1. Mechanical Properties
• 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?
• Hardness: What is hardness of a material and how do we measure it?

2. How materials deform as a function of applied load 
Testing methods and language for mechanical properties of materials.
Stress,  (MPa)
Strain,  (mm / mm)

3. Elastic Deformation d F F d 1. Initial 2. Small load 3. Unload
bonds
stretch
return to
initial F d
Linear-
elastic
Non-Linear-
Elastic means reversible!

4. Plastic Deformation (Metals)
1. Initial
2. Small load
3. Unload p
lanes
still
sheared F d
elastic + plastic
bonds
stretch
& planes
shear
plastic F d
linear
elastic
plastic
Plastic means permanent!

5. Tensile – applied loads “pull” the sample
Forces and Responses
Tensile – applied loads “pull” the sample

6. Linear Elastic Properties
• Modulus of Elasticity, E:
(also known as Young's modulus) F
simple
tension
test
• Hooke's Law:
s = E e s
Linear-
elastic E e

7. Tensile Forces Gripping Zone Gripping Zone Failure Zone ¾ inch ½ inch
8 ½ inches

8. Forces and Responses
Compression: applied loads “squeeze” the sample

9. Mechanical Properties
Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal
Adapted from Fig. 6.7,
Callister 7e.

10. Other Elastic Properties
• Elastic Shear
modulus, G: t G g
t = G g
• Special relation for isotropic materials:
2(1 + n) E G =

11. Poisson's ratio, n e n = - eL e - n • Poisson's ratio, n: Units:
metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40 eL e - n
Units:
E: [GPa] or [psi]
n: dimensionless

12. Plastic Deformation

13. (Ultimate) Tensile Strength, TS
• Maximum stress on engineering stress-strain curve. y
strain
Typical response of a metal
F = fracture or
ultimate
strength
Neck – acts as stress concentrator
engineering TS
stress
engineering strain
Adapted from Fig. 6.11, Callister 7e.

14. Ductility
Measures how much the material can be stretched before fracture
High ductility: platinum, steel, copper
Good ductility: aluminum
Low ductility (brittle): chalk, glass, graphite

15. Ductility (%EL and %RA)
• Plastic tensile strain at failure:
Adapted from Fig. 6.13, Callister 7e.

16. Toughness • The ability to absorb energy up to fracture =
the total area under the strain-stress curve up to fracture
Units: the energy per unit volume, e.g. J/m3
very small toughness
(unreinforced polymers)
Engineering tensile strain, e E
ngineering
tensile
stress, s
small toughness (ceramics)
large toughness (metals)
Adapted from Fig. 6.13, Callister 7e.
Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy

17. Toughness Impact (toughness) – applied loads “hit” the sample
Impact (charpy, dart)

18. Resilience, Ur 2 1 U e s @ Ability of a material to store energy
Energy stored best in elastic region
If we assume a linear stress-strain curve this simplifies to y r 2 1 U e s @
Adapted from Fig. 6.15, Callister 7e.

19. True Stress & Strain True stress True Strain
Adapted from Fig. 6.16, Callister 7e.

20. Elastic Solid Stress-strain What happens when force is removed?
Recovery

21. Elastic Strain Recovery
Adapted from Fig. 6.17, Callister 7e.

22. ( ) Hardening s e • An increase in sy due to plastic deformation.
large hardening
small hardening y 1
• Curve fit to the stress-strain response: s T = K e ( ) n
“true” stress (F/A)
“true” strain: ln(L/Lo)
hardening exponent:
n =
0.15 (some steels)
to n =
0.5 (some coppers)

23. 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)

24. Hardness • Resistance to permanently indenting the surface.
• Large hardness means:
--resistance to plastic deformation or cracking in
compression.
--better wear properties.
e.g.,
10 mm sphere
apply known force
measure size
of indent after
removing load d D
Smaller indents
mean larger
hardness.
increasing hardness
most
plastics
brasses
Al alloys
easy to machine
steels
file hard
cutting
tools
nitrided
diamond
Adapted from Fig

25. Hardness Testers

26. Hardness: Measurement
Rockwell
No major sample damage
Each scale runs to 130 but only useful in range
Minor load kg
Major load (A), 100 (B) & 150 (C) kg
A = diamond, B = 1/16 in. ball, C = diamond
HB = Brinell Hardness
TS (MPa) = 3.45 x HB
TS (psi) = 500 x HB

27. Conversion of Hardness Scales c07f30
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

29. Variability in Material Properties
Elastic modulus is material property
Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability.
Statistics
Mean
Standard Deviation
All samples have same value
Because of large variability must have safety margin in engineering specifications
where n is the number of data points

30. c07f32 Property Variability and Design/Safety Factors
Average and standard deviation
c07f32

31. 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
• Example: 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
carbon steel: s y
= 310 MPa
TS = 565 MPa
F = 220,000N d L o 5
d = m = 6.7 cm

32. 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.