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Crystal structure
There are two main forms of solid substance, characterizing
different atoms arrangement in theirmicrostructures: amorphous and
crystalline.
Amorphous solid
Amorphous solid substance does not possess long-range order of
atoms positions. Some liquids
when cooled become more and more viscous and then rigid,
retaining random atom characteristic
distribution.
This state is called undercooled liquid or amorphous solid.
ommon glass, most of !olymers,
glues and some of eramics are amorphous solids. Some of the
"etals may be prepared in
amorphous solid form by rapid cooling from molten state.
Crystalline solid
rystalline solid substance is characterized by atoms arranged in
a regular pattern, e#tending inall three dimensions. The
crystalline structure is described in terms of crystal lattice,
which is a
lattice with atoms or ions attached to the lattice points. The
smallest possible part of crystal
lattice, determining the structure, is called primitive unit
cell.
$#amples of typical crystal lattice are presented in the
picture:
Metal crystal structure and specific metal properties are
determined by metallic bonding %force, holding together the
atoms of a metal. $ach of the atoms of the metal contributes
its
valence electrons to the crystal lattice, forming an
electron cloud or electron &gas', surrounding
positive metal ions. These free electrons belong to
the whole metal crystal.
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Ability of the valence free electrons to travel throughout the
solid e#plains both the high
electrical conductivity and thermal conductivity of metals.
(ther specific metal features are: luster or shine of their
surface )when polished*, theirmalleability )ability to be hammered*
and ductility )ability to be drawn*.
These properties are also associated with the metallic bonding
and presence of free electrons in
the crystal lattice.
The following elements are common metals:
aluminum)Al*, barium)+a*, beryllium)+e*, bismuth)+i*,
cadmium)d*, calcium)a*,
cerium)e*, cesium)s*, chromium)r*, cobalt)o*, copper)u*,
gold)Au*, indium)n*,
iridium)r*, iron)e*, lead)!b*, lithium)i*, magnesium)"g*,
manganese)"n*, mercury)/g*,molybdenum)"o*,
nic0el)1i*, osmium)(s*, palladium)!d*, platinum)!t*,
potassium)2*,
radium)3a*, rhodium)3h*, silver)Ag*, sodium)1a*, tantalum)Ta*,
thallium)Tl*, thorium)Th*,
tin)Sn*, titanium)Ti*, tungsten)4*, uranium)5*, vanadium)6*,
zinc)7n*.
Thermal properties
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Thermal Conductivity
Thermal Conductivity (λ) is amount of heat passing in unit
time through unit surface in adirection normal to this surface when
this transfer is driven by unite temperature gradient under
steady state conditions.
Thermal conductivity may be e#pressed and calculated from the
Fourier’s law:
ΔQ/ Δt !"# "ΔT/ Δ$
4here
Q -heat, passing through the surface #8
Δt - change in time8
! - thermal conductivity8
# - surface area, normal to the heat transfer
direction8
ΔT/Δ$-temperature gradient along $ % direction of the heat
transfer.
ourier9s law is analogue of the irst ic09s law, describing
diffusion in steady state.
"etals have high thermal conductivity. /eat is transferred
through the metal crystal by freeelectrons. ompare:
! of alumina ;< +T5=)lb>?* )@. 4=)m>2**.
! of Al B@CC +T5=)lb>?* )DB 4=)m>2**.
Coefcient o Thermal Expansion
Thermal Expansion ( Coefficient of Thermal
Expansion ) is relative increase in length per unite
temperature rise:
% Δ&/ '&oΔT(
4here
% -coefficient of thermal e#pansion )CT)*8
Δ& % length increase8
&o % initial length8
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ΔT % temperature rise.
Thermal e#pansion of metals is generally higher, than that of
ceramics.
ompare:
CT) of Si D. ?EF );.C ?EF*.
CT) of Al B ?EF )D ?EF*.
Specic Heat Capacity
Heat Capacity is amount of heat required to raise
material temperature by one unit.
Specific Heat Capacity is amount of heat required to raise
temperature of unit mass of material by one unit:
c ΔQ=)mΔT(
4here
c -specific heat capacity8
ΔQ % amount of heat8
m % material mass8
ΔT % temperature rise.
Specific /eat apacity of metals is lower, than that of
ceramics.
ompare:
*c+ of alumina C.DC +T5=)lb>?* )GHC I=)0g>2**.
*c+ of steel C.BBH +T5=)lb>?* );GB I=)0g>2**.
Magnetic properties
"ost of metals are slightly magnetic, but only few of them
)iron, nic0el, cobalt and their alloys*
display pronounced magnetic properties, called
ferromagnetism.
• Magnetically soft metals – metals, which are demagnetized
after themagnetic eld is removed. Magnetically soft metals are used
in electricmotors and transformers.
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• Magnetically hard metals – metals, retaining their
magnetization after themagnetic eld is removed.Magnetically hard
metals are used for permanentmagnets.
• Magnetostriction – eect of changing dimensions of a
ferromagnetic metalwhen its magnetization is changed.
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Tensile test and Stress-Strain Diagram
#tress,#train -iagram e#presses a relationship between a
load applied to a material and the
deformation of the material, caused by the load .
Stress-Strain Jiagram is determined by tensile test.
Tensile tests are conducted in tensile test machines, providing
controlled uniformly increasingtension force, applied to the
specimen.
The specimen9s ends are gripped and fi#ed in the machine and its
gauge length &. )a calibrated
distance between two mar0s on the specimen surface* is
continuously measured until the rupture.
Test specimen may be round or flat in the cross-section.
n the round specimens it is accepted, that &. "
diameter.
The specimen deformation )strain* is the ratio of the increase
of the specimen gauge length to its
original gauge length:
0 '& 1 &.( / &.
Tensile stress is the ratio of the tensile load
F applied to the specimen to its original cross-
sectional area #.:
2 F / #.
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The initial straight line ).3*of the curve characterizes
proportional relationship between the
stress and the deformation )strain*.
The stress value at the point 3 is called the limit of
proportionality:
2p F3 / #.
This behavior conforms to the 4oo5’s &aw:
2 )"0
4here ) is a constant, 0nown as 6oung’s Modulus
or Modulus of )lasticity.
The value of Koung9s "odulus is determined mainly by the nature
of the material and is nearly
insensitive to the heat treatment and composition.
"odulus of elasticity determines stiffness - resistance of
a body to elastic deformation caused byan applied force.
The line .) in the Stress-Strain curve indicates the range
of elastic deformation % removal of
the load at any point of this part of the curve results in
return of the specimen length to its
original value.
The elastic behavior is characterized by the elasticity
limit )stress value at the point )*:
2el F) / #.
or the most materials the points 3 and ) coincide and
therefore 2el2p.
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A point where the stress causes sudden deformation without any
increase in the force is calledyield limit 'yield stress7 yield
strength(:
2y F6 / #.
The highest stress )point 68* , occurring before the sudden
deformation is called upper yield
limit .
The lower stress value, causing the sudden deformation )point
6&* is called lower yield limit.
The commonly used parameter of yield limit is actually lower
yield limit.
f the load reaches the yield point the specimen
undergoes plastic deformation % it does not
return to its original length after removal of the load.
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/ard steels and non-ferrous metals do not have defined yield
limit, therefore a stress,
corresponding to a definite deformation )C.BL or C.DL* is
commonly used instead of yield limit.
This stress is called proof stress or offset yield limit 'offset
yield strength(9
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(ther important characteristic of metals is ductility -
ability of a material to deform under
tension without rupture.
Two ductility parameters may be obtain from the tensile
test:
=elative elongation - ratio between the increase of the specimen
length before its rupture and itsoriginal length:
0 '&m 1 &.( / &.
4here &m % ma#imum specimen length.
=elative reduction of area , ratio between the decrease of the
specimen cross-section area
before its rupture and its original cross-section
area9
> '#. 1 #min( / #.
Where Smin– minimum specimen cross-section area.
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Fracture Toughness
Fracture is a process of brea0ing a solid into pieces as a
result of stress.
There are two principal stages of the fracture process:
• Crac5 formation
• Crac5 propagation
-uctile fracture
Juctile materials undergo observable plastic
deformation and absorb significant energy before
fracture.
A crac0, formed as a result of the ductile fracture, propagates
slowly and when the stress is
increased.
!lastic deformation of a multi- phase material causes
formation and coalescence of voids on the
phase and inclusions boundaries. These voids are
responsible for the specific appearance of the
ductile fracture surface, consisting of numerous spherical
micro-cavities )dimples*, initiatingformation of the crac0.
Tensile specimen fractured by the ductile mechanism is
characterized by the cap and cone
appearance of the fracture.
Single-phase alloys and pure metals are more ductile, than
metals, containing second phases or
inclusions.
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?rittle fracture
+rittle fracture is characterized by very low plastic
deformation and low energy absorption prior
to brea0ing.
A crac0, formed as a result of the brittle fracture, propagates
fast and without increase of the
stress applied to the material.
The brittle crac0 is perpendicular to the stress direction.
There are two possible mechanisms of the brittle fracture:
transcrystalline 'transgranular7
cleavage( or intercrystalline
'intergranular(:
Cleavage crac0s pass along crystallographic
planes through the grains.
@ntercrystalline fracture occurs through the grain
boundaries, embrittled by segregatedimpurities, second phase
inclusions and other defects.
The brittle fractures usually possess bright granular
appearance.
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Toughness
Toughness is ability of material to resist fracture.
The general factors, affecting the toughness of a material are:
temperature, strain rate,relationship between the
strength and ductility of the material and presence of
stress
concentration )notch* on the specimen surface.
racture toughness is indicated by the area below the curve on
strain-stress diagram )see the
figure*:
As seen from the diagram toughness of the ductile materials is
higher than toughness of brittle
materials.
Stress-intensity Factor () is a quantitative parameter of
fracture toughness determining a
ma#imum value of stress which may be applied to a specimen
containing a crac0 )notch* of a
certain length.
Jepending on the direction of the specimen loading and the
specimen thic0ness, four types ofstress-intensity factors are used:
C7 @C @@C @@@C.
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C % stress-intensity factor of a specimen, thic0ness
of which is less than a critical value.
C depends on the specimen thic0ness. This condition
is called plane stress.
@C7 @@C7 @@@C % stress-intensity factors,
relating to the specimens, thic0ness of which is above
the critical value therefore the values of
@C @@C @@@C do not depend on the
specimen thic0ness.This condition is called plane strain.
@@C and @@@C % stress-intensity factors
relating to the fracture modes in which the loading
direction is parallel to the crac0 plane. These factors are
rarely used for metals and are not used
for ceramics8
@C % plane strain stress-intensity factor relating to
the fracture modes in which the loading
direction is normal to the crac0 plane. This factor is widely
used for both metallic and ceramic
materials.
@C is used for estimation critical stress applied to
a specimen with a given crac0 length:
2C B @C /'6' a(D(
4here
@C % stress-intensity factor, measured in
"!a>mM8
2C % the critical stress applied to the specimen8
a % the crac0 length for edge crac0 or half crac0 length
for internal crac08
6 % geometry factor.
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(ne of the most popular impact tests is the Charpy Test,
schematically presented in the figure
below:
The hammer stri0ing energy in the harpy test is DDC ft>lbf
)CC I*.
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FatigueFatigue is a type of failure of a material, occurring
under alternating loads.
"ost of the failures of machine details are caused by
fatigue.
Fatigue life is the number of cycling stresses, causing failure
of the material.
requency of these stresses is not important.
Fatigue limit is the ma#imum value of repeatedly applied stress
that the material can withstand
after an infinite number of cycles )BC-DC mln. ycles in
practice*.
Fatigue strength at E cycles is the load, producing the material
fracture after 1 cyclingapplications of the load.
atigue limit of a material is much lower, than its ultimate
tensile strength.
atigue tests are carried out in the 4Nhler-type machine,
schematically shown in the picture.
The rotating specimen in form of a cantilever is driven by an
electric motor. The specimen is
loaded by the force , applied to the ball bearing, mounted on
the end of the specimen.
Since the force direction does not change, the direction of the
stress applied to the specimen will be reversed each BGC? of
the shaft rotation.
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This scheme provides cycling loading of the specimen, presented
in the equivalent scheme.
To find the fatigue limit the fatigue test is repeated at
different loads.
The tests results are presented in form of #,E
curve )stress vs. number of cycles*:
atigue fracture is characterized by presence of two different
types of the surface:
(ne part is smooth and discolored with ripple-li0e mar0s,
indicating slow crac0 growth from the
center of the crac0 formation. Another part of the surface has
coarse crystalline appearanceresulted from the final catastrophic
crac0 propagation.
The following factors affect fatigue fracture:
• #urface factor
atigue crac0s form and initiate on the specimen surface
therefore hardened and smooth surface
)without stress concentrations - notch, flaw* will increase the
fatigue limit.
• Compressive stress
ompressive stresses, produced in the specimen surface by Shot
peening, cold wor0 or heattreatment result in
considerable increase of fatigue limit.
• Micro,structure defects
1on-metallic inclusions and other micro-defects may
initiate formation of fatigue crac0s.
• )nvironmental factoratigue in the presence of corrosive
environment )orrosion
fatigue* occurs at lower cycling stresses and after lower number
of cycles.
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Creep
Creep is a phenomenon of slow plastic
deformation )elongation* of a metal at high temperature
under a constant load.
The creep mechanism9
At low stresses the creep is controlled by
the diffusion of atoms through the grain boundaries.
Athigher stresses the creep strain proceeds due to
the dislocations movement.
The rate of creep is a function of the material, the
applied stress value, the temperature, and the
time e#posure.
onsiderable creep deformation, causing damage of machines and
structures occur at high
temperatures )about a half of the melting point measured in the
absolute temperature scale*.
Therefore this phenomenon is ta0en into account in design and
operation of heat e#changers,steam boilers and pipes, Oet engines
and other loaded equipment, wor0ing at high temperatures.
Soft metals )lead, tin* may e#perience creep at room
temperature.
A typical creep behavior is presented in the diagram:
The initial strain is not time dependent and it is caused mainly
by elastic deformation.
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The first stage creep is characterized by relatively
fast plastic deformation occurring at
decreasing rate. Juring this stage resistance creep increases
causing decrease the deformation
rate.
The second stage creep occurs at a constant and relatively low
deformation rate. This rate is
used in the engineering design.
The rate of creep at the second stage depends on both the load
)stress* and the temperature.
The third stage creep is associated with accelerated strain rate
caused by decrease of the cross
sectional area of the specimen )nec0ing*. This stage is
finalized by the specimen fracture.
At room temperature creep is negligible at any stress below the
yield point.
The quantity, which is used in precise design of machines and
structures wor0ing at elevated
temperatures, is creep strength.
Creep strength is a stress which causes a definite creep
strain after a specified period of time at
a given temperature.
reep strength of a material is much lower, than its tensile
strength.
f a large amount of deformation is tolerated rupture strength is
used in design.
=upture strength is a stress which causes a fracture of a
metal after a specified period of time at
a given temperature.
reep strength and rupture strength are determined in
stress-rupture tests conducted in PTensiletest and Stress-Strain
JiagramQtensile testRR machines equipped with a furnace providing
uniform
heating of the tested specimens.
This machine records amount of strain at every moment after the
test has started and until the
specimen failure.
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Fracture toughness tests of ceramics
Fracture is a process of brea0ing a solid into pieces as a
result of stress.
There are two principal stages of the fracture process:
• Crack formation
• Crack propagation
There are two fracture mechanisms: ductile fracture and brittle
fracture.
eramic materials have e#tremely low ductility, therefore they
failure by brittle mechanism.
• Brittle fracture• Fracture Toughness
• Flexure Test
• Indentation Fracture Test
?rittle fracture
+rittle fracture is characterized by very low !lastic
deformation and low energy absorption priorto brea0ing.
A crac0, formed as a result of the brittle fracture, propagates
fast and without increase of the
stress applied to the material.
The brittle crac0 is perpendicular to the stress direction.
There are two possible mechanisms of the brittle fracture:
transcrystalline 'transgranular7
cleavage( or intercrystalline
'intergranular(:
Cleavage crac0s pass along crystallographic planes through
the grains.
@ntercrystalline fracture occurs through the grain
boundaries, embrittled by segregated
impurities, second phase inclusions and other
defects.
The brittle fractures usually possess bright granular
appearance.
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Fracture Toughness
Fracture Toughness is ability of material to resist
fracture when a crac0 is present.
The general factors, affecting the fracture toughness of a
material are: temperature, strain rate, presence of structure
defects and presence of stress concentration )notch* on the
specimen
surface.
#tress,intensity Factor '( is a quantitative parameter of
fracture toughness determining a
ma#imum value of stress which may be applied to a specimen
containing a crac0 )notch* of acertain length.
Jepending on the direction of the specimen loading and the
specimen thic0ness, four types of
stress-intensity factors are used: C, @C, @@C,
@@@C.
C % stress-intensity factor of a specimen, thic0ness
of which is less than a critical value.
C depends on the specimen thic0ness. This condition
is called plane stress.
@C7 @@C7 @@@C % stress-intensity factors,
relating to the specimens, thic0ness of which is above thecritical
value therefore the values of @C7 @@C7 @@@C do
not depend on the specimen thic0ness.
This condition is called plane strain.
@@C and @@@C % stress-intensity factors
relating to the fracture modes in which the loading
direction is parallel to the crac0 plane. These factors are
rarely used for metallic materials and are
not used for ceramics8
@C % plane strain stress-intensity factor relating to
the fracture modes in which the loading
direction is normal to the crac0 plane. This factor is widely
used for both metallic and ceramic materials.
@C is used for estimation critical stress applied to
a specimen with a given crac0 length:
2C B @C /'6' a(D(
4here
@C % stress-intensity factor, measured in
"!a>mM8
2C % the critical stress applied to the specimen8
a % the crac0 length for edge crac0 or half crac0 length
for internal crac08
6 % geometry factor.
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Two test methods are used for measuring fracture toughness
parameter )stress-intensity factor* of
ceramic materials: le#ure Test and ndentation racture Test.
Flexure Test
The test method is similar to that which is used for measuring
le#ural Strength, howevernotched specimens are used.
ndentation Fracture Test
6ic0ers /ardness "ethod is used for this test.
!olished surface of a ceramic sample is indented by 6ic0ers
ndenter , resulting in formation offour crac0s emanating
from the indent corners.
The crac0s length is inversely proportion to the material
toughness8 therefore @C may be
estimated by measuring the crac0s length.
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4ardness test methods4ardness is resistance of material
to plastic deformation caused by indentation.
Sometimes hardness refers to resistance of material to
scratching or abrasion.
n some cases relatively quic0 and simple hardness test may
substitute tensile test.
/ardness may be measured from a small sample of material without
destroying it.
There are hardness methods, allowing to measure hardness
onsite.
3rinciple of any hardness test method is forcing an
indenter into the sample surface followed
by measuring dimensions of the indentation )depth or
actual surface area of the indentation*.
/ardness is not fundamental property and its value depends on
the combination of yield strength,
tensile strength and modulus of elasticity.
Benefits of hardness test:
• $asy
• ne#pensive
• uic0
• 1on-destructive
• "ay be applied to the samples of various dimensions and
shapes
• "ay be performed in-situ
Jepending on the loading force value and the indentation
dimensions, hardness is defined as a
macro- , micro- or nano-hardness.
Macro,hardness tests '=oc5well7 ?rinell7 ic5ers( are the most
widely used methods for rapidroutine hardness measurements. The
indenting forces in macro-hardness tests are in the range of
HC1 to CCCC1.
Micro,hardness tests 'micro,ic5ers7 noop( is applicable
when hardness of coatings, surface
hardness, or hardness of different phases in the
multi-phase material is measured. Small diamond pyramid is
used as indenter loaded with a small force of BC to BCCCgf.
Eano,hardness test uses minor loads of about B nano-1ewton
followed by precise measuring
depth of indentation.
• ?rinell 4ardness Test
• =oc5well 4ardness Test
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• =oc5well #uperficial 4ardness Test
• ic5ers 4ardness Test
• noop 4ardness Test
• #hore #cleroscope 4ardness Test
?rinell 4ardness Test
n this test a hardened steel ball of D.H, H or BC mm in diameter
is used as indenter.
The loading force is in the range of CC1 to CCCC1 )CC1 for
testing lead alloys, HCCC1 for
testing aluminum alloys, BCCCC1 for copper alloys, CCCC1 for
testing steels*. The +rinell/ardness 1umber )/+* is calculated by
the formula:
4? ;F/ 'G:HI-"'-,'-J , -iJ(D((
4here
F- applied load, 0g
- % indenter diameter, mm
-i % indentation diameter, mm.
n order to eliminate an influence of the specimen supporting
base, the specimen should be seven
times )as minimum* thic0er than indentation depth for hard
alloys and fifteen times thic0er than
indentation depth for soft alloys.
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=oc5well 4ardness Test
n the 3oc0well test the depth of the
indenter penetration into the specimen surface is measured. The
indenter may be either ahardened steel ball with diameter B=B@',
B=G' or a spherical diamond cone of BDC? angle )+rale*.
oading procedure starts from applying a minor load of BC 0gf
)0gf in 3oc0well Superficial
Test* and then the indicator, measuring the penetration depth,
is set to zero. After that the maOor
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load )@C, BCC or BHC 0gf*is applied. The penetration depth is
measured after removal of the maOor
load.
/ardness is measured in different scales )A, +, , J, $, , , /,
2* and in numbers, having nounits )in contrast to +rinell and
6ic0ers methods*.
Aluminum alloys, copper alloys and soft steels are
tested with B=B@' diameter steel ball at BCC
0gf load )=oc5well hardness scale ?*.
/arder alloys and hard cast iron are tested with the diamond
cone at BHC 0gf )=oc5well
hardness scale C*.
An e#ample of 3oc0well test result: H /3. t means H units,
measured in the scale by the
method /3 )/ardness 3oc0well*.
=oc5well #uperficial 4ardness Test
=oc5well #uperficial Test is applied for thin strips, coatings,
carburized surfaces.
3educed loads )BH 0gf, C 0gf, and C 0gf* as a maOor load and
deduced preload )0gf* are usedin the superficial test.
Jepending on the indenter, two scales of 3oc0well Superficial
method may be used: T )B=B@'
steel ball* or 1 )diamond cone*.
@D 3CT means @D units, measured in the scale CT )C 0gf, B=B@'
steel ball indenter* by the
3oc0well Superficial method )3*.
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ic5ers 4ardness Test
The principle of the 6ic0ers /ardness method is similar to the
+rinell method.
The 6ic0ers indenter is a B@ degrees square-based diamond
pyramid.
The impression, produced by the 6ic0ers indenter is clearer,
than the impression of +rinellindenter, therefore this method is
more accurate.
The load, varying from B0gf to BDC 0gf, is usually applied for C
seconds.
The 6ic0ers number )/6* is calculated by the formula:
4 H:KI"F/ -J
4here
F-applied load, 0g
- % length of the impression diagonal, mm
The length of the impression diagonal is measured by means of a
microscope, which is usually
an integral part of the 6ic0ers Tester.
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noop 4ardness Test
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The appliance consists of a diamond-tipped hammer, falling in a
graduated glass tube from a
definite height. The tube is divided into B;C equal parts.
The height of the first rebound is the hardness inde# of the
material.
The harder the material, the higher the rebound.
The Shore method is widely used for measuring hardness of large
machine components li0e rolls,
gears, dies, etc.
The Shore scleroscope is not only small and mobile, it also
leaves no impressions on the tested
surface.
4ardness Conversion Table
)submitted by the website administration*
=A
.
?rale
=?
H..
H/H+
=C
H.
?rale
=-
H..
?rale
=HE
?rale
=G.E
?rale
=IE
?rale
=HT
H/H+
=G.T
H/H+
=IT
H/H+
4?
..
H.mm
4?
G...
H.mm
4
-iamond
3yramid
#hore
UD - GC G< U< UD G< - - - - - BG@H -
UD -
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@B UU DB ;C.U @U.U ;D. DC.< UD.H GB.H
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#ule of $ixtures is a method of approach to
appro#imate estimation of composite material
properties, based on an assumption that a composite
property is the volume weighed average of
the phases )matri# and dispersed phase* properties.
According to 3ule of "i#tures properties of composite materials
are estimated as follows:
• Density• Coecient of Thermal Expansion
• Modulus of Elasticity
• Shear modulus
• !oisson"s ratio
• Tensile strength
Density
dc dm"m N df "f
4here
dc,dm,df % densities of the composite, matri# and
dispersed phase respectively8
m,f % volume fraction of the matri# and dispersed
phase respectively.
Coefcient o Thermal Expansion
• Coefcient o Thermal Expansion ( CTE ) in
longitudinal direction (along thebers)
%cl '%m")m"m N %f ")f "f (/'m"m N
)f "f (
4here
%cl, %m, %f % CT) of composite in longitudinal
direction, matri# and dispersed phase )fiber*
respectively8
)m,)f % modulus of elasticity of matri# and
dispersed phase )fiber* respectively.
• Coefcient o Thermal Expansion ( CTE ) in transverse
direction (perpendicular to the bers)
%ct 'HNOm( %m "m N %f " f
4here
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Om % !oisson9s ratio of matri#.
%oisson&s ratio is the ratio of transverse
contraction strain to longitudinal e#tension strain in the
direction of applied force.
!odulus o Elasticity
&ong align fibers
• Modulus o Elasticity in longitudinal direction
( Ecl )
)cl )m"m N )f "f
• Modulus o Elasticity in transverse direction
( Ect )
H/)ct m/)m N f /)f
#hort fibers
)cl P.P&f )f N m)m
P& H , ;/&"tanh'& /;(
RK Sm/')f -Jln';=/-((D
where:
)f % modulus of elasticity of fiber material8
)m % modulus of elasticity of matri# material8Sm -
shear modulus of matri# material8
P& % length correction factor8
& % fibers length8
- % fibers diameter8
;= % distance between fibers8
P. - fiber orientation distribution factor.
P. C.C align fibers in transverse direction
P. B=H random orientation in any direction )J*
P. =G random orientation in plane )DJ*
P. B=D bia#ial parallel to the fibers
P. B.C unidirectional parallel to the fibers
#hear modulus
Sct Sf Sm/'f Sm N
mSf (
4here:
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Sf % shear modulus of elasticity of fiber
material8
Sm % shear modulus of elasticity of matri# material8
3oissonUs ratio
OH; vf Of N mOm
4here:
Of % !oisson9s ratio of fiber material8
Om % !oisson9s ratio of matri# material8
Tensile Strength
• Tensile strength o long-ber reinorced composite in
longitudinal direction
2c 2m"m N 2f "f
4here
2c, 2m, 2f % tensile strength of the composite,
matri# and dispersed phase )fiber* respectively.
• Tensile strength o short-ber composite in longitudinal
direction
)fiber length is less than critical value &c*
&c 2f "d/Vc
4here
d % diameter of the fiber8
Vc %shear strength of the bond between the matri# and
dispersed phase )fiber*.
2c 2m"m N 2f "f "'H 1
&c/;&(
4here
& % length of the fiber
• Tensile strength o short-ber composite in longitudinal
direction
)fiber length is greater than critical value &c*
2c 2m"m N &" Vc"f /d
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Classi#cation of composites
Composite material is a material composed of t$o or more
distinct
phases %matrix phase and dispersed phase& and ha'ing
(ulk
properties signi#cantly di)erent form those of any of the
constituents*
• Matrix phase
The primary phase, having a continuous character, is called
matri#. "atri# is usually more
ductile and less hard phase. t holds the dispersed phase
and shares a load with it.
• Dispersed %reinforcing& phase
The second phase )or phases* is embedded in the matri# in a
discontinuous form. This secondary phase is called dispersed
phase. Jispersed phase is usually stronger than the matri#,
therefore it
is sometimes called reinforcing phase.
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"any of common materials
)metal alloys, doped eramics and
!olymers mi#ed with additives*
also have a small amount of dispersed phases in their
structures, however they are not considered
as composite materials since their properties are similar to
those of their base constituents) physical properties of
steel are similar to those of pure iron*.
There are two classification systems of composite
materials. (ne of them is based on the matri#material )metal,
ceramic, polymer* and the second is based on the material
structure:
Classification of composites @
)based on matri# material*
!etal !atrix Composites "!!C#
"etal "atri# omposites are composed of a metallic matri#
)aluminum, magnesium, iron,
cobalt, copper * and a dispersed ceramic
)o#ides, carbides* or metallic )lead, tungsten,
molybdenum* phase.
Ceramic !atrix Composites "C!C#
eramic "atri# omposites are composed of a ceramic matri#
and embedded fibers of other
ceramic material )dispersed phase*.
$olymer !atrix Composites "$!C#
!olymer "atri# omposites are composed of a matri# from
thermoset )5nsaturated !olyester
)5!*, $po#iy )$!** or thermoplastic )!olycarbonate
)!*, !olyvinylchloride, 1ylon,
!olysterene* and embedded glass, carbon, steel or
2evlar fibers )dispersed phase*.
Classification of composite materials @@
)based on reinforcing material structure*
$articulate Composites
!articulate omposites consist of a matri# reinforced by a
dispersed phase in form of particles.
1. Composites $ith random orientation of particles*. Composites
$ith preferred orientation of particles* !ispersed phase
ofthese materials consists of two-dimensional "at platelets
#"a$es%, laid parallelto each other.
Fi%rous Composites
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1. Short+#(er reinforced composites* &hort-'er
reinforced compositesconsist of a matri( reinforced 'y a dispersed
phase in form of discontinuous'ers #length ) 1**+diameter%.
1. Composites $ith random orientation of #(ers*
. Composites $ith preferred orientation of #(ers*
. ,ong+#(er reinforced composites* ong-'er reinforced
compositesconsist of a matri( reinforced 'y a dispersed phase in
form of continuous'ers.
1. -nidirectional orientation of #(ers*
. Bidirectional orientation of #(ers %$o'en&*
&aminate Composites
4hen a fiber reinforced composite consists of several layers
with different fiber orientations, it is
called multilayer 'angle,ply( composite.
Structure of composites
Structure of a composite material determines
its properties to a significant e#tent.
Structure factors affecting properties of composites are as
follows:
• Bonding strength on the interface 'etween the dispersed
phase andmatri(
• Shape of the dispersed phase inclusions #particles,
"a$es, 'ers,laminates%
• .rientation of the dispersed phase inclusions #random or
preferred%.
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@nterfacial bonding
ood bonding )adhesion* between matri# phase and dispersed phase
provides transfer of load,
applied to the material to the dispersed phase via the
interface. Adhesion is necessary forachieving high level of
mechanical properties of the composite.
There are three forms of interface between the two phases:
1. !irect 'onding with no intermediate layer. n this case
adhesion #/wetting/% isprovided 'y either covalent 'onding or
van der Waals force.
. ntermediate layer #inter-phase% is in form of solid
solution of the matri( anddispersed phases constituents.
0. ntermediate layer is in form of a third 'onding phase
#adhesive%.
#hape and orientation of dispersed phase
mportance of these structure parameters is confirmed by the
fact, that one of the systems oflassification of composites is
based on them.
• !articulate Composites• Fi(rous Composites
• ,aminate Composites
$articulate Composites
!articulate omposites consist of a matri# reinforced with a
dispersed phase in form of particles.
$ffect of the dispersed particles on the composite properties
depends on the particles dimensions.
6ery small particles )less than C.DH micron in diameter* finely
distributed in the matri# impede
movement of dislocations and deformation of the
material. Such strengthening effect is similar to
the precipitation hardening. n contrast to the
precipitation hardening, which disappears atelevated temperatures
when the precipitated particles dissolve in the matri#, dispersed
phase of
particulate composites )ceramic particles* is usually
stable at high temperatures, so the
strengthening effect is retained. "any of composite materials
are designed to wor0 in hightemperature applications.
arge dispersed phase particles have low strengthening effect but
they are capable to share loadapplied to the material, resulting in
increase of stiffness and decrease of ductility.
/ard particles dispersed in a softer matri# increase wear and
abrasion resistance.
Soft dispersed particles in a harder matri# improve
machinability )lead particles in steel orcopper matri#* and reduce
coefficient of friction )tin in aluminum matri# or lead in
copper
matri#*.
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omposites with high electrical conductivity matrices )copper,
silver* and with refractory
dispersed phase )tungsten, molybdenum* wor0 in high temperature
electrical applications.
4hen dispersed phase of these materials consists of
two-dimensional flat platelets )fla0es* whichare laid parallel to
each other, material e#hibits anisotropy (dependence of the
properties on the
axis or plane along which they were measured). n the case of
fla0es oriented parallel to a particular plane, material
demonstrates equal properties in all directions parallel to the
plane and
different properties in the direction normal to the plane.
Fi%rous Composites
Jispersed phase in form of fibers )ibrous omposites* improves
strength, stiffness and ractureToughness of the material,
impeding crac0 growth in the directions normal to the fiber.
$ffect of the strength increase becomes much more significant
when the fibers are arranged in a
particular direction )preferred orientation* and a stress
is applied along the same direction.
The strengthening effect is higher in long-fiber
)continuous-fiber* reinforced composites than in
short-fiber )discontinuous-fiber* reinforced
composites.
Short-fiber reinforced composites, consisting of a matri#
reinforced with a dispersed phase in
form discontinuous fibers )length V BCC>diameter*, has a
limited ability to share load.
oad, applied to a long-fiber reinforced composite, is carried
mostly by the dispersed phase -
fibers. "atri# in such materials serves only as a binder of the
fibers 0eeping them in a desiredshape and protecting them from
mechanical or chemical damages.
&aminate Composites
aminate composites consist of layers with different
anisotropic orientations or of a matri#reinforced with a dispersed
phase in form of sheets.
4hen a fiber reinforced composite consists of several layers
with different fiber orientations, it is
called multilayer )angle-ply* composite.
aminate composites provide increased mechanical strength in
two directions and only in one
direction, perpendicular to the preferred orientations of the
fibers or sheet, mechanical propertiesof the material are low.
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