2nd International Conf. on Airworthiness & Fatigue - 8th ICSAELS Series Conf. 14-18July, 2014 Patras, Greece
A Multi-scale FE Modeling Approach for Predicting Strength of Carbon Nanotube-Doped Composite Structures A. Chanteli, K.I. Tserpes Laboratory of Technology & Strength of Materials Department of MechanicalEngineering&Aeronautics University of Patras, Patras, 26500, Greece, http://ltsm.mead.upatras.gr/ Corresponding Author Email：
[email protected]
Abstract A multi-scale FE modeling approach was developed for predicting strength of composite structures containing carbon nanotube (CNT)-doped veils which have been inserted between composite plies to enhance delamination resistance. The multi-scale approach was based on the development of 3D FE models lying from the nano- to the macro-length scale. In the FE models, all material and geometrical parameters that could affect the effectiveness of reinforcement were considered. Keywords: Carbon nanotubes; Multi-scale modeling; Finite element analysis; Progressive damage modeling
1. Introduction In the latter years, the aircraft industry is increasingly using carbon fiber reinforced plastics (CFRPs) in primary structural parts aiming to significantly reduce the aircraft gross weight. Indicative examples of this strategy are the Airbus A380, the Boeing 787 and the new Airbus A350 which use 24%, 50% and 53% composites, respectively. Traditional unidirectional (UD) composites, widely used in aerospace applications, suffer from matrix dominated failures (e.g. delamination and matrix cracking) due to the relatively low fracture toughness of the matrix. These failures make UD composites prone to fatigue and impact. In the last decade, a continuous research effort is ongoing to increase the matrix-dominated mechanical properties of the composite materials. In this frame, there have been proposed new material architectures (e.g. 2D and 3D woven composites), new reinforcement solutions (e.g. stitching, doping with carbon nanotubes (CNTs)) and chemically-improved matrices with enhanced properties. Manufacturing of CNT-doped materials systems (e.g. veils)and their integration into CFRP structural parts haveattracted much interest in the last 2-3 years.Yokozeki et al. [1] showed that the introduction of CNTs increase compressive strength of composite laminates.Gorbatikh et al. [2] examined three examples of reinforcement locations and suggested that CNT-reinforcement should target to the enhancement of damage-related properties. In this frame, they managed to increase by 80% the interlaminar fracture toughness of UD carbon-fiber composites, to double the interfacial shear strength of glass-fiber composites and the damage threshold during tensile loading of carbon-fabric composites.Wang et al. [3] reviewed the available literature in mechanical and functional properties of multi-scale hybrid composites manufactured using CNTs. The authors stated that in order to produce a trully enhanced multi-scale composite material, homogeneous dispersion and targeted orientationof CNTs should be achieved. To the date there are two main reinforcing methods for improvinginterlaminar mechanical propertiesof CFRPs. The first is the production of three-phase composites using nano-reinforced matrix. By implementing this approach Yokozeki et al. [1] enhanced the interlaminar fracture toughness of CFRP laminates by adding 5wt % of cup-stacked carbon nanotubes as modified matrix.Shan et al. [4] developed a spraying technique that was assisted with spraying E20 epoxy resin for the deposition of MWCNTs on the surface of carbon fiber fabric. They reported that the composites with CNT-deposited with E20 exhibited high interlaminar fracture toughness and preserved in-plane mechanical properties including tensile and flexural properties.The second category is the fabrication of nano-reinforced interlayers that reinforce the interface between the CFRP pre-preg layers. By implementing this approach Li et al. [5] studied the powder of vapor grown carbon fiber as an interface reinforcement of a CFRP laminate under double cantilever beam tests and compared the experimental and numerical results. White et al. [6]studied the improvement of the delamination toughness of fiber-reinforced composites using epoxy interlayers that contained 20wt% polyamide-12 (PA) particles and 1wt% multi-walled carbon nanotubes. The authors reported the ability of the MWCNT network to facilitate stress redistribution within the resin-rich region. In all works of both categories several manufacturing-related parameters that influence the degree of enhancement in the matrix-dominated properties of CFRPs by the addition of CNTs have been recognized. Thus, models capable of assessing the effects of these parameters on the mechanical properties of CNT-doped CFRPs and performing virtual design and optimization of the three-phase composites are needed.
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In the present work, a multi-scale FE modeling approach was developed for predicting strength of composite structures containing CNT-doped veils by considering all material and geometrical parameters that could affect the effectiveness of reinforcement. 2. The multi-scale approach The proposed multi-scale approach is schematically described in Fig.1. It comprises 5 steps. In the present work, the models and results from the first 4 steps up to the modeling of the CNT-doped carbon-fiber composites are presented. All models have been developed using the ANSYS FE code. At all steps all possible parameters that may influence the mechanical properties of the materials have been taken into account. Where necessary input from molecular mechanics or analytics performed on specimens have been used as input to the models.
Fig. 1: Schematic representation of the multi-scale modeling approach.
3. Materials 3.1 Veils In this study, two types of nano-modified interlayer materials (veils) were considered for the enhancement of delamination resistance. The first type is a mixture of polyamide and MWCNTs with a volume fraction of VCNT-POL=5% and the second type is a mixture of RTM6 resin and multi-wall CNTs with a volume fraction of VCNT-POL=1.5%. The elastic properties and strength values of the matrix materials are listed in Tables 1 and 2, respectively.The CNTs were treated as isotropic materials with a Young’s of 1 TPa and a Poisson’s ratio of 0.3. Table 1.Elastic properties of the matrix interlayer materials. Elastic properties
Polyamide
RTM6
Elastic modulus, E
2400 MPa
2290 MPa
0.3
0.3
Poisson’s ratio, v Table 2.Strength values of the matrix interlayer materials. Elastic moduli
Polyamide/RTM6
Tension Z
75 MPa
Compression Z
200 MPa
Shear
67 MPa
3.2 Carbon-fiber composites The CFRP materials that were considered as reference materials are an11-ply [0o]11IM7/M21 composite material and an 8-ply [0o]8RTM6/HTA 5131 composite material with a fiber volume fraction of 60%. The elastic properties that were considered in the numerical analyses for the carbon-fiber layers are listed in Table 3.
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A. Chanteli and K.I. Tserpes / Proceedings of ICAF-2014 Table 3.Elastic properties of the reference CFRP materials. Material properties
11-ply model
8-ply model
Elastic modulus, EX
145000 MPa
120000 MPa
Elastic modulus, EY
10300 MPa
11300 MPa
Elastic modulus, EZ
10300 MPa
11300 MPa
Shear modulus, GXY
5300 MPa
5300 MPa
Shear modulus, GXZ
5275 MPa
5275 MPa
Shear modulus, GYZ
3950 MPa
3480 MPa
Poisson’s ratio, v
0.2
0.2
4. Evaluation of the properties of the CNT-doped veil The material properties of the CNT-doped veil were evaluated using a FE model of a RVE of a multiwalledCNT(MWCNT) oriented into an angle of 45o degrees within the epoxy matrix. The FE mesh of the RVE is shown in Fig.2. The specific angle of orientation of the MWCNT was chosen as an average value between full alignment (0o) and vertical alignment (90o). A perfect bonding between the MWCNT and the matrix is assumed as a first approach of this method. The MWCNT consists of seven hollow single-walled CNTs all gathered to the outer diameter. The outer diameter of the MWCNT is 9.5 nm and the thickness of each tube is 0.34 nm. The outer dimensions of the RVE are defined according to the desired nanotube volume fractionVCNTtaken as the ratio of nanotube's volume to RVE's volume. The nanotube length LCNTis determined according to the desiredVCNT.The constituents of the RVE were represented using the ANSYS 3D SOLID185 element. Linear isotropic material properties were assigned to all the elements of the FE model and the loading conditions applied are tension and compression along the thickness direction of the RVE (z-axis) and interlaminar shear, y-z and x-z planes. Periodic boundary conditions were properly assigned in order to obtain the homogenized engineering behavior of the RVE that reflects the macroscopic behavior of the material.
Fig. 2: FE mesh of the RVE (zero thickness interface).
The purpose of the numerical analyses is the prediction of the homogenized tensile, compressive and shears strengths of the RVE. In order to introduce damage in the matrix elements of the 3D elastic model we used the Progressive Damage Modeling (PDM) module. The prediction of failure initiation wasdone using the von Mises failure criterion. In addition, the material property degradation is achieved on case-by-case selected/calibrated rules. The implementation of the PDM technique in the 3D FE model was achieved with a specially designed routine in ANSYS FE code. The numerical results are given in Tables4 and 5. Table 4.Predicted elastic properties of the 45o CNT-doped interlayers. Elastic properties
Polyamide/CNT
RTM6/CNT
Elastic modulus, E
7306 MPa
2195 MPa
Poisson’s ratio, v
0.3
0.3
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A. Chanteli and K.I. Tserpes / Proceedings of ICAF-2014 Table5.Predicted strength values of the 45o CNT-doped interlayers. Interlayer
Tension Z
Compression Z
Shear X-Z
Shear Y-Z
CNT-doped polyamide
117.4 MPa
254 MPa
200 MPa
230 MPa
CNT-doped RTM6
100.45 MPa
245.2 MPa
52 MPa
70 MPa
5.
Progressive damage modeling The mechanical properties of the composite material were evaluated using PDM onthe compression (in-plane and transverse) specimens. Two reference composite materials were considered, a 11-ply and a 8-ply. Between each pair of adjacent composite layers an interlayer was placed. Fig.3 shows the FE mesh of the two doped composite specimens. The interlayer thickness was derived by / . The derived values of interlayer thickness for the two CNT-doped composites are 0.0044 mm and 0.03 mm,respectively. The dimensions of the coupons used for longitudinal compression analysis were defined by the EN 2850 Type A standard while for the transverse compression analysis by the standard EN 2850 Type B. This was done in order to enable comparison of numerical predictions with experimental results.
a.
b.
Fig. 3.Iso-view of the FE mesh of (a) the 8-ply interlayered material and (b) the 11-ply interlayered material. With red color the elements of the interlayers are shown.
The composite layers were modelled as orthotropic material. Failure analysis of the layers was performed using the Hashin-type failure criteria and the Maximum Stress criterion. The mathematical expressions of the failure criteria for each failure mode are:
Matrix tensile cracking for
0: 1
(1)
Matrix compressive cracking for
0:
1
Fiber tensile failure for !! 0:
" 1
Fiber compressive failure for !! 0:
" 1
Delamination in tension for ## 0:
Delamination in tension for ## 0:
$
$
(2) (3) (4)
1
(5)
1
(6)
where %& are the stress components in the ij direction and at the denominators are the respective strengths. Index “T” denotes tension and index “C” denotes compression. Failure of the CNT-doped interlayer was predicted using the Brewer-Lagace failure criterion
$ $ 1
(7)
The strength values of the composite materials used for the numerical analyses are listed in Table 6. For the CNTdoped interlayers, the homogenized material properties derived using the RVE described in section 4 were used. As soon as a failure was predicted in a ply its elastic properties were degraded using the property degradation rules listed in Table 7.
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A. Chanteli and K.I. Tserpes / Proceedings of ICAF-2014 Table 6. Strength values of the composite reference materials. Strength values Tensile strength, XC
IM7/8552 2558 MPa
HTA/6376 2250 MPa
Compressive strength, XT
1500 MPa
1600 MPa
Tensile strength, YT
64 MPa
64 MPa
Compressive strength, YC
285 MPa
290 MPa
Tensile strength, ZT Compressive strength, ZC In plane shear strength, SXY
76 MPa 285 MPa 91.2 MPa
94 MPa 290 MPa 98 MPa
Shear strength, SYZ Shear strength, SXZ
118 MPa 91.2 MPa
30 MPa 98 MPa
Table 7.Material property degradation rules. Types of failure
Degradation rule
Matrix tensile cracking
EYˊ=0.2EY, GXYˊ=0.2GXY, GYZˊ=0.2GYZ, NUXYˊ=0.2NUXY
Matrix compressive cracking
EYˊ=0.2EY, GXYˊ=0.2GXY, GYZˊ=0.2GYZ, NUXYˊ=0.2NUXY
Fibre tensile failure
EXˊ=0.07EX
Fibre compressive failure
EXˊ=0.07EX
Fibre-matrix shear out
GXYˊ=0.2GXY
Delamination in tension
EZˊ=0.2EY, GYZˊ=0.2GXY, GXZˊ=0.2GXZ, NUXZˊ=0.2NUXZ,NUYZˊ=0.2NUYZ
Delamination in compression
EZˊ=0.2EY, GYZˊ=0.2GXY, GXZˊ=0.2GXZ, NUXZˊ=0.2NUXZ, NUYZˊ=0.2NUYZ
Interlayer failure
EZˊ=0.2EY, GYZˊ=0.2GXY, GXZˊ=0.2GXZ, NUXZˊ=0.2NUXZ, NUYZˊ=0.2NUYZ
6. Evaluation of the mechanical properties composites containing CNT-doped veils In Fig.4a and b the predicted longitudinal compression moduli of CNT-doped compositesare compared with the experimental values [7] for the 8-ply and 11-ply composite materials, respectively. In the figure, the experimental and numerical moduli of the reference materials are also included. In general, there is a good agreement between numerical and experimental moduli for the reference and reinforced materials.Both methods show a decrease in the modulus of composite specimens due to the addition of the CNT-doped interlayer. This is because the added interlayer although has increased properties compared to the matrix (polyamide or RTM6), it has much lower properties compared to the composite layers. In Fig.5 and 6 the predicted transverse and longitudinal compression strength values of CNT-doped composites are compared with the respective experimental values [7] for the 8-ply and 11-ply materials, respectively.In the figures, the experimental and numerical strength values of the reference materials are also included. A good agreement (less than 10% deviation) is obtained between the model and the tests for the strength of both reference and reinforced materials except for the transverse compression strength of the 11-ply material for which the deviation is about 30%. The model in all cases predicts an increase in strength of the composite materials due to the increase in delamination resistance between composite layers. An increase in strength is also measured from the tests except for the cases of transverse compression of the 8-ply and longitudinal compression of the 11-ply. These two findings are possibly attributed to parameters such as agglomerations of CNTs which have not been considered in the model.
a.
b.
Fig. 4.Comparison between numerical and experimental longitudinal compression moduli: (a) 8-ply composite material, (b) 11-ply composite material. 221
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a.
b.
Fig.5.Comparison between numerical and experimental compression strength valuesfor the 8-ply material: (a) transverse compression strength and (b) longitudinal compression strength.
c.
d.
Fig.6. Comparison between numerical and experimental compression strength valuesfor the 11-ply material: (a) transverse compression strength and (b) longitudinal compression strength.
7. Conclusions In the present work, a multi-scale FE modeling approachwas developed for predicting strength of CFRP composites containing CNT-doped interlayers. 11-ply and 8-ply composite specimens were modeled and their predicted moduli and strength valueswere compared with experimental values for the load-cases of longitudinal and transverse compression. In general, a good agreement was obtained between the model and experiments. Both methods show that the presence of CNT-doped interlayers leads to a enhancement decrease of axial elastic modulus and to a increase of compression strength of the reinforced composites. The model tends to overestimate the strength increase compared to the tests due to the non-consideration of parameters that counterbalance reinforcing effectiveness such as agglomeration of CNTs, weak CNT/polymer interface, weak CNTs, etc. However, the model is fully parametric and has the capability to consider the effect of these parameters occurring at different scales. This process is currently being undertaken by the authors. Acknowledgements The research leading to these results has gratefully receivedfunding from the European Union Seventh Framework Programme(FP7/2007- 2013) under Grant Agreement no 284562. References [1] [2] [3] [4]
[5]
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Kevin L. White, Hung-Jue Sue. Delamination toughness of fiber-reinforced composites containing a carbonnanotube/polyamide-12 epoxy thin film interlayer. Polymer 53 (2012) 37e42. SARISTU Technical Report A_DEU_D93_2_Test data and analysis of elements and trade-offv4, 2012.
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