1. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Elastic and Plastic Deformation
Elastic Deformation :
If a metal deformed by a force returns to its original
dimensions after the force is removed, the metal is said
to be elastically deformed.
During elastic deformation the metal atoms are displaced from their original positions but not to the extent that they take up new positions. Thus, when the force removed, the metal atoms return to their original positions and the metal takes back its original shape.

2. Elastic
Deformation :

3. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Elastic and Plastic Deformation
Plastic Deformation :
If a metal deformed by a force dose not returns to its original
dimensions after the force is removed, the metal is said
to be plastically deformed.
During plastic deformation the metal atoms are permanently displaced from their
original positions and take up new positions.

4. Plastic
Deformation :

5. Plastic Deformation :
The ability of some metals to b extensively plastically deformed without fracture is one
of the most useful engineering properties of metals.
Example; the extensive plastic deformability of steel enables automobile parts to be stamped out mechanically without the metal fracturing.

6. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals lo Ao
Engineering Stress and Engineering Strain
Engineering Stress( σ segma):
Average uniaxial force divided by the original cross-sectional
Area.
Units: U.S system
SI systemm

7. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Engineering Stress and Engineering Strain
Engineering Stress( σ segma):.
Example 1: A 0.5 in diameter aluminum bar is subjected to a force of 2500 lbf. Calculate the engineering stress in pounds per square inch (psi) on the bar.
Example 2: A 1.5 cm diameter bar is subjected to a load of 2500 kg. Calculate the engineering stress in megapascal (MPa) on the bar.

8. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Engineering Stress and Engineering Strain
Engineering Stress( σ segma):. F Δl lo l lo Ao
Δl=l-lo

9. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals F Δl lo l
Stress and Strain in metals
Engineering Stress and Engineering Strain
Engineering Strain ( ε epsilon):
Changes in length of sample divided by the original length of
sample.
Units: U.S system inches per inch (in./in.)
SI system : meters per meter (m/m)
It is common to convert eng. Strain into percent strain or percent elongation:
% engineering strain= eng. Strain *100%=% elongation

10. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Engineering Stress and Engineering Strain
Engineering Strain ( ε epsilon):
In most cases engineering strain is determined by using a small length, usually 2 in.,
called the gage lengthy, within a much longer, for example, 8 In.:
2 in.
2.65 in.
Gage marking
8 in. F
Unstressed
sample
Stressed

11. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Engineering Stress and Engineering Strain
Engineering Strain ( ε epsilon):
Example 3:
A sample of commercially pure aluminum in. wide, in. thick, and 8 in. long
that has gage markings 2.00 in. apart in the middle of the sample is strained so that the
gage marking are 2.65 in. apart (Fig.) . Calculate the engineering strain and the percent
engineering strain that the sample undergoes.
2 in.
2.65 in.
Gage marking
8 in. F
Unstressed
sample
Stressed

12. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Engineering Stress and Engineering Strain
Poisson’s Ratio( ν nu):
A longitudinal elastic deformation of a metal produces an accompanying lateral
dimensional change. A tensile stress segma produces an axial strain and
lateral contraction of and
For ideal material, nu=0.5, for real materials nu = (average 0.3)

13. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Shear Stress and Shear Strain
Shear stress ( τ tau):
Shear force S divided by the area A over which the shear force
acts

14. Mechanical properties of metals Stress and Strain in metals
Engineering Materials
Mechanical properties of metals
Stress and Strain in metals
Shear Stress and Shear Strain
Shear strain ( γ gamma):
Shear displacement (D) divided by the distance (H) over which the shear act;
The relationship between shear stress
and shear strain is
G=elastic modulus