MULTI-SCALE MODELLING OF COMPOSITE MATERIALS

Vikas TiwariMDM12B025

Guided By:Dr. Venkata Timmaraju Mallina

INTRODUCTION

It is a new advanced method of modeling bodies by considering their behavior at various scales(in context with size) i.e. at

- Atomic scale

- Microscopic level

- Macroscopic level It has great importance as it gives accurate results as less

assumptions have to be made. Contd.

Multi-scale modelling results are in close agreement with experimental values confirming the validity of the multi-scale scheme.

Atomistic models are studied under “molecular dynamics”.

At both microscopic and macroscopic level finite element method is used for evaluation of required properties.

MOTIVATION

This project makes way to enter into philosophy of “complexifying design” .

Very less dependence on experimentation as prediction of properties using this method are accurate.

It needs knowledge of both materials science and finite element method for correct outcome.

WHY COMPOSITE MATERIALS?

Composite materials are rapidly increasing in terms of their use ,they are replacing the conventional materials.

The properties are adjustable according to design parameters such as the nature, rate, orientation and fiber architecture, arrangement of folds and the nature of the matrix .

So analyzing their behavior accurately will not only save time but also money used in numerous trials for experimentation

OBJECTIVE

Here the matrix of epoxy thermoset is used and long continuous fibers of glass will be reinforced and will be modelled to study the behaviour analytically.

RVE (Representative Volume Element) of the above mentioned material is to be made based on FEM (Finite Element Method).

Figure 1:FEM based RVE model of continuous fiber embedded in a matrix

(Reference: Analytical Estimation of Elastic Properties of Polypropylene Fiber Matrix Composite by Finite Element Analysis. http://dx.doi.org/10.4236/ampc.2012.21004)

WORK DONEAnalytical Formulation: Halphin-Tsai relation EL=Ef *Vf+ Em *(1-Vf) -1 1/ET=Vf/Ef+(1-Vf/Vm) -2 υL=υf *Vf +υm(1-Vf) -3

Contd.

Matrix and composite filler properties put in compliance matrix to get transverse geometric properties:-

Properties->

Fibre Diametre

Density(ρ),Kg/m3

Young’s modulus(E),MPa

Shear modulus(G),MPa

Poisson’s Ratio(υ)

Epoxy(matrix)

  1200 4500 1600 0.4

E glass(filler)

16 μm. 2600 74000 30000 0.25

Calculated values for transversely isotropic model using formulation for 10% volume fraction:-

ξ=2 (for circular fibers arranged in a square array)E1=11450 MPaυL=0.385η= 0.8373 (for calculating E2) E2=5733.697 MPaη=0.8554 (for calculating GL)GL=2048.999 MPa

The compliance matrix of transversely isotropic material is given below which is used in modelling RVE and later compare FEM results with the analytical formulation:

WORK TO BE DONE

ANSYS simulation for the above mathematical model is to be done by making the RVE and properties to be compared with Halphin-Tsai relations.

After the successful completion of above task, that approach will be adopted in making complex arrangement of fillers in matrix such as nanotubes, Nano platelets fillers in polymer matrix.

THANK YOU