modelling face-core bonding in sandwich manufacturing thermoplastic faces and rigid closed-cell foam...

8/6/2019 Modelling Face-Core Bonding in Sandwich Manufacturing Thermoplastic Faces and Rigid Closed-Cell Foam Core

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ELSEVIER PI I : S1359-835X(98)00001-3

Composites Part A 29A (1998) 485-4940 1998 Published by Elsevier Science Limited

Printed in Great Britain. A ll rights reserved1359~835x/98/$19.00

Modelling face-core bonding in sandwichmanufacturing: thermoplastic faces and rigid,closed-cell foam core

Malin ikermo* and 6. Toma s htriimDepartment of Aeronautics, Kungl Tekniska Hijgskolan, SE- 100 4 4 Stockholm, Sweden(Received 23 June 1997; revised 75 December 1997; accepted 22 December 1997)

A model to predict the bond strength between thermoplastic faces and rigid, closed-cell foam cores in structuralsandwich components is presented. The model is based on the assumption that the bond strength is proportional tothe amount of resin that flows during manufacturing into the open surface cells of the core to bond the constituentsto each other. Following model formulation, a numerical example considering bonding of glass reinforcedpolyamide 12 faces to an expanded polymethacrylimide core is used to illustrate the relative influence of theindependent processing parameters. The numerical example is compared to a preliminary experimentalinvestigation carried out with the same material system and a favourable, albeit preliminary, correlation betweenmodel predictions and experimentally determined bond strengths is found. 0 199 8 Published by Elsevier ScienceLimited . All rights reserved.(Keywords: E. thermoplastic resin; E. resin flow; rigid foam core: sandwich)

NomenclatureA

4:

A

b

cD

h

ho

DhKn

nu

Permeation area [m]First permeation area of surface cell1mlSecond permeation area of surfacecell [m]In-core cell permeation area [m*]Position of matrix flow front andmatrix penetration depth [m]Gas concentration [cm3(STP)/cm3]Diffusion coefficient [m*/s]Acceleration of gravity [m/s21Height of matrix layer adjacent tocore [m]Initial height of matrix layer adjacentto core [m]Activation energy of matrix [Umol]Gas solubility coefficient [s]Number of moles of gas [mol]Initial number of moles of gas in oneopen cell [mol]

P

PP.

p PP

PP

Q

4rRRrTt

T,TretVY

Permeabi ty coefficient of?corematerial PBarrer, 10 - lo m]Pressure [Pa. N/m]Ambient pressure [Pa. N/m]Applied processing pressure [Pa. N/m-1Gas pressure within each cell [Pa. N/m]Number of moles of gas to have per-meated a cell wall [mol]Volume flux m cylindrical or spheri-cal channel [m/s]Molar gas constant (J/mol K]Radius of flow channel [m]Radius of spherical core cells [m]Instantaneous temperature [K]Time [slAmbient temperature [K]Reference temperature [K]Cell volume lm]Velocity vector [m/s]

* Author to whom correspondence should be addressed


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Modeling face-core bonding: M. Akermo and B. T. htrom

Nomenclature continued,WGreeksa

Volume of gas in one cell [m]Thickness of core cell wall [m]

Angle between flow lines and channelaxis [Radians]PPmf

Matrix viscosity [Pa*s, Ns/m]Matrix viscosity at reference tem-perature [Pa-s, Ns/m]

P Matrix density [kg/m31

INTRODUCTION

Bonding o f two thermoplastic polymer components isprimarily established through intimate, molecular contactbetween the components and diffusion of polymer mole-cules across the interface, which upon cooling results inmolecular interlocking. The degree of diffusion (or mixing)of molecules at the interface depends on the compatibility ofthe two surfaces to be bonded and on the bondingtemperature, which m ust be above the glass transitiontemperature of the polymer. In bonding of two identicalpolymer components, mixing may be complete, i.e. thecomponents are bonded into one solid component withoutany boundary visible in-betw een. At this stage the interfacehas reached the same strength as that of the virgin material*-4. Based on the theory of molecular diffusion between twocomponents of the same polymer, a model of bonding of all-thermoplastic honeycomb core sandwich components hasbeen developed by the authors5. In the bonding ofincompatible polymers, the degree of molecular mixing atthe interface is limited and a weak bond is thus established.Howev er, a second, and often dominating, bondingmechanism may occur as matrix from one surface flow sinto and solidifies in irregularities of the other surface andthus mechanically locks the components together.

This paper considers bonding of thermoplastic faces to arigid closed-cell foam core. Bonding is in this case governedby matrix flow into the core during processing, since theflow both increases the contact area between face and core,making a limited deg ree of molecular mixing possible and,at the same time, enabling mechanical locking of thecomponents. No further effort is dedicated to determiningthe actual bonding mechanism, but it is assumed that thebond strength is to some extent proportional to the matrixpenetration depth into the open surface cells of the core. Thematrix flow at the face-core interface has therefore beenmodelled with the intent of developing a tool to determinehow process parameters and material p roperties influencethe matrix penetration depth into the core and therebyindirectly the face-core bond strength. That matrix reallydoes how into the open surface cells during processing isillustrated by Figure 1, showing a near half-spherical matrixbubble left on the face following face-core failure.

46 6

Following model formulation, a numerical example ispresented to illustrate the predicted matrix flow in bondingof glass fabric reinforced polyamide 12 (PA 12) faces to anexpanded closed-cell polymethacrylimide (PMI) foam core.The results o f the numerical example is compared to resultsof an initial experimental study on compression moulding ofsandwich components using the same materials as used inthe numerical example.

PROBLEM STATEMENTThe techniques used to manufacture sandwich componentsdiffer widely depending on the application and theprocessing requirements of the materials used. A reviewof the current state-of-the-art of sandwich manufacturing,which largely involves thermoset rather than thermoplasticmatrices, can be found in reference 6. Howev er, in themodel presented herein, quite general processing conditionsare considered. The thermoplastic faces are heated to atemperature above the matrix melting point using adedicated oven. Faces and core are then stacked andplaced in the cooled mould, where the sandwich componentis consolidated under constant p ressure. To enable makingthe necessary assumptions on problem geometry, the modelis limited to unreinforced or fabric reinforced thermoplasticfaces and rigid, expanded closed cell foam cores (or similarmaterials). Howev er, the model is easily adopted to otherface material systems by making appropriate assumptionsregarding the matrix pressure gradient within the face.While some assumptions are introduced during modelformulation, the ones defining model geometry, boundaryconditions and fluid behaviour are stated below:?? Figure 2 shows that the core surface cells are similar to

irregular polyhedrons cut open at different locations.

Figure 1 Matrix bubbles remaining on the face fracture surface followingface-core failure. The face material is glass fabric reinforced PA 12 with aPA 12 resin film added on top


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Modeling face-core bonding: M. Akermo and B. T. Astrom

Howev er, to simplify m odel formulation, the surface cellsare assumed to be perfect half-spheres, whose shaperemains unaffected by the process.In order to model the matrix flow into the core the matrixpressure gradient m ust be known. Co mposite laminatesoften have matrix-rich surfaces and face-core bonding isgenerally enhanced when a neat resin film is addedbetween face and core. Figure 3 shows a glass fabricreinforced PA 12 laminate with a black PA 12 resinfilm (pigmented for visibility) laminated onto one side.Since the transverse permeability of tight fabrics is quitelow and melted thermoplastics generally have very highviscosities, transverse flow within the face during mould-ing is assumed negligible. The pressure in the matrix-richlayer adjacent to the core is therefore assumed equal tothe applied moulding pressure.Although thermoplastic melts are generally shear thin-ning, this tendency is in this mod el ver sion neglectedand a Newtonian fluid model is consequently used.The face-core consolidation step in sandwich manufac-turing is assumed isothermal. Where as heat transfer

during compression moulding of foam core sandwichcomponents has been modelled globally as part of anextensive in-house study, microscopic modelling consid-ering the irregular geometry of the core surface andincluding material convection is beyond the scope ofthis model version. Temperature nevertheless remains aparameter in the model.

THEORETICAL APPROACH

Matrix jlow int o open s&ace cell

Consider the matrix-rich layer adjacent to the core andone half-spherical surface cell, as illustrated in Figure 4.Initially the matrix is concentrated to the matrix-rich layer.By applying consolidation pressure onto the face, a gradientdevelops within the matrix, thus forcing the matrix into thecell. Assuming that every surf ace cell has the same radius.the flow can be considered as restricted to the v-direction,

Figure 2 Machined surface of expanded closed-cell polymer foam. The tigure shows a PM1 core (Rohacell I lOA). but the general ceil structure is shared bymost expanded polymers. Published with permission from RGhm, Darmstadt. Germany

Figure 3 Glass fabric reinforced PA 12 laminate. The woven fabric is visible as white layers. An extra PA 12 resin layer, in this case pigmented black forvisibility. has been added on top as a bonding aid

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Modeling face-core bonding: M. Akermo and B. T. Astrom

i.e. into the core. The pressure in the gas (air) initiallytrapped in the cell increases when matrix flows into the cell,thus reducing the pressure gradient and consequently thematrix flow rate. Due to the increased gas pressure in thesurface cell, the gas is assumed to permeate through the thincell walls further into the core.

The matrix flow into the half-spherical cell is neitherlaminar nor steady, which makes the problem difficult tosolve analytically. Therefore, in order to further simplify theproblem, two additional assumptions are made:

During a sufficiently short time increment, the flow intoand within the half-sphere is assumed to be steady. T henon-steady process can thus be solved by discretizing theprocess with respect to time, solving the steady-stateproblem for each time increment and summing up thecontributions. The increasing gas pressure within thecell and the position of the matrix flow front thus needsto be recalculated for each time step.During each incremental time step, the matrix flow withinthe cell is assumed to be laminar. This m ight seem a crudeapproximation, but it can be explained by considering theNavier-Stokes equation describing the motion ofNewtonian fluids. The non-laminar flow gives rise toinertia forces exp ressed as nonlinear terms [vVV] in theacceleration force term of the Navier-Stokes equation (vis the velocity vector). C onsidering steady flow through achannel of varying radius it can be shown that these iner-tia forces can be neglected if7

PVRff-< 1 (1 )where (Y s angle between flow lines and channel axis, pdensity, v velocity, R channel radius, p Newtonian visc-osity. This expression was determined by considering they-component of the flow given by the Navier-Stokesequation, balancing its compo nents and requiring theacceleration force term to be negligibly small. Eqn (1)may be interpreted as stating that the acceleration forcecan be neglected if the variation in cross-section area withstreamwise distance within the channel is sufficientlyslow. Keeping in mind that the viscosity of melted ther-moplastics is on the order of lo-105, their density on theorder of unity, the channel radius on the order of 10v4, andthe velocity intuitively high only when the change in chan-nel radius, (Y, s slow, one finds that eqn (1 ) always holdstrue for the present flow situation. (Representative numer-ical data are given in Table I.)These approximations reduce the equation of motion

within each time step to the Hagen-Poiseuille equation,thus giving the volume flux of matrix, qy r as

(2 )where R is the average radius during the time step, p t h ematrix pressure and g the acceleration of gravity.

The matrix flow front, at y = b (cf. Figure 4), supports thegas pressure, while the top of the matrix-rich layer (at y = -h), supports the applied pressure, p a p p . T h e pressure drop

between the two ends of this virtual flow channel isdetermined by integrating over its length:

Pg-papp= -WY: Jb -L-Iv+ b- R (=J)~ J_,P&3)Integration of eqn (3), using R(y) = r for - h I y 5 0 andR (y) = (r - y*)* (cf. Figure 4) for 0 I y 5 b yields

sY = (pg(b + h) - (Ps -pap,))XT r48~ (4)h -

where the expression for the instantaneous gas pressure, p g,is derived below.

Since the matrix is assumed to be incompressible, thematrix volume is conserved during processing and thevolume flux of matrix can also be expressed in terms of they-position of the matrix flow front. However, due to thespherical geometry, an exact calculation of how muchfurther into the surface cell the matrix has flowed during atime increment requires solution of a third degree equation.Considering the matrix flow during a very short timeincrement, the change in channel radius at the flow front is

Table 1 Data corresponding to a closed cell PM1 foam core and glass/PA12 faces, used in numerical exampleVariable Value ReferenceCore thicknessDhPrefPaPaPPP(PMMA)rPT,T efw

1omm23 kJ/mol175 Nm/s0.1 MPa0.8 MPa0.01 Barrer0.13 mm1.01 kg/m23C220C0.004 mm

eqn (14)**

82gure

Figure 2*Based on experimental data from Hills.

PWP

Figure 4 Matrix flow into one half-spherical open surface cell. The radiusof the sphere is r and the instantaneous channel radius R. The matrix-richlayer adjacent to the core is of instantaneous height h and in the figure thematrix has flowed distance b into the cell. pw and ps denote appliedpressure and gas pressure in the open cell, respectively


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Modeiiing face-core bonding: M. hkermo and 6. T. hrom

very small and the time derivative of the position of thematrix flow front can be approximated by

db qydt=7FR(b)2 (5 )

Gas permeationIf a thin wall of thickness w separates two chambers

containing gas at different pressure, the gas will permeate inthe direction of the negative pressure gradient. In theproblem considered herein, the gas permeates into the coresince the matrix inflow increases the gas pressure in thesurface cells. The matrix flow is assumed uniform over thecore surface, meaning that the gas pressure within one layerof cells in the core is uniform and that gas permeationparallel to the core surface therefore may be neglected.Since cores are normally stored in ambient conditions for along time prior to processing the gas diffusion may beconsidered steady. It is also assumed that Henrys law applies to both interfaces of the cell wall, i.e. that asolubility coefficien t, K, exists so that

K=S=c?PI P? (6 )

where Cl and C2 are the gas concentrations and p , and p,the gas pressures at the respective surfaces. Henrys law wasdeveloped for rubbery polymer membranes at temperaturesabove their glass transition temperature, but describes oneof the two contributions to the sorption of gases in glassypolymers with intersegmental packing defects frozen intothe structure. The other contribution comes from the so-called Langmuir sites arising from the packing defects dur-ing solidification of the polymer. The permeating moleculestrapped in the Langmuir sites are much less mobile thanthose obeying Henrys law and molecules in the Langmuirsites are therefore for the purpose of this treatment consid-ered immobile . Ficks first law then holds, stating that forsteady-state diffusion the gas flux through the thin wall isproportional to the gas concentration gradient through thewall. i.e.

Q = - DAt(C2 - C,)/w (7)where Q is the number of moles of gas that has diffusedthrough a wall of area A and thickness w during time t,

cell layer:3

i-lIi+l

where D is the diffusion coefficient. The permeabilitycoefficient of the core wall, P, is defined as the product ofthe diffusion coefficien t and the solubility coefficien t.Using eqns (6) and (7), the total number of moles of gasthat has passed through the wall separating the surface cellfrom the immediately underlying cell at ambient pressure paduring time t can therefore be expressed as

Q= _,,,!%@w

In reality the core cells are more similar to polyhedrons thanhalf-spheres and the contact areas between different cellswithin one layer are therefore not single points, as forspheres. but rather surfaces. Since no permeation occursbetween cells within one layer, the initial permeation areabetwee n surfac e cells and underlying cells. A: is assumedequal to the projected area of the half-sphere, i.e. At = 1rr.Howev er, the permeation area decreases as the matrix fillsthe cell. At b > r/2 the surface area of the gas filled part ofthe half-spherical cell given by A: = 2mfr - b) (cf. Figure4), decreases below the assumed initial permeation area.The latter permeation area, AZ , is therefore from that pointon used to calculate the permeation area between the cells.

As gas permeates into the next layer of cells, the gaspressure is built up also within these cells, thus forcing thegas to permeate further into the core. see Figure 5. Th eincreased number of moles of gas within cell layer i in thecore at time f is

Qi= _pA*,(2P& -P&+1 -p,,w

The permeation area between two cells within the core, A,,is equal to the projected area of the sphere. Note that twodifferent permeation areas, equal to the surface cell permea-tion area, A,, and the in-core cell permeation area, A,, mustbe considered when calculating the increased number ofmoles of gas within the second layer of cells (immediatelybelow the surface cells).

Gas pressure in open cell

Before faces and core are brought together, the surfacecells are filled with air at ambient temperature, T,, andambient pressure, pa. By considering the air as an ideal gas,

core surface--

Figure 5 The core cells are idealised as arranged in layers. The increased number of moles of gas within cell layer i, pi, depends on the gas pressure. pg.within the surrounding cells, here ps,+, 5 peC 5 pgl_,


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Modelling face-core bonding: M, Akermo and B. T. Astrom

the instantaneous gas pressure can be determined byrecalculating the original pressure, volume an d temperatureinto the instantaneous volume and temperature of the gas.The ideal gas law gives the initial number of moles of gas noin a cell as

P ,Vn o = R T , (10)where R is the molar gas constant and V the cell volume.During processing air permeates through the core wall andthe remaining moles of gas in the cell continuouslydecreases. T he instantaneou s gas pressure w ithin each cellis given by

nR TPg = - V z s (11)where V , is gas volume, T instantaneous gas temperatureand n instantaneou s num ber of moles of gas in the cell,which is given by n=no-Q (12)

P r ed ic te d m a tr i x p e n et r a t io n d e p thEqn (5) provides an expression for the matrix penetrationdepth (distance) into the core. In the model, the process is

discretized with respect to time and the final penetrationdepth is therefore found by sum ming up the contributionsfrom each time increment:

where qy is given by eqn (4). The boundary conditions, i.e.the position of the matrix flow front and the gas pressure, arerecalculated in-between each time step. The instantaneousgas pressure is calculated using eqns (8 ), (9) and (11). Notethat this expression for the matrix penetration depth is onlyvalid if the amount of matrix initially available at the face-core interface exceeds the amount needed to fill every opencell at the core surface. Since the matrix viscosity is stronglytemperature dependent, thebe used in eqn (13).

NUMERICAL EXAMPLE

instantaneous viscosity should

This section provides a numerical example using thepresented model. The material data used correspond toglass fabric reinforced PA 12 faces, in this case Vestopreg@from Hi& , and a closed cell PM 1 foam core, in this caseRohacell@ 1lOA from Rohrn. While this core is partlycrosslinked and therefore can not melt, it softens uponexcessive heating. For the purpose of the model presentedherein it is nevertheless considered rigid throughoutprocessing. The average cell radius and cell wall thicknesswere determined from Figure 2. It is assumed that extraPA 12 resin is added to the face-core interface as a bondingaid. The available amount of matrix at the face-core

interface thus exceeds the amount needed to fill every opencell at the core surface and the matrix content at theinterface does not limit the flow into the cells. Matrixviscosity data for three different temperatures as function ofshear rate (provided by Htils) were fitted to the Carreau-Yasu da model. Since the presented m odel only considersNewtonian fluid behaviour, the zero-shear rate viscosity wasused in the predictions. The temperature dependency of theviscosity was accounted for using the Arrhenius shiftfactor:

(14)The behaviour predicted by the Arrhenius shift factor isobserved in molten polym ers 100C or more above theirrespective glass transition temperatures. Eqn (14) washerein used to predict the matrix viscosity at temperaturesabove the melting tem perature of PA 1 2, which at about180C is more than 120C above the glass transitiontemperature of 54C . The reference viscosity , p ref, andtemperature, TIe f , used in this example are given in T a b leI , together with the activation energy, &, which wascalculated from the viscosity data. Since the permeabilitycoefficient of PM1 could not be found in the literature, itsvalue was approximated by the permeability coefficient of achemically related polymer, poly(mety1 metbacrylate),PM MA . The permeability coefficient is reported in thecustomary unit Barrers9, where 1 Barrer equals lo-[cm3(STP) cm/(cm2s cm Hg)]. The permeabilitycoefficient depends on the permeating medium and thevalue given in Table I corresponds to the coefficient fornitrogen (Nz).

The model was numerically implemented in MATLABusing a time increment of 10 e5 s. First the new position ofthe matrix flow front after one time increment is calculatedand then the gas pressure within the surface cell andunderlying cells is calculated. T his procedure is repeateduntil the entire surface cell is filled, until a set processingtime is reached or, more likely, until the matrix solidifies.The temperature within the ga s filled cell is in this exampleassum ed equal to the face temperature, which is anoverestimation. The real gas temperature is probably closeto the average tem perature of face and core, but exactdetermination of the gas temperature requires more detailedheat transfer modelling than so far carried out.Two different values for the gas permeability coefficientof PMMA were found in the literature. In addition to thevalue given in Table I , reference 8 gives the gaspermeability of PMM A a s 0.1 Barrer, i.e. an order ofmagn itude higher. In this reference the permeating mediumis not stated an d the lower value of the gas permeability istherefore used in most of the examples, although both valuesare used for the predictions in Figure 6 to illustrate theimportance of gas permeation. The figure shows thepredicted matrix penetration depth for two differentpressures, 0.2 MPa and 0.8 MPa, and for both gaspermeabilities. In these calculations, the process is assum edisothermal at 200C and the matrix within the face isconsequently assumed melted throughout the process. The

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Modeling face-core bonding: M , hermo and B. T. horn

model predicts that the main part of the matrix flow occursduring the first tenth of a second of processing (which isdifficult to make out from the figure). The linear increase inmatrix penetration depth occurring thereafter is due to gaspermeation from the surface cell, which reduces the gaspressure in the cell and thus enables further matrix flow.Figure 7 is essentially a magnification of the time axis forthe first 0.06 s of the predictions in Figure 6, but only thepredictions em ploying the lower permeability coefficientare shown. The figure clearly illustrates that under theseprocessing conditions little additional matrix flows into thesurface cells after the first few hundredths of a second.

The time until the matrix solidifies mainly depends uponthe temperatures of mou ld, faces and core. Both throughheat transfer modelling and experimental work, it was foundthat with realistic face temperatures and the mould atamb ient temperature, the sandwich component is cooled tobelow the matrix melting temperature within a matter ofseconds following mould closure. The gas permeationduring su ch a short time frame is negligibly small according

0.14

f 0.12g5 0.10%uc 0.08.g$ 0.06Ep?! 0.04t$ 0.02

n

to the curves corresponding to the lower permeabilitycoefficient in Figure 6. Using a cooled mould, the matrixflow most probably ceases at a point where the gas pressurein the surface cell is balanced by the applied processingpressure; this point is hereinafter referred to as theequilibrium point. Figure 8 shows the predicted equilibriumpoint for two different tem peratures, 200C and 250C asfunction of moulding pressure. The figure shows that thepredicted matrix penetration depth at the equilibrium pointincreases with increasing pressure. The increase is sig-nificant at low pressures, bu t levels off above 1.5 MP a toasymptotically approach the core cell radius. Figure 8 alsosuggests that the equilibrium point exhibits a weaktemperature dependency, which is further illustrated inFigure 9 (note the different length scales of these twofigures). The reason for this dependency is that, although theinitial flow rate increases with increasing face temperaturedue to the reduced matrix viscosity, the equilibrium point isreached sooner since the gas pressure within the cell alsoincreases w ith temperature. Observe once again that if the

cell radius

p=O.8 MPa-

~E0.1 Barrer

eO.01 Barrer

p=O.2 MPa @=O.lBarrer

eO.01 Barrer

1

-0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Processing time (8)

Figure 6 Predicted matrix penetration depth into the core as function of time for two different pressures, two different gas permeabilities and a facetemperature of 200C

0.14P cell radiusg 0.12 -5g 0.10 p=O.8 MPa-_-.---- -_---_-_-_._---_- ____u

1

0.00 0.01 0.02 0.03 0.04 0.05 0.06Processing time (8)

Figure 7 Predicted matrix penetration depth as function of processing time during the first 0.06 s for two different pressures and a face temperature of 200C

4 9 1


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Modeling face-core bonding: M. Akermo and B. T, As from

available am ount of matrix at the face-core interface islimited, predictions such as these may not hold, since thematrix penetration depth into the core cannot significantlyexceed the initial height of the matrix-rich layer.

COMP ARISON TO EXPERIMENTAL STUDYThe aim of developing the presented model w as to increasethe understan ding of bonding of thermoplastic faces to rigid,closed-cell foam cores. To further this goal, some of theresults of the numerical example above have therefore beencompared to an initial experimental study on compressionmoulding of glass/PA12-PM1 foam core sandwich compo-nents , i.e. the same material system a s considered in thenumerical examples above. In this study, a two-levelTaguchi design13 was used to investigate which processingparameters most significantly influence the transversetensile strength of the manufactured components. Consoli-dation was performed either keeping the mould at ambien ttemperature or heated to 80C and the consolidation timewas therefore short. The transverse tensile strength w ascharacterized according to AST M C297 . The weaker

0 . 1 4E -L 0 . 1 2c=4

0 . 1 0

cell a d i u s

5 0 . 0 8' EE 0 . 0 8tg 0 . 0 4X; 0 . 0 2z

0 . 0 0

T = 2 0 0 " C

p r

IIi0.0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5

specimen s all failed at the face-core interface, whereas inthe stronger specimens failure took place in the core and theface-core bond strength was then apparently higher than thetensile strength of the core. In this initial study severaldifferent processing variables were investigated and in orderto reduce the num ber of experiments, a fractional factorialdesign w as used13. This study therefore cannot provideunambiguous information on how the processing para-meters influence the bond strength and the results aretherefore merely used for qualitative comparisons in orderto detect trends in the bond strength dependency on theinvestigated parameters.

Not surprisingly, the study indicates that the parametersmost significantly influencing the bond strength are thosedetermining the amou nt of matrix at the face-core interface.Two different kinds of face materials were used in the study:preconsolidated 1 mm thick faces and single prepreg plies.The preconsolidated faces appeared to have resin richsurfaces, while the unconsolidated prepregs, wh ich arepowder im pregnated, appear resin starved on the surfaceprior to consolidation. Through m icroscopy it was observedthat neither of these materials seemed to have enough resinon the surface to allow filling of the open cells of the core

Pressure (MPa)Figure 8 The predicted equilibrium point as function of the applied pressure for two different face temperatures

0 . 1 0 0 I2E. 0.098 -cZ* 0.098 -c.s2 -0.0945IL 0.092 -!!2m= 0.090 I I I I I I I I c I I

1 8 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0Temperature (C)

Figure 9 The predicted temperature dependency of the equilibrium point

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Modeling face-core bonding: M. Akermo and B. T. istrom

surface. A 0.1 mm thick PA 12 resin film w as thereforeadded to the interface as a bonding aid in some of thespecimens. The results sho w that the transverse tensilestrength of the components increases significantly withincreasing amount of matrix available at the face-coreinterface, see Figure 10. The single prepreg faces withoutresin film added did not seem to bond to the core at all.Howev er, use of prepreg faces and an extra resin filmresulted in higher strength than when using preconsolidatedfaces without resin film added. The highest strength wasachieved with preconsolidated faces and resin film added.

The experimental study also shows that the processingpressure influences the bond strength in the fashionpredicted by the model. The transverse tensile strengthincreased by 25% when the pressure was increased from0.55 to 0.9 MPa . The model predicts that the matrixpenetration depth should increase by 0.02 mm, equal to24%, for such a pressure increase.

As the face preheating temperature was increased from200C to 220C the transverse tensile strength decreased .Part of the explanation might be referred to Figure 9, whichshows that increasing moulding temperature also reducesmatrix penetration into the core. Howev er, the predicteddependency is far too weak to account for the significantdecrease in bond strength observed and some othermechanism must at least be partially responsible.

DISCUSSIONIn the model presented above the matrix viscosity isassumed Newtonian, although polymer melts, includingthe one considered in the numerical example, are shear-thinning (non-New tonian). This assump tion simplifiesmodelling but of course makes the result less exact. Themain purpose of developing the model was to gainunderstanding of how the process param eters influencebonding between thermoplastic faces and a rigid foam core.It is argued that bonding is proportional to the amount ofmatrix penetrating into the core surface during p rocessing

and the final penetration depth is therefore of greatestimportance. Howev er, the presented model, which, due tothe Newtonian assumption, overestimates the matrixviscosity, shows that matrix penetration is a very rapidprocess and that the final penetration depth m ay be reachedwithin less than 1 s. Incorporating the instantaneous shearrate dependent viscosity into the model will not alter thepredicted ultimate penetration depth, although it will bereached in an even shorter time. Thus, for the purpose ofgaining a qualitative understanding of bonding t hrou ghmatrix flow, this simplified model version is likelysufficient. Howev er, in order to enable quantitativelyrealistic predictions of all aspects of the matrix flowduring processing. a non-Newtonian fluid descriptionshould be used.

Since the gas permeability coefficient of PMI. needed inthe model, was not available from the core manufacturerand could not be found in the literature, it had to beapproximated using the permeability coefficient of achemically related polymer, PM MA . Two different valuesof the permeability coefficient for PMM A were found in theliterature, each giving its specific required processing timeto till the core surface cells. The difference between the twopredictions is quite significant. The lower of the two valuesindicates that gas diffusion between adjacent cells may beneglected under conditions such as those investigatedherein, whereas the higher of the two values suggests theopposite, since gas diffusion already plays an important rolefor short consolidation times. This difference illustrates thatthe permeability coefficient of the core in question must beknown to allow accurate predictions.

The model d oes not include modelling of heat transferduring processing. The material temperature is of interestfor several reasons: the gas pressure in the surface cellsdepends on gas temperature, the matrix can only flow attemperatures above its melt temperature (or glass transitiontemperature for amorphous thermoplastics ) and rapid coolingof the manufactured sandwich component thus effectivelylimits the matrix penetration into the core. Considering allthese temperature-dependent parameters. not knowing the

2s5 1200- Increasing matrix content5 lOOO- at face-core interfaceFEfn EOO-P,5 600-s

www laminate n%XrZn laminatematrix filmFigure 10 Experimentally determined transverse tensile strength of sandwich panels with different face material configurations and different matrix contentat face-core interface. Tensile strength of virgin core is 2.8-3.5 MPa

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Modelling face-core bonding: M. Akermo and B. T. htrom

temperature developm ent at the face-core interface duringprocessing is a weakness of the model, which must beovercome in order to ensure quantitatively realistic predictions.

The pressure distribution at the face-core interface is aninteraction between core, matrix and reinforcement. Apply-ing pressure onto an unlimited amount of matrix on the coresurface, the matrix penetrates into the core, thus increasingthe gas pressure within each cell and evenly distributing thepressure over the entire core. If the applied pressure isexcessive, the core cell walls may rupture du e to the highgas pressure. If pressure is applied by reinforcement indirect contact with the core cell walls, the uppermost part ofthe walls have to sustain the entire applied pressure, whichmay cause the walls to buckle. Increasing the temperature ofthe face, the core is heated further and the maximum loadthe core can withstand decreases further. The modelassum es that the core cell walls remain unaffected bypressure a nd temperature, which is obviously true onlywithin a limited processing window. It is thereforeimportant to consider the compressive strength of the corebefore blindly implementing the model predictions tooptimize the matrix penetration depth.

This paper does not include any dedicated experimentalverification of the presented model, although initialexperimental work appears to substantiatepredictions. H owever, an extensive experimen talunderway in order to further verify the model.

modelstudy is

CONCLUSIONSA model has been developed to predict the matrix flow intoa rigid, closed cell foam core during bonding of sandwichcomponents. The model is used in a numerical exampleconsidering bonding of glass fabric reinforced PA 12faces to a closed cell P M1 foam core. T he permeab ilitycoefficient of PM1 could not be found an d was thereforeapproximated with two different permeability coefficientsfound for PMMA. Matrix penetration during isothermalprocessing at 200C was predicted using these two differentvalues and it was found that with the lower of the twovalues, the influence of gas permeation on the matrixpenetration depth is weak enough to be neglected for shortprocessing times. If gas permeation is neglected, matrixflow ceases as the gas pressure within the cell is balanced bythe applied pressure.

The model predicts that the matrix penetration depthsignificantly increases with increased pressure up to about1 MP a. The model further p redicts that 70% of themaxim um m atrix penetration depth is reached within0.005 s at a pressure of 0.8 M Pa and a face temp erature of200C. The model also shows that the matrix penetrationdepth decreases with increasing face temperature, since thegas pressure within the core surface cells increases when thegas is heated by the face.In conclusion, the model predicts that maximum matrixpenetration into the core surface cells (and thus, accordingto the main model assumption, maximum face-coreinterfacial bo nd strength) is obtained us ing as high a

pressure as the core can sustain and as low a temperature aspossible (above the matrix melting temperature). Thepredicted processing time is very short, less than 0.1 s, butneeds to be substantially increased when the pressure isreduced. Using lower pressures, the required processingtime to enable filling the core surface cells mainly dependson the gas permeability coefficient of the core. However, inreality the processing time may not be arbitrarily chosen,since it is determined by the heat transfer situation at theface-core interface.

The numerical results are compared to an initialexperimental study on compression mou lding of sandw ichcomponents using the same materials as considered in thenum erical example. The face-core interfacial bond strengthwas characterized in terms of the transverse tensile strength.It is assumed that this strength is proportional to the amou ntof matrix having penetrated into the core surface cellsduring processing and this assumption is partly substantiatedby the experimental study. The experiments also show thesame pressure and temperature dependence as predicted bythe model, but further experimental work is needed to draw afirm conclusion on the quantitative accuracy of the model.

ACKNOWLEDGEMENTSThis work has been supported by the Commission of theEuropean Union under Brite-EuRam contract no. BRB2-CT94-0912. Material and material data were generouslysupplied by Hills, Marl, Germany, and Rohm, Darmstadt,Germany. Special thanks are due to Dr Hellermann and MrSeibert, who have been helpful contacts at their respectivecompany.

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