Project report on application of finite element method to find longitudinal Young's modulus of continuous fibre-reinforced composites

1. Vikas Tiwari
MDM12B025
Guided By
Dr. Venkata Timmaraju Mallina

2. 
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.

3. 
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

4. 
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.

5. 
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.

6. Contd.
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.

7. Contd.
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.

8. 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.
Contd.
Contd.

9. Contd.
Results and Validation:
Figure 3&4: Stress & Strain distribution of RVE in z-direction
Contd.

10. 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.
1.105
2.21
3.32
4.42
5.525
0
1
2
3
4
5
6
0 1 2 3 4 5 6
Stress(x10MPa)
Strain (x10^-3)
Stress vs Strain

11. 
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.

12. 
Thank You!!!