Resin pressure evolution during autoclave curing of epoxy matrix composites.
Advanced polymer matrix composites are finding applications in a wide range of industries and the technology for their manufacturing is continually evolving . High performance structural components are often manufactured by autoclave processing of prepregs. A stack of prepreg plies is usually covered by a bleeder, used to absorb the excess resin, and is sealed with a vacuum bag and de-bulked to consolidate the laminate by removing entrapped air. Then, the assembly is cured in the autoclave where pressure and temperature are simultaneously applied to assure to the component the required mechanical properties and low porosity [2-4]. The porosity threshold is very low for autoclave processed composites for aeronautic applications, being lower than 1% or 2% depending on the structural role of the parts , Higher porosities can lead to a detrimental effect on matrix dominated properties such as fatigue properties and intcrlaminar shear strength [6-12]. Despite several studies present in the literature, the mechanisms of void formation and growth in laminates produced from prepregs are still not well understood. It is widely accepted that voids are formed either due to the dissolution of dissolved gases within the resin, mostly water absorbed during prepreg exposure to a humid environment, or due to air entrapment during lay-up. However, there is no agreement on which is the dominant cause of voids [13-16]. It is also generally recognized that void growth occurs when the pressure within a void exceeds the hydrostatic pressure in the surrounding resin and this process is favored by high curing temperatures and low resin viscosity. A limited flow, even if relevant lor the force balance responsible of the transfer of autoclave gas pressure to the resin, is allowed for many stacks including a bleeder. At higher temperatures, as viscosity increases after reaction is started, close to the resin gel point, the voids eventually formed remain entrapped in the matrix. The recent use of a new generation of thermosetting resins, mixed with toughening agents and characterized by an increased viscosity, can considerably reduce the resin flow modifying the pressure distribution in the resin [17, 18].
Several mathematical models for resin flow in composite laminates have been developed with the aim of predicting void growth [6, 17, 19, 20]. These models generally assume that resin pressure is equal to the applied pressure without considering the role of the bleeder plies [14, 17]. More recently, some researchers have considered the flow through the fiber stack and/or in the bleeder [21, 22]. However, in these studies the nonlinearity arising from the viscosity changes associated with the temperature and degree of reaction evolution, were not considered. Actually, during the curing process, when resin flows out from the laminate into the bleeder, a pressure drop is established through the laminate thickness. Furthermore, a fraction of the autoclave pressure is transferred to the fiber stack, characterized by an elastic behavior in compression. Experimental measurements from Campbell  indicated that the hydrostatic pressure in the resin is not necessarily equal to that in the autoclave since a fraction of the autoclave pressure can be supported by the intrinsic stiffness of the reinforcement stack. This arises as a consequence of a resin flow into the bleeder, which although very limited, plays a key role in the force balance. This balance must consider the mentioned compressive behavior of the reinforcement as well as the dependence on temperature and degree of reaction of the resin viscosity during a curing cycle [24-26]. Since the evolution of hydrostatic pressure dominates the final content of porosities, modeling of resin flow and hydrostatic pressure is a key issue for predicting the conditions possibly leading to voids generation.
In this work, a viscoelastic model able to predict the evolution of the resin pressure during an autoclave cycle accounting for the effects of the temperature, degree of reaction, and viscosity changes, has been developed. The model also includes a kinetic and a rheological model whose input parameters have been experimentally determined by differential scanning calorimetry (DSC) and rheological analysis. The predicted resin pressure for three case studies associated to different composite and bleeder thicknesses and reinforcement materials have been discussed. The aim of the model is to calculate the hydrostatic resin pressure, which can be related to the thermodynamic conditions required for void growth at a given cure temperature.
The investigated resin was CYCOM 977-2, a toughened epoxy resin produced by Cytec Engineered Materials, formulated for autoclave and press molding technology.
The adopted reinforcement should mimic the compression behavior of those used to fabricate prepregs, usually compressed either during impregnation either during lay up, vacuum bagging and autoclave curing, so that the volume fraction of fiber ([V.sub.f]) is close to 60%. Two kinds of dry fiber stacks were used. A first fiber stack, labeled as a "Stiff fiber stack" was obtained using the carbon fiber reinforcement supplied by Cytec with the commercial name of UD-24K-IMS65-194-6.35. A dry UD fiber stack, characterized by a [.sub.40] lay-up and a [V.sub.f] of 57%, was used. Preforms with 8 mm thickness (200 x 100 [mm.sup.2]) were obtained by Automated Fiber Placement with a Coriolis robot in the facilities of Novotec (Avetrana, Italy) adopting a set point temperature of 80[degrees]C to obtain a stable high [V.sub.f] dry fabric preform.
The second fiber stack was characterized by high compressibility and labeled as "Compliant fiber stack." It was prepared in press at 80[degrees]C using a satin HexForceG0926 5-H carbon fiber fabric, supplied by Hexcel. The stacking sequence was [.sub.21].
Compression test was performed on a LLOYD LR50K dynamometer on 8-mm thick specimens (35 x 35 [mm.sup.2]) using a crosshead speed of 1 mm/min. The results were the average of five replicates.
The preforms with 8-mm thickness were also used to measure the transversal saturated permeability according to the classical Darcy experiment  under a pressure gradient of 1 bar.
A carbon fiber preform was placed between two glass plates sealed by a silicone seal. The volumetric flow rate was monitored with and the permeability was obtained by the slope of the volumetric flow rate versus the square root of time. A through thickness permeability [K.sub.f] = 7 x [10.sup.-13] [m.sup.2] was obtained for both stiff and compliant fiber stack as the average values of five measurements.
DSC was used to study the cure kinetics of the epoxy matrix. A Mettler Toledo DSC 822 calorimeter was used performing dynamic runs on uncured resin samples from 25[degrees]C to 300[degrees]C at constant heating rates (0.5[degrees]C/min, 0.75[degrees]C/min, 1[degrees]C/min) in a nitrogen atmosphere. At least three measurements were carried out at each heating rate.
Rheological measurements were carried out in a straincontrolled rheometer (ARES, Rheometrics Scientific) equipped with a parallel plate geometry (25 mm plate diameter) in dynamic mode at 1 Hz. The samples were subjected to an oscillatory shear strain of known amplitude and frequency while imposing a specified temperature cycle. The tests were performed from 30[degrees]C to 300[degrees]C at the same heating rates used in the DSC analysis. At least three measurements were carried out at each heating rate.
A finite element (FE) software (FlexPDE from PDE Solutions Inc.) capable to solve unsteady-state problems (initial conditions differential equations) in ID was used. It is a numeric solver able to transform a system of partial differential equations in a FE model using quadratic interpolating polynomials in the elements. Initial condition differential equations are solved adopting a four point finite difference discretization approach. The software is provided with a text editor in which the equations can be edited together with the problem geometry, the initial and boundary conditions.
RESULTS AND DISCUSSION
The changes of pressure in the resin and the compression stress taken from the reinforcement stack have been modeled using a simple Kelvin-Voigt model, considering a spring and a dashpot in parallel. The first accounts for the load taken by the reinforcement stack and the second for the load necessary for the reinforcement to sink into the resin.
A sketch of the thickness evolution and resin How during autoclave curing is shown in Fig. 1. At low temperature (Fig. la), the resin in a prepreg is virtually solid and no compressive strain occurs. At this stage, the composite stack is kept under vacuum, in particular the top ply of the composite is in contact with vacuum (between -700 and -980 mbar depending on the process). At room temperature, autoclave gas pressure reduces the thickness of dry bleeder until reaches its equilibrium thickness at the beginning of curing. The prepreg lay up can be sketched as a dashpot and a spring in parallel (a Maxwell-Voigt viscoelastic element). The spring represents the stiffness of the reinforcement while the dashpot the viscous drag due to resin flow through the fiber stack.
On heating (Fig. lb), the resin viscosity decreases and a pressure gradient is developed across the lay up. As shown in Fig. 1b, the resin fills the bleeder thanks to the compaction of the reinforcement: resin flow occurs until the bleeder thickness is filled under autoclave pressure (in plane flow is neglected). The upper resin layer is still under vacuum during bleeder filling. The composite thickness is reduced as the bleeder absorbs more and more resin. At this stage, the autoclave pressure is sustained either by the reinforcement (the spring in the model) either by the dashpot (the pressure needed for resin flow).
As the temperature increases, the reduction in resin viscosity leads to the complete filling of the bleeder. At this stage, the flow ends. The pressure is distributed between that supported by the reinforcement, under compressive strain, and the hydrostatic pressure in the resin, now constant but in general lower than the autoclave pressure. Until this tilling time, [t.sub.f], the resin surface is kept under vacuum. For times longer than [t.sub.f], a hydrostatic pressure build up almost instantaneously occurs (Fig. 1c). However, the resin pressure is not equal to the autoclave pressure if a fraction of the load is borne by the reinforcement whose thickness is reduced. After tf, resin flow from the composite surface stops and only an undesired lateral flow can eventually occur.
The Darcy flow can also end for other two reasons: (i) the spring takes all the load, that is, the total autoclave pressure is supported by the fiber stack with virtually zero pressure in the resin; (ii) the resin viscosity increases as the gel point approaches, before the bleeder is filled, until the dashpot takes all the load. In this case, the pressure is transferred to the resin only when its viscosity is very high and flow is ended. In these cases, the production of porosities due to volatiles (e.g., absorbed water) evolution is very likely to occur.
The Voigt model of Fig. 1 under a constant load (autoclave gas pressure, [P.sub.aut], in this case) is:
[P.sub.sp] + [P.sub.dp] = [P.sub.aut] (1)
where [P.sub.sp] is the pressure in the spring (elastic reaction of fiber stack) and [P.sub.dp] is that in the dashpot (hydrostatic pressure in the resin).
[P.sub.sp] has been obtained performing compression tests on stacks of the fabrics. As shown in Fig. 2, the compression lest results are characterized by a strong non linearity. The experimental data in Fig. 2 have been fitted with a simple exponential growth function:
[P.sub.sp] = [A.sub.0]exp([epsilon]/[A.sub.1])--[A.sub.0] (2)
where [A.sub.0] and [A.sub.1] are parameters of the model and the deformation, [epsilon], is given by the resin flow across the bleeder induced by autoclave pressure and is dependent on spring and damper properties. The elastic reaction of the bleeder was neglected.
Indicating with [x.sub.f] the advancing resin front through the bleeder (Fig. 1b), [epsilon] can be written as:
[epsilon] = ([X.sub.f] - [t.sub.tot])/[t.sub.tot] (3)
where [t.sub.tot] = [t.sub.c] + [t.sub.b] is the total initial thickness given by the sum of initial thicknesses of the composite and of the bleeder, respectively.
The analysis of the pressure supported by the dashpot is based on the hypothesis that a Darcy type flow occurs across the reinforcement fabric. For the sake of simplicity, only the permeability, [K.sub.f], of the reinforcement has been considered, assumed much lower than that of the bleeder. Then, a 1D Darcy flow has been considered using as an unknown the resin front position [x.sub.f] (Fig. 1), that is, a fictive flow has been assumed where the resin is flowing even if it is the bleeder which sinks into the resin, compacting the reinforcement:
[dx.sub.f]/dt =-[[K.sub.f]/[eta](T,[alpha])]([P.sub.dp]/[x.sub.f]) (4)
where the viscosity, [eta], is a function of the temperature, T, and the degree of reaction, [alpha]. Equation 4 can be rearranged introducing [x.sub.f] and the strain [epsilon], and then [P.sub.dp] can be obtained:
[P.sub.dp] = [(d[epsilon]/dt) [t.sub.tot][eta](T, [alpha])/[K.sub.f]]([t.sub.c] - [epsilon][t.sub.tot]) (5)
Combining Eq. 2 and 5 with Eq. 1, a first order differential equation is obtained, where [epsilon][[alpha](T, t), [eta]([alpha], T) is the unknown:
[P.sub.aut] = [(d[epsilon]/dt) [t.sub.tot][eta](T, [alpha])/[K.sub.f]]([t.sub.c] -[epsilon][t.sub.tot])+[A.sub.0]exp([epsilon]/[A.sub.1])-[A.sub.0] (6)
The initial conditions for Eq. 6 are [epsilon] = 0 at t = 0 and T = [T.sub.room]. In this first approach, the temperature across the composite has been considered uniform, following a time dependence according to the cure cycle adopted. As shown in Eq. 6, [K.sub.f] has been assumed constant while the viscosity is a function of the temperature, T, and [alpha], so a kinetic and a rheological model must be solved together with Eq. 6. In synthesis, the simplifying assumptions adopted are: (i) ID Darcy How through the fabric; (ii) negligible permeability of the bleeder; (iii) constant permeability of the reinforcement fabric; and (iv) uniform temperature across the composite specimen.
Chemorheological Analysis of the Thermosetting Matrix
The cure kinetics has been analyzed performing either isothermal either dynamic scans on the resin at the typical heating rates found in autoclave curing. The experimental results have been initially modeled using the well known Kamal's model [28-31]:
d[alpha].dt = ([k.sub.1] + [k.sub.2][[alpha].sup.m]) [(1-[alpha]).sup.n] (7)
where [alpha] is the degree of reaction, m and n are reaction orders and the kinetic constants [k.sub.i] have an Arrhenius dependence on temperature [k.sub.i] = [k.sub.0i]exp(-[E.sub.i]/RT) i= 1,2. Then, a better fit with the experimental DSC results have been obtained using Karkanas and Partridge's model [32, 33], a modification of the Kamal's model:
D[alpha]/dt =[k.sub.1][(1-[alpha]).sup.n1] + [k.sub.2][[alpha].sup.m][(1-[alpha]).sup.n2] (8)
where [alpha] is the degree of reaction, [n.sub.1], [n.sub.2] and m are reaction orders and the kinetic constants [k.sub.i] have an Arrhenius dependence on temperature [k.sub.i] = [k.sub.0i]exp(-[E.sub.i]/RT) i = 1,2. The initial conditions for Eq. 7 are [alpha] = 0 for t = 0. The comparison between the experimental DSC data and the prediction of the kinetic models are reported in Fig. 3. The improvement brought by Karkanas and Partridge's can be observed in Fig. 3b.
The evolution of viscosity as a function of temperature has been modeled using a chemorheological model based on a modified version of Kenny and Opalicki model [24. 34. 35]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)
where [[eta].sub.g0] is the viscosity of the unreacted resin at the initial glass transition temperature [T.sub.g0], [[alpha].sub.g] the degree of reaction at gel temperature and [C.sub.1], [C.sub.2], A, and B constant parameters. The proposed model accounts for the twofold effect of the temperature: an increase of the temperature lowers the viscosity of the resin but simultaneously promotes the curing reaction and therefore increases the viscosity. Equation 9 provides a good fitting of the experimental viscosity as shown in Fig. 4. The parameters used in Eq. 8 and 9 are reported in Table 1.
Equations 6, 7, and 8 have been simultaneously solved with FlexPDE under a temperature program given by a constant heating rate followed by an isotherm at 180[degrees]C, which is the cure temperature of the resin, as suggested by the manufacturer. Three case studies have been considered:
* Case 1: thick bleeder and stiff fiber stack;
* Case 2: thick bleeder and compliant fiber stack;
* Case 3: thick laminate, thick bleeder, and compliant fiber stack with low penneability.
In the Case 1, a stiff carbon fiber preform of 4 mm thickness, with a bleeder thickness of 0.5 mm under an autoclave pressure of 5.5 bar, was adopted. The adopted bleeder thickness, being 1/8 of the composite thickness, can be considered a condition of "overbleeding." Figure 5 shows the evolution of the resin front Xf and of the compressive strain in the reinforcement as a function of temperature assuming a heating rate of 0.5[degrees]C/min.
It is clearly evidenced that a stiff fiber stack prevents the complete filling of the bleeder as the resin flow ends when [x.sub.f] is about 4.14 mm instead of 4.50 mm. The corresponding evolution of viscosity and pressure in the resin and in the reinforcement is reported in Fig. 6. During the flow, the hydrostatic pressure in the resin changes and its final value depends on the fraction of pressure taken from the reinforcement stack. The presence of a thick bleeder (like an over-bleeding condition) and stiff fiber stack leads to an incomplete filling of bleeder. As shown in Fig. 6, at temperatures higher than 75[degrees]C, all the auto clave pressure is supported by the elastic reaction of the fiber stack and is not transferred to the resin. The resin pressure becomes zero before the minimum of viscosity is reached, as shown in Fig. 6, where the resin viscosity is still decreasing and the cure reaction is not yet started. This condition can be highly favorable to the formation of porosities arising from volatiles, mainly water, characterized by a higher vapor pressure as their boiling point is approached.
In the second case study, a compliant carbon fiber preform of 4 mm thickness, with a bleeder thickness of 0.5 mm under an autoclave pressure of 5.5 bar. Also in this case, the adopted bleeder thickness, being 1/8 of the composite thickness can be considered a condition of "overbleeding," Fig. 7 shows the evolution of the hydrostatic resin pressure, the resin viscosity and of the compressive stress in the reinforcement as a function of temperature assuming a heating rate of 0.5[degrees]C/min. The compliant fiber stack can be strained under compression more than 0.5 mm, and, when the bleeder is filled, the pressure in the resin decrease up to 2.6 bar.
In the third case study, the behavior of a 12-mm thick composite made using a compliant carbon fiber stack, was considered. A very low permeability of 1 x [10.sup.-15] [m.sup.2] was adopted in case study 3 to delay the resin flow above the minimum in the viscosity. A bleeder thickness of 0.5 mm under an autoclave pressure of 5.5 bar is still used, that is, a normal bleeding condition is reproduced. The evolution of the resin front position and viscosity with the temperature is reported in Fig. 8, while Fig. 9 shows the evolution of the hydrostatic resin pressure, the resin front position and the compressive stress in the reinforcement as a function of temperature assuming a heating rate of 0.5[degrees]C/min. At low permeability, the flow is slow and occurs at higher temperature than in the former case studies, even continuing when viscosity increases. In this case, the resin flow is limited by viscosity increase, that is, gelation prevents full transfer of autoclave pressure to liquid resin and the bleeder is not completely filled.
The results predicted by these simulations are in good agreement, even if qualitatively, with the experimental measurements of hydrostatic pressure performed by Campbell et al. [23, 36] on thick composites with a standard bleeder and a thick bleeder (overbleeding condition). In the first case, the resin pressure follows the autoclave pressure as reported in Fig. 10a. This condition is predicted by our model as shown in the case study 3, where a very limited pressure decrease was predicted (Fig. 9). A similar condition can be predicted by the model when a compliant fiber stack and a very thin bleeder is used, to significantly limit the resin flow.
When overbleeding conditions were used by Campbell et al. [23, 36], resin How is not limited by the "capacity" of the bleeder allowing high strains in the fiber stack up to its equilibrium strain under he applied pressure. In this case, after some flow and an initial pressure increase, the resin pressure decreases to zero very rapidly (Fig. 10b). Also this case has been qualitatively predicted by our model as shown in the first case study. In particular, as shown in Fig. 6, an excess in resin flow due to an "overbleeding" condition, associated with a stiff fiber stack, capable take the autoclave pressure with a limited compressive strain, leads to a decrease to zero of the hydrostatic resin pressure.
A model capable to predict the pressure changes occurring during an autoclave cycle has been presented. The model takes into account the out-of-plane flow in the bleeder and simulates the unreacted preprcg using a Kelvin Voigt model. The dashpot behavior has been simulated considering a Darcy flow through the reinforcement and a simple exponential growth function has been adopted for the nonlinear elastic behavior of a fabric reinforcement under compression. Furthermore, a full simulation of the cure behavior has been performed considering the dependence of the resin viscosity from temperature and degree of reaction. The effect of the flow and of the reinforcement compression indicates that only a fraction of the autoclave gas pressure is transferred as a hydrostatic pressure in the resin.
As future work, the introduction of an energy balance in the model is envisaged. The effect of volatile diffusion under vacuum before bleeder is filled by the resin and the variability of permeability with the fiber volume fraction will be also considered.
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Francesca Lionetto (iD), (1) Giuseppe Buccoliero, (2) Silvio Pappada, (2) Alfonso Maffezzoli (1)
Contract grant sponsor: Italian Ministry of Education, University and Scientific Research in the framework of Project PON03PE_00067_2 DITECO "Difetti, danneggiamenti e tecniche di riparazione nei process iproduttivi di grandi strutlure in composito."
This paper was presented at 8th International Conference on Times of Polymers & Composites-TOP 2016 held in Ischia, Italy, June 19-23, 2016
(1) Department of Engineering for Innovation, University of Salento, via per Monteroni, Lecce 73100, Italy
(2) Consorzio CETMA, Departments of Materials and Structures Engineering, Technologies and Processes Area, SS7-Km706 + 300, Brindisi 72100, Italy
Correspondence to: F. Lionetto; e-mail: email@example.com
Caption: FIG. 1. Simplified sketch of strain and flow phenomena occurring during autoclave cure. [Color figure can be viewed at wileyonlinelibrary.com]
Caption: FIG. 2. Comparison between Eq. 2 predictions and experimental compression test.
Caption: FIG. 3. Comparison between Eqs. 7 and 8 predictions and experimental DSC data.
Caption: FIG. 4. Comparison between Eq. 9 predictions and experimental viscosity data.
Caption: FIG. 5. Model results for Case 1 (stiff fiber stack): evolution of strain and resin front, until complete filling of the bleeder.
Caption: FIG. 6. Model results for Case 1 (stiff fiber stack): evolution of viscosity and pressure in the resin and in the reinforcement.
Caption: FIG. 7. Model results for Case 2 (compliant fiber slack): evolution of pressure, elastic stress, and viscosity.
Caption: FIG. 8. Model results for Case 3 (compliant fiber slack with a low permeability): evolution of viscosity and resin front.
Caption: FIG. 9. Model results for Case 3 (compliant fiber stack with a low permeability): evolution of resin front and pressure in the resin and in the reinforcement.
Caption: FIG. 10. Measurements of hydrostatic pressure on 40-ply AS-4/3501-6 epoxy laminate in (a) normal bleeder and (b) overbleed condition.
TABLE 1. Parameters of the chemorheological model. [A.sub.0] [A.sub.1] m [n.sub.1] (MPa) 0.396 0.0325 0.58 0.79 [E.sub.2] [[eta].sub.0] (Pa s) [T.sub.go] (K) [C.sub.1] (kJ/mol) 45.12 6.05 x [10.sup.10] 266 34.52 [A.sub.0] [n.sub.2] [K.sub.10] [E.sub.1] [K.sub.20] (MPa) ([s.sup.-1]) (kJ/mol) ([s.sup.-1]) 0.396 1.99 [1.15.sup.*] 127.0 140 [10.sup.10] [E.sub.2] [C.sub.2] (K) [[alpha]. A B (kJ/mol) sub.g] 45.12 53.09 0.455 5.98 8.05
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|Author:||Lionetto, Francesca; Buccoliero, Giuseppe; Pappada, Silvio; Maffezzoli, Alfonso|
|Publication:||Polymer Engineering and Science|
|Date:||Jun 1, 2017|
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