1. CHAPTER 6: MECHANICAL PROPERTIES
ISSUES TO ADDRESS...
• Stress and strain: What are they and why are
they used instead of load and deformation?
• Elastic behavior: When loads are small, how much
deformation occurs? What materials deform least?
• Plastic behavior: At what point do dislocations
cause permanent deformation? What materials are
most resistant to permanent deformation?
• Toughness and ductility: What are they and how
do we measure them? 1

2. Chapter 6: Mechanical Properties of Metals 6.1 Introduction
Why Study the Mechanical Properties of Metals ?
It is important for engineers to understand
How the various mechanical properties are measured, and
What these properties represent
The role of structural engineers is to determine stresses and stress distributions within members that are subjected to well-defined loads
By experimental testing
Theoretical and mathematical stress analysis.
Design structures/components using predetermined materials such that unacceptable levels of deformation and/or failure will not occur.

3. 6.2 Concepts of Stress and Strain
Static load  changes relatively slowly with time
Applied uniformly over a cross-section or surface of a member.
Tension
Compression
Shear
Torsion

4. 6.2 Concepts of Stress and Strain (Contd.)
TENSION TEST
Most common mechanical stress-strain test
Used to ascertain several mechanical properties that are important in design
A specimen is deformed, usually to fracture, with a gradually increasing tensile load that is applied uniaxially along the long axis of the specimen.
A standard specimen is shown in Figure 6-2.

5. 6.2 Concepts of Stress and Strain (Contd.)
The specimen is mounted by its ends into the holding grips of the testing apparatus (Figure 6-3).
Tensile testing machine
To elongate the specimen at a constant rate
To continuously and simultaneously measure the instantaneous load and the resulting extension
Load using load cell
Extension using extensometer
Takes few minutes and is destructive.

6. 6.2 Concepts of Stress and Strain (Contd.)
Engineering Stress (s) = Instantaneous applied load (F) / Original Area (Ao)
Unit: MPa, GPa, psi
Engineering strain (e)
li = instantaneous length
lo = original length
COMPRESSION TESTS
Similar to tensile test, compressive load
Sign convention, compressive force is taken negative  stress negative
Since lo > li , negative strain

7. 6.2 Concepts of Stress and Strain (Contd.)
SHEAR AND TORSIONAL TESTS
Shear stress : t = F / Ao
F: Load or force imposed parallel to the upper and lower faces
Ao: shear or parallel area
Shear strain (g) is defined as the tangent of the strain angle q.

8. 6.2 Concepts of Stress and Strain (Contd.)
GEOMETRIC CONSIDERATIONS OF THE STRESS STATE
Stress is a function of orientations of the planes

9. Elastic means reversible!
ELASTIC DEFORMATION
1. Initial
2. Small load
3. Unload
Elastic means reversible! 2

10. ELASTIC DEFORMATION 6.3 Stress-Strain Behavior
Non-permanent, completely reversible, conservative
Follow same loading and unloading path
Linear elastic deformation
Hooke’s Law
Modulus of elasticity or Young’s Modulus  stiffness or a material’s resistance to elastic deformation

11. 6.3 Stress-Strain Behavior (Contd.)

12. Nonlinear Elastic Behavior
Gray cast iron, concrete, many polymers
Not possible to determine a modulus of elasticity
Either tangent or secant modulus is normally used.

13. 6.3 Stress-Strain Behavior (Contd.)
On an atomic scale, macroscopic elastic strain is manifested as small changes in the interatomic spacing and the stretching of interatomic bonds.
 E is a measure of the resistance to separation of adjacent atoms
Modulus is proportional to the slope of the interatomic force-separation curve (Fig 2.8a) at equilibrium spacing

14. 6.3 Stress-Strain Behavior (Contd.)
With increasing temperature, the modulus of elasticity diminishes
Shear stress and strain are proportional to each other:
Shear modulus or modulus of rigidity ( Table 6.1)

15. 6.4 Anelasticity Up to this point, it is assumed that
Elastic deformation is time-independent
An applied stress produces an instantaneous elastic strain
Strain remains constant over the period of time the stress is maintained
Upon release of the load, strain is totally recovered (immediately returns to zero)
In most engineering materials, there will also exist a time-dependent elastic strain component , i.e.
elastic deformation will continue after stress application
Upon load release some finite time is required for complete recovery
Loading and unloading path are different
Anelasticity : time-dependent elastic behavior
For metals, the anelastic component is normally small and neglected.
For some polymers, it is significant and known as viscoelastic behavior (Sec. 16.7)

16. 6.5 Elastic Properties of Materials
Poisson’s ratio
E = 2G(1 + n)
Example 6.1
Example 6.2

17. Stress not proportional to strain (Hooke’s law cease to be valid)
PLASTIC DEFORMATION
For most metals, elastic deformation persists only to strains of about 0.005
Plastic deformation
Stress not proportional to strain (Hooke’s law cease to be valid)
Permanent
Nonrecoverable
Non-conservative
Transition from elastic to plastic deformation
Gradual for most metals
Some curvature results at the onset of plastic deformation

18. PLASTIC DEFORMATION (METALS)
1. Initial
2. Small load
3. Unload
Plastic means permanent! 3

19. PLASTIC (PERMANENT) DEFORMATION
(at lower temperatures, T < Tmelt/3)
• Simple tension test: 14

20. Plastic deformation (Contd.)
From as atomic perspective
Plastic deformation corresponds to the breaking of bonds with original atom neighbors
Reforming bonds with new neighbors
Large number of atoms and molecules move relative to one another
Upon removal of stress, they do not return to their original position
Mechanism of plastic deformation:
Crystalline Solids:
accomplished by a process called slip
Involves the motion of dislocations (Sec 7.2)
Non-crystalline solids (as well liquids)
Occurs by a viscous flow mechanism (Sec 13.9)

21. • Stress at which noticeable plastic deformation has occurred.
YIELD STRENGTH, sy
• Stress at which noticeable plastic deformation has
occurred.
when ep = 0.002 15

22. 6.6 Tensile Properties
YIELDING and YIELD STRESS
Typical stress strain behavior (Figure)
Proportional Limit (P)
Yielding
Yield strength
In most cases, the position of yield point may not be determined precisely.
Established convention: a straight line is constructed parallel to the elastic portion at some specified strain offset, usually (0.2%) Fig. 6.10a  corresponding intersection point gives yield strength.

23. 6.6 Tensile Properties (Contd.)
Some steels and other materials exhibit the behavior as shown in Fig 6.10b
The yield strength is taken as the average stress that is associate with the lower yield point.
Magnitude of yield strength is a measure of its resistance to plastic deformation
Range from 35 MPa to 1400 MPa
35 MPa for low-strength aluminum
1400 MPa for high-strength steel

24. 6.6 Tensile Properties (Contd.)
TENSILE STRENGTH
Tensile strength TS (MPa or psi) is the stress at the maximum on the engineering stress-strain curve
All deformation up to this point is uniform.
Onset of necking at this stress at some point  all subsequent deformation at this neck.
Range: MPa
50 MPa for aluminum
3000 MPa for high strength steel

25. • Plastic tensile strain at failure:
DUCTILITY, %EL
• Plastic tensile strain at failure:
Adapted from Fig. 6.13, Callister 6e.
• Another ductility measure:
• Note: %AR and %EL are often comparable.
--Reason: crystal slip does not change material volume.
--%AR > %EL possible if internal voids form in neck. 19

27. Effect of Temperature
As with modulus of elasticity (E), the magnitudes of both yield and tensile strengths decline with increasing temperature
Ductility usually increases with temperature
Figure shown stress-strain behavior of iron

28. RESILIENCE
Resilience is the capacity of a material to absorb energy when it is deformed elastically and then, upon unloading, to have this energy recovered.
Modulus of resilience (Ur)
Associated property
Area under the engineering stress-strain curve
Strain energy per unit volume required to stress from an unloaded state to yielding
Mathematically,

29. • Energy to break a unit volume of material
TOUGHNESS
• Energy to break a unit volume of material
• Approximate by the area under the stress-strain
curve. 20

30. TOUGHNESS
A measure of the ability of a material to absorb energy up to fracture.
Specimen geometry and the manner of load application are important in toughness determination:
Notch toughness: dynamic (high strain rate) loading, specimen with notch (or point of stress concentration) (Sec 8.6)
Fracture toughness: property indicative of a materials resistance to fracture when crack is present (Sec 8.5)
For static (low strain rate) condition, modulus of toughness is equal to the total area under the stress-strain curve (up to fracture ):
For Ductile Material : For Brittle Material:

31. 6.7 True Stress and Strain
Engineering stress-strain curve beyond maximum point (M) seems to indicate that the material is becoming weaker.
Not true, rather it becomes stronger.
Since cross-sectional area is decreasing at the neck  reduces load bearing capacity of the material
True stress: Actual or current or instantaneous force divided by the instantaneous cross-sectional area.
True Strain: Change in length per unit instantaneous length

32. 6.7 True Stress and Strain (Contd.)
Relation between two definitions
Above equations are valid only to the onset of necking; beyond this point true stress and strain should be computed from actual load, area and gauge length.
Schematic comparison in Figure 6.16
Corrected takes into account complex stress state with in neck region.

33. 6.7 True Stress and Strain (Contd.)
For some metals and alloys, the true stress-strain curve is approximated as
Parameter n
strain-hardening exponent
A value less than unity
Slope on log-log plot
Parameter K
Known as strength coefficient
True stress at unit true strain

35. 6.8 Elastic Recovery During Plastic Deformation
Upon release of load, some fraction of total strain is recovered as elastic strain
During unloading, straight path parallel to elastic loading
Reloading
Yielding at new yield strength

36. Solve Examples in Class
6.3
6.4
6.5
6.6
Design Example 6.1