Composite Materials

1. 1
Gaziantep University
College of Engineering
Civil Engineering Department
Report on
Three composite models in stress , strain
and elastic modulus
Submitted by
Mohammed Layth Abbas
Student No:201444956
Supervisor
Assoc.Prof. Erhan Güneyisi
CE 543
(composite Materials)

2. 2
Introduction
A composite material is made by combining two or more materials –
often ones that have very different properties. The two materials
work together to give the composite unique properties. However,
within the composite you can easily tell the different materials apart
as they do not dissolve or blend into each other.
Why use composites?
The biggest advantage of modern composite materials is that they
are light as well as strong. By choosing an appropriate combination of
matrix and reinforcement material, a new material can be made that
exactly meets the requirements of a particular application.
Composites also provide design flexibility because many of them can
be molded into complex shapes. The downside is often the cost.
Although the resulting product is more efficient, the raw materials
are often expensive.
Some of the properties that can be improved by forming a composite
material are:-
Strength , stiffness , corrosion resistance , wear resistance ,
attractive ness , weight , fatigue life , temperature dependent
behavior , thermal insulation .
Unit cell models of the composites

3. 3
There are three types of the unit cell models composite material as
indicated below
1- Parallel phase model
Dispersed phaseMatrix phase
For the parallel phase model
Determination of E1
The first modulus to be determined is that one of the composite
material in the 1- direction that is in the fiber direction from the
figure below
….1ɛ1=
Where ɛ1 applies for both the fibers and the matrix according to the
basic assumption. Then if both constituent materials behave
elasticity the stress in the fiber direction are

.....m = Em F = EF1
The average stress 1 acts on cross sectional area A of the
representative volume element , F acts on the cross sectional area of
the fibers Af and m acts on the cross sectional area of of the matrix
Am .The resultant force of the reprehensive volume element of the
composite material is
.…3P=1 A =f Af +=f Af

4. 4
By substitution of equation (2 ) in equation (3 )and recognition from
micromechanics that
….41 = E11
Apparently
…..5Em+E1= Ef
but the volume friction of fiber and matrix can be written as
Vf=Af/A Vm=Am/A ….6
Thus
…..7EmVm+E1 = EfVf
2-Series phase model
The modulus of the matrix material is Em and the modulus of the
dispersed material is Ed where is the modulus of the composite
material is E the volume friction of the constituents are Vm and Vd
such that
….1Vm+Vd=1
Obviously any relationship for the composite modulus E must yield
E=Em for Vm =1 and E = Ed for Vd=1
One of the simplest relationships that satisfies the foregoing
restrictions is the rule of mixtures
….2E=EmVm+EdVd

5. 5
Where in the constituents of the composite material are presumed to
contribute to the composite stiffness in direct proportion to their own
stiffness and volume frictions. The rule of mixtures will be shown to
provide an upper bound on the composite modulus E for the special
case in which
….3Vm=Vd=V
Another simple relationship between the constituent moduli results
from the observation that the compliance of the composite material
1/E, must agree with the compliance of the matrix. 1/Em, when Vm=1
and with the compliance of the dispersed material when Vd= 1 the
resulting rule of mixtures for compliance is
….4
3-Dispersed phase (Maxwell modell)