# Mechanical properties of metals by malj

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```									     Mechanical properties of
metals

How do metals respond to external loads?
•Stress& strain
•Elastic deformation.
•Plastic deformation.
STRESS-STRAIN TESTING
• Typical tensile specimen                     • Typical tensile
test machine
Adapted from Fig. 6.2,
Callister 6e.

• Other types of tests:            Adapted from Fig. 6.3, Callister 6e.
(Fig. 6.3 is taken from H.W. Hayden,
--compression: brittle          W.G. Moffatt, and J. Wulff, The
Structure and Properties of
materials (e.g., concrete)    Materials, Vol. III, Mechanical
Behavior, p. 2, John Wiley and Sons,
--torsion: cylindrical tubes,   New York, 1965.)
shafts.                                                       9
Raw Data Obtained
Total Elongation
Uniform Deformation

X

Maximum
Elastic
Deformation                    Pf

Elongation, DL (mm)
Engineering Stress-Strain Curve
Elongation

Sy
Engineering Stress, S=P/Ao

0.2% offset
yield stress

E                  (Ultimate)

Su
E

Proportional Limit

Engineering Strain, e = DL/Lo)
Stress-strain behavior
Elastic behavior
• In brittle materials   • In ductile materials
• Non linear elastic     • Linear elastic behavior
behavior
Hooke’s Law
Elastic Deformation
• Elastic deformation is not permanent; it means that when
the load is removed, the part returns to its original shape
and dimensions.
• For most metals, the elastic region is linear. For some
materials, including metals such as cast iron, polymers,
and concrete, the elastic region is non-linear.
• If the behavior is linear elastic, or nearly linear-elastic,
Hooke’s Law may be applied:
S  Ee
• Where E is the modulus of elasticity (MPa)
Elastic properties of materials
• Poisson’s ratio:
When a metal is
strained in one
direction, there are
corresponding
strains in all other
directions.
ex  ey
          For most metals,
ez  ez
0.25 <  < 0.35
in the elastic range
Stress-strain behavior
• Elastic deformation
• Reversible: when the stress is
removed, the material returns to
the dimension it had before the
(except for the case of plastics).
• Plastic deformation
• Irreversible: when the stress
• is removed, the material
• previous dimension.
Elastic Recovery
Stress

Strain                                 Strain
elastic strain
Elastic and Plastic Strain
P (σ,Ɛ)
Ɛ=Ɛe+Ɛp
Total strain =
Stress

elastic strain + plastic strain
Ɛe= σ/E
Ɛp=Ɛ- Ɛe
Total Strain

The 0.2% offset yield stress
Strain           is the stress that gives a plastic
Plastic                              (permanent) strain of 0.002.
Elastic
Ɛp          Ɛe
Tensile properties: Yielding

• Yield strength σy - is chosen
as that causing a permanent
strain of 0.002
• Yield point P - the strain
deviates from being
proportional to the stress (the
proportional limit)
• The yield stress is a measure
of resistance to plastic
deformation
Tensile properties: Yielding
• For a low-carbon steel,
the stress vs. strain
curve includes both an
upper and lower yield
point.

The yield strength is
defined in this case as
the average stress at
the lower yield point.
Tensile Strength
• For structural applications,
the yield stress is usually a
more important property
than the tensile strength,
since once the it is passed,
the structure has deformed
beyond acceptable limits
Ductility
• Ductility is a measure
of the deformation at
L f  Lo              fracture
EL%               x 100
Lo                • Define as elongation
percent or reduction in
area
•        L f  Lo
EL%                  x 100
Lo
Ao  A f
AR%               x 100
Ao
Ductile Vs Brittle Materials
• Only Ductile materials will exhibit
necking.
• Ductile if EL%>8% (approximately)
• Brittle if EL% < 5% (approximately)
Engineering Stress

Engineering Strain
Example problem
Determine the mechanical properties for metal which have the
stress-strain curve as shown below.
• The elastic modulus is the slope in the linear elastic
region

For the yield strength, the 0.002 strain offset line is
drawn dashed. It intersects the stress-strain curve at
approximately 285 MPa
• (d) The tensile strength is approximately 370
MPa, corresponding to the maximum stress on
the complete stress-strain plot.
• If the gauge length (L0) = 12 cm , the length at
fracture (Lf) = 16 cm, original diameter (d0)= 12
mm, the diameter at fracture (df) = 8mm.
Then the ductility =

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