Multi-Scale Modelling of Composite Materials

Vikas TiwariMDM12B025

Guided ByDr. 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. from atomic scale to macroscopic scale.

At both microscopic and macroscopic level FEM is used to evaluate required properties.

Very less dependence on experimentation as it’s a combination of both material science and FEM approach.

Motivation

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 is reinforced and is to study the behaviour analytically using ANSYS 12.

RVE (Representative Volume Element) of the above mentioned material is to be made based on FEM (Finite Element Method) in ANSYS 12.

For simple arrangement of fibre-reinforced matrix, empirical relation like Rule of Mixtures and Halphin-Tsai formula exists from which elastic properties evaluated from FEM is to be validated.

Design and Implementation

Rule of Mixtures calculation for longitudinal Young’s modulus for 10 % volume fraction came out to be 11450 Mpa.

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

)1( fmffL VEVEE

Contd.

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Assumptions made for modelling composite material:

Macroscopically homogeneous

Linearly elastic

Macroscopically transversely isotropic

Initially stress free (no thermal stress) Joint between filler material and matrix is rigid i.e. under load they will not

separate away from each other. This is achieved by using ‘glue’ in ANSYS 12.

Contd.

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Element Type and Material Property: SOLID 20 node 186 tetrahedral element is used to model RVE i.e. a cube (134.52 ×

134.52 × 100 μm3) and having 10% volume fraction of fibres. Fibre(glass) and matrix(epoxy) properties are applied (from the table shown before)

Figure 2:Finite Element meshed model of RVE (in x-y-z coordinate system

Figure 1:Finite Element model of RVE (Continuous fibre of glass embedded in epoxy matrix).

Contd.

Boundary Condition and Load applied: In this work the boundary condition with normal pressure (stress) applied in z

direction are as follows. u(LF) = 0, v(BF) = 0, w(BKF) = 0 Other faces are free to move in any direction.Here pressure is applied to have uniform

load distribution ,so that both fibres and matrix undergo same deformation.

Then problem is solved for various pressure applied and stress and displacement values at half section of model is recorded.

From the FEM results stress vs strain curve is plotted to get EL and verified with the empirical relation.

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Results and Validation:

Figure 3&4: Stress & Strain distribution of RVE in z-direction

Contd.

Results and Validation: Stress vs Strain curve gives EL to be approximately 10908.19 Mpa. giving us 4.732%

error from result (11450 Mpa.) calculated from empirical relation.

Contd.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

1

2

3

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[Y VALUE]

[Y VALUE]

[Y VALUE]

[Y VALUE]

[Y VALUE]

Stress vs StrainStrain (x10^-3)

Stre

ss (x

10 M

Pa)

Conclusion and Future Work

So, we can conclude that our FEM approach is credible although there was slight deviation from the original values due to various assumptions made.

We can pursue our future work of solving more complicated problems for which no empirical relation exists and also to include molecular dynamics to reduce the error

In future, we plan to implement this approach in making complex arrangement of fillers in matrix such as nanotubes, nano platelets fillers in polymer matrix.

Thank You!!!