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Phase DiagramsPhase Diagrams A phase is a physically distinct, chemically homogeneous and
mechanically separable portion of a substance.It has a well defined structure, uniform composition and distinct boundaries
or interfaces.
A phase can be continuous or discontinuous. Example, Draw macrostructure
Alloy may be homogeneous (uniform) or mixtures. A homogeneous alloyconsist of single phase or multiple-phases.
The relationship between phases in a system as a function of
Temperature, Pressure and Composition depicted in the form of Map is a
phase diagram. The diagram in equilibrium condition is known asequilibrium phase diagram.
Equilibrium condition- very slow heating or cooling
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The simplest phase diagram is a pressure temperature diagram for a
fixed composition material e.g. water, iron (phases present are ice,
water and water vapour).
mp
Temp.
allotropic trans.
Eq. diagram of pure metal
For most of the reactions occurring at atmospheric pressure, it is
temperature (vertical axis)-composition (horizontal axis) diagram.
For pure metals, the diagram is a vertical straight line. The melting/
boiling/ allotropic transformation temperatures are points on the lines.
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A phase diagram consisting two phases - binary diagram
three phases- ternary
multiple phases multiple phase diagram
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Time-temperature Cooling CurvesTime-temperature Cooling Curves
The alloy phase diagrams are constructed from a series of time-temperature cooling curves. When a pure metal (alloy in some cases)
solidifies from liquid state there is a arrest of temperature due to release
of latent heat. As a result arrest of temperature. In other cases (alloys)
there may be fall of temperature during solidification.
temperature
time
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Cooling Curve of a Binary Phase SolutionCooling Curve of a Binary Phase Solution
Fig (a) is the cooling curve of pure metal (solidification at a fixed temp.).
Fig (b) Binary alloy with completely soluble liquid and solid phases(solidification over a range of temp.). .
Fig (c ) Binary system with completely soluble liquid and mixed solid phases
(eutectic). Eutectic phase formation also occurs at a fixed temperature.
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Isomorphous SystemIsomorphous System
When components are completely soluble in both liquid and solid state
and no chemical reaction takes place.
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System with Partially Soluble ComponentsSystem with Partially Soluble Components
When components are completely soluble in liquid state and partially
soluble in solid state and no chemical compound formation. E.g.Eutectic and Peritectic systems.
Only solid solutions and . A phase mixture of and phases (Eutectic).
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Gibbs Phase RuleGibbs Phase RuleStability of phases depend on temperature, pressure, concentration,
composition. From thermodynamics consideration of equilibrium, Gibbsderived the following phase rule.
F = C P + 2
Where F = Degree of freedom of system (e.g. temperature,pressure, concentration, composition of phases)
C = Number of components forming the system
(i.e. elements or compounds)
P = Number of phases in the alloys (in equilibrium system)
2 = Number of external factors (temperature and pressure )
Metals are mostly used at atmospheric pressure. Thus, the pressurehas not any appreciable effect on equilibrium of alloys in solid andliquid states.
Thus, equilibrium can be modified as
F = C P + 1
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Apply the above equation to pure metal at the solidification
temperature.
The solid phase and liquid phases co-exit at a particular temperaturei.e. solidification temperature. Hence, the equation will be solved asfollows:
F = 1 2 + 1 = 0 (fixed temp of solidification, degree of
freedom zero)
After the pure metal has solidified there will be one degree of freedom,i.e. the temperature:
F = 1 + 1 1 = 1
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A mixture consisting of two metals which have a solidification range asagainst a fixed solidification temperature of a pure metal, when thealloy is partly solid and partly liquid:
F = 2 2 + 1 = 1 (solidification over a range of temp., withoutdisturbing the equilibrium of the two phase )
When the alloy has completely solidified, it will have two degree offreedom without any change in the equilibrium of the system:
F = 2 1 + 1 = 2 (Temp. and Comp. )
The maximum number of phases a binary alloy can have in equilibriumwithout any degree of freedom is worked out as follows:
F = 0
0 = C + 1 P
= 2 + 1 P
P = 3
This means that there can be three separate phase in equilibrium in abinary alloy.
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In a ternary alloy the number of phases in equilibrium with no degree of
freedom is worked out as follows:
F = 0
0 = C + 1 P= 3 + 1 P
P = 4
The degree of freedom cannot be a fraction or less than zero
C P + 1 > 0
or C + 1 > P, P < C + 1Hence number of phases present will not be more than the number of
components + 1.
In case of binary alloys the maximum number of phases can be 3 and for
ternary alloy, it can be 4.
The phase rule predicts maximum number of phase present in the alloy under
equilibrium conditions at any point of diagram. If number of phase are known,
we can know the degree of freedom from phase rule. Then it will be known
whether the temperature or composition of phase or both can be changed at
the time without changing the structure of the alloy.
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Phase analysisChemical Composition of Phase
Tie line ruleLet us consider the chemical composition of alloy of metal A and B at temperature T1 shown in Fig. 9.8
Chemical composition of the phase, at any temperature, in two phase region, is determined by tie line
rule I, i.e. by drawing a horizontal line XY from temperature T1. The line XY is called tie line. From
points X and Y draw vertical lines cut the base line at points a and b respectively. The composition of
phase (solid solution phase) is 88% A and 12% B corresponding to point a as shown in Fig. 9.8.
Similarly composition of liquid phase is 60 A and 40 B corresponding to point b.
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Amount of Phases
The amount of each phase present in the two region is determine by
lever rule. Let us say, we are interested to find the amount of liquidphase and solid phase for 75%A 25%B alloy at temperature T1. Draw
a horizontal line representing temperature T1. Also draw a vertical line
ab, representing alloy composition. The horizontal and vertical lines cut
at point Z as shown in Fig. 9.9 (a). The point Z is considered as fulcrum
of the lever system. The lengths XZ and YZ are considered as leverarms as shown in Fig. 9.9 (b). The entire line XY represents 100% or
total weight of two phases at temperature T1. From lever rule we can
find the amount of liquid phase and solid phase ().
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Percentage of liquid phase =
Percentage of solid phase =
The numerical value of XY, ZY and XZ are interested and the amount
of phase is determined. The value of phase are as under.
XZ = 13ZY= 15, XY = 28
Hence, the percentage of liquid phase =
The percentage of solid phase =
100xXY
XZ
100xXY
ZY
4.4610028
13!x
6.531002815 !x
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Hence the amount of solid is proportional to the distance from the
fulcrum to be end of lever marking the liquid composition. The amount
of liquid is proportional to the distance from the fulcrum to the other
end, which marks the solid composition. The inverse relationship, whichputs the fulcrum at the centre of gravity between phase, is the simple
rule for calculating relative amount of phases.
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Solid Solutions
A solid solution forms when, the solute atoms are added to the host
materials, the crystal structure is maintained, and no new may/ may not
structure are formed. Perhaps it is useful to draw an analogy with a
liquid solution. If two liquids soluble in each other are combined, a liquid
solution is produced as the molecules intermix, and its composition is
homogeneous throughout. A solid solution is also compositionally
homogeneous; the impurity atoms are randomly and uniformlydispersed within the solid.
Solid solution is composed of two parts
1. Solute: The solute is the minor part of the solution or the material
which is dissolved.
2.Solvent: Solvent constitutes the major portion of the solution. Bothsolute and solvent can be solid, liquid or gas.
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Unsaturated Solid Solution
If the solvent if dissolving very small amount of solute lower than thelimiting value at a given temperature or pressure, it is called
unsaturated solid solution.
Saturated Solid Solution
If the solvent is dissolving limiting amount of solute, it is calledsaturated solid solution.
Super Saturated Solid Solution
If it is dissolving more amount of solute than it should, under equilibriumcondition and it is called supersaturated solid solution.
Super saturated condition can be accomplished by stirring, by rapidlycooling the solution, etc. The super saturated condition are unstable.When enough time is given or energy is supplied, the solid solutionbecomes saturated by rejection or precipitating the excess solute.
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A solid solution is simply a solution in the solid state and consists of two
types of atoms combined in one type of lattice. Solute is more soluble
in liquid state than in solid state. Most of the solid solution solidify over
a range of temperature.
Solid Solution Alloy
Let an alloy consists of two metal A and B. The melting point of the
alloy will be in between the melting points of metal A and B. Theliquidus and solidus line can be shown as in Fig. 9.10 (a) and (b).
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These line have minimum and maximum value of temperature. At
composition K1 the alloy behaves as pure metal i.e. its solidification
takes place at one constant temperature and there is no change in
composition. The cooling curve of alloy of composition K shown ahorizontal line. Such alloys are called congruent melting alloys. These
diagrams are eutectic diagrams and such alloys are called
pseudoeutectic alloys. Alloys showing the behaviour as shown in Fig.
9.10 (b) (i.e. liquidus and solidus lines pass through a maximum) are
very rare.
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Heat Treatment VariablesThe main aim of any heat treatment process, whether at some intermediate stage intermediate
stage of processing, or in the final stage, is to produce the desired changes in themicrostructure of metal and alloys This is done to ensuring desired properties inthe metals and alloys. There are a number of factors, or heat treatment process variables, whichhave to be chosen properly and controlled as these affect the attainment of proper microstructure.
The important variables which affect the heat treatment process are:
a)Temperature of heating (generally austenitising),
b)Time of heating and soaking.c)Rate of heating.
d)Furnace atmosphere, etc.
The process variables also include variables during multiple heating stages,interrupted heating, cooling to sub-zero temperature, interrupted quenching,multiple tempering, etc.
The chemical composition of alloy, original microstructure of the part, size andshape of the part, ultimate properties desired in the part and economic of theprocess, or processes control the exact method, or duration of the cycle, orcycles.
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Objectives of Heat Treatment
Heat treatment may be done to derive one, or more of the following objectives:
1. To enhance ductility , softness and machinability.
2. To increase hardness, wear resistance and cutting ability.
3. To increase toughness, i.e. obtain both high tensile strength and good ductility to
withstand high impact and absorb large energy during plastic deformation and ultimately fractire.4. To refine grain size.
5. To remove internal and residual stresses induced during working/ non-
uniform cooling (of heated parts) / casting / welding.
6. To improve specific properties such as high surface hardness with a tough
core, of high temperature properties, or corrosion resistance etc.
7. To improve electrical/ magnetic properties.
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Allotropy of iron
-iron (bcc, a=1.241 at 20C, Lattice parameter=2.92 at 1394C), iron (fcc,
a=1.270 at 20C,L=3.591 at 20C), , iron and iron (bcc) (a=1.241 at
20C,L=2.863 at 20C ).
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Structure bccand fcc Iron
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Phases in Iron-cementite equilibrium system
i. Alpha ferrite( just ferrite): Ferrite is an interstitial solid solution of carbon in- iron and this is bcc. The maximum solubility of carbon in ferrite is 0.02%
at 727C (point T in Fig. 1.22), which decreases with the fail of temperature
to negative amount of 00C (< 0.0008% at 200C). It is soft and ductile phase.
95 VHN
ii. Austenite: It is an interstitial solid solution of carbon in iron and has fcc
structure. The maximum solability of carbon in austenite is 2.11% at11470C, which decreases to 0.8/ 0.77% carbon at 7270C. Austenite is soft,
ductile tough and malleable (fcc structure) and paramagnetic. Steels are
commonly rolled and forged above about 11000C when they are in
austenitic state due to its high ductility and malleability, which is also due to
its fcc structure. 395 VHN
iii. Delta ferrite: It is an interstitial solid solution of carbon in - iron havingbcc structure. It has maximum solubility of carbon of 0.09% at 14950C. It is
a high temperature phase.
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Cementite or Iron carbide, Fe3C: It is an interstitial intermediate
compound with carbon 6.67%. Complex orthorhombic crystal stucture (12
Fe and 4 C atoms per unit cell). Brittle and very hard 800 VHN
Graphite: Pure form of carbon found in Fe-C system. A phase in gray castirons.
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Reactions in Fe Fe3C diagram
Three important invariant (at a constant temperature) reactions take place asdescribed below:
Peritectic Reaction: A peritectic reaction, in general, can be represented byan equation:
Where, L represents a liquid of fixed composition, S1 and S2 are two differentsolids of fixed composition each Fig. 1.23 illustrate the peritectic region of Fe-Fe3C diagram. The variant peritectic reaction in Fe-Fe3C diagram is given by:
21 SHeating
CoolingSL
C
FCCAustenite
Cooling
C
Cof
BCCferrite
Cof
L
%17.0(
)(1495
%09.0(
)(
%53.0(
0
p
H
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Eutectic Reaction:
An eutectic reaction in general can be represented by an equation:
L (of eutectic composition)
21 SSHeating
CoolingL (of eutectic composition)
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Eutectic reaction in Iron-cementile phase diagram
Austenite
Austenite+ Cementite
Pearlite+ Cementite
Pearlite=Ferrite+Cementite
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Eutectoid Reaction: The eutectoid invariant reaction is a solid
state version of eutectic reaction and in general can be
represented by an equation:
S1 S2 + S3
Where S1, S2 and S3 are three different solids each of fixed
composition. The Fig. 1.25 illustrates the eutectoid region of Fe-
Fe3C diagram. The invariant eutectoid reaction in Fe-Fe3C
diagram is given by equation:
Heating
ooling
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Effect of Carbon on Iron
Allotropy of iron: Carbon significant affects the allotropy of iron, as is illustrate
in Fe-Fe3C diagram. The crystal structures of bcc -Fe and the fcc -Fe are
modified by adding carbon atoms in the interstices of iron atoms (Fig. 1.19)
Carbon addition decreases the freezing temperature of iron to become-11470C at 4.3%C in cast iron. A lowering of temperature of about 4000C, helps
to melt and cast the cast irons, easily as compared to steels.
Carbon is an austenite stabilizer and expands greatly the austenite field and
also lower the fields of ferrite (BCC).
New phases: This introduces another phase and reaction (eutectoid) on slow
cooling. High rate of cooling still another phase, martensitr (super saturatedsolid solution of carbon in -iron)
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Effect of Carbon on Mechanical Properties
of Annealed Steels
As the carbon content of slowly cooled plain carbon steels increase, theamount of pearlite from 0%C to 100%C at 0.77%C, the remaining other phase
being ferrite.
Pearlite: A mixture of two phases, i.e. hard and brittle cementite, embedded in
soft and ductile ferrite, makes the steel stronger and stronger as its amount
increase to 100%.
The cementite plates in pearlite acts as a barrier to the motion of dislocations in ferrite (see Fig.1.33), thereby increase the resistance to deformation and thus the strength but,
reduces the ductility and toughness. As the carbon content increases, amount
of cementite (hard and brittle) increases, thus the hardness increases with
decrease of % eleongation % reduction in area and impact strength.
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According to the micro structure
in the annealed state
Hypo eutectoid Steels: Microstructure of these steels contains
varying proportions of proecutectioid ferrite (also called free ferrite) and
pearlite, i.e. the amount of pearlite increase from 0% upto 100% as the
carbon content of the steel increase to 0.77%.
Eutectoid Steel: The steel with 0.77% carbon has 100% pearlite in its
microstructure.
Hyper eutectoid Steels: Microstructure of these steels contains
varying proportions of proecutectioid cementite (also called free
cementite) and pearlite, i.e. the amount of pearlite increase from 0%upto 100% as the carbon content of the steel increase to 0.77%.
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Steels and Cast irons
Iron-carbon alloy containing carbon less than 2.11% C
Cast irons Iron-carbon alloy containing more than 2.11% C
These definitions are applicable to pure Iron-carbon systems
The above mentioned limit may change with addition of alloying elements
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Transformation on cooling in Iron-cementile phase
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Commercial Classification
1. Low Carbon Steels: carbon upto 0.25%.
2. Medium Carbon Steels: carbon from 0.25% to 0.55%.
3. High Carbon Steels: carbon from 0.55% to ideally a maximum of
2.11% but commonly upto 1.5% max. in commercial steels.
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Low Carbon Steels:
Carbon content is low (upto 0.25%) in these steels.
Combination of fair strength with high ductility with excellent fabrication
properties (for rolling, drawing, pressing, welding etc.).These steels are not hardened as the hardenability is low to producemartensite. The hardness of martensite (if produced) is low.
Conventional Low Carbon Steels:
These steels contain upto 0.1% carbon with 0.3-0.4% manganese andare cold worked low carbon steels.
These steels have yield strength of 200 300 MPa. Tensile strength of350 370 MPa and percentage elongation of 28 40%
Conventional Mild Steels:These steels have carbon content between 0.15% to 0.25%, i.e. highercarbon content than conventional low carbon steels, and thus, havehigher strength but lower ductility and thus are usually hot workedsteels.
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High Carbon Steels (Carbon more than 0.55%)
These are heat treatable steels.
Heat treatment is done to develope high hardness, wear resistance,
cutting properties and have least ductility. These are mainly tool steels.
% Carbon Applications
0.55 0.65% C Railways
0.65 0.75% C Saws
0.75 0.85% C Car bumpers
0.85 0.95% C Small cold chisels
0.95 1.10% C Dies
1.10 1.40% C Razors
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Indian Standard Specifications
Steels have been classified on the basis of properties and the chemicalcomposition, though mainly it is based on the latter.
Code Designation Based on Mechanical properties
It uses the tensile strength or the yield strength for designation,
Fe = minimum tensile strength in N/mm2
Fe E = minimum yield strength in N/mm2, Fe E 210
Code Designation Based on Chemical Composition
Specification Codedesignation
Average Composition
C15 C = 0.15%C
30C5 C 0.30, Mn = 0.5%
15Ni2Cr1Mo15 C = 0.15, Ni = 2, Cr =1,
Mo = 0.15%
15Cr3Mo55 C = 0.15, Cr = 3, Mo =
0.55%
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AISI Specification (The American Iron and Steel Institute)
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Function of Alloying Elements
Plain carbon steels are ironcarbon alloys in which the propertiesare primarily derived from the presence of carbon. Some incidentalelements like Mn, Si, S and P are present in small amount usually
introduced during iron/steel making.
Alloying steels are those which contain one or more alloyingelements intentionally introduced to enhance or impart certain
properties.
It is difficult to distinct boundary between plain carbon and alloy steels.
AISI definition: All steels containing Mn \> 1.65, Si \> 0.60 and
Cu \> 0.60% are plain carbon steels and all other are regarded as alloy
steels.
Common alloying elements: Mn, Ni, Cr, V, Si, W, Cu, Mo etc.
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Limitation of Plain Carbon Steels
The largest tonnage of metallic materials produced are plain carbon
steels, signifying their extensive applications. More over, carbon steelsare cheap and available in large quantities in quite a large variations of
shapes and sizes. Their heat treatments are simple. An engineer
should try to use as far as possible the carbon steels.
The most important limitations of carbon steels are:
1.Low hardenability.
2.Low corrosion and oxidation resistance.
3.Major loss of hardness on stress relieving tempering treatment.
4.Poor high temperature properties.
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The limitations of carbon steels are overcomed by the use of alloy
steels.
The presence of alloying elements not only enhance the outstandingcharacteristics of plain carbon steels, but also improves some other
properties or even induce specific properties.
The effects of alloying elements
1. improve the hardenability
2. improve corrosion and oxidation resistance3. increase resistance to softening on tempering
4. increase high temperature properties
5. but also increase resistance to abrasion
6. increase strength of the part that cannot be subjected to quenching due to
physical limitation of part or the structure in which it is employed.
Alloy steels are expensive and may require more elaborate processing,
handling and even heat treatment cycles.
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Types of Iron Binary Diagrams
1. Phase diagram with Open -field. (austenite stabilizer)
2. Phase diagram with Expanded -field. (austenite stabilizer)
3. Phase diagram with Closed -field. (ferrite stabilizer)
4. Phase diagram with contracted -field. (ferrite stabilizer)
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Classification of Alloying Elements
Based on stabilizing Austenite or Ferrite:i. Austenite Stabilizer : Mn, Ni, Co, Cu, Zn increase the range in which -
phase, or austenite is stable (by raising A4 and lowering A3 temperature). Fig. 1.42 (1) and (2) andalso tend to retard the separation of carbides. These elements have -phase-FCC crystal structure (or similar structure) in which these segregate(dissolve) in austenite in preference to ferrite. Elements like carbon and nitrogen(interstitial solid solution forming elements) are also austenite
stabilizers.
ii. Ferrite Stabilizers: Cr, W, Mo, V, Si, Al, Be, Nb, P, Sn, Ti, Zr (Fig. 1.44for Cr) increase the range of -phase. Majority of carbide formers are alsoferrite formers.
iii. (by lowering A4 and lowering A3 temperatures). These elements have -phase-BCC crystal structure (orsimilar structure) and thus in ( + ) two phase equilibrium, these elements segregate (dissolve) in ferrite in
preference to austenite. These elements decrease the amount of carbon soluble in austenite and thus tendto increase the volume of free carbide in the steel for a given carbon content. Majority of carbideformers are also ferrite formers. Chromium is a special of these elements as at lowconcentrations, chromium lowers A) temperature and raises. A4 temperature and raises A3 but at highconcentrations raises A3. Overall, the stability of austenite is continuously decreased Transformer steel with
hardly carbon and around 3% silicon is ferrite steel.
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Based on carbide forming tendency
i. Carbide forming elements: Important elements, in this class are
arranged in order of increasing affinity for carbon and thus the carbide
forming potential of the elements (as compared to iron):Fe Mn Cr W Mo V Ti Nb Ta Zr.
If say, vanadium is added in steel having chromium and molybdenum with insufficient carbon, then vanadium
first removes carbon from chromium carbide, the remaining vanadium then removes carbon frommolybdenum carbide and forms its own carbide. The released chromium and molybdenum dissolve to form
solid solution in austenite. Several ferrite formers are also carbide formers.
ii. Graphitising elements: Si, Ni, Cu, Al are common graphitisers. Small
amount of these elements in steels can graphitise it and thus impair the properties ofsteel unless elements of group (i) as present to counteract the effect.
iii. Natural element: Co is the only element which neither forms carbide,
nor causes graphitisation.
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Effects of Alloying Elements in Steels
1. They may form substitutional solid solution in ferrite or austenite,
resulting in solidsolution strengthening.Structural steels, because of their physical dimensions cannot be heattreated and are used in hot rolled conditions can be strengthened by solidsolution hardening particularly the weldable type of steels wheremanganese content may be increased to 1.3 1.7%.
2. They may dissolve in carbide. Mn may dissolve in cementite to formalloyed cementite, (Fe, Mn)3C.
3. Alloying elements may form their own carbide or nitrides, like NbC, VN,WC, Cr23, V4C3.
4. They may form intermediate phase like sigma phase FeCr in stainlesssteel a brittle phase. They may form intermetallic compounds Ni3T3, NiAletc.
5. They may form non metallic inclusions such as oxides.
6. They may be present as insoluble metals like copper or lead.
7. Alloying element may influence the critical range in Fe-Fe3C diagram(change in eutectoid temperature)
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7. Alloying element may influence the critical range in Fe-Fe3C diagram in
one or more of the following ways:
a) Change the carbon content of eutectoid (Fig. 1.47). All the elements lowerthe eutectoid carbon content. Titanium and molybdenum are the most
effective in lowering it e.g. a steel with 5%C has its eutectoid point at
0.5%C as compared to 0.77% in carbon steels. High speed steel (18/4/1)
has eutectoid point at 0.25% carbon.
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b) Change the eutectoid temperature: the eutectoid temperature in plain
carbon steels is 7270C. Elements lime Ni, Mn, i.e. the austentie stabiliser
lower this temperature. Ferrite stabilizer (Cr, V, W, etc.) raise the
eutectoid temperature above 727
0
C as the concentration is increased . Tiand Mo are most effective in raising the eutectoid temperature. For
example 3% Ni lower the A4 temperature by 300C. High speed steel
(18/4/1) has eutectoid temperature raised from 7270C to 8400C. It is to be
noted the manganese and nickel are the only common elements that
lower the eutectoid temperature and all other raise it (Fig. 1.48).
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Some other effects of alloying elements
Effect on GrainGrowth: Strong carbide and nitride forming elements play animportant role in limiting the grain growth during heating.
Effect on Resistance to Softening on Tempering: The hardened plain carbonsteels soften rapidly with increasing tempering temperature (Fig. 1.52).
Effect on Corrosion and Oxidation Resistance: Alloying elements like
chromium, aluminium and silicon make the steel resistance to oxidation andcorrosion, though chromium is most outstanding. A minimum of 12% chromiumis needed for protection against oxidation atmospheres.
The amount of chromium needed has to be increased to give resistance to scaling at high temperatureas the temperature of application increase. Stainless irons (virtually free of carbon) have 13%chromium are ferritic, but are used for furnace components. Cutlery steels require high carbon to gethard martensite to have sharp, had cutting edge and thus, are made to 0.6 0.75% carbon with 17
18% chromium.
In 18/8 austenitic stainless steel (0.1% C), addition of nickel further improvescorrosion resistance apart from converting the alloy steel to metastableaustenite (FCC). This impart ductility toughness and excellent cold workingproperties and the steel find use in kitchen wares surgical instruments and inchemical plants.
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