10.6.3 10.6.4 10.6.5 10.6.6 10.6.7 10.6.8 10.7. Summary References Sensitivity Factor Analysis 10.6.3.1 Heat Treatment of Duplex Stainless Steels 10.6.3.2 t The simplicity of modelling in 'substance'-type calculations meant that com- ,f plex systems could be studied at an early stage of CALPHAD development. The SolGasMix programme of Eriksson (1975) was one of the first to provide such a capability, and within a decade very complex systems were being routinely :;j handled; two good examples are given in the CALPHAD volume dedicated to Eriksson in 1983. Lindemer (1983) was able to look at gas-phase reactions in a fission reaction involving U-Cs-I-Ba-Zr-Mo considering 18 gaseous species and 20 condensed substances. Another interesting example of a calculation based mainly on a substance database is given in the work of Lorenz et al. (1983) who were interested in the stability of SiC-based ceramics containing Zr02 and other oxides. This involved the quaternary system SiC-ZrO2-Al2O3-Si02 reacting in inert argon gas, and gave rise to 36 gaseous species and 22 stoichiometric, solid substances. Calculations of the reaction for various composite mixtures of SiC and oxides were then made as functions of temperature and pressure. Calculations %\ involving so many phases were not being routinely handled at this time for systems such as steels, where non-ideal mixing in most of the solid phases is the , I norm. ; j There now exists a thriving community of researchers who regularly publish thermodynamic assessments for binary and ternary systems. Many are extremely accurate and, due to a formalisation of unary data proposed by SGTE (Dinsdale :. ] 1991), these can be combined with existing or future work in the establishment of multi-component solution databases, where the promise of CALPHAD methods is greatest. In many ways an accurate thermodynamic assessment of a binary or ternary system only proves again the validity of the fundamental concepts laid | down in earlier years. The models have improved and, therefore, levels of accuracy level have improved, but most commonly used materials are multi-component in nature and the degree to which binary and ternary assessments can be applied per se is fundamentally limited. The key issue is how to extend the CALPHAD route to % 'real' rather than 'ideal' materials, and the next section will concentrate on this ^| issue. >\ References are listed on pp. 402—408. CALPHAD—A Comprehensive Guide 309 10.3. GENERAL BACKGROUND TO MULTI-COMPONENT CALCULATIONS 10.3.1 Introduction From their earliest days CALPHAD methods have always promised to be extendable to complex materials. Certainly, the necessary mathematical formulations to handle multi-component systems have existed for some time and have been programmed into the various software packages for calculation of phase equilibria. However, it is interesting to note that, until quite recently (with the exception of steels), there has been little actual application to complex systems which exist in technological or industrial practice, other than through calculations using simple stoichiometric substances, ideal gas reactions and dilute solution models. The latter have been used for some time, as it is not intensive in computational terms, and some industrially important materials, although containing many elements, are actually low in total alloy or impurity content, e.g., HSLA steels. Examples in this area can be found in Kirkaldy et al. (1978), Bhadeshia and Edmond (1980), Hack and Spencer (1985) and Kroupa and Kirkaldy (1993). The limitations of dilute solution models have been discussed earlier in Chapter 5 and, although useful for certain limited applications, they are not applicable in a generalised way and could not begin to handle, with any accuracy, complex alloy types such as stainless steels or Ni-based superalloys. Substance calculations, while containing large numbers of species and condensed phases, are, in many ways, even more limited in their application to alloys as they do not consider interactions in phases involving substantial mixing of the components. The main areas of application for more generalised models have, until recently, been restricted to binary and ternary systems or limited to 'ideal industrial materials' where only major elements were included. The key to general application of CALPHAD methods in multi-component systems is the development of sound, validated thermodynamic databases which can be accessed by the computing software and, until recently, there has been a dearth of such databases. The notable exception to this trend was steels and, in particular, stainless and high-speed steels where alloy contents can rise to well above 20wt%. For such alloys a concentrated solution database (Fe-base) has existed since 1978, based on work done at the Royal Institute of Technology (KTH), Stockholm, Sweden. However, although it is far more generalised than dilute solution databases, its range of applicability is limited in temperature to between 700° and 1200°C. Work since 1978, mainly by the Royal Institute of Technology, has seen the development of a new steel database, TCFe, for use in Thermo-Calc. This work now forms the basis for steel calculations in the SGTE solution database. More recently, TCFe has been extended and improved by Saunders and Sundman (1996). These newer databases have a number of distinct advantages over the old Fe-base, not least in that liquid-phase equilibria is now taken into account. The lack of similar databases for other material types presented severe problems for CALPHAD calculations with any of the other commonly used materials and led to a concentration of application to steels. However, in the past four years further multi-component databases have been developed for use with A1-, Ni-, Ti- and TiAl-based alloys (Saunders 1996a-c, 1997a,b). These databases have been created mainly for use with industrial, complex alloys and the accuracy of computed results has been validated to an extent not previously attempted. Simple, statistical analysis of average deviation of calculated result from experimental measurement in 'real', highly alloyed, multi-component alloys has demonstrated that CALPHAD methods can provide predictions for phase equilibria whose accuracy lies close to that of experimental measurements. The importance of validation of computed results cannot be stressed too highly. We are now in a position where computational speed has allowed the development of modelling in many related areas. These models often rely on input data which can be time-consuming to measure but can be readily predicted via CALPHAD and related methods. Therefore, CALPHAD results may be used as input for other models, for example, in the manufacture of a steel starting from the initial stages in a blast furnace, through the refinement stages to a casting shop, followed by heat treatment and thermomechanical processing to the final product form. All of these stages can be modelled and all use input data which can be provided either directly or indirectly from CALPHAD calculations. Such a future total modelling capability will never materialise properly until confidence can be placed in the predictions of each of the building blocks. In the case of CALPHAD methods, the key to this is the availability of high-quality databases and the rest of this section will concentrate on databases and discuss some of the strategies in their construction. 10.3.2 Databases 10.3.2.1 'Substance' databases. Basically substance databases have little complexity as they are assemblages of assessed data for stoichiometric condensed phases and gaseous species. They have none of the difficulties associated with non-ideal mixing of substances, which is the case for a 'solution' database. However, an internal self-consistency must still be maintained. For example, thermodynamic data for CCs), 02 and C02 are held as individual entries, which provide their requisite properties as a function of temperature and pressure. However, when put together in a calculation, they must combine to give the correct Gibbs energy change for the reaction C(s)+02;?=iC02. This is a simple example, but substance databases can contain more than 10,000 different substances and, therefore, it is a major task to ensure internal self-consistency so that all experimentally known Gibbs energies of reaction are well represented. Examples of substance databases of this type can be found in the review of Bale and Eriksson (1990). 10.3.2.2 'Solution' databases. Solution databases, unlike substance databases, consider thermodynamic descriptions for phases which have potentially wide ranges of existence both in terms of temperature and composition. For example, the liquid-phase can usually extend across the whole of the compositional space encompassed by complete mixing of all of the elements. Unlike an ideal solution, the shape of the Gibbs energy space which arises from non-ideal interactions can become extremely complex, especially if non-regular terms are used. Although it may seem an obvious statement, it is nevertheless important to remember that thermodynamic calculations for complex systems are multi-dimensional in nature. This means that it becomes impossible to visualise the types of Gibbs energy curves illustrated in earlier chapters which lead to the easy conceptualisation of miscibility gaps, invariant reactions, etc. In multi-component space such things are often difficult to understand, let alone conceptualise. Miscibility gaps can appear in ternary and higher-order systems even though no miscibility gap exists in the lower-order systems. The Gibbs phase rule becomes vitally important in understanding reaction sequences, but often one has to accept the computer predictions which can be surprising at times. This emphasises the need to validate the database for multi-component systems and leads inexorably to the concept of two types of database. 10.3.3 The database as a collection of lower order assessments Essentially this is the basic concept of any database, but an unthinking application of this concept is dangerous. It can be easily demonstrated that in multi-component calculations the properties of some substances, or lower-order interactions in solution phases, are ineffective in modifying phase equilibria, while in other cases some are extremely critical. This may be because the total energy of the system is very exothermic and a particular Gibbs energy term is close to ideal. In this case a change of a few hundred percent in a binary value actually alters things very little. Other reasons may exist for the precise value of an interaction being non-critical. For example, the equilibrium solubility of elements in a particular phase may be small and the Ya X)j xixj solubility product subsequently produces small changes in total energy, even if interaction coefficients are heavily modified. This leads to a number of important questions and concepts. The first and most important question is how many of the constituent substances or lower-order interactions must be accurately represented before a successful calculation can be guaranteed. Let us take the example of a simple commercial alloy such as Ti-6A1-4V. This is the most popular structural Ti alloy used worldwide. Essentially one would need to consider Ti-Al, Ti-V and Al-V binary interactions and Ti-Al-V ternary interactions. Unfortunately, although called Ti-6A1-4V, this alloy also contains small amounts of O, C, N and Fe and it therefore exists in the multi-component space within the Ti-Al-V-O-C-N-Fe system. There are then 21 potential binary References are listed on pp. 402-408. interactions and 35 possible ternary interactions to consider. The number of thermodynamic assessments necessary to obtain all of these parameters is obviously massive, and the inclusion of an additional element to the alloy means a further 7 binary and 21 ternary assessments would potentially need to be made. This would make a total of 28 binary and 56 ternary assessments. The effort to do all of this is so large that it is much easier (and cheaper) to consider an almost exclusively experimental route to determining phase equilibria in the commercial TJ-6A1-4V alloy. This can be enhanced with regression analysis techniques to specify the effect of various elements on critical features such as the temperature when the alloy becomes fully /?. Fortunately, it is not necessary to perform all of these thermodynamic assessments. In essence one should ensure that all of the binary systems are completed, but the levels of C and N are so low that it is possible to effectively ignore interaction parameters between these two elements, even if they were possible to determine. The percentage of ternary assessments which is necessary to provide an accurate calculation is, in reality, small, mainly because the ternary Si J2j Y,k XiXjXk solubility product can be small for the minor elements. For example, the effect of including ternary parameters for Fe-C-N, which are basically impurity elements, is negligible and little effect is found from the Fe-V-N system even though it contains one of the major elements. It can therefore be seen that if we wish to consider making calculations for the Ti-6A1-4V alloy, the actual amount of work is much reduced from the theoretical number of permutations. However, this is a particularly simple Ti-alloy and another type such as IMI 834 typically contains Ti, Al, Sn, Zr, Nb, Si, C, O, N and Fe, where seven elements have a significant effect on phase equilibria. The general problem, therefore, remains as to how to judge the number of the potential interactions which must be included, so that a successful multi-component calculation can be made. This cannot be answered in a simple fashion and the position is considerably exacerbated if one wishes to make a generalised database applicable for many material types. If reliable and accurate multi-component calculations are to be made, new paradigms are required and it is no longer possible to consider using databases which are basically constructed as collections of assessed binary and ternary systems which might be available at the time. The database itself must be assessed. ternary systems have been assessed and calculated results have been validated as It being successful. The words italicised in the previous sentence hold the key : { paradigms which need to be employed when designing an assessed database. J Composition space. It is firstly of critical importance that a well-understood and \ properly circumscribed composition space is defined. This is best done by consider--f ing databases for use with particular material types, for example steels, conven- '! tional Ti alloys, etc. This firstly limits the number of elements which need to be \ considered and also helps to define concentration limits for these elements. ; Critical systems. It is impossible just by looking at a list of elements to decide which are the critical binary and ternary systems that must be critically assessed. However, some clear pointers can be gained by looking at the composition space in - which the database is to be used. For example, B levels in Ni-based superalloys as a ■'! rule do not exceed 0. lwt% and, therefore, assessment of B-rich ternary and higher- order alloys is unnecessary. There are, however, critical B-containing ternary systems which must be assessed to understand the thermodynamics of the M3B2 phase which can appear. Likewise, the thermodynamics of the MC carbide must be j well defined and this includes a large number of carbon-containing ternary systems. , i On the other hand, although Ti, Ta and Nb may appear in the alloy in much larger amounts than B and C, a ternary assessment of Ti-Ta-Nb is not critical as the magnitude of the thermodynamic interactions are small which, combined with the solubility product term, makes for small Gibbs energy changes. The understanding of the critical systems in an assessed database is in the hands of j the developer of the database and can often only be understood after a series of I multi-component calculations are made. | Validation of the database. This is the final part in producing an assessed database and must be undertaken systematically. There are certain critical features such as melting points which are well documented for complex industrial alloys. In steels, volume fractions of austenite and ferrite in duplex stainless steels are also well I documented, as are 7' solvus temperatures (7's) in Ni-based superalloys. These must be well matched and preferably some form of statistics for the accuracy of calculated results should be given. Only after at least these three steps are taken can a database then be considered as an assessed database and used with confidence in an application involving a complex multi-component alloy. 10.3.4 Assessed databases By definition 'assessed databases' are focused, usually on material types. The recent A1-, Ni- and Ti-databases (Saunders 1996a~c) and, to a large degree, the Fe-databases produced by KTH in Stockholm are good examples. They contain up to 15 elements and have been designed for use within the composition space associated with the different material types. All, or most, of the critical binary and 10.4. STEP-BY-STEP EXAMPLES OF MULTI-COMPONENT CALCULATIONS This section will take three commercial alloys and analyse how the final calculated result took form, starting with some of the important constituent binary and ternary diagrams, and seeing how the various features of the final alloy are controlled by these underlying systems. References are listed on pp. 402-408. 10.4.1 A high-strength versatile Ti-alloy (Ti-6Al-4V) Ti-6A1-4V is probably the most widely used Ti alloy in the world. It is an alloy with a duplex structure containing solid solutions based on the a, c.p.h._A3 and /3, b.c.c._A2 allotropes of Ti. In its final heat-treated form it consists predominantly of a and its high strength is partly derived from its final microstructure which is manipulated by a series of thermomechanical treatments that include hot isothermal forging just below its 0 transus temperature (T^). The interest is, in the first place, to predict and how the amounts of a and 0 vary with temperature. There are empirical relationships which relate alloy content to T@, but these are not usually applicable to all types of Ti alloy and can suffer from a lack of accuracy. Significantly, there are no such relationships which can be generally used for predicting the amount of a and /? in commercial alloys as a function of temperature and composition and little work has been undertaken to quantitatively understand the partitioning of elements between the a and 0 phases. The alloy combines the features of two different binary systems, Ti-Al and Ti-V (Figs 10.11 and 10.12). Al is an 'a-stabiliser' while V is a strong '/^-stabiliser'. It is the combination of these two types of diagram which produces a wide two-phase a + /? region, and Fig. 10.13 shows the behaviour of the basic ternary alloy as a function of temperature. Although more heavily alloyed in Al, the alloy never 1800 (Al) too MOLE ^PERCENT AL Figure 10.11 Calculated Ti-Al phase diagram. References are listed on pp. 402-408. 20 40 60 MOLEJPERCENT V Figure 10.12 Calculated Ti-V phase diagram. 80 600 700 800 900 1000 TEMPERATU RE_CELS1 US 1100 Figure 10.13 Calculated mole % a vs temperature plot for a Ti-6A1-4V ternary alloy. 316 N. Saunders ana A. f. Mioaowntlc becomes fully a, as just enough V is added to retain some j3. The basic behaviour of the alloy is thus defined by the Ti-Al-V ternary but Ti alloys always contain significant levels of O and N, and in the case of Ti-6A1-4V usually some Fe. At high levels (>5000 ppm) O generally acts as an embrittling agent, but at lower levels (2000 ppm) it can be used to enhance strength (Jaffee 1958) and is therefore a deliberate addition to 'conventional' alloys such as Ti-6A1—4V. Apart from the physical effects of O, this also produces significant phase-boundary shifts even at low levels of-uptake, and it is therefore necessary to include the effects of at least this element in the calculations. Figure 10.14 shows the calculated Ti-O diagram from Lee and Saunders (1997). In the composition range of interest it is of a simple type but O has a powerful effect on This effect is carried over to the critical ternary system Ti-Al-0 and Figs 10.15 and 10.16 show how the Ti-Al system changes as O is added (Lee and Saunders 1997). No such information is available for Ti-V-0 but it is interesting to note the predicted effect of O on Ti-V. Figure 10.17 shows a section through 2400 ^/i.L,rnnu—a i^omprenensive vuiae Figure 10.14 Calculated Ti-0 phase diagram (from Lee and Saunders 1997). 1400 1300 D 3? J 1200 u i w OS 3 1100 £ iooo s t- 900 800 0.05 w1%0 - p 1 a 1 1 5 10 15 MOLE PERCENT AL 20 Figure 10.15 Calculated vertical section through Ti-Al-0 at 0.05wt%O. 1400 1300 CO o < Pi w CL, S W H 1100 1000 900 800 - P / ci+P - a I I 1.0 wt%0 1 5 10 15 MOLE PERCENT AL 20 Figure 10.16 Calculated vertical section through Ti-Al-0 at 1.0wt%O. References are listed on pp. 402-408. 1000 0.25 w<%0 5 10 55 MOLE PERCENT V 20 Figure 10.17 Calculated vertical section through Ti-V-O at 0.25wt%O. Ti-V-O at a constant 2500 ppm of O and the effect of O on T0 is significant, while the effect on the position of the a-phase boundary is minimal. Taking the necessary binary assessments for the inclusion of C, N and Fe and the assessments for Ti-Al-O and Ti-V-O, the effect of O on the of Ti-6A1-^V with typical C, N and Fe impurity levels, was calculated and compared with experiment. The agreement between the calculations and experimental results of Kahveci and Welsch (1986) is good (Fig. 10.18). Figure 10.19 further shows some calculated phase % vs temperature plots for three Ti-6Al-4V commercial alloys and compares these with experiment. The advantage of the CALPHAD route becomes increasingly apparent because, as well predicting the calculations have also given good results for the amounts of a and 0. Furthermore, it is now possible to look at the partitioning of the various elements to the a and 0 phases and Fig. 10.20 shows comparisons with experiment for the various metallic elements. One of the V results for the 0 phase has an arrow indicating that the true experimental result was considered to be higher than that shown in Fig. 10.20 (Lasalmonie and Loubradou 1979). This is because the 0 grains were so small that some overlap with the a matrix occurred during measurement by EPMA, resulting in a V reading that is almost certainly too low. As previously stated, the levels of the light elements such as O are important in determining physical properties of Ti and it is also possible to look at the partitioning of O between the a and 0 phases (Fig. 10.21). It can be seen that the level of O in a just below is extremely high. This has significant consequences for thermomechanical processing for Ti-6A1-4V at these temperatures as yield References are listed on pp. 402-408. J 1200 0-2 0.4 0.6 0.S WEIGHT PERCENT O 1.0 Figure 10.18 Comparison between calculated and observed /3-transus for Ti-6A1-4V alloys as a function of O concentration. QBIenkinsop(!993) © Kahveci and Welsch (1986) XLee etal. (1991) 500 600 700 800 900 1000 tlOO TEMPERATURE CELSIUS Figure 10.19 Calculated mole % phase vs temperature plots for three Ti-6A1-4V alloys with experimental data superimposed. 15 H & Q ffl H < tj < u 10 A—►./ — A A> 1 5 — (T) (wt%AI) Lasolmonie and Loubradou (1979) A (wt%V) Lasoloionie and Loubradou (1979) H, (wt%Fe) Lasolmonie and Loubradou (1979) •fe (wt°/oAl) Ishikawa et al (1992) <> (wt%V) Ishikawa etttl. (1992) + (wt%Fe) Ishikawa e( at. (1992) 5 10 OBSERVED WT% is Figure 10.20 Comparison between calculated and experimental values for the concentration of Al, V and Fe in the a and & phase in Ti-6A1-4V alloys. 0.6 O H 2 a u ft! & a o 3 200 400 600 800 1000 TEMPERATURE CELSIUS 1200 Figure 10.21 Calculated concentration of O in the a and /3 phase for a Ti-6A1-4V alloy. strengths in a will be higher and ductility levels lower than would be expected by just taking total levels of impurity as a guide. 10.4.2 A high-tonnage Al casting alloy (AA3004) Aluminium alloys form one of the most widely used groups of materials in existence. They make products which are often cheap and can be applied to many different areas. Extensive work has been done on the experimental determination of binary and ternary phase diagrams, mainly during the mid-part of this century, and researchers such as Phillips (1961) and Mondolfo (1976) have produced detailed reviews of the literature which provide industry standard publications. However, although some important Al-alloys are based on ternary systems, such as the LM25/ 356 casting alloy based on Al-Mg-Si, in practice they inevitably include small amounts of Cu, Mn, Fe, Ti etc., all of which can significantly modify the castability and properties of the final product. The situation is further exacerbated by the use of scrap material. It is therefore useful to be able to predict phase equilibria in multi-component alloys. The modelling issues for Al alloys turn out to be reasonably straightforward. Unlike superalloys or steels there are few intermetallic phases with wide regions of stoichiometry. A large number of the compounds tend to be stoichiometric in nature, for example, Mg2Si and Al2CuMg. Where there is substantial solubility, such as in the Al^Mn and a-AlFeMnSi phases, the transition metals basically mix on one sub-lattice while Si mixes on the Al sub-lattice. The phases can be then treated as conventional line compounds and complexities of modelling associated with phases such as a and 7', where many elements may mix on more than one sub-lattice, do not arise. There is also limited solubility in the Al solid solution for most elements which are usually added to Al alloys which means that, for this phase, the effect of most ternary interactions is completely negligible. Nevertheless, Al alloys more than make up for this simplicity in modelling by exhibiting reaction schemes which can be far more complex than usually found in systems involving more complex models. Because of their inherent simplicity in modelling terms, Al systems offer a good example of how a database can be constructed and the AA3004 alloy, which is based on the Al-Fe-Mn-Si system, will now be discussed in more detail. The Al-Si diagram and Al-rich regions of the Al-Mn and Al-Fe diagrams are shown in Figs 10.22-10.24. The Al-Mn and Al-Fe systems are modifications based on the work of Jansson (1992) and Saunders and Rivlin (1987). Unless stated, all other diagrams are from Saunders (1996b). The Al-Mn and Al-Fe diagrams are complex but in terms of Al alloys only the Al6Mn, AL4Mn and Al3Fe phases are of importance. This leads to a large degree of simplification in considering the ternary modelling. Figure 10.25 shows the liquidus projection for the Al-Fe-Mn system which is characterised by a substantial extension of the AlgMn phase into the ternary and References are listed on pp. 402-408. 1500 C/3 3 — U «' bS Oh S 5 20 40 60 80 WEIGHTPERCENT SI Figure 10.22 Calculated Al-Si phase diagram. 100 5 10 15 20 25 WEIGHT PERCENT MN 35 Figure 10.23 Calculated Al-rich region of the Al-Mn phase diagram. 10 15 20 25 30 35 40 45 WEIGHT PERCENT FE Figure 10.24 Calculated Al-rich region of the Al-Fe phase diagram. a, a o « x - Al3Fe —" AI4Mn Al6Mn ' 1.0 0.5 0 AljFe / otAlFeSi _________--\ pAlFeSi (Al) 1 1 1 1 1 1 Si 0 2 4 6 8 10 12 14 WEIGHT PERCENT SI Figure 10.26 Calculated liquidus projection for Al-Fe-Si. •a References are listed on pp. 402-408. 2 4 6 WEIGHT PERCENT SI 10 Figure 10.27 Calculated liquidus projection for Al-Mn-Si. a-AlFeSi phase was considered to be isomorphous with a-AlMnSi. Later work showed this not to be the case and its stable structure is hexagonal (Munson 1967, Mondolfo 1976, Rivlin and Raynor 1988). The addition of Fe to the a-AlMnSi phase is simply achieved by making the Gibbs energy of the cubic AlFeSi compound only just metastable. Other elements such as Cr and V also partition to the cubic a phase and this can also be taken into account. Combining this quaternary with Mg, and in particular Al-Mg-Si, it is now possible to consider a reasonably pure AA3004 alloy which is used extensively for thin-walled containers such as drink cans. Figures 10.28(a,b) show phase % vs temperature plots for an alloy Al-lMn-l.2Mg-0.5Fe-O.2Si (in wt%). On solidification the primary phase is Al, with Al6Mn appearing soon afterwards. There is a subsequent peritectic reaction involving a-AlFeMnSi (which will now just be called a) which partly consumes the AlftMn phase. The amount of a increases as the alloy is cooled below its solidus and it becomes the dominant solid-state intermetallic just below 600°C. However, it disappears around 400°C, as Si is taken up by the formation of Mg2Si which acts as a precipitation hardening phase. The interplay between the a and Al6Mn is critical, as the surface finish during fabrication of cans is much improved if a particles, rather than Al6Mn, predominate in 3XXX alloys of this type (Anyalebechi 1992, Marshall 1996). It is therefore now possible for CALPHAD methods to be used as a tool in helping to model and control this reaction. Cama et al. (1997) studied an alloy with the same composition as used in the last iv. oaunuern una a. ivnoaownm (a) 100 - w < X o 2 80 60 40 20 (Al) AI.Mn T ± X Liq CALftiAU—A Comprehensive (Juide 327 100 I 300 400 500 600 700 M&2Si TEMPERATURE CELSIUS < id O 100 200 300 400 500 600 TEMPERATURE CELSIUS 700 Figure 10.28 (a) Calculated mole % phase vs temperature plot for a AA3004 alloy, (b) Expanded region of Fig. 10.26(a). calculation, but with 0.2wt%Cu added, and performed long-term anneals between 550° and 630°C. They measured the relative levels of Al6Mn and a and reported results as a percentage of a observed. Calculations were therefore made for their alloy so that computed results could be compared with experiment. Experimental results varied between 61 and 39% while the calculations predict values of 53-33%. The calculations suggest some small amount of liquid would be present at 630°C and the lower value is quoted at 620°C. The results, while underestimating the measured values, are still in very reasonable agreement and the temperature dependency of the conversion of Al6Mn to a is almost exactly predicted. Furthermore, Marshall (1996) reported results for the closely related AA3104 alloy where the transition from Mg2Si to a is observed somewhere between 350 and 400°C. Although Marshall (1996) did not provide a composition for the alloys which were used, calculations for an ideal 3104 composition, following Sigli et al. (1996), suggest this transition occurs between 360° and 440°C, in good agreement with observation. In alloys such as AA3004 some of the major issues concern solidification and therefore it is interesting to look at this in detail. However, as solidification in Al alloys rarely occurs under equilibrium conditions, a more detailed examination of this issue will be found in the next chapter. J0.4.3 A versatile corrosion-resistant duplex stainless steel (SAF2205) Duplex stainless steels are a highly formable, strong, yet highly corrosion-resistant series of alloys. The 'ideal' duplex structure is aimed to be a 50/50 mixture of austenite (7) and ferrite (a). The microstructure can be manipulated by thermo-mechanical processing to produce an alloy with high strength. They also have a high Pitting Resistance Equivalent (PRE), where PRE can be related to the levels of Cr, Mo, W and N by the empirical formula (Hertzman 1995) PRE = wt%Cr + 3.3(wt%Mo + wt%W) + 16wt%N. A popular alloy of this type is SAF 2205. The alloy is predominantly an Fe-Cr-Ni alloy with significant additions of Mo, Mn, Si, C and N. The composition may typically be Fe-22Cr-5.5Ni-3Mo-l.7Mn-0.4Si-0.14N-0.024C (in wt%). Figure 10.29 shows an isothermal section for Fe-Cr-Ni at 1000°C and Fig. 10.30 shows a phase% vs temperature plot for a Fe-22Cr-5.5Ni alloy. It has a narrow liquid+solid region and it is already duplex below 1216°C, reaching a 50/50 7 + a mixture at 1015°C, close to the final annealing temperature of the full composition alloy. The a phase forms below 730°C at the expense of a, but this is low compared to the temperature where it is observed in real SAF2205 (Thorvaldsson et al. 1985). The PRE number for this ternary alloy is only 22 and values around 30-40 are necessary for adequate corrosion resistance. The addition of 3%Mo improves its pitting resistance equivalent (PRE) but causes substantial changes (Fig. 10.31). The level of austenite is substantially decreased, only forming below 1134°C and never reaching more than 40% in the References are listed on pp. 402-^408. 100 - 20 40 60 WEIGHT PERCENT NI 80 100 Figure 10.29 Calculated isothermal section for Fe-Cr-Ni at 1000°C. 600 800 1000 1200 1400 1600 TEMPERATURE_CELSIUS Figure 10.30 Calculated mole % phase vs temperature plots for a Fe-22Cr-5.5Ni alloy. References are listed on pp. 402-408. < x w o 600 800 1000 1200 1400 TEMPERATURE CELSIUS 1600 Figure 1031 Calculated mole % phase vs temperature plots for a Fe-22Cr-5.5Ni-3Mo alloy. duplex region. The stability of cr is markedly increased: it now forms below 875°C and some x forms below 800°C. Both a and x are actually seen in SAF2205. Figure 10.32 shows an isothermal section for Fe-Cr-Mo which shows the expansive region of cr and the formation of a ternary x phase. 20 40 60 80 100 WEIGHT.PERCENT MO Figure 1032 Calculated isothermal section for Fe-Cr-Mo at 1000°C. i 600 800 1000 1200 1400 1600 TEMPERATURE_CELSIUS Figure 10.33 Calculated mole % phase vs temperature plots for a Fe-22Cr-5.5Ni-3Mo-l.7Mn alloy. The addition of 1.7%Mn does not make such a large difference as the Mo addition (Fig. 10.33), It is, however, noticeable that all of the a has disappeared between 670-850°C by the reaction to form (7 + a). This is because Mn is both a 7 stabiliser and it enhances the formation of a which competes with a for a-stabilising elements such as Cr and Mo. The addition of 0.4wt%Si does not alter the general behaviour of the alloy significantly (Fig. 10.34). It is known that a ternary a phase forms in Fe-Cr-Si but Si is also a powerful a stabiliser. It is noticeable that there has been sufficient a stabilisation to delay the onset of the a —► (7 4- c) transformation and a is stable to lower temperatures than previously but, in the end, the level of addition of Si is insufficient to make significant changes. The next major changes occur with addition of N which substantially stabilises 7 (Fig. 10.35). The alloy is now close to its final composition and it can be seen that the N has stabilised 7 sufficiently such that it becomes the predominant phase below 1050°C while the formation of a and x is relatively unchanged. A new phase is now observed, M2N, based on Cr2N. This is an important phase as it can cause sensitisation to corrosion resistance. In SAF2205 its temperature of formation is close to that of a. The addition of C additionally causes the formation of M23C6 below 900°C (Fig. 10.36) and slightly lowers the solidus. The final predicted behaviour for SAF2205 is close to that found in practice. The amount of 7 in the alloy as a function of temperature is in excellent agreement with experimental results (Hayes 1985) and the behaviour of the minor phases is also 600 800 1000 1200 1400 1600 ■i TEMPERATURE_CELSIUS \ Figure 10.34 Calculated mole % phase vs temperature plots for a Fe-22Cr-5.5Ni-3Mo-l.7Mn-0.4Si alloy. Figure 10.35 Calculated mole % phase vs temperature plots for a : Fe-22Cr-5.5Ni-3Mc-l.7Mn-0.4Si~O.14N alloy. References are listed on pp. 402-408. 800 [000 1200 1400 '' TEMPERATURE CELSIUS 1600 Figure 1036 Calculated mole % phase vs temperature plots for a SAF2205 alloy with composition Fe-22Cr-5.5Ni-3Mc-l.7Mn-0.4Si-O.14N-0.24C. well predicted. The temperature of a and M2N formation is close to that observed in practice and the M23C6 and \ phases are predicted to form as observed (Thorvaldsson et al. 1985). The behaviour of the x phase is interesting as it is commonly seen as one of the first minor phases to form in practice. Thorvaldsson et al. (1985) showed that in SAF2205 the sequence of phase formation at 850°C would be x followed by a, with a finally being the stable phase and x disappearing after long anneals. The predicted solvus temperature for x is close to that of a but at 850°C it is not yet stable when solid transformation. Calculations for the liquidus and solidus were made for these alloys using the Fe-DATA database (Saunders and Sundman 1996) and compared with the results obtained at the lowest cooling rate. Figure 10.37 shows the results of this comparison and the accuracy of the predictions is impressive, particularly for the liquidus values which exhibit an average deviation from experiment (d) of only 6°C. It is also pleasing to note how well the solidus values are predicted with an average deviation of just under 10°C. Three solidus values are not matched so well and are highlighted. In these alloys low-melting eutectics were observed, but not predicted, and it is uncertain if the difference is due to an inherent inaccuracy in the prediction or to the persistence of non-equilibrium segregation during solidification. 10.5.1.2 Ti alloys. In Ti alloys there are numerous measurements of the T'3 as this is a very critical temperature for these alloys. Figure 10.38 shows the comparison between predicted and measured values for Ti alloys of all types, ranging from f3-type alloys such as Ti-10V-2Al-3Fe through to the a types such as IMI834. The results exhibit an average deviation from experiment of less than 15°C which is very good for the measurements of a solid-state transformation such as References are listed on pp. 402-408. 334 N. Saunders and A. P. Miodownik Sugimoto et al. (1985) A Yoder et al. (1984) A Ishikawa et al. (1992) M Matsumoto (1993) 0 Blenkinsop (1993) + Lampman (1990) 1100 700 800 900 1000 OBSERVED BETA-TRAN S US Figure 10.38 Comparison between calculated and experimental /Mransus temperatures in Ti-alloys (from Saunders 1996a). References are listed on rm. 407-AMi CALPHAD—A Comprehensive Guide 335 10.5.1.3 Ni-based super alloys. In Ni-based superailoys, containing high volumes of 7', the temperature window where an alloy can be heat treated in the fully 7 state is a critical feature both in alloy design and practical usage. This heat treatment window is controlled both by 7^ and the solidus and there have therefore been numerous experimental measurements of these properties. A further key experimental feature for cast alloys is the liquidus and, similarly, numerous measurements have also been made for this temperature. Figure 10.39 shows a comparison plot for 7^, liquidus and solidus for wide variety of Ni-base superalloys and average deviations from experiment are typically the same as for steels and Ti alloys, with d for liquidus and solidus being 6°C and 10°C respectively while d for the 7^ is less than 15°C. 10.5.2 Calculations for duplex and multi-phase materials 10.5.2.1 Duplex stainless steels. Duplex stainless steels have provided a fruitful area for CALPHAD calculations and have been an example of where high levels of success have been achieved for practical materials. An early study (Hayes 1985) was able to demonstrate that reasonable predictions for amounts of austenite could be obtained for a variety of different duplex stainless steels, demonstrating the □ 7', Small (1993) T, Small (1993) Small (1993) Honnarat etal. (t971) Van der Molen et al. (1971) Betteridge and Heslop (1974) Brinegar et al. (1984) 7; Dharwadkar et al. (1992) TJTi Dharwadkar et al. (1992) 7', Shaw (1992) T./T, Shaw (1992) *7', Wlodek« OS o 10 15 CALCULATED % AL Kriege and Bans (1969) Kriege and Bans (1969) Loomis et al. (1972) Dreshfield and Wallace (1974) Dreshfleld and Wallace (1974) ShimaniAi et al. (1976) Shimanuki etal. (1976) Caron and Khan (1983) Delargy and Smith (1983) Delargy and Smith (1983) Khan et al. (1984) Meng et al. (1984) Meng et al. (1984) Blavette et al. (1988) Blavette et al. (1988) Harada et al. (1988) Harada el al. (1988) Trinckhauf and Nembach (1991) Schmidt and Feller-Kniepmeier (1992) Duval et al. (1994) Duval et al. (1994) Figure 10.45 Comparison between calculated and observed compositions of 7 and 7' in Ni-based superalloys: (a) Al, (b) Co, (c) Cr, (d) Mo and (e) W. (at %) (from Saunders 1996c) IVA It/Ul/P'C/UfV 40 35 30 25 20 15 10 5 0 0» — — — o rt «■ ! 1 O 7' a y a 7 M 7' + 7' 2 7 M 7' * 7' ffl 7 M 7' V 7 * 7' + 7 Y 7' A 7 X 7' a 7 o 7' © 7 Kriege and Baris (1969) Kriege and Baris (1969) Shimanuki etal. (1976) Shimanuki etal. (1976) Caron and Khan (1933) Deiargy and Smith (1983) Delaigy and Smith (1983) Khan et a!. (1984) Meng et at. (1984) Meng et al. (1984) Blavette et al. (1988) Blavette el a/. (1988) Harada el a/. (1988) Harada et al. (1988) Tiinckhauf and Nembach, (1991) Schmidt and Feller-Kniepmeier (1992) Duval etat. (1994) Duval etat. (1994) O 2 w on a o 10 15 20 25 30 35 40 CALCULATED % CO © 7' Kriege and Baris (1969) * 7 Kriege and Baris (1969) * 7' Loomis « al. (1972) Q 7' Dreshfield and Wallace (1974) A 7 Dreshfield and Wallace (1974) M 7' Caron and Khan (1983) X 7' Khan « a/. (1984) «7' Meng el a/. (1984) B 7 Meng el a/. (1984) * 7' Harada era/. (1988) + 7 Harada etal. (1988) Y 7' Tiinckhauf and & 7 Nembach, (1991) O 7' Duval etal. (1994) O 7 Duval et al. (1994) 2 4 6 CALCULATED % MO © 7' Kriege and Bans (1969) * 7 Kriege and Bans (1969) O 7' Loomis el al. (1972) □ 7' Dreshfield and Wallace (1974) *7 Dreshfield and Wallace (1974) A 7' Shimanuki el a/. (1976) B 7 Shimanuki ft a/. (1976) M 7' Caron and Khan (1983) + 7' Deiargy and Smith (1983) X 7 Deiargy and Smith (1983) M 7' Khan el a/. (1984) * 7' Meng e( a/. (1984) ffl 7 Meng el a/. (1984) M 7' Blavette el al. (1988) V7 Blavette el al. (1988) * 7' Harada et at. (1938) + 7 Harada el at. (1938) Y 7' Tiinckhauf and 47 Nembach, (1991) X 7' Schmidt and 07 Feller-Kniepmeier (1992) O 7' Duval «* al. (1994) 0 7 Duval el a/. (1994) Q I PS O □ 7' Dreshfield and Wallace (1974) ft 7 Dreshfield and Wallace (1974) M 7' Caron and Khan (1983) + 7' Deiargy and Smith (1983) X 7 Deiargy and Smith (1983) M 7' Khan era/. (1984) M 7' Blavette et al. (1988) -» 7 Blavette era/. (1988) * 7' Harada et al. (1988) + 7 Harada et al. (1988) X 7' Schmidt and O 7 Feller-Kniepmeier (1992) a 7' Duval eta/. (1994) O 7 Duval el al. (1994) 10 15 20 25 30 CALCULATED % CR 35 40 2 4 6 8 10 CALCULATED % W Figure 10.45 (b) and (c). Figure 10.45 (d) and (e). References are listed on pp. 402-408. 10,5.3 Summary It is clear from the results shown in this section that the CALPHAD route is providing predictions whose accuracy lies close to that expected from experimental measurement. This has significant consequences when considering CALPHAD methods in both alloy design and general everyday usage as the combination of a high quality, assessed database and suitable software package can, for a wide range of practical purposes, be considered as an information source which can legitimately replace experimental measurement. The next sections discuss more complex types of calculations which are geared to specific, practical problems. 10.6. SELECTED EXAMPLES 10.6.1 Formation of deleterious phases Formation of secondary phases is a feature of many materials and, in the context used here, is defined as the formation of phases other than the primary hardening phases or the predominant phases in duplex alloys. Embrittling phases can be carbides, borides, topologically close-packed (TCP) phases such as o or y,, or 'insoluble' compounds such as Al7Cu2Fe in Al alloys. They can also be beneficial, providing secondary hardening reactions as for example in the low-temperature precipitation of 77 phase in the 7'-hardened alloy IN939 (Delargy and Smith 1983). But, more often, they produce a degradation in mechanical properties as is found with a formation in stainless steels. The understanding of the formation of these phases is therefore critical in material design and processing. For Ni-based super-alloys, the formation of a and related phases has concerned alloy designers for many years. They are major materials in aerospace gas turbine engines where failure of critical components can have catastrophic consequences. The next two sub-sections will therefore show examples of how CALPHAD methods can be used to understand and help control TCP phases. 10.6.1.1 o-Phase Formation in Ni-based Superalloys. The concept of '<7-safety' has been one of the most important design criteria in the design of superalloys (Sims 1987), and in the past the most usual method of predicting this was by techniques such as PHACOMP which rely on the concept of an average electron hole number, Nv, made up of a weighted average of Nv values for the various elements. In itself the concept behind PHACOMP is simple and it is easy to use, but there are a number of questions concerning its use and theoretical justification. For example, the values of JV„ used to calculate Nv are usually empirically adjusted to fit experience and the model fails to explain why a appears in the Ni-Cr-Mo ternary but is not observed in binary Ni-Cr or Ni-Mo. Furthermore, although it supposedly correlates with the phase boundary of 7 and o, it gives no information on the temperature range where a may be stable, nor does it provide any information on the interaction of this boundary with the 7//1 or 7/Laves boundaries. Using the CALPHAD route an actual cr-solvus temperature can now be calculated which defines the temperature below which a will form and can be unambiguously used to help define V-safety'. A good example of this concept is in Udimet® 720 (U720) whose composition is given below (Keefe et al. 1992). Cr Co Mo W Ti Al B Zr U720 0.035 U720LI 0.01 18.0 16.0 14.7 14.7 3.0 3.0 1.25 1.25 5.0 5.0 2.5 2.5 0.033 0.015 0.03 0.03 This alloy was first used in land-based gas turbine engines and for long-term use at up to 900°C (Keefe et al. 1992), but its excellent all-round properties suggested that it could also be used as an aerospace disc alloy. Unfortunately, while long-term exposure at high temperatures produced only minor susceptibility to cr, its use at 750°C quickly led to large amounts of 0 being formed (Keefe et al. 1992). Clearly the alloy was either close to, or just below, its cr-solvus at the higher temperature and it was found necessary to reduce Cr levels to destabilise a at lower temperatures. This led to the development of U720LI with 2wt% less Cr than for U720. C and B levels were also lowered to reduce formation of borides and carbides which acted as nucleation sites for a formation. Figure 10.46 shows a calculated phase % vs temperature plot for U720 and it can be seen that its a-solvus is indeed close to 900"C and at 750°C the alloy would w 3 o S 100 U720 / \ Liq 80 / \ 60 40 I 20 \ J 0 600 borides' carbides 900 1200 TEMPERATURE CELSIUS 1500 Fifliirc 10 46 Calculated mole % phase vs temperature plot for U720 (from * ' Saunders 1996c). References are listed on pp. 402-408.