1 st method : Homogenization

1. Poster 75 – JNC17 – Poitiers 2011 – Aurélie Cordelle Nano-Reinforcement of thermosetting polymers using CNTs Feifei Zhao1, M. DRISSI-HABTI1* *Pour toute correspondance : monssef.drissi-habti@ifsttar.fr Background: The project aims to seek the influence of the orientation angle of the CNTs inside the polymer regarding the applied stress during the reinforcement process. The 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, the unit cell in nano scale of the domain was selected to simulated Problématique : The high var der Waals (vdW) force between the CNTs and the surrounding polymers can not be ignored Constants 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 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 The volume fraction is 1% which is the most widely used. 1st method : Homogenization Based on the satisfy of 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): • 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. 2nd method : Stress-Strain curve • Some conclusions can be obtained from the figure: • 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 more strong. • If take the slop of the first time step as the Young’s Modulus of the composite, the result will be opposite with that of the homogenization method, this is because of……. • 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 is elasticity. • The Maxwell model is used to evaluated the behavior of viscoelastic. The governing equation is then: Conclusions : • Applied the homogenization method with the Effective Interface Model to calculated the elastic Young’s Modulus of the Nano-Reinforcement composite. • Compared two kinds of different homogenization boundary conditions: KUBC and PBC. The effects of elimination of the edge effect of the PBC is obvious. • The elastic Young’s Modulus of the composite decreases with the increase of the orientation angle. • Imposed the viscoelastici behavior for the themosetting polymer and the assumed interface, the stress-strain curve was obtained. • With the increase of the orientation angle, the stress-strain curve increase which is opposite with the result of the homogenization. Preview : • All the work can be refine with more powerful computer and then more accurate result can be obtained • All the work can be transferred for the Nano-Reinforeced composite with graphene. 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.