what is the driving force for phase transformation of austenite to pearlite?

Ferrite Phase Transformation

Increase Model Predictive Capabilities by Multiscale Modeling

Maciej Pietrzyk , ... Danuta Szeliga , in Computational Materials Engineering, 2015

v.2.2 Phase transformations

The austenite-ferrite phase transformation is a temperature-activated phenomenon that leads to significant changes of the microstructure properties during the cooling process. The developed CA model is designed to simulate this transformation during cooling in the 2D space. The phase transformation algorithm on the ground of CA technique is presented in Effigy 5.24.

Figure 5.24. The concept of the CA stage transformation algorithm.

Each CA cell is described by several country and internal variables in order to properly depict physical state of the material. The jail cell tin can be in iii different states: ferrite (α), austenite (γ), and ferrite-austenite (α/γ), every bit shown in Effigy 5.25. The last state is used to describe CA cells located at the interface betwixt austenite and ferrite grains. Additionally, internal variables are defined to describe other necessary microstructure features. Cells contain information, for case, how many ferrite phase is in a particular cell F _i,j , what is the carbon concentration in each cell C _i,j , the growth length l _i,j of the ferrite-austenite prison cell into the austenite prison cell or the growth velocity V _i,j of the interface cell. These internal variables are used in the transition rules to replicate mechanisms of stage transformation.

Effigy 5.25. Analogy of the nucleus of the ferrite phase and the surrounding cells in the ferrite-austenite (α/γ) state.

Similar to the SRX model, there are ii major parts used to replicate the nucleation and growth of the ferrite grains in the austenitic matrix. Nucleation is stochastic in nature, thus diverse approaches to describe this process tin be used. In the nowadays model, to replicate the stochastic character of nucleation, a number of nuclei n is calculated in a probabilistic manner at the kickoff of each time step:

(5.17) $\mathrm{northward}=N(T_i){\left(\frac{B_i}{B_0}\right)}^{\mathrm{three}}P(\tau )$

(five.xviii) $\mathrm{Due\; north}(T_i)=\frac{a_1}{\mathrm{one}+\exp \left[{\displaystyle \frac{(A_{e3}-T_i)-a_2}{a_{\mathrm{iii}}}}\right]}\left(\frac{xy}{40,000}\right)$

(5.19) $P(\tau )=\frac{2}{3}\tau R(0,1)$

where B ₀, B _i are the mean amounts of γ cells at the beginning and ithursday time step, respectively, N is the full number of α nuclei, a ₁, a ₂, a ₃ are the model parameters, A _eastwardiii is the start temperature of the austenite-ferrite transformation, 10, y are the width and height of the CA space, P is the probability, and τ the fourth dimension step.

Beyond this, locations of grain nuclei are as well generated randomly along austenite grain boundaries. When a cell is selected every bit a nuclei, the state of this cell changes from austenite (γ) to ferrite (α). At the same time, all the neighboring cells of the ferrite (α) cell change their state to ferrite-austenite (α/γ). The carbon content, which was in the austenite prison cell is shared between all neighboring cells, which are in the country α/γ. Nucleation procedure has a continuous character and it occurs during the entire CA simulation until the finish of transformation. Afterward nucleus appears in the CA space, the growth of ferrite phase is calculated in the following steps.

Ferrite growth is controlled by the carbon diffusion, thus the carbon distribution across the microstructure is evaluated past the solution of the diffusion equation on the basis of the finite difference (FD) method:

(5.20) $\frac{\partial {\mathrm{ten}}_{\phi }^e}{\partial t}=D_{\phi }{\nabla }^2{x}_{\phi }^{\mathrm{east}}$

(5.21) $C_{i,j}^h=\frac{D\mathrm{\Delta }t}{\mathrm{\Delta }{x}^{\mathrm{ii}}}(C_{i-\mathrm{ane},j}^{h-1}+C_{i+\mathrm{ane},j}^{h-1}+C_{\mathrm{i},j-1}^{h-\mathrm{i}}+C_{i1,j+\mathrm{i}}^{h-1}-\mathrm{iv}{C}_{i,j}^{h-1})+C_{i,j}^{h-1}$

Due to very small carbon content in ferrite, model assumes carbon diffusion only within the austenite phase. Every bit a result, in the case when, for example, one of the neighbors (i+one,j) is in ferrite country then Eq. (five.21) is modified as:

(5.22) $C_{i,j}^h=\frac{D\mathrm{\Delta }t}{\mathrm{\Delta }{x}^2}(C_{i-\mathrm{one},j}^{h-1}+0+C_{1,j-1}^{h-\mathrm{i}}+C_{i1,j+1}^{h-1}-\mathrm{three}{C}_{i,j}^{h-\mathrm{one}})+C_{i,j}^{h-1}$

The transition rules describing growth of ferrite grains during phase transformation are designed to replicate experimental observations of mechanisms responsible for this procedure [198]. It is well known that the recently formed ferrite nuclei grow into the austenite phase. The velocity of the α/γ interface is assumed to be a product of the mobility M and the driving force for interface migration F:

(5.23) $\mathrm{Five}=MP=K_{0}D(T)F={\mathrm{One\; thousand}}_0{D}_0\exp \left(\frac{Q}{RT}\right)F$

where Grand ₀ is the mobility coefficient, T the absolute temperature, and D ₀ the improvidence coefficient.

The driving force for the phase transformation F in the present model is composed of chemical driving force F _chem and driving force related to grain boundary curvature. The former is due to the differences in the carbon concentration in equilibrium atmospheric condition and carbon concentration in each cell:

(5.24) $F_{\mathrm{chem}}=\beta \left[C_{\mathrm{eq}}(T_i)-C_{i,j}^{\gamma }\right]$

where β is the model coefficient, C _eq the equilibrium carbon concentration calculated using ThermoCalc software, C _i,j the carbon concentration in the (i,j) CA cell.

The latter is due to the shape and crystallographic orientation of the grain purlieus and tin be expressed as:

(five.25) $F_{\mathrm{fb}}=\gamma \kappa$

(five.26) $\gamma ={\gamma }_m\left(\frac{\theta }{{\theta }^m}\right)\left[1-\ln \left(\frac{\theta }{{\theta }^m}\right)\right]$

The $\kappa$ is described similar to the SRX model by Eq. (5.14).

The following transition rules are proposed in the book to replicate the phenomena occurring at the austenite-ferrite boundary. When the ferrite phase is present in the material, the CA ferrite cells grow into the austenite phase. In the current time step t, the growth length of the austenite-ferrite cell with indexes (i,j) toward an austenite neighboring cell with indexes (chiliad,50) is described equally:

(five.27) $l_{i,j}^t={\int }_{t_0}^t{5}_{i,j}\mathrm{d}t$

where t ₀ is the time when the CA cell (i,j) inverse into the ferrite state, and 5 _i,j the growth velocity of the CA cell (i,j).

The growth velocity V is obtained from Eq. (v.23) and so the ferrite book fraction in the CA cell (m,l) is calculated equally a outcome of the ferrite growth:

(five.28) $F_{k,l}=\sum _1^{N_{\mathrm{neigh}}}\frac{l_{i,j}^t}{L_{\mathrm{CA}}}$

where F _g,l is the total ferrite volume fraction in the CA cell (g,fifty), as a contribution from all the neighboring austenite-ferrite CA cells, L _CA the dimension of the CA cell in the CA space, and t the time step.

Based on these calculations the transition rules are defined as follows:

(v.29) $Y_{k,l}^{t+1}=\{\begin{array}{l}\mathrm{\alpha }/\mathrm{\gamma }\iff Y_{k,\mathrm{fifty}}^t=\mathrm{\gamma }{\wedge }^M{Y}_{i,j}^{t^t}=\mathrm{\alpha }/\mathrm{\gamma }\wedge F_{k,\mathrm{50}}^t>F_{\mathrm{cr}}\\ Y_{\mathrm{grand},l}^t\end{array}$

(5.30) $Y_{\mathrm{thousand},\mathrm{fifty}}^{t+1}=\{\begin{array}{l}\mathrm{\alpha }\iff Y_{k,\mathrm{50}}^t=\mathrm{\alpha }/\mathrm{\gamma }\\ Y_{k,\mathrm{50}}^t\end{array}$

where $Y_{\mathrm{grand},l}^t$ is the state of the cell (k,l) in the time step ${t,}^M{Y}_{i,j}^{t^t}$ the state of the Moore neighboring (M) cell (i,j) in the fourth dimension step t, F _cr the critical value of the volume fraction of ferrite in the CA cell.

The CA prison cell changes the state from austenite into austenite-ferrite when ferrite volume fraction in this cell exceeds the critical value F _cr. Otherwise the cell remains in the austenite state. When the cell changes its state to austenite-ferrite, all the neighboring cells in the austenite-ferrite state change their states into the ferrite. When a change in the cell land occurs, the corresponding carbon concentration changes according to the FeC diagram.

Examples of obtained results on the footing of the model implemented within the CA framework are presented in Figure 5.26. Figure five.26 presents evolution of microstructure morphology and corresponding carbon distribution changes during cooling with the cooling rate at five°C/due south. The size of the investigated CA infinite is 200×200   μm.

Figure 5.26. (a) Development of microstructure morphology and (b) carbon distribution changes during cooling with the cooling rate at 5°C/s.

As seen in Figure 5.26, the growth of newly formed ferrite nuclei is directly related with carbon concentration controlled by the diffusion procedure. Influence of crystallographic concentration on grain growth is neglected at this stage of the research, thus circular growth of ferrite grains is observed.

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Modelling stage transformations in steel

M. Pietrzyk , R. Kuziak , in Microstructure Development in Metallic Forming Processes, 2012

Differential equation model

A more than physically formulated model was proposed past some Japanese scientists (Suehiro et al., 1992; Senuma et al., 1992). This model is based on a differential equation, and therefore it tin can be applied easily to varying temperature weather. In add-on, several physical parameters are introduced into this model. In the remainder of this chapter, the model based on differential equations will be referred to equally 'model B'. The basic principles of this model are explained using the ferritic transformation as an example.

Two differential equations are used to describe austenite-ferrite phase transformation kinetics:

•

for nucleation and growth,

[6.fourteen] $\frac{\text{d}{\mathrm{10}}_{\text{f}}}{\text{d}t}=a_5{\left(SI{K}^3\right)}^{0.25}{\left[\ln \left(\frac{1}{\mathrm{i}-X_{\text{f}}}\right)\right]}^{0.75}(1-X_{\text{f}})$

•

for site saturation,

[6.15] $\frac{\text{d}{\mathrm{10}}_{\text{f}}}{\text{d}t}=a_6\times {10}^{-12}\exp \left(\frac{a_8}{RT}\right)\frac{6}{D_{\text{γ}}}\mathrm{Thou}(1-{\mathrm{10}}_{\text{f}})$

where 10 _f is the transformed volume fraction, I is the charge per unit of nucleation, G is the rate of transformation, South is the specific expanse of grain boundaries and D_γ is the austenite grain size.

The equations used to calculate the parameters in Eq. 6.xiv are given in Tabular array 6.1 (Suehiro et al., 1992; Senuma et al., 1992; Pietrzyk and Kuziak, 1999), with the following notation: R, gas constant; T, temperature in °C; $\stackrel{⌢}{T}$ , absolute temperature in Thou; ΔT = Ae ₃ – T, temperature drop below Ae ₃; ΔG, Gibbs free energy calculated using ThermoCalc; r, radius of curvature of the advancing phase; D, diffusion coefficient of carbon in austenite; C_γ , average carbon content in austenite; C_α , carbon content in ferrite; C ₀, initial carbon content in the steel; C_γα , carbon content in austenite at the γ–α phase boundary; C_γβ , carbon content in austenite at the γ–cementite stage boundary; K _p, velocity of the motion of the austenite/pearlite boundary; Q, heat generated during transformation; and ρ, density. All of the thermodynamic parameters, such equally the equilibrium temperatures Ae _one and Ae ₃ and the relations between the compositions C_γα , C_γβ , C_α and the temperature, were determined using Thermo Calc for the chemic composition of the steel.

Tabular array 6.1. Equations describing the parameters in the differential equation model

$I=\frac{D}{\sqrt{\stackrel{⌢}{T}}}\text{exp}\left(\frac{-{\text{α}}_7\times {10}^{\mathrm{nine}}}{R\stackrel{⌢}{T}\text{Δ}{G}^2}\right)$	$\mathrm{Thousand}=\frac{\mathrm{ane}}{2r}D\frac{C_{\text{γα}}-C_{\text{γ}}}{C_{\text{γ}}-C_{\text{α}}}$	$S=\frac{\mathrm{half-dozen}}{D_{\text{γ}}^4}$
$C_{\text{γ}}=\frac{(C_0-X_{\text{f}}{C}_{\text{α}})}{\mathrm{i}-{\mathrm{10}}_{\text{f}}}$	$r=\frac{1.14D^{0.5}(C_{\text{γ}}-C_0)}{\sqrt{(C_{\text{γ}}-C_{\text{α}})(C_0-C_{\text{α}})}}{t}^{0.5}$	$Q=\rho \text{Δ}H\frac{\text{Δ}X}{\text{Δ}t}$
$X_{\text{f}0}=\frac{C_{\text{γα}}-C_0}{C_{\text{γα}}-C_{\text{α}}}$

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Application of synchrotron and neutron scattering techniques for tracking phase transformations in steels

S.S. Babu , in Phase Transformations in Steels: Diffusionless Transformations High Forcefulness Steels Modelling and Advanced Analytical Techniques, 2012

Austenite to depression-temperature α-ferrite and/or pearlite

In the literature, the austenite to a -ferrite stage transformation has been studied extensively by using post-characterization techniques ( Bhadeshia, 1985) and past many groups atomic number 82 by Johnson and Mehl (1939, reprinted in 2010), Aaronson (2005) and Hillert (1997). Fifty-fifty later these extensive works, there are even so unanswered questions including, activation free energy for nucleation, transition from local equilibrium to paraequilibrium, competition betwixt nucleation rate and growth of grain boundary allotriomorphs, interface structure and partitioning, and mixed manner (interface and improvidence-controlled growth) transformation. Some of the above questions are beingness answered by conscientious experimentation involving selective field ion beam machining and atom probe field ion microscopy. However, the in-situ tracking of these transformations has merely been performed using resistance, magnetic and dilatometry methods, the latter beingness the nearly pop. In this regard, straight tracking of crystal structure and its carbon concentration would be ideal. Offerman et al. (2002) accept used in-situ synchrotron diffraction to rail the nucleation and growth states under irksome cooling weather. Based on the data, they ended that the experimentally measured activation energy for nucleation of ferrite is much lower than that predicted by thermodynamic models. Such data are influencing the development of robust austenite to ferrite transformation models (Van Dijk et al., 2007). Offerman et al. (2003) besides used neutron depolarization techniques to evaluate the nucleation and growth charge per unit of pearlite. Readers are referred to these classic papers for more details.

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Nucleation and growth during the austenite-to-ferrite phase transformation in steels after plastic deformation

J. Sietsma , in Phase Transformations in Steels: Fundamentals and Diffusion-Controlled Transformations, 2012

Abstract:

High temperature plastic deformation of austenite prior to the austenite-to-ferrite phase transformation during cooling can significantly influence the evolution of the microstructure during this transformation. This forms the basis for the germination of ultra-fine ferrite in steels. The basic processes of the phase transformation and the way in which these are affected past deformation defects in the parent structure are discussed in this affiliate. Both experimental and modelling studies bespeak the ascendant influence of prior plastic deformation on the nucleation process. Since the nucleus density is found to increase more strongly than the defect density before the transformation, a distinct increase in the nucleation potency is identified.

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Continuous Casting of Steel

Seppo Louhenkilpi , in Treatise on Process Metallurgy: Industrial Processes, 2014

1.8.4.3 Solidification Paths

Effigy 1.8.20 shows the left uppermost function of the Atomic number 26–C equilibrium phase diagram. We tin can see three important points, which divide the steel solidification modes or paths into four different areas. The points are C%   =   0.1, C%   =   0.18, and C%   =   0.51. The signal C%   =   0.xviii is called the peritectic betoken. The four areas are (one) C   =   0–0.one%, (2) C   =   0.i–0.18%, (3) C   =   0.18–0.51%, and (4) C   >   0.51%. It must be noticed that these values are only for binary Fe–C blend and for equilibrium conditions and alloying and nonequilibrium conditions change these values a lot. Merely typically, all steels solidify according to one of these 4 solidification modes. When a new steel course is bandage and produced, it would be skillful to calculate the exact phenomena and solidification paths using a good solidification model.

Figure 1.8.20. The left uppermost role of the Fe–C equilibrium phase diagram. The three points in the figure divide the solidification of the Fe–C steels into four different areas. The four areas are: (1) C   =   0–0.1%, (2) C   =   0.one–0.18%, (iii) C   =   0.18–0.51%, and (4) C   >   0.51%.

Area 1 (C   =   0–0.1%). The solidification takes place only with liquid to δ-ferrite stage transformation and then that at solidus the dendrite is fully ferritic. Microsegregation is small considering the diffusion coefficients are high in the ferrite. So these steels are not very sensitive to hot slap-up. Below the solidus, the δ-ferrite transforms to austenite and the steel shrinks (about 0.6%) during this transformation. If this transformation starts close to solidus, as in Effigy i.8.21 is the case for steels close to 0.1%, the steel is very sensitive to many kinds of surface defects. The reason is that when this shrinkage takes identify at a thin shell shut to solidus, the beat is non strong plenty to resist deformation. The deformation leads to the formation of air gaps betwixt the crush and the mold and uneven estrus transfer and shell growth. The air gap ways besides reduced heat transfer leading to crush reheating and grain growth. These steels are sensitive to hot spots and surface bully. Uneven heat transfer and shell reheating may likewise cause longitudinal surface cracking. If the phase transformation takes place at lower temperature, non shut to solidus, the shell is stronger to resist its deformation. The ferrite phase is quite soft, and if the amount of ferrite is large in the strand, the strand should exist cooled and supported well to foreclose bulging.

Figure one.viii.21. Beginning of solidification of 0.ane C% steel in the mold with air gap formation which causes reduced heat transfer and grain growth at the surface.

Courtesy of Aalto University/J. Miettinen.

Area 2 (C   =   0.i–0.xviii%). The solidification starts with liquid to δ-ferrite phase transformation. When the carbon content is C   =   0.one% or close to that, the δ-ferrite transforms to austenite just below to the solidus temperature. These kinds of steels are very sensitive to surface defects (encounter the text of the Area i). Figure i.8.22 shows this miracle schematically. The ferrite to austenite transformations starts simply below the solidus leading to air gap formation between the crush and the mold. A schematic quality index bend for surface defects is also presented in the effigy. The dendrite is fully ferritic when the carbon content is 0.1%. When the carbon content is higher, the solidification starts with δ-ferrite, only when the temperature has decreased to the peritectic temperature in a higher place the solidus, the solidification continues with peritectic reaction. In the peritectic reaction, the already solidified δ-ferrite reacts with liquid forming solid austenite. This reaction takes place with carbon content from 0.ane% to 0.51%. The reaction starts from the dendrite surface where δ-ferrite and liquid react to austenite when the temperature has decreased to the peritectic temperature (see Figure ane.8.23). When the temperature is decreasing, the reaction continues so that the austenite is forming betwixt the liquid and δ-ferrite phases. So the austenite grows toward both the solid and liquid directions (Figure 1.8.23). The peritectic reaction ends when either the liquid or δ-ferrite stage has disappeared. When the carbon content is 0.18%, the peritectic reaction ends because both the liquid and δ-ferrite disappear at the same time and so at the solidus, the structure is fully austenitic. With less carbon content than C   =   0.18%, the reaction ends because liquid phase is disappearing. The remaining δ-ferrite continues to transform to austenite just below the solidus. And every bit mentioned before, the closer the content is to C   =   0.one%, the stronger is this phenomenon leading to surface quality problems. When the main solidification phase is ferrite, the microsegregation is relatively small considering the diffusion of the alloying and tramp elements is much faster in ferrite than in austenite. The smaller the microsegregation is, the more than the solidification occurs with liquid to ferrite reaction and so microsegregation is in general relatively depression in depression carbon steels compared with the college carbon steels. Microsegregation increases the sensitivity to hot smashing, and so low carbon steels are not very sensitive to these kinds of defects. When the carbon content is around C   =   0.18%, the austenite grain size volition exist relatively high and this increases the sensitivity to cracking (run across Section 1.8.four.1).

Figure 1.8.22. Carbon steels with around C   =   0.1% are very sensitive to surface defects (figures left). Carbon steels with effectually C   =   0.18% take high austenite grain size and this increases the sensitivity to cracking (figures right). Cooling rate has small outcome on these phenomena [half dozen,x].

Courtesy of Aalto University/J.Miettinen.

Effigy 1.eight.23. Schematic presentation of the solidification phenomena of carbon steels with C   =   0.18–0.51%. The solidification occurs with three reactions: (ane) liquid to ferrite, (2) peritectic reaction, and (3) liquid to austenite. The concentration at liquid remains quite high [10].

Courtesy of Aalto University/J. Miettinen.

Surface area 3 (C   =   0.18–0.51%). The solidification starts again with liquid to δ-ferrite phase transformation and when the temperature decreases to the peritectic temperature the peritectic reaction starts (see Figure i.8.23). But now the peritectic reaction ends already above the liquidus because δ-ferrite is disappearing. For these steels, a third solidification reaction is occurring during solidification and it is that the remaining liquid afterwards peritectic reaction transforms to austenite. At solidus, these steels are fully austenitic. The trend to microsegregation increases with increasing carbon content considering the solidification reaction, liquid to austenite, is increasing. The length of the mushy zone (liquidus temperature minus solidus temperature) is too increasing with higher carbon content. Stronger microsegregation and larger mushy zone brand these steels sensitive to internal defects like hot cracking and macrosegregation.

Area 4 (C   >   0.51%). Only 1 solidification reaction occurs in these steels; the liquid transforms to austenite. The dendrite is fully austenitic and then the structure at solidus too. The trend to microsegregation is highest compared with the steels of other Areas 1–iii. The length of the mushy zone increases with increasing carbon content. These steels are very sensitive to internal defects like hot cracking, porosity, and macrosegregation. Hot slap-up tendency can be evaluated by calculating the length of the temperature interval from temperature at which at that place is about ii% cook left to the solidus temperature. Higher value means higher hot dandy trend. Microsegregation has a big result on this value. Figure 1.8.24 shows schematically the effect of carbon content and cooling rate on this index. Cooling rate has two twofold effects on microsegregation: fast cooling charge per unit reduces the diffusion time only likewise reduces the diffusion lengths because thinner arms are forming. The starting time i has a negative effect and the second ane a positive effect for reducing microsegregation.

Figure 1.8.24. The outcome of carbon content and cooling charge per unit on the tendency of internal quality. High carbon steels are in general sensitive to internal defects because of the potent microsegregation and the long solidification interval. Calculated by IDS tool [half-dozen,10].

Courtesy of Aalto University/J. Miettinen.

When the carbon content is college than two%, the compositions are typically already named as cast irons, not steels. The solidification of cast irons typically starts with dendritic solidification of liquid to austenite reaction, but when the temperature is reaching the so-chosen eutectic temperature, the solidification continues with eutectic reaction. In eutectic reaction, the liquid transforms to two solid phases forming a lamellar (eutectic) structure. The solidification morphology of cast irons is then dendritic–eutectic structure, whereas in steels, the solidification structure is fully dendritic. If the carbon content in cast irons is higher than the eutectic point (~   4.2%), the primary phase can besides be graphite or cementite.

It should exist noted that even if the microsegregation is strong, the homogenization of the structure beneath the solidus temperature is in general fast because the improvidence rates are high at high temperatures. This is peculiarly the case for interstitial elements like C, B, N, O, and H.

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Stage transformations in microalloyed high strength low blend (HSLA) steels

R.C. Cochrane , in Stage Transformations in Steels: Diffusionless Transformations High Forcefulness Steels Modelling and Advanced Analytical Techniques, 2012

6.8 Conclusions and future trends

While the microalloying concept has proved of slap-up benefit in terms of producing steels capable of satisfying the mechanical belongings requirements demanded past users, the process of developing new steels still succeeds on an empirical basis although guided past the metallurgical principles described. The increasing need to validate models to predict microstructure will expose some shortcomings in the understanding of the details of the austenite to ferrite phase transformation, specifically nucleation. Austenite grain size prediction from noesis of the rolling functioning and the steel limerick already gives realistic results for laboratory simulations used for studying controlled rolling. The office of Nb in the evolution of the deformation substructures is also approaching a stage where information technology can realistically exist anticipated that the 'conditioned' state of the austenite at a relevant length calibration can be predicted for some commercial rolling operations. There seems, even so, no simple method of predicting ferrite grain size straight from the country of the austenite. Almost all of the current approaches rely on empirical relationships between the final ferrite grain size and the state of the 'conditioned' austenite. Given the complexity of the ferrite grain coarsening which is evident from more recent studies, it is unlikely, in the writer's opinion, that this task will be an easy ane. Moreover, the development of the 'ultra-fine', quasi-polygonal, 'bainitic' or acicular ferrite microstructures feature of the recent generation of low carbon TMCP steels has all the same to be clarified and related in particular to the transformation behaviour. It would appear that there is a much greater spread in grain mis-orientation in these TMCP steels than is observed in more than conventional TMCR steels, suggesting that the features noted for ferrite grain coarsening may operate at lower transformation temperatures. Furthermore, the observation of groups of laths with characteristics of bainite together with groups of grains of appreciably larger mis-orientations might imply the diffusional ferrite transformation is promoted or accelerated at particular austenite grain mis-orientations or within the grain interiors by retained deformation. At that place have been studies on the effects of deformation of weld metals which testify an dispatch of the AF reaction, but in one case it was judged that strain accumulation effectually inclusions raised the AF transformation start temperature ( Yang et al., 1995). This finding seems compatible with the microstructural changes noted in some HSLA steels where retained deformation appears to promote AF over GB (granular bainite) in a temperature range where displacive transformation predominates (Jun et al., 2006) (Fig. 6.44).

6.44. Outcome of deformation (b) in replacing bainitic ferrite (BF) past acicular ferrite (AF) over the cooling rate range ~1–20°C/sec. GB: grain boundary ferrite, Chiliad: martensite. Boron treated 0.05%C-0.25%Si-1.92%Mn-0.067Nb+Ti-1.ane total Mo+Cr+Ni.

From Jun et al. (2006).

There are new approaches which should shed some calorie-free on the mechanisms responsible for the microstructures plant in TMCP steels noted in a higher place. Applying molecular dynamics (MD) and Monte Carlo (MC) computational methods to the dynamics of clusters of solute atoms of the type detected by atom probe studies should lead to a better understanding of the events leading to ferrite nucleation (run across Tateyama et al., 2010; Nagano and Enomoto, 2010). Information technology can be argued, for instance, that strong interactions between Iron and solutes in alloy systems showing intermetallic formation, Fe-V, Atomic number 26-Ti, Atomic number 26-Nb or Fe-Al, would change the Fe-X(any solute)-Atomic number 26 cluster dynamics leading to nucleation, both in the austenite matrix just likewise at grain boundaries, hence influencing nucleation rates of ferrite. The question over the significance of epitaxial nucleation events for acicular ferrite nucleation may also be clarified past such processes; some relevant studies have been carried out on Al alloys (Bunn et al., 1998), where similar epitaxial events are thought to be implicated in grain refinement from the as-cast state (Schumacher et al., 1998).

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Identification of Cloth Models and Purlieus Conditions

Maciej Pietrzyk , ... Danuta Szeliga , in Computational Materials Engineering, 2015

iv.ii.one.3 Phase transformation models

The review of various phase transformation models was presented in Section iii.six. For wide range of metal-forming application, the model selection has to be made by searching for a balance between the model predictive capabilities and computing costs. The modified JMAK model described in Department iii.6.1 is a compromise solution. Due to a big number of parameters of this model, the objective of the investigations was to validate the model construction with the SA provided in Section two.i.iii, especially global sensitivity methods, to identify the model parameters of the highest bear upon to the model outputs to make the identification procedure, see the algorithm 2.viii in Section 2.one.three, more than reliable and efficient by reducing the dimension of the input parameters space.

The modified JMAK model is defined by Eqs. (3.123)–(3.138) Eq. 3.123 Eq. 3.124 Eq. three.125 Eq. three.126 Eq. 3.127 Eq. 3.128 Eq. iii.129 Eq. 3.130 Eq. iii.131 Eq. three.132 Eq. 3.133 Eq. 3.134 Eq. iii.135 Eq. three.136 Eq. 3.137 Eq. 3.138 , Section 3.6.1. For a item material, for cooling process, model parameters a ₄, …, a ₂₇ should be identified. The goal function defined in the identification algorithm two.eight for this problem is multimodal, thus SA was performed every bit a preliminary step of identification.

Sensitivity of the modified JMAK phase transformation model with respect to the model parameters was estimated using iii global sensitivity methods from Department 2.1.3.2: the Morris blueprint, correlation ratios, and Sobol' indices. The model inputs were: x={cr, a}, where cr is the cooling rate, $\mathbf{a}=(a_4,\cdots ,a_{27},D_{\gamma })$ the parameters of the JMAK model for cooling process, and $D_{\gamma }$ the austenite grain size at the offset of the transformations. Ten model outputs y=(T _ij , X _i ) were analyzed, where T is the temperature, X _i the phase volume fraction, $i\in \{\mathrm{f},\mathrm{p},\mathrm{b},\mathrm{grand}\}$ indicates ferrite, pearlite, bainite, or martensite phase, and $j\in \left\{\mathrm{s},\mathrm{e}\right\}$ indicates start/end of phase transformation, respectively. The modified JMAK model includes information on steel chemic composition as well as information on phase equilibrium weather. Hence, the model validation was performed for the selected dual stage steels. The chemical composition of the steels is listed in Table four.1 every bit DP600 A and DP600 B. The parameters describing carbon concentrations equilibrium, determined with ThermoCalc software, are provided in Table 4.2.

Table iv.2. Parameters in Eq. (3.130) describing equilibrium carbon concentrations

	c γα0	c γα1	c γβ0	c γβ1
DP600 A	4.57	−0.005412	−0.94	0.00228
DP600 B	4.8513	−0.005776	−i.46583	0.002887
	$c_{\alpha }=\{\begin{array}{ll}-0.069+0.000435T-9.1658\times {10}^{-\mathrm{vii}}{T}^2+6.487\times {\mathrm{ten}}^{-\mathrm{x}}{T}^{\mathrm{iii}}\hfill & \mathrm{f}\mathrm{o}\mathrm{r}T\<{637}^{\mathrm{o}}\mathrm{C}\hfill \\ -0.0487268+0.00017839T-1.50788\times {10}^{-\mathrm{vii}}{T}^2\hfill & \mathrm{f}\mathrm{o}\mathrm{r}T\ge {637}^{\mathrm{o}}\mathrm{C}\hfill \end{array}$

The sensitivity results for all parameters a={a _iv, …, a ₂₇, D _γ } obtained for the investigated steel by Morris blueprint are presented in Figure four.17. It is observed that some of the model parameters practise not bear on whatever model outputs; some of them influence the model outputs in negligible way. These parameters cannot be identified based on analyzed model outputs and/or they should be eliminated from the model.

Figure 4.17. SA results obtained past Morris design for the modified JMAK model of the cooling process.

The conclusions are formulated every bit the summary results from the application of three sensitivity methods: Morris pattern, correlation ratios, and Sobol' indices:

•

Ferrite. The results for ferrite transformation obtained from all sensitivity methods are presented in Effigy 4.18. Starting time temperature of ferrite transformation is the well-nigh sensitive to a ₇ (parameter in k _f Eq. (iii.123))—high impact of this parameter on T _fs and X _f is observed. Post-obit remarks are made for the next parameters: a ₄ (exponent due north in Eq. (3.91))—slight sensitivity to the temperature start T _fs, higher sensitivity to the volume fraction X _f, a ₅ (parameter in thou _max Eq. (3.124)) and a _six (parameter in T _nose Eq. (iii.125))—both outputs: T _fs and X _f are sensitive to these parameters, a _eight (parameter in k Eq. (three.123))—depression impact of this parameter on T _fs and X _f, a ₂₀ (parameter in B _southward Eq. (3.134) and bainite incubation time τ _b in Eq. (3.129))—it determines B _southward and information technology indirectly influences X _f—thus college sensitivity to X _f, low sensitivity to T _fs, D _γ (parameter in k _max Eq. (iii.124))—the same sensitivity conclusions as for a ₂₀. Proffer: parameter a ₈ can be eliminated in modeling ferrite phase transformation. The lack of the model sensitivity on D _γ parameter is questionable. It should exist pointed out that the dilatometric tests were performed only for one austenite grain size, thus dependence of the transformation kinetics on D _γ is non reliable. This problem should exist further investigated by performing dilatometric tests for various grain sizes.

Figure iv.18. Ferrite phase sensitivity indices calculated with respect to parameters of modified JMAK model estimated by methods: (a) Morris design, (b) Correlation ratios, and (c) Sobol'.

•

Pearlite. For the considered chemical composition of steel the contribution of pearlite transformation is negligible and observed for low cooling rates, below 1°C/south. The conclusions on model sensitivity are formulated based on Morris pattern calculations—Effigy four.17. The start phase transformation temperature T _ps is sensitive to a ₅ parameter in k _max Eq. (3.124) for ferrite transformation, which indirectly impacts on the beginning of the pearlite transformation. The end stage transformation temperature T _pe and stage volume fraction X _p are sensitive starting time of all to a ₁₄ parameter in one thousand _p Eq. (3.126) for pearlite. Some sensitivity is observed for parameters a ₄ and a _vii defended to ferrite phase. For dual stage steel that was chosen for analysis, those parameters determine if the pearlite transformation starts, hence their impact on the pearlite model outputs. The pearlite transformation for dual phase steels is observed only for low cooling rates (lower than 1°C/due south), regarding the fact that the model of the pearlite transformation for DP steels can exist simplified.

•

Bainite. The results for bainite transformation obtained from all sensitivity methods are presented in Figure four.19. Three bainite phase model outputs: stage transformation temperature start/cease B _{due south}/B _eastward and phase volume fraction 10 _b are sensitive to a _twenty parameter from B _s Eq. (iii.134) and bainite k _b Eq. (iii.127) and next to a ₂₆ parameter from equation M _s (3.134) defining stage start temperature of martensite. Side by side, B _south is sensitive to a ₁₉ and a ₁₈—parameters from bainite incubation time τ _b (Eq. (three.129)). Low sensitivity to these parameters is observed for B _east. The model output B _e is sensitive to a ₂₄, which is the exponent n in Eq. (iii.91)). Latter parameters defining bainite transformation are: a ₁₇, a ₂₁, a ₂₂, a ₂₃ practice not bear upon the bainite model outputs or their affect is very low. Suggestion: the bainitic transformation model tin can be simplified.

Figure 4.nineteen. Bainite phase sensitivity indices calculated with respect to parameters of modified JMAK model estimated by methods: (a) Morris design, (b) Correlation ratios, and (c) Sobol'.

•

Martensite. The results for martensite transformation obtained from all sensitivity methods are presented in Figure iv.20. Phase temperature start M _south is sensitive to a ₂₀ parameter from B _s Eq. (3.134) and next to a ₂₆ parameter from M _s Eq. (three.134). The results for phase volume fraction X _m are not consistent only the impact of the to a higher place-listed parameters a _twenty and a ₂₆ is observed. Moreover, slight influence of a ₄–a ₇, a ₁₄, and a ₂₃ is noticed. Proffer: parameter a ₂₇ from Eq. (3.134) should not be modeled.

Effigy 4.xx. Martensite phase sensitivity indices calculated with respect to parameters of modified JMAK model estimated by methods: (a) Morris design, (b) Correlation ratios, and (c) Sobol'.

To sum upwards, the SA indicated the ready of parameters of the highest impact on the model outputs and in the parameters identification process they should exist adamant. The parameters of the depression impact should exist stock-still or, if it is possible, eliminated from the model of the investigated steels. Based on the obtained results, identification procedure presented in this section was applied for selected steels.

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Kinetics of phase transformations in steels

Southward. van der Zwaag , in Phase Transformations in Steels: Fundamentals and Diffusion-Controlled Transformations, 2012

iv.1 Introduction

As is well known, and clearly presented in the other chapters in this book, lean and assimilated steels can exist in dissimilar phases or mixtures of phases depending on the chemic composition and the actual temperature. Different many other metal systems, steels can undergo not just the liquid-solid phase transformation merely also many solid-solid stage transformations. These solid-solid phase transformations, the nature of which depend on the cooling rate in going from ane (stable or metastable) phase to another (stable or metastable) phase, offer a unique tool to tailor the microstructure of steels and thereby to tune the mechanical backdrop of steels of a fixed chemical composition over a broad range of strength and ductility values. Given the wide range of steel compositions in combination with the many phase transformations and resulting microstructures, it is impossible to bargain with all options and conditions within the context of a single affiliate. Hence, in this chapter the attention is focused on the austenite-ferrite phase transformation which plays a dominant role in any thermomechanical process route for low alloy or lean steels. This is not unreasonable because low alloyed steels with either a simple or a complex multiphase microstructure form about 80% of all steels currently produced. For virtually of these steels the allotriomorphic ferrite forms a large fraction of the full microstructure. The handling of merely this type of transformation hither is, on the one hand, specific as other solid state transformations related to austenite decomposition, such equally pearlite, upper and lower bainite and martensite formation, have other specific characteristics. On the other hand, the clarification of this type of transformation is generic every bit the interacting aspects of nucleation, growth and initial microstructure will play a role in all sorts of transformations. The chief purpose of this chapter is to testify the complexity of the kinetics of phase transformations and to demonstrate that for seemingly identical weather condition the kinetics can be rather different. Furthermore, the treatment will evidence that a single transformation-time curve, can never be reconstructed unambiguously into all the factors and processes which played a part in the transformation kinetics. Implicitly the handling too explains why steels of a stock-still composition made on dissimilar installations can have unlike microstructures and hence properties.

The chapter starts with the well-known macroscopic description of solid land phase transformations based on a sequence of nucleation and growth processes, the Johnson–Mehl–Avrami–Kolmogorov (JMAK) approach. To stay in line with the subsequent handling of the physics of the nucleation and growth processes, attention is focused on isothermal transformations. While it is possible to derive the exact values of the primal parameters in the JMA model assuming a microstructure free continuum as the starting condition for the transformation, and by making additional assumptions on the nucleation and growth processes, information technology is incommunicable to invert the process and to derive hard evidence for either the nature of the nucleation or growth procedure by plumbing fixtures JMA equations to experimental transformation curves. In this chapter the effect of the microstructure on the apparent JMA parameters for a given transformation process is shown.

Nonetheless its pivotal function in phase transformations, as a conditio sine qua non, the precise physics of the nucleation process remain rather unclear. This is partially due to the impossibility to monitor non-invasively the rearrangements of the small number of atoms (estimated at values as depression as a hundred or less) making the transition of being in the parent phase to forming the nucleus in the relevant fourth dimension scale (estimated at values less than a microsecond). In this chapter we will summarize a recent generic model for nucleation processes, which explains why information technology is impossible to quantitatively predict the nucleation kinetics for steels as a function of composition and undercooling.

While the growth of ferrite grains from the parent austenite seems easier to address as information technology gain on a larger scale (typically micron scale) and over longer fourth dimension scales (seconds to minutes), exact prediction of kinetics remains hard every bit the growth involves both short distance diminutive rearrangements at the austenite-ferrite interface, as well as long distance diffusional transport of interstitial and substitutional alloying elements with widely differing intrinsic mobilities. In this chapter nosotros discuss recent findings on the nature of the ferrite growth suggesting that unlike growth mechanisms may apply to different grains in the same sample undergoing a unmarried thermal treatment. Finally, the chapter concludes with a curt section discussing the relevance of a good understanding of the transformation kinetics for the steel industry.

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Recent Development in Focused Ion Beam Nanofabrication

Charlie Kong , ... Richard D. Tilley , in Comprehensive Nanoscience and Nanotechnology (Second Edition), 2019

ii.15.4.1 Surface Modifications

FIB was used for creating high resolution patterns of maskless implantation doping on silicon in the very early phase [2]. Recently, Ocelic and Hillenbrand demonstrated that the surface phonon polaritions could be confined past gallium implantation on SiC with a FIB, equally shown in Fig. 7 [278]. They found that gentle ion implantation with simple patterns could induce local surface amorphization without significantly altering the chemical composition of the surface. So the local backdrop of surface phonon polaritons could be controlled with a single step Ga implantation procedure.

Fig. seven. Infrared near-field amplitude images of Ga⁺ FIB implanted structures of a checkerboard pattern taken at 891 cm^–1. The inset shows a zoom-in scan of the 200 nm squares.

Reprinted with permission from Ocelic, N., Hillenbrand, R., 2004. Subwavelength-scale tailoring of surface phonon polaritons by focused ion-beam implantation. Nature Materials 3(9), 606–609. Copyright © 2004 Nature Publishing Group.

It was found that Ga ion implantation would induce microstructural modifications about the surface in a number of materials. The Ga modification effects were investigated on thin films of Cu, Au, and West respectively [279]. It was found that the Ga implantation could result in microstructural alterations including texture development in surface layers. These modifications were more significant in fine-grained materials, but non so in big grained materials. Babu et al. [280] studied the kinetics of the austenite-to-ferrite stage transformation occurred on the surface of 316 L austenitic stainless steel during Ga implantation in FIB. They plant that this type of phase transformation may be in relation to the grain orientation of parent austenite.

Ga implantation was applied to the nanofabrication process on the surface of diamond. Kawasegi et al. [281] demonstrated a texture fabrication process of the nanopolycrystallined diamond (NPD) using the combination of FIB irradiation and heat handling. The selected area on the diamond surface could be converted to non-diamond phases by Ga ion implantation in a FIB, and then oxidized to CO and CO_two during the heat treatment. So the desired surface roughness formed on the diamond. This grouping too presented another method for patterning the surface of a single crystalline diamond in the sub-micrometer scale with a combination of FIB and deep ultraviolet (DUV) light amplification by stimulated emission of radiation irradiations [282]. The surface area of the diamond irradiated by the FIB was selectively machined down to a maximum depth of 80 nm using a low-ability DUV light amplification by stimulated emission of radiation, whereas the non-FIB-irradiated area was inappreciably machined.

Ga implantation has too been applied to manipulate properties of nanostructures, such as nanowires (NWs). Burchhart et al. [283] reported to have tuned the electrical behavior of germanium-nanowire (Ge-NW) MOSFETs devices with Ga implantation. With the Ω-shaped metallic gate acting as implantation mask, highly doped source/drain (S/D) contacts were formed in a self-aligned procedure by FIB implantation. Recently, Scholz et al. [284] demonstrated a method to grow perpendicularly ordered pure monocrystalline InAs NWs with FIB implantation. A special dual beam FIB-SEM system with AuGa liquid blend ion source was operated at 30 kV. The unmarried charged Au ions purified with an ExB mass filter were implanted on the substrate of GaAs with the user-defined patterns. The produced high quality NWs showed no stacking faults and loftier aspect ratios up to ane:300. In the other report, Ga implantation in FIB has also been used to fabricate ZnS NW device [285]. The ZnS NWs were single-crystalline with a wurtzite structure synthesized via a vapor–liquid–solid mechanism. Ga ions were used as the dopant species by implantation.

The surface modification with Ga implantation has been used to fabricate special nanostructured devices. Shahmoon et al. [286] presented a method to deposit charged nanoparticles into specific patterns made past FIB milling. The degradation procedure relied upon the Ga implantation on an insulated material, which resulted in the nanoparticles trapped in the narrow gaps on the substrate to form a desired nanodevice. Curtz et al. [287] demonstrated a novel approach of fabricating nanodevices from the thin moving-picture show of loftier temperature superconducting (HTS) materials by FIB technique. Ga implantation converted the unwanted HTS region into an insulating phase, which acted as a passivation layer effectually the sidewalls of the unaffected nanostructure. More recently, Lam et al. [288] further modified this procedure and made nanoscale HTS YBa_iiCu_threeO_seven (YBCO) constrictions using a progressive trimming procedure with Ga implantation, which converted the outer layer of YBCO to a insulating protective layer, while the inner layer of YBCO film was nonetheless unaffected. This controllable procedure was used to justify the extent of YBCO surface modification and hence, tuning the final characteristics of the superconducting nanobridge.

It is interesting to notation that Shukla et al. [289] reported a novel method to make nano or micro metallic patterns on substrate with Ga implantation in FIB. They demonstrated the idea past patterning on Au coated SiO₂/Si substrate followed by but skin-off. It was found that the patterned Au dots were printed and stuck on the substrate due to Ga implantation. The method is suitable for materials of which the adhesion to the substrate can exist improved by ion bombardment.

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An overview of the recurrent failures of duplex stainless steels

Cesar Roberto de Farias Azevedo , ... Angelo Fernando Padilha , in Technology Failure Analysis, 2019

2.one Wrought DSSs (0.01 wt% ≤ C ≤ 0.08 wt%)

This sub-group of DSS shows values of prices between US$ 5.8 /kg to United states$ 7.viii/g, yield strength betwixt 460 and 620 MPa, fracture toughness between 71 and 212 MPa.m^1/2 and PREN between 24.five and 45.seven. The most popular form of wrought DSS (UNS S31803, see Tabular array i) presents in the annealed condition a very interesting combination of mechanical strength, ductility and toughness at 20 °C (yield forcefulness higher than 450 MPa, elongation higher than 25% and Charpy V captivated energy of 300 J) [1–ii,9,13–fifteen].

During the solidification of these ingots there is the formation of a fully ferritic microstructure (liquid→ liquid + ferrite) and the austenite stage, divers every bit secondary austenite, is formed by solid state phase transformation (ferrite→ ferrite + secondary austenite), see Fig. 1a. The nucleation and growth of the secondary austenite phase take place between 1250 and 600 °C by the partial decomposition of the ferrite stage (see Fig. anea) and its kinetics features a typical C-curve when represented in a TTT diagram [14]. The hot working of DSSs betwixt 1200 and 1050 °C promotes the germination of a duplex microstructure with a defined proportion of the ferrite and austenite phases (see Fig. anea). After hot working, a solution annealing estrus treatment (between 1000 and 1100 °C) is necessary maintain the correct proportion and morphology of ferrite and austenite phases in gild to reach the required mechanical and corrosion properties.

Wrought DSSs are usually supplied in the solution-annealed condition, exhibiting a duplex microstructure containing between 40 and threescore vol% of austenite phase [1,2,9,13]. The resulting microstructure features alternating ferrite and austenite lamellae (see Fig. 3a and b , showing the ferrite/austenite interfaces but non the ferritic and austenitic grain-boundaries). Fig. iiic shows the corresponding grain boundaries, allowing the effective evaluation of the morphology and the grain size of the austenite and ferrite phases in the wrought DSS. As the ferrite/austenite interface energy is lower than the ferritic and austenitic grain boundary energies, the thermodynamic rest induces the formation of the typical lamellar duplex microstructure [1–two,15–16].

Fig. 3. Duplex microstructure. (a) Three-dimensional microstructure of a rolled DSS sail (UNS S31803, encounter Table 1), where the ferrite is the darker phase. Optical microscopy, Behara II etching [fifteen]; (b) EBSD image of ferrite and austenite of a rolled UNS S32750 DSS; (c) Orientation paradigm map - aforementioned field shown in (b) - for the effective visualization of the grain boundaries of the austenite and ferrite phases in the lamellar DSS [16].

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