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Computational Approaches for Modeling the Multiphysics in Pultrusion Process

Carlone P Baran Ismet Hattel Jesper Henri Palazzo GS

Published inAdvances in Mechanical Engineering

Link to article DOI1011552013301875

Publication date2013

Document VersionPublishers PDF also known as Version of record

Link back to DTU Orbit

Citation (APA)Carlone P Baran I Hattel J H amp Palazzo G S (2013) Computational Approaches for Modeling theMultiphysics in Pultrusion Process Advances in Mechanical Engineering 2013 [301875]httpsdoiorg1011552013301875

Hindawi Publishing CorporationAdvances in Mechanical EngineeringVolume 2013 Article ID 301875 14 pageshttpdxdoiorg1011552013301875

Research ArticleComputational Approaches for Modeling the Multiphysics inPultrusion Process

P Carlone1 I Baran2 J H Hattel2 and G S Palazzo1

1 Department of Industrial Engineering University of Salerno Via Giovanni Paolo II 84084 Fisciano Italy2 Department of Mechanical Engineering Technical University of Denmark 2800 Kgs Lyngby Denmark

Correspondence should be addressed to P Carlone pcarloneunisait

Received 30 August 2013 Accepted 4 November 2013

Academic Editor Nao-Aki Noda

Copyright copy 2013 P Carlone et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Pultrusion is a continuousmanufacturing process used to produce high strength composite profiles with constant cross sectionThemutual interactions between heat transfer resin flow and cure reaction variation in the material properties and stressdistortionevolutions strongly affect the process dynamics together with the mechanical properties and the geometrical precision of the finalproduct In the present work pultrusion process simulations are performed for a unidirectional (UD) graphiteepoxy compositerod including several processing physics such as fluid flow heat transfer chemical reaction and solid mechanics The pressureincrease and the resin flow at the tapered inlet of the die are calculated by means of a computational fluid dynamics (CFD) finitevolumemodel Several models based on different homogenization levels and solution schemes are proposed and compared for theevaluation of the temperature and the degree of cure distributions inside the heating die and at the postdie region The transientstresses distortions and pull force are predicted using a sequentially coupled three-dimensional (3D) thermochemical analysistogether with a 2D plane strain mechanical analysis using the finite element method and compared with results obtained from asemianalytical approach

1 Introduction

Pultrusion is a continuous manufacturing process used torealize constant cross sectional composite profiles In recentyears the pultrusion process experienced a remarkable grow-ing within the composite industry due to its cost-effect-iveness automation and high quality of products Nowadaysthe process is widely used to manufacture highly strength-ened structures such as wind turbine blades window profilesdoor panels and reinforcing bars for concrete Moreover insome applicative sectors such as in the automotive industrythe environmental impact of pultruded composite structuresover the entire life cycles results is lower than other engi-neeringmaterials [1] A schematic view of the pultrusion pro-cess is depicted in Figure 1 During the process the reinforce-ment fibers in the form of rovings or mat are pulled throughguiders and impregnated by the resin material in an openbath or employing a resin injection chamberWetted out rein-forcements are then pulled via a pulling mechanism throughthe heating die The die inlet is typically characterized by a

tapered or a conical convergent shape in order to promote thedesired impregnation and compaction of the reinforcementthe removal of the air and the excess resin In the straightportion of the die the heat provided by means of electricalheaters or hot oil activates the exothermic cure reaction ofthe thermoset resin As a consequence the material changesits status from reactive liquid to gel and then vitrifiedsolid [2 3] The thermochemical behavior of the processingthermoset resin generally represented by time-temperature-transformation (TTT) diagrams [2ndash4] is a crucial issueDuring the curing process the resin shrinks because of thechemical reaction (cross linking) promoting the contractionof the work piece Besides that the part continues contractingdue to the cooling effect for example convective cooling atthe postdie region At the end of the process the cured andsolidified product is cut into desired lengths

Even if the process is conceptually quite simple the anal-ysis of its dynamics and the definition of optimal processingparameters are a complex task due to themutual interactionsbetween involved physical phenomenamainly related to heat

2 Advances in Mechanical Engineering

FibersFiber guides

Resin bath

Heating die Puller Saw

Pulling direction

Figure 1 Schematic view of the pultrusion domain for the compos-ite rod

transfer species conversion and phase changes die-materialcontact and stress-strain development Several researchershave performed numerical and experimental investigationson different aspects inherent to the pultrusion processmainly focusing on issues related to heat transfer and cure[5ndash11] pressure distribution [12 13] and pulling force [14ndash20] However proposedmodels often neglect the interactionsbetween involved phenomena on the base of some simpli-fying assumptions Most of the published works convergeon the conclusion that the mechanical properties and thequality of the pultruded composite are strongly affected bythe degree of cure (DOC) distribution and the applied pullingforce The aforementioned features in turn depend on thepull speed die temperature die geometry constituentsrsquo typeand volume fractions Furthermore the pulling force consistsof different contributions such as the bulk compaction forcedue to the pressure increase in the tapered portion of the diethe viscous drag acting in the liquid zone and the frictionalforce due to the contact between the internal surface ofthe die and the solidified processing material [2 3 18ndash21]Experimental outcomes reported in [14] by Price and Cup-schalk showed the impact of the materials volume fractionsdie temperature and pull speed on the pull force It wasalso indicated that for a constant temperature and pullingspeed the force increases exponentially with the volumeof material Lackey and Vaughan carried on an extensiveexperimental and statistical investigation on the influence ofprocess parameters on the pulling force and flexural strengthof pultruded products employing a five-factor half-factorialcentral composite design (CCD) It was concluded that theprocess parameters affect the pulling force according to com-plex interactions whose overall effect may vary significantlyusing resin systems characterized by different cure kinetics[15] Considering the elevated number of variables involvedin the aforementioned problem a satisfactory experimentalanalysis could result in undesired time and money spendingFurthermore pure experimental tests may have no solidpredictive capability As a consequence the development ofsuitablemultiphysicsmodels is highly required for compositemanufacturing processes In-plane stresses and deformationsin composite laminates can also be related to the interactionbetween the tool and the part [22] Besides the temperatureand the DOC gradients through the composite thicknessalso promote the development of residual stresses in themanufactured part [23] A better understanding of thesephenomena which take place in the heating die as well asin the postdie region is highly required to reduce processinduced shape distortions and residual stresses and to obtain

a realistic analysis of inservice loading scenarios and reliabil-ity assessments [24 25] It should be noted that the generalmechanical behavior of the composite material is orthotropic(transversely isotropic if only unidirectional fibers are used)and the coefficient of thermal expansion (CTE) of thepolymer-matrix materials is usually much higher than that ofthe fibersHence dimensional variations and internal stressesare induced mainly due to the curing shrinkage of resin andthe mismatch in the CTE of the fibers and the resin matrix[26]

In the present work several processing models dealingwith different phenomena are combined to simulate themanufacturing of a pultruded productThis approach has notbeen considered up to now for the analysis of the pultrusionproviding a better understanding of the entire process at aglance A schematic representation of the implementedmod-els including outputs and relative connections is depicted inFigure 2

In particular pultrusion process simulations are per-formed for a unidirectional (UD) graphiteepoxy compositerod including different processing physics with the aim topredict the pulling force and the stressdistortion evolutionsin the processingmaterial All the contributions to the overallpulling force have been accounted for in the present workThe pressure increase which is responsible for the bulk com-paction force has been derived by means of a computationalfluid dynamics (CFD) model of the resin flow field atthe inlet and solved using a finite volume (FV) approachThe reinforcing fibers have been modeled as an anisotropicporous media with directional permeability in accordancewith the Gebart modelThe temperature and the DOC distri-butions inside the heating die and at the postdie region areobtained by means of a three-dimensional (3D) thermo-chemical analysis Two different modeling approaches areimplemented a continuous finite element (FE) model and aporous FV model based on different homogenization levelsand solution schemes Bothmodels provide the viscosity fieldallowing one to infer the viscous drag acting in the liquidzone Furthermore two solution strategies have been devel-oped and compared for the prediction of the normal pres-sure which generates the frictional force between the pro-cessing material and the internal die surface after resin gela-tion In the first case numerical outcomes provided by the FVporous model have been analytically processed consideringthe well-established relations of the continuous mechanicsresulting in a semianalytical method (SAM) In the secondapproach the transient stresses distortions and frictionalpull force are predicted using a sequentially coupled 3Dthermochemical analysis together with a 2D plane strainmechanical analysis using the finite element method (FEM)In both cases the evolution of the mechanical properties ofthe processingmaterial is computed using the cure hardeninginstantaneous linear elastic (CHILE) approach [25 27] Thepaper is organized as follows in Section 2 the theoreticalmodeling and the governing equations are described in detailwhile in Section 3 the obtained results are exposed anddiscussed Finally in Section 4 the relevant findings and thefuture perspectives of this research are highlighted

Advances in Mechanical Engineering 3

Impregnation model

Thermochemicalmodel

Mechanical model

Compacting pressure Compaction force

Pull force

Residual stresses

Work-piece distortions

TemperatureDegree of cure

Resin viscosity

Physical and mechanical properties

Viscous drag

Die-composite pressure

Stress-strain distribution

Therm

al stra

in

Chemica

l strai

n

Figure 2 Implemented models and coupling effects in pultrusion

z

Heating platens

Gel zone Solid phase

Detachment pointDie

Pultruded composite

product

Impregnated fibers

Viscous force

Frictional force

Compaction force

Gelation point

Pull direction

Thermal contact resistance

Liquid phase

Figure 3 Phase changes and force contributions in pultrusion

2 Theoretical Modeling andNumerical Implementation

21 Pull Force Model As aforementioned four differentcontributions to the overall pulling force in pultrusion havebeen identified in the literature [2 3 14ndash21] the collimationforce 119865col the bulk compaction force 119865bulk the viscous drag119865vis and the frictional force 119865fric These contributions arestrictly related to the geometrical features of the die-workpiece system and to the resin transitions from liquid to geland then solid status as schematized in Figure 3

The first contribution 119865col is due to resistances arisingfrom the creel to the die inlet and it is generally assumed tobe negligible As a consequence the pulling force 119865pul can beexpressed as follows

119865pul = 119865col + 119865bulk + 119865vis + 119865fric asymp 119865bulk + 119865vis + 119865fric (1)

119865bulk is related to the increase in the resin pressuretypically observed in the initial part of the die that is whenthe resin is still in liquid phase The die inlet is generallydesigned as tapered (120579 le 10∘) or rounded shapes [4] in orderto promote the constituents compaction reducing fibers dam-age Moreover the resulting over-pressure allows the resin tocompletely fill the reinforcingmaterial porosities At the sametime this overpressure forces the excess resin to flow back asdepicted in Figure 4The excess resin is usually recovered and

Straight die

Intersection point

Resin backflow

Compacting

Tapered

Impregnated fibers

pressure p

120579

length Li

Figure 4 Resin flow and pressure increase at the die inlet

redriven to the open bath for the fiber impregnation Whilethe resin is in a liquid status at the die entrance the force dueto the applied pressure acts along a direction normal to thedie surfaces As a consequence it does not affect the pullingforce except at the tapered die entrance (Figure 4) Definingthe local resin pressure as 119901 the die taper angle as 120579 and theinlet surface as 119860

1 the bulk compaction term can be written

as follows

119865bulk = ∬1198601

119901 sin 120579 119889119860 (2)

In the straight portion of the die the increase in thetemperature of the processing resin due to the heat providedby the heaters activates the exothermic cure reaction Thecrosslinking of the thermosetmonomers in conjunctionwiththe existing temperature field provides two relevant pheno-mena namely gelation and vitrification inwhich the status ofthe resin is changedThe term gelation refers to the transitionof the catalyzed resin from viscous liquid to gelled (rubbery)solid This transition is associated with the achievementof a certain degree of cure or polymerization (degree of


Moving fibers

Die wall Resin

120582

Figure 5 Couette flow in the liquid region

cure at gelation 120572gel) which corresponds also to a sharpincrease of the resin viscosity Vitrification (glass transition)is not rigorously associated with a specific extent of thecure reaction but with the (120572-dependent) glass transitiontemperature (119879

119892) If the resin temperature is below 119879

119892 it

behaves as a vitrified (glassy) solid Differently from gelationvitrification is a reversible phase change

Before the gel point viscous drag occurs at the die wallThis resistance is imputable to the presence of a thin liquidlayer between the travelling fibers and the stationary diesurface Thus a plane Couette flow is induced in whichthe reinforcing fibers are assumed to be the moving platetranslated at a constant pull speed and the die surface as thefixed plate A schematic view is shown in Figure 5 [17] Theviscous force can be written analytically as follows

119865vis =Vpul120582

∬1198602

120578 (120572 119879) 119889119860 (3)

where 120582 is the thickness of the resin layer between the solidboundary and themoving fibers 120578 denotes the resin viscosityVpul is the fiber pull speed and 1198602 is the surface interested byviscous effects whose length is determined by the gel-pointSeveral approaches for the estimation of 120582 have been adoptedin the literature mainly based on the fiber packing the radius119903119891 the volume fraction V

119891 or permeability considerations

[16 17] In the present investigation the following relation hasbeen employed [17]

120582 = 119903119891(1 minus

1

2

radicradic3120587119881

119891

2) (4)

The rheological behavior is herein modeled following thewell-recognized three parameters correlation model [12 1316 17] which is expressed as follows

120578 = 120578infinexp(

Δ119864120578

119877119879+ 119870120572) (5)

where119877 is the gas constant119879 is the absolute temperature 120578infin

Δ119864120578and119870 arematerial parameters provided by experimental

data fittingAfter the gel point the resin flow and the viscous

effects are obviously inhibited and the composite is mechan-ically pulled through the die Consequently the interaction

between the processingmaterial and the die surface is mainlycharacterized by frictional effects Generally the entity of thefrictional force can be inferred by considering the frictioncoefficient 120583 and the contact pressure 120590 according to thefollowing equation

119865fric = int1198603

120583 sdot 120590 119889119860 (6)

being1198603the die surface from the gel-point to the detachment

point It should be noted that the value of the frictioncoefficient depends on theDOCduring the resin gelation andfurther varies at the glass transition However due to the lackof thorough experimental data generally the averaged valuesare utilized [14ndash21] Regarding the magnitude of the contactpressure 120590 is considered to be affected by two contrastingconditions the transverse thermal expansion of the compos-ite due to the increase in temperature and pressure and theresin chemical shrinkage related to crosslinking reactionThelatter phenomenon leads to a progressive reduction in the sizeof the composite cross section until it shrinks away from thedie internal wall (detachment point)

It is worth noting that the separation of the processingmaterial from the die cavity induces the formation of a thin(thermally insulating) air layer As a consequence a thermalcontact resistance (TCR) is interposed between the heated dieand the processingmaterial In the present investigation eachcontribution has been computed using the numerical and thesemianalytical models as explained in detail in the following

22 Impregnation Analysis In a conventional pultrusionprocess reinforcing fibers are wetted out inside the resin bathbefore entering the heating die After the impregnation thewetted fibers typically show an excess of resin with respect tothe amount needed for the final product As a consequencein the tapered zone of the die (inlet) the processing materialis compacted resulting in a pressure increase with respectto the atmospheric value Material compaction is affectedby several factors such as the volume fraction and thepermeability of the reinforcement the resin viscosity andthe geometrical features of the die-material system [12] Theimpregnation model describes the pressure distribution andthe resin flow in the first part of the die including thetapered or rounded zone and a portion of the straight die(Figure 4) Velocity and pressure in the reinforcement-freezones of the domain are inferred by means of the conjunctsolution of the well-known mass and momentum equationsIn particular since the early part of the die is not heated inorder to avoid premature resin gelation it is assumed thatthe temperature and the DOC variations are negligible andtherefore the resin viscosity remains constant Furthermoreunder the hypothesis of incompressibility of the liquid resinand neglecting body forces the equilibrium equations can bewritten as follows

120597119906

120597119909+120597V120597119910

+120597119908

120597119911= 0

120578(1205972

119906

1205971199092+1205972

119906

1205971199102+1205972

119906

1205971199112) minus

120597119901

120597119909= 0


120578(1205972V

1205971199092+1205972V1205971199102

+1205972V1205971199112

) minus120597119901

120597119910= 0

120578 (1205972

119908

1205971199092+1205972

119908

1205971199102+1205972

119908

1205971199112) minus

120597119901

120597119911= 0

(7)

where 119906 V and 119908 are the velocity components of the resinalong the 119909 119910 and 119911 directions respectively and 119901 is theliquid pressure The reinforcing fibers have been treated asa moving porous media in which the porosity and thepermeability vary according to geometrical considerationsensuring always the final fiber volume The following mod-ified Darcy model has been solved in the porous region

119906 = 119880 minus119870119909119909

120578Φ

120597119875

120597119909

V = 119881 minus

119870119910119910

120578Φ

120597119875

120597119910

119908 = 119882 minus119870119911119911

120578Φ

120597119875

120597119911

(8)

where 119880 119881 and119882 represent the velocity components of theporous media along the 119909 119910 and 119911 directions respectively Itshould be noted that assuming that 119911-direction is the pulldirection the component 119882 is constant and it is the onlynonzero term in the straight portions of the domain whileother components should be locally modified consideringthe geometric configuration of the tapered zone [12] Towpermeability has been defined according to the Gebart modelas follows

119870119909119909

= 119870119910119910

= 1198621(radic

119881119891max119881119891

minus 1) 119903119891

2

119870119911119911=

8119903119891

2

119888

(1 minus 119881119891)3

119881119891

2

(9)

where 119903119891is the fiber radius 119881

119891max the maximum achievablefiber volume fraction 119862

1and 119888 are constants equal to 0231

and 53 respectively [13] The impregnation model has beenimplemented and solved using a FV schemeThe commercialsoftware ANSYS-CFX has been employed for this purposeThe pressure distribution provided by the impregnationmodel is then used in (2) to evaluate 119865bulk

23 Thermochemical Analysis In this section theoreticalbackgrounds of the implemented continuous and porousmodels are presented

231 Continuous Model The basic assumption of the con-tinuous (homogenized) model is that in each location of theprocessing composite material all the constituents experi-ence the same temperature As a consequence the wholetemperature field is established solving a unique nonlinear

equation using the lumped material properties [4ndash11 16ndash18]which can be written as follows

120588119888119862119901119888

(120597119879

120597119905+ Vpul

120597119879

120597119911)

= 119896119909119888

1205972

119879

1205971199092+ 119896119910119888

1205972

119879

1205971199102+ 119896119911119888

1205972

119879

1205971199112+ 119881119903119902

(10)

where 119879 is the temperature 119905 is the time 120588119888is the density

119862119901119888

is the specific heat 119896119909119888 119896119910119888 and 119896

119911119888are the thermal

conductivities of the composite material along 119909 119910 and 119911

directions respectively and 119881119903is the resin volume fraction

Material properties are assumed to be constant throughoutthe processThe source term 119902 in (10) is related to the internalheat generation due to the exothermic resin reaction and isexpressed as follows

119902 = 120588119903119867119905119903119877119903 (11)

where 119877119903is the reaction rate119867

119905119903is the total heat of reaction

and 120588119903is the resin density

Several kinetic models have been proposed and discussedin the inherent literature to describe the evolution of the curereaction In the present investigation thewell-established 119899th-order model has been adopted assuming an Arrhenius typedependence on the absolute temperature

119877119903(120572 119879) =

120597120572

120597119905=

1

119867119905119903

119889119867 (119905)

119889119905= 1198700exp(minusΔ119864

119877119879) (1 minus 120572)

119899

(12)

where 120572 is the degree of cure and 119867(119905) is the heat generatedduring cure The above equations have been solved in a3D domain using a FE approach The evaluation of theDOC and the reaction rate has been obtained by meansof an iterative inhouse developed routine implemented intothe commercial software package ABAQUS [28] until thematching of temperature and DOC tolerances to reach thesteady state The DOC is obtained by using the followingdiscretization [7 25]

(120597120572

120597119905+ Vpul

120597120572

120597119911) = 119877

119903(120572 119879) (13)

232 Porous Model Differently from the continuous modelthe porous model treats the pultrusion process as a reactiveliquid (resin) flow through a moving porous media (rein-forcement) inside a defined rigid boundary (die cavity) Inother words it is a CFDbased nonthermal equilibriummodelconsidering each component as a different entity on macro-scale therefore a finite difference between the reinforcementand the matrix temperatures is admitted As a consequencebesides the continuity and the momentum equations for thefluid phase one energy balance equation for each compo-nent is needed This allows heat to be transferred betweencontiguous phases Assuming that the processing compositeis only composed by the reacting resin and the fibrousreinforcement that is neglecting voids and porosity effects


the temperature field can be obtained by solving the followingequations

120593119891120588119891119862119901119891

120597119879119891

120597119905+ 120588119891119862119901119891

Vpul120597119879119891

120597119911

= 120593119891(119896119909119891

1205972

119879119891

1205971199092+ 119896119910119891

1205972

119879119891

1205971199102+ 119896119911119891

1205972

119879119891

1205971199112) + 119876

119903119891

(14)

120593120588119903119862119901119903

120597119879119903

120597119905+ 120588119903119862119901119903

(119906120597119879119903

120597119909+ V

120597119879119903

120597119910+ 119908

120597119879119903

120597119911)

= 120593(119896119903

1205972

119879119903

1205971199092+ 119896119903

1205972

119879119903

1205971199102+ 119896119903

1205972

119879119903

1205971199112) + 120593119902 + 119876

119891119903

(15)

where the subscripts 119903 and 119891 refer to the resin and fiberrespectively In the above equations 120593 = 1minus120593

119891represents the

volume porosity of the medium (ratio between the volumeavailable for fluid flow and the total volume) Assumingthe absence of voids 120593 coincides with the resin volumefraction 119881

119903= 1 minus 119881

119891sdot 119876119903119891

= minus119876119891119903

is the interfacial heattransfer between the fluid and the solid depending on thetemperature difference the interfacial area density and thephysical properties of the two phases It should be borne inmind that in the porous model the DOC is treated as anadditional scalar variable with transport properties existingonly in the fluid phase and varying according to a sourceterm generated by the reaction rate previously defined in(12) Similarly the heat generation term 119902 in (11) is restrictedto the reactive resin and the exothermic reaction affects thefiber temperature by means of conductive heat transfer Asfor the impregnation model the software ANSYS-CFX [29]has been used to solve the porous thermal model employinga FV numerical scheme The temperature and the DOCdistributions are utilized to compute the resin viscosity andthe viscous drag according to (5) and (3) respectively

24 Mechanical Analysis As mentioned above the pro-cess induced stress and distortions including also the die-composite contact pressure are predicted using the twodifferent procedures The former approach is based on thesolution of a 2D quasi-static FE mechanical model sequen-tially coupled with the 3D continuous thermochemical FEmodel The latter is a semianalytical approach based on theapplications of the well-established principles of the linearelasticity to the results provided by the above describedporous model

241 FE Model In this model the 2D cross section of thepart is assumed to bemoved along the pulling direction whiletracking the corresponding temperature and DOC profilesprovided by the FE model A detailed description of thisprocedure that is the mapping of the predicted fields (119879120572) to the 2D mechanical plain-strain model is shown inFigure 6 The implemented mechanical FE model assumesthat the longitudinal strains that is parallel to the pullingdirection are negligiblewith respect to the transverse compo-nents of the strain tensor This approximation is well jus-tified considering the remarkable difference for pultruded

products between in plane (cross sectional) and out of plane(product length) dimensions being the former of few squaremillimeters and the latter of several meters before the cutoutAs a consequence the problem can be reduced to a twodimensional plane strain analysis as discussed in [25] Thecorresponding transient distortions and the evolution of theprocess induced stresses and strains are calculated consider-ing the temperature and the cure distributions assuming thefollowing contributions to the incremental total strain (Δ120576tot)

Δ120576tot = Δ120576mech + Δ120576th + Δ120576ch (16)

where Δ120576mech is the incremental mechanical strain Δ120576th isthe incremental thermal strain and Δ120576ch is the incrementalchemical strain due to the volumetric shrinkage of the resinThe details of the relations between the stress and straintensors used in the present FE approach can be found in [25]

The CHILE approach [25 27] has been implemented bymeans of user-routines in the commercial package ABAQUSto derive the instantaneous local resin elastic modulus (119864

119903)

assuming a linear relation of the stress and strain tensorsThe corresponding expression for the resin elastic modulusassuming secondary effects of temperature as negligible isgiven as follows

119864119903=

1198640

119903

119879lowast

lt 1198791198621

1198640

119903

+119879lowast

minus 1198791198621

1198791198622

minus 1198791198621

(119864infin

119903

minus 1198640

119903

) for 1198791198621

le 119879lowast

le 1198791198622

119864infin

119903

119879lowast

gt 1198791198622

(17)

The fictitious temperature 119879lowast is defined as the difference

between the 119879119892and the actual resin temperature 119879 and

expressed as follows

119879lowast

= 119879119892minus 119879 = (119879

0

119892

+ 119886119879119892120572) minus 119879 (18)

where 1198790119892

represents the glass transition temperature of theuncured resin and 119886

119879119892describes the dependence of the glass

transition temperature on the degree of cure According tothe CHILE approach during the cure reaction 119864

119903varies

linearly with 119879lowast from the uncured (1198640

119903

) to the fully cured(119864infin119903

) resin moduli 1198791198621

and 1198791198622

are the critical temperaturesdefining the beginning and the end of modulus development[27] The effective mechanical properties of the compositeare calculated using the self-consisting field micromechanics(SCFM) relationships as reported in detail in [25] For theproposed approach shown in Figure 6 the die is assumed tobe rigid and therefore rigid body surfaces are added at thedie-part interface instead of including the meshing for thewhole die Between the rigid surfaces and the composite parta mechanical contact formulation is defined which restrictsany expansion of the composite beyond the tool interfacehowever any separation due to resin shrinkage is allowedIn this approach the friction force at the contact conditionis assumed to be zero (sliding condition) A generic view ofthe plane strain model including the rigid surfaces and themechanical boundary conditions (BCs) is shown in Figure 6It should be noted that even if the constitutive behavior of the


3D transient thermochemical analysis(Eulerian frame) 3D composite part

Movingpulling direction

2D plane strain quasi-static mechanical analysis(Lagrangian frame)

y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend

middot middot middot


2D plane-strain model

Rigid body

Temperature (T)

Cure degree (120572)

2D cross section

Figure 6 Representation of the coupling of the 3D Eulerian thermochemical model with the 2D Lagrangian plain-strain mechanical modelincluding the rigid body surfaces and the mechanical BCs

homogenized material is linear elastic the solved boundaryvalue problem is significantly nonlinear due to the spaceand time variations of all physical and mechanical propertiesinvolved

242 Semianalytical Analysis ofDistortions andPressure Theproposed semianalytical approach is based on the computa-tion of a virtual unconstrained cross section of the processingmaterial It is assumed that during the process the positionof the center of mass (barycenter) of the cross section isalways preserved [11]The composite distortions are related tothe thermal expansion of each component and the chemicalshrinkage of the reactive resin As a consequence eachvirtual dimension of the 119894th control volume can be computedmultiplying its initial value by the correction factor as follows

120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894

are the variations of a unit dimension ofthe 119894th volume entirely filled with resin and fiber respectivelyDefining the CTEs of the resin as 120572

119903and of the fibers in the

transverse direction as 120572119891119905 and the percentage volumetric

shrinkage of the fully cured resin as 120574119903 it follows

120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)

where the subscripts 119903 and 119891 refers to resin and fiber respec-tively Here the utilized temperature and the DOC valuesare the volume averaged values calculated by consideringthe results of the porous model described in Section 232

With reference to the circular cross section investigated thedimensional variation Δ

119903119894of the 119894th volume along the radial

direction is given by

Δ119903119894= 119903119894(120575119888119894minus 1) (21)

The total displacement Δ119903= ΣΔ

119903119894and the virtual radius

119903V can be evaluated by extending equation (21) to the wholeradius In particular from the die inlet until the detachmentpoint due to the prevalence of the thermal expansion onthe chemical shrinkage the virtual section of the processingcomposite results reasonably greater than the die cavityConsequently the pultruded part is compressed by the dieinternal walls In this case the contact pressure is evaluatedfollowing the well-known principles of materials science forthick walled cylinders schematizing the virtual section as aseries of concentric and contiguous annulus (delaminationphenomena are not included) and assuming plane strainhypothesis As for the FE model described in Section 241material elastic properties are evaluated according to localtemperature and DOC using the CHILE approach and theSCFM relationships Taking into account this the continuityof thematerial imposes the congruence of the circumferentialstrains 120576

120579and the radial stress 120590

119903at the boundaries between

adjacent layers using the subscript 119895 to identify each annulus(increasing with the radial position) and the subscripts intand ext to localize the strain at the inner or outer radius ofthe annulus respectively which results in the following

120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall

Imposed displacement

Virtual section

jth layer(j + 1)th layer

Congruence equations at layers boundary

Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1

Δ ron the outer radius

ext

ext

int

int

Figure 7 Pressure calculation scheme

Furthermore considering that the enlargement of the realcross section is prevented by the rigid die walls (the uncon-strained section previously computed is a purely virtual one)the circumferential strain on the external radius results in thefollowing

120576120579= minus

Δ119903

119903V (23)

providing the closure to the considered problem A schematicrepresentation of the calculation procedure is depicted inFigure 7 It is trivial to outline that in correspondence withthe external radius the radial solicitation 120590

119903equals to the

opposite of the pressure 120590 acting on the die internal wallallowing one to derive the frictional contribution using (6)

Frictional resistance vanishes when the shrinkage effectprevails inducing the detachment of the material from thedie In this case an additional TCR is induced between thedie and the composite TCR values are computed in the cor-responding locations assuming that the empty space betweenthe die surface and the processing composite is fulfilled byair Since radial displacements and TCR values along thedie length are not known as a priori an iterative procedureconnecting the thermochemical model with the dimensionalchange model has been implemented until reaching theconvergence of a temperature criterion

3 Results and Discussion

31 Case Study The pultrusion process of a UD graphiteepoxy composite rod with circular cross section is simu-lated to compare the numerical outcomes provided by theproposed models as well as with results discussed in theliterature [6 13]The radius of the processing rod is 475mmwhile the length 119871die of heating die is 914mm which areadopted for the numerical and experimental analysis detailedin [6] It should be noted that in the performed simulationsthe temperature distribution on the internal die surface isused to provide the required closure of the above describedthermochemical problem that is the die is not included inthe calculation domain as also done in [6] Despite the imple-mented thermochemical models that allow one to definemore complex boundary conditions this relatively simplercase has been reproduced in order to compare numerical

results with data reported in [6] The inlet temperature isassumed to be equal to the resin bath temperature (38∘C)while the matrix material is assumed to be totally uncured(120572 = 0) at the same cross section Only a quarter of the 3Dmodel has been considered due to the symmetry and in orderto reduce the computational effort A schematic view of thesimulation domain is depicted in Figure 8

The variation of the internal section in the tapered inlet isnot taken into account in the thermochemical model as wellas for the stress and distortions calculations in themechanicalmodel The reason is that the size of the tapered section isrelatively small and there is almost no heat transfer curingand stress development observed in that region

In addition considering that the composite material inthe die exit section is still at elevated temperature it isreasonable to suppose that the cure reaction proceeds alsoin the postdie region leading to a certain amount of DOCincrease as already discussed in [6 25] This aspect has beenincluded in the model extending the length of the pultrudedcomposite to the postdie region The postdie is characterizedby a total length 119871post-die equal to 1370mm ensuring that nofurther reaction will take place in the material In the postdieregion convective cooling in the room temperature (27∘C)is imposed as a boundary condition on the external surfaceof the pultruded product The dependence of the convectivecooling coefficient on the surface temperature is definedusing the well-known principle of heat transfer for horizontalcylinder The pull speed Vpull has been defined as 5mms [6]

The pultruded composite rod consists of Shell Epon94209470537 resin and Graphite Hercules AS4-12K fibers(119903119891= 13 120583m) The properties of components and the resin

kinetic parameters are listed in Tables 1 and 2 respectivelyThe parameters used in the CHILE approach are given inTable 3

32 Impregnation Analysis The impregnation model is con-sidered for the first 30mm of the die assuming that after thislength flow perturbations induced by the convergent sectionof the inlet vanish The tapered inlet has been modeledassuming a rounded shape with length 119871

119905and radius119877

119905being

equal to 6 and 635mm respectively [13] The preform ratiodefined as the ratio between the cross sectional area of theimpregnated material before and after the compaction due tothe tapered inlet is assumed to be 144 neglecting shape vari-ations of the pulled material As a consequence the wettedfibers approaching to the inlet have been modeled as a cylin-drical porous medium with radius being equal to 57mm

As aforementioned a constant viscosity assumption isadopted taking into account that generally in the very earlypart of the die no significant reaction is observed The refer-ence viscosity value has been obtained according to (5) con-sidering the resin as fully uncured (120572 = 0) at a temperatureequal to 38∘C as for the thermochemical models It shouldbe noted however that the catalyzed resin before the impre-gnation and entering of the die lays into the open bathfor some time During this period a small amount of reac-tion cannot be excluded a priori Even if the degree of cross-linking in the resin bath does not significantly affect the evo-lution of the solidification process it can influence the


Pulling direction

Heating Convective cooling

Composite475

Ldie = 914 Lpost-die = 1370

yy

xz

Top

Center

Centerline(Symmetric BC)

Figure 8 Schematic view of the pultrusion domain for the composite rod All dimensions are inmm

Table 1 Material physical properties and concentration [6 9ndash11]

Property Graphite Epoxy120588 [kgmminus3] 1790 1260119888119901

[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911

(1∘C) minus90119864 minus 7 45119864 minus 5

120574119903

() mdash 4Volume fraction 06 04

viscosity for the impregnation and compaction analysis Thissituation is investigated in the present work by simulatingthe compaction process using three different viscosity values105 Pasdots (120572 = 0) 15 Pasdots (120572 = 0008) [13] and 260 Pasdots(120572 = 002) In the impregnation model the die surfaces aremodeled as rigid walls defined with a no slip condition Aninlet condition is imposed to the inlet surface correspondingto the preform while an opening condition allowing thecreation of the resin backflow is applied on the surroundingsurface In both cases a zero relative pressure is defined Thevelocity of the processing material crossing the outlet sectionhas been assumed to be equal to the pull speed

In Figures 9ndash11 the results provided by the impregnationmodel are reported which show the pressure profiles at thecenterline of the processing material (Figure 9) a streamlineplot of the resin flow in the tapered region (Figure 10) andthe calculated bulk compaction force (Figure 11) For all thesimulated conditions an increase in the pressure has beenpredicted before the intersection point which is identifiedby the contact between the reinforced preform and the die

0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point

Gadam et al [13]Present model

150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00

Figure 9 Centerline pressure rise in the tapered region of the die

internal surface and is depicted in Figure 9 by the verticaldashed line This pressure variation is due to the effect of theresin backflow (well highlighted by the streamlines oppositeto the pulling speed in Figure 10) which prevents the free flowof the resin inside the preform towards the nonreinforcedzonesThe samefigure also highlights the excellent agreementbetween the obtained pressure profiles and the data reportedin [13] confirming the validity of the implemented numericalmodel Furthermore as already indicated in [13] for theconsidered configuration more than half of the total pressureincrease has already developed at the intersection point It isalso worth noting in Figure 10 that at the very beginning ofthe straight portion of the die the resin velocity converges onthe pull speed imposed to the reinforcing fibers

Obtained outcomes also show that the activation of thecure reaction inside the resin bath is quite undesirable evenif the degree of crosslinking achieved before entering thedie is reduced Indeed the premature crosslinking of thecatalyzed resin increases its viscosity and as a consequencehigher pressures are needed to squeeze the excess resin outof the preform This results also in a proportional increaseof the pulling force contribution due to material compaction(Figure 11)

33Thermochemical Analysis The calculated centerline tem-perature and DOC profiles are shown in Figure 12 togetherwith the temperature profile imposed on the diewall It is seen


Table 2 Epoxy resin rheological parameters [6 9ndash12]

1198700

[sminus1] Δ119864 [Jmolminus1] 119899 119867tr [J kgminus1] 120578

infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450

Table 3 Resin properties for modulus calculation (CHILE and glass transition) [25 27]

1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow

Porous medium Symmetry planes

50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)

Figure 10 Streamline of the resin flow in the tapered region of thedie

0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)

Viscosity (Pamiddots)

489694

120572 = 0)

Figure 11 Influence of the resin viscosity (initial degree of cure) onthe compaction term of the pulling force

that the predicted results match quite well with the availableexperimental data in [6] This evidences that the numericalschemes adopted for the continuous homogeneous FEmodel(denoted as ldquoCMrdquo in Figure 12) and the porous nonhomoge-neous FV model (denoted as ldquoPMrdquo in Figure 12) are stableand converged to a reliable solution The temperature in thecenter of the composite rod becomes higher than the die walltemperature after approximately 390mm from the die inletdue to the internal heat generation of the epoxy resin At thatpoint a peak of the reaction rate is obtained inducing a sharpincrease of the DOC The maximum composite temperatureis calculated approximately as 208∘C What is more at thepostdie region the DOC is increased slightly which indicatesthat the curing still takes place after the die exit as alsoobserved in [6] The centerline DOC is increased from 084

00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)

Die temperature [6]Temperature at center [6]Temperature at center (PM)Temperature at top (PM)Temperature at center (CM)Temperature at top (CM)

Degree of cure at center [6]Degree of cure at center (PM)Degree of cure at top (PM)Degree of cure at center (CM)Degree of cure at top (CM)

Die exit Postdie region

Tem

pera

ture

(∘C)

Top

Center

Figure 12 Temperature and DOC profiles comparison of thepresent outcomes with the reference data [6]

(at the die exit) to 087 (at the end of the process) while atthe surface it varies from 080 to 083 indicating a globalpercentage increase of approximately 36

The depicted DOC profiles in Figure 12 show an earlieractivation of the cure reaction at the composite surface dueto the rapid temperature increase related to conductive heattransfer from the die wall As a consequence the DOC at theexternal radius initially results higher than at the center Thistrend varies after the activation of the reaction in the core ofthe material indeed the relatively low thermal conductivityof the resin prevents the heat generated at the center toflow towards the external zones inducing a significant andlocalized temperature increase at the center which stronglypromotes monomers crosslinking It is worth noting that thecure crossover (intersection between the DOC profiles at thecenter and at the top) is reached approximately at 120572 = 05that is well above the gel point (120572 = 0265) of the consideredresin system indicating a delay in the establishment of thedesired in-out solidification direction Indeed as evidencedby the viscosity profiles depicted in Figure 13 the activationof the cure reaction implies a sharp viscosity increase at gela-tion occurring earlier at the top surface at a distance approxi-mately equal to 360mm from die entrance and separatingthe liquid zone (where viscous drag acts) from the gel


471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)

Viscosity at center (FVM)Viscosity at center (FEM)Viscosity at top (FVM)

Viscosity at top (FEM)Work piece radius (SAM)Workpiece radius (CM)

Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103

Figure 13 Extension of the liquid gel and solid zone as evidencedby viscosity profiles at top and work piece radius

zone (dominated by frictional resistance)The same viscositytrend is observed at the center of the composite rod afterapproximately 405mm from the die entrance It should bealso noted that in the first 200mm from the inlet the tem-perature increase leads to a slight viscosity reduction beforethe beginning of crosslinking phenomena as also highlightedin Figure 13

In the same figure (Figure 13) the work piece radius as afunction of the axial distance is reported As highlighted bynumerical outcomes in the liquid zone the materials thermalexpansion prevails on chemical shrinkage leading to a virtualradius of the work piece greater than the die internal radiusAs a consequence a further pressure increase (shown in whatfollows) is to be expected Even if this pressure increasedoes not theoretically implies further contributions to thetotal pulling force (being the wall surface parallel to 119865pull)from a practical point of view it is very interesting since inconjunction with the aforementioned viscosity reduction itpromotes the reduction of voids in the final product As canbe seen bothmodels fairly agree with the individuation of thedetachment point which is the intersection point betweenthe virtual radius and the die internal radius during shrink-age Please note that the zero radial displacement providedby the FE model (CM) is due in agreement with realityto the nonpenetrating condition applied at the mechanicalcontact between the composite and the rigid die surface [25]The detachment point for the outer surface of the compositerod is found to be approximately at 540mm from the inlet(more precisely 535mm and 545mm for the FEM and SAM)as a consequence the die length interested by the frictionaleffect (gel zone) is estimated to be approximately 180mmThe delayed position of the detachment point predictedby the SAM with respect to the FEM suggests also that arelatively major computation of the virtual radius (or radialdisplacement of the cross section) This aspect can be relatedto the assumption of the lumped CTE employed in the FEmodel in contrast with the usage of a different CTE for eachconstituent (when the resin is in liquid phase) adopted by theSAMAfter the detachment point TCRs are induced between

the work piece and the die Nevertheless very negligibledifferences (less than 05∘C) in the temperature distributionshave been found with and without the TCR inclusion in thecalculations The work piece radius in the exit section asprovided by the analytical calculation coupled to the finitevolume model results 4742mm in good agreement withthe value (4739mm) reported in [11] A slight difference(sim0003mm = 3120583m) regarding the work piece radius at theexit calculated using the FE model and the semianalyticalprocedure has been found As can be seen in Figure 13 afterthe detachment point the evolution of the radial distortiondiffers between the aforementioned approaches The reasonfor this deviation could be found in the oversimplification ofthe semianalytical model (SAM) in which the displacementsare calculated only in the radial direction without takingthe effect of the mechanical behaviors in the longitudinaldirection into account

34 Mechanical Analysis The evolution of the processinduced transverse normal stresses in the 119909-direction (119878

11)

is shown in Figure 14(a) It is seen that at the end of theprocess tensile stresses prevail at the inner region (center)and compression stresses occur at the outer region (top)while upholding the self-static equilibrium in which thereis no applied external load This observation resembles withthe one presented in [25] The stress levels are found to berelatively small (lt1MPa) The main reason is that there arean almost uniform temperature andDOCdevelopments overthe cross section of the composite rod which provides rela-tively lower through-thickness gradients promoting almostno residual stresses at the end of the process The variationin 11987811

is due to the internal competition between expansionand contraction of the partThe effective longitudinal and thetransversemoduli (calculated by the SCFM) of the compositerod at the end of the process are found to be 1302GPaand 97GPa respectively which agrees well with typicalvalues given in [30] for T300 carbonepoxy with a fibervolume fraction of 60 In Figure 14(b) the resin modulusdevelopment due to monomers crosslinking is depicted It isseen that almost same evolution pattern is obtained using theCHILE model in FEMmodel and SAMmodel

Undeformed contour plots of the stresses 11987811

(in 119909-direction) and 119878

22(in the 119910-direction) are shown in Figure 15

As expected the 11987811distribution is almost symmetricwith the

11987822distribution with respect to the diagonal of the composite

rod since all the mechanical boundary conditions are thesameThemaximumnormal tensile and compression stressesare found to be approximately 026MPa and minus082MParespectively for 119878

11and 11987822

In Figure 16 the contact pressure profiles (between inter-nal die surface and the outer surface of the part that is toppoint indicated in figure) provided by the implementedmod-els (FEM SAM) are shown Both models highlighted a pro-gressive pressure increase (up to approximately 02MPa forthe FEMand027 for the SAM) from the die inlet to the strongactivation of the resin reaction since the composite part triesto expand because of the temperature increase however theinternal die surface restricts this expansion The difference


00

02

04

0 400 800 1200 1600 2000 2400Axial distance (mm)

Stress at center (FEM)Stress at top (FEM)

Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)

Center (FEM)Center (SAM)

Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)

Figure 14 In-plane stresses (11987811

) evolution at the center and at the top of the composite rod (a) and resin modulus development at the samelocations as a function of the axial distance (b)

+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)

Figure 15 The undeformed contour plots of the inplane stresses 11987811

(a) and 11987822

(b)

between these two predictions is due to the aforementionedconsiderations in virtual section calculations which relieson the specific assumptions in the FEM and in the SAMAfterwards due to resin chemical shrinkage a continuouspressure reduction is observed until the detachment occurs

According to the calculated viscosity and pressure pro-files in the thermochemical analysis the total pulling forcetogether with its components is predicted (Figure 17) For thecalculation of the frictional resistance the friction coefficient120583 has been assumed to be 025 as also used in [19] Numericaloutcomes show that for the simulated process the viscousforce represents the principal amount of the total resistancebeing 119865bulk = 49N 119865vis = 3137N and 119865fric = 1841Nas predicted by the semianalytical procedure A relativelysmaller frictional resistance (1129N) is predicted by theFE mechanical model due to the lower contact pressure

profile in Figure 16 The key role played by the viscous dragwith respect to the frictional force can be related to thereduced die length affected by the frictional phenomena andto the delayed development of the resin (and the composite)modulus The contribution due to the material compactionis found to be not significant as compared to other amountsbeing less than 1 of the total load

4 Conclusions

In the present work different approaches for modelingand simulations of several physical aspects such as fluidflow heat transfer chemical reaction and solid mechanicsinvolved in a conventional pultrusion process are proposedand compared The proposed models are based on differentnumerical techniques (FEM FVM) as well as the analytical


000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)

Finite element modelSemianalytical model

Detachment point

Die exit

Top

Figure 16 Contact pressure profiles

0

100

200

300

400

500

600

49

3137

1841

5027

Compaction forceViscous force

Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4

Figure 17 Contribution to the pulling force as provided by theimpregnation viscous and frictional models (SAM) assumingchemical shrinkage and initial viscosity to be 4mdash105 Pasdots

calculation Taking into account the discussed outcomes itcan be concluded that

(i) the resin pressure increases at the tapered die inletpromoting the backflow of the excess resin howeveras soon as the straight portion of the die beginsa flat velocity profile is enforced It is found thatthe compaction force increases with the viscosity (ordegree of cure) of the resin in the impregnation bath

(ii) adopted numerical schemes (FEM FVM) are foundto be accurate and converged to a reliable solutionsince the predicted values match well with the ref-erence data [6] Moreover both models fairly agreein the evaluation of viscosity profiles dimensional

variations and extension of the three zones (ieliquid gel and solid) The inclusion of the thermalcontact resistance due to material contraction insidethe die in pultrusion modeling does not affect thesimulation results significantly

(iii) in the initial portion of the curing die the thermalexpansion of the processing materials dominates theresin shrinkage which induces a progressive contactpressure increase and consequently frictional resis-tance after gelation However as the cure reactionproceeds the chemical contraction of the reactiveresin prevails causing the detachment of the workpiece from the die internal surface and the vanishingof the contact pressure as well as the frictional force

(iv) in the residual stress model relatively small residualstress values were predicted at the end of the processdue to the uniform distribution of the tempera-ture and degree of cure over the cross section ofthe composite part having a relatively small diam-eter (95mm) The thickness of the composite parttogether with the total volumetric shrinkage of theresin has an important effect on the residual stressevolution [25] At the end of the process it is foundthat tension stresses prevail for the center of the partsince it cured later and faster as compared to the outerregions where compression stresses were obtainedwhile upholding the self-static equilibrium

(v) the viscous drag is found to be the main contributionas the frictional force to the overall pulling forcewhile the contribution due to material compaction atthe inlet is found to be negligible

Investigating the several aforementioned processingphysics simultaneously provides a better understanding ofthe entire pultrusion dynamics at a glance and thereforethis study would be very much of interest to the compositemanufacturing processing community and especially to sci-entists and engineers in the field of manufacturing processmodeling

Acknowledgment

This work is a part of DeepWind project which has beengranted by the European Commission (EC) under FP7 Pro-gram Platform Future Emerging Technology

References

[1] Y S Song J R Youn and T G Gutowski ldquoLife cycle energyanalysis of fiber-reinforced compositesrdquo Composites A vol 40no 8 pp 1257ndash1265 2009

[2] T F Starr Pultrusion for Engineers Woodhead Publishing2000

[3] T G Gutowski Advanced Composites Manufacturing JohnWiley amp Sons New York NY USA 1997

[4] R S Dave andAC LoosProcessing of Composites CarlHanserMunich Germany 2000


[5] X Lin Liu I G Crouch and Y C Lam ldquoSimulation of heattransfer and cure in pultrusion with a general-purpose finiteelement packagerdquo Composites Science and Technology vol 60no 6 pp 857ndash864 2000

[6] M Valliappan J A Roux J G Vaughan and E S Arafat ldquoDieand post-die temperature and cure in graphiteepoxy compo-sitesrdquo Composites B vol 27 no 1 pp 1ndash9 1996

[7] P Carlone G S Palazzo and R Pasquino ldquoPultrusion man-ufacturing process development by computational modellingand methodsrdquo Mathematical and Computer Modelling vol 44no 7-8 pp 701ndash709 2006

[8] P Carlone G S Palazzo and R Pasquino ldquoPultrusion man-ufacturing process development cure optimization by hybridcomputational methodsrdquo Computers and Mathematics withApplications vol 53 no 9 pp 1464ndash1471 2007

[9] I Baran C C Tutum and J H Hattel ldquoOptimization of thethermosetting pultrusion process by using hybrid and mixedinteger genetic algorithmsrdquo Applied Composite Materials vol20 pp 449ndash463 2013

[10] I Baran C C Tutum and J H Hattel ldquoThe effect of thermalcontact resistance on the thermosetting pultrusion processrdquoComposites B vol 95 pp 995ndash1000 2013

[11] S C Joshi and Y C Lam ldquoThree-dimensional finite-elementnodal-control-volume simulation of the pultrusion processwith temperature-dependent material properties includingresin shrinkagerdquo Composites Science and Technology vol 61 no11 pp 1539ndash1547 2001

[12] K S Raper J A Roux T AMcCarty and J G Vaughan ldquoInves-tigation of the pressure behavior in a pultrusion die for graph-iteepoxy compositesrdquo Composites A vol 30 no 9 pp 1123ndash1132 1999

[13] S U K Gadam J A Roux T A McCarty and J G VaughanldquoThe impact of pultrusion processing parameters on resin pres-sure rise inside a tapered cylindrical die for glass-fibreepoxycompositesrdquo Composites Science and Technology vol 60 no 6pp 945ndash958 2000

[14] H L Price and S G Cupschalk ldquoPulling force and its variationin compositematerials pultrusionrdquo in Polymer Blends and Com-posites in Multiphase Systems pp 301ndash322 ACS Publications1984

[15] E Lackey and J G Vaughan ldquoAn analysis of factors affectingpull force for the pultrusion of graphiteepoxy compositesrdquoJournal of Reinforced Plastics and Composites vol 13 no 3 pp188ndash198 1994

[16] P Carlone and G S Palazzo ldquoViscous pull force evaluationin the pultrusion process by a finite element thermo-chemicalrheological modelrdquo International Journal of Material Formingvol 1 no 1 pp 831ndash834 2008

[17] D Srinivasagupta S Potaraju J L Kardos and B JosephldquoSteady state and dynamic analysis of a bench-scale injectedpultrusion processrdquo Composites A vol 34 no 9 pp 835ndash8462003

[18] S MMoschiar MM Reboredo H Larrondo and A VazquezldquoPultrusion of epoxy matrix composites pulling force modeland thermal stress analysisrdquo Polymer Composites vol 17 no 6pp 850ndash858 1996

[19] M S Yun and W I Lee ldquoAnalysis of pulling force during pul-trusion process of phenolic foam compositesrdquo Composites Sci-ence and Technology vol 68 no 1 pp 140ndash146 2008

[20] S Li L Xu Z Ding L J Lee and H Engelen ldquoExperimentaland theoretical analysis of pulling force in pultrusion and resin

injection pultrusion (RIP)mdashpart II modeling and simulationrdquoJournal of Composite Materials vol 37 no 3 pp 195ndash216 2003

[21] S Li L Xu Z Ding L J Lee and H Engelen ldquoExperimentaland theoretical analysis of pulling force in pultrusion and resininjection pultrusion (RIP)mdashpart I experimentalrdquo Journal ofComposite Materials vol 37 no 2 pp 163ndash189 2003

[22] M R Wisnom M Gigliotti N Ersoy M Campbell and K DPotter ldquoMechanisms generating residual stresses and distortionduring manufacture of polymer-matrix composite structuresrdquoComposites A vol 37 no 4 pp 522ndash529 2006

[23] Y Abou Msallem F Jacquemin N Boyard A Poitou DDelaunay and S Chatel ldquoMaterial characterization and residualstresses simulation during the manufacturing process of epoxymatrix compositesrdquo Composites A vol 41 no 1 pp 108ndash1152010

[24] I Baran C C Tutum and J H Hattel ldquoThe internal stressevaluation of the pultruded blades for a Darrieus wind turbinerdquoKey Engineering Materials vol 554ndash557 pp 2127ndash2137 2013

[25] I Baran C C Tutum M W Nielsen and J H Hattel ldquoProcessinduced residual stresses and distortions in pultrusionrdquo Com-posites B vol 51 pp 148ndash161 2013

[26] C Dong ldquoModeling the process-induced dimensional varia-tions of general curved composite components and assembliesrdquoComposites A vol 40 no 8 pp 1210ndash1216 2009

[27] A Johnston An integrated model of the development of process-induced deformation in autoclave processing of composites struc-tures [PhD thesis] The University of British Columbia Van-couver Canada 1997

[28] ldquoABAQUS 6 11 Reference Guiderdquo Dassault Systems 2011[29] ldquoANSYS CFX 13 0 Reference Guiderdquo ANSYS 2010[30] D Zenkert and M Battley Laminate and Sandwich Structures

Foundations of Fibre Composites Polyteknisk Forlag LyngbyDenmark 2nd edition 2009

Impact Factor 173028 Days Fast Track Peer ReviewAll Subject Areas of ScienceSubmit at httpwwwtswjcom

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawi Publishing Corporation httpwwwhindawicom Volume 2013

The Scientific World Journal

Hindawi Publishing CorporationAdvances in Mechanical EngineeringVolume 2013 Article ID 301875 14 pageshttpdxdoiorg1011552013301875

Research ArticleComputational Approaches for Modeling the Multiphysics inPultrusion Process

P Carlone1 I Baran2 J H Hattel2 and G S Palazzo1

1 Department of Industrial Engineering University of Salerno Via Giovanni Paolo II 84084 Fisciano Italy2 Department of Mechanical Engineering Technical University of Denmark 2800 Kgs Lyngby Denmark

Correspondence should be addressed to P Carlone pcarloneunisait

Received 30 August 2013 Accepted 4 November 2013

Academic Editor Nao-Aki Noda

Copyright copy 2013 P Carlone et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Pultrusion is a continuousmanufacturing process used to produce high strength composite profiles with constant cross sectionThemutual interactions between heat transfer resin flow and cure reaction variation in the material properties and stressdistortionevolutions strongly affect the process dynamics together with the mechanical properties and the geometrical precision of the finalproduct In the present work pultrusion process simulations are performed for a unidirectional (UD) graphiteepoxy compositerod including several processing physics such as fluid flow heat transfer chemical reaction and solid mechanics The pressureincrease and the resin flow at the tapered inlet of the die are calculated by means of a computational fluid dynamics (CFD) finitevolumemodel Several models based on different homogenization levels and solution schemes are proposed and compared for theevaluation of the temperature and the degree of cure distributions inside the heating die and at the postdie region The transientstresses distortions and pull force are predicted using a sequentially coupled three-dimensional (3D) thermochemical analysistogether with a 2D plane strain mechanical analysis using the finite element method and compared with results obtained from asemianalytical approach

1 Introduction

Pultrusion is a continuous manufacturing process used torealize constant cross sectional composite profiles In recentyears the pultrusion process experienced a remarkable grow-ing within the composite industry due to its cost-effect-iveness automation and high quality of products Nowadaysthe process is widely used to manufacture highly strength-ened structures such as wind turbine blades window profilesdoor panels and reinforcing bars for concrete Moreover insome applicative sectors such as in the automotive industrythe environmental impact of pultruded composite structuresover the entire life cycles results is lower than other engi-neeringmaterials [1] A schematic view of the pultrusion pro-cess is depicted in Figure 1 During the process the reinforce-ment fibers in the form of rovings or mat are pulled throughguiders and impregnated by the resin material in an openbath or employing a resin injection chamberWetted out rein-forcements are then pulled via a pulling mechanism throughthe heating die The die inlet is typically characterized by a

tapered or a conical convergent shape in order to promote thedesired impregnation and compaction of the reinforcementthe removal of the air and the excess resin In the straightportion of the die the heat provided by means of electricalheaters or hot oil activates the exothermic cure reaction ofthe thermoset resin As a consequence the material changesits status from reactive liquid to gel and then vitrifiedsolid [2 3] The thermochemical behavior of the processingthermoset resin generally represented by time-temperature-transformation (TTT) diagrams [2ndash4] is a crucial issueDuring the curing process the resin shrinks because of thechemical reaction (cross linking) promoting the contractionof the work piece Besides that the part continues contractingdue to the cooling effect for example convective cooling atthe postdie region At the end of the process the cured andsolidified product is cut into desired lengths

Even if the process is conceptually quite simple the anal-ysis of its dynamics and the definition of optimal processingparameters are a complex task due to themutual interactionsbetween involved physical phenomenamainly related to heat


FibersFiber guides

Resin bath


Pulling direction







Impregnation model

Thermochemicalmodel

Mechanical model


Pull force

Residual stresses



Resin viscosity


Viscous drag



Therm

al stra

in

Chemica

l strai

n


z

Heating platens


Detachment pointDie

Pultruded composite

product

Impregnated fibers

Viscous force

Frictional force

Compaction force

Gelation point

Pull direction


Liquid phase







Straight die

Intersection point

Resin backflow

Compacting

Tapered

Impregnated fibers

pressure p

120579

length Li




as follows

119865bulk = ∬1198601

119901 sin 120579 119889119860 (2)



Moving fibers

Die wall Resin

120582




119892 it



119865vis =Vpul120582

∬1198602

120578 (120572 119879) 119889119860 (3)




120582 = 119903119891(1 minus

1

2


119891

2) (4)


120578 = 120578infinexp(

Δ119864120578

119877119879+ 119870120572) (5)






119865fric = int1198603

120583 sdot 120590 119889119860 (6)





120597119906

120597119909+120597V120597119910

+120597119908

120597119911= 0

120578(1205972

119906

1205971199092+1205972

119906

1205971199102+1205972

119906

1205971199112) minus

120597119901

120597119909= 0


120578(1205972V

1205971199092+1205972V1205971199102

+1205972V1205971199112

) minus120597119901

120597119910= 0

120578 (1205972

119908

1205971199092+1205972

119908

1205971199102+1205972

119908

1205971199112) minus

120597119901

120597119911= 0

(7)


119906 = 119880 minus119870119909119909

120578Φ

120597119875

120597119909

V = 119881 minus

119870119910119910

120578Φ

120597119875

120597119910

119908 = 119882 minus119870119911119911

120578Φ

120597119875

120597119911

(8)


119870119909119909

= 119870119910119910

= 1198621(radic

119881119891max119881119891

minus 1) 119903119891

2

119870119911119911=

8119903119891

2

119888

(1 minus 119881119891)3

119881119891

2

(9)








120588119888119862119901119888

(120597119879

120597119905+ Vpul

120597119879

120597119911)

= 119896119909119888

1205972

119879

1205971199092+ 119896119910119888

1205972

119879

1205971199102+ 119896119911119888

1205972

119879

1205971199112+ 119881119903119902

(10)


119862119901119888






119902 = 120588119903119867119905119903119877119903 (11)





119877119903(120572 119879) =

120597120572

120597119905=

1

119867119905119903

119889119867 (119905)

119889119905= 1198700exp(minusΔ119864

119877119879) (1 minus 120572)

119899

(12)


(120597120572

120597119905+ Vpul

120597120572

120597119911) = 119877

119903(120572 119879) (13)




120593119891120588119891119862119901119891

120597119879119891

120597119905+ 120588119891119862119901119891

Vpul120597119879119891

120597119911

= 120593119891(119896119909119891

1205972

119879119891

1205971199092+ 119896119910119891

1205972

119879119891

1205971199102+ 119896119911119891

1205972

119879119891

1205971199112) + 119876

119903119891

(14)

120593120588119903119862119901119903

120597119879119903

120597119905+ 120588119903119862119901119903

(119906120597119879119903

120597119909+ V

120597119879119903

120597119910+ 119908

120597119879119903

120597119911)

= 120593(119896119903

1205972

119879119903

1205971199092+ 119896119903

1205972

119879119903

1205971199102+ 119896119903

1205972

119879119903

1205971199112) + 120593119902 + 119876

119891119903

(15)




119903= 1 minus 119881

119891sdot 119876119903119891

= minus119876119891119903








119903)


119864119903=

1198640

119903

119879lowast

lt 1198791198621

1198640

119903

+119879lowast

minus 1198791198621

1198791198622

minus 1198791198621

(119864infin

119903

minus 1198640

119903

) for 1198791198621

le 119879lowast

le 1198791198622

119864infin

119903

119879lowast

gt 1198791198622

(17)




119879lowast

= 119879119892minus 119879 = (119879

0

119892

+ 119886119879119892120572) minus 119879 (18)

where 1198790119892




119903varies


119903


) resin moduli 1198791198621

and 1198791198622






y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend




Rigid body

Temperature (T)


2D cross section




120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894





120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)





Δ119903119894= 119903119894(120575119888119894minus 1) (21)







120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































FibersFiber guides

Resin bath


Pulling direction







Impregnation model

Thermochemicalmodel

Mechanical model


Pull force

Residual stresses



Resin viscosity


Viscous drag



Therm

al stra

in

Chemica

l strai

n


z

Heating platens


Detachment pointDie

Pultruded composite

product

Impregnated fibers

Viscous force

Frictional force

Compaction force

Gelation point

Pull direction


Liquid phase







Straight die

Intersection point

Resin backflow

Compacting

Tapered

Impregnated fibers

pressure p

120579

length Li




as follows

119865bulk = ∬1198601

119901 sin 120579 119889119860 (2)



Moving fibers

Die wall Resin

120582




119892 it



119865vis =Vpul120582

∬1198602

120578 (120572 119879) 119889119860 (3)




120582 = 119903119891(1 minus

1

2


119891

2) (4)


120578 = 120578infinexp(

Δ119864120578

119877119879+ 119870120572) (5)






119865fric = int1198603

120583 sdot 120590 119889119860 (6)





120597119906

120597119909+120597V120597119910

+120597119908

120597119911= 0

120578(1205972

119906

1205971199092+1205972

119906

1205971199102+1205972

119906

1205971199112) minus

120597119901

120597119909= 0


120578(1205972V

1205971199092+1205972V1205971199102

+1205972V1205971199112

) minus120597119901

120597119910= 0

120578 (1205972

119908

1205971199092+1205972

119908

1205971199102+1205972

119908

1205971199112) minus

120597119901

120597119911= 0

(7)


119906 = 119880 minus119870119909119909

120578Φ

120597119875

120597119909

V = 119881 minus

119870119910119910

120578Φ

120597119875

120597119910

119908 = 119882 minus119870119911119911

120578Φ

120597119875

120597119911

(8)


119870119909119909

= 119870119910119910

= 1198621(radic

119881119891max119881119891

minus 1) 119903119891

2

119870119911119911=

8119903119891

2

119888

(1 minus 119881119891)3

119881119891

2

(9)








120588119888119862119901119888

(120597119879

120597119905+ Vpul

120597119879

120597119911)

= 119896119909119888

1205972

119879

1205971199092+ 119896119910119888

1205972

119879

1205971199102+ 119896119911119888

1205972

119879

1205971199112+ 119881119903119902

(10)


119862119901119888






119902 = 120588119903119867119905119903119877119903 (11)





119877119903(120572 119879) =

120597120572

120597119905=

1

119867119905119903

119889119867 (119905)

119889119905= 1198700exp(minusΔ119864

119877119879) (1 minus 120572)

119899

(12)


(120597120572

120597119905+ Vpul

120597120572

120597119911) = 119877

119903(120572 119879) (13)




120593119891120588119891119862119901119891

120597119879119891

120597119905+ 120588119891119862119901119891

Vpul120597119879119891

120597119911

= 120593119891(119896119909119891

1205972

119879119891

1205971199092+ 119896119910119891

1205972

119879119891

1205971199102+ 119896119911119891

1205972

119879119891

1205971199112) + 119876

119903119891

(14)

120593120588119903119862119901119903

120597119879119903

120597119905+ 120588119903119862119901119903

(119906120597119879119903

120597119909+ V

120597119879119903

120597119910+ 119908

120597119879119903

120597119911)

= 120593(119896119903

1205972

119879119903

1205971199092+ 119896119903

1205972

119879119903

1205971199102+ 119896119903

1205972

119879119903

1205971199112) + 120593119902 + 119876

119891119903

(15)




119903= 1 minus 119881

119891sdot 119876119903119891

= minus119876119891119903








119903)


119864119903=

1198640

119903

119879lowast

lt 1198791198621

1198640

119903

+119879lowast

minus 1198791198621

1198791198622

minus 1198791198621

(119864infin

119903

minus 1198640

119903

) for 1198791198621

le 119879lowast

le 1198791198622

119864infin

119903

119879lowast

gt 1198791198622

(17)




119879lowast

= 119879119892minus 119879 = (119879

0

119892

+ 119886119879119892120572) minus 119879 (18)

where 1198790119892




119903varies


119903


) resin moduli 1198791198621

and 1198791198622






y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend




Rigid body

Temperature (T)


2D cross section




120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894





120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)





Δ119903119894= 119903119894(120575119888119894minus 1) (21)







120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































Impregnation model

Thermochemicalmodel

Mechanical model


Pull force

Residual stresses



Resin viscosity


Viscous drag



Therm

al stra

in

Chemica

l strai

n


z

Heating platens


Detachment pointDie

Pultruded composite

product

Impregnated fibers

Viscous force

Frictional force

Compaction force

Gelation point

Pull direction


Liquid phase







Straight die

Intersection point

Resin backflow

Compacting

Tapered

Impregnated fibers

pressure p

120579

length Li




as follows

119865bulk = ∬1198601

119901 sin 120579 119889119860 (2)



Moving fibers

Die wall Resin

120582




119892 it



119865vis =Vpul120582

∬1198602

120578 (120572 119879) 119889119860 (3)




120582 = 119903119891(1 minus

1

2


119891

2) (4)


120578 = 120578infinexp(

Δ119864120578

119877119879+ 119870120572) (5)






119865fric = int1198603

120583 sdot 120590 119889119860 (6)





120597119906

120597119909+120597V120597119910

+120597119908

120597119911= 0

120578(1205972

119906

1205971199092+1205972

119906

1205971199102+1205972

119906

1205971199112) minus

120597119901

120597119909= 0


120578(1205972V

1205971199092+1205972V1205971199102

+1205972V1205971199112

) minus120597119901

120597119910= 0

120578 (1205972

119908

1205971199092+1205972

119908

1205971199102+1205972

119908

1205971199112) minus

120597119901

120597119911= 0

(7)


119906 = 119880 minus119870119909119909

120578Φ

120597119875

120597119909

V = 119881 minus

119870119910119910

120578Φ

120597119875

120597119910

119908 = 119882 minus119870119911119911

120578Φ

120597119875

120597119911

(8)


119870119909119909

= 119870119910119910

= 1198621(radic

119881119891max119881119891

minus 1) 119903119891

2

119870119911119911=

8119903119891

2

119888

(1 minus 119881119891)3

119881119891

2

(9)








120588119888119862119901119888

(120597119879

120597119905+ Vpul

120597119879

120597119911)

= 119896119909119888

1205972

119879

1205971199092+ 119896119910119888

1205972

119879

1205971199102+ 119896119911119888

1205972

119879

1205971199112+ 119881119903119902

(10)


119862119901119888






119902 = 120588119903119867119905119903119877119903 (11)





119877119903(120572 119879) =

120597120572

120597119905=

1

119867119905119903

119889119867 (119905)

119889119905= 1198700exp(minusΔ119864

119877119879) (1 minus 120572)

119899

(12)


(120597120572

120597119905+ Vpul

120597120572

120597119911) = 119877

119903(120572 119879) (13)




120593119891120588119891119862119901119891

120597119879119891

120597119905+ 120588119891119862119901119891

Vpul120597119879119891

120597119911

= 120593119891(119896119909119891

1205972

119879119891

1205971199092+ 119896119910119891

1205972

119879119891

1205971199102+ 119896119911119891

1205972

119879119891

1205971199112) + 119876

119903119891

(14)

120593120588119903119862119901119903

120597119879119903

120597119905+ 120588119903119862119901119903

(119906120597119879119903

120597119909+ V

120597119879119903

120597119910+ 119908

120597119879119903

120597119911)

= 120593(119896119903

1205972

119879119903

1205971199092+ 119896119903

1205972

119879119903

1205971199102+ 119896119903

1205972

119879119903

1205971199112) + 120593119902 + 119876

119891119903

(15)




119903= 1 minus 119881

119891sdot 119876119903119891

= minus119876119891119903








119903)


119864119903=

1198640

119903

119879lowast

lt 1198791198621

1198640

119903

+119879lowast

minus 1198791198621

1198791198622

minus 1198791198621

(119864infin

119903

minus 1198640

119903

) for 1198791198621

le 119879lowast

le 1198791198622

119864infin

119903

119879lowast

gt 1198791198622

(17)




119879lowast

= 119879119892minus 119879 = (119879

0

119892

+ 119886119879119892120572) minus 119879 (18)

where 1198790119892




119903varies


119903


) resin moduli 1198791198621

and 1198791198622






y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend




Rigid body

Temperature (T)


2D cross section




120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894





120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)





Δ119903119894= 119903119894(120575119888119894minus 1) (21)







120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































Moving fibers

Die wall Resin

120582




119892 it



119865vis =Vpul120582

∬1198602

120578 (120572 119879) 119889119860 (3)




120582 = 119903119891(1 minus

1

2


119891

2) (4)


120578 = 120578infinexp(

Δ119864120578

119877119879+ 119870120572) (5)






119865fric = int1198603

120583 sdot 120590 119889119860 (6)





120597119906

120597119909+120597V120597119910

+120597119908

120597119911= 0

120578(1205972

119906

1205971199092+1205972

119906

1205971199102+1205972

119906

1205971199112) minus

120597119901

120597119909= 0


120578(1205972V

1205971199092+1205972V1205971199102

+1205972V1205971199112

) minus120597119901

120597119910= 0

120578 (1205972

119908

1205971199092+1205972

119908

1205971199102+1205972

119908

1205971199112) minus

120597119901

120597119911= 0

(7)


119906 = 119880 minus119870119909119909

120578Φ

120597119875

120597119909

V = 119881 minus

119870119910119910

120578Φ

120597119875

120597119910

119908 = 119882 minus119870119911119911

120578Φ

120597119875

120597119911

(8)


119870119909119909

= 119870119910119910

= 1198621(radic

119881119891max119881119891

minus 1) 119903119891

2

119870119911119911=

8119903119891

2

119888

(1 minus 119881119891)3

119881119891

2

(9)








120588119888119862119901119888

(120597119879

120597119905+ Vpul

120597119879

120597119911)

= 119896119909119888

1205972

119879

1205971199092+ 119896119910119888

1205972

119879

1205971199102+ 119896119911119888

1205972

119879

1205971199112+ 119881119903119902

(10)


119862119901119888






119902 = 120588119903119867119905119903119877119903 (11)





119877119903(120572 119879) =

120597120572

120597119905=

1

119867119905119903

119889119867 (119905)

119889119905= 1198700exp(minusΔ119864

119877119879) (1 minus 120572)

119899

(12)


(120597120572

120597119905+ Vpul

120597120572

120597119911) = 119877

119903(120572 119879) (13)




120593119891120588119891119862119901119891

120597119879119891

120597119905+ 120588119891119862119901119891

Vpul120597119879119891

120597119911

= 120593119891(119896119909119891

1205972

119879119891

1205971199092+ 119896119910119891

1205972

119879119891

1205971199102+ 119896119911119891

1205972

119879119891

1205971199112) + 119876

119903119891

(14)

120593120588119903119862119901119903

120597119879119903

120597119905+ 120588119903119862119901119903

(119906120597119879119903

120597119909+ V

120597119879119903

120597119910+ 119908

120597119879119903

120597119911)

= 120593(119896119903

1205972

119879119903

1205971199092+ 119896119903

1205972

119879119903

1205971199102+ 119896119903

1205972

119879119903

1205971199112) + 120593119902 + 119876

119891119903

(15)




119903= 1 minus 119881

119891sdot 119876119903119891

= minus119876119891119903








119903)


119864119903=

1198640

119903

119879lowast

lt 1198791198621

1198640

119903

+119879lowast

minus 1198791198621

1198791198622

minus 1198791198621

(119864infin

119903

minus 1198640

119903

) for 1198791198621

le 119879lowast

le 1198791198622

119864infin

119903

119879lowast

gt 1198791198622

(17)




119879lowast

= 119879119892minus 119879 = (119879

0

119892

+ 119886119879119892120572) minus 119879 (18)

where 1198790119892




119903varies


119903


) resin moduli 1198791198621

and 1198791198622






y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend




Rigid body

Temperature (T)


2D cross section




120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894





120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)





Δ119903119894= 119903119894(120575119888119894minus 1) (21)







120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































120578(1205972V

1205971199092+1205972V1205971199102

+1205972V1205971199112

) minus120597119901

120597119910= 0

120578 (1205972

119908

1205971199092+1205972

119908

1205971199102+1205972

119908

1205971199112) minus

120597119901

120597119911= 0

(7)


119906 = 119880 minus119870119909119909

120578Φ

120597119875

120597119909

V = 119881 minus

119870119910119910

120578Φ

120597119875

120597119910

119908 = 119882 minus119870119911119911

120578Φ

120597119875

120597119911

(8)


119870119909119909

= 119870119910119910

= 1198621(radic

119881119891max119881119891

minus 1) 119903119891

2

119870119911119911=

8119903119891

2

119888

(1 minus 119881119891)3

119881119891

2

(9)








120588119888119862119901119888

(120597119879

120597119905+ Vpul

120597119879

120597119911)

= 119896119909119888

1205972

119879

1205971199092+ 119896119910119888

1205972

119879

1205971199102+ 119896119911119888

1205972

119879

1205971199112+ 119881119903119902

(10)


119862119901119888






119902 = 120588119903119867119905119903119877119903 (11)





119877119903(120572 119879) =

120597120572

120597119905=

1

119867119905119903

119889119867 (119905)

119889119905= 1198700exp(minusΔ119864

119877119879) (1 minus 120572)

119899

(12)


(120597120572

120597119905+ Vpul

120597120572

120597119911) = 119877

119903(120572 119879) (13)




120593119891120588119891119862119901119891

120597119879119891

120597119905+ 120588119891119862119901119891

Vpul120597119879119891

120597119911

= 120593119891(119896119909119891

1205972

119879119891

1205971199092+ 119896119910119891

1205972

119879119891

1205971199102+ 119896119911119891

1205972

119879119891

1205971199112) + 119876

119903119891

(14)

120593120588119903119862119901119903

120597119879119903

120597119905+ 120588119903119862119901119903

(119906120597119879119903

120597119909+ V

120597119879119903

120597119910+ 119908

120597119879119903

120597119911)

= 120593(119896119903

1205972

119879119903

1205971199092+ 119896119903

1205972

119879119903

1205971199102+ 119896119903

1205972

119879119903

1205971199112) + 120593119902 + 119876

119891119903

(15)




119903= 1 minus 119881

119891sdot 119876119903119891

= minus119876119891119903








119903)


119864119903=

1198640

119903

119879lowast

lt 1198791198621

1198640

119903

+119879lowast

minus 1198791198621

1198791198622

minus 1198791198621

(119864infin

119903

minus 1198640

119903

) for 1198791198621

le 119879lowast

le 1198791198622

119864infin

119903

119879lowast

gt 1198791198622

(17)




119879lowast

= 119879119892minus 119879 = (119879

0

119892

+ 119886119879119892120572) minus 119879 (18)

where 1198790119892




119903varies


119903


) resin moduli 1198791198621

and 1198791198622






y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend




Rigid body

Temperature (T)


2D cross section




120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894





120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)





Δ119903119894= 119903119894(120575119888119894minus 1) (21)







120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References





































120593119891120588119891119862119901119891

120597119879119891

120597119905+ 120588119891119862119901119891

Vpul120597119879119891

120597119911

= 120593119891(119896119909119891

1205972

119879119891

1205971199092+ 119896119910119891

1205972

119879119891

1205971199102+ 119896119911119891

1205972

119879119891

1205971199112) + 119876

119903119891

(14)

120593120588119903119862119901119903

120597119879119903

120597119905+ 120588119903119862119901119903

(119906120597119879119903

120597119909+ V

120597119879119903

120597119910+ 119908

120597119879119903

120597119911)

= 120593(119896119903

1205972

119879119903

1205971199092+ 119896119903

1205972

119879119903

1205971199102+ 119896119903

1205972

119879119903

1205971199112) + 120593119902 + 119876

119891119903

(15)




119903= 1 minus 119881

119891sdot 119876119903119891

= minus119876119891119903








119903)


119864119903=

1198640

119903

119879lowast

lt 1198791198621

1198640

119903

+119879lowast

minus 1198791198621

1198791198622

minus 1198791198621

(119864infin

119903

minus 1198640

119903

) for 1198791198621

le 119879lowast

le 1198791198622

119864infin

119903

119879lowast

gt 1198791198622

(17)




119879lowast

= 119879119892minus 119879 = (119879

0

119892

+ 119886119879119892120572) minus 119879 (18)

where 1198790119892




119903varies


119903


) resin moduli 1198791198621

and 1198791198622






y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend




Rigid body

Temperature (T)


2D cross section




120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894





120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)





Δ119903119894= 119903119894(120575119888119894minus 1) (21)







120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References







































y

z x

y

z

x

y

x

z = zend

z = z2

z = x13z = 0

t = 0t = t1

t = t2

t = tend




Rigid body

Temperature (T)


2D cross section




120575119888119894= 119881119903120575119903119894+ 119881119891120575119891119894 (19)

where 120575119903119894

and 120575119891119894





120575119903119894= (1 + 120572

119903(119879119903119894minus 1198790)) sdot (1 minus

120574119903120572119894

100)

13

120575119891119894= (1 + 120572

119891119905(119879119891119894minus 1198790))

(20)





Δ119903119894= 119903119894(120575119888119894minus 1) (21)







120576120579119895ext = 120576

120579119895+1int

120590119903119895ext = 120590

119903119895+1int(22)


Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































Die wall


Virtual section



Section barycenter

120576120579119895 = 120576120579119895+1120590r119895 = 120590r119895+1


ext

ext

int

int



120576120579= minus

Δ119903

119903V (23)


119903equals to the












119905being




Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































Pulling direction


Composite475


yy

xz

Top

Center





[J kgminus1 Kminus1] 712 1255119896119909

[Wmminus1 Kminus1] 116 02119896119910

[Wmminus1 Kminus1] 116 02119896119911

[Wmminus1 Kminus1] 66 02119864119909

[GPa] 2068119864 + 1 mdash119864119910

[GPa] 2068119864 + 1 mdash119864119911

[GPa] 2068119864 + 2 mdash]119911119909

02 035]119911119910

02 035]119909119910

05 035119866119911119909

[GPa] 2758119864 + 1 mdash119866119910119911

[GPa] 2758119864 + 1 mdash119866119909119910

[GPa] 6894119864 + 0 mdash120572119909

(1∘C) 72119864 minus 6 45119864 minus 5

120572119910

(1∘C) 72119864 minus 6 45119864 minus 5

120572119911


120574119903




0 1 2 3 4 5 6

Pres

sure

rise

(Pa)

Axial distance (mm)

Intersection point


150 Pamiddots

260 Pamiddots

250 Pamiddots

105 Pamiddots

70E + 05

60E + 05

50E + 05

40E + 05

30E + 05

20E + 05

10E + 05

00E + 00







1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References





































1198700


infin

[Pasdots] 998779119864120578

[Jmolminus1] 119870

1914119864 + 4 605119864 + 3 169 3237119864 + 3 512119864 minus 7 376119864 + 4 450


1198791198621

[∘C] 119879

1198622

[∘C] 119879

0

119892

[∘C] 119886

119879119892

[∘C] 119864

0

119903

[MPa] 119864infin

119903

[MPa]minus45 12 0 195 3447 3447

Pulldirection

Resinbackflow


50e minus 003

40e minus 003

30e minus 003

20e minus 003

10e minus 003

00e + 000

Velo

city

stre

amlin

e 1 (m

sminus1)


0246

81012

14

489694

1204

Com

pact

ion

forc

e (N

)

26 (120572 = 002)15 (120572 = 0008)

105 (120572 = 0)


489694

120572 = 0)



00

02

04

06

08

10

0

50

100

150

200

250

0 400 800 1200 1600 2000 2400

Deg

ree o

f cur

e

Axial distance (mm)




Tem

pera

ture

(∘C)

Top

Center





471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































471

472

473

474

475

476

477

0 400 800 1200 1600 2000 2400

Wor

k pi

ece r

adiu

s (m

m)

Axial distance (mm)



Detachment point

Gel zone

Liquid zone

Nominal radius

Visc

osity

(Pamiddot

s)

Top

Center

8400 100 200 300 400

Die exit

12

10

8

6

4

2

0

times103






11)









11and 11987822



00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































00

02

04



Die exit

minus02

minus04

minus06

minus08

Top

Center

In-p

lane

stre

ssS

11(M

Pa)

(a)

0 200 400 600 800 1000 1200

Resin

mod

ulus

(Pa)

Axial distance (mm)


Top (FEM)Top (SAM)

Die exit

40E + 09

35E + 09

30E + 09

25E + 09

20E + 09

15E + 09

10E + 09

50E + 08

00E + 00

Top

Center

(b)



+2592e + 05

+1690e + 05

+7874e + 04

minus1150e + 04

minus1017e + 05

minus1920e + 05

minus2822e + 05

minus3724e + 05

minus4627e + 05

minus5529e + 05

minus6432e + 05

minus7334e + 05

minus8236e + 05y

zx

SS 1

1(A

vg 7

5)

(a)

+2595e + 05

+1693e + 05

+7908e + 04

minus1111e + 04

minus1013e + 05

minus1915e + 05

minus2817e + 05

minus3719e + 05

minus4621e + 05

minus5523e + 05

minus6424e + 05

minus7326e + 05

minus8228e + 05y

zx

SS 2

2(A

vg 7

5)

(b)


(a) and 11987822

(b)




4 Conclusions



000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































000

005

010

015

020

025

030

035

040

0 200 400 600 800 1000

Con

tact

pre

ssur

e (M

Pa)

Axial distance (mm)


Detachment point

Die exit

Top


0

100

200

300

400

500

600

49

3137

1841

5027


Frictional force

(N)

Pulling force

49

3137

1841

120574r = 4










Acknowledgment


References




































































Date post:	30-Mar-2021
Category:	Documents
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Computational Approaches for Modeling the Multiphysics in … · transformation (TTT) diagrams...

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