Simulation of bleeder flow and curing of thick composites with pressure and temperature dependent properties

Simulation Modelling Practice and Theory 32 (2013) 64–82

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Simulation of bleeder flow and curing of thick composites with pressure and temperature dependent properties A.S. Ganapathi a,⇑, Sunil C. Joshi a, Zhong Chen b a b

Division of Aerospace Engineering, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639 798, Singapore Division of Material Science, School of Materials Science and Engineering, Nanyang Technological University, Singapore 639 798, Singapore

a r t i c l e

i n f o

Article history: Received 13 August 2012 Received in revised form 14 November 2012 Accepted 10 December 2012 Available online 7 January 2013 Keywords: Laminate Bleeder Resin flow Curing Consolidation

a b s t r a c t A two-dimensional transient heat transfer, one-dimensional compaction and two-dimensional resin flow analysis of a thick laminated composites fabrication assembly including the bleeders and vacuum bagging is carried out in a fully coupled manner. Resin distribution within the laminate and the bleeders is controlled by their respective compaction behavior as well as permeability of the fiber network. Compaction behavior of dry bleeders is obtained from compression experiments carried out in-house and the derived relevant empirical parameters are used in the numerical simulation. The variations in the resin volume fraction within the laminate due to the resin outflow to the surrounding bleeder were tracked and updated as a function of time in the cure simulation. Four case studies were performed with temperature dependent as well as independent resin properties and pressure dependent and also pressure independent resin volume fractions. These simulations were carried out to understand the behavior of resin flow through the bleeder and its impact on the local variations in the resin content of the laminate. The results obtained show a significant disparity in the thermal overshoot at the center of the laminate and the pressure distribution within the laminate and the bleeder, when a complete coupling and the parametric changes as in the real situation are ignored in numerical simulation. It is shown that the complete coupling of various real-time phenomena helps in accurate prediction of temperature, pressure, resin viscosity, bleeder and fiber compaction, resin flow and associated changes in fiber volume content, and degree of cure distributions for thick composites as they are cured. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction The performance of laminated composites greatly depends on the type of manufacturing process employed. Autoclave curing, where reasonably high pressure, temperature, and vacuum can be applied during curing, is widely used to manufacture composites. The compaction or consolidation pressure applied during curing plays a major role in enhancing performance of the resultant composite laminates. Within a curing laminate the consolidation process depends on the resin viscosity, degree of cure and temperature distribution in thick laminates and study of these various parameters and the associated processes has been of research interest. A one-dimensional (1-D) sequential compaction model by Springer et al. [1] explains well the resin flow transverse to fiber direction and calculates the resin flow rate for known constant viscosity fluids. Lee et al. [2] measured the viscosity, the heat generated during curing reaction and the extent of reaction for Hercules 3501-6 resin system and developed ⇑ Corresponding author. Tel.: +65 85086835. E-mail address: [email protected] (A.S. Ganapathi). 1569-190X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.simpat.2012.12.002

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analytical models to represent each parameter. A three-dimensional (3-D) laminate compaction model based on soil consolidation theory and flow through porous media shows the interaction between the flows in different directions and gives a nonlinear compaction behavior model [3,4]. Gutowski et al. [5,6] conducted consolidation experiments and concluded that the Carman–Kozeny equation should be modified to represent permeability of a porous fibrous media in transverse directions. These consolidation experiments gave a suitable expression for fiber effective stress and permeability. Rate of consolidation of fiber reinforcement affects permeability of the laminate [7–9]. Increase in the rate reduces permeability in the transverse direction and it should therefore be updated continuously in the numerical simulation process [9,10]. A 1-D as well as 3-D consolidation study of thick laminated composite concludes that a minimum compaction pressure should be applied to achieve complete consolidation [11–13]. A multi-physics numerical simulation of 2-D consolidation of laminated composites shows the influence of fiber parameters on the compaction behavior [14,15]. For curved laminates, the fiber bed shear modulus at the corners greatly influences compaction behavior of the laminate and alters its final shape [16]. Any gap left between the tool and the curved laminate due to improper compaction leads to resin rich zones and creates residual stresses and part-to-part variations in the geometry [17,18]. One such issue is addressed experimentally by Dong [18] for an angle-shaped part. An analytical model was developed to identify the formation of resin rich zones. An inverse method is proposed to obtain the parameters that relate the pressure in the laminate and the compaction stresses. This emphasizes the importance of multi-physics modeling of the manufacturing process. These simulation methods considered constant resin content in the laminate and focused on thermo-chemical–mechanical–elastic–rheological coupling. But, coupling the resin flow and compaction in the process simulation, which is also important, was ignored. Sun et al. [19] simulated the tool-part interaction induced residual shear stresses during the consolidation of L-shaped laminates. Mechanical properties of the tool also play a role in the transfer of autoclave pressure to the laminate and its consolidation. Initial curing reaction rate is relatively insignificant in altering the temperature and viscosity variations in resin matrix [20]. For thick laminates, the change in viscosity in thickness direction is not uniform and mostly thermal overshoot is observed at the center of the laminate during curing. Joshi et al. [21] proposed a method to use a general purpose finite element (FE) package to simulate the cure kinetics of epoxy resins with two user programs. It was observed that convective heat transfer from autoclave air to the mold and thickness of the bleeders affect the temperature profile and thermal overshoot in the laminate [22]. Shin and Hahn [23] developed a 1-D numerical model to simulate resin flow through bleeders with the assumption that bleeder plies do not change their thickness during curing. Commercial FE package can be used to model heat transfer and compaction-flow model for flow thorough porous media [24]. Li et al. [25] introduced an FE procedure to study 2-D resin flow and compaction of laminates. To achieve uniform compaction and void free composite laminates, the excessive resin in the laminates shall be removed effectively. Darcy’s law combined with 1-D consolidation can be used to model the bleeder flow [26]. There is a large pressure drop at the laminate bleeder interface, which leads to a variation in the fiber volume fraction, void content and resin flow distribution within the laminate. Fiber volume fraction and resin pressure inside the laminate are interdependent. Monitoring the resin pressure during the autoclave process is challenging and needs special measuring systems [27]. Keeping the laminate boundary at zero pressure leads to a uniform fiber volume fraction which is not to true in real situations. Resin flow in transverse and in-plane directions results in variable fiber volume fraction throughout the laminate when bleeders are used to absorb excess resin. Process induced residual stresses are of great importance in determining the final laminate quality. The residual stresses are calculated from the temperature difference and volumetric shrinkage of the resin [28]. These lead to distortion of final laminates and there is a need for a simulation method for predicting the residual stresses and deformations in an integrated manner for industrial manufacturing [29]. As seen, a number of numerical simulations were performed by previous researchers to optimize cure temperature and pressure profiles [4,11–13,15,20–22,24,25], but only few simulations dealt with the effect of resin flow through bleeder [23,26]. Bleeder is a porous, thick layer of material that absorbs and holds resin that flows out from the curing laminate in addition to allowing the volatiles to escape. In the work on bleeders so far, a zero bleeder pressure at the laminate bleeder interface was assumed throughout the process. In reality, the laminate–bleeder interface pressure varies throughout the curing process depending upon the amount of resin that flows out from the laminate to the bleeder. The drawback in the previous numerical simulations was that none coupled heat transfer analysis with the resin flow and the lay-up compaction analyses. Variation in resin properties and resin volume fractions due to the resin outflow were not accounted for in the cure simulation. As a result, an inflated value of the thermal overshoot was arrived at the center of the laminate during curing; which led to inaccurate prediction of temperature and pressure cure cycles and the resulting laminate properties. Several specific FE programs were developed to model transient heat transfer and resin flow compaction of thick laminated composites. These methods are time consuming and expensive. A general purpose commercial FE software packages may be used for process simulation, however, these packages do not have the facility to couple heat transfer and resin flow. Separate user subroutines are required to be written to calculate the viscosity and degree of cure, and update them at each time step. Again, this is a time consuming process. Therefore, it is necessary to develop a simulation process that simultaneously accounts for all physical phenomena involved in a composites manufacturing process such as heat transfer, cure kinetics, viscosity, resin flow, compaction, process induced stresses, thermal shrinkage of resin and void formation [30]. This paper attempted to accomplish this by coupling heat transfer, cure kinetics, rheology, 1-D consolidation and 2-D resin flow within and out of curing laminates in a transient manner.

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A multi-physics software COMSOL is used to model a typical composites manufacturing process. Heat transfer and subsurface flow modules are used to simulate cure and resin flow associated compaction behavior. The viscosity and degree of cure are calculated with the help of partial differential equation (PDE) module. In the present study, 1. Effect of thermal conductivities of vacuum bag, breather, caul plate, peel ply and bleeders is accounted in cure simulation, which alters temperature distribution within the laminate. 2. The temperature dependency of resin properties on parameters such as density, specific heat and thermal conductivity is taken into consideration, which is mostly ignored and kept constant in several previous numerical studies. 3. Resin flow and compaction behavior of bleeder was simulated under the applied curing pressure with proper initial and boundary conditions. 4. The loss of resin volume fraction at various locations in a curing laminate due to resin flow from the laminate to the bleeders is updated for accurate determination of the source term in the transient heat transfer analysis of the laminate. It was found that by considering the variable resin volume fraction and resin properties the thermal overshoot temperature comes down, which is otherwise over-predicted. Consolidation of the laminates is controlled by the resin holding capacity and the location of the bleeders around the lay-up. The resin absorption in the side bleeders is more compared to the top bleeder layers due to the high resistance offered by the compacted fibers to the resin flow in the laminate thickness direction. 2. Background theory 2.1. Transient heat transfer The presence of resin within the laminate and bleeders generates exothermic heat through species reaction. This can be accounted as internal heat source term. Convective heat transfer is negligible due to small resin velocities. At a specific processing time and location, constituent materials are at the same temperatures. Therefore, energy equation that governs the transient heat transfer within the laminate/bleeder including the source term can be written as [21,31]

qC p @T=@t ¼ @=@xðK x @T=@xÞ þ @=@yðK y @T=@yÞ þ @=@zðK z @T=@zÞ þ @Q=@t

ð1Þ

With constant thermal conductivities and by neglecting the internal heat generation term, the energy equation for vacuum bag accessories and the mold or tool can be written as

qC p @T=@t ¼ Kð@ 2 T=@x2 þ @ 2 T=@y2 þ @ 2 T=@z2 Þ

ð2Þ

where q, cp, Ki (i = x, y, z) are density, specific heat and thermal conductivity respectively, and T is temperature. The source term in Eq. (1) can be obtained from differential scanning calorimeter experiment as formulated in [21]

dQ=dt ¼ qr V r Q t ðda=dtÞ

ð3Þ

where qr, Vr, Qt, a, da/dt are density, volume fraction, reaction heat per unit mass, degree of cure and rate of exothermic reaction respectively of resin. 2.2. Curing reaction kinetics Differential scanning calorimetry is most widely used to fit the Arrhenius type reaction kinetics equation for epoxy resins. One such set of equation, Eq. (4), for cure reaction kinetics of Hercules 3501-6 resin system is [2]

da=dt ¼ ðB1 X 1 þ B2 X 2 aÞð1  aÞð0:47  aÞ for a 6 A

ð4aÞ

da=dt ¼ B3 X 3 ð1  aÞ for a > A

ð4bÞ

where

X i ¼ expðDEi =RTÞ i ¼ 1; 2; 3:

ð5Þ

and R is the universal gas constant, Bi, the pre-exponential factors, DEi represent activation energies. 2.3. Viscosity model A viscosity model for Hercules 3501-6 resin was reported by Lee et al. [2]. It is the function of the process temperature distribution and degree of cure as shown in

l ¼ lo expðDEi =RT þ baÞ i ¼ 4: where lo is viscosity constant and b temperature independent constant.

ð6Þ

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2.4. Resin flow-compaction model for laminate/bleeder It is assumed that the laminate is fully saturated with resin and the autoclave pressure is shared by the resin, fibers and bleeder at any instant of the compaction process. The stress seen at any point in the laminate is described as in [3,11,22,24,25]

Pa ¼ Pr þ r

ð7Þ

where Pa is the autoclave applied pressure, Pr is the resin pressure, and r is the fiber/bleeder effective stress. By combining Darcy’s law with effective compaction stress, the flow continuity equation can be described as [11] 0

@Pr =@t ¼ ð1=mv Þdiv :ðj =l grad Pr Þ

ð8Þ

0

where j is the permeability tensor of fiber/bleeder [12], mv is the volume change coefficient of fiber/bleeder. A modified Carman–Kozeny equation for the permeability of the fibers is given in Tables 3 and 4. The volume change co-efficient for fiber/bleeder is given by Eq. (9) as [11]

mv ¼ av =ð1 þ eo Þ

ð9Þ

where eo is the initial void ratio and av is @e/@ r. The void ratio can be related to the either fiber or bleeder volume fraction as [24]

e ¼ ð1=V f Þ  1

ð10Þ

From the consolidation experiments on carbon fibers impregnated in silicon oil, Young fitted a relationship between void ratio and the fiber effective stress as [12,24]

e ¼ 1:552  106 r þ 0:81 for 0 6 r 6 68:95  103 Pa e ¼ 0:247log10 r þ 1:899 for

r P 68:95  103 Pa

ð11aÞ ð11bÞ

From the compaction experiments on dry bleeders the instantaneous change in porosity can be obtained as

u ¼ uo ðInstantaneous volume of bleeder=Initial volume of bleederÞ

ð12Þ

where uo is the initial porosity of the bleeder. The porosity can be related to the bleeder void ratio by

u ¼ e=ð1 þ eÞ

ð13Þ

A relationship between the void ratio and bleeder effective stress can be obtained from compression experiments on bleeders. Note that since data on bleeder was not readily available, the authors conducted necessary experiments. The resulting Eq. (14) for bleeder, which is similar to Eq. (11), is

e ¼ 0:111log10 r þ 1:446 for 0 6 r 6 63; 870 Pa

ð14aÞ

e ¼ 0:056log10 r þ 0:8188 for

ð14bÞ

r P 63; 870 Pa

3. Case studies description In order to simulate the autoclave curing process, a thick composite laminate made up of 140 plies, graphite/epoxy (AS4/ 3501-6) prepregs was taken into consideration [21]. The tool is made up of aluminum alloy. The non-porous peel ply between the tool and the laminate is thin enough to not to affect the heat transfer significantly and may be ignored. The bagging that covers the laminate lay-up consists of one layer each of breather, vacuum bagging film, caul plate and the porous peel ply. Bleeders are laid up at the top and the sides of the laminate to allow 2-D resin flow out of the laminate. The thickness and arrangement of the each material in the fabrication assembly is illustrated in Fig. 1. The necessary properties of the each material used for simulation are given in Tables 1–5. The simulation is performed for the following four (cases A to D) different cases in order to underline the shortcomings of the earlier numerical simulation procedures by various researchers. Case Case Case Case

A: Variable laminate properties and constant resin volume fractions. B: Variable laminate properties and variable resin volume fractions. C: Constant laminate properties and variable resin volume fractions. D: Constant laminate properties and constant resin volume fractions.

In case A, the density, thermal conductivity and specific heat co-efficient of resin are taken as the functions of the degree of cure and they vary at each time step (Table 1). This dependence of resin properties has to be updated by re-calculating the

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Fig. 1. Geometry of 140 layers, graphite/epoxy (AS4/3501-6) laminate manufacturing assembly.

Table 1 Properties of 3501-6 resin [7,16]. Density Specific heat Thermal conductivity Heat of reaction Viscosity parameters

qm Cm Km Qt DE4 b

lo Cure parameters

B1 B2 B3 DE1 DE2 DE3

Density variation with cure

qm

Specific heat variation with cure Thermal conductivity with cure

Cm Km

1260 1260 0.167 4.736  105 9.08  104 14.1 7.93  1014 2.101  109 2.014  109 1.960  105 8.07  104 7.78  104 5.66  104 0.09a + 1.232 for a 6 0.45 1.272 for a > 0.45 4.184(0.468 + 5.975  104T  0.141a)  103 0.04184(3.85 + (0.035T  0.41)a)

kg/m3 J/kg K W/mK J/kg J/mol – Pa s min1 min1 min1 J/mol J/mol J/mol kg/m3 J/kg K W/mK

Table 2 Properties of AS4 fibers [7,16]. Density Specific heat Thermal conductivity Permeability

qf Cf Kf kx ky

Fiber radius Final fiber volume fraction

rf Va

1790 712 26 r 2f ð1  V f Þ3 =ð2:8V 2f Þ r 2f ðsqrtðV a =V f Þ  1Þ3 =ð17:4ðV a =V f Þ þ 1Þ 6

4  10 0.83

kg/m3 J/kg K W/mK m2 m2 m

Table 3 Properties of air weave N 10 bleeders [16]. Density Specific heat Thermal conductivity Permeability

qb Cb Kb kxb kyb

Fiber radius Initial porosity Final bleeder volume fraction

rb

uo Va

90 1350 0.1668 r 2b ð1  V b Þ3 =ð2:8V 2b Þ r 2b ðsqrtðV a =V b Þ  1Þ3 =ð17:4ðV a =V b Þ þ 1Þ 2  106 0.66 0.83

kg/m3 J/kg K W/mK m2 m2 m – –

laminate properties at every time step with the help of rule of mixtures. It is assumed that the resin volume fraction at the source term is constant throughout the curing process.

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A.S. Ganapathi et al. / Simulation Modelling Practice and Theory 32 (2013) 64–82 Table 4 Properties of vacuum bag assembly. Density Specific heat Thermal conductivity

qvb Cvb Kvb

982 1250 0.1979

kg/m3 J/kg K W/mK

2692.1 916.9 216.3

kg/m3 J/kg K W/mK

Table 5 Properties of tool [14]. Density Specific heat Thermal conductivity

qT CT KT

In case B, changes in resin volume fractions due to the continuous compaction of the laminate during curing is taken into consideration. The net resin volume fraction at each time step is calculated from the change in the fiber volume fraction and updated in the source term. The variable resin properties also were updated in heat source term. In case C, the density, thermal conductivity and specific heat of laminate are kept constant. The change in the resin volume fractions at each time step is updated. In case D, the material properties and resin volume fractions of the thick laminated composite are kept constant throughout the simulation. Each of these cases is also analyzed with and without internal heat generation term to know its impact. 4. Numerical simulation A coupled analysis is carried out to study the interaction between different parameters involved in laminate curing and compaction processes. One-dimensional compaction and 2-D flow equations with Darcy’s law are used to simulate resin flow through the laminates and the surrounding bleeders. The temperature distribution is modeled using 2-D energy equations. The entire procedure adopted is shown as a flow diagram in Fig. 2 and discussed below. 4.1. Modeling procedure After creating the FE model of the thick composite laminate fabrication assembly, temperature distribution at each and every point within the assembly was obtained using heat transfer module by applying an autoclave cure cycle at the boundaries. The degree and rate of cure within the laminate were modeled with the help of PDE module. The exothermic heat generated during the chemical reaction of the resin was calculated by updating the rate of cure. Subsequently, the source term was updated in the heat transfer module for the resin-filled laminate and bleeder layers. Secondly, viscosity of the resin was calculated using the temperature distribution within the laminate/bleeder. The resulting viscosity distribution was then used to calculate the resin pressure distribution with the help of subsurface flow module by applying the autoclave pressure cycle at the boundaries. The subsurface flow module contains the flow continuity equation combined with Darcy’s law and the 1-D consolidation. This module was used to obtain the resin flow distribution within the laminate/bleeder. The pressure equilibrium equation was employed to find the fiber/bleeder effective stress, which was then used to calculate the real-time fiber/bleeder volume fractions. Finally, the resin volume fractions were updated in the source term of the heat transfer module to obtain accurate temperature distribution to account for the resin loss from the laminate or the resin gain by the bleeder. 4.2. Two dimensional finite element modeling The length of the laminate was considered large as compared with the other two dimensions. Hence, it was possible to model the laminate cross section as a 2-D problem involving energy and momentum transfers. The laminate assembly was discretized using QUAD 4 elements. The mesh geometry adopted is as shown in Fig. 3. The Galerkin weighted residual approach was used to solve the PDE equations involved in this simulation process. 4.3. Boundary conditions and initial conditions A set of initial and boundary conditions was applied to solve each PDE simultaneously involving resin flow, fiber and bleeder compaction, and the heat transfer processes. These are specified in Table 6. The tool–laminate interface was assumed as an impermeable layer with no resin taking place through it. The laminate and the bleeder were at different initial conditions. There was an average pressure build up at the laminate–bleeder interface. The autoclave cure temperature and the pressure profiles used are given in Fig. 4.

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Autoclave cure temperature

Transient heat transfer analysis

Temperature distribution

Heat source term

Rate/Degree of cure

Viscosity calculation

Resin flow and compaction analysis

Resin pressure distribution in laminate/bleeder Autoclave applied pressure Fiber/Bleeder effective stress

Fiber/Bleeder volume fraction

Resin volume fraction Fig. 2. Numerical simulation procedure.

Fig. 3. Finite element mesh of 140 layers, graphite/epoxy (AS4/3501-6) laminate manufacturing assembly.

5. Results and discussions A process simulation inclusive of heat transfer, resin flow and compaction of thick laminated composites has been established and shown that the coupling between these phenomena as well as the inclusion of bleeder into the process simulation are important and make difference. The resin volume fractions depend on resin flow within and out of the laminate, and compaction behavior of the laminate and the bleeder. The changes in resin volume fraction modify the temperature distribution within the laminate. Subsequently, temperature distribution alters the degree of cure and viscosity of the resin. Again, viscosity and degree of cure affect the resin flow within the laminate and the bleeder. This cycle continuous until curing of the resin completes. The results with and without the heat source term are presented to emphasize the importance of the accurate heat source term in altering the trends of all the parameters involved in this process simulation.

A.S. Ganapathi et al. / Simulation Modelling Practice and Theory 32 (2013) 64–82 Table 6 Initial and boundary conditions [3,11,15,16,18].

Heat transfer analysis Degree of cure Flow and compaction

Heat transfer analysis Flow and compaction

Initial condition

Region

At At At At

Domain Domain Domain Domain

t = 0 s, t = 0 s, t = 0 s, t = 0 s,

T = 293 K a=0 P = 0.689 MPa P = 0 MPa

laminate assembly. laminate/bleeder laminate bleeder

Boundary condition

Region

Convective heat flux with h = 70 W/m2 K P = 0 MPa No flow

Boundary of laminate Assembly. Boundary of bleeders Laminate–tool interface

1.00

150 100

0.50 Temperature

50

Pressure (MPa)

200

Temperature (°C)

of of of of

Pressure 0 0

100

200

0.00 400

300

Time (min) Fig. 4. Autoclave cure temperature and pressure profile.

Temperature ( °C)

200 180

Input

160

Case: A

140

Case: B Case: C

120

Case: D 100 80

100

120

140

160

Time (min)

(a) Excluding heat generation term. 220

Temperature (°C)

200 Input

180

Case: A

160

Case: B

140

Case: C

120

Case: D

100 80

100

120

140

160

Time (min)

(b) Including heat generation term. Fig. 5. Temperature profile at the center of 140 layer 25 mm thick, AS4/3501-6, graphite epoxy, prepreg laminate.

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In summary, various coupling and parametric transitions considered were as listed below in case studies A, B, C and D. Parameters

Case A

Case B

Case C

Case D

Resin volume fraction in heat source term

Constant through the simulation

Updated at each time step

Updated at each time step

Resin density

Updated at each time step

Updated at each time step

Constant through the simulation

Resin thermal conductivity

Updated at each time step

Updated at each time step

Constant through the simulation

Resin specific heat capacity

Updated at each time step

Updated at each time step

Constant through the simulation

Temperature at center of the laminate without heat source term (no thermal overshoot observed) at 100–120th minute Thermal over shoot temperature at center of laminate with heat source term at 100–120th minute Cure kinetics at the center of laminate without source term

Matches with case B and less than remaining cases

Matches with case A

Higher than remaining cases

Constant through the simulation Constant through the simulation Constant through the simulation Constant through the simulation Less than case C and higher than case A and B

Less than case D and higher than remaining cases

Less than remaining cases

Less than cases A and D and higher than case B

Higher than remaining cases

Slower than cases C and D and overlaps with case B Faster than case B and slower than cases C and D Same as case A

Slower than remaining cases

Faster than remaining cases

Slower than remaining cases

Slower than case D and rapid than cases A and B

Same as case B and higher than remaining cases at first ramp, at second ramp same as remaining cases Same as case A and higher than remaining cases at ramp up, less than remaining cases at first dwell Less than remaining cases

Same as case D and lesser than remaining cases at first ramp, at second ramp same as remaining cases Same as case D at first ramp and second ramp and higher than remaining cases at first dwell Similar to case A

Slower than case C and rapid than cases A and B Faster than remaining cases Same as case C

Less than remaining cases

Higher than case B and less than remaining cases

Cure kinetics at the center of laminate with source term Minimum Viscosity at the center of laminate without source term

Minimum Viscosity at the center of laminate with source term

Resin loss at the center of laminate without source term Resin loss at the center of laminate with source term

Same as case B at first ramp, and lesser than remaining cases at second ramp Higher than case B and less than case D Higher than remaining cases

Same as case C at ramp up and less than case C at first dwell Higher than remaining cases Less than case A and higher than remaining cases

5.1. Temperature Fig. 5 shows the transient temperature distribution at the center of the laminate with and without the heat source term for a range of 80–160 min of the curing time. A major variation in the temperature profile can be observed in this range of time period. The temperature distribution mainly depends on the thermal conductivities of the materials in the fabrication assembly. As a result, temperature at the center of the laminate approaches the applied autoclave temperature gradually. With neglected heat source term, in which heat transfer due to conduction alone is considered, temperature at the center

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of the laminate is lower than the autoclave cure cycle temperature up to 160 min of curing as shown in Fig. 5a. Resin volume fraction in the source term plays no role in modifying the temperature profile. There is a significant difference in temperature profile which can be obtained by comparing variable and constant laminate property cases. Resin properties depend on the degree of cure (Table 1) and the degree of cure changes due to the resin flow out of the laminate which alters the temperature distribution. In cases A and B, even though the local heat is not contributing to the changes in degree of cure, the loss of resin from the laminate alters the degree of cure as well the resin properties. In cases C and D, the resin properties are constant irrespective of the resin outflow of the laminate. These cases show higher temperature profiles. There is a maximum temperature difference of 8 °C at the center of laminate that can be observed between cases A and C at around 115 min of curing. When the heat generation term is included in the transient heat transfer equation, there is a thermal peak observed at the second dwell period of the cure cycle. At high temperatures, local heat generation at the center of the thick laminates from the resin cure kinetics reaction is observed. In Fig. 5b there is a significant deviation in temperature distribution at the center of the laminate from 91 to 125 min into the cure cycle. For variable resin (as well as laminate) properties, the variable and constant resin volume fraction assumptions (i.e. cases A and B) result in a maximum temperature difference of 6.39 °C at around 114th minute into the cure cycle; the peak temperature for case A is 211.9 °C and for case B it is 205.51 °C at 114th minute. At these temperatures with moderate extent of chemical reaction close to a = 0.5, viscosity of the resin reaches its minimum value. There is a resin flow from the laminate to the bleeder due to the applied compaction pressure at the low viscosity. Subsequently, resin content at the center of the laminate decreases. With the decreased resin volume fraction (case B), contribution of the heat source term to the temperature distribution lowers when compared to the constant resin volume fraction case (case A). In these cases A and B, decrease in resin (laminate) properties takes place for both cases. But, the decrease in the resin properties such as density, thermal conductivity and specific heat capacity for case B is more rapid than case A due to the variable resin volume fraction in the source term. This again results in lower temperature distribution in case B than case A as seen in Fig. 5b. For constant resin (laminate) properties, the variable and constant resin volume fractions (i.e. cases C and D) have resulted in the temperature difference of 5.95 °C around 108 min of curing. At 108th minute, the peak temperature for case D is 215.5 °C and for case C it is 209.5 °C. In these cases the resin volume fraction is the key factor that to alters the temperature distribution. For cases D and A, a temperature difference of 9.49 °C is observed around 107 min of curing. The peak temperature in case D, 215.43 °C, is higher than the peak temperature in case A, 205.94 °C, at 107th minute into the cure cycle. Eventually, this results in a lower temperature distribution in case A as shown in Fig. 5b. For variable resin volume fraction in the source term, the variable and the constant resin (laminate) properties (i.e. cases B and C) result in a temperature difference of 7.55 °C at around 108th minute. The peak temperature in case B, 202 °C, is lower than in case C, 209.55 °C, after 108 min of curing. Even though the resin volume fraction in the source term is updated at every time step, the decrease in the resin properties leads to a lower resin volume fraction in case B than in case C. This ends up with a lower thermal peak temperature in case B as shown in Fig. 5b. Finally, the constant resin (laminate) properties and volume fractions case is compared with the variable resin (laminate) properties and volume fractions case (i.e. cases D and B). There is a maximum difference in the temperature distribution of 15.05 °C at 107th minute. The peak temperature in case D is 215.43 °C and case B is 200.38 °C at 107 min, which is higher than the second dwell temperature of the autoclave cure cycle of 197 °C. Therefore, keeping the resin volume fraction and the resin properties constant while determining the heat source term over-estimates the overshoot temperature at center of the thick laminated composites. From this comparison it is evident that the coupled analysis, that is case B, gives more realistic prediction of temperature distribution and thermal overshoot within the laminate. Even though we include the heat source term in the transient heat transfer analysis, it is important to update the resin volume fractions at every time step to avoid over-prediction of the thermal overshoot. Otherwise this results in a rapid cross-linking of polymers and gives under-predicted fiber volume fractions. 5.2. Degree of cure Fig. 6a indicates the chemical reaction kinetics with excluded heat source term for different cases. Constant laminate properties cases progress at a faster rate than the variable laminate properties cases. These curves are directly related to the temperature profile at the center of the laminate due to the temperature dependency of the degree of cure. Curves for cases A and B match each other throughout the curing process. From this, it is evident that the resin volume fraction plays no role in altering the chemical reaction rate of the resin for cases A and B. But, the degree-of-cure-dependant resin properties swerve the cure kinetics for cases A and B from cases C and D. Polymerization in case C is faster than any other cases due to the constant properties with a considerable resin loss from the laminate, which changes the overall thermal conductivity, specific heat and density of the laminate. The cure reaction for all four cases completes at around 166th minute. Fig. 6b shows the degree of reaction profile with heat source term for all four cases. A linear change in the degree of cure is noticed for all during the first dwell of the cure temperature profile. Thereafter the degree of cure increases rapidly at the second ramp of the cure cycle. After the first dwell, the chemical reaction of resin in case A progresses faster than case B due to the constant resin volume fraction in the source term. Since resin volume fraction is updated at each time step, the reaction kinetics of resin for case C is slower than case D in the range of 91–125 min. As a result of constant resin parameters, the cure reaction kinetics for case D is faster than other three cases. Even though the resin volume fraction is updated at each time step, the resin cure kinetics for case C is faster than for case B. This results in a decrease in resin (laminate) prop-

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Degree of Cure

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erties in case B in comparison with case C. The cure kinetics reaction for case D occurs faster than for case B at high temperatures in the laminate and the bleeder. Here, case D represents the uncoupled situation of transient heat transfer and resin flow analyses. Due to the coupled nature of the problem, cure kinetics for case B is slower than the other cases. 5.3. Viscosity Fig. 7a gives viscosity profile for Hercules 3501-6 resin with excluded heat generation term. Viscosity is a function of temperature distribution and degree of cure within laminate. When temperature increases, viscosity of resin tends to decrease first and increase afterwards with degree of cure. The viscosity of Hercules 3501-6 starts to decrease from its initial value of 1222 Pa s with the increase in temperature with no cross-linking of the resin taking place. It reaches a minimum value at 41st minute with the degree of cure of 0.034 at 107 °C with constant laminate properties. From Fig. 7a it is evident that the constant resin properties lead to a minimum viscosity of 0.7 Pa s around 41 min when compared to the variable resin properties where viscosity reaches 1.0 Pa s at 41st minute. Further increase in temperature enhances the chemical reaction and the viscosity starts to increase till the end of the first dwell at 69 min of curing. After this first dwell, again the increase in temperature reduces the viscosity to 0.8 Pa s without any significant difference in the minimum viscosities for between the different cases. During the first temperature dwell, the resin polymerization starts slowly. When the temperature is increased further (second ramp), the viscosity drops with the slow polymerization, then rises dramatically as the cross linking of the resin progresses rapidly. This is the reason that a little peak is observed in the viscosity profile at 70th minute of the cure cycle. Since, the temperature profile and degree of cure for case C are higher than any other case; the viscosity profile reaches its highest value faster than the other cases. This means that case C has the highest fiber volume fraction than any other cases due to the improved thermal conductivity and the resin flow out of the laminate. With the inclusion of the heat source term at low temperature and the degree of cure, the viscosity profile remains similar as in Fig. 7a until 41 min into the cure cycle. This is because of the slow polymerization taking place with no contribution from the heat source term in the first ramp. This can also be observed from the degree of cure profile. If we examine Fig. 7b clearly, after 41th minute, there is a significant deviation in the viscosity profile with the contribution from the heat source term due to cross linking of polymer chains. The viscosity of 0.66 Pa s for constant resin (laminate) properties cases (i.e. cases C and D) is less than the variable property cases (cases A and B); it is 0.94 Pa s at 41st minute, irrespective of the slight variations in the resin volume fraction. At the first dwell, the degree of cure increases linearly. It also causes the viscosity to rise, which after reaching a little local peak, starts to fall again at the second ramp in temperature. Immediately after

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the first dwell, the degree of cure and temperature profiles for case A rise slower than the remaining cases. Therefore, the viscosity reaches a minimum value of 0.75 Pa s at 93rd minute. This is because, both resin (laminate) properties and resin volume fractions are updated in the source term for the heat transfer analysis. When these are kept constant, like in case D, then the temperature and degree of cure increase rapidly and the viscosity reaches its maximum value faster than any other case, as seen from Fig. 7b. These studies also confirm that the coupled analysis, that is case B, gives more realistic prediction of the resin matrix viscosity. The main idea to compare the profiles with and without the heat source term is to understand the shifts in the curves for different cases due to the resin volume fractions and the associated heat generation. It is clear from the comparison that a small change in resin volume fraction affects the overall cure kinetics, viscosity, temperature distribution and the final fiber volume fraction of the laminate. 5.4. Resin pressure within laminate Two dimensional resin flow analysis has been carried out to find out the compaction and flow behavior of a thick laminated composites. Initial pressure in the laminate is 0.689 MPa and the bleeder is 0 MPa. A pressure of 0 MPa is applied at the bleeder boundaries. As a result, the pressure at the laminate–bleeder interface is 0.3445 MPa. Initially there is no flow of resin taking place from the laminate to the bleeder until the minimum viscosity of the resin is reached. The resin pressure at the center of the laminate for different cases is shown in Fig. 8. Though a constant pressure is applied throughout the curing process, the flow of resin from the laminate to the bleeder is driven by the temperature, degree of cure and the viscosity of the resin. Without the source term, the flow of resin from the laminate to the bleeder takes place first for case D where viscosity starts to decrease rapidly than the remaining cases. A large amount of resin is transferred from the laminate to the bleeder for case D as compared to any other cases, as seen in Fig. 8a. If we examine Fig. 8a closely, the resin flow starts at 21st minute and ends around 101 min for all four cases. At the 21st minute, the viscosity for cases C and D is around 3 Pa s, and for cases A and B, it is around 6 Pa s During this time period, there is no significant difference in temperature, degree of cure and viscosity between cases C and D and, similarly for cases A and B. No difference in resin pressure drop is noticed between case A and case B. By comparing cases B and D, i.e. the variable resin (laminate) properties and resin volume fraction case with the

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constant resin properties and volume fractions case, case D has larger viscosity variations than case B. As a result, the resin pressure drop in case B is less than in case D. Beyond 101 min of curing the resin pressure does not change, which means the cross-linking of resin is completed and the viscosity has reached its maximum value. The resin flow out of the laminate into the bleeder for case B is less than for the remaining cases due to the slow polymerization, lower thermal peak temperatures and high viscosities. In case D, constant resin properties and volume fractions result in rise in the thermal peak, reduction in the minimum viscosity and speeding up of the chemical cure reaction. With the source term in transient heat transfer analysis, the resin pressure drop takes place rapidly in the range of 21– 101 min similar to Fig. 8a. Cases C and D have the same viscosity and resin pressure profiles till the 48 min of curing. Similarly, cases A and B have overlapping viscosity and resin pressure profiles up to 48th minute. In this time range, temperature and degree of cure profiles also overlaps. But, there is a difference in the resin pressure drop for cases B and D due to the difference in the minimum viscosities as stated earlier. Beyond 48th minute, the viscosity in case A starts to decrease rapidly than in case D due to the variable resin (laminate) properties, which are updated in the source term. For case A, density, thermal conductivity and specific heat, all increase with degree of cure with the constant resin volume fraction. This leads to an increased pressure drop in case A than in case D as seen in Fig. 8b. While comparing case A and case B, due to the variable resin volume fraction case B has lower temperature and degree of cure distributions. The temperature overshoot is less than in case A. This resulted in higher viscosity and lower resin pressure drop for case B than for case A, again leading to the same conclusion that case B provides the most realistic simulation of the prepreg molding process in autoclave.

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5.5. Resin pressure within bleeder

Resin Pressure (kPa)

Figs. 9 and 10 show the resin pressure distribution at the center of the top and side bleeder layers. The permeability of the laminate in in-plane direction is more than in transverse direction. Hence, the resin flow velocity in the in-plane direction is higher than the transverse direction velocity as seen in Fig. 11. This results in more resin flow to the side bleeders than to the top bleeders. The variation in resin pressure distribution in the top and side bleeders for different cases depends on the laminate pressure drop. At the initial stages, the top bleeder has negative resin pressure developed due to the dry compaction of the bleeder with high transverse permeability until 21st minute. Since, viscosity of the resin near the sides of the laminate

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decreases faster than the top of the laminate due to the high thermal conductivity of the tool (faster temperature rise) and the smaller dimensions of the bleeder in the thickness direction of the laminate, there is a positive pressure distribution at the beginning of the curing in the side bleeder till 21st minute. Further increase in the temperature minimizes viscosity of the resin and the resin flow from one location to another within the laminate as well as out of the laminate starts. It is clear from Figs. 9 and 10 that, the loss of laminate resin pressure for cases C and D is high compared to for cases A and B at the initial stages. This leads to higher pressure gain at the mid of the top and the side bleeders. After 42 min, there is a cross-over between the viscosity plots for different cases due to the chemical kinetics of the resin and its effect on the resin properties

(a) 60 minutes.

(b) 120 minutes.

(c) 180 minutes.

(d) 240 minutes.

(e) 300 minutes. Fig. 13. Contour plot for temperature (K) distribution of 140 layer 25 mm thick, AS4/3501-6, graphite epoxy, prepreg laminate for case B.

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and resin volume fractions. This leads to a cross-over between pressure distributions in different cases. After 85 min, viscosity in case A drops rapidly and as a result, the resin pressure drops in the laminate and increases in the bleeder layers. This is the reason that resin pressure gain in the bleeders is higher for case A than the remaining cases. There is an oscillation in the resin pressure distribution due to the variable volume fraction of resin in the heat source term and nonlinear compaction behavior of the bleeder. From Figs. 9 and 10, it may be concluded that case B has less resin gain into the bleeder due to the lowest viscosity compared to the remaining cases. From the above results, it is evident that case B gives the more realistic process simulation. The temperature and pressure distributions at various locations in the laminate and the bleeder for variable resin properties and resin volume fractions for case B are shown respectively in Figs. 12–14. Fig. 12 shows the pressure distribution at various locations in the fabrication

(a) 60 minutes.

(b) 120 minutes.

(c) 180 minutes.

(d) 240 minutes.

(e) 300 minutes. Fig. 14. Contour plot for resin pressure  105 (Pa) distribution of 140 layer 25 mm thick, AS4/3501-6, graphite epoxy, prepreg laminate for case B.

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assembly. Figs. 13 and 14 present the contour plots showing the step-by-step distribution of the pressure and temperature. Initially, the interface pressure is the average of initial pressure of the laminate and the bleeder. Once the resin starts to flow, the interface pressure starts to increase. After reaching a maximum value its starts to decrease. Because of the high resistance of the fiber beds in the transverse direction, the resin pressure distribution at the top bleeder is less than the side bleeders. The pressure at the side interface reaches the applied pressure due to the high resin flow velocity in the axial direction than the transverse direction. Comparing to the middle and top of the laminate, bottom of the laminate has high resin pressure due to the sequential compaction response of the laminate and the bleeder. There are resin rich regions at the bottom of the laminate and resin starved regions at the edges of the laminate. This essentially means, for each product, the applied autoclave pressure and the bleeder arrangement shall be carefully optimized to get uniform resin distribution and consolidation. Application of lower autoclave pressure will lead to resin rich laminate whereas higher autoclave pressure will compress the bleeder fully until the bleeder volume fraction reaches a maximum value. At high volume fractions the resin holding capacity of the bleeder will drop, which again will lead to resin rich regions in the laminate. An optimum autoclave pressure cycle should be chosen to get optimum resin pressure distribution. It is also necessary to account for variations in resin properties and resin volume fractions as a function of the compaction pressure as well as the temperature in a coupled manner so that the real-time phenomena in composite manufacturing process are simulated accurately. These studies corroborate that the accounting of the bleeder compression, the resin flow into the bleeder and its effects on the entire curing process is done in a more realistic manner in the coupled analysis as in case B.

5.6. Fiber volume fraction

Fiber Volume Fraction

Comparison of variations in the fiber volume fractions with respect to time at the center of the laminate for different cases is shown in Fig. 15. The consolidation of the lay-up starts at the same time in all four cases due to the applied autoclave pressure and the drop in the viscosity. By keeping zero pressure at the boundary of the laminate throughout the simulation leads to higher fiber volume fraction in the laminate. There is no outside control over the resin flow coming out of the laminate once the flow is initiated. As a result, the consolidation takes place very fast and the permeability of the laminate decreases rapidly. In real situations, resin flow is controlled by the bleeder characteristics and the final fiber volume fraction is less than the simulated value. So, the pressure at the boundary should be updated at every time step. In other words, resin flow into and through the bleeders should be included in the process simulation. For the reason that the compressibility and resin flow are related to each other, case B has less fiber volume fraction and resin pressure drop than the other three cases and the

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consolidation therein takes place in a linear fashion. The reductions in the thickness of the laminate for zero boundary pressure and instantaneous boundary pressure are shown in Fig. 16. The unrestricted flow of resin out from the laminate gives a thickness reduction of 4.8 mm. The flow of resin out of the laminate to the bleeder, if accounted for, it leads to 1.1 mm reduction in the thickness. The resin flow out from the laminate is controlled by various parameters such as the bleeder permeability, fiber porosity and the compaction behavior. To achieve a desirable fiber volume fraction, laminate thickness and the laminate quality, it is vital to select a bleeder with appropriate thickness, permeability and other parameters. 6. Conclusions Aerospace industries are keen to develop thick laminated composite structures to replace the metal ribs and stiffeners of the wings, landing gear drag brace and primary load carrying members. It, not only saves weight, but also the cost of manufacturing. It is difficult to manufacture thick complex shaped parts without prior understanding of the physical phenomena involved in the manufacturing process. Therefore, a detailed process simulation shall be carried out by considering all the major parameters that make significant contribution to the final quality of the composite part. It is found through this fully coupled and inclusive process simulation that the slow but continuous loss of resin from a curing laminate depends on the thickness, permeability, resin holding capacity and compaction characteristics of the bleeder and it is vital to include this resin loss from the laminate to the bleeder in the process simulation. This will help the manufacturers to select a bleeder with exact porosity and permeability to absorb the controlled amount of resin out of the laminate. Since, the permeability of the bleeder controls the resin absorbing capacity, bad selection of bleeder results in a resin rich and resin starved regions within the laminate affecting the laminate quality. It is also important to account for the compaction behavior of the bleeder layers in the process simulation which was generally ignored by previous researchers. Moreover, fiber volume fraction of the laminate is a function of resin pressure distribution. This simulation addresses all these shortcomings. This eventually will avoid the trial and error process of selecting bleeder parameters. Further, the constant resin properties and resin volume fractions in the source term appear to over-estimate the thermal overshoot at the center of the curing laminate. Variations in resin properties and resin volume fractions due to the resin flow from the laminate to the bleeder shall be updated in the heat source term of the transient heat transfer analysis to predict well-optimized temperature and pressure cycles to minimize thermal overshoot. The residual stresses depend on the temperature difference and the thermal shrinkage of resin. Hence, it is vital to predict the temperature distribution within the laminate accurately. The current method of the process simulation can be easily extended to predict realistic and optimized residual stresses by considering instantaneous resin volume fractions and the temperature distribution. Acknowledgements The first author gratefully acknowledges Nanyang Technological University (NTU) and the Energy Research Institute @ NTU for financial and other support. References [1] G.S. Springer, Resin flow during the cure of fiber reinforced composites, Journal of Composite Materials 16 (5) (1982) 400–410. [2] W.I. 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