1. Introduction to Materials Science and Engineering
Chapter 6: Mechanical Properties of Metals
Textbook: Chapter 8

2. Content Introduction Stress and Strain Elastic Deformation
Plastic Deformation
Toughness and Hardness
Summary

3. 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 does permanent deformation occur? What materials are most resistant to permanent deformation?
Toughness and Ductility: What are they and how
do we measure them?

4. Technological Significance:
Aircraft, such as the one shown here, makes use of aluminum alloys and carbon-fiber reinforced composites. (Courtesy of Getty Images.)
The materials used in sports equipment must be lightweight, stiff, tough, and impact resistant. (Courtesy of Getty Images.)

5. History of Strength Test:
(a)
(b)
(c)
(a) Tensile Test of Wire by Leonardo da Vinci
(b) Galileo’s Illustration of Bending Test
(c) Galileo’s Illustration of Tensile Test

6. 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.

7. Content Introduction Stress and Strain Elastic Deformation
Plastic Deformation
Toughness and Hardness
Summary

8. Tensile Test:
Measures the resistance of a material to a static or slowly applied force.
As the force is applied the metal deforms (elongated).
• Typical tensile specimen

9. Engineering Stress: (Force divided by the original area A0)
• Tensile stress, σ:
• Shear stress, τ:
Stress has units:
N/m2 or lb/in2

10. Engineering Strain: • Tensile Strain (e): • Lateral strain:
• Shear Strain (g):
Strain is always
dimensionless.

11. Schematic Illustration of Different Stress State

12. Schematic Representation of Normal and Tensile Stresses

13. Content Introduction Stress and Strain Elastic Deformation
Plastic Deformation
Toughness and Hardness
Summary

14. Linear Elastic Properties:
• Modulus of Elasticity, E:
(also known as Young's modulus)
• Hooke's Law:
• Poisson's Ratio, ν:
Metals: ν ~ 0.33
Ceramics: ~0.25
Polymers: ~0.40
Units:
E: [GPa] or [psi]
n: Dimensionless

15. Elastic Properties:
Schematic stress-strain diagram showing linear elastic deformation for loading and unloading cycles.
Schematic stress-strain diagram showing nonlinear elastic deformation, and how secant and tangent moduli are determined.

16. Properties from Bonding : E
Elastic (Young’s) Modulus, E (Y)
E ~ Curvature at ro (The Bottom of The Well)
E is larger
if Eo is larger

17. Force versus Interatomic Separation:

18. 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)

19. Other Elastic Properties:
• Elastic Shear
Modulus, G:
Simple torsion
test
• Elastic Bulk
Modulus, K:
Pressure test:
Initial vol =Vo.
Vol change = DV
• Special Relations for Isotropic Materials:

20. Bulk Modulus

21. Elastic Modulus

22. Content Introduction Stress and Strain Elastic Deformation
Plastic Deformation
Toughness and Hardness
Summary

23. Stress at which noticeable plastic deformation has occurred.
Yield Strength, σy
Stress at which noticeable plastic deformation has occurred.

24. Yield Strength Comparison:

25. Tensile Strength, TS:
• Maximum Possible Engineering Stress in Tension.
Adapted from Fig. 6.11, Callister 6e.
• Metals: Occurs when noticeable necking starts.
• Ceramics: Occurs when crack propagation starts.
• Polymers: Occurs when polymer backbones are
aligned and about to break.

26. Plastic Deformation
Necking starts to form
Cup and cone failure

27. Tensile Test: 1. Modulus of Elasticity, E 2. Yield Strength, Y.S.
3. Tensile Strength, T.S.
4. Ductility, 100 x  failure
5. Toughness

28. Tensile Strength Comparison
Room Temp. Values
Based on data in Table B4,
Callister 6e.
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered
AFRE, GFRE, & CFRE =
aramid, glass, & carbon
fiber-reinforced epoxy
composites, with 60 vol%
fibers.

29. True Stress and True Strain
True Stress : σt
True Strain : εt
If no volume change occurs during deformation, namely,

30. Comparison of Engineering and True Stress-Strain Curves

31. Comparison of Engineering and True Stress-Strain Curves

32. Temperature Effect

33. Testing of Ceramics
- Four Point Bend Test

34. Bend Test
Flexile Strength
(Modulus of Rupture)
Flexile Modulus

35. Testing of Polymers Polyester Nylon66 Semicrystalline Thermoplastic
Spherulite
Polyester
Nylon66

36. Plastic Deformation of Polymers

37. 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.

38. Content Introduction Stress and Strain Elastic Deformation
Plastic Deformation
Toughness and Hardness
Summary

39. Toughness • Energy to break a unit volume of material.
• Approximate by the area under the stress-strain curve.

40. Hardness A measure of a material’s resistance Test
to plastic deformation.
Test
- A hard indenter is pressed into the specimen. Standard load applied.
Magnitude of indentation is measured: Area of Indentation, or Depth of Indentation.

41. Hardness Resistance to Permanently Indenting the Surface
A Measure of a Material’s Resistance to Localized Plastic Deformation
Large hardness means:
Better Resistance to Plastic Deformation or Cracking in Compression
Better Wear Properties
Indentation/indentor; Mohs scale, BHN, etc.

42. Rockwell Hardness Test
Rockwell Hardness Tester

43. Hardness Measurement

44. ) Hardness • An Increase in σy due to Plastic Deformation.
• Curve Fit to the Stress-Strain Response:
Hardening Exponent: ) n n=
0.15
(Some Steels) σ = C ε T T
to n=
0.5
(Some Copper)
True Stress (F/A)
True Strain: ln(l/l0)

45. Hardness Measurement

46. Hardness vs. Tensile Properties

47. Design or Safety Factors
• Design uncertainties mean we do not push the limit.
• Factor of Safety, N
Often N is between
1.2 and 4
• Ex: Calculate a diameter, d, to ensure that yield does
not occur in the 1045 carbon steel rod below. Use a
factor of safety of 5.
1045 plain s y
=310MPa
TS=565MPa
F = 220,000N d L o
carbon steel: 5

48. Strength vs. Density

49. Summary
• Stress and Strain: These are size-independent measures of load and displacement, respectively.
• Elastic Behavior: This reversible behavior often shows a linear relation between stress and strain.
To minimize deformation, select a material with a large elastic modulus (E or G).
• Plastic Behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches σy.
• Toughness: The energy needed to break a unit volume of material.
• Ductility: The plastic strain at failure.