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                                                             G.V. Seretis et alii, Frattura ed Integrità Strutturale, 50 (2019) 517-525; DOI: 10.3221/IGF-ESIS.50.43 
 

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Focused on the research activities of the Greek Society of Experimental Mechanics of Materials 

 
 
 
  
Multi-parameter analysis of curing cycle for GNPs/glass fabric/ 
epoxy laminated nanocomposites 
 
 
Georgios V. Seretis 
National Technical University of Athens, School of Mechanical Engineering, 15780 Zografou, Athens, Greece 
ELVALHALCOR S.A., Copper Tubes Division (HALCOR), 32011, Oinofyta, Viotia, Greece 
gio.seretis@yahoo.com / gseretis@halcor.com, http://orcid.org/0000-0003-2824-3576 
 
Aikaterini K. Polyzou, Dimitrios E. Manolakos, Christopher G. Provatidis 
National Technical University of Athens, School of Mechanical Engineering, 15780 Zografou, Athens, Greece 
k.polyzou@gmail.com; manolako@central.ntua.gr; cprovat@central.ntua.gr 
 
 
 
ABSTRACT. In this study, a multi-parameter analysis, using Taguchi method 
for design of experiments, has been conducted to investigate the optimum 
curing conditions for GNPs/E-glass fabric/epoxy laminated nanocomposites. 
The independent variables in the L25 Taguchi orthogonal array were heating 
rate, curing temperature and curing time, addressing five levels each. Tensile 
and 3-point bending tests were performed for each experiment number (run 
number) of the Taguchi L25. The analysis shown that the most significant para-
meter for tensile strength is the time and for flexural strength is the tempera-
ture. Also, it shown that the optimum performance was obtained for tempera-
ture values greater than the glass transition temperature Tg. 
  
KEYWORDS. Polymer-matrix composites; Nanocomposites; Graphene nano-
platelets; Curing; Mechanical testing; Multi-parameter analysis. 
 

 

 
 

Citation: Seretis, G.V., Polyzou, A.K., Mano-
lakos, D.E., Provatidis, C.G., Multi-parameter 
analysis of curing cycle for GNPs/glass fabric/ 
epoxy laminated nanocomposites, Frattura ed 
Integrità Strutturale, 50 (2019) 517-525. 
 
Received: 19.01.2019  
Accepted: 22.05.2019  
Published: 01.10.2019  
 
Copyright: © 2019 This is an open access 
article under the terms of the CC-BY 4.0, 
which permits unrestricted use, distribution, 
and reproduction in any medium, provided 
the original author and source are credited. 

 

 
 
INTRODUCTION  
 

omposites of epoxy matrix are of the most commonly used polymer matrix composites. For this kind of composites 
several different types of reinforcement have been tested. However, the reinforcing material is not the only signifi-
cant factor for the final properties of the produced epoxy matrix composites. The curing process, due to the great 

number of properties it affects or controls [1,2], also plays a key role. For this reason, to accurately control the results of a 
curing process, it is necessary to understand the effects of all the affecting parameters. Therefore, the parameters which are 
known to affect a curing process, such as curing temperature and time, have been widely investigated [3-10]. For example, 
the relation between the curing temperature (Tcure) and the glass transition temperature (Tg) has been found to controls the 
applied curing mechanism and, therefore, it is of great importance [11]. Also, related research works have been focused on 
alternative curing processes [12-14], such as curing using microwaves. 

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G.V. Seretis et alii, Frattura ed Integrità Strutturale, 50 (2019) 517-525; DOI: 10.3221/IGF-ESIS.50.43                                                               
 

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Taguchi analysis is widely used in the research of composite materials. For example, it is used to investigate the influence 
of surface treatment on the composites’ performance [15] and the importance of V-ring indenter parameters [16], to deter-
mine the optimum machining conditions leading to minimum surface roughness in drilling of GFRP composite [17], to de-
velop multiphase hybrid epoxy matrix composites reinforced with glass-fiber and filled with rice husk particulates [18], etc. 
Analysis of Variance (ANOVA) and Regression or Multiple Regression models regularly follow the Taguchi method to 
create an effective prediction model. The commonly used Multiple Regression models [16,17] are not always able to achieve 
high accuracy in prediction. Therefore, researchers started working on more accurate multiple regression models [19,20]. 
In this study, a multi-parameter analysis, using Taguchi method for design of experiments, has been conducted to investigate 
the optimum curing conditions for GNPs/E-glass fabric/epoxy laminated nanocomposites. The independent variables in 
the L25 Taguchi orthogonal array were heating rate, curing temperature and curing time, addressing five levels each. Tensile 
and 3-point bending tests were performed for each experiment number (run number) of the Taguchi L25. According to the 
analysis of variance, the significant parameter for tensile performance was the curing time and for flexural performance was 
the curing temperature, at a 95% confidence level. The Full Quadratic regression model was used to predict the tensile 
response of the nanocomposites, since the respective main effects plots were more linear or shown clear trends. On the 
other hand, for the flexural performance, where the respective main effects plots neither were linear nor shown clear 
trends, the Poisson regression model was used to achieve high accuracy in prediction. The R2 of the regression models 
used was greater than 90% for the prediction of both tensile and flexural values.  
 
 
EXPERIMENTAL PROTOCOL 
 
Materials 

he matrix material used for the nanocomposite specimens was the low-viscosity Araldite GY 783 epoxy resin 
together with the low-viscosity, phenol free, modified cycloaliphatic polyamine hardener. The glass transition 
temperature (Tg) was 100°C and the gel time for the specific matrix composition at 20°C and 65% relative humidity 

(RH), conditioning requirements which were obeyed during the preparation of the nanocomposites laminates, was 35 min. 
Woven E-glass fabric of 282 g/m2 density was used for matrix reinforcement, as presented in Fig.1. Table 1 presents the 
characteristics of the fabric used. The warp direction is the enhanced one, as can be seen in, and therefore it was the main 
weave direction. Thus, the laminae orientations in the stacking sequence of the composites will be based on the warp 
direction. Graphene nanoplatelets (GNPs) by Alfa Aesar of surface area (S.A.) 500 m2/g were also used as filler material. 
 

 
 

Figure 1: The woven E-glass fabric used in positioning angle (layer orientation) 0º. 
 

Characteristics Warp Weft 

Fiber description Glass EC11 204 fiber Glass EC11 204 fiber 

Thread count (ends/cm) 8 6 

Weight distribution (%) 57 43 
 

Table 1: E-glass fabric’s characteristics. 
 
Preparation of E-glass fabric/epoxy laminated composites  
To prepare the GNPs-reinforced matrix, weighed amount of pre-dried graphene nanoplatelets were stirred gently into the 
epoxy resin using a laboratory mixer for mechanical stirring for a process time of 25 min at 200 rpm, to ensure homogeneity 
of the suspension [22]. Weighed amount of hardener was added into the GNPs reinforced epoxy resin mixture at the manu-

T 



 

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facturer recommended resin/hardener proportion, which was a 100:50 by weight ratio, and stirred gently using a laboratory 
mixer for mechanical stirring for a process time of 5 min at 200 rpm. Subsequently, the matrix mixture was coated and hand-
rolled on E-glass fabrics in layer sequence under constant stirring [22-25]. For each hand lay-up procedure, four layers of 
E-glass fabric were employed in [0˚/45˚/-45˚/0˚]T sequence. The GNPs w.t. contents used for UD laminates reinforcement 
were 5%. The selection of the GNPs content was made based on literature on the content that provides the best perform-
ance of the specific nanocomposites [22]. Before the first layer coating, the surface on which the specimens were produced 
was covered by release paste wax. The hand lay-up procedure applied is well-known and has been presented in explosive 
view mode in other published works [22,23]. To achieve a 40±1% by volume epoxy proportion in all specimens, both the 
fabric and the matrix mixture used for coating were weighed before each hand lay-up process and after solidification. 
 
Curing cycle 
All specimens left in ambient temperature for 6 hours before the curing conditions of the Taguchi design of experiments 
were applied. Therefore, the complete curing cycle applied is presented in Fig.2, where parameter a, T1 and h1 represent 
the heating rate [°C/min], the temperature of the first curing step [°C] and the duration of the first curing step [h], res-
pectively. The selected values for each parameter under study (i.e. the design of experiment levels) can be found in Table 2. 
 

 
 

Figure 2: The curing cycle applied with the parameters of the Taguchi design of experiments noted. 
 

Control factor 
Level 

1 2 3 4 5 

A: Heating Rate [oC/min] 1 2 3 4 5 

B: Temperature [oC] 50 80 100 120 140 

C: Time [h] 2 4 6 8 10 
 

Table 2: Design of Experiments (DOE) factors and their levels. 
 
The curing temperature (Tcure) can be either higher or lower of the glass transition temperature (Tg) [3-5,22-25]. When 
Tcure>Tg, the reaction proceeds rapidly at a rate driven by chemical kinetics. When Tcure=Tg, vitrification takes place (i.e., 
material solidifies). Finally, when Tcure<Tg, the reaction rate decelerates and becomes diffusion-controlled. To include all 
these mechanisms in the Taguchi design of experiments, apart from the Tg temperature, two different temperatures both 
under and over Tg were selected as presented in Table 2. 
The dimensions of each specimen which underwent 3-point bending tests were 93.6 × 12.7 ×1.1 mm, according to the 
ASTM D790-03 test method. The specimens which underwent tensile test had a total size of 102 × 6 × 1.1 mm in accord-
ance with ASTM D3039/3039M. All specimens were cut at their testing dimensions using a Struers Discotom-2 along 
with a 40A25 cut-off wheel. To evaluate if tabs were needed on the holding regions of the specimens, the theoretical tab 
limits were marked on the specimens, as indicated from the above ASTM standard method [22,23]. Since the failure occurred 
into the theoretical control region no tabs are recommended by the ASTM standard used.  
For each experiment number (run number) of the Taguchi design of experiments, five specimens were prepared and under-
went each test (five specimens for each tensile and five for each flexural test). 
 
Experimental set-up and tests 
An Instron 4482 test machine of 100 kN capacity was used for the both tensile and 3-point bending tests. In accordance 
with the ASTM standard methods D790-03 and D3039/3039M, all tests were performed in a standard laboratory atmo-



 

G.V. Seretis et alii, Frattura ed Integrità Strutturale, 50 (2019) 517-525; DOI: 10.3221/IGF-ESIS.50.43                                                               
 

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sphere (23±1˚C and 50±5% relative humidity). Test conditioning was kept constant for 6 hours before each test. To meet 
the test method’s span-to-depth specification, the support span was set at 52 mm for the flexural tests. The recommended 
from the ASTM methods test speed of 2 mm/min was applied on both tensile and 3-point bending tests. 
 
Taguchi design of experiments 
Taguchi’s method uses a special design of orthogonal arrays to study the entire process parameter space with just a small 
number of experiments. Using Taguchi’s method the number of experiments to evaluate the influence of control parameters 
on certain quality properties or characteristics is considerably reduced as compared to a full factorial approach [23,24]. 
There are three ways of transformation to calculate the loss function, depending on the desired characteristic of the 
measured value. The characteristic of the desired value can either be the-lower-the-better, the-higher-the-better or the-
nominal-the better. The loss function of the ‘‘the-higher-the-better’’ quality characteristic (yk), which was used for this 
study, with m as the mean of the target quality parameter is calculated as shown in Eq.(1) where Lij is the loss function of 
the ith performance characteristic in the jth experiment [23,24]. 
 

      𝐿 ∑             (1) 

In the Taguchi method, the S/N ratio nij for the ith performance characteristic in the jth experiment, which can be 
calculated using Eq.(2), is used to determine the deviation of the performance characteristic from the desired [23,24]: 
 

    𝑛 10log 𝐿       (2) 

Regardless of the category of the performance characteristic, a larger S/N ratio indicates a performance of a better quality. 
Therefore, the optimal level of the process parameters is the level with the highest S/N ratio. 
The selection of control factors is the most important step in a design of experiments. It is known that heating rate (a), 
temperature (T1), time (t1) are three factors which affect the mechanical behavior of an epoxy matrix and, consequently, of 
a laminated composite [23,24]. Therefore, it is expected that these three factors also affect the mechanical behavior in the 
case of epoxy matrix nanocomposites. In this work, the impact of these three factors on tensile and flexural strength of 
GNPs/glass fabric/epoxy laminated nanocomposites is studied using an L25 orthogonal array design. The selected levels 
of the three control factors are presented in Table 2. 
 
 
ANALYSIS OF VARIANCE (ANOVA)  

 
nalysis of variance (ANOVA) is a statistical tool which examines the hypothesis that the means of two or more 
populations are equal and, subsequently, it evaluates the significance of one or more factors, by comparing the 
response variable means at the different factor levels. The significant factors for both tensile and flexural per-

formance were temperature and time in this study, at 95% confidence level (see Tables 3 and 4). Specifically, the tensile 
performance is mostly affected by curing time (31.18%). On the other hand, the flexural performance is mostly affected 
by curing temperature (32.67%) and secondarily by curing time (18.32%). The main effects plot for the main effect terms 
in ultimate tensile strength (UTS) and flexural strength for factors a, T1, and t1 are shown in Figs.3 and 4, respectively. Ad-
ditional tests were conducted to confirm the results of the above analysis (see Tables 5 and 6). The error achieved was 
lower than 1% in both cases. The optimal values can be predicted using Eq.(3) [23,24]. 
 

𝑛 𝑛 ∑ 𝑛 𝑛   (3) 

where: nm is the total mean of the response (UTS and flexural strength, respectively) and characteristic under consideration; ni 
is the mean values at the optimum level and q is the number of control factors that significantly affects curing process of 
composite. 
 
Results and discussion 
The main effects plot for the main effect terms in UTS for factors a, T1, h1 are shown in Fig.3. From the main effect plots, it 
has been observed that the UTS of the composite significantly increase for temperature increase from 50 °C to 80 °C. Tem-
perature increase up to 120°C does not cause any change in the tensile performance, while further increase again increases 

A 



 

                                                             G.V. Seretis et alii, Frattura ed Integrità Strutturale, 50 (2019) 517-525; DOI: 10.3221/IGF-ESIS.50.43 
 

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Figure 3: Main effect plots for UTS for a, T1 and h1 factors. 
 

 
 

Figure 4: Main effect plots for flexural strength for a, T1 and h1 factors. 
 

Source dF Sum of squares Mean square F-value P value C (%)

A: Heating Rate [oC/min] 4 661.7 165.4 0.51 0.73 9.23 

B: Temperature [oC] 4 423,2 105,8 0.31 0.865 5.9 

C: Time [h] 4 2235 558.6 2.26 0.098 31.18
 

Table 3: ANOVA results for tensile tests without interaction, * Significant at 95% confidence level. 
 

Source dF Sum of squares Mean square F-value P value C (%) 

A: Heating Rate [oC/min] 4 2644 661 0.54 0.711 9.68 

B: Temperature [oC] 4 8925 2231.2 2.43 0.082 32.67 

C: Time [h] 4 5004 1251 1.12 0.374 18.32 
 

Table 4: ANOVA results for flexural tests without interaction, * Significant at 95% confidence level. 
 

Parameter Optimal Parameters 
 A3B5C1 
 Experimental Predicted 

UTS (MPa) 214.65 218.848 
Error % 1.95 % 

 

Table 5: Confirmation table for optimum tensile performance. 



 

G.V. Seretis et alii, Frattura ed Integrità Strutturale, 50 (2019) 517-525; DOI: 10.3221/IGF-ESIS.50.43                                                               
 

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Parameter Optimal Parameters
 A2B5C1 
 Experimental Predicted 

Flexural Strength (MPa) 285 278.007 
Error % 2.45 % 

 

Table 6: Confirmation table for optimum flexural performance. 
 
the tensile performance of the nanocomposites. It seems that the nanofillers act like cooling points within the epoxy matrix, 
negating in this manner the previously reported negative effect of temperature increase on E-glass fabric/ epoxy composite 
specimens’ performance. The heating rate, when it increases from 1°C/min to 2°C/min, results in a slight tensile increase, 
while greater increase of its value tend to decrease the tensile performance of the material. Specifically, for heating rate 
values ranging from 2°C/min to 3°C/min a significant performance drop can be observed. Subsequently, for heating rate 
value increase up to 4°C/min the tensile performance slightly increases and for further increase of a it decreases again. 
Overall, for heating rate values greater than 2οC/min the UTS values are considerably low. The curing time increase up to 
6 hours leads to a consequent significant performance drop. However, for further curing time increase, up to 10 hours, the 
tensile performance increases again, overpassing the performance that corresponds to a curing time equal to 2 hours. 
The main effects plot for the main effect terms in flexural strength for factors a, T1, and h1 are shown in Fig.4. The heating 
rate increase leads to an initial flexural performance increase, for heating rate value increase from 1°C/min to 2°C/min, 
and subsequently, for further increase of the heating rate value, to a flexural performance drop. Slight curing temperature 
increase, i.e. from 50°C to 80°C, dramatically decrease the flexural strength of the material. Further temperature increase 
causes a consequent increase in flexural performance. A progressive increase of the curing time significantly decreases the 
flexural strength of the material. 
 
 
MULTIPLE REGRESSION ANALYSIS 

 
he above analysis was followed by a regression analysis, which was applied to create a model for prediction of the 
performance of the nanocomposites as regards both tensile and flexural performance. The commonly used full 
quadratic regression model, involving only the main factors as they occurred from the ANOVA analysis, achieved 

significantly low prediction accuracy in the case of the nanocomposite materials (about 62%). Due to the low accuracy of 
this regression model led to the necessity for a more leviable and accurate regression model. Therefore, a Poisson regression 
model was used to improve the prediction accuracy for the flexural performance and the full quadratic regression model 
enhanced with the interaction between the second order terms (modified full quadratic model) was used for tensile perform-
ance prediction. The accuracy of these models was 94.9% and 90.99%, respectively. The backwards elimination method 
was applied again on all the parameters included in the regression. The Fout factor for terms removal was selected equal to 4. 
All three curing process parameters selected were considered as independent variables. Therefore, two different regression 
models were created, i.e. a Poisson regression model for the flexural performance prediction and a modified full quadratic 
regression model for the tensile performance prediction of the nanocomposites. These two regression models are 
presented in Eqs.(4) and (5), respectively. 
 

𝐹𝑙𝑒𝑥𝑢𝑟𝑎𝑙 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ  𝑒    (4) 
 
where 
 

𝑌 6.09 4.10 𝑎  0.0054 𝑇 4.703 ℎ 1.105 𝑎 0.001897 𝑇 0.12 ℎ
0.063 𝑎 𝑇 0.841 𝑎 ℎ 0.03293 𝑇 ℎ 0.33 𝑎 0.00001 𝑇
0.0401 ℎ 0.0914 𝑎 ℎ 0.0001 𝑎 𝑇 0.001283 𝑎 ℎ 𝑇
0.01888 𝑎 0.001775 ℎ 0.01132 𝑎 ℎ  

 
𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑆𝑡𝑟𝑒𝑛𝑔𝑡ℎ  𝑌                    (5) 

 
where 

T 



 

                                                             G.V. Seretis et alii, Frattura ed Integrità Strutturale, 50 (2019) 517-525; DOI: 10.3221/IGF-ESIS.50.43 
 

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𝑌 407 166 𝑎  10.29 𝑇 2.4 ℎ 55.8 𝑎 0.0491 𝑇 19.22 ℎ 11.77 𝑎 𝑇
84.7 𝑎 ℎ 1.399 𝑇 ℎ 2.403 𝑎 𝑇 18.51 𝑎 ℎ 0.0654 𝑎 𝑇
9.31 𝑎 ℎ 0.01051 𝑎 𝑇 1.597 𝑎 ℎ  

 
Results and discussion 
Fig.5 presents the performance of the modified full quadratic regression model used for the tensile performance prediction. 
Fig.6 presents the performance of the Poisson regression model used for the flexural performance prediction. The above 
results when compared to the respective ones for laminated composites without GNPs reinforcement [23], lead to the con-
clusion that the GNPs reinforcement does not affect which is the most significant parameter for both tensile and flexural 
performance. Thus, for the tensile performance of the specific composites, with and without GNPs reinforcement, the most 
significant parameter is the curing time and for the flexural performance the curing temperature. 
However, in the case of GNPs reinforced nanocomposites, the less significant parameter for the tensile performance is 
temperature, when the respective one for the composites without GNPs reinforcement is heating rate [23]. This may be 
related to the significantly different thermal expansion coefficient between matrix, fibers and graphene nanoparticles [25]. 
 

 
 

Figure 5: Experimental and theoretical values of tensile strength (calculated using the modified full quadratic regression model). 
 

 
 

Figure 6: Experimental and theoretical values of flexural strength (calculated using the Poisson regression model). 
 
 

CONCLUSIONS 
 

NPs/woven E-glass fabric/epoxy laminated nanocomposites were produced using a hand lay-up process and 
underwent tensile and flexural testing according to a L25 Taguchi design of experiments. Based on the experimental 
results as well as the subsequent statistical analysis, the following remarks may be drawn: G



 

G.V. Seretis et alii, Frattura ed Integrità Strutturale, 50 (2019) 517-525; DOI: 10.3221/IGF-ESIS.50.43                                                               
 

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(a) The most significant parameter for tensile strength is the time and for flexural strength is the temperature. Therefore, 
for slow temperature increase values, i.e. 1-5 °C/min, the effect of the heating rate on both the tensile and the flexural 
performance of the cured laminated nanocomposites is not considerable. 

(b) The optimum performance was obtained for temperature values greater than the glass transition temperature Tg. It is 
known that when Tcure˃Tg, the reaction proceeds rapidly at a rate driven by chemical kinetics. Therefore, it is obvious 
that both tensile and flexural performance of the epoxy matrix laminated nanocomposites is mainly controlled by the 
chemical kinetics. 

(c) The Full Quadratic regression model was used to predict the tensile response of the nanocomposites, since the respect-
ive main effects plots were more linear or shown clear trends. On the other hand, for the flexural performance, where 
the respective main effects plots neither were linear nor shown clear trends, the Poisson regression model was used to 
achieve high accuracy in prediction. 

 
 
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curing of graphene nanoplatelets reinforced hand lay-up glass fabric/epoxy nanocomposites, Compos. Part B-Eng., 
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    /ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing.  Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
  >>
  /Namespace [
    (Adobe)
    (Common)
    (1.0)
  ]
  /OtherNamespaces [
    <<
      /AsReaderSpreads false
      /CropImagesToFrames true
      /ErrorControl /WarnAndContinue
      /FlattenerIgnoreSpreadOverrides false
      /IncludeGuidesGrids false
      /IncludeNonPrinting false
      /IncludeSlug false
      /Namespace [
        (Adobe)
        (InDesign)
        (4.0)
      ]
      /OmitPlacedBitmaps false
      /OmitPlacedEPS false
      /OmitPlacedPDF false
      /SimulateOverprint /Legacy
    >>
    <<
      /AddBleedMarks false
      /AddColorBars false
      /AddCropMarks false
      /AddPageInfo false
      /AddRegMarks false
      /ConvertColors /ConvertToCMYK
      /DestinationProfileName ()
      /DestinationProfileSelector /DocumentCMYK
      /Downsample16BitImages true
      /FlattenerPreset <<
        /PresetSelector /MediumResolution
      >>
      /FormElements false
      /GenerateStructure false
      /IncludeBookmarks false
      /IncludeHyperlinks false
      /IncludeInteractive false
      /IncludeLayers false
      /IncludeProfiles false
      /MultimediaHandling /UseObjectSettings
      /Namespace [
        (Adobe)
        (CreativeSuite)
        (2.0)
      ]
      /PDFXOutputIntentProfileSelector /DocumentCMYK
      /PreserveEditing true
      /UntaggedCMYKHandling /LeaveUntagged
      /UntaggedRGBHandling /UseDocumentProfile
      /UseDocumentBleed false
    >>
  ]
>> setdistillerparams
<<
  /HWResolution [2400 2400]
  /PageSize [612.000 792.000]
>> setpagedevice