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1st step : Simulation of the stiffness
Problématique : The high van der Waals (vdW) force between the CNTs and the surrounding polymers cannot be ignored
Modelling of the Nano-Reinforcement of Thermosetting Polymers Using CNTsFeifei Zhao1, M. DRISSI-HABTI1*
1 PRES LUNAM, IFSTTAR, Département Mesure, Auscultation et Calcul Scientifique (MACS)44344 Bouguenais Cedex, France
For correspondence : * [email protected]
Ce travail a été conduit dans le cadre du projet FUI (fonds uniques interministériels de la DGE), Decid2. MDH tient à remercier ces fonds, ainsi que la Région Pays de la Loire pour le soutien financier.
Background: The project aims to model the influence of the orientation angle of the CNTs inside thermosetting polymers regarding the applied stress, during the reinforcement process. The compressive stress, σ, is imposed at the top of the domain while the CNT disperses inside the domain with an orientation angle α. To do that, instead of analyzing the whole domain of the material, a unit nano-cell of the domain was selected to be simulated
Odegard et al. developed the Effective Interface Model (EIF) to consider the high vdW force of the reinforcement process.The assumed interface between the CNT and the surrounding polymer is actually the layer of space between them
Constants
Material E(Gpa) ν
Polymer 4.2 0.4
Interface 3.5 0.4
CNT 88.7 0.26
The influence of the orientation angle was simulated from two aspects:
1, The elastic Young’s Modulus of the final composite was calculated using homogenization method.
2,The stress-strain curve of the final composite with the propagation of the deformation or stress
To satisfy the Hill condition (1), two kinds of boundary conditions were used for the simulation:
1, Uniform displacement (Dirichlet, Kinematic, KUBC) boundary condition
2, Periodic boundary condition (PBC):
: : : (1)E
0( ) (2)u x E x x
0( ) (3)per
u x E x u x
2nd step : Simulation of the Stress-Strain curve
As the polymer is always viscoelasticity, the stress-strain curve can be used to measure the damage with the propagation of the stress applied on the top of the domain.
As the properties of the interface is close to that of the polymer, it can be assumed to be also viscoelasticity.
The CNT behaves elastic
The Maxwell model is used to evaluated the behavior of viscoelastic. The governing equation is then:
(4)k
The different lines in one figure represents different number of elements along one direction: from 10 to 60 for KUBC and from 10 to 40 for PBC. With the increase of the number of the elements, the solution is getting convergence. Because of the elimination of the edge effects, the results of the PBC is more realistic. With the increase of the orientation angle, the Young’s Modulus decreases.
The volume fraction is 1% which is the most widely used.
Some conclusions : The different lines in the figure represents different orientation angle: from 0 to 40
With the increase the orientation angle, the stress-strain curve getting higher which means the composite is getting stronger.
Some refinements are needed to simulate properly the initial slopes of stress-strain curves so that preceding results will be displayed
Conclusions : The homogenization method with the Effective Interface Model was used to calculate the elastic Young’s Modulus of the Nano-Reinforced composite.
Two kinds of different homogenization boundary conditions: KUBC and PBC was used. There is no effects of elimination of edge effects when using KUBC conditions.
The elastic Young’s Modulus of the composite decreases with the increase of the orientation angle.
Imposing viscoelastic behavior for the themosetting polymer as well as a visco-elastic interface, the stress-strain curve was properly simulated.
