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8/12/2019 Metalurgia Mecnica - Reviso (Eng)
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direct stress examples
Engineering StressLoad, P
P
Area
Ao
Lo
L/2
L/2
Load, P
P
Area
Ao
Lo
L/2
L/2
o
o
LLe
AP
=
=
Engineering Strain
Direct Stress - Tension Direct Stress - Compression
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tension test
Loa
d,
P(k
N)
Elongation, L (mm)
Uniform DeformationTotal Elongation
Elastic
Deformation
X
MaximumLoad, Pmax
Load, Pf
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Elongation
0.2% offset
yield stress
Proportional Limit
E
E
(Ultimate)
Engineering Strain, e = L/Lo)
Eng
ineeringStress,=
P/Ao Sy
Su
engineering stress-strain curve N
mm2 MPa
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Hookes 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,
Hookes Law may be applied:
where E is the modulus of elasticity (MPa)
Ee=
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modulus of elasticity - stiffness
0.0100.0080.0060.0040.0020.0000
100
200
300
400
500
CONTINUED
Stress(MPa)
Strain
E=Se
=(300 0) Pa(0.015 0.0)
= 2x105MPa
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shear stress and strain
Shear Stress,ShearStrain,
GShearStress
Shear Strain
shear stress, = Shear Load / Areashear strain, = angle of deformation (radians)
shear modulus, G = / (elastic region)
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Poissons ratio,
= exez
= eyez
for most metals,
0.25 < < 0.35in the elastic range
furthermore:
E= 2G(1+)
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plastic deformation
Stress
Strain0.002 0.002 0.002
y
y
y
Elastic Plastic Elastic Plastic
Elastic Plastic
Most Metals - Al, Cu Clad Al-Alloys Low carbon Steel
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elastic and plastic strain
Stress
Strain
Plastic Elasticeeep
P
Total Strain
(e,)
ep
e
pe
eee
Ee
eee
=
=
+=
The 0.2% offset yield stress
is the stress that gives a plastic
(permanent) strain of 0.002.
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elastic recovery
Strain
Stress
Loading
Unloading
Loading
Unloading
Reloading
elastic strain Strain
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Elongation
Area Reduction
EL%=LfLo
Lo
x 100
AR%=AoAfAo
x 100
Lo
Ao
Lf
Af
ductility EL% and AR%
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ductile vs brittle materials
only ductile materials will exhibit necking.
ductile if EL%>8% (approximately)
brittle if EL% < 5% (approximately)
X
XXA
B C
XD Brittle DuctileA & B C & D
Enginee
ringStres
s
Engineering Strain
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toughness and resilience
toughness: a measure of the ability of a material toabsorb energy without fracture.
(J/m3 or N.mm/mm3= MPa)
resilience: a measure of the ability of a material toabsorb energy without plastic or permanent
deformation.(J/m3 or N.mm/mm3= MPa)
note: both are determined as energy/unit volume
t h U
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toughness, Ut
X
+
=
100
%
2
)( EL
deU
uy
e
o
t
f
uy
Eng
ineeringStress,=P/Ao
Engineering Strain, e = L/Lo)
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t i l h i l ti
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typical mechanical properties
metals in annealed (soft) condition
Material Yield Stress(MPa)
Ultimate
Stress (MPa)
Ductility
EL%
Elastic Modulus
(MPa)
Poissons
Ratio
1040 Steel 350 520 30 207000 0.301080 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 0.36AZ80 Mg Alloy 285 340 11 45000 0.29
str ct ral origins of plasticit
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structural 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.
structural origins of plasticity
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structural origins of plasticity
C04edge4.mov C04disje.mov C04dragb.movC04bubb1.mov
C0445deg.mov
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C04frank.mov
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Kink:
degrau
na LD
no PE
Jog:
degrau na LD
em outro PE
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C04climb.mov
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Resultante da tenso de cisalhamento
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Relao do escorregamento com estrutura cristalina
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Resultante critica da tenso de cisalhamento
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Escorregamento mltiplo
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Escorregamento mltiplo
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Encruamento e escorregamento
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Deformao por maclagem
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