Finite Element Analysis of Polymer Nano Composites

Presented byRaj Kiran (20123025)

Nayan Patil (20123116)Project AdvisorDr. D.K. Shukla

Assistant Professor , MED

Objectives to be achieved

• Analysis of polymer nanocomposites using commercial finite element software ABAQUS.

• To learn about nanocomposites, their modelling and how nanofillers affect their properties.

• Different mechanical properties will be studied.

B.Tech-7th Semester Work

Following things have been completed in last semester-

• Learning ABAQUS through different tutorials. • Literature review of polymer nanocomposites. • To learn about geometric modelling of nanofillers. • Finally to prepare the geometric model in

ABAQUS.

B.Tech-8th Semester Work Plan

Following things will be completed by end of this semester-

• To carry out the analysis with spherical and ellipsoidal shaped inclusions and compare the results.

• To extend the study to fracture mechanics and comment on Stress Intensity Factor.

What is a polymer?• Polymer is a large molecule composed of many repeated

subunits. • Synthetic and natural polymers play an essential role in

everyday life.• Synthetic plastics such as polystyrene • Natural biopolymers such as DNA and proteins

Polystyrene DNA

Composite• Composite material is a material made from two or more constituent materials

with significantly different physical or chemical properties that, when combined, produce a material with characteristics different from the individual components.

• Properties of composites are function of the properties of constituent phases, their relative amounts and geometry of dispersed phase.

• Wood which consists of strong cellulose fibres surrounded by a material known as lignin.

Basics of Composites

• Matrix • Continuous phase • Transfers stresses to other phases • Classified into: MMC, CMC, PMC• Dispersed phase (Reinforcing phase) • Remains in discontinuous form in matrix • Stronger than matrix, enhances matrix properties • Particulate materials, fibrous materials

What are Nano Composites? Nano composites are a class of materials in which one or

more phases with nano scale dimensions ( 10nm-100nm) are embedded in a metal, ceramic or polymer matrix.

Why Nano composites? • High surface to volume ratio • Strength is increased • Heat resistant

Polymer Nano Composites

• Combination of a polymer matrix and inclusions that have at least one dimension(i.e. length, width, or thickness) in nanometer size range are known as polymer nano composites

• Polymers are light weight• Corrosion resistant materials• Matrix can be of polymeric materials such as

thermoplastics, thermosets or elastomers.

Dispersed Phase

• Nanoscale reinforcing phase can be grouped into 3 categories

• Nanoparticles • Nanotubes • Nanoplates

• Depending on type of Nanoparticles added, the mechanical, electrical, optical and thermal properties of polymer nanocomposites can be altered

Types of Nano Phases

Nanoparticles Nano Tubes

Nano Plates

Methodologies for Analysis of Nano composites

• Molecular Dynamics • Molecular dynamics (MD) is a computer simulation of physical

movements of atoms and molecules.

• Multiscale Modeling • Modeling in which multiple models at different scales are used to

model different phases of a system.

• Finite Element Method • In mathematics, the finite element method (FEM) is a numerical

technique for finding approximate solutions to differential equations.

• In this project we will adopt the methodology of FEM for analysis of nanocomposites using analysis software ‘ABAQUS’.

Finite Element Method

Finite element analysis of the composites requires:

• Modeling of Representative Volume Element• Material properties• Suitable loads and boundary conditions• Interpretation of results

What is Representative Volume Element?

• In composites, it is the smallest volume over which if a measurement is made that will yield a value representative of the whole.

• In other words, they represent a composite as a whole, give an over all idea about the composite.

• They also reduce the overall computational time.

More About RVE

• They have the same effective Young’s Modulus and Volume Fraction as that of the composite.

Square array with square RVE Hexagonal Array with Triangular RVE

Different Types of Nanoparticles

Different nanoparticles impart different properties to the nanocomposites, so according to application these particles are chosen. Some of these are-

• Carbon nanofibres• Carbon nanotubes• Nanoaluminium Oxide• Nanotitanium Oxide

Properties of Nano Particles Properties Titanium Oxide Aluminium Oxide

Density (g/cc) 3.97 4.00

Elastic Modulus (GPa) 288 375

Poisson’s Ratio 0.29 0.23

Synthesis of Polymer Nanocomposites

• Sol gel process: Very versatile and simple process. Metal precursor is dissolved in a solvent called sol which is converted into a 3-D network called gel by inducing a reaction known as hydrolysis.

• In Situ process

Cost of Nanoparticles Quantity Aluminium Oxide Titanium Oxide

50 gm Rs. 7830.71 19406.76

• Cost of nanoparticles is so high that it is not practical and economically possible to carry out experiments directly on the nanocomposites and determine the properties through it by hit and trial method. So, using FEA is a good approach.

Source: www.sigmaaldrich.com

Modelling of Polymer Nano Composites

• For FEA geometry of the RVE is required which can represent the composite as a whole.

• RVEs have been developed using algorithm known as Random Sequential Adsorption Algorithm.

Main Steps of the RSA Algorithm

• Generation of a filler particle with given dimensions.

• Check that the filler resides within the RVE.• Check that the filler is not penetrating through

any other filler particles.• Update the current volume fraction of RVE.• Repeat the above steps till desired volume

fraction is reached.

Start

I/P Parameters Radius,S.Vol.Fra

Generate Random

Coordinate

Inside RVE?

Draw filler

Penetrating with others?

Update Volume Frac

Vol. Frac=S.Vol.Fra

Stop

NO

YESYES

NO

YES

NO

Flowchart of RSA Algorithm

Generation of the RVE• The RVE was generated using RSA algorithm to

provide for user specified minimum distance between neighbour fillers.

• The centre distance was kept 3r, r is the radius of the filler i.e. 4 nm.

• If the surface of any filler penetrates into that of other or that of the RVE then it is discarded.

• Using above steps MATLAB code was developed and random co-ordinates were generated and 2D and 3D RVEs were modelled.

3-D RVEs With Random Spheres

Cubic RVE with of side 424 nm and weight fraction 1% randomly generated spherical inclusions

3-D RVEs With Random Ellipsoids

Cubic RVE with of side 424 nm and weight fraction 1% randomly generated ellipsoidal inclusions

Properties of Materials

Property Matrix Filler Young’s Modulus 3.054 GPa 375 GPa

Poisson’s Ratio 0.375 0.23

•Nanofillers of Alumina and Matrix of Epoxy has been used for analysis.

MATLAB and PYTHON Script

• It is very tedious and cumbersome process to insert each and every particle in the matrix. So, we directly interacted with kernel of ABAQUS instead of using GUI.

• PYTHON script was written to solve this problem.

• MATLAB codes were developed to generate the script!

RVEs used for Analysis

• We have used RVEs with different weight fractions with same length for the analysis purpose.

• Different weight fractions were obtained by changing the number of inclusions.

• Weight fractions ranged from 0.5% to 4% and corresponding number of particles ranged from 30 to 246.

Boundary Conditions

• For the analysis symmetrical boundary conditions were used.

• On three adjacent faces of the RVE, the displacement components normal to the faces were constrained so as to prevent rigid body motion.

• Two of the remaining faces were forced to remain parallel to themselves during deformation.

Boundary Conditions...

•All the nodes of the remaining face were given a fixed displacement of 5nm.

Symmetrical Boundary Conditions

Element Convergence Test• Element Convergence test was carried out for

weight fraction 0.5% with 10 number of particles.

It was concluded that 200000 elements were sufficient for analysis.

0 50000 100000 150000 200000 250000 300000 3500003.8

3.805

3.81

3.815

3.82

Number of Elements

E in

GPa

A glimpse of RVEs used

Weight fraction 0.5% with 30 inclusions Weight fraction 1% with 60 inclusions

More RVEs

Weight fraction 2% with 191 inclusions Weight fraction 4% with 246 inclusions

RVE Convergence Test• Average Young’s Moduli were calculated for

different orientations with different weight fractions and different number of inclusions.

• So, the RVEs converged at 30 inclusions and corresponding size was 771 nm. So 771 nm was taken as RVE size and weight fraction was varied.

For 0.5% w.f.

Comparison of E/Em

It is concluded that as the weight fraction of spherical and ellipsoidal inclusions increase Young’s Modulus of the composite also increases in same ratio.

Non-Linear Analysis•After elastic analysis was carried out non-linear response was studied for different weight fractions. •For practical purposes it becomes necessary to know about the plastic behaviour of the PNCs.•Initially the response of the PNCs is linear from which elastic modulus can be calculated.•As weight fraction increases the slope increases indicating increase in elastic modulus.

Non-Linear Response

Stress- Strain curve for PNCS for different weight fractions

Fracture Mechanics

• Assumes there is always a crack in materials.• Cracks may exist due to some manufacturing

defects, during welding or due to inclusion of some foreign particles.

• Due to these cracks and flaws the strength of the material reduces.

• These inherent flaws effect the life of the structure and their performance.

Modes of Fracture Failure

• Mode-I Fracture: Opening mode and tensile stress is applied normal to the crack surface.

• Mode-II Fracture: Sliding mode and shear stresses act parallel to the plane of crack.

• Mode-III Fracture: Tearing mode and displacement is parallel to the crack front and thus causes tearing.

Modes of Fracture Failure

Three modes of fracture failure

Stress Intensity Factor• If a plate having centre crack of length 2a is

loaded by far field stress σ , then stresses at crack tip are much higher than the applied stress.

Infinite plate having centre crack of length 2a

SIF for mode-I• Stress Intensity Factor also known as SIF gives

an idea about the state of stress at the crack tip.• SIF for mode-I loading for infinite plate having

edge crack of length a is given as : KI = σ√πa

• For plate of finite dimensions it is given as: KI = f(a/w) σ√πa Where w is the width of plate

Finite Element Modeling of Cracks• Here, we found out KI only for 2D RVEs.• 2D cracks are modeled by lines while 3D

cracks as planes.

Crack in 2D RVE

Finite Element Modeling of Cracks

• This line or plane is known as SEAM.

• Analysis is performed using seam as a crack and this seam creates edges that are free to move apart.

• Crack front is the forward part of the crack.

Loading and Boundary Conditions• Bottom edge was fixed and load was applied

on the upper edge of 1E-6 N/nm2.

Load and Boundary Conditions for Mode-I loading

Evaluation of KI for Spherical and Elliptical inclusions

• Once the crack is modeled, load is applied and boundary conditions are imposed KI was calculated and compared for 2D RVEs at different area fractions for spherical and elliptical inclusions.

• It was observed that the value of KI decreases as the area fraction increases upto a certain area fraction and then became constant.

Comparison of KI for Spherical and Elliptical inclusions

Comparison of KI for spherical and elliptical inclusions

THANK YOU !