Composites: Part A 36 (2005) 806–826

www.elsevier.com/locate/compositesa

Numerical analysis of cure temperature and internal stresses in thin and

thick RTM parts
Edu Ruiz*, François Trochu1
Centre de Recherches Appliquées Sur les Polymères (CRASP), Département de Génie Mécanique, École Polytechnique de l’Université de Montréal,
Montreal, Que., Canada H3C 3A7
Received 27 November 2003; revised 12 September 2004; accepted 7 October 2004

Abstract
Resin transfer molding (RTM) is a widely used manufacturing technique of composite parts. Proper selection of processing parameters is
critical in order to produce successful molding and to obtain a good part. Notably, when thermosetting resins are processed, the shrinkage that
results from resin polymerization increases the complexity of the problem. Numerical prediction of internal stresses during composite
manufacturing has three objectives: (1) to improve knowledge about the process; (2) to analyze the effects of processing parameters on the
mechanical integrity of the part; and (3) to validate the principles of thermal optimization. This investigation aims to predict residual stresses
and part deformation (i.e. warpage) in thin and thick composites. Accurate characterization of materials is essential for effective numerical
analysis of phenomena which determine the generation of processing stresses. For this purpose, a reaction kinetics model of the resin is
presented, together with a description of mechanical properties as a function of the degree of polymerization and glass transition temperature.
A linear model is used to predict volume changes in glass–polyester composites. A finite difference analysis is used to simulate the effect of
thermal and rheological changes during the processing of sample plates. Classical laminate theory is applied to calculate the internal stresses
that result from processing conditions. These stresses are compared to determine different curing strategies for thick composite parts. Finally,
a thermal optimization algorithm is applied to demonstrate the advantages of transient heating and cooling, to minimize processing stresses
and avoid thermal degradation of the material or composite delamination.
q 2004 Published by Elsevier Ltd.

Keywords: B. Cure behaviour; B. Residual/internal stress; B. Thermomechanical; C. Numerical analysis; E. Resin transfer moulding (RTM)

1. Introduction significant thermal gradients and temperature peaks and,

in turn generate residual stresses and possibly, polymer
As the composite industry grows, thick parts and pieces degradation. In order to improve the quality of thick
of complex shape become more common. Composite composites, processing temperatures need to be controlled
components for structural applications require larger to minimize thermal gradients throughout the part. This
cross-sections. The curing of thick parts remains a challenge means the mold temperature must be lower for thick parts
because of the low thermal conductivity of the composite than for thin ones. Moreover, the chemorheology and cure
and the high heat of reaction generated during cross-linking kinetics may be considerably different from what is
polymerization. This combination of low conductivity and observed at higher temperatures. The reinforcing fibers are
high heat sources in the part during cure can foster not really affected during the process cycle, but the polymer
matrix can shrink during cross-linking, in some cases by as
much as 9% [1].
* Corresponding author. Address: P.O. Box 6079, Station ‘Centre- Both chemically induced shrinkage and thermal defor-
Ville’, Montreal, Que., Canada H3C 3A7. Tel.: C1 514 340 4711x5844; mations are generated during composite processing. The
fax: C1 514 340 5867.
E-mail addresses: eduardo.ruiz@polymtl.ca (E. Ruiz), francois.
fibers possess a small thermal expansion coefficient along
trochu@polymtl.ca (F. Trochu). their longitudinal axis and that produces little deformation
1
Tel.: C1 514 340 4711x4280. during resin cure. The polymer matrix has a much higher
1359-835X/$ - see front matter q 2004 Published by Elsevier Ltd.
doi:10.1016/j.compositesa.2004.10.021
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 807

thermal expansion coefficient and is thus more susceptible

to temperature changes. During processing, different
thermal behaviors produce residual stresses. During the
cure of fiber-reinforced composites, the residual stresses
generated can have considerable effects on the part quality
and on its mechanical properties, promoting warpage or
initiating matrix cracks and delamination [2]. Thick parts
are often too rigid to relieve internal stresses by distortion,
so matrix damage is more likely to occur [3]. The processing
of thick composites at a lower temperature should reduce
thermally induced residual stresses [4]. However, a
minimum temperature must be reached to initiate the
cross-linking chemical reaction. At low temperature, the
cure reaction takes longer and the number of links created
may not be high enough to obtain the required mechanical
properties. In the processing of composite materials by
Resin Transfer Molding (RTM), the three key processing
parameters are curing time, temperature and pressure.
Appropriate choice of these parameters will produce a
material which is fully cured, well compacted and of high
quality.
As depicted in Fig. 1, a number of surface and structural
defects may appear in the processing of composite parts by
RTM. Inappropriate processing parameters result in typical
problems such as distorted surface appearance, waviness,
warpage or ‘spring-in’, matrix degradation or delamination.
The effect of processing parameters on these defects may be
examined by rule-based heuristic expert systems or
numerical analysis of the physical phenomena involved
during composite processing [1–6,8–13]. Heuristic methods
may initially seem to be faster in terms of computer time
and do not require detailed material characterization.
However, the results strongly depend on the knowledge of
the expert. It is difficult to asses the level of optimization
reached. As understanding of material behavior grows, Fig. 1. Investigations required to assess and control part quality in RTM
manufacturing. The global problems need to be stated, requirements of
numerical analysis is increasingly chosen in process
material characterization defined and appropriate objective functions
optimization [4]. Still, the implementation of computational derived, for process optimization.
methods is limited by the wide requirements of material
characterization. In addition, the results of numerical
demonstrated the ability to follow resin cure, Differential
simulations depend on the quality of experimental data,
Scanning Calorimetry (DSC) seems to be the most effective
(i.e. on the repeatability of experiments executed to
characterize a specific material property). The property experimental technique for that purpose. Calorimetric
investigated can only be studied on a given experimental studies have been widely used and kinetic models are
domain. This restricts the space available for numerical based primary on the autocatalytic assumptions. Yousefi-
analysis and optimization. Then, for process optimization, Moshirabad [19] has determined the dependence of kinetic
one needs to define the global problem to be studied and parameters on temperature, as well as the effect of low-
state the requirements of material characterization. Finally, curing temperature on gel time and final degree of
one needs to develop comprehensive objective functions to polymerization. More recently, Edu Ruiz and Trochu [17]
reflect the complexity of composite processing. established a methodology to determine parameters of
In reference to material characterization, prediction of several kinetic models using genetic algorithms.
reaction kinetics is a key element in the processing of The evolution of mechanical properties during resin cure
thermosetting materials. The reaction kinetics of epoxy and is another issue that limits the scope of numerical
polyester resins has been widely investigated by several predictions of processing stresses. Many previous investi-
authors [2–8,14–20]. Although recently, new measurement gators have assumed the mechanical properties of the
methods, such as optical fiber sensors [5] or Fourier composite are elastic and vary linearly with the degree of
Transformed Infrared Spectroscopy (FTIR), have polymerization of the matrix [21–23]. Although this method
808 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

is the simplest way to compute internal stresses during Both models depend on fiber volume fractions, temperature
processing, viscoelastic effects and glass transition of the and degree of polymerization. A methodology based on
resin limit the accuracy of calculations. Viscoelastic Classical Laminated Plate Theory (CLT) [25] is developed to
modeling [8,11–13,17] is well suited for material charac- predict residual stresses during the cure of composite
terization of relaxation and glass transition effects. Never- laminates. The thermo-chemical model predicts the tem-
theless, the requirement of time integrals and close loop perature and degree of polymerization through the thickness
iterations make these models difficult to implement in of the part. The mechanical model (based on CLT) evaluates
numerical optimization schemes, which require a large the through-thickness strain and stresses as a function of the
number of iterative calculations. To simplify this problem thermo-chemical evolution of the material. On one hand,
and to avoid time integration, some authors [24] have differential dilatation of the plies generates thermal stresses.
considered the existence of a ‘free-stress’ temperature On the other hand, differences in the polymerization degree
(i.e. the temperature at which the composite would reach a result in a non-uniform shrinkage of the polymer matrix and
‘stress-free’ state). Another possibility, still accurate and create residual stresses of chemical origin.
without requiring excessive computational time, consists of The former thermo-chemical and mechanical models
modeling mechanical properties in their unrelaxed and fully enable processing stresses to be calculated and compared
relaxed stages [17], where a function of the glass transition for three different curing strategies through the thickness of
temperature describes the phase transformation. the composite laminate: (1) outside-to-inside cure; (2)
Various researchers have conducted numerical predic- inside-to-outside cure; and (3) one-side cure. First, the
tions of the composite curing stresses using analytical curing and cooling of asymmetrical thin laminates is
equations or finite element (FE) formulations. Svanberg investigated. Predictions of warpage for a series of thin
et al. [27,28] developed a simplified, mechanical constitutive plate samples have been validated through experiment.
model applicable to homogenized composites during resin Next, the analysis of processing stresses is carried out for
cure. The model replaced the viscoelastic time dependence thick composite plates. The advantage and drawbacks of
by a path dependence on the state variables, namely strain, three possible curing scenarios are compared and the best
degree of cure and temperature. The model was also heating strategy is identified. Finally, a thermal optimiz-
implemented in a general purpose FE software program ation algorithm illustrates the time gains of more optimized
and verified against analytical test cases. Based on the simple heating and cooling temperature profiles. This minimizes
beam bending test, Saham et al. [29] conducted experiments processing stresses and at the same time material thermal
to monitor the evolution of residual stresses in epoxy degradation and/or composite delamination.
compounds for electronic packaging applications. The
authors explained how the relationship between the stresses
evaluated and various curing phenomena such as polymer
cross-linking and temperature differentials. Di Francia et al. 2. Thermo-mechanical analysis
[30] used the single-fiber pull-out test to evaluate the
deformation of an adhesively bonded composite patch In a non-isothermal RTM injection, the mold is typically
during cure. Experimental studies were also conducted at a higher temperature than the resin and fibers.
using a three-point bending fixture, showing a good Temperature variations in the part are produced by the
match with analytical predictions. Fernlund et al. [31] heat exchanged between the preform, resin and mold walls
implemented a FE approach to compute curing stresses of during resin injection. Sometimes, curing is affected by the
laminated carbon composites in ‘L’ and ‘C’ shapes. A heat transfer in the cavity during the filling stage. However,
validation with experimental results showed that the when thermal effects during filling have little effect on the
approach presented provided a good numerical prediction initial polymerization degree of the resin, it is possible to
of curing stresses. Although the FE solutions seems to be decouple filling and curing as two distinct stages of the
accurate to calculate the stain–stress behavior during resin manufacturing process. In order to verify if the chemical
cure for composites parts of complex shape, these methods reaction can be omitted during mold-filling, a non-dimen-
require excessive computer time for cure cycle optimization. sional number called the gelling ratio (Ge) is used. This
In this sense, analytical solutions of simple shape composites number conveys the time required to fill up the mold
seem to be more appropriate for implementation in looping (injection time) with the time needed to cure the part
optimizations. (reaction time). For a small Ge, it is possible to decouple the
The purpose of this paper is to show how a numerical curing process from the filling stage. In the case of
model of trough-thickness heat transfer can assist in finding polyester-based resin systems, the free radicals generated
optimal temperature cycles. First, the physical phenomena are initially deactivated by reacting with an inhibitor, so the
that govern curing are presented together with the thermal Ge can be defined as the ratio of the filling time (tf) over the
equation that models the heat exchanged between the part inhibition time (tin) at mold temperature. From this
and its surroundings. Models are presented for volume definition, a Ge smaller than unity means that the curing
changes and material behavior during composite processing. process can be decoupled from mold filling, which is
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 809

the case assumed in this investigation. K3 ðT; aÞ Z ðamax K aÞn

injection time filling time t
Ge Z Z Z f !1 (1) The term K1(T) is an Arrhenius factor that depends on
reaction time inhibition time tin
temperature. Function K2(a) is a fit with a polynomial of
degree m. Function K3(T,a) accounts for the maximum
2.1. Heat transfer equation degree of polymerization amax that depends on temperature.
Finally, K4(Id) is a characteristic function that models the
In this study, the resin cure is analyzed through the effect of the inhibitors: K4(Id)Z1, if induction time IdO0,
thickness of the composite. At each period in time, an and K4(Id)Z0 otherwise. For the unsaturated polyester resin
instantaneous equilibrium temperature is assumed to exist used in this investigation (T580-63 from AOC), kinetic
between the resin and the fibers. This corresponds to the measurements were performed with a DSC 910 from
lumped approach of Lin et al. [6]. The transient absolute DuPont Instruments. An ultimate heat of reaction of 365 J/g
temperature T(z,t) at position z and time t, through the total was found when 1.5 phr of Andonox Pulcat-A peroxide was
part thickness H is given by the one-dimensional Fourier’s added as catalyst. Fig. 2 compares the degree of cure in time
heat conduction equation measured by dynamic DSC measurements for different
heating rates with predictions derived from the kinetic
vT v2 T
~
r~ Cp Z k~ 2 C Q 0% z% H (2) equation (3). The autocatalytic model seems to predict
vt vz accurately the cross-linking evolution in all the cases
where the density r,
~ heat capacity Cp~ and conductivity k~ of considered.
the composite are defined as the effective properties The final resin conversion, or maximum extent of cure,
obtained by the rule of mixture [6] depends on temperature up to a temperature high enough to
rr rf provide sufficient molecular mobility so as to permit all
~ Z Cpr wr C Cpf wf
Cp r~ Z species to react within the system [2]. The final polymeriz-
rr wr C rf wf
ation degree is commonly less than one for the curing
temperatures typically used to process thick parts (i.e. not all
kr kf f=rf
k~ Z wr Z polymerization links can be developed at low temperature).
kr wr C kf wf ðf=rf Þ C ð1 K f=rr Þ Note that a temperature dependent parameter amax is
introduced in the kinetic equation to account for the
wf Z 1 K wr incomplete chemical reaction. By using the conversion
In the above equations, f is the porosity and wr, wf denote methodology proposed by Atarsia and Boukhili [7] to
the weight fractions of resin and fibers, respectively. convert dynamic DSC tests for a series of constant heating
The subscript f stands for the fibers and r for the resin. ramps to isothermal results, the maximum cure degree can
The thermal properties of the resin are considered to be a be derived from dynamic DSC data and modeled as a
function of temperature and degree of polymerization. The polynomial function of temperature of degree N
source term Q represents the instantaneous heat generated
by the cross-linking polymerization of the resin. Q is X
N
assumed to be proportional to reaction rate. amax Z fi T i with T in 8C (5)
iZ0

2.2. Chemical reaction

Fig. 3 shows the maximum degree of polymerization
attained as a function of cure temperature for the AOC resin.
Resin cure is modeled by an empirical, autocatalytic,
kinetic equation that describes free-radical polymerization.
Let a denote the degree of polymerization, (i.e. the ratio of 2.3. Induction time
the instantaneous heat released by the reaction to the
ultimate heat of reaction). The rate of conversion da/dt is In polyester-based formulations, inhibitors are placed in
given by the following equations [15] resin systems to increase shelf-life. They combine with the
free radicals that initiate polyester–styrene cross-linking.
da
Z K1 ðTÞK2 ðaÞK3 ðT; aÞK4 ðId Þ (3) Inhibition agents in the resin system increase the curing time
dt significantly. While these inhibitors disappear quickly at

 high curing temperatures, the kinetics of the inhibitor
Tref
K1 ðTÞ Z kref EXP KA K1 deactivation can be very slow at the lower temperatures
T required to successfully cure thick parts. Assuming that the
(4) polyester–styrene linkage begins only when the inhibitor
X
m
i
K2 ðaÞ Z ai a concentration reaches zero, the induction time Id(T,t)
iZ0 required initiating the chemical reaction can be represented
810 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

Fig. 2. Comparison of DSC measurements of the resin degree of polymerization with predictions of the resin cure kinetics model: DSC experiments from room
temperature to 180 8C at heating ramps between 5 and 35 8C/min show good agreement with model predictions.

by a time integral of the thermal history [16]. induction reference temperature. The weight function
ðt

 K4(Id) of Eq. (3) is then set to 1 when the induction time
T is zero. Measured versus predicted induction times are
Id ðT; tÞ Z trefK exp KCind ind K 1 dt;
0 T compared in Fig. 3 for a wide range of curing temperatures
( (6) of the AOC resin T580-63. Note that for low processing
Z 0 if Id O 0 temperatures (i.e. less than 60 8C), larger induction periods
K4 ðId Þ Z
Z 1 if Id % 0 (w20 min) are required before polymerization begins. The
ultimate polymerization degree may not exceed 40%. The
where tref, Cind and Tind are fitting coefficients called, resin manufacturer recommends that composite parts made
respectively, reference time, induction constant and with this resin system should be processed within the range

Fig. 3. Maximum degree of resin polymerization and induction time as a function of curing temperature: these results were obtained from DSC measurements
data after applying the conversion methodology.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 811

of 90–120 8C. This will decrease the processing time and below) and two functions to account for the dependency on
also reach an adequate level of polymerization. the polymerization degree (Fr(a)) and glass transition
temperature (Wr(Tg)) [17]
2.4. Thermo-chemical dependence of mechanical properties Er ðT; aÞ Z Eagp ðTÞ C ½Ec ðTÞ K Eagp ðTÞFr ðaÞWr ðTg Þ (7)

In order to accurately assess the quality and control the Ec0 0

Eagp
manufacturing process, it is imperative to be able to predict Ec ðTÞ Z Eagp ðTÞ Z (8)
coshða1 TÞb1 coshða2 TÞb2
the intrinsic behavior of the material and the properties of
the final part. Similarly, much like thermo-kinetic proper- a K aagp
ties, the mechanical properties of the resin vary during the Fr ðaÞ Z c expðdaÞ
^ C ea^ a^ Z (9)
ault K aagp
curing process. Some authors [8–10] have reported a linear
correlation between the mechanical properties and the

Tg ðaÞ K T
degree of polymerization for different thermosetting poly- Wr ðTg Þ Z h exp
mers. In this work, mechanical properties were measured Tg ðaÞ K Tref

K1 (10)
with a dynamic mechanical analyzer (DTMA 2980 from TA
Kbg
Instruments) as a function of temperature and degree of Tg ðaÞ Z ag exp
polymerization. It was found that long after the gel point, 1 K a^
the resin elastic modulus is still very low (below 10 MPa) The expression Fr(a) is as the sum of a linear plus an
for a polymerization degree less than 40%. This polymeriz- exponential function of the polymerization degree that can
ation degree, called After Gel Point (AGP) [17], was then be estimated from the curve of Fig. 5. A convenient rule of
taken as base line to analyze the evolution of mechanical mixtures ðaÞ^ is used here in order to approximate the
properties for higher polymerization levels. Resin samples variations of material properties between the AGP level
cured until the AGP stage were mechanically tested with the (aagp) and the cure degree for which E 0 reaches its ultimate
DMA during a specified curing cycle. Fig. 4 shows that the value (for aultz97%). Further, the model presented
elastic modulus has an initial value defined at AGP (E 0 agp) accounts for the glass transition temperature dependence
and then increases, until it reaches a maximum considered of the resin elastic modulus by a temperature shift factor
as the fully cured modulus (E 0 c) for 97% of total resin (Wr(Tg)). This factor considers the transition to complete
polymerization. viscoelastic relaxation at vitrification (or when the material
Fig. 5 depicts a non-linear correlation between Young’s is in a rubbery state, i.e. when TRTg). Constants a, b, c, d
modulus and the polymerization degree. This relationship and e of Eqs. (7)–(10) were obtained by implementing a
was modeled by introducing hyperbolic cosine laws that Genetic Algorithms Search Engine that properly fit the
properly describe the temperature dependence of the elastic models to the measured data. Subscripts r, c, g and agp of
moduli of the AGP and fully cured resin (see equations these constants denote, respectively, resin, composite, glass

Fig. 4. Comparison of the resin Young’s modulus (E 0 ) and degree of polymerization during a specified curing cycle: E 0 is measured with a DMA while the
degree of polymerization comes from DSC measurements.
812 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

Fig. 5. A non-linear correlation between E 0 and the degree of polymerization is observed for the polyester resin tested: DMA measurements of E 0 are plotted as
a function of the degree of polymerization obtained from DSC results.

transition and after gel point. Fig. 6 shows the temperature relatively good agreement with experimental data for all
shift factor of fully relaxed coefficients for polymerization tested samples.
degrees above AGP. Glass transition temperatures are also In the case of shear properties, two possible approaches
depicted in the same graphic, showing that the initial glass may be used. In the first case, Levitsky and Shaffer [11]
transition Tg0 stands around 55 8C, while the fully cured assumed the plain strain bulk modulus to be constant during
transition TgN is at about 110 8C (TgN was practically taken as cure, so that the elastic moduli and Poisson’s ratio vary as
the glass transition temperature for 95% of total resin the part cures. In the second case, Bogetti and Gillespie [8]
conversion). Fig. 7 shows DMA measurements of the elastic assumed that Poisson’s ratio remains constant during
modulus for several resin specimens cured at different processing. They found that differences in the resin
polymerization degrees between aagp and ault. The predic- Poisson’s ratio during cure have no significant influence
tions of the proposed thermo-chemical model exhibit a on the properties of the macroscopic composite, on

Fig. 6. Temperature shift factor as a function of temperature for various degrees of polymerization: the glass transition temperature Tg is also drawn as a
function of the degree of polymerization.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 813

Fig. 7. Comparison of the model predictions and DMA measurements of Young’s modulus E 0 for partially and fully cured resin samples (the lines present
model predictions).

process-induced strains and on residual stresses. Both volume fractions Vf in the two principal fiber directions
models predicted nearly identical values of elastic and


shear moduli. Poisson’s ratio is also expected to relax to i Vf ðEfi K Er ðT; aÞÞ Er ðT; aÞ
Ecomp Z C Eagp ðTÞ
w0.5 as the thermosetting polymer approaches the rubbery 1 C Ai expðBi TÞ Er ðT; 1Þ
state, nevertheless it was found by O’Brien et al. [12] that
the effect on the shear modulus is relatively minor. with i Z 1; 2
According to these researchers, variations of Poisson’s (12)
ratio do not play an important role. For that reason, in
where Ai and Bi are fitting constants for each material
this investigation a constant value nrZ0.35 was used, as
direction (iZ1,2). Indexes r, f and comp stand for resin,
measured at room temperature for a fully cured sample. The
fiber and composite, respectively.
instantaneous resin shear modulus during cure is based on
Two reinforcing materials have been used in this study to
the classical relationship for isotropic materials
analyze thermal effects on processing stresses: a continuous
glass random mat U101 from Vetrotex and one bi-directional
Er ðT; aÞ balanced non-crimp glass fabric NCS 82620 from J.B.
Gr ðT; aÞ Z (11) Martin. Fig. 8 shows measurement results of Young’s
2ð1 C nr Þ 1 2
modulus in both directions (Ecomp , Ecomp ) for a composite
plate made with NCS-82620 bidirectional fabric (VfZ42%).
For the partially and fully cured samples, the mechanical
model approaches the experimental curves at temperatures
2.5. Composite effective mechanical properties
close to Tg. Young modulus of composite specimens with
these materials were measured and fitted by Eq. (12). As
The effective, homogeneous mechanical properties of the
depicted in Fig. 9, between two and three fiber volume
composite laminate are highly dependent on those of the
contents were tested for each material. Note that the rule of
matrix and reinforcement, as well as on the fiber volume
mixture used here may be accurate only around measured
fraction. The thermal and mechanical properties of the
values of fiber volume content. The range of validity
reinforcement may be considered constant, independent of
considered for the materials tested is presented in Fig. 10.
temperature and of the polymerization degree. But, accord-
ing to the models previously presented matrix properties
vary during processing. Although Whitney’s self-consistent, 2.6. Volume changes
micro-mechanical model [13] was initially used to deter-
mine reinforcement properties, they were over-estimated at Some experimental studies have been conducted to gain
temperatures close to the matrix glass transition. Empirical insight on the volumetric changes that occur during
models were then used to estimate the composite elastic thermosetting polymer processing. Hill et al. [14] measured
1;2
modulus Ecomp as a function of temperature T and fiber the volume changes of unsaturated polyesters during resin
814 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

Fig. 8. Measured and predicted Young’s modulus E 0 in both directions for a composite with volume fraction VfZ42% of NCS-82620 for fully and partially
cured samples.

cure due to variations of temperature and degree of The first term on the right hand side represents the bulk
polymerization. Hill proposed that the overall volumetric thermal expansion/contraction contribution, which can be
changes of a thermoset resin during cure be considered as a expressed by
combination of thermal expansion or contraction and

1 dV
polymerization shrinkage as follows
Vo dt Thermal Contribution


1 dV dT dT (14)
Z bgel C½ðbcured Kbgel Þa
Vo dt overall dt dt



1 dV 1 dV bcured ; bgel Z a0 Cb0 T
Z K
Vo dt thermal contribution Vo dt polymerization shrinkage where bgel and bcured are the coefficients of thermal
(13) expansion (CTE) of the gelled and fully cured resin,

Fig. 9. Measured and predicted E 0 for different fiber volume fractions Vf of fully cured composite samples made of NCS-82620 fabric and U101 mat.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 815

Fig. 10. Rule of mixtures for E 0 as a function of fiber volume fraction Vf: regions A and B represent the experimental domain of validity of Vf for U101 and NCS
materials, respectively.

respectively. These coefficients are assumed to vary linearly shrinkage lchem for the fully cured sample was about 7%.
with temperature, and a0 and b0 are the constants of the

1 dV da
linear fitting. Eq. (14) means that the thermal expansion or Z lchem (15)
Vo dt polymerization shrinkage dt
contraction is assumed to vary monotonically with the
polymerization degree a. The second term on the right hand
side of Eq. (13) represents the contribution of chemical 2.7. Longitudinal and transverse coefficient of thermal
shrinkage (i.e. the volume shrinkage induced by the resin expansions (CTE)
cross-linking during polymerization). Resin shrinkage was
measured with a thermomechanical analyzer (TMA 2940 The CTE of pure resin samples and composite plates
from TA Instruments) as a function of the degree of were also measured with the thermo-mechanical analyzer.
polymerization. As observed in Fig. 11, the linear As presented in Fig. 12, thermal expansions of uncured resin
relationship of Eq. (15) was derived experimentally for samples (i.e. for aZ0), partially cured (for aZ0.45 and
the polyester resin tested. The total polymerization 0.80) and fully cured ones have been experimentally

Fig. 11. Linearization of chemical shrinkage induced by resin polymerization (TMA versus DSC measurements).
816 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

Fig. 12. Coefficients of thermal expansion for partially and fully cured resin samples (from TMA measurements).

determined. During curing, the CTE of the resin decreases directions (i.e. longitudinal, transverse and through-thick-
almost in proportion with the degree of polymerization. ness). The model follows the rule of mixture
Based on this assumption, experimental data can be fitted by
a bilinear function of temperature and degree of polymeriz- CTEdcompZ CTEr ðT; aÞð1 K Vf Þ C CTEdfiber Vf
(17)
ation. Then, the resin CTE can be written as a rule of
where d Z L; T; and T  T
mixture between the uncured (After Gel Point) and cured
CTE
2.8. Strain–stress modeling
CTEr ðT; aÞ Z CTEagp ðTÞð1 K aÞ
^ C CTEcured ðTÞa^ (16)
The present analysis assumes that the Classical Lami-
where a^ is the normalized degree of cure given by Eq. (9). nated Theory (CLT) is applicable to the infinitesimal region
Composite samples of NCS 82620 and U101 reinforce- of a composite unit cell. By introducing the expressions of
ments were also measured (see Fig. 13) in the three principal thermo-chemically dependent mechanical properties into

Fig. 13. Coefficients of thermal expansion for fully cured composite samples of NCS-82620 fabric: d1 and d2 indicate the principal planar directions of the
fabric, while T refers to the transverse direction.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 817

the CLT formulation, we get for thermal and chemical Table 1

loadings [25] Summary of dimensions and curvatures of eight thin plate samples after
demolding: reported thicknesses are the average of 10 measurements along
ðt 
v3j the plates
fsj gt Z ½Cj t dt; for j Z 1–N plies (18)
tðAGPÞ vt Test NCS 82620 U101 Length Thickness X curvature
number (# of plies) (# of plies) (mm) (mm) (1/m)
where the strain vector is defined as
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2 2 515 2.7 0.314
3j Z 3thermal
j C 3chem
j ; 3chem
j Z 3 1 C ðlchem aÞK1 2 3 2 489 2.7 0.356
3 2 2 493 2.6 0.292
Here 3chem
j is the incremental isotropic shrinkage strain 4 4 2 499 2.7 0.496
defined by Bogetti and Gillespie [8]. In order to account for 5 5 2 499 2.8 0.506
6 6 2 504 2.8 0.428
the potentially nonlinear behavior of the material, the 7 4 2 500 2.7 0.375
stiffness matrix [Cj] (that depends of the composite 8 5 2 499 2.8 0.404
temperature and resin degree of cure) must be calculated
Curvatures along the X-axis are calculated from 10 measurements.
at each processing time. In this way, [Cj] is the algebraic
average of [Cj]t and [Cj]tCdt. A step-by-step calculation has
been used to predict the thermo-chemical response of the manufacture varies between 2.6 and 2.8 mm with an
laminate during processing. At each step, planar stresses and average of 2.7 mm.
out-of-plane curvatures are calculated from the strains Differences in the linear CTE and mechanical properties
induced by thermal gradients and chemical changes in the of each ply obviously generate warpage in molded plates.
composite. Thermocouples were embedded between plies to measure
through-thickness temperature profiles during processing.
As depicted in Fig. 15, the warpage of plates cured at 120 8C
resulted in a curved shape along the longitudinal and
3. Analysis of thin composite plate cooling
transverse directions. Because of the existence of a
transverse curvature, one single measurement is the center
Internal stresses strongly effect the properties and
is insufficient to estimate the longitudinal curvature. For each
durability of composite parts manufactured with thermoset-
material combination, the longitudinal deflections of the
ting polymers. The source of internal stresses depends on
material properties and processing conditions. These stresses plate samples (after manufacture) were measured using a
are most commonly created during composite manufacturing Linear Variable Displacement Transducer (LVDT) at several
and result from thermal and mechanical differences of locations on the middle axis of the samples. The longitudinal
behavior among phases of the constitutive materials. Internal plate curvature was then estimated from these measures
stresses may lead to defects in the part in the form of voids along the sample length. As presented in Table 1, the
and micro-cracking during processing, or warpage, spring- longitudinal curvature of the samples after demolding varied
in, premature delamination or debonding after manufacture. for the different material combinations tested. While for test
In order to identify defects caused by internal stresses #2 (two plies of U101 and two of NCS 82620) a curvature of
during cooling, a total of 16 3 mm thick composite plates of 0.292 mK1 was obtained, for test #5 (two plies of U101 and
50 cm by 10 cm were molded using several combinations of five of NCS 82620) a curvature of 0.506 mK1 was measured.
NCS-82620 fabric and U101 mat. As shown in Fig. 14, NCS Special care must be taken in the specimen preparation,
and U101 plies were asymmetrically layered. The samples mainly due to surface density variations of the U101 mat.
contained between two and six plies of NCS 82620 fabric Non-uniform surface density of the mat results in variable
together with two plies of U101 mat. The thickness of the plate thickness after curing, so the assumption
plates was measured at 10 locations and averaged. The of cylindrical deflection may not correctly predict
stacking sequence, length and thickness of eight samples are
reported in Table 1. The thickness of the plates after

Fig. 14. Stacking sequence for thin plates: the number of NCS plies was Fig. 15. Warpage appearing in thin composite plates after manufacture due
changed while mold thickness remained constant; two plies of U101 were to unbalanced lay-up: total deflection in the plate center is the sum of
used for all the test samples. longitudinal and transverse deflections.
818 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

Fig. 16. Measure of typical plate deflection during cooling from above the glass transition temperature. The sample has two plies of NCS-82620 fabric and two
plies of U101 mat. While temperature decreases from 140 8C to room temperature, plate deflection increases from 5 to 17 mm.

the experimental values. After demolding, a number of Transducer (LVDT) was placed to measure the deflection
plates were re-heated and maintained during 20 min at of the plates at the gravity center. While sample
150 8C, which is above their glass transition temperatures, temperature decreases, the deflection in the center
so as to allow relaxation of the matrix. Once processing increases from 5 to 17 mm.
and demolding stresses have relaxed, the flat plates were The measured temperatures were then used as thermal
cooled to room temperature. As illustrated in Fig. 16, boundary conditions for the thermo-mechanical model. The
temperatures at different thickness and length positions deflection of the specimens was calculated by solving
were recorded during cooling. The bottom, mid-plane and iteratively Eqs. (2), (12), (17) and (18). The results of the
top temperatures decreased uniformly enough to neglect proposed model are compared to experimental values in
transverse thermal effects. A Linear Variable Displacement Fig. 17. A minimum of three measures were carried out for

Fig. 17. Comparison of measured plate deflection during cooling with the numerical prediction of the thermo-mechanical model: three measurements were
performed for each plate; the two samples show a good agreement with predicted values.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 819

Table 2 The progression of the curing front through the thickness

Comparison of ultimate plate deflection during cooling after re-heating at is another important issue connected with the development
150 8C: numerical and measured deflections are taken at room temperature
of internal stresses. Fig. 19 illustrates three basic scenarios
Test number Measured Numerical Error that commonly appear when curing thick parts [18]: (1)
deflection (mm) deflection (mm) (%) inside-to-outside; (2) outside-to-inside; and (3) one-side
2 12.808 13.0372 1.79 curing. To study these curing scenarios, numerical
4 14.964 14.7746 1.27 simulations were carried out for a 15 mm thick plate
6 12.732 12.8714 1.09
made of NCS-82620 fabric with 48% fiber volume fraction
7 14.424 14.4051 0.13
8 12.609 12.6558 0.37 and AOC polyester resin matrix. Figs. 20–29 present the
calculated values of temperature, degree of polymerization,
Young’s modulus E 0 and internal stresses for these three
each plate to analyze the dispersion of the experiments. scenarios.
Note that it is essential to ensure uniformity of the fibrous
reinforcement all along the specimen in order to ensure 4.1. Outside-to-inside cure
reproducibility of mechanical properties. Non-uniformities
and small thermal variations during tests may lead to In the first case, when curing progresses from the
variations in the plate deflection. A comparison for two outward surfaces towards the middle (outside-to-inside
specimens is presented that shows compatibility between cure), the surfaces gel and vitrify before the core. When the
predictions of the thermo-mechanical model and measured gelled material at the core cures and shrinks, the already
deflections. Based on the same procedure, the deflections of rigid surfaces resist the deformation. This produces high
all the composite plates were measured in time. The internal stresses and promotes void formation or possible
deflections measured at the end of cooling are compared composite delamination in the center. This happens when
with calculated values in Table 2. A review of the results for thick parts are cured at temperatures typically used for thin
the five plates tested shows an error of less than 2%. These plates. Fig. 20 displays numerical calculations of tempera-
tests on thin plates provide an experimental validation of the ture and Young’s modulus E 0 when processing the 15 mm
proposed thermo-mechanical model. Accurate predictions thick composite plates at a mold temperature of 120 8C.
were obtained for residual stresses of thermal origin on non- Heating at this temperature results in an outside-to-inside
balanced plates. cure. The evolution of the degree of polymerization at
different locations through the thickness of the sample is
plotted in Fig. 21. Point A shows that the surface reaches the
AGP polymerization level prior to the core. Point B shows a
4. Analysis and optimization of thick plate processing fast curing in the center occurring when the surfaces are
already cured. Internal stresses calculated along the
The processing of thermosetting composites creates longitudinal X-axis are plotted in Fig. 22 for this curing
internal stresses during resin cure. Volume mismatch scenario. Stresses mainly developed during the curing
between composite plies causes thermally induced defor- phase, between 10 and 11 min. Although mechanical
mations and chemically induced shrinkage to occur. properties at that time just begin their evolution, resin
Residual stresses also occur in the composite. To study polymerization shrinkage is important enough to create high
processing defects in thick composites, 15 mm thick plates stresses in the part. Fig. 23 displays the strain calculated
were cured at different mold temperatures. As shown in through the thickness of the part at different periods of time
Fig. 18, processing thick plates at mold temperatures around AGP. At about 10.7 min, fast curing of the core
normally used for thin plates results in important residual generates high chemical strain gradients that result in
stresses, which in some cases were high enough to cause growing internal stresses, called curing stresses. At this
matrix cracking and/or composite delamination. To avoid stage, the stresses can become critical and cause matrix
these defects, lower curing temperatures are required for cracking and/or delamination, because of the low tensile
thick composites. strength of the partially cured resin.

Fig. 18. Two examples of matrix cracking and delamination during processing of thick composite plates. Defects appear commonly in thick composites
processed at high mold temperature.
820 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

cure, high-temperature processing of thick composite parts

must absolutely be avoided.

4.2. Inside-to-outside cure

In the second case, when the cure front progresses from

the middle thickness towards the surfaces of the part
(inside-to-outside cure), the core gels and vitrifies before
the exterior surface. A solid core surrounded by a gelled
material is created. As the rigid core continues to cure
inside the gelled material, minimal internal stresses are
generated at the interface. This progression of the cure
front can be achieved by processing the 15 mm thick
part at a lower temperature, as presented in the analysis of
Figs. 24 and 25. In Fig. 24, numerical values of through-
thickness temperatures and degrees of polymerization are
depicted for a 70 8C processing temperature. Exothermic
temperature peaks are much reduced in this case. The
internal stresses calculated for this curing scenario are
Fig. 19. Schematics of the evolution of the curing front through the shown in Fig. 25. Here, compared to the outside-to-inside
thickness of a thick part: Outside-to-Inside, Inside-to-Outside and One-
Inside cure scenarios are considered.
cure, processing stresses are inverted. In the inside-to-
outside cure strategy, compression stresses appear in the
core and tensile stresses at the surface. The quarter
The outside-to-inside cure generates high exothermic thickness shows nearly no stress, but it is surrounded by
temperature peaks produced by the fast curing of the core. two inverted states of stresses. So shear stresses will then
This is due to the high resin reactivity and low thermal appear at this position inside the composite. Although this
conductivity of the composite. During cooling of the part cure scenario presents many interesting features concern-
from the exothermic peak to room temperature, internal ing reduction of internal stresses, two main disadvantages
stresses, also called cooling stresses, continue to develop due must be noticed: (1) longer processing times are required to
to balanced (or proportional) thermal gradients. Conse- successfully cure the composite, and (2) low mechanical
quently, because of all the disadvantages of outside-to-inside properties will result from an incomplete resin cure.

Fig. 20. Numerical calculation of temperature and Young’s modulus E 0 for a 15 mm thick composite cured at a mold temperature of 120 8C: high exothermic
temperature peaks are observed.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 821

Fig. 21. Through-thickness calculation of polymerization degrees during outside-to-inside cure of a 15 mm thick composite: A and B denote the AGP level at
the surface and middle thickness, respectively.

Note this latter disadvantage, however, can be overcome through a gelled material. A one-side cure progression can
with a post-cure. be achieved when processing the 15 mm thick composite at
different temperatures on the upper and lower mold
4.3. One-side cure surfaces. Simulation results are presented in Figs. 26 and
27 for mold temperatures of 70 and 90 8C on the top and
The above disadvantages compel us to consider a third bottom surfaces, respectively. The temperature profiles of
case: it consists of having the curing front move from one Fig. 26 show that curing temperature can be higher without
surface of the part to the opposite one. In such a one-side really increasing the exothermic peak. This results in a
cure strategy, the generation of processing stresses can be significant reduction in curing time. The internal stresses
explained by simulating the displacement of the curing front calculated for this processing strategy are drawn in Fig. 27.

Fig. 22. Calculated stresses developed during outside-to-inside cure: internal stresses rapidly develop during cure after 10 min., due to resin shrinkage in the core.
822 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

Fig. 23. Through-thickness chemical strains induced by resin polymerization shrinkage for an outside-to-inside cure: at about 10.7 min, fast curing of the core
generates high chemical strains.

The major disadvantage of the one-side cure strategy is the mechanical performance, an optimized processing cycle can
resulting unsymmetrical pattern of residual stresses. It can now be outlined. In order to minimize the internal stresses
lead to deformations and geometric distortion of the generated during resin cure, ideally, the degree of
composite part. polymerization through the thickness should remain con-
stant at each instant. In fact, minimizing chemically induced
strain gradients between plies will result in a net reduction
5. Optimization of cure cycle of curing stresses. In the same way, if through-thickness
thermal gradients are minimized during cure and subsequent
Based on the understanding of different curing strategies cooling, residual stresses will also be decreased and
previously examined and their effects on part distortion and processing defects avoided.

Fig. 24. Numerical calculation of temperature and through-thickness degree of polymerization for an inside-to-outside cure: the thick plate is processed at a
temperature of 70 8C.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 823

Fig. 25. Computed internal stresses during inside-to-outside cure (plate processed at 70 8C): while no stress develops during the cure phase, contraction stresses
appear in the core due to thermal variations.

In this study, an optimization methodology based on thermal and curing gradients. A second heating ramp is
genetic algorithms was used to determine the mold necessary to successfully cure the part up to the desired final
temperatures that could minimize residual stresses and polymerization degree, while avoiding high exothermic
processing time [26]. Figs. 28 and 29 present calculations temperature peaks. The internal stresses calculated during
for the same 15 mm thick composite plates processed this the optimized cure cycle are drawn in Fig. 29 and illustrate
time with optimized mold temperatures. Fig. 28 shows how curing and cooling stresses are significantly reduced by
numerical results of internal temperature and degree of this approach. These results demonstrate that numerical
polymerization. Initial mold overheating helps to decrease optimization of the thermal boundary condition can be a
processing time while minimizing through-thickness useful tool to minimize residual stresses, and especially in

Fig. 26. Calculated temperature and degree of polymerization during one-side cure: resin polymerization evolves from the hot to cold surface, resulting in a
high exothermic peak in the regions close to the cold surface.
824 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826

Fig. 27. Numerical internal stresses during one-side cure: internal stresses grow up in the regions close to the cold surface during resin polymerization (after
around 24 min).

the case of thick composites increase mechanical perform- two reinforcing materials (NCS-82620 fabric and U101
ance of the cured part while minimizing processing time. mat) embedded in a polyester resin (T580-63 from AOC). A
kinetic model, including inhibition times induced by
inhibitor decomposition, is also proposed to describe the
6. Summary resin polymerization during processing. The energy
equation was solved by finite differences through the
In this paper, models are proposed to describe changes of thickness of the part. The analysis of process-induced
composite mechanical properties as a function of (1) fiber stresses in the composite is based on Classical Laminated
volume content; (2) temperature; and (3) degree of Theory. Asymmetrically layered thin plates were first
polymerization of the resin. These models were used for processed to validate the thermo-mechanical model by

Fig. 28. Numerical calculation of temperature and degree of cure for an optimized curing cycle: initial mold overheating and appropriate heating ramps result in
a quasi-constant through-thickness progression of polymerization and minimization of temperature gradients.
 E. Ruiz, F. Trochu / Composites: Part A 36 (2005) 806–826 825

Fig. 29. Calculation of through-thickness internal stresses during optimized curing cycle: low residual stresses are found after processing while final
polymerization degree is maximized.

comparing calculated and measured plate deflections during Acknowledgements

cooling. The predictions of the model were verified with an
accuracy of less than 2%. To identify processing defects in The authors are grateful to the National Science and
thick composites, 15 mm plates were fabricated by RTM at Engineering Research Council of Canada (NSERC) and
different mold temperatures. Processing these plates in the Fonds Québécois de Recherche sur la Nature et la
range of molding temperatures normally used for thin plates Technologie (FQRNT) for their financial support. The
resulted in important residual stresses, which in some cases contribution of Auto 21 and Ford Motor Co. for the
were high enough to cause matrix cracking and/or composite development of characterization molds is also gratefully
delamination. In this analysis, it was shown that the acknowledged as well as the support of the Bourses
progression of the curing front through the thickness of the d’Excellence du Ministère de l’Education du Québec. The
composite is critical to the development of internal stresses. authors would like to thank Vetrotex for the reinforcement
High-processing temperature produces an outside-to- samples and Nicolas Juillard from J.B. Martin for his
inside progression of the curing front that leads to important constant support during the last 15 years.
internal stresses. Low temperature processing generates an
inside-to-outside cure that prevents matrix cracking.
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