1. Mechanical Properties Of Metals - I
6-1

2. Calculate the percent cold reduction after cold rolling 0
Calculate the percent cold reduction after cold rolling in-thick aluminum sheet to in.
Solution:

3. Stress and Strain in Metals
Metals undergo deformation under uniaxial tensile force.
Elastic deformation: Metal
returns to its original
dimension after tensile
force is removed.
Plastic deformation: The
metal is deformed to
such an extent such
that it cannot return
to its original dimension
6-10

4. Engineering Stress and Strain
F (Average uniaxial tensile force)
Engineering stress = σ =
A0 (Original cross-sectional area)
Engineering stress σ = F
Units of Stress are PSI or N/M2 (Pascals) Δl A0
1 PSI = 6.89 x 103 Pa
Change in length
Engineering strain = ε =
Original length A
Units of strain are in/in or m/m. F
6-11

5. Calculate the engineering stress in SI units on a 2
Calculate the engineering stress in SI units on a 2.00-cm-diameter rod that is subjected to a load of 1300 kg.

6. Mechanical Properties
Modulus of elasticity (E) : Stress and strain are linearly related in elastic region. (Hooks law)
Higher the bonding strength,
higher is the modulus of elasticity.
Examples: Modulus of Elasticity of steel is 207 Gpa.
Modulus of elasticity of Aluminum is 76 Gpa
σ (Stress) Δσ
E =
E =
Strain Δε
ε (Strain) Δσ Δε
Stress
Linear portion of the
stress strain curve
6-17

7. Yield Strength Yield strength is strength at which
metal or alloy show significant
amount of plastic deformation.
0.2% offset yield strength is that
strength at which 0.2% plastic
deformation takes place.
Construction line, starting at 0.2%
strain and parallel to elastic region
is drawn to fiend 0.2% offset yield
strength.
Figure 5.23
6-18

8. Ultimate tensile strength
Ultimate tensile strength (UTS) is the maximum strength reached by the engineering stress strain curve.
Necking starts after UTS is reached.
More ductile the metal is, more
is the necking before failure.
Stress increases till failure. Drop
in stress strain curve is due to stress
calculation based on original area.
Al 2024-Tempered S T R E
Mpa
Necking Point
Al 2024-Annealed
Strain
Stress strain curves of
Al 2024 With two different
heat treatments. Ductile
annealed sample necks more
6-19

9. Tensile Strength
Figure 7.11 Typical engineering stress-strain behavior to fracture, point F. The tensile strength is indicated at point M.
Very familiar property and widely used for identification of a material. It is used for the purposes of specifications and for quality control of a product.

10. Ductility
It is a measure of the degree of plastic deformation that has been sustained at fracture.
A material that experiences very little or no plastic deformation upon fracture is termed brittle.
Figure 7.13 Schematic representations of tensile stress-strain behavior for brittle and ductile materials loaded to fracture.

11. Percent Elongation
Percent elongation is a measure of ductility of a material.
It is the elongation of the metal before fracture expressed as percentage of original length.
% Elongation =
Measured using a caliper fitting the fractured metal together.
Example:- Percent elongation of pure aluminum is 35%
For 7076-T6 aluminum alloy it is 11%
Final length – initial Length
Initial Length
6-20

12. Percent Reduction in Area
Percent reduction area is also a measure of ductility.
The diameter of fractured
end of specimen is meas-
ured using caliper.
Percent reduction in area
in metals decreases in case
of presence of porosity.
% Reduction
Area
Initial area – Final area =
Final area
Stress-strain curves of different metals
6-21

13. True Stress – True Strain
True stress and true strain are based upon instantaneous cross-sectional area and length.
True Stress = σt =
True Strain = εt = F
Ai (instantaneous area)
6-22

14. Hardness and Hardness Testing
Hardness is a measure of the resistance of a metal to permanent (plastic) deformation.
General procedure:
Press the indenter that
is harder than the metal
Into metal surface.
Withdraw the indenter
Measure hardness by
measuring depth or
width of indentation.
Rockwell hardness
tester
Figure 5.27
6-27

15. Hardness Tests
Table 5.2
6-28

16. Tensile Testing of Aluminum Alloy
Example 1:
Tensile Testing of Aluminum Alloy
Convert the change in length data in Table 6-1 to engineering stress and strain and plot a stress-strain curve.

17. Example 1: SOLUTION

18. Young’s Modulus of Aluminum Alloy
Example 2 :
Young’s Modulus of Aluminum Alloy
From the data in Example 1, calculate the modulus of elasticity of the aluminum alloy. Use the modulus to determine the length after deformation of a bar of initial length of 50 in. Assume that a level of stress of 30,000 psi is applied.
Example :SOLUTION

19. Ductility of an Aluminum Alloy
Example 3 :
Ductility of an Aluminum Alloy
The aluminum alloy in Example 1 has a final length after failure of in. and a final diameter of in. at the fractured surface. Calculate the ductility of this alloy.
Example 3 :SOLUTION

20. True Stress and True Strain Calculation
Example 4:
True Stress and True Strain Calculation
Compare engineering stress and strain with true stress and strain for the aluminum alloy in Example 6.1 at (a) the maximum load and (b) fracture. The diameter at maximum load is in. and at fracture is in.
Example 4: SOLUTION

21. Example 4 : SOLUTION (Continued)

22. Example Problem 5
A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile tested to fracture and found to have an engineering fracture strength (σf) of 460 MPa. If its cross-sectional diameter at fracture is 10.7 mm, determine:
(a) The ductility in terms of percent reduction in area
(b) The true stress at fracture