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Mechanical Properties of Metals by rt3463df

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```									Mechanical Properties
of Metals
500

CONTINUED
400
Stress (MPa)

300

200

100

0
0.000 0.002 0.004 0.006 0.008 0.010
Strain
Mechanical Properties
• Stiffness - Elastic Modulus or Young’s Modulus (MPa)
• Strength - Yield, Ultimate, Fracture, Proof, Offset Yield.
Measured as stress (MPa)
• Ductility - Measure of ability to deform plastically
without fracture - Elongation, Area Reduction, Fracture
Strain - (no units or mm/mm)
• Toughness, Resilience - Measure of ability to absorb
energy (J/m3).
• Hardness - Resistance to indentation/abrasion (Various
scales, e.g.; Rockwell, Brinell, Vickers.)
Stress and Strain
• In a simplistic sense, stress may be thought
• Similarly, strain is the deformation of the
component/original length.
• A stress may be direct, shear, or torsional -
• Stress cannot be measured directly, but
deformation can be.
Direct Stress Examples
L/2

P                           L/2

S
Lo           Area
Ao
Lo           Area

L
Ao
Ao

e
Lo
L/2                                                      L/2
P
Engineering Strain
P

Direct Stress - Tension                    Direct Stress - Compression
Tension Test
Measures P

Extensometer
Measures L

Typical Universal
Testing Machine
Modern Materials Testing System

Hydraulic
Wedge
Grips

Specimen
Extensometer
ASTM Tension Test Specimen
Ao=0.20 in2
0.505" Dia

2” Gauge Length

Lo
Raw Data Obtained
Total Elongation
Uniform Deformation

X

Maximum
Elastic
Deformation                      Pf

Elongation, L (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 = L/Lo)
Duke’s Quick Tip!

• Express Load in Newtons (N) and Area in
mm2 to get Stress in MPa.
N
2  MPa
mm
• Mechanical properties of metals are almost
always given in MPa or ksi.
• Imperial units: Load in kips (1000 lbf) &
Area as in2 gives Stress in ksi (kips/in2)
• 1000 psi = 1 ksi = 6.89 MPa
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)
Modulus of Elasticity - Stiffness
500

CONTINUED
400
Stress (MPa)

300

200             S (300  0)MPa
E                    2x10 5 MPa
e (0.015  0.0)

100

0
0.000   0.002    0.004      0.006     0.008   0.010
Strain
Atomic Origin of Stiffness
dF 
E   
 dr ro
Net Interatomic Force
Strongly Bonded

Weakly Bonded

Interatomic Distance
Shear Stress and Strain
Shear Stress,
Strain,
Shear

Shear Stress
Shear Strain

shear stress,  = Shear Load / Area
shear strain,  = angle of deformation (radians)
shear modulus, G =  /(elastic region)
Elastic Properties of Materials
• Poisson’s ratio: When a metal is strained in
one direction, there are corresponding
strains in all other directions.
• For a uniaxial tension strain, the lateral strains are
constrictive.
• Conversely, for a uniaxial compressive strain, the
lateral strains are expansive.
• i.e.; the lateral strains are opposite in sign to the
axial strain.
• The ratio of lateral to axial strains is known as
Poisson’s ratio, n.
Poisson’s Ratio, n

ex  ey
n  
ez  ez
For most metals,
0.25 < n< 0.35
in the elastic range
Furthermore:
E  2G(1  n )
Plastic Deformation
Elastic Plastic            Elastic Plastic
Elastic Plastic
Sy
Sy
Sy
Stress

0.002               0.002    Strain            0.002

Most Metals - Al, Cu       Clad Al-Alloys           Low carbon Steel
Microstructural Origins of Plasticity
• Slip, Climb and Slide of atoms in the crystal structure.
• Slip and Climb occur at Dislocations and Slide occurs
at Grain Boundaries.




Elastic and Plastic Strain
P (e,S)         e  ee  e p
S
ee 
E
Stress

e p  e  ee
Total Strain

The 0.2% offset yield stress
Strain    is the stress that gives a plastic
Plastic                       (permanent) strain of 0.002.
Elastic
ep          ee
Elastic Recovery
Stress

Strain                                 Strain
elastic strain
Ductility - EL% & AR%
• Elongation
L f  Lo
EL%                x 100
Lo           Lo
Lf
• Area Reduction
Ao  A f           Ao   Af
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
Toughness & Resilience
• Toughness: A measure of the ability of a
material to absorb energy without fracture.
(J/m3 or N.mm/mm3= MPa)
• Resilience: A measure of the ability of a
material to absorb energy without plastic or
permanent deformation.
(J/m3 or N.mm/mm3= MPa)
• Note: Both are determined as
energy/unit volume
Toughness, Ut

Su
Sy
Engineering Stress, S=P/Ao

ef
Ut   S de
o
(S y  Su ) EL%
                  
2       100 

Engineering Strain, e = L/Lo)
Resilience, Ur

Sy                    Su
Engineering Stress, S=P/Ao

ey            X
U r   S de
o
Sy e y

E                           2
Sy 2

2E
ey
Engineering Strain, e = L/Lo)
Typical Mechanical Properties
Metals in annealed (soft) condition

Material              Yield Stress     Ultimate     Ductility   Elastic Modulus   Poisson’s
(MPa)        Stress (MPa)    EL%             (MPa)          Ratio
1040 Steel                350             520            30         207000            0.30
1080 Steel                380             615            25         207000            0.30
2024 Al Alloy             100             200            18           72000           0.33
316 Stainless Steel       210             550            60         195000            0.30
70/30 Brass                75             300            70         110000            0.35
6-4 Ti Alloy              942            1000            14         107000            0.36
AZ80 Mg Alloy             285             340            11           45000           0.29

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