# Outline: • Ductility • Resilience • Toughness • Hardness • Example

```Effect of Testing Temperature on Mechanical Behavior
Outline:
• Ductility
• Resilience
• Toughness
• Hardness
• Example
• Slip Systems
• The yield and tensile strengths ………… with increasing temperature.
• Ductility ……………. with temperature.
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/1
Dr. M. Medraj
DUCTILITY
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/2
DUCTILITY
Ductility measures the amount of plastic deformation that a material
goes through by the time it breaks.
• Ductility is a measure of how much strain a given stress produces.
• Highly ductile metals can exhibit significant strain before
fracturing, whereas brittle materials frequently display very little
strain.
• An overly simplistic way of viewing ductility is the degree to
which a material is “forgiving” of local deformation without the
occurrence of fracture.
Two measures of ductility:
1) Percent Elongation (%El )
% El =
Final length - Initial length
x 100
Initial length
Brittle materials: %EL  5% at fracture
2) Percent Reduction In Area
Ductile materials: %EL and %RA both  25%
Initial Area - Final Area
%RA =
x 100
Initial Area
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/3
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/4
RESILIENCE
Typical Mechanical Properties of Metals
Ability of material to absorb energy during elastic deformation and
then to give it back when unloaded.
• Measured with Modulus of Resilience, Ur
• Ur, is area under  -  curve up to yielding:
U r  0 y  d
• Assuming a linear elastic region:
Ur 
1 
2 y y

1  
2 y
 y   2y
 
 E  2E
• Units are J/m3 (equivalent to ……)
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Dr. M. Medraj
Mech 221 lecture 12/5
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/6
Toughness Measurement: Impact Testing
TOUGHNESS
Ability to absorb energy before fracture
•
•
Charpy and Izod tests measure impact energy or
notch toughness
Charpy V- notch (CVN) most common
Charpy Test
•
•
•
• Toughness is the area under  -  curve up to fracture.
•
- Similar to Resilience (same units J/m3).
- Larger area  tougher material.
•
• So tough materials have a combination of ……….. and ………..
• Can be measured by an impact test (Chapter 8).
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/7
•
use standard sized bar specimens with a
central notch
weighted pendulum released from a
height, h
impacts the specimen behind the notch
(stress concentration)
fracture of specimen occurs and energy is
absorbed
the pendulum travels to point, h´, where
h´< h
obtain the amount of absorbed energy
from scale
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/8
HARDNESS
Vickers
Hardness is a measure of the material’s resistance to localized
plastic deformation (e.g. dent or scratch)
Brinell
HARDNESS
Quantitative Hardness:
 Different types of quantitative hardness test has been designed
• Rockwell
• Brinell
• Vickers
• Knoop
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/9
• The depth or size of indentation is
measured.
Rockwell
 Moh’s scale, determined by the ability of a material to scratch
another material:
from 1 (softest = talc) to 10 (hardest = diamond)
Knoop
Qualitative Hardness:
• Usually a small indenter (sphere, cone,
or pyramid) is forced into the surface of
a material under conditions of controlled
• The tests somewhat approximate, but
popular because they are easy and nondestructive (except for the small dent).
Where,
P (the applied load) is in kg,
D is the indenter's diameter
d is the diameter of the resulted indentation
Dr. M. Medraj
Example
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/10
Plastic Deformation
A cylindrical metal specimen having an original diameter of
12.8 mm (0.505 in.) and gauge length of 50.80 mm (2.000 in.)
is pulled in tension until fracture occurs. The diameter at the
point of fracture is 6.60 mm (0.260 in.), and the fractured
gauge length is 72.14 mm (2.840 in.). Calculate the ductility
in terms of percent reduction in area and percent elongation.
 Why metals could be plastically deformed?
 Why the plastic deformation properties could be changed
to a very large degree by forging without changing the
chemical composition?
 Why plastic deformation occurs at stresses that are much
smaller than the theoretical strength of perfect crystals?
 Plastic deformation – the force to break all bonds in the
slip plane is much higher than the force needed to cause the
deformation. Why?
These questions can be answered based on the idea proposed in
1934 by Taylor, Orowan and Polyani: Plastic deformation is
due to the motion of a large number of ……………..
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/11
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/12
Dislocations allow deformation at much lower
stress than in a perfect crystal, How?!
Dislocations and Plastic Deformation
Under applied shear stress, dislocations can move by breaking bonds
CONSECUTIVELY (rather than simultaneously) Requires less energy.
This is the reason why experimental shear strength is lower.
Deformation by dislocations movement is called SLIP.
• The combination of C-P plane (the slip plane) and C-P direction
(the slip direction) is called a …………...
Recall:
The movement of the dislocation (to the right in this sequence) requires
the breaking (and formation) of only ONE set of bonds per step.
SLIP SYSTEMS DEPEND ON
THE CRYSTAL STRUCTURE
OF THE MATERIAL!
Dislocations move in ………………. directions within
……………………. planes.
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/13
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/14
Dislocations and Plastic Deformation
Next Topic:
Phase Diagrams
The more slip systems available, the easier it is for dislocations to
move, which is why (on the average) FCC and BCC metals are
more ductile than HCP metals.
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/15
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech 221 lecture 12/16
```
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