy transport bytypical plies used in tape winding ，tply/ Wpl≤advection due to ply motion ，respectively .1 , so that variations in the axial( z ) directionThe first two terms on the right-hand side ofare negligible ; the problem is thereby reducedEq.( 1 ) are energy transport by thermal dif-to two dimensions : R and θ. The laser ener- fusion along the fiber and transverse fiber di-gy is assumed to be incident upon a given arc .rections , respectively. The last term on thelength of the cylinder' s periphery. All the ra- right-hand side of Eq.( 1 )is the rate of heatdiant energy deposition and primary heatreleased by chemical reaction .transfer are assumed to occur in a thin surfaceThe boundary conditions for Eq.( 1 ) arelayer of radial thickness H (《D/2 ) com-assumed as described below .prised of the n outermost plies. It is furtherSurfaces( 1 ) and (3 ) are connected toassumed that 2H/D≤1 ,so that the curva- each other ,so :ture of the surface layer can be neglected andAdiabatic condition of Surfaces ( 1 ) andthe annular physical domain can be simplified ( 3 ):into the rectangular computational domain( X, Y)( Fig.2 ). In the model，the com-x=0(2 )Convective condition of Surface( 2 ):Moving lasern the grid with laser heat input :heat sourceConvectiveSurface (2)heat losshe= -h( T- T.)+ sq (3)Ply"where sq is rate of laser heat input，h is con-Surface(1)(3)vective heat transfer coefficient .In the grid without laser heat input :中国煤化工一Tu)(4 )AdialPly2YHCNMH Gace(4):Ply1Surface (4)戈=0(5 )2. Cure kinetics equationComputation domainDue to its wide use in industry and the .164WU Cunzhen , SUN Zhjjian et al.availability of a cure kinetics model( Loos et rameters are asfollows : convective heatal.，1983 ), the Hercules AS/3501-6 resin transfer coefficient h : W/ m2. K ); plysystem is used in the present study. I oos'thickness ( in y direction )tpl， : m ; rate ofmodel is used to estimate the heat release dQ/laser heat input sq :W/ m- ; thermal conduc-dt as a function of the degree of cure a andtivity along fiber axis direction hl : W/( m'temperature T. In this model a is defined toK ); tape speed U : m/s. The steep ramp-upbe the ratio of the exothermic heat releasedon the right-hand of each ply is primarily dueQch until some intermediate time to the totalto the laser heat input because the last twoexothermic heat released Qiot when all cross-points along the X axis are the points thatlinking reactions are complete. The incoming have just got the laser heat input under thetape is assumed to be totally uncured : a = 0.moving laser heat source assumption. It canalso be seen from Fig.3 that the temperature3. Numerical method of the modelof the later- wound ply is higher than the pre-Control volume formulation is employed tovious ply temperature ; and that the trans-solve the energy equation. Detailed derivation verse-fiber diffusion is less. The relativelyof the two-dimensional discretization equationhigher temperature on the left side of the firstwas given by Patankar( 1980 ). The resulting ply is due to the sy mmetrical matching condi-algebraic equations were solved by SLURtion for the first ply. The effects of some pro-method. After obtaining the new temperature cess parameters on the temperature distribu-fields，the degree of cure is determined bytion are considered here and shown in Figs.4solving the cure kinetics equations.- 6. W hen one parameter is considered , oth-ers are kept constant. The temperature in theRESULT AND DISCUSSIONply decreases with the increase of the tapespeed( Fig.4 ) and the increase of the tapethickness( Fig.5 ). It can be seen from Fig.6The most primitive results of the analysisthat the greater the laser heat input，theare the ply-by-ply temperature profiles during higher is the temperature in the ply. Yet toothe curing process. In Figs. 3-6，the hori- great heat input will cause material degrada-zontal axis shows the grid points of compositetion , which must be prevented. The effect ofply along X-axis. The values of the Y-axis the convective heat transfer coefficient be-indicate the temperature of the ply when itstween the air and composite on the tempera-layout has just finished. The unit for the pa-ture is relatively small .600 ;-1-415550600 F- -1025500500年老450I是450400 E350中国煤化工300335*30-33YRCNMHG510 3sGrid points along X-axis0nd points along X-axisFig.3 Temperature distribution in the pliesFig.4Effect of tape speed on the tempera-tpy=1x 10-4，sq=0.5x 106 ,5 ,kl=6, U=0.15tpy=2x 10-4 ,h=5 sq=1x10° ,kl=6Numerical prediction of temperature distribution in thermoset composites165751 fr。7010+ 120650E -123650600 -18600是s50兰55500450400101520253035Grid points alone x-axisOrid poimnts along XaxsFig.6 Effect of laser heat input on the tem-Fig.5Effect of tape thickness on the tem-peratureh=5 ,kl=6, U=0.1，l= 1.194x 10-4sq=0.75x 106 ,h=5，kl=6, U=0.1continuous curing process for thermoset poly mercomposites. Part I : modeling and demonstration .CONCLUSIONSJournal of Com posite materials , 29( 1 ): 1222 -1234 .A numerical thermo-chemical model forKim ,D.H. , Han,P.G. ,Jin G. H. et al. , 1997. Amodel for thermosetting composite pultrusion pro-the on-line curing of thermoset composite iscess. Journal of Composite Materials ，31( 20 ):established. The temperature distribution in2105 - 2122 .the composite is presented. The effects of Kinsey ,S.P. , Haji-Sheikh ,A. , Lou ,D.Y.S. , 1997.various process parameters on the temperatureA thermal model for cure of thermoset compositesJournal of Materials Processing Technology ，63 :are also discussed. Since the model can pre-442-449.dict the temperature distribution in the com-Loos A.C. ,Springer ,G.S.，1983. Curing of Graphite/posite during the curing process , the methodEpoxy Composites , Ph. D. Dissertation , Universitydeveloped can serve as design tool for the on-of Michigan , Ann Arbor，M ichiganline laser curing of thermoset composite.Patankar ,S. 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