1. Poisons Ratio Poisons ratio = . w0 w Usually poisons ratio ranges from
υ ( nu)
Poisons ratio = . w0 w
Usually poisons ratio ranges from
0.25 to 0.4.
Example: Stainless steel
Copper
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 1 1

2. Table 6.1

3. Mechanical Property obtained from the Engineering Tensile Test
Modulus of elasticity
Yield strength at 0.2 percent offset
Ultimate tensile strength
Percent elongation at fracture
Percent reduction in area at fracture

4. Physical Properties Stiffness - a measure of the resistance
offered by an elastic body to elastic
deformation
Elastic – determine how much a material will
compress under a given amount of pressure
without undergoing deformation
Strength – is the ability to withstand an applied
stress without failure
Toughness - used to describe combination
of strong and ductile

5. Malleable - a material that can be Straighten without fructure
Ductility - a measure of degree of plastic deformation that has been
sustained at fracture
Malleable - a material that can be
Straighten without fructure
Strain – the amount of deformation
Brittle – a material that experience very little or no plastic deformation upon fracture

6. Sample Problem
6.25. The following engineering stress-strain data were obtained for a 0.2% C plain-carbon steel (a) Plot the engineering stress-strain curve. (b) Determine the tensile elastic modulus of this steel (c ) Elastic limit (d ) Determine the 0.2 percent offset yield strength for this steel (e) Ultimate tensile strength of the alloy (c) Determine the percent elongation at fracture

7. Stress
Strain 30
0.001 55
0.002 60
0.005 68
0.01 72
0.02 74
0.04 75
0.06 76
0.08
0.1 73
0.12 69
0.14 65
0.16 56
0.18 51
0.19

8. Stress and Strain in metals
Engineering Stress-Strain Diagram
Experimental plot of engineering stress (σ)
Versus
Engineering strain (ε);
σ is normally plotted as the y axis and ε as the x axis.

9. Mechanical properties of metals
Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram
1. Modulus of Elasticity (E)
The linear elastic region (OP): linear means that the relationship between stress and strain obeys the uniaxial Hook’s law.
σ=E ε
E (modulus of elasticity)
can be determine by measuring
the slope of the curve in this
region.
E= σ/ε
Units of psi or Pa

10. Higher the bonding strength, higher is the modulus of elasticity.
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 10 10

12. Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram
2. The Elastic Limit (E)
Upon continued loading past point P, a transition to a new region takes place. In this region (PE), the relationship between stress and strain is no longer linear but the behavior is still elastic.
Point E called the elastic limit. Up to point E, if one removes the load, the specimen will regain its original shape and dimensions.

13. 3. Yield Strength (point) (Y)
Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram
3. Yield Strength (point) (Y)
With additional loading applied to the specimen, past point E,
the material reaches the yield point (Y). The deformation experienced by the material past point Y is permanent and is called plastic deformation.

14. 3. Yield Strength (point) (Y)
Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram
3. Yield Strength (point) (Y)
The stress at which yield occurs, is called the yield strength of the material.
In order to have a unified standard, the 0.2 % offset yield strength is used. Engineers often design various components to protect against yield.
Calculation method of the yield strength

15. 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. 15 15

16. 4. Ultimate Tensile strength (UTS)
Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram
4. Ultimate Tensile strength (UTS)
With continued loading past the yield point (Y), the specimen undergoes severe plastic deformation.
Although the specimen becomes longer and thinner in this region, it retains its cylindrical shape up to point U.
The stress corresponding to point U is called ultimate strength of the metal. It represents the largest stress or the peak point in the stress-strain diagram.

17. 4. Ultimate Tensile strength (UTS)
Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram
4. Ultimate Tensile strength (UTS)
In region YU, as the metal plastically deforms, it becomes stronger, i.e, one needs to apply larger loads to cause the same level of deformation. This phenomenon is called strain hardening).
Also in this region (YU), as the length increases, the cross-sectional area of the specimen becomes smaller. This is called Poissons effect.

18. 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. 18 18

19. Tensile Test (Cont) Commonly used Test specimen Typical Stress-strain
curve 19 19

20. Mechanical property data obtained from Tensile test and the Engineering Stress-Strain Diagram
Necking
This is the point at which the specimen undergoes extensive necking; where the diameter drops sharply in an unstable manner. Necking occurs at point U.

21. Mechanical properties of metals Stress and Strain in metals

22. Mechanical property data obtained from Tensile test
and the Engineering Stress-Strain Diagram
5. Percent Elongation
The amount of elongation that a tensile specimen undergoes
during testing provides a value for the ductility of a metal.
Ductility of metals is most commonly expressed as percent
elongation.
Percent elongation is a measure of the ductility of the metal and is also an index of quality of the metal.

23. Mechanical property data obtained from Tensile test
and the Engineering Stress-Strain Diagram
6. Percent reduction in area
The ductility of a metal or alloy can also be expressed in terms
of the percent reduction in area.
Percent reduction in area is a measure of the ductility of the metal and is also
an index of quality.

24. 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.
Initial area – Final area
% Reduction
Area =
Final area
Stress-strain curves of different metals 24 24

25. Seatwork : Mechanical Properties of Metal
The following engineering stress-strain data were obtained at the beginning of a tensile test for a 0.2% C plain-carbon steel. (a) Plot the engineering stress-strain curve for these data. (b) Determine the modulus of elasticity of this steel (c) Determine the 0.2 percent offset yield strength for this steel (d ) Elastic limit (e) Ultimate tensile strength

26. Problems 1
A cylindrical aluminum specimen of diameter 1.28 cm and length 10 cm is loaded in tension to 10,000N. The yield strength of the metal is given to be 250 MPa and the modulus of elasticity is given to be 70 GPa. Under the action of this force, compute for the stress and the strain in the specimen.

27. Problems 2
A cylinder metal specimen 15.0 mm in diameter and 150 mm long is to be subjected to a tensile stress of 50 MPa; at this stress level the resulting deformation will be totally elastic. If the elongation must be less than mm, which of the metals in the Table 6.1 below are suitable candidates ? Why ?