By the end of this chapter, a
student will be able to :
1-Explain the Stress &Strain
2-Define the Mechanical Tests
3-Use Hooks Low
4-Classify Elastic coefficients .
It is the ability of a substance to restore its
original shape and size after deformation.
Materials that restore its original shape and size
after deformation .
The Types of stress.
1-Tensile (Longitudinal) Stress.
Tension results in a body when the body is acted by two
forces equal in a magnitude directed away from each
other and acting along the same line. The tensile
stress increases the body length
Tensile Stress σ L = Fn
Fn is the force acting perpendicular
A is the cross sectional area
Compression Stress in a body when the
body is acted by two forces equal in a
magnitude directed toward from
each other and acting along the
same line .The compression stress
decreases the body length.
Compression Stress σ V = Fn
Shearing Stress is result applied to the body which are
directed toward from each other but not acted along
the same straight line .
Shear Stress (σ s ) = Fn
The Types of strain.
It is produced due to the tensile stress
L = ∆L/L0
It is produced due to the compressive stress
which causes a change in the volume
ϵ V = ∆V/V0
It is produced due to the shear stress which causes
a change in the shape of the body without change
ϵS = tanφ
5: Hook's law
Hook's law states that :in elastic region the force
applied to the spring is directly proportional to the
F = KX
X is the distance that the spring has been stretched or
compressed away from the equilibrium position,
which is the position where the spring would
naturally come to rest (usually in meters)
F is the restoring force exerted by the material (usually
K is the force constant (or spring constant).
According to the types of stress applied to a body and
the accompanied type of strain produced in the body,
there are different types of elastic module
The Types elastic coefficients.
It is the ratio between the longitudinal stress to the
E= Longitudinal stress σ L = F/A
It is the ratio between the shear stress to the shear strain.
G= Shear stress σ s = F/A
Shear strain ϵs tanΦ
tanΦ = x/h
Bulk modulus is the ratio between the compressive
stress to the volume strain
B= Compressive stress σ V = F/A
Volume strain ϵV ∆V/V0
7: Mechanical Tests
In order to study mechanical properties of
materials, there are different mechanical
methods or test should be followed .These
1-The stress – strain test
4-The creep test
1-The stress –strain test
Stress strain test involves relation between the
stress and strain from which a stress strain
curve is obtained
A:The proportional limit A
The proportional limit A is the stress at which the
material still obey Hooks law
B:The elastic limit B
Elastic limit is the maximum stress
C:The Yield strengthC
The Yield strengthC is the stress at which the
material behaves plastically.
D:The ultimate strength D
The ultimate strength D is the maximum stress
that a material can with stand just before
fracture or rupture.
It is deformation produced in amaterial
under the application of cyclic stress.
It is the ability of the surface of a
material to resist penetration by a
point under a specific load.
4:The Creep test
Creep test involves the relation
between stain and time at constant
stress. It is usually occurs at
temperature near to the softening point
of the material.
1-Wire 12.5 m long is stretched to a length
A) What is the strain of the stretched wire?
B) If the wire is copper whose Young's
modulus (E) =120x109 N/m2 ,what is the
stress required to produce this strain?
C) If the cross sectional area of the wire is
4x10-5 m2 ,what is the tension stretched