Module 31. Heat treatment of steel I. Lecture 31. Heat treatment of steel I

Module 31 Heat treatment of steel I Lecture 31 Heat treatment of steel I 1

Keywords : Transformation characteristics of eutectoid steel, isothermal diagram, microstructures of pearlite, bainite and martensite, mechanisms of nucleation & growth, impingement factor, extended volume, inter lamellar spacing, effect of super cooling on inter lamellar spacing of pearlite Introduction In the last two modules we learnt how the strength of certain types of alloys can be improved significantly by a heat treatment called age hardening. It is a two stage process consisting of solution treatment and ageing. The alloy is first transformed into a super saturated state by heating it to a suitable temperature to dissolve the precipitates. It is subsequently quenched to suppress precipitation to retain excess solute in the solid solution. The alloy is soft under this condition. Its strength increases on ageing at a suitable temperature due to the formation of a fine array of precipitates. If such a treatment is given to common grades of steel we find it becomes very hard and brittle on quenching after homogenization in the austenitic state (similar to solution treatment). It has to be given a treatment similar to ageing (called tempering) to make it soft and ductile. This is primarily due to the special features of the iron carbon phase diagram. We are already familiar how by controlling the carbon content a wide range of structure and properties can be obtained in steel. The range can be further enhanced by subsequent heat treatment. We shall learn about it in the next 6 modules. Transformation characteristics of eutectoid steel: Let us recall the important features of eutectoid steel. It has around 0.8% carbon. If it is heated to a little above 723 C it transforms into austenite. If it is cooled slowly from austenite to room temperature it decomposes into a mixture of ferrite and cementite. It has a characteristic lamellar structure called pearlite. The widths of the ferrite and cementite plates are in the ratio 7:1. It is relatively soft and ductile. As against this if it is quenched from austenite you get martensite instead of pearlite. It is a super saturated solid solution of carbon in ferrite. It is extremely hard and brittle. Ferrite is BCC whereas austenite is FCC. Carbon atoms are accommodated within the interstices of the two lattices. The size of the interstices in BCC is much smaller than that in FCC. The lattice gets distorted if excess carbon atoms are retained within BCC structure. As a result it transforms into martensite having BCT structure. 2

910 723 760 t s t f + Cm 723 + Cm + Pearlite Pearlite + Cm Hypo eutectoid Hyper eutectoid 0 0.02 0.08 0.002 (a) 1.5 T M s M f M + + Cm + M Log (time) (b) Pearlite Bainite Fig 1 Figure 1 (a) shows the relevant part of the Fe Fe 3 C (Cm) phase diagram & the TTT diagram of eutectoid steel. Depending on carbon content steel may have widely different structure. If % C is less than the solubility limit it consists of 100% ferrite. It is soft and ductile. If % C lies between 0.002 to 0.02 it consists of a fine dispersion of Fe 3 C in a matrix of ferrite. The amount of % carbide can be estimated using lever rule. It comes out to be very low (~0.25%). Steel having %C between 0.02 and 0.8 is known as hypo eutectoid steel. It consists of pro eutectoid ferrite and pearlite. The amounts of the two constituents would depend on % C in the steel. The amount of pearlite is zero if %C is 0.02 whereas it is nearly 100% as %C approaches the eutectoid composition (0.8). Steel having %C beyond 0.8% is known as hyper eutectoid steel. It consists of pro eutectoid cement and pearlite. Commercial grades of steel rarely have greater than 1.5% carbon. The maximum amount of pro eutectoid cementite in steel may around 10 12%. Usually it appears in the form of a thin network along the grain boundary of austenite before it transform into pearlite. This makes the steel brittle. It is prone to inter granular cracking. It has to be given a suitable heat treatment to avoid the formation of such a network. We shall learn more about it in subsequent modules. This is all that we can infer about the structure of steel from its phase diagram. It does not tell us about the effect of cooling rate or the transformation temperature on the evolution of the structure in steel. It is major limitation of phase diagram. It only gives the structure of steel under thermodynamic equilibrium. Initial structure Structure at t > t s Structure at t > t f 3 Fig 2 100% A few pearlite nodules 100% pearlite NPTEL Phase II : IIT Kharagpur : Prof. at R. N. boundary Ghosh, Dept of Metallurgical and Materials Engineering (a) (b) (c)

Figure 1 (b) gives a schematic time temperature transformation (TTT) diagram of eutectoid steel. The concept was introduced in module 24. The decomposition of austenite to pearlite (a mixture of ferrite and cementite) is a solid state transformation. Diffusion of carbon in the austenite plays a major role. It takes place through a process called nucleation and growth. The first phase to nucleate is cementite. It forms preferably at the austenite grain boundary and grows into the grain. This is associated with the creation of a new interface having a definite energy. It also draws excess carbon from the surrounding area. As a result the area adjacent to the cementite nucleus gets depleted of carbon. When it falls below a certain limit ferrite plates nucleate on the two sides of the cementite nucleus. This is how the process continues. The features of the transformation are illustrated by a set of schematic structures shown in fig 2. If the steel is kept for a sufficiently long time at (say) 760 C (a little above the eutectoid temperature) it gets transformed into austenite. Let this now be transferred to a bath maintained at a temperature a little below the eutectoid temperature (675 C). It is now in a super cooled state. Let the degree of super cooling be represented as T. In this case T is around 50 C. This is measure of the driving force for the transformation of austenite into pearlite. Since it is associated with creation of new interfaces and diffusion of carbon in solid state does not take place instantaneously; the initial structure at this temperature is still 100% austenite as shown in fig 2(a). It takes some time (t s ) for the first pearlite nodule to form. This indicates the start of the transformation. Thereafter more nodules nucleate and the older ones keep growing. Figure 2(b) shows a schematic structure of the steel at time t > t s. Note that there are 3 nodules that have formed. They are of different sizes. The larger ones are those that have nucleated earlier. Pearlite is made of two different phases. They have different etching contrast. The line represents a cementite plate and the white areas on the two sides of it are ferrite plates. A nodule of pearlite consists of several alternate plates of cementite and ferrite. The term nodule is used to represent different pearlitic areas. Note that the orientations of the plates differ from nodule to nodule. The process of nucleation and growth of pearlite nodules continue until the entire area is covered by pearlite. It happens at a time t f. This denotes the time at which the decomposition of austenite is over (finished). Figure 2(c) gives a schematic representation of the structure of this steel at a time t > t f. Note that several nodules of pearlite may nucleate in a grain of austenite. Once a nodule nucleates it continues to grow until it impinges against another nodule beside it. As a consequence each grain of austenite transforms into several nodules of pearlite having different orientations. This is illustrates in fig 2(c). 4 The time at which the transformation of a super cooled austenite starts (t s ) and the time at which it finishes (t f ) depend on the temperature. If these are plotted against temperature a set of two C shaped plots are obtained. The details of the experimental methods to determine these were described in module 24. Figure 1(b) shows a schematic TTT diagram of eutectoid steel. The transformation product above the knee of the C shaped TTT diagram is pearlite. The

pearlite that forms near the eutectoid temperature is coarse whereas the pearlite that forms near the knee of the plot is fine. The inter lamellar spacing is a measure of its fineness. It is inversely proportional to the degree of super cooling. Figure 3(a) gives an enlarged appearance of lamellar structure of coarse & fine pearlites. Coarse Pearlite (a) (b) (c) Fine M or Upper Lower Bainite Cm Fe 2.4 C Martensite Fig 3 Cm The product of isothermal transformation in eutectoid steel below the knee of the TTT diagram is called bainite. It is also a mixture of ferrite and carbide. The bainite that forms just below the knee of the TTT diagram consists of broken platelets of cementite in a matrix of ferrite. The distribution is extremely fine. It cannot be seen under optical microscope. Since the transformation takes place at a low temperature the distance covered by carbon atoms is less. This is why the platelets are very small. This type of transformation product is known as upper bainite or feathery bainite. Figure 3(b) gives an enlarged view of the microstructure of upper (or feathery) bainite. The nature of bainite that forms at a still lower temperature is entirely different. It consists of a still finer dispersion of carbide (Fe 2.4 C) in a matrix of ferrite having an acicular shape. The carbides are aligned at a specific angle with respect to the axis of the needle. It is known as lower bainite or acicular bainite. Figure 3(b) gives an enlarged view of the microstructure of lower (or acicular) bainite. 5 If the steel is quenched directly to room temperature from 760 C it transforms in a manner that is entirely different from that of pearlitic or bainitic transformation. The cooling rate is so fast that the excess carbon cannot precipitate as carbides. Precipitation involves diffusion. Fast cooling does not allow enough time for carbon atoms to diffuse. The transformation that takes (a) place is known as diffusion less transformation and the product is called martensite. It has a different crystal structure than that of austenite which is FCC. The crystal structure of martensite in eutectoid steel is body centered tetragonal. Its c/a ratio is around 1.08. This means that the crystal structure of martensite is not very much different from that of ferrite which is BCC (where c/a = 1). Carbon forms interstitial solid solution with iron. The interstitial

6 gaps in FCC structure are symmetric and relatively large whereas the similar sites in BCC are asymmetric and smaller. This is why the solubility of carbon in austenite is more than that in ferrite. Carbon occupies octahedral sites in austenite (FCC) since these are the largest. Recall that a FCC unit cell has four lattice sites and four octahedral sites. Thus the number of sites to accommodate carbon in austenite lattice is quite large. A quick conversion of the weight % carbon in eutectoid steel to atomic % would show that only a very small fraction of these sites are occupied by carbon atom. Atom fraction of carbon in eutectoid steel is approximately = 0.8 x (atomic weight of carbon / atomic weight of iron) = 0.8 x (56/12)/100 = 0.037. This suggests that approximately amongst every 100 atoms of iron in austenite there are only four carbon atoms. This is equivalent to having only four carbon atoms in every 25 unit cells of austenite. On quenching if austenite were to transform into ferrite it would amount to a conversion of 25 FCC unit cell to 50 BCC unit cells (recall that FCC has 4 atoms / unit cell whereas BCC has 2 atoms / unit cell). The latter being less closely packed it would be accompanied by an overall expansion in volume (around 4%). In reality there is an expansion along certain directions and contraction along another. As a result the symmetric octahedral site in FCC gets converted into an asymmetric octahedral site in BCC. Quenching does not allow the carbon atoms to come out of the lattice in the form of precipitates. The presence of excess carbon atoms in the octahedral sites results in an asymmetric distortion of the lattice. This is why instead of BCC we now have a BCT lattice. This type of transformation occurs by deformation (shear). The process is extremely fast. It occurs at the speed of sound. Such a transformation is often termed as athermal. It takes place only by nucleation. There is no growth. It occurs in super cooled austenite is below a critical temperature called Ms. It is the temperature at which martensitic transformation starts. The process continues as long as is it is cooled. There is a temperature denoted as M f at which the transformation is nearly complete and no further transformation takes place on cooling. If the steel is quenched to a temperature below M f it is almost 100% martensite. Figure 3(c) shows an enlarged view of lens shaped matensite needles that form within an austenite grain. Once a needle nucleates it extends to the boundary. It does not cross the boundary or intersect another martensite plate or needle. The presence of excess solute, the associated lattice distortion and extremely fine size of the needles make martensite so strong. In short eutectoid steel can be transformed into a wide variety of microstructures simply by controlling the transformation temperature. If it is allowed to transform at a temperature a little below 723 C it transforms into coarse lamellar pearlite. As the transformation temperature is reduced the structure becomes finer and the steel becomes stronger. The eutectoid steel has the maximum hardness if it is converted into martensite. Coarse pearlite has the lowest strength. It can also be converted into bainite which is harder than pearlite but softer than martensite. Slide 1 gives the hardness of various products of transformation in Rockwell C scale along with its TTT diagram. It is also known as isothermal transformation diagram.

A 1 T M s M f Isothermal transformation diagram P f R P C 5-20 Coarse s Pearlite time B s B f R C 30-40 Fine Pearlite R C 40-50 Upper Bainite R C 50-60 Lower Bainite Martensite R C : 64 Slide 1 Isothermal transformation diagram A 1 T +cm B f Coarse Pearlite Feathery Bainite (a) (b) Slide 2 M s (c) B s M f Martensite (d) time Fine Pearlite + Acicular Bainite + Martensite 7 Slide 2 shows how by adopting different cooling schemes it is possible to get different types of structure in eutectoid steel. It shows four different cooling schemes. One of these consists of direct quenching from a temperature a little above A 1 (the lower critical temperature or the eutectoid temperature) where the steel is totally austenite. The cooling rate is extremely fast. Martensitic transformation starts as soon as the temperature drops below M s. It continues until M f, the temperature at which the martensitic transformation is nearly complete. This is the final structure of the steel if such a cooling scheme is adopted. Note that martensitic transformation

is an athermal transformation. It occurs in the steel within a specified temperature range as long as it cools even if the rate of cooling is extremely fast. The transformation stops if it is kept at an intermediate temperature between M s and M f. The M s temperature of a steel is a function of its composition. There are steels whose M f temperature is lower than room temperature. In such a case the microstructure of steel on quenching will consist of both austenite and martensite. The other 3 cooling schemes have one or more stages of isothermal hold. If the temperature of iso thermal hold is a little below A 1 temperature the transformation starts when the hold time exceeds t s and it continues until it reaches t f. Once the hold time exceeds t f the transformation is complete. It means hereafter if you cool fast or slow the microstructure of the steel would remain unaltered. The final microstructure is a function of the temperature of isothermal hold. In case (a) (see slide 2) the final structure is coarse pearlite whereas in case (b) the final structure is feathery or upper bainite. The cooling scheme (c) in slide 2 consists of two isothermal steps with hold times as shown. The first isothermal hold is in the temperature range where you expect the austenite to transform into fine pearlite. The transformation begins when the hold time intersects the C curve representing the start of pearlitic transformation. It continues for a while and then it is quenched to a bath at a temperature where the austenite could transform into acicular bainite. The transformation begins when the hold time exceeds the time needed for the bainitic transformation to begin. Note that the cooling curve crosses the C curve labeled as B s but after a while it is quenched to room temperature. During this stage the remaining austenite transforms into martensite. The final microstructure therefore consists of fine pearlite, acicular bainite and martensite. Pearlitic transformation: 8 Pearlite is a product of eutectoid transformation in steel. It forms within austenite having a fixed amount of carbon (0.8%C) during isothermal hold at a temperature below 723 C (A 1 ) but above 550 C (the knee of the TTT diagram). It has a lamellar structure consisting of alternate plates of cementite and ferrite. The distance between two consecutive cementite plates is known as its inter lamellar spacing (). The cementite plates are more widely spaced in coarse pearlite. The finer details of coarse pearlitic structure are visible under optical microscopes. Nital (2% nitric acid in alcohol) the most common etching reagent for steel attacks only the boundary between ferrite and cementite. However the width of a cementite plate is so thin that it appears as a dark line. Its width is approximately 1/7 th the width of a ferrite plate. Let us now look at the mechanism of decomposition of austenite into pearlite in a little more detail. This is shown in slide 3 by a set of sketches representing the redistribution of carbon within austenite resulting in the nucleation of a pearlite nodule.

Pearlitic transformation (a) Cm plate %C (b) plate 0.8% 0.8% 0.8% 0.8% Distance Slide 3 %C as a function of distance %C as a function of distance 0.8% 0.8% (c) The sketch (a) in slide 3 shows how % carbon in austenite would change when a tiny plate of cementite (Cm) forms. Recall that % C in eutectoid austenite and Cm are 0.8 and 6.67 respectively. When a tiny plate of Cm forms the carbon content at the interface drops significantly. However %C in austenite away from the interface still remains at 0.8%. This is represented schematically as a plot of %C as a function of distance on the two sides of a Cm plate. The carbon profile keeps changing with time as the Cm plate becomes thicker. When %C at the interface drops below a critical limit ferrite plates nucleate on the two sides of the Cm plate. %C in ferrite is as low as 0.02%. Therefore nucleation of ferrite is accompanied by the rejection of excess carbon into austenite. The %C in austenite increases beyond 0.8%. The sketch (b) in slide 3 shows the variation of %C as a function of distance from the ferrite austenite interface. This too keeps changing with time. When it exceeds beyond a critical point Cm plates nucleate at the two ferrite austenite interfaces as shown in sketch (c) of slide 3. This too is accompanied by a change in carbon concentration at the interfaces. This is how the pearlitic transformation in steel may be assumed to be taking place. On the basis of this assumption it is possible to find a relation between the lamellar spacing () of pearlite and the temperature of isothermal hold. This is illustrated in slide 4. 9 The sketch (a) in slide 4 shows a pearlite nodule consisting of alternate layers of ferrite and cementite. The sketch (b) shows the relevant part of the Fe Fe 3 C phase diagram. The dotted horizontal line denotes the temperature at which the pearlite nodule has formed. The line representing the composition of austenite that can coexist with ferrite as a function of temperature has been extended to intersect the dotted horizontal line denoting temperature at

a point. This represents the concentration of carbon at the / interface. The line representing the composition of austenite that can coexist with cementite as a function of temperature has been extended to intersect the dotted horizontal line at a point. This represents the concentration of carbon at the Cm/ interface. Note that. Therefore the growth of the nodule should be determined by the flow of carbon atoms from the / interface to the Cm/ interface. The real interfaces are curved not straight (see Fig 4). Pearlite growth kinetics Assumption: growth depends only on carbon diffusion within austenite from interface to /cm interface (a) Pearlite C cm C austenite (b) Pearlite C cm C T Growth depends on diffusion. G increases initially with increasing T as T decreases diffusivity becomes low & the growth becomes slow C m 0.8 Slide 4 Cm C Cm C J G Direction of flow of carbon Fig 4: The interface between austenite and ferrite is not straight as shown in slide 4 but curved as in this figure. The cementite plate is too thin. Therefore the curvature is not visible. Figure 4 indicates the direction of growth of pearlite. The growth may be assumed to be determined by the flow of carbon atom. This is governed by Fick s law of diffusion. J denotes the flux of carbon atoms. Its direction is denoted by the arrow labeled J in figure 4. 10 (1)

The growth rate (G) is is determined by J. It is directly proportional to the diffusivity of carbon in austenite and the concentration gradient that depends on the difference in carbon concentration within a specified zone of austenite. Note that (see sketch (b) in slide 4). It is therefore obvious from equation 1 that as T approaches zero (the isothermal transformation temperature is close to the eutectoid temperature) the growth rate is expected to be very slow. This is why the magnitudes of both t s & t f are large. As T increases the growth rate increases; the magnitude of t s & t f decreases. When the temperature becomes too low the transformation rate is dominated by the diffusivity of carbon in austenite. Therefore the growth rate again becomes slow and the magnitudes of t s & t f start increasing. This explains the C shaped nature of the transformation diagram. Isothermal transformation of austenite to pearlite: We have just seen how a nucleus of pearlite once formed could grow within a grain of super cooled austenite. The effect of nucleation rate was ignored. Yet it is possible to explain why the time temperature transformation diagram of a diffusion controlled transformation has a characteristic C shape. The nucleation rate too like the growth rate depends on the degree of super cooling. Let us now look at the process of transformation at a constant temperature. The kinetics of transformation at a constant temperature is best followed by monitoring fraction transformed as a function of time. Module 24 explains various ways of monitoring the kinetics of such transformation. Slide 5 shows the isothermal transformation (or TTT) diagram of eutectoid steel and beside it there is a plot of fraction transformed (f) as a function of time (t) at a constant temperature (T). The temperature at which the transformation has been monitored is shown as a horizontal dotted line on the TTT diagram (sketch (a) in slide (5)). The sketch (b) in slide 5 gives a plot of f as a function of time at a constant temperature T. Note that it has a characteristic S shape. The transformation starts when the hold time t exceeds t s. Initially the rate of transformation is slow but it increases until it reaches a maximum. Thereafter the rate of transformation keeps decreasing until the transformation is complete at time t = t f. 11

Pearlitic transformation t 0.5 1 t s T t f f 0.5 Slide 5 t 0.5 time 0 t s time t f (a) (b) A S shaped plot can be represented by the following equation where is a characteristic time and n is a constant that depends on the nature of the transformation. 1 (2) Equation 2 can also be expressed as: (3) This suggests a method of estimating n & from the plot in the sketch (b) of slide 5. A plot of versus ln(t) is linear. The slope of the plot = n whereas the intercept = nln((see fig 5). Slope = tan( = n 1 1 Intercept = nln() Fig 5 12 0

The slope n tells us about the mechanism of transformation. Slide 6 illustrates with the help of a set of sketches the most commonly cited nucleation and growth mechanisms of isothermal transformation. Nucleation & growth process (a) Constant nucleation & growth rate Austenite (t 1 ) (t 2 ) (t 3 ) (b) Nucleation followed by constant growth Slide 6 (c) Austenite Cellular transformation with fixed nucleation Effect of impingement t Pearlite Slide 6 explains with the help of sketches at three different times how the transformation proceeds by nucleation and growth. The case (a) represents a situation where both nucleation and growth occur at a constant rate. At time t 1 there are four nodules of pearlite within a grain of austenite whereas at time t 2 two more nodules have formed. Note that the nodules that were present at t 1 have grown bigger. At a still higher time (t 3 ) the number of nodules increases and the pre existing nodules grow in size. Note that the diameters of the nodules are different. The larger nodules are amongst the first to have formed. The case (b) in slide 6 represent a situation where growth starts only after nucleation is complete. This represents a sequential process. There are fixed sites within an austenite grain where a nodule of pearlite may nucleate. Once all of these sites are occupied by pearlite nodules then only growth sets in. This is often referred to as site saturation model. Note that in this case the dimensions of all the nodules are identical. 13 The case (c) shows the effect of impingement. It can occur in either of the two situations described above although the sketches shown are applicable for the case (b). As long as the nodules are small they can grow in all directions (see the sketches at time t 1 ). When the nodules become bigger they may impinge on a neighbor as shown in the sketch at time t 2 of case (c). The nodules can no longer grow in these directions. On completion of transformation

in this case a single grain gets divided into four nodules. It is shown by a set of lines. Having introduced the physical concept of transformation let us now try to derive an expression for fraction transformed (f) in terms of number of nucleation site / unit volume (N), growth rate (G), and time (t). Slide 7 explains how to account for the effect of impingement by introducing a concept of extended volume fraction. Extended volume fraction: concept Pearlite nodule Pearlite nodule (a) (b) V 1 V 2 V 1 V 2 Slide 7 Austenite Austenite The sketch (a) in slide 7 shows two pearlite nodules of volume V 1 & V 2 within an austenite grain of volume V T. If these are wide apart (there is no impingement) the volume fraction (f) is given by: (4) It represents the true volume fraction of pearlite. However if there is overlapping as shown in the sketch (b) of slide 7 the volume fraction estimated by equation (4) is going to be more than the true volume fraction. Let this be represented as the extended volume fraction (f ext ). (5) The relation between infinitesimal changes in true and extended volume fractions is given by 14 1 (6) Note that effect of overlap or impingement is negligible if the magnitude of f is low. The effect shows up as f increases.

Assume that N = the number of nucleation site / unit volume, G = rate of growth in mm / sec, r = average radius of the nodules = Gt. At any instant t the extended volume of all the nodules is given by: (7) Differentiation of equation 7 gives 3 (8) On substituting equation 8 in equation 6: 14 (9) Integrate equation 9 & substitute the initial condition that at t = 0, f =0 to get: 1 (10) Where the parameter is given by / (11) Note that is a characteristic time. It corresponds to a fixed value of f = f c. Put t = in equation 10. This gives: 1 0.632 (12) The characteristic time corresponds to 63% of transformation. The method of estimating n & has already been explained. If n = 3 it may be concluded that the transformation takes place at a constant growth rate after nucleation has occurred at all the available sites. Summary: 15 In this module we looked at how by proper selection of transformation temperatures and / or direct quenching from austenite a wide range of properties can be obtained in eutectoid steel. This is best described by an isothermal transformation (IT) or time temperature transformation (TTT) diagram. The transformation below the critical temperature (723 C) and above M s results in a mixture of ferrite and carbide. It is controlled by diffusion. At a given temperature it takes some time for the transformation to start (t s ) but it can go to completion at the same temperature after a time t f. The transformation occurs by nucleation and growth. The fraction transformed at a given temperature is zero until time t reaches t s. Thereafter it increases at

increasing rate till the transformed regions touch each other. Beyond this f still continues to increase but at reduced rate until time t f when the transformation is complete. The f versus t plot at a given temperature has a characteristic S shape. We also discussed how this can be explained by simple models based on nucleation & growth. The transformation product above the knee of the TTT diagram is called pearlite and that below it is called bainite. The kinetics of this transformation is a function of both time and temperature. We have seen how it can be explained in terms of diffusivity of carbon in austenite. The low temperature transformation products are much finer those at higher temperatures. As against these the transformation that takes place below M s is entirely different. There is no diffusion at all. It occurs as long as temperature keeps dropping. The transformation ceases if the temperature is held constant. The product is a super saturated solid solution (known as Martensite). There is no precipitate. It is extremely hard. The wide variety of transformation characteristics forms the basis of a wide range of heat treatments that can be given to steel. We shall learn more about it in subsequent modules. Exercise: 16 1. If a piece of steel having 0.2% carbon is quenched after soaking at a temperature just above A 1 what type of structure will you get? Estimate approximate amounts of phases present and their compositions. 2. In a hypothetical experiment on steel having 0.2%C, a sample after soaking above A 3 is quenched in a lead bath at 800⁰C and the structural change is followed with time. Assume that after some time austenite () boundary is covered by a thin layer of ferrite () and it continues to grow. This is known to be a diffusion controlled process. (a) Draw carbon profile perpendicular to interface after some time has elapsed. (b) Derive an approximate expression for the thickness of ferrite as a function of time (c) If diffusivity of carbon in austenite at 800⁰C is 3x10 12 m 2 /s 2 plot thickness as a function of time. 3. Carbon atoms occupy octahedral interstitial sites in austenite and ferrite. Estimate fraction of these sites that are occupied in these if carbon contents are 0.1 and 0.01wt% respectively. 4. Use Fick s first law to derive an expression for growth rate of pearlite nodule. 5. Show that the inter lamellar spacing of pearlite is inversely proportional to the degree of under cooling. 6. Microstructure of isothermally transformed pearlite should have identical spacing in all colonies. However often its microstructure often shows that lamellar spacing varies from colony to colony. Why is it so?

Answer: 1. A piece of steel when kept at just above A 1 temperature will have ferrite and austenite. % ferrite = (0.8 0.2)/0.8x100 = 75%. Assumption: %C in austenite =0.8% where as that in ferrite is negligible. If quenched 25% austenite present at soaking temperature will convert into Martensite. The structure at room temperature will consist of 75%ferrite and 25%Martensite having 0.8% carbon. 2. (a) Carbon profile on the two sides of interface is as follows: 0.2 Growth direction GB 0.47 0.02 910 800 723 0 c 0.8 910 800 0.8 0.47 910 723 (b) To derive a simple relation we assume: densities of austenite and ferrite are the same. Therefore wt % =vol %. Area of interface = 1. Carbon gradient in austenite is constant. This is given by following sketch 17 C 0 austenite x From the above one gets: L C C On substituting L : On integration thickness of ferrite layer at any time t =.. ferrite x Carbon gradient in = flux of carbon crossing the interface in time dt to move this by dx = This is equal to flux of carbon rejected by as it grows by dx =. L is obtained by equating the hatched area of the adjoining figure. /2 (c) 10 2.33.. 10 or 1.53 10 Note that this estimate is valid only for short time.

3. Number of octahedral site in austenite = 1 / atom of Fe. Atomic wt of carbon = 12 and Fe = 56. Atom fraction carbon in austenite =.... 0.0047. In one unit cell there are 4 Fe atoms and 4 interstitial sites. Fraction of these that are occupied = 0.0047. This mean amongst 100 unit cell the number of carbon atom is approximately 2 (~400x0.0047). Whereas in ferrite the number of such sites / Fe atom = 3. Atom fraction carbon. 0.00047. In one unit cell there are 2Fe atoms. Number of carbon atom = 0.00094. There are 6 sites / unit cell. Fraction of these that are occupied = 0.00094/12 = 7.8x10 5. This means there is approximately one carbon atom in approximately 1000 unit cells. 4. Super cooling is necessary for Pearlite to nucleate: T E T 0 cm Pearlite colony grows as carbon diffuses from / interface to cm / interface. Flux of C / unit area = %C 5. Super cooling is necessary to overcome activation hill arising due to creation of new surface. 18 G at T E T G 0 For inter lamellar spacing of the total interface area = 2/ m 2 / unit volume. G for this to form is given by where V m is molar volume, is surface energy and is free energy for formation of pearlite having infinite inter lamellar spacing. The transformation will not occur unless G <0. Thus: Cm

6. Pealite is made of alternate layers of ferrite and cementite. Ferrite plates are 7 time wider than those of cementite. Microstructure gives a sectional view. Colonies of Pearlite in a microstructure are randomly oriented. The plane of microstructure may intersect these at different angles. Wherever the plane is perpendicular to ferrite / cementite plates the spacing between two plates will be the minimum. Whereas those intersected at an angle will appear to have larger spacing. This is shown in following sketch: Pearlite colony Microstructure plane B A On plane B spacing would appear significantly larger. If transformation occurs at a fixed temperature the minimum spacing is the correct estimate of lamellar distance.. 19