Finite Element Tensile Analysis on Failure and Response of Fiberglass Fabric Epoxy Composite Material

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Chapter: 1 INTRODUCTION

1.1 Background Study

The use of composite material in aviation field has been widely used from non-structural

components until primary parts. Composite materials are defined as combinations of two

or more materials that differ in composition and form that is constituents or element will

retain their own individual identity. There are two types of composite construction which

are laminate and sandwich construction. Laminate is material constructed by several plies

that are stack together with different fiber orientation and cured by chemical

polymerization. On the other hand, sandwich construction is core that is bonded between

the laminate.

Composite materials are anistropic material that is having some advantages over

isotropic material. The advantages are its ability to be designed and oriented in according

to the strength needed to every different parts or components. Beside that it also high

strength to weight ration, high stiffness and resistance corrosion.

Composite also have some drawbacks. One of the major problems usually is the

first ply failure (FPF). Strength of a laminate is often defined by the first ply failure

(FPF), which is simply the inner envelope of all plies. When external loading reaches the

FPF, micro cracking or fiber failure can begin.

To claim additional load-carrying capability of the laminate, plies that have

reached the FPF must be degraded by an iterative procedure until the ultimate strength of

the laminate is reached. First ply failure can be predict by study finite element analysis in

the design of orientation plies stacking in composite laminate material under tensile load.

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1.2 The Objective of The Present Paper

Objective of the thesis is to construct geometry design and modeling fiberglass fabric

epoxy laminate structure based on ASTM D3039 Test Method for Tensile Properties of

Polymer Matrix Composite Materials in MSC.Patran computerized software.

All the input data such as material properties, fabric orientation sequence, and tensile

load fulfilled in MSC.Patran program and the MSC.Nastran program will process the data

for analysis and result. To compile, analyze and records all the data’s and make a

conclusion from it.

1.3 Problem Statement

The finite element tensile analysis on failure and response of fiberglass fabric epoxy

composite material only given result which is to predict failure of laminate tested in

theoretically manner but somehow the theory manner only can be proven in practically

manner.

1.4 Importance of Present Work

The important of our present work is to observe the failure and response of fiberglass

fabric epoxy composite material laminates under tensile loads. Beside that, we also do

design analysis from all the tested composite laminate to gain it ultimate tensile strength.

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Chapter: 2 LITERATURE REVIEW

2.1 Introduction

Composite materials are combination of two or more materials that are differs in

composition or form. The constituent or elements that make up the composite retains

their individual identities. Since composites has been introduced to aviation industry late

1970’s, the aviation industry has started fabricate and replace aluminum parts of the

aircraft due to weight ratio, ease of maintenance and absolutely to eliminate fatigue stress

problem.

It is important to get better understanding in composite, especially in composite

failure because safety is the main priority in aviation industry nowadays.

2.2 Basic Concepts of Material Properties

Conventional monolithic materials can be divided into three broad categories: metals,

ceramics, and polymers. Although there is considerable variability in properties within

each category, each group of materials has some characteristic properties that are more

distinct for that group by refer to Table 1.1. [1]

2.2.1 Type of Material

Depending on the number of its constituents or phases, a material is called single-phase

(or monolithic), two-phase (or bi-phase), three-phase, and multiphase. The different

phases of the structural composite have distinct physical and mechanical properties and

characteristic dimensions much larger than molecular or grain dimensions. [1]

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Table1.1 Structural Performance Ranking of Conventional Material

2.2.2 Homogeneity

A material is called homogeneous if its properties are the same at every point or are

independent of location. The concept of homogeneity is associated with a scale or

characteristic volume and the definition of the properties involved. The material can be

more homogeneous or less homogeneous, depending on the scale or volume observed.

The material is referred as to as quasi-homogeneous, if the variability from point to point

on a macroscopic scale is low. [1]

2.2.3 Heterogeneity or Inhomogeneity

If the properties of the material vary from point to point, the material called heterogeneity

or inhomogeneity. The concept of heterogeneity is associated with a scale or

characteristic volume. As the scale decreases, the same material can be regarded as

homogeneous, quasi-homogeneous, or heterogeneous. [1]

2.2.4 Isotropy

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A material called isotropic when its properties are the same in all directions or are

independent of the orientation of reference axes. [1]

2.2.5 Anisotropic/ Orthotropic

A material called anisotropic when its properties at a point vary with direction or depend

on the orientation of reference axes. If the properties of the material along any direction

are the same as those along a symmetric direction with respect to a plane, then that plane

is defined as a plane of material symmetry. A material may have zero, one, two, three, or

an infinite number of planes of material symmetry though a point. A material without any

planes or symmetry is called general anisotropic (or aeolotropic). At the other extreme,

an isotropic material has an infinite number of planes of symmetry. [1]

Of special relevance to composite materials are orthotropic materials, that is,

materials having at least three mutually perpendicular planes of symmetry. An

isotropic/anisotropic also associated with a scale or characteristic volume. For example,

the composite material in Figure 2.1 is considered homogeneous and anisotropic on a

macroscopic scale, because it has a similar composition at different locations (A and B)

as shown in figure 2.1 below, but properties varying with orientation. On a microscopic

scale, the material is heterogeneous having different properties within characteristic

volumes a and b. [1]

Figure 2.1 Macroscopic (A, B) and microscopic (a, b) scales of observation in a

unidirectional composite layer.

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2.2.6 Material Response under Load

Some of the instinct characteristics of the materials discussed before are revealed in their

response to simple mechanical loading, for example, uniaxial normal stress and pure

shear stress as illustrated in figure 2.2. [1]

An isotropic material under uniaxial tensile loading undergoes an axial

deformation (strain), εx, in the loading direction, a transverse deformation (strain), εy, and

no shear deformation:

Figure 2.2 Response of various types of material under uniaxial normal and pure shear loading.

Isotropic

Orthotropic

Anisotropic

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2.3 Continuous-Fiber Composites

A continuous-fiber composite are reinforced by long continuous fibers and are the most

efficient from the point of view of stiffness and strength. The continuous fibers can be all

parallel (unidirectional continuous-fiber composite), can be oriented at right angles to

each other (crossply or woven fabric continuous-fiber composite), or can be oriented

along several directions (multidirectional continuous-fiber composite). The composite

can be characterized as a quasi-isotropic material for a certain number of fiber directions

and distribution of fibers. [1]

In addition, composite can be in laminate which consisting of thin layers of

different materials bonded together, such as bimetals, clad metals, plywood, and so on.

2.4 Lamina and Laminate - Characteristic and Configurations

A lamina, or ply, is a plane (or curved) layer of unidirectional fibers or woven fabric in a

matrix. In a case of unidirectional fibers, it is also referred to as unidirectional lamina.

The lamina is an orthotropic material with principal material axes in the direction of the

fibers (longitudinal), normal to the fibers in the plane of the lamina (in-plane transverse),

and normal to the plane of the lamina (Figure 2.2). The axes are designated as 1, 2, and 3

respectively. In the case of a woven fabric composite, the warp and fill directions are the

in-plane 1 and 2 principal directions, respectively (Figure 2.2). [1]

Figure 2.3 Lamina and principal coordinate axes: (a) unidirectional reinforcement and (b)

woven fabric reinforcement.

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A laminate is made up of two or more unidirectional laminae or plies stacked

together at various orientations (Figure 2.3). The laminae (or plies, or layers) can be of

various thicknesses and consist of different materials. Since the orientation of the

principal material axes varies from ply to ply, it is more suitable to analyze laminates

using a fixed system or coordinates (x, y, z) as shown. The orientation of a given ply is

given by the angle between the reference x-axis and the major principal material axis

(fiber orientation or warp direction) of the ply, measured in a counterclockwise direction

on the x-y plane. [1]

Composite laminates containing plies of two or more different types of materials

are called hybrid composites, and more specifically interply hybrid composites. For

example, a composite laminate may be up of unidirectional glass/ epoxy, carbon/ epoxy

and aramid/ epoxy layers stacked together in a specified sequence. In some cases it may

be advantageous to intermingle different types of fibers, such as glass and carbon or

aramid and carbon, within the same unidirectional ply. Such composites are called

intraply hybrid composites. [1]

Figure 2.4 Multidirectional laminate and reference coordinate system.

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2.5 Laminate Configurations

2.5.1 Symmetric laminates

A laminate is called symmetric when for each layer on one side of a reference plane

(middle surface) there is a corresponding layer at an equal distance from the reference

plane on the other side with identical thickness, orientation, and properties. The laminate

is symmetric in both geometry and material properties. [1]

Example:

[0° / 30° /60°] s

2.5.2 Symmetric Crossply Laminates

A symmetric laminate with special orthotropic layers, the principal axes of each layer

coincide with the laminate axes. [1]

Example:

[0° / 90°/ 0°] and [0°/ 90°] s

2.5.3 Symmetric Angle-Ply Laminates

A laminates containing plies oriented at +θ and –θ directions. They can be symmetric or

asymmetric. If the laminate consists of an odd number of alternating +θ and –θ plies of

equal thickness, then it is considered as symmetric. [1]

Example:

[θ/ -θ/ θ/ -θ/ θ] = [±θ/ θ] s

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2.5.4 Balanced Laminates

A balanced laminates consists of pairs of layers with identical thickness and elastic

properties but having +θ and –θ orientations of their principal material axes with respect

to the laminate principal axes. Balanced laminate can be symmetric, asymmetric, or

antisymmetric. [1]

Example:

Symmetric: [±θ1/ ±θ2] s

Antisymmetric: [θ1/ θ2/ -θ2/ -θ1]

Asymmetric: [θ1/ θ2/ -θ1/ -θ2]

2.5.5 Antisymmetric Laminates

A laminates where the material and thickness of the plies are the same above and below

midplane, but the ply orientations at the same distance above and below of the midplane

are negative to each other. [1]

Example:

[45°/ 60°/ -60°/ -45°]

2.5.6 Quasi-Isotropic Laminates

A quasi-isotropic laminate where it extensional stiffness matrix [A] behave like that of an

isotropic material. [1]

Example:

[0°/ 60°/ -60°] and [0°/ ±45°/ 90°]

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2.6 Strength of Material

2.6.1 Stress

Stress is used to analyze how strong a structure is by factoring out the size and shape

affected which:

Normal stress: tensile and compressive stress, σ

σ = F/ A or P/ A

Where,

F = Tension force

P = Compression force

A = Cross-sectional area

Shear stress, τ Shear stress (torque), τ

τ = F/A τ = Tr/ J

Where,

F = Shear force

A = Cross-sectional area

Tr = Total radius

J = Polar moment inertia (depends on shape)

Figure 2.5 Tensile and Compression Force

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2.6.2 Tensile Properties

Tensile properties indicate how the material will react to forces being applied in tension.

A tensile test is a fundamental mechanical test where a carefully prepared specimen is

loaded in a very controlled manner while measuring the applied load and the elongation

of the specimen over some distance. Tensile tests are used to determine the modulus of

elasticity, elastic limit, elongation, proportional limit, reduction in area, tensile strength,

yield point, yield strength Poisson’s ratio and other tensile properties. [2]

The main product of a tensile test is a load versus elongation curve which is then

converted into a stress versus strain curve. The stress-strain curve relates the applied

stress to the resulting strain and each material has its own unique stress-strain curve. A

typical engineering stress-strain curve is shown in figure 2.4. If the true stress, based on

the actual cross-sectional area of the specimen, is used, it is found that the stress-strain

curve increases continuously up to fracture. [2]

Figure 2.6 Example of graphs which illustrating the difference between nominal stress

and strain and true stress and strain in the tensile test.

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2.7 Linear-Elastic Region and Elastic Constants

As can be seen in the figure 2.5, the stress and strain initially increase with a linear

relationship. This is the linear elastic portion of the curve and it indicates that no plastic

deformation has occurred. In this region of the curve, when the stress is reduced, the

material will return to its original shape. In this linear region, the line obeys the

relationship defined as Hooke's Law where the ratio of stress to strain is a constant. [2]

Figure 2.7 Graphs illustrating the difference between nominal stress and strain and true stress and strain.

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The slope of the line in this region where stress is proportional to strain is called

the modulus of elasticity or Young's modulus. The modulus of elasticity (E) defines the

properties of a material as it undergoes stress, deforms, and then returns to its original

shape after the stress is removed. It is a measure of the stiffness of a given material. To

compute the modulus of elastic, simply divide the stress by the strain in the material.

Since strain is unit less, the modulus will have the same units as the stress, such as kpi or

MPa. The modulus of elasticity applies specifically to the situation of a component being

stretched with a tensile force. This modulus is of interest when it is necessary to compute

how much a rod or wire stretches under a tensile load. [2]

There are several different kinds of moduli depending on the way the material is

being stretched, bent, or otherwise distorted. When a component is subjected to pure

shear, for instance, a cylindrical bar under torsion, the shear modulus describes the linear-

elastic stress-strain relationship. [2]

2.8 Shear Modulus

Shear modulus is the ratio of shear stress to shear strain. Testing is performed using a

torsional pendulum. A test specimen of uniform cross-section is clamped at ends, one end

fixed and the other to a weighted disc that acts as an inertial member. The system is put

into motion and the oscillation period and amplitude is measured and plotted as a

function of time. [2]

For isotropic materials the shear modulus can be related to the tensile modulus with the

formula:

G = E / [2(1+ν)]

Where,

G is the shear modulus.

E is the tensile modulus or Young modulus.

ν is the Poisson's ratio of the material.

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Axial strain is always accompanied by lateral strains of opposite sign in the two

directions mutually perpendicular to the axial strain. Strains that result from an increase

in length are designated as positive (+) and those that result in a decrease in length are

designated as negative (-). Poisson's ratio is defined as the negative of the ratio of the

lateral strain to the axial strain for a uniaxial stress state. [2]

Poisson's ratio is sometimes also defined as the ratio of the absolute values of

lateral and axial strain. This ratio, like strain, is unitless since both strains are unitless.

2.9 Poisson’s Ratio

An important material property used in elastic analysis is Poisson's ratio. Poisson’s ratio

is defined as the ratio of transverse to longitudinal strains of a loaded specimen. This

concept is illustrated in Figure 2.6. [2]

Generally, ‘stiffer’ materials will have lower Poisson’s ratios than ‘softer’

materials (see Table 1.2). You might see Poisson’s ratios larger than 0.5 reported in the

literature; this implies that the material was stressed to cracking, experimental error, etc.

Table 1.2 Typical values for Poisson’s Ratio

Material Poisson’s Ratio

Steel 0.25 - 0.30 Aluminum 0.33 PCC 0.15 – 0.20 Flexible Pavement Asphalt Concrete Crushed Stone Soils (fine - grained)

0.35 (±) 0.40 (±) 0.45 (±)

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Figure 2.8 Poisson’s ratio example.

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2.10 Finite Element Analysis (FEA)

2.10.1 Introduction

The term of analysis in engineering means the application of an acceptable analytical

procedure to a design problem based on established engineering principle.

Is to verify the structure or thermal integrity of a design, usually this can be done

using handbook or analytical procedure for simple design. This analysis is being

performed using numerical analysis and computers to predict structure or product

performance. [5]

2.10.2 Complexity of Analysis/ Design

The micro-mechanics terms is establishes the relation between the properties of the

constituents and those of the unit composite ply. On the other hand, macro-mechanics

(laminate plate theory) is relies on measured ply data to establish optimum laminates for

a structural application.

Ply stacking sequence is importance to obtain the stiffness and strength properties

of the efficient laminate. This will prevent from warping during fabrication and service.

Beside that, another term always used is delamination. Delamination is the result of

interlaminate stresses and is of particular concern at the boundary layer along the free

edges of a laminate composite. [5]

2.10.3 Failure Criteria

This failure criterion is used as a guide design and material improvement. This is

typically for empirical development. All off these are depend on ply lay up, ply material,

and the history of loading.

To analyze the strength of a laminate, strength theories are required. Laminate

strength is influenced by the presence of residual stresses, stress concentration, and

interlaminar stress which manifest at the free edge of a laminate.

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This progress will take placed at first-ply-failure (fpf) to last-ply-failure (lpf).

Lastly, as the failure criteria have been developing, the analyses of the theory are

including maximum stress, maximum strain and etc. [5]

2.10.4 Environmental Consideration

A change of temperature or the absorption of fluids or gases from the environment will

result in a dimensional change in the lamina. This will include thermal expansion or

contraction.

Only balance and symmetrical laminates can sustain a volumetric strain without

producing an out-of-plane deformation. Composite are typically resistance to chemicals

and corrosion. [5]

2.10.5 Composite Analysis/ Design

The programs can be used or general purpose analysis program, with appropriate

capabilities, can be used for design and analysis of composite structure and product.

Material identification, layer thicknesses, layer location, and ply angle. After

solving the composite problem, post-processing is required to interrogate the result of the

analysis in term of both laminate and ply orientation. [5]

2.10.6 Sequence of Finite Element Analysis (FEA)

Below shows the sequence of Finite Element Analysis (FEA) been applied for composite

laminate model:

I. Define material properties of plies used in the laminate.

II. Define ply properties from material properties and micro-mechanic

procedure.

III. Build plies into laminate, define laminate lay-up:

i. Define stacking sequence, ply group, and stack of ply group.

ii. Symmetric, anti-symmetric and repeat stacking

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iii. Specify ply material orientation so that laminate constitutive

matrix can be formed.

IV. Assign laminate properties to FEA model, assign laminate material property

table to elements.

V. Define boundary condition, load, constraints and etc.

VI. Display and evaluate result.

VII. Access ply-by-ply stress and strain result, interlaminar shear stresses and

etc.

VIII. Evaluate failure criteria.

2.10.7 Design Consideration

There is several design consideration must be caution during modeling the element in

finite element analysis as stated:

I. Low to moderate modulus of elasticity which may not be linear in the

regions of interest.

II. Core material may be used to increased dimension, increasing stiffness and

strength properties of the laminate.

III. Susceptibleness to deformation under long term load.

IV. Adequate material property data may be difficult to obtain

V. Boundary condition may be difficult to specify.

VI. Laminate code must be fully understood to prevent ply configuration errors.

VII. Must know how published orthotropic material properties are derived

VIII. Structure symmetry not usable if in-plane and out-of-plane coupling exist

IX. Element size at material boundary must be small enough to accurately

resolve interlaminate shear stress.

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2.11 General Information of PATRAN/NASTRAN

2.11.1 MSC.Patran

MSC.Patran is the world’s most widely used pre/post-processing software for Finite

Element Analysis (FEA), providing solid modeling, meshing, and analysis setup for

Nastran, Marc, Abaqus, LS-DYNA, ANSYS, and Pam-Crash.

Designers, engineers, and CAE analysts tasked with creating and analyzing virtual

prototypes are faced with a number of tedious, time-wasting tasks. These include CAD

geometry translation, geometry cleanup, manual meshing processes, assembly connection

definition, and editing of input decks to setup jobs for analysis by various solvers. Pre-

processing is still widely considered the most time consuming aspect of CAE, consuming

up to 60% of users’ time. Assembling results into reports that can be shared with

colleagues and managers is also still a very labor intensive, tedious activity.

MSC.Patran provides a rich set of tools that streamline the creation of analysis

ready models for linear, nonlinear, explicit dynamics, thermal, and other finite element

solvers. From geometry cleanup tools that make it easy for engineers to deal with gaps

and slivers in CAD, to solid modeling tools that enable creation of models from scratch,

MSC.Patran makes it easy for anyone to create FE models.

Meshes are easily created on surfaces and solids alike using fully automated

meshing routines (including hex meshing), manual methods that provide more control, or

combinations of both. Finally, loads, boundary conditions, and analysis setup for most

popular FE solvers is built in, minimizing the need to edit input decks. Patran’s

comprehensive and industry tested capabilities ensure that your virtual prototyping efforts

provide results fast so that you can evaluate product performance against requirements

and optimize your designs. [4]

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2.11.2 MSC.Nastran

This software is most powerful general purpose digital computer program for the finite-

element structural analysis of small to large and complex physical device and system.

Nastran has been a proven standard tool in the field of structural analysis for decades. It

provides a wide range of modeling and analysis capabilities, including linear static,

displacement, strain, stress, vibration, heat transfer, and more.

NASTRAN can handle any material type from plastic and metal to composites

and hyperelastic materials. NASTRAN is written primarily in FOTRAN and contain over

one million lone of code. NASTRAN is compatible with a large variety of computer and

operating system, ranging from small workstation to the largest supercomputer, and the

applications of NASTRAN are stated below:

The strength and fatigue of aircraft structures, such as fuselage, wings and flaps,

and landing gear.

The strength and durability, and vibration of car, truck, and train structures such

as body, chassis, suspension, steering, and wheels.

The ability of any product to withstand being improperly handled, dropped,

crashed, or other types of catastrophic events.

Today, NASTRAN is widely used throughout the world in the aerospace,

automotive, and maritime industries. It is considered the industry standard for the

analysis of aerospace structures. [3]

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Chapter: 3 METHODOLOGY

3.1 Introduction

Methodology for this project is done by design a composite laminate model in

MSC.Patran software and then the model submitted to MSC.Natran for analysis. There

are several of model which is has same dimension of length and width, same material,

same material properties, different numbers of plies, and different angle of plies

orientation.

3.2 Material Selection

In this project, we have been choose the Fiberglass Prepreg Fabric, Class III Grade 1,

Type 1581 fabric (BMS 8-79-1581) material properties for the data need to be input in

define material properties in MSC.Patran program.

This material is widely used by Boeing aircraft manufacturer as example in

fabrication of horizontal stabilizer skin panel station number from 39.02-213.32 for

Boeing 737-400 aircraft.

Figure 3.1 Horizontal stabilizer skin panels. (Courtesy of Boeing 737-400 SRM)

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The BMS 8-79-1581 equivalent to Hexcel glass face sheet is its F155TM resin with

an 8 harness satin weave. F155TM is an advance modified epoxy formulation designed for

autoclave curing to offer very high laminate strengths with increased fracture toughness

and adhesive properties. The cure cycle of F155™ is 250ºF (121ºC) for 90 minutes.

Typical applications of this controlled flow epoxy resin are co-curing onto honeycomb

and bonding to metal.

Table 3.1 Fiberglass Prepreg Fabric, Class III Grade 1, Type 1581 fabric BMS 8-79

(Hexcel F155) properties.

Hexcel Designation 1581-38”-F155 Compression Strength 517 MPa Compression Modulus 25.5 GPa Ultimate Tensile Strength 483 MPa Compression inter-laminar shear strength 23.4 GPa Compression inter-laminar shear strength 68.9 MPa F155 Resin Tensile Modulus 3.24 GPa Fiber Volume Fraction 45% Elastic Modulus 29.7e9 Poisson Ratio 0.17 Shear Modulus 5.3e9 Density 2200

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3.3 Model Dimension

In design the model size and configuration, we have followed the Standard Test Method

for Tensile Properties of Fiber-Resin Composite (D 3039) that are provided and approved

from American Society Test Method (ASTM).

L = Length W = Width 3.4 Force Calculation

To test the design by giving tensile load, there are must be a suitable and applicable load

for the area and design size. To find the suitable force will be acting for tensile force to

be acting in Patran software, we have used the equation for ultimate stress is equal to

force per unit area as stated below:

Since from the material properties table 3.1, the ultimate stress value was 483

MPa, and the area from the design was 3225.5mm2. So, the calculation to define the force

value can be calculated as below:

L=127mm (5 inch)

W=25.4mm (1 inch)

σu = F/A

σu = F/A 483Mpa = F/ 3225.5mm2 F = 3225.5mm2 x 483Mpa F = 1558061.4 N * 1 Pascal is equal to 1.0E-6 Newton/square millimeter

Figure 3.2 Model dimension.

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3.4.1 Load Distribution After do the calculation for the needs of load action to the model design has been done,

the force must be divided equal at the all 4 node of the X axis in the direction of force

will be acting.

So, the value of force in paragraph 3.4 must be divided into three, for node

number 2 and 3, and one other value must be dividing into two for node number 1 and 4.

So, the calculation to define the force value for every node can be calculated as below:

In doing this, it is important to distribute the force acting on the element evenly

and also for sure for the accuracy of result, data analysis and data interpretation.

F = 1558061.4 N

Node no. 2 & 3 = 1558061.4 N ÷ 3 = 519353.8N

Node no. 1 & 4 = 519353.8 N ÷ 2 = 10223.5 N

Force direction

Node no. 1 (10223.5 N)

Node no. 2 (519353.8N)

Node no. 3 (519353.8N)

Node no. 4 (10223.5 N)

Figure 3.3 Force direction and value.

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3.5 Patran Model Design

3.5.1 Patran Modeling Design Steps

There are few step must be need to followed in design the composite laminate to get the

perfect result of the analysis. First of all, the geometry model must be created by selected

the plane of X, Y, Z axis and insert it vector coordinate value as shown in figure 3.4.

Next, the element model has been selected to create mesh surface of the element

shape. The purpose of the mesh is to divide the load applied into the small area as shown

in figure 3.5.

After that, a fixed load has been set up at the left end side of the element node by

created zero displacement on X, Y, Z axis (<0 0 0>). In this case, by creating fix

displacement to prevent the model from any movement such as rotation. The step has

shown in figure 3.6.

Next, the force values have been inserted at the force direction in right end node

side as shown in figure 3.7. The value can be referring as per paragraph 3.4.1. After that,

we must define the material properties data in the material input options as shown in

figure 3.8. The material properties must be according to the manufacturer specification as

per as Table 3.1.

Next, we need to define the data of material names, thickness per ply and it

orientation by filled up in the laminated composite section as per as figure 3.9. The

thickness per ply must be referring to ASTM.

After all the data has been filled up in every table properties, a new file has been

created and it now can be run in Nastran for analysis as shown in figure 3.10. In this

process the Nastran program will determine and analyze the requested data.

Finally, run Patran program again, the result can be access by generate the .bdx

file that carrying the data has been extracted in Nastran before. The result can be go

through by select stress tensor as shown in figure 3.11.Beside that, we also can see the

result of each ply with different views.

Figure 3.4 Create Geometry.

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Figure 3.5 Create a Finite Element Mesh.

29

Figure 3.6 Create Constraints on the Laminate.

30

Figure 3.7 Create Constraints on the Laminate.

31

Figure 3.8 Defining Ply Material Properties.

32

Figure 3.9 Define Composite material names, thickness per ply and it orientation.

33

Figure 3.10 Submit the Model to MSC.Nastarn for Analysis.

34

Figure 3.11 View the Result.

3.5.2 Model In this project, we have design 14 model of fiberglass laminate to test in Pastran and

Nastran software. The design has been created by moderate the fabric ply layer and it ply

orientation. Beside that, the maximum thickness of the tested model has been refer to

Tensile Properties of Fiber-Resin Composite (D 3039) that are provided and approved

from American Society Test Method (ASTM) in TABLE 2 Recommended Thicknesses

For various Reinforcements.

The design also was created by taking the present of percentages of 45° and 0/90°

ply orientation. Table below shown percentages of 45° and 0/90° ply orientation and the

design has been tested for this research:

MODEL ORIENTATION ORIENTATION

% THICKNESS PER

PLY THICKNESS TOTAL PLY

4A [ 0,90/ 45]s 50% of 45°

4B [ 45/ 0,90]s 50% of 0°/90°

MODEL ORIENTATION ORIENTATION %

THICKNESS PER PLY

THICKNESS TOTAL PLY

8A [ 45/ (0,90) / (0,90) / (0,90) ]s 25% of 45°

8B [ (0,90)/ 45/(0,90)/(0,90) ]s 25% of 45° 8C [ (0,90)/(0,90)/45/(0,90) ]s 25% of 45° 8D [ (0,90)/ (0,90)/ (0,90) / 45 ]s 25% of 45° 8E [ 45/ 45/ 0,90/ 0,90]s 50% of 45°

50% of 0°/90° 8F [ 0, 90/ 0, 90/ 45/ 45]s 50% of 45°

50% of 0°/90° 8G [0, 90/ 45/ 0,90/ 45]s 50% of 45°

50% of 0°/90° 8H [45/(0,90)/45/(0,90)]s 50% of 45°

50% of 0°/90° 8I [(0,90)/ 45/45/(0,90)]s 50% of 45°

50% of 0°/90° 8J [ 45/ (0,90)/(0,90)/45]s 50% of 45°

50% of 0°/90° 8K [ 0, 90 / 45/ 45 /45]s 25% of 0°/90°

Table 3.2 4 Plies

Table 3.2 8 Plies

0.0078125 INCHES 0.03125 INCHES

0.0078125 INCHES 0.125 INCHES

36

8L [ 45/ 0, 90/ 45/ 45 ]s 75% of 45° 8M [ 45/ 45 / 0, 90 / 45]s 75% of 45° 8N [ 45/ 45/ 45 / 0,90]s 75% of 45°

37

Chapter: 4 RESULTS & DISCUSSION

4.1 Result By aid of Patran/ Nastran, all data that required has been successfully includes in the

program as per as required in the manual. In this case, a fixed boundary condition (BC)

has been applied at one end (as shown at figure 3.6).The BC set to <0, 0, 0>. This show

the ends are not allowed to move at any directions. The force assigned at the other end as

shown at figure 3.7.

The rotation and moment set to < 0, 0, 0>, this means no rotation and moment

allowed during this test. Also, the material specifications have been included as per as

ASTM. Then, certain orientations have been set as per as table 4.1 and 4.2. According to

the tested data in 3.5.2, the result has been recorded as shown below:

Model Orientations Stress value Layers

4A

[ 0,90/ 45]s

2.58 + 006 1 1.40 + 006 2 1.40 + 006 3 2.58 + 006 4

4B

[ 45/ 0,90]s

1.40 + 006 1 2.58 + 006 2 2.58 + 006 3 1.40 + 006 4

Table 4.1 4 Layers Lamina

38

Model Orientations Stress values Layers 8A [ 45/ 0,90 / 0,90 / 0,90 ]s 6.42+005 1

1.11+006 2 1.11+006 3 1.11+006 4 1.11+006 5 1.11+006 6 1.11+006 7 6.42+005 8

8B [ 0,90/ 45/0,90/0,90 ]s 1.11+006 1 6.42+005 2 1.11+006 3 1.11+006 4 1.11+006 5 1.11+006 6 6.42+005 7 1.11+006 8

8C [ 0,90/0,90/45/0,90 ]s 1.11+006 1 1.11+006 2 6.42+005 3 1.11+006 4 1.11+006 5 6.42+005 6 1.11+006 7 1.11+006 8

8D [ 0,90/ 0,90/ 0,90 / 45 ]s 1.11+006 1 1.11+006 2 1.11+006 3 6.42+005 4 6.42+005 5 1.11+006 6 1.11+006 7 1.11+006 8

Table 4.2 8 Layers Lamina

39

Model Orientations Stress values Layers 8E [45/0,90/45/0,90]s 7.01+005 1

1.29+006 2 7.01+005 3 1.29+006 4 1.29+006 5 7.01+005 6 1.29+006 7 7.01+005 8

8F [0,90/ 45/45/0,90]s 1.29+006 1 7.01+005 2 7.01+005 3 1.29+006 4 1.29+006 5 7.01+005 6 7.01+005 7 1.29+006 8

8G [ 45/ 0,90/0,90/45]s 7.01+005 1 1.29+006 2 1.29+006 3 7.01+005 4 7.01+005 5 1.29+006 6 1.29+006 7 7.01+005 8

8H [ 0, 90/ 0, 90/ 45/ 45]s 1.29 + 005 1 1.29 + 005 2 7.01 + 006 3 7.01 + 006 4 7.01 + 006 5 7.01 + 006 6 1.29 + 005 7 1.29 + 005 8

8I [0, 90/ 45/ 0,90/ 45]s

1.29 + 005 1 7.01 + 006 2 1.29 + 005 3 7.01 + 006 4 7.01 + 006 5 1.29 + 005 6 7.01 + 006 7 1.29 + 005 8

40

Model Orientations Stress values Layers 8J [ 45/ 45/ 0,90/ 0,90]s 7.01 + 006 1

7.01 + 006 2 1.29 + 005 3 1.29 + 005 4 1.29 + 005 5 1.29 + 005 6 7.01 + 006 7 7.01 + 006 8

8K [ 0, 90 / 45/ 45 /45]s 1.58 + 006 1 7.95 + 005 2 7.95 + 005 3 7.95 + 005 4 7.95 + 005 5 7.95 + 005 6 7.95 + 005 7 1.58 + 006 8

8L [ 45/ 0, 90/ 45/ 45 ]s 7.95 + 005 1 1.58 + 006 2 7.95 + 005 3 7.95 + 005 4 7.95 + 005 5

7.95 + 005 6 1.58 + 006 7 7.95 + 005 8

8M [ 45/ 45 / 0, 90 / 45]s 7.95 + 005 1 7.95 + 005 2 1.58 + 006 3 7.95 + 005 4 7.95 + 005 5 1.58 + 006 6 7.95 + 005 7 7.95 + 005 8

8N [ 45/ 45/ 45 / 0,90]s 7.95 + 005 1 7.95 + 005 2 7.95 + 005 3 1.58 + 006 4

41

1.58 + 006 5 7.95 + 005 6 7.95 + 005 7 7.95 + 005 8

NOTE: 4 layers of 50% of 45° orientations - max 2.58 + 006

4 layers of 50% of 0° orientations - min 1.40 + 006

8 layers of 25% of 45° orientations - max 6.85+005 - min 6.35+005 8 layers of 50% of 45° orientations - max 7.51+005 - min 6.93+005 8 layers of 75% of 45° orientations - max 8.42+005 - min 7.84+005 8 layers of 25% of 0° orientations - max 1.60+006 - min 1.27+006 8 layers of 50% of 0° orientations - max 1.30+006 - min 1.13+006 8 layers of 75% of 0° orientations - max 1.11+006 - min 1.03+006

By referring to the shown data, the stress value has been evaluated per ply for both 4

layers lamina and 8 layers lamina. The data has shown the different stress value for each

of the ply with respect to the orientations.

For 4 layers lamina, the stress value for orientation 0°, 90° found slightly higher

than the 45° which is 2.58 – 006 (Table 4.1). For 8 layers lamina, the stress value for

orientation 45° found higher than 0°, 90° regardless of the number of orientation 45° of

the laminate (Table 4.2). It is because the number of ply for orientation 0°, 90° is more

than 45° ply, this means the stress has been distributed to each ply of orientation 0°, 90°.

42

4.2 Discussion 4.2.1 Stress Analysis Stress is defined as the internal resistance set up by a body when it is deformed. The

purpose of analysis of the stress in this test is to give some comparison and also will

clearly show which the best of laminate configuration being tested in Pantran and Nastran

program.

According to the result in paragraph 4.1, with aided by Patran and Nastran

program, there were several analysis and interpretations can be discussed. Below,

represent percentage of ply orientation 45 or 0/90 must be added to show the stress occur

on when the load act on X axis.

4.2.1.1 Maximum Stress Value

The value of stress deformation shown at certain nodes and will be color coded to

show stress value. From the result, we can see clearly the differences of maximum stress

value between 4 and 8 plies with various orientations where the load and boundary

condition are constant as per table 5.1 below:

Model Orientations Max. Stress Value 4A [ 0,90/ 45]s 2.61 + 006 8B [0,90 /45 / 0,90 / 0,90 ]s 1.10+006 8E [45/0,90/45/0,90]s 1.30+006 8K [ 0, 90 / 45/ 45 /45]s 1.60+ 006

Table 5.1 Differences of Max. Stress Values

43

Figure 4.1 Differences of Max. Stress Values

From the graph, we assumed that as the number of ply has increase, the stress value also

increases. That means the number of ply is directly proportional to the stress value.

Generally, the laminate with high thickness absolutely will be much stronger than low

thickness when the load applied is constant.

Beside that, the orientation also will influence the effectiveness of stress value.. In

this case, the 45° ply is better for counter the shear load with regard to the direction of the

loading applied. Generally 0°/90° ply used to counter the axial loads for both

compression and tension.

Further more, from the model 4A, 8B, 8E, and 8K we have calculate the

percentage of tensile load has been hold for 45° and 0°/90° ply orientation. For the

result, we have found the percentage of 0°/90° orientation hold much more tensile load

rather than 45° ply orientation. So, the expectation of 0°/90° ply orientation hold much

more tensile load has been clearly proved from the percentage calculation and finite

element tensile analysis. Table 5.2 below shown the percentage value of tensile load has

been hold by 45° and 0°/90° ply orientation.

0

0.5

1

1.5

2

2.5

3

Model

Max

. Str

ess

Valu

e

4A 8B 8E 8K

44

4.2.1.2 Stress Deformation Structure

Under certain loading condition, each model will tend to deform cause of stress act on it.

For every model, the deformation can be view by access in result in Patran program. The

maximum and minimum stress values have been existed at certain node. For comparison

of deform structure for model 4A, 8A, 8E, and 8K, the deformations are shown at figure

4.2 as per below:

Model [0,90]% [45]%

4A 64.8 35.2 8B 83.8 16.2 8E 64.8 35.2 8K 40 60

Figure 4.2 Model 4A After Deformation

Table 5.2 The percentage value of tensile load has been hold by 45° and 0°/90° ply orientation

45

Figure 4.2 above shown the deformation structure occur along the model after

giving load. For Model 4A, the maximum stress value occurred at node 20 and minimum

stress values were existed at node 17.

Deformation that occurred on model 8A under certain loading has shown in

Figure 4.3. The result shows the maximum value occurred at node 1, and the minimum

value occurred at node 3. It also shows an extension of the model after certain loading

condition.

Figure 4.3 Model 8A After Deformation

46

For the next model, 8E, that goes through under certain loading condition with

result as shown in Figure 4.4. The result has shown the maximum stress value that

occurred on the model at node 20 and the minimum stress value occurred at node 17.

Figure 4.4 Model 8E After Deformation

47

The 8K model which is also goes through under certain loading condition as the

other model before has shown in Figure 4.5. The result shows the maximum stress value

occurred at node 20 and the minimum stress value occurred at node 17.

After has been analyzed precisely, the model with different number of layer and

orientation will result in different maximum and minimum stress value under certain

loading condition regardless of the location of the nodes. Obviously, the stress that acts

on the model will cause deformation of the model structure which result an extension

toward the loading direction.

Figure 4.5 Model 8K After Deformation

48

From the stress deformation structure data that has been obtained, we can see the

relationship between stress value and locations of the node. This is mean the maximum

and minimum stress value can be predict at certain location of deformation occurs along

the models after load has been applied. The location of node and it maximum value for

model 4A, 8A, 8E, and 8K are shown in table 5.2 below:

Model Location of Node Max. Stress Value 4A 20 2.58 + 006 8A 1 6.42+005 8E 20 7.01+005 8K 20 7.95 + 005

Table 5.2 Locations of Node and It Max. Stress Value

49

Chapter: 5 CONCLUSION

As a conclusion, various models are tested to analyze the finite element tensile analysis

on failure and response of laminate composites model in several of ply orientation and

certain number of ply. Finite element analyses on solid laminate fiberglass fabric epoxy

material were performed with aided of MSC.Patran/Nastran program under tensile load

where the direction of the load are constant. Based on the result, we can conclude that:

1. As the number of ply increase, the maximum stress value of the laminate

increase.

2. The orientation in each ply will influence the strength of the laminate

under certain loading indirectly increases it maximum stress value.

Practically, from the test, we can predict the failure can be occurs on aircraft

composite structure under certain loading condition by knowing stress value with regard

to the location. Beside that, we also can use this test for composite part design purposes.

By doing this, the failure of the laminate structure can be minimized and the cost of

maintenance also can be reduced.

Consequently, the quality of the laminate composite product will achieve the

standard requirement. Beside that, this also will promote durability of the product for

their serviceable life.

Eventually, from observation that was done, some improvement should be made

to get better test result. Our suggestion that composite laminate model also need to be test

under various loading such as compression and shear loading to obtain the compression

and shear strength. This is important in define the composite laminate part total strength.

By having tensile, compressive and shear strength data, we can evaluate the part total

strength properties for it suitable application.

50

REFERENCES:

[1] Isaac M. Daniel, Ori Ishai, 2006. Engineering Mechanics of Composite Materials,

Second Edition. Pp 18 – 42. Oxford University Press, Inc.

[2] CMMok, An Introduction of mechanical Testing Pictorial tutorial

http://www.sut.ac.th/Engineering/Metal/course.html. Accessed on 2nd May 2006.

[3] Article, NASTRAN from Wikipedia, the free encyclopedia

http://en.wikipedia.org/wiki/Nastran. Accessed on 28 June 2009.

[4] MSC Software Cooperation, http://www.mscsoftware.com/Contents/Product/CAE-

Tools/Patran.aspx. Accessed on 30 June 2009.

[5] Edward Simon Lee, E-Learning Article, http://www.cseinc.orgt/tutorial.htm.

Accessed on 3 July 2009.