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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.
2
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.
3
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]
4
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
5
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.
6
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
7
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.
8
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.
9
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
10
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°]
11
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
12
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.
13
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.
14
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.
15
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 (±)
16
Figure 2.8 Poisson’s ratio example.
17
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.
18
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
19
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.
20
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]
21
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]
22
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)
23
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
24
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.
25
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.
26
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.
28
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.