1. MECHANICAL PROPERTIES
Chapter 7:
MECHANICAL PROPERTIES

2. Chapter Outline Terminology for Mechanical Properties
The Tensile Test: Stress-Strain Diagram
Properties Obtained from a Tensile Test
True Stress and True Strain
The Bend Test for Brittle Materials
Hardness of Materials

3. Questions to Think About
• 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?
Ceramic Materials: What special provisions/tests are made for ceramic materials?

4. Stress-Strain Test
specimen
machine

5. Tensile Test

6. Important Mechanical Properties from a Tensile Test
Young's Modulus: This is the slope of the linear portion of the stress-strain curve, it is usually specific to each material; a constant, known value.
Yield Strength: This is the value of stress at the yield point, calculated by plotting young's modulus at a specified percent of offset (usually offset = 0.2%).
Ultimate Tensile Strength: This is the highest value of stress on the stress-strain curve.
Percent Elongation: This is the change in gauge length divided by the original gauge length.

7. Terminology Load - The force applied to a material during testing.
Strain gage or Extensometer - A device used for measuring change in length (strain).
Engineering stress - The applied load, or force, divided by the original cross-sectional area of the material.
Engineering strain - The amount that a material deforms per unit length in a tensile test.

8. Elastic Deformation 1. Initial 2. Small load 3. Unload
Elastic means reversible.

9. Plastic Deformation (Metals)
1. Initial
2. Small load
3. Unload
Plastic means permanent.

10. c07f10ab
Typical stress-strain behavior for a metal showing elastic and plastic deformations, the proportional limit P and the yield strength σy, as determined using the strain offset method (where there is noticeable plastic deformation). P is the gradual elastic to plastic transition.

11. Plastic Deformation (permanent)
From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then reforming bonds with new neighbors.
After removal of the stress, the large number of atoms that have relocated, do not return to original position.
Yield strength is a measure of resistance to plastic deformation.

12. c07f25

13. The image shows necked region in a fractured sample
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Localized deformation of a ductile material during a tensile test produces a necked region.
The image shows necked region in a fractured sample

14. Permanent Deformation
Permanent deformation for metals is accomplished by means of a process called slip, which involves the motion of dislocations.
Most structures are designed to ensure that only elastic deformation results when stress is applied.
A structure that has plastically deformed, or experienced a permanent change in shape, may not be capable of functioning as intended.

15. Yield Strength, sy

16. Stress-Strain Diagram
ultimate
tensile strength 3
necking
Slope=E
Strain
Hardening
yield
strength
Fracture 5 2
Elastic region
slope =Young’s (elastic) modulus
yield strength
Plastic region
ultimate tensile strength
strain hardening
fracture
Plastic
Region
Stress (F/A)
Elastic
Region 4 1
Strain ( ) (DL/Lo)

17. Stress-Strain Diagram (cont)
Elastic Region (Point 1 –2)
- The material will return to its original shape
after the material is unloaded( like a rubber band).
- The stress is linearly proportional to the strain in
this region. or
: Stress(psi)
E : Elastic modulus (Young’s Modulus) (psi)
: Strain (in/in)
Point 2 : Yield Strength : a point where permanent
deformation occurs. ( If it is passed, the material will
no longer return to its original length.)

18. Stress-Strain Diagram (cont)
Strain Hardening
- If the material is loaded again from Point 4, the
curve will follow back to Point 3 with the same
Elastic Modulus (slope).
- The material now has a higher yield strength of
Point 4.
- Raising the yield strength by permanently straining
the material is called Strain Hardening.

19. Stress-Strain Diagram (cont)
Tensile Strength (Point 3)
- The largest value of stress on the diagram is called
Tensile Strength(TS) or Ultimate Tensile Strength
(UTS)
- It is the maximum stress which the material can
support without breaking.
Fracture (Point 5)
- If the material is stretched beyond Point 3, the stress
decreases as necking and non-uniform deformation
occur.
- Fracture will finally occur at Point 5.

20. The stress-strain curve for an aluminum alloy.
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

21. Stress-strain behavior found for some steels with yield point phenomenon.

22. T E N S I L P R O
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23. Yield Strength: Comparison
Room T values
a = annealed
hr = hot rolled
ag = aged
cd = cold drawn
cw = cold worked
qt = quenched & tempered

24. Tensile Strength, TS
After yielding, the stress necessary to continue plastic deformation in metals increases to a maximum point (M) and then decreases to the eventual fracture point (F).
All deformation up to the maximum stress is uniform throughout the tensile sample.
However, at max stress, a small constriction or neck begins to form.
Subsequent deformation will be confined to this neck area.
Fracture strength corresponds to the stress at fracture.
Region between M and F:
Metals: occurs when noticeable necking starts.
• Ceramics: occurs when crack propagation starts.
• Polymers: occurs when polymer backbones are aligned and about to break.

25. In an undeformed thermoplastic polymer tensile sample,
the polymer chains are randomly oriented.
When a stress is applied, a neck develops as chains become aligned locally. The neck continues to grow until the chains in the entire gage length have aligned.
The strength of the polymer is increased

26. Tensile Strength: Comparison
Room T 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.

27. Engineering Stress • Tensile stress, s: • Shear stress, t:
Stress has units: N/m2 or lb/in2 27

28. VMSE http://www.wiley.com/college/callister/0470125373/vmse/index.htm

29. Tensile Testing of Aluminum Alloy
Example 1
Tensile Testing of Aluminum Alloy
Convert the change in length data in the table to engineering stress and strain and plot a stress-strain curve.

30. Example 1 SOLUTION

31. Ductility, %EL
Ductility is a measure of the plastic deformation that has been sustained at fracture:
A material that suffers very little plastic deformation is brittle.
• Another ductility measure:
• Ductility may be expressed as either percent elongation (% plastic strain at fracture) or percent reduction in area.
%AR > %EL is possible if internal voids form in neck.

32. Toughness
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Toughness is the ability to absorb energy up to fracture (energy per unit volume of material).
A “tough” material has strength and ductility.
Approximated by the area under the stress-strain
curve.
Lower toughness: ceramics
Higher toughness: metals

33. Toughness • Energy to break a unit volume of material
• Approximate by the area under the stress-strain
curve. 21

34. Linear Elastic Properties
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Linear Elastic Properties
s = E e
• Hooke's Law:
n = ex/ey
• Poisson's ratio:
metals: n ~ 0.33
ceramics: n ~0.25
polymers: n ~0.40
Modulus of Elasticity, E:
(Young's modulus)
Units:
E: [GPa] or [psi]
n: dimensionless

35. c07prob
Engineering Strain
Strain is dimensionless. 35

36. c07f09
Axial (z) elongation (positive strain) and lateral (x and y) contractions (negative strains) in response to an imposed tensile stress. 36

37. True Stress and True Strain
True stress The load divided by the actual cross-sectional area of the specimen at that load.
True strain The strain calculated using actual and not original dimensions, given by εt ln(l/l0).
The relation between the true stress-true strain diagram and engineering stress-engineering strain diagram.
The curves are identical to the yield point.

38. Stress-Strain Results for Steel Sample

39. Example 2: Young’s Modulus - Aluminum Alloy
From the data in Example 1, calculate the modulus of elasticity of the aluminum alloy.

40. Example 2: Young’s Modulus - Aluminum Alloy - continued
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.

41. Young’s Moduli: Comparison
Graphite
Ceramics
Semicond
Metals
Alloys
Composites
/fibers
Polymers
E(GPa)
Composite data based on
reinforced epoxy with 60 vol%
of aligned carbon (CFRE),
aramid (AFRE), or glass (GFRE)
fibers.

42. Example 3: True Stress and True Strain Calculation
Compare engineering stress and strain with true stress and strain for the aluminum alloy in Example 1 at (a) the maximum load. The diameter at maximum load is in. and at fracture is in.
Example 3 SOLUTION

43. c07f17
Strain Hardening
An increase in sy due to plastic deformation.

44. Strain Hardening (n, K or C values)

45. c07f12

46. c07f33

47. Mechanical Behavior - Ceramics
The stress-strain behavior of brittle ceramics is not usually obtained by a tensile test.
It is difficult to prepare and test specimens with specific geometry.
It is difficult to grip brittle materials without fracturing them.
Ceramics fail after roughly 0.1% strain; specimen have to be perfectly aligned.

48. The Bend Test for Brittle Materials
Bend test - Application of a force to the center of a bar that is supported on each end to determine the resistance of the material to a static or slowly applied load.
Flexural strength or modulus of rupture -The stress required to fracture a specimen in a bend test.
Flexural modulus - The modulus of elasticity calculated from the results of a bend test, giving the slope of the stress-deflection curve.

49. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
The stress-strain behavior of brittle materials compared with that of more ductile materials

50. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
(a) The bend test often used for measuring the strength of brittle materials, and (b) the deflection δ obtained by bending

51. Flexural Strength c07f18 Schematic for a 3-point bending test.
Able to measure the stress-strain behavior and flexural strength of brittle ceramics.
Flexural strength (modulus of rupture or bend strength) is the stress at fracture.
See Table 7.2 for more values.

52. MEASURING ELASTIC MODULUS
• Room T behavior is usually elastic, with brittle failure.
• 3-Point Bend Testing often used.
--tensile tests are difficult for brittle materials.
• Determine elastic modulus according to: 23

53. MEASURING STRENGTH • 3-point bend test to measure room T strength.
• Flexural strength:
• Typ. values:
Si nitride
Si carbide
Al oxide
glass (soda) 69
300
430
390 69
Data from Table 12.5, Callister 6e. 24

54. Stress-Strain Behavior: Elastomers
3 different responses:
A – brittle failure
B – plastic failure
C - highly elastic (elastomer)
--brittle response (aligned chain, cross linked & networked case)
--plastic response (semi-crystalline case)

55. Hardness of Materials
Hardness test - Measures the resistance of a material to penetration by a sharp object.
Macrohardness - Overall bulk hardness of materials measured using loads >2 N.
Microhardness Hardness of materials typically measured using loads less than 2 N using such test as Knoop (HK).
Nano-hardness - Hardness of materials measured at 1–10 nm length scale using extremely small (~100 µN) forces.

56. Hardness
Hardness is a measure of a material’s resistance to localized plastic deformation (a small dent or scratch).
Quantitative hardness techniques have been developed where a small indenter is forced into the surface of a material.
The depth or size of the indentation is measured, and corresponds to a hardness number.
The softer the material, the larger and deeper the indentation (and lower hardness number).

57. Hardness • Resistance to permanently indenting the surface.
• Large hardness means:
--resistance to plastic deformation or cracking in
compression.
--better wear properties.
Adapted from Fig. 6.18, Callister 6e. (Fig is adapted from G.F. Kinney, Engineering Properties and Applications of Plastics, p. 202, John Wiley and Sons, 1957.)

58. Hardness Testers

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60. Conversion of Hardness Scales
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Conversion of Hardness Scales
Also see: ASTM E
Volume 03.01
Standard Hardness Conversion Tables for Metals Relationship Among Brinell Hardness, Vickers Hardness, Rockwell Hardness, Superficial Hardness, Knoop Hardness, and Scleroscope Hardness

61. Correlation between Hardness and Tensile Strength
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Correlation between Hardness and Tensile Strength
Both hardness and tensile strength are indicators of a metal’s resistance to plastic deformation.
For cast iron, steel and brass, the two are roughly proportional.
Tensile strength (psi) = 500*BHR

63. 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 sy.
• Toughness: The energy needed to break a unit
volume of material.
• Ductility: The plastic strain at failure.