Cerâmicos
avançados
Cerâmicos
porosos
Ligas metálicas
Metals are dense because they
have heavy atoms and close
packing; ceramics have lower
densities than metals because they
contain light atoms, either C, N or
O; polymers have low densities
because they consist of light atoms
in chains.
0,1
Compósitos de
f ibras
The density clearly depends on the
mass of the atoms, their size and
the way they are packed.
1
Polímeros
estruturais
The reciprocal of the density is the
specific volume v, while the product
of v and the relative atomic mass W
is known as the atomic volume Ω.
10
Elastómeros
Density defined as the mass per
unit volume of a material, increases
regularly with increasing atomic
numbers in each sub-group.
DENSIDADE
[ton/m^3]
Madeiras
1. densidade
100
Espumas
poliméricas
propriedades físicas
1. densidade
1. densidade
propriedades físicas
2. propriedades térmicas: expansão térmica
The change in dimensions with temperature is usually expressed in terms of the linear coefficient of
expansion, given by:
α = (1/l)(dl/dT)
where l is the original length of the specimen and T is the absolute temperature.
Because of the anisotropic nature of crystals, the value of α usually varies with the direction of
measurement and even in a particular crystallographic direction the dimensional change with temperature
may not always be uniform.
The change in volume with temperature is important in many metallurgical operations such as casting,
welding and heat treatment. Of particular importance is the volume change associated with the melting or,
alternatively, the freezing phenomenon since this is responsible for many of the defects, both of a
macroscopic and microscopic size, which exist in crystals.
Most metals increase their volume by about 3% on melting, although those metals which have
crystal structures of lower coordination, such as bismuth, antimony or gallium, contract on
melting.
This volume change is quite small, and while the liquid structure is more open than the solid structure, it is
clear that the liquid state resembles the solid state more closely than it does the gaseous phase.
For the simple metals the latent heat of melting, which is merely the work done in separating the atoms
from the close-packed structure of the solid to the more open liquid structure, is only about one thirtieth of
the latent heat of evaporation, while the electrical and thermal conductivities are reduced only to threequarters to one-half of the solid state values.
2. propriedades térmicas: capacidade calorífica ou calor
específico
The specific heat is another thermal
property important in the processing
operations of casting or heat
treatment, since it determines the
amount of heat required in the
process. Thus, the specific heat
(denoted by Cp, when dealing with
the specific heat at constant
pressure) controls the increase in
temperature, dT, produced by the
addition of a given quantity of heat,
dQ, to one gram of matter so that:
dQ = Cp dT
The specific heat of a metal is due
almost entirely to the vibrational
motion of the ions. However, a small
part of the specific heat is due to the
motion of the free electrons, which
becomes important at high
temperatures, especially in transition
metals with electrons in incomplete
shells.
2. propriedades térmicas: capacidade calorífica ou calor
específico
When the specific heat is experimentally
determined, it is the specific heat at
constant
pressure, Cp, which is measured,
2. propriedades térmicas: capacidade calorífica ou calor
específico
2. propriedades térmicas: capacidade calorífica ou calor
específico
3. propriedades elétricas
One of the most important electronic properties
of metals is the electrical conductivity, σ , and
the reciprocal of the conductivity (known as the
resistivity, ρ), defined as:
ρ = RA / l
where R is the resistance, l is the length and A is
the cross-sectional area.
A characteristic feature of a metal is its high
electrical conductivity which arises from the ease
with which the electrons can migrate through the
lattice.
The high thermal conduction of metals also has
a similar explanation, and the Wiedmann–Franz
law shows that the ratio of the electrical and
thermal conductivities is nearly the same for all
metals at the same temperature.
Since conductivity arises from the motion of
conduction electrons through the lattice,
resistance must be caused by the scattering of
electron waves by any kind of irregularity in the
lattice arrangement. Irregularities can arise from
any one of several sources, such as
temperature, alloying, deformation or nuclear
irradiation, since all will disturb, to some extent,
the periodicity of the lattice.
3. propriedades elétricas
The effect of
temperature is
particularly important
and, as shown in Figure
6.19, the resistance
increases linearly with
temperature above
about 100 K up to the
melting point.
On melting, the
resistance
increases markedly
because of the
exceptional disorder
of the liquid state.
3. propriedades elétricas
4. propriedades mecânicas
propriedades mecânicas
propriedades mecânicas
COMPÓSITOS
METAIS
CERÂMICOS
POLÍMEROS
propriedades mecânicas
Stress (MPa)
500
CONTINUED
400
300
200
100
0
0.000 0.002 0.004 0.006 0.008 0.010
Strain
propriedades mecânicas
• 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.)
propriedades mecânicas
Load, P
Engineering Stress
Load, P
∆L/2
∆L/2
Lo
P
σ=
Ao
Area
Ao
Lo
Area
Ao
∆L
e=
Lo
∆L/2
∆L/2
P
Engineering Strain
P
Direct Stress - Tension
Direct Stress - Compression
tension test
Total Elongation
Load, P
(kN)
Uniform Deformation
X
Maximum
Load, Pmax
Elastic
Deformation
Elongation, ∆L (mm)
Load,
Pf
Engineering Stress, σ = P/Ao
engineering stress-strain curve
Elongation
Sy
0.2% offset
yield stress
(Ultimate)
E
Su
E
Proportional Limit
Engineering Strain, e = ∆L/Lo)
stress-strain curve
• express Load in Newtons (N) and Area in mm2 to get
stress in MPa.
• mechanical properties are usually given in 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:
σ = Ee
where E is the modulus of elasticity (MPa)
modulus of elasticity - stiffness
Stress (MPa)
500
CONTINUED
400
300
200
100
0
0.000
0.002
0.004
0.006
Strain
0.008
0.010
atomic origin of stiffness
Net Interatomic Force
Strongly Bonded
Weakly Bonded
Interatomic Distance
Shear Stress
shear stress and strain
Shear Strain
shear stress, τ = Shear Load / Area
shear strain, γ = angle of deformation (radians)
shear modulus, G = τ /γ (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,
υ.
Poisson’s ratio, ν
for most metals,
0.25 < ν < 0.35
in the elastic range
furthermore:
plastic deformation
Elastic Plastic
Elastic Plastic
σy
σy
Elastic Plastic
Stress
σy
0.002
Most Metals - Al, Cu
0.002
Strain
Clad Al-Alloys
0.002
Low carbon Steel
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.
τ
τ
elastic and plastic strain
P (e,σ)
e = ee + e p
σ
Stress
ee =
E
e p =e− ee
Total Strain
Strain
Plastic
ep
ee
Elastic
The 0.2% offset yield stress
is the stress that gives a plasti
(permanent) strain of 0.002.
elastic recovery
Loading
Reloading
Stress
Loading
Unloading
Unloading
Strain
elastic strain
Strain
ductility – EL% and AR%
• Elongation
Lo
Lf
• Area Reduction
Ao
Af
ductile vs brittle materials
Engineering Stress
• only ductile materials will exhibit
necking.
• ductile if EL%>8% (approximately)
• brittle if EL% < 5% (approximately)
Engineering Strain
toughness and 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
Engineering Stress, σ=P/Ao
toughness, Ut
σu
σy
ef
U t = ∫ σ de
o
(σ y + σ u )  EL% 
≈


2
 100 
Engineering Strain, e = ∆L/Lo)
Engineering Stress, S=P/Ao
resilience, Ur
σu
σy
ey
U r = ∫ σ de
o
≈
E
=
σ y ey
2
σ y2
2E
ey
Engineering Strain, e = ∆L/Lo)
X
typical mechanical properties
metals in annealed (soft) condition
Material
1040 Steel
1080 Steel
2024 Al Alloy
316 Stainless Steel
70/30 Brass
6-4 Ti Alloy
AZ80 Mg Alloy
Yield Stress
(MPa)
350
380
100
210
75
942
285
Ultimate
Stress (MPa)
520
615
200
550
300
1000
340
Ductility
EL%
30
25
18
60
70
14
11
Elastic Modulus
(MPa)
207000
207000
72000
195000
110000
107000
45000
Poisson’s
Ratio
0.30
0.30
0.33
0.30
0.35
0.36
0.29
creep test
(ASTM E – 139)
creep behavior
creep behavior
fatigue test
fatigue failure
fatigue strength
fatigue mechanism
impact test - ASTM – E 23
impact test - ASTM – E 23
fracture
fracture
fracture
fracture
propriedades magnéticas
propriedades magnéticas
propriedades magnéticas
H – magnetic field necessary to induce a field of strength B inside the material
removing of the field H, a
certain residual magnetism
is left on the specimen
A field Hc, called the coercive force,
must be applied in the opposite force
to remove the residual magnetism
(residual remanence)