Gardner’s motivation theory

Computational approach to metallurgical alloy design to realize optimum material properties required through microstructural and constitutional selection and control has made significant strides in the last decade. Computational techniques, such as first princi-ple calculations and the Monte Carlo simulation, have been increasingly utilized in the

Table 7 Retardation Effect of Alloying Elements Element Retardation=1% addition

calculation of phase diagrams. Several databases for calculating phase diagrams of com-mercial alloy systems using CALPHAD approach have been developed. A wealth of infor-mation concerning various aspects of phase equilibria have been extracted, such as stable and metastable phase equilibria, the temperature of T₀ as a function of composition, volume fractions of the phase constituents under specific conditions, value of activity and enthalpy of solutions, Gibb’s energy of formation, driving force for phase transforma-tions, etc. Several instances of the computational approach which is related to designing with C-, low alloy and medium-alloy steels are briefly reviewed.

(A) SEGREGATION AND PERITECTIC REACTION. The degree of segregation of a solute is quantitatively analyzed by the distribution (or partition) coefficient of the solute.

It is defined by kxs=l¼xxs=xxl

, where xxs

and xxl

are the concentrations of solute in the solid and liquid phases, respectively. 1 k is defined as segregation coefficient which can be used to quantify the rejection of the solute at the interface during the solidification process [81]. As a result of solute additions, changes in the relative positions of liquidus and soli-dus lines are directly related to the segregation coefficients. Thermodynamic calculations have been utilized in calculating these coefficients for several solutes and such calculations have been extended for estimating the partition coefficients of g-loop forming elements, even though there exists no direct phase equilibrium between austenite and liquid phase in the steel. Table 8 lists some of the equilibrium partition coefficients of alloying elements between austenite and liquid or between ferrite and liquid in steel, and the effect of adding 1 wt% alloying elements on the variation in the position of the liquidus and the solidus lines of the steel [82]. Sulfur, phosphorus, and carbon have low values of k in steel and, therefore, have a strong tendency to segregate during solidification.

The characteristics of the peritectic reaction and thereby the solidification behavior are also affected by the addition of the alloying elements. Figure 57 shows the results from

Table 8 Effect of Alloying Elements on Solid=Liquid Equilibria in Iron Base Alloys Change in liquidus and solidus=% element

Partition coefficient Liquidus Solidus

thermodynamic calculations predicting the effect of alloying elements on the temperature and composition of the peritectic reaction in Fe–C system.

(B) CONTROL OF INCLUSION MORPHOLOGY. The morphology of MnS in steels can be broadly classified into three types: (1) randomly dispersed globular sulfides, (2) rod-like fine sulfides, and (3) angular sulfides. Globular or droplet MnS would form only when the solidification path involves the monotectic reaction (L¼ Fe(s) þ L). However, based on the stable equilibrium phase diagram of Fe–MnS pseudo-binary system (Fig. 58(a)) the primary Fe phase would be expected to solidify first, then followed by eutectic reaction L¼ Fe(s) þ MnS(s). This would preclude the formation of any globular type MnS. But in practice the globular MnS has always been observed in Fe–Mn–S ternary alloys cooled from liquid state in the normal way. This dilemma can be resolved now by the calculated meta-stable phase diagram represented by the dotted line in Fig. 58(b). The calculated dif-ference between the eutectic temperature (e) and the monotectic temperature (m) is so small (only 38C ) that a monotectic reaction seems possible. The deciding factor that tips the balance in favor of globular MnS is the magnitude of interfacial energy between Fe(L1)= MnS(L2) boundary which is estimated to be lower than that of the Fe(L1)=MnS(s) bound-Figure 57 Effect of alloying elements on (a) the peritectic composition, and (b) temperature of Fe–

C system. (From Ref. 82.)

Figure 58 Pseudo-binary Fe–MnS phase diagrams in stable and metastable systems: (a) schematic, and (b) calculated one in Fe-rich portion. (From Ref. 82.)

ary; the energy barrier for the nucleation of MnS(L2) is energetically more favored and the metastable monotectic reaction predominates over the stable eutectic reaction.

Alloying element addition in steel strongly affects the morphology of MnS inclusions [84,84]. The changes in morphology of MnS inclusions brought about by the additions of C, Si, Al, and Ti in hypo and hyper eutectic Fe–MnS system are summarized in Figs. 59 and 60. TiN crystallites act as nucleation catalysts for MnS(s) in Fe–MnS alloys contain-ing Si (melted under N2) and Al2O3crystallites act as nuclei in Fe–MnS alloys containing Al (melted under Ar), promoting primary crystallization of the MnS(s) phase and the eutectic reaction associated with the stable system. When the same alloys containing Ti Figure 59 Morphology of MnS in hypoeutectic (monotectic) alloys containing C, Si, and Ti.

(From Refs. 83,84.)

Figure 60 Morphology of primary MnS in hypereutectic (monotectic) alloy. (From Refs. 83,84.)

are melted under Ar atmosphere, only oxides TiO2and SiO2are formed which tend to react with MnO forming compounds with lower melting temperatures, although its own melting temperature is about 1008C higher than that of Fe. As a result, liquid oxide dro-plets are formed first and act as nucleants for MnS (L2), thereby facing the metastable monotectic reaction leading to monotectic morphology of MnS. The addition of C and Si lowers the melting point of iron and raises the activity of sulfur, resulting in an expan-sion of the two phase region and an increase in the slope of the liquidus line for iron, leads to an increase in the temperature difference between the metastable monotectic and the stable eutectic points, as shown in Fig. 61. The magnitude of this difference is estimated to be about 108C in the Fe–1% Mn–0.3% S–1% Si alloy, which could explain the prefer-ence of stable eutectic over the metastable monotectic reaction in these alloys.

(C) SURFACE FISSURE IN CU-CONTAINING STEELS. During hot rolling, surface fissure defects occur in steels containing residual copper which comes from the ferrous scrap.

Copper has a weaker oxidation tendency as compared to that of iron in steel. Cu is not oxidized during the heating stage prior to hot working and remains as a dissolved solute in iron-based solution. When the concentration of Cu in the surface layer exceeds the solubility limit of Cu in solid Fe, liquid Cu forms at the interface between steel and the oxide. This liquid penetrates the grain boundaries of Fe matrix during hot rolling and gen-erates surface crack. Figure 62 is a calculated 12008C isothermal section of Fe–Cu–Sn phase diagram [85] and superimposes some experimental points obtained for the composi-tion of the liquid phase formed at the interface between the matrix and oxide in specimens containing Cu and Sn heated at 12008C in air. It should be noted that the liquid phase in the specimen is located on the boundary of the two phase field (gþ L), i.e., the liquid is in equilibrium with austenite. It is evident that the surface fissure is closely related to the aus-tenite=liquid phase equilibrium in the Fe–Cu system. The solubility of Cu in Fe is effected by alloying additions. Figure 63 shows the calculated and the experimental results. It can be seen that Ni and Co increase the solubility of Cu while Al decreases up to2.5% and then increases it in ferrite. All the other elements such as Si, V, Mn, Cr, and Sn decrease the solubility of Cu. Sn drastically decreases the solubility of Cu. The calculated results Figure 61 Change in phase equilibria in the pseudo-binary system by alloying with carbon and silicon. (From Refs. 137,138.)

can explain the origin of the surface fissure due to liquid embrittlement in steel containing residual Cu, which is suppressed by Ni and promoted by Sn.

(D) EFFECT OF ALLOYING ELEMENT ON THE RELATIVE STABILITY OF FERRITE AND AUSTENITE. Various types of high-strength low alloy steels with good ductility have been developed by thermo-mechanical treatment, i.e., controlled rolling combined with con-trolled cooling. Dual phase steel and low alloy TRIP-type steels (a group of C–Mn–Si), are processed by intercritical treatment, consisting of heating the steel to a temperature range in the (aþ g) region followed by austempering. During the austempering treatment, Si suppresses the formation of cementite in bainite and promotes carbon enrichment of austenite, which in turn depresses the Mstemperature of the austenite. In the case of both Figure 62 Composition of liquid phase formed at the interface of matrix and oxide in the Fe–Cu–

Sn system projecting the calculated phase at 12008C. (From Ref. 85.)

Figure 63 Effect of alloying elements on the solubility of Cu in solid phases. (From Ref. 86.)

dual phase and low alloy TRIP-type steels, the intercritical treatment in the (aþg) two phases field is a decisively important step in controlling the final microstructure. The extent of the dual phase field, volume fraction of the phases and their equilibrium compo-sitions and Ae3temperature are critical processing parameters for a successful intercritical treatment. All these parameters can now be accurately predicted using information from thermodynamic databases shown in Table 9.

The partition coefficient k_x^a=g¼xx a=xx

g is one of the most important factors that determine the a=g phase equilibrium. It directly relates to the partial molar Gibb’s energy change at infinite dilute solution of the element x accompanying the a=g transformation [87]. Figure 64 shows the calculated kxa=gas a function of temperature [88]. Most of the elements exhibit strong temperature dependence.

The calculated Ae3is illustrated in Fig. 65. There is a significant agreement between the calculated and the observed value [89].

(E) CALCULATION OF MSTEMPERATURE. The effect of the alloying element addition on the martensitic transformation start temperature can be calculated by the thermody-namic approach [90]. This has been done by dividing the free energy change accompanying the martensitic transformation into chemical and non-chemical parts. The chemical free energy is estimated from the change in partial molar Gibb’s energy associated with the a! g transformation. The non-chemical part arises mainly as a result of the change in fric-tion stress required to move dislocafric-tions which is related to the strengthening mechanism in austenite. The calculated chemical and mechanical contributions of alloying elements to Table 9 Data Base of Calculated Phase Diagrams of Low Alloy Steels

Steels Systems Phases

Low alloy steels Fe(C, N, Si, Mn, Cr, Mo, Ni, Co, Al, Nb, V, Ti, W)

L, a, g, carbide, nitride Micro-alloying

steels

(C, N, S, Mn, Si, Al, Cr, Ti, Nb, V) L, a, g, carbide, nitride, sulfide

Figure 64 Temperature dependence of the distribution of alloying elements between a and g phases. (From Ref. 88.)

Msare shown in Fig. 66. Based on such a calculation, Mstemperature relates to the chem-istry of low alloy steels:

M_sð^CÞ ¼ 545  330C þ 2Al þ 7Co  14Cr  13Cu  23Mn

 5Mo  4Nb  13Ni  7Si þ 3Ti þ 4V þ 0W ð84Þ

(F) CARBIDES AND NITRIDES IN MICRO-ALLOYED STEELS. The solubility of carbides, nitrides and carbonitrides in both liquid and solid state of steel is of fundamental impor-tance for exercising microstructural control in micro-alloyed steels.

Figure 67 shows the solubility products of various carbides, nitrides and sulfides in austenite and ferrite. It can be seen that the overall solubilities of nitrides are smaller than those of carbides, while both the compounds are more soluble in austenite than in ferrite.

Figure 65 Comparison of calculated Ae3 temperatures and observed ones. (From Ref. 89.)

Figure 66 Effect of alloying elements on Mstemperature. (From Ref. 90.)

Figure 68 illustrates the effect of micro-alloying elements on the g field in Fe–C alloys [91], a very small additional amount significantly changed the extent of the phase field. Figure 69 shows the calculated phase equilibria between austenite and (Nb, Ti) (C, N) at 12008C in a steel where the total Nbþ Ti content in austenite is kept at 0.02% [92]. A small increase in the content of Ti (from 0.00001 to 0.0001) would result in a phase separation of carbonitride and the three phase field (gþ TiN þ NbC) appears.

Figure 67 Solubility products of carbides, nitrides, and sulfides in g and a. (From Ref. 91.)

Figure 68 Effect of micro-alloying elements on the austenite region of Fe–C alloy. (From Ref. 91.)

Figure 70 shows the calculated miscibility gap contours in carbonitrides (NaCl type) consisting of Ti, Nb, and V. The miscibility gap in NbC–VC pseudo-binary system and the miscibility island in double-pseudo-binary system of (Nb, Ti) (C, N), (Nb, V) (C, N) and (V, Ti) (C, N) are formed due to the large difference in lattice parameters between NbC and VC and the difference in Gibb’s energy of formation of the compounds, respectively [93]. These calculated phase diagrams may be utilized in predicating phase separation in steels.

Figure 69 Phase equilibria between g and (Nb, Ti)(C, N) at 12008C keeping (NbþTi)¼0.02% by mass percentage. (From Ref. 92.)

Figure 70 Miscibility gaps of complex carbonitrides. (From Ref. 93.)

IV. CASE ANALYSIS AND APPLICATION OF THE METALLURGICAL