prediction of recrystallization in investment cast single ... · prediction of recrystallization in...

Available online at www.sciencedirect.com

www.elsevier.com/locate/actamat

Acta Materialia 61 (2013) 51–66

Prediction of recrystallization in investment cast single-crystalsuperalloys

Chinnapat Panwisawas a, Harshal Mathur b, Jean-Christophe Gebelin a, Duncan Putman c,Catherine M.F. Rae b, Roger C. Reed a,⇑

a Department of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham B15 2TT, UKb Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK

c Rolls-Royce plc., P.O. Box 31, Derby DE24 8BJ, UK

Received 13 June 2012; received in revised form 30 August 2012; accepted 5 September 2012Available online 24 October 2012

Abstract

Modelling and targeted experimentation are used to quantify the processing conditions which cause recrystallization in a single-crystalsuperalloy. The plasticity needed is traced to the differential thermal contractions of the metal and its ceramic mould during processing.For typical cooling rates, the plasticity causing recrystallization is induced above 1000 �C, thus over a temperature interval of approx-imately 300 �C after solidification is complete. The total accumulated plastic strain needed for recrystallization is estimated to be in therange of 2–3%. Modelling is used to rationalize the influence of mould thickness, stress concentration factor and geometry on the inducedplasticity. Negligible plastic strains were predicted in a solid casting with no stress concentration features, as found experimentally. How-ever, recrystallization occurred in thin-walled sections, particularly beneath shroud-like features due to the plasticity induced there. Themodel provides the foundation for a systems-based approach which enables recrystallization to be predicted and thus avoided in newdesigns of turbine blade aerofoil.� 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Mechanical deformation; Solidification; Investment casting; Superalloys

1. Introduction

Turbine blades for gas turbine applications are invest-ment cast, often into single-crystal form. During process-ing, deformation is induced in the nickel-based superalloyduring solidification and subsequent cooling; this is dueto differential thermal contraction of the metal, mouldand core, arising from their differing thermal expansioncoefficients [1]. In practice, this effect has a number of ram-ifications which need to be recognized. First, account needsto be taken of the shrinkages which occur – the final castingwill not exhibit the same dimensions as the wax model towhich it is related. Second, and perhaps of greater practicalimportance, plastic strains are produced which can be large

1359-6454/$36.00 � 2012 Acta Materialia Inc. Published by Elsevier Ltd. All

http://dx.doi.org/10.1016/j.actamat.2012.09.013

⇑ Corresponding author. Tel.: +44 121 414 7080.E-mail address: [email protected] (R.C. Reed).

enough to induce recrystallization during subsequentheat treatment [2–5]. Particularly for components cast insingle-crystal form, the occurrence of recrystallizationcannot be tolerated – the associated high-angle grainboundaries degrade the creep [6,7] and fatigue [8–10]properties significantly. Work has been done to study therecrystallization behaviour of single-crystal superalloysunder the influence of different annealing conditions [11–13]and microstructural features [14–16]. However, very littleattention has been given to developing a systematicapproach for design purposes.

This paper is concerned with the mathematical model-ling of the investment casting of single-crystal superalloys,with particular emphasis on thermal–mechanical effects sothat processing-induced plasticity can be predicted andrationalized. One aim is to elucidate the amount of plasticstrain needed for recrystallization to occur, and to infer the

rights reserved.


mailto:[email protected]


52 C. Panwisawas et al. / Acta Materialia 61 (2013) 51–66

temperature range over which this is induced in the mate-rial. The overarching goal is to build a physics-based toolfor the prediction of recrystallization during the processingof single-crystal castings. Traditionally, the avoidance ofrecrystallization has been dealt with in a rather empiricalway, with reliance placed on existing casting practice, expe-rience or else rules of thumb. Mathematical modellingallows the physical effects causing recrystallization to beanticipated, which is obviously advantageous. Such model-ling might be used for the optimization of processing con-ditions, so that the likelihood of recrystallization can bereduced. If sufficiently robust, it might also be used duringthe early stages of design process to influence the geometrychosen for the turbine blade – as part of a systems-basedapproach to component design.

2. Methods

2.1. Modelling approach

A simplified geometry was designed to represent an ana-logue of a turbine blade aerofoil, of comparable size andcontaining flanges to simulate the mechanical constraintsprovided by platforms and shrouds. Fig. 1 illustrates thedetails of the test piece analysed, which has been christenedthe “bobbin” geometry. Fillet radii of 2 mm were introducedbetween the three platforms/shroud flanges of thickness5 mm, consistent with a stress concentration factor of 1.80.The three gauge lengths of diameter 15 mm are identifiedaccording to the notation L1, L2 and L3, with L1 and L3 beingthe first and last to solidify, respectively, during processing.In some cases – in order to introduce greater complexity –

Fig. 1. Geometry of turbine blade analogue: (a) casting with notches incentral locations of gauge lengths and (b) schematic illustration of thegeometry, where /core, / and W are core diameter, gauge diameter andwall thickness, respectively.

further stress concentration features of known factor Kt wereintroduced into the gauge lengths, and in other cases a cera-mic core was used to facilitate the casting of hollow testpieces of wall thickness as little as 1.5 mm. The details ofthe various geometries considered are summarized in Table1. The nominal thickness of the shell used was �5 mm.

For the modelling, calculations were carried out usingthe finite element method and commercially available soft-ware. Thermal–elastic–plastic analysis was carried out,with the high-temperature plasticity assumed to be rateindependent. This assumption is critiqued later in Section3.6. Temperature-dependent material parameters for theCMSX-4 superalloy were assumed. Thus, the followingthermal and mechanical properties of CMSX-4 were used:density, specific heat capacity, thermal conductivity, yieldstress, ultimate yield strength, hardening exponent, thermalexpansion coefficient, Young’s modulus and Poisson’sratio, taken in the h001i solidification direction. The stres-ses and strains, especially the plastic strains, are of primaryinterest here; since radial symmetry was present in all cases,it proved sufficient to model a 30 degree section of the com-ponents for the mechanical part of the calculation. For thesuperalloy, an elastic–plastic formulation was employed,together with the von Mises criterion; elastic isotropy wasassumed. In what follows, consideration of the effective(accumulated) plastic strain is made and this is denoted��pl. For the definition of ��pl, the flow function for an iso-tropically hardening material is introduced in the form

f fr; jf�plgg ¼ �rfrg � rff�plg ð1Þ

where the effective stress �rfrg is defined as

�rfrg �ffiffiffiffiffiffiffiffiffiffiffiffiffi3

2r : r

rð2Þ

and the plastic flow stress due to isotropic hardening,rf{�

pl}, is defined by

rff�plg � r1 þ ðry � r1Þ expf�H�plg ð3Þwhere r1, ry and H are the ultimate yield stress, teh yieldstrength and the hardening exponent, respectively. There-fore, from the isotropic hardening criterion, one obtains�rfrg ¼ rff�plg. This gives rises to the definition of effective(accumulated) plastic strain as

��pl �Z �pl

0

d��pl ¼Z �pl

0

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

3�pl : �pl

rð4Þ

Note that the definition of d��pl is such that stored energy isconserved:

dW ¼ rd�pl ¼ �rd��pl ð5ÞFor the superalloy, model parameters were adopted

from Refs. [17–20]. For the shell and core, representativevalues for alumina-and silica-based shell materials adaptedfrom Refs. [21–23] were used. The variation in the flowstress with temperature for CMSX-4 is plotted in Fig. 2;the data are taken from Ref. [1].

Table 1Details of the bobbin castings which were modelled (those chosen for experimental casting are labelled by�)

No. Label Gauge diameter (/) (mm) Notch position Kt Wall thickness (W) (mm) Core diameter (mm) (/core)

L1 L2 L3

1 SB15� 15 – – – – – –2 SB9 9 – – – – – –3 MSB15� 15 Middle 1.6 2.0 2.6 – –4 TSB15 15 Top 1.6 2.0 2.6 – –5 CB3.0� 15 – – – – 3.0 96 MSB9 9 Middle 1.6 2.0 2.6 – –7 CB1.5� 15 – – – – 1.5 128 TSB9 9 Top 1.6 2.0 2.6 – –9 MCB 15 Middle 1.6 2.0 2.6 1.5 6W 6 3.5 910 TCB 15 Top 1.6 2.0 2.6 1.5 6W 6 3.5 911 MSB-1 15 Middle 1.6 1.6 1.6 – –12 MSB-2 15 Middle 2.0 2.0 2.0 – –13 MSB-3� 15 Middle 2.6 2.6 2.6 – –14 TSB-1 15 Top 1.6 1.6 1.6 – –15 TSB-2 15 Top 2.0 2.0 2.0 – –16 TSB-3 15 Top 2.6 2.6 2.6 – –

Fig. 2. Yield strength of CMSX-4 material used in the simulation. Data are from Ref. [1].

C. Panwisawas et al. / Acta Materialia 61 (2013) 51–66 53

2.2. Validation studies – investment casting

For the purposes of model validation, some of thegeometries identified in Table 1 were fabricated from theCMSX-4 single-crystal superalloy. A semi-industrial-scalesingle-shot investment casting facility at the University ofBirmingham was employed. Moulds were prepared usingwax assembly, ceramic processing and steam-autoclavedewaxing methods, following standard procedures.

The casting cycle followed is shown in Fig. 3. The moltenmetal was poured under vacuum conditions at 1500 �C intothe mould, and withdrawn thereafter at 0.06 mm s�1; whenall of the mould had passed the baffle, cooling was allowedto proceed in air. Some of the castings were instrumented

using Rh/Pt Type B thermocouples, which have measure-ment capability up to 1750 �C, with use being made of alu-mina sheaths of 4 mm outside diameter, 2 mm insidediameter and 15 mm length. All castings received a standardsolution heat treatment, consisting of a final solutioning stepof 1315 �C/6 h [1]. An electrolytic etching process involvingHCl/H2O2 etch was used to reveal whether recrystallizationhad occurred.

2.3. Transmission electron microscopy

Transmission electron microscopy (TEM) was used tostudy the deformation induced during the investment cast-ing process. CMSX-4 superalloy in the as-cast condition

Fig. 3. Heating cycle used during the investment casting trials.


was used for this purpose. For sample preparation, discs of�3 mm diameter and 0.2–0.3 mm thickness were subjectedto twin-jet electropolishing with 10% perchloric acidsolution in methanol; 20.5 V and � 5 �C were the workingconditions. A JEOL 200CX transmission electron micro-scope was used at an accelerating voltage of 200 kV forbright-field imaging of the deformed microstructure.

Fig. 4. As-cast tensile (a) wax part, (b) casting mould and (c) test piececast in a single-shot furnace at the University of Birmingham.

2.4. Mechanical testing – critical plastic strain for

recrystallization

For later parts of the study, as-cast tensile test pieces ofCMSX-4 of diameter 5.85 mm and gauge length 29 mmwere cast. To ensure that the surface finish of the test pieceswas representative of that arising from the investment cast-ing furnace, tensile test pieces were cast in such as way thatthe gauge length remained in the as-cast condition; only theshoulders and grips of the test pieces were subjected to elec-trical discharge machining (see Fig. 4). Care was taken toensure that only test pieces cast within 20 � of h001i wereemployed for the tensile testing. To evaluate the criticalstraining conditions necessary for recrystallization,mechanical testing was subsequently carried out in tensionat different temperatures at a strain rate of 0.2% min�1, toinduce various levels of plastic strain into the material. Theyield stress data were extracted from the mechanical testingresults for modelling purposes. Typical stress–strain curvesare given in Fig. 5 and the variation in the flow stress withtemperature is given in Fig. 5. Subsequently, samplespulled in tension to various strain levels were subjected tothe standard solution heat treatment for CMSX-4. Thesamples were then sectioned longitudinally along h001ifor examination. The electrolytic etching process was usedas before, to reveal any recrystallization.

Fig. 5. (a) Stress–strain curves and (b) variation in flow stress with temperature for as-cast CMSX-4.


3. Results

In this section our results are presented as follows. First,some basic considerations relevant to the problem are dis-cussed; results from a basic one-dimensional model are given.Next, results from (i) the thermal and (ii) thermal–mechanicalfinite element modelling are presented. There follows a sensi-tivity analysis, which explores the effects of the important pro-cessing parameters. Finally, the predictions are comparedwith the results from our experimental studies.

3.1. Preliminary considerations

Consider the situation of a solid cylinder of a single-crystal superalloy held within a mould assumed to be

totally rigid; this simple test case can be modelled in onedimension using an elasto-plastic material law under theassumption of isotropic elasticity. The cooling rate isassumed to be uniform at 0.06 mm s�1, consistent withthe experimental work. The plastic strain �pl{T} at eachtemperature is determined using

�plfTg �Z T

T solidus

@�pl

@t=@T@t

dT ð6Þ

The results (see Fig. 6) indicate that about 0.1% plasticstrain is induced at temperatures in excess of 1200 �C (seethe zone A marked in the figure). On further cooling, fur-ther thermal strain can be accommodated elastically inzone B down to a temperature of approximately 600 �C.

Fig. 6. Strain evolution during cooling from 1300 �C, as predicted by one-dimensional modelling. The terms �th, �el and �pl are the magnitudes of the totalthermal strain, elastic strain and plastic strain, respectively.

Fig. 7. Comparison between predicted thermal fields and thermocouple measurements of the casting SB15.


Further plastic strain is induced only when the temperaturefalls below 600 �C, building up substantially thereafter(zone C). These calculations suggest the possibility of theplasticity causing recrystallization being introduced at tem-peratures in excess of 1000 �C, soon after solidification iscompleted.

3.2. Thermal model

Thermocouple measurements were made at the loca-tions L1 and L2 during the casting of the bobbin test pieceSB15 of Table 1. In Fig. 7, the thermocouple readings are

compared with the predictions from the model. Consistentwith the location of the thermocouples, the readings fromL2 are higher than those from L1 at any given time; amaximum difference of up to 150 �C was measured. Themodel predictions are in good agreement with the experi-mental results between approximately 1515 and 1000 �C.

The important temperature range for this study isbetween 1300 and 1000 �C, since strain accumulationoccurs only below the solidus temperature of the alloy,which is about 1330 �C; this is consistent with the predic-tions in Fig. 6. Below 1000 �C, the model underestimatesthe cooling rates somewhat, due to the rather complicated

Fig. 8. Results of mesh sensitivity study for plastic strain in SB15 geometry.

Fig. 9. Variation in predicted effective plastic strain accumulation with shell thickness and stress concentration factors, in different locations.


heat transfer effects, which are not accounted for perfectly.However, as will be confirmed later, only temperaturesabove 1000 �C are significant for recrystallization, so the

results in Fig. 7 demonstrate that the thermal characteris-tics of the furnace used are captured sufficiently well forthe present purposes.


3.3. Thermal–mechanical model

Thermal–mechanical modelling was carried out to quan-tify the effects of geometry, stress concentration features,shell thickness, shell type, core diameter and core type. Insummarizing the results, the notation of Table 1 is used.Preliminary work was carried out first to confirm the nec-essary scale of mesh discretization needed for the finite ele-ment analysis. The geometry SB15 was used for thispurpose. Fig. 8 illustrates the variation in the computedplastic strain for this geometry at three distinct locations.No significant benefit is gained from using a mesh size lessthan 1 mm; this was used for the work reported in this restof the paper.

Fig. 9 illustrates the influences of shell thickness andstress concentration factor, which have been found forthe solid test pieces MSB-1 to TSB-3 of Table 1. One iden-tifies first that the shell thickness has an important influ-ence, particularly at larger stress concentration factors.The effect is greatest when the stress concentration factorKt is as high as 2.6. The plastic strains produced by Kt

Fig. 10. Evolution of solid fraction (a), temperature (b), effective plastic strain (

values of 1.6 and 2.0 were found to be approximately thesame and not strongly influenced by shell thickness.

The plastic strains predicted by the model were found tobe consistently higher for the L3 location than for L1, and ingeneral were in the order L3 > L2 > L1. This can be rational-ized in the following way. For illustrative purposes, con-sider results for the CB1.5 casting (see Fig. 10). The lowerpart of the casting solidifies first (Fig. 10a) and therefore,during its cooling towards 1000 �C, the material above it(which has yet to solidify) remains in the liquid state, so thatlittle stress builds up. Thus the stress at location L2 does notrise markedly until location L1 solidifies. Location L3 passesthrough the critical temperature range towards 1000 �Cwith the material below it already solidified, so that greaterstresses can be set up on it. Also important are the rates ofcooling, which then relate directly to the rate of plasticstraining. The cooling rates are higher at location L1 thanat L3, due to its greater proximity to the water-cooled chillplate on which the casting sits. The definition of plasticstrain in Eq. (6) then helps to rationalize the greater plasticstrain at lower cooling rates, consistent with L3 – for which

c) and von Mises stress (d) with time during solidification of CB1.5 casting.

Fig. 11. Variation in predicted effective plastic strain with different shell materials, for SB15 and MSB15 geometries.

Fig. 12. Variation in predicted effective plastic strain with withdrawal rates for the MSB15 casting.


the cooling rate is lowest – experiencing the highest plasticstrain. Note the greater rate of increase of the plastic strainwith time for location L3 (see Fig. 10c). The maximum plas-tic strain predicted is also affected by the location of thenotch, e.g. whether it is placed at the very middle of thegauge length or alternatively directly under the flange (seeFig. 1). Higher plastic strains were found in the latter cases,due to the superposition of stresses arising from the filletradii (under the flanges) with those due to the machinednotches introduced for their stress concentration effect.

In addition to the above, a sensitivity analysis for plasticstrain accumulation was carried out to explore the effects ofshell material. Two distinct shell systems were studied: analumina-based one (referred to here as Shell1) and asilica-based one (Shell2). Thermal expansion coefficientsand Young’s moduli were assumed to be linear functions

of temperature, and thus, given the materials used, Shell1is appreciably stiffer than Shell2; consequently, more plas-tic strain might be anticipated within the metal cast inShell1 than in Shell2. Calculations were carried out forthe SB15 and MSB15 geometries (see Fig. 11). The pre-dicted plastic strain induced in the unnotched solid testpiece SB15 is small and not appreciably influenced by shelltype; moreover, the plastic strain was distributed uniformlyalong the casting. For the notched test piece MSB15, thestrain was concentrated strongly around the notch, andfor Shell2 in particular it showed again the tendencyL3 > L2 > L1. For Shell1 the plastic strain did not varystrongly from gauge length to gauge length. Slower with-drawal rates caused slower cooling rates, hence lower strainrates for deformation and thus lower plastic strains. Fig. 12illustrates the quantitative data associated with this cooling

Fig. 13. Variation in predicted effective plastic strain with different core materials and wall thicknesses, for CB1.5 and CB3.0 test pieces.

Fig. 14. Variation in the predicted plastic strain at ambient temperature for the different geometries at location L3.


rate effect. More deformation was found around thenotches of MSB15 than under the flange features. Thesefindings emphasize the importance of shell properties.

Finally, the influence of the material used for the corewas studied. The larger values are typical of alumina-basedshells and cores, and the smaller ones representative ofsilica-based ones. The test piece CB1.5 is emphasized here,since it is this one which was found to exhibit extensiverecrystallization when an alumina core was employed.Fig. 13 summarizes the results of the analysis. Castingsproduced with an alumina-based core are predicted to havean induced plastic strain of about 2%, which varies slightlywith position along the casting. When a silica-based core isused, the induced plasticity is reduced by a factor of

approximately half. Hence one advantage of using asilica-based core – in addition to the ease by which it canbe leached out of the casting – is a reduced propensityfor recrystallization to occur.

To summarize, the castings listed in Table 1 were mod-elled to examine the effects of casting cross-section, thestress concentration factor, its location and the presenceof a core. Fig. 14 plots the maximum plastic strain gener-ated in the different castings and confirms that there is astrong influence of casting geometry. In the solid castings,the induced strain is low and approximately constant irre-spective of the gauge diameter and, for the thicker castings,the stress concentration features. However, as the gaugecross-sections were reduced and when a ceramic core is

Fig. 15. Variation in predicted effective plastic strain predicted in the cast test pieces and associated experimental observations of recrystallization aftersolution heat treatment.

Fig. 16. Recrystallization in cored test piece CB1.5 after solution heat treatment.


introduced, the plastic strains increase significantly. Theintroduction of stress concentration features enhances theaccumulated strains. Notches in the top positions of thegauge generated the highest strains; for the TCB test piece,a total accumulated plastic strain of 13% plastic strain waspredicted.

3.4. Comparison of predictions with experimental casting

trials

In order to assess the accuracy of the modelling, targetedmodel-driven experimentation was carried out by castingsome of the geometries modelled above experimentally.

Fig. 17. Plastic strain evolution during casting of bobbin test pieces SB15 and CB1.5 at different locations.

Fig. 18. Distribution of effective plastic strains and average normalstresses in the solid and cored test pieces on completion of the casting (30degree sections).


The castings fabricated are identified in Fig. 15, beingplotted in order of increasing predicted plastic strain. Aftersubsequent solution heat treatment, the solid castings of15 mm gauge diameter were never found to recrystallize;however, when an alumina core was used to reduce thecasting wall thickness to 1.5 mm, recrystallization was pro-duced consistently over the entire length of the casting (seeFig. 16). In Fig. 17, the evolution of the plastic strain in thegauge sections of the simple solid casting and the coredcasting are compared. During cooling, a plastic strain ofonly 0.35–0.4% is predicted in the former, and �2.5% inthe latter. The sense of the stress field is also important.Fig. 18 compares the distribution of effective plastic strainand average normal stresses on a longitudinal section andthe surface, for both the solid and cored castings. The nor-mal stresses within the gauge regions are primarily tensile,consistent with the lower thermal expansion coefficient ofthe ceramic mould. However, the intensity and distributionof normal stresses increases with solidification height, asthe cooling of the lower regions imparts contraction stres-ses on the regions above which remain at higher tempera-tures; this is consistent with the results presented inFig. 9. This, consequently, is reflected in the strain distribu-tion. Fig. 17 shows that during cooling of the cored castingposition L3 is strained first and L1 last. To summarize, theresults confirm conclusively that the critical level of accu-mulated plastic strain for recrystallization to occur is about�2.5%, and that this strain – consistent with the one-dimensional analysis presented in Section 3.1 – is inducedbefore the temperature drops to 1000 �C.

The analysis revealed further effects which should benoted. When a core is present, the predicted plastic strainis higher on the inner surface than on the outer one; on theother hand, the normal stresses are lower on the inner sur-face than on the outer one. Furthermore, in the cored

castings, the fillet radii between the flanges and the gaugesdid not cause any substantial stress concentration; conse-quently, no plastic strain was observed in these regions.However, stress concentration was observed in the filletregions of the solid casting; it was primarily tensile in nature,but the fillet region below L1 also showed compressive stres-ses. In the cored casting, the ratio of the gauge cross-sectionto the flange thickness is much smaller than in the solid


casting. Hence, in the cored casting the gauge regions are themost susceptible to developing the very highest plasticstrains (�2.5%). On the other hand, in the solid casting,strains concentrated on features such as fillet regions, andthe gauge regions develop only half the maximum strain atmost (60.15%). In the solid casting, strain concentrationwas observed only in the fillet regions below the flanges,due to the effect of axial contraction during cooling. In allcastings, the gauge regions closest to the flanges displayedhigher normal stresses, and consequently higher plasticstrains. In cored castings, the middle two flanges showedlocal compressive stresses at the interfaces with the gaugeregions. These developed plastic strains of 0.5–1%; suchregions might be additional sites for recrystallization.

One of the hollow castings (CB1.5) which exhibitedrecrystallization after solution heat treatment was exam-

Fig. 19. Longitudinal cross-section of cored casting at location

ined in detail. Material from location L1 was electrical dis-charge machining wire cut longitudinally (see Fig. 19a) andtransversely (see Fig. 20a), and characterized in the as-castcondition. The horizontal section was examined usingscanning electron microscopy, and showed that recrystalli-zation was evident right across the wall thickness (seeFig. 19b and Fig. 20b).

3.5. Transmission electron microscopy

As a further test of the modelling predictions, the micro-structure of the as-cast CMSX-4 was examined using TEM.Solid bars were used for this purpose. The dendrite cores –which are characterized by cubic c0 of �100–400 nm – aremore or less dislocation-free (see Fig. 21a). However, asthe interdendritic regions were approached – comprising

L1: (a) as-cast condition, (b) after solution heat treatment.


�200–1000 nm irregular c0 and large c/c0 eutectic pools – anappreciable increase in the dislocation density was observed(see Fig. 21b). The dislocations in the as-cast microstructurewere primarily at the c/c0 interface, forming loops around theprecipitates.

To place these observations into context, deformation inas-cast samples strained at various temperatures were stud-ied. Between 20 and 550 �C, shearing by dislocations alongthe {111}h1 10i slip systems was the primary deformationmechanism, with dislocation dipoles, loops and pairs in thec0 being found (see Fig. 21c). However, with deformation at750 �C, stacking faults were also observed within the c0 (seeFig. 21d); these form due to the activation of {111}h1 1,2islip systems. At the higher temperatures of 1050 and1200 �C, dislocation networks formed at the c/c0 interface(see Fig. 21e and f), leaving both c and c0 relatively disloca-tion free. These observations are consistent with thosereported in the literature [1,24,25].

The dislocation structure within an as-cast microstruc-ture is rarely reported, and it is significant that a high dis-location density is observed. The conventional solutionheat treatment would dissolve the c0, allowing the loops

Fig. 20. Transverse cross-section of cored casting at location L

to annihilate to give the more familiar dislocation-freemicrostructure. The simple bar geometry examined experi-ences the lowest possible stresses during casting, yet clearlyundergoes deformation at the yield stress appropriate tothe deformation temperature; according to Fig. 18, theinduced plastic strain in the bar is estimated to be60.15%. Comparison of the microstructures in Fig. 21shows that the as-cast microstructures of Fig. 21a and bmost nearly resemble the higher-temperature deformationof Fig. 21e and f, evidenced by the absence of stackingfaults, dislocation dipoles and loops within the c0. It shouldbe noted that the coarser c0 in the strained samples is due tothe longer soak time at temperature during the strainingtests.

The inhomogeneous dislocation density in Fig. 21a andb supports the deduced temperature range over which cast-ing deformation is induced. This is consistent with resultsfrom the process modelling of the bobbin test pieces(Fig. 17). From the TEM, there is no evidence of plasticdeformation below 600 �C, and the necessary stresses foryield at 600 �C are probably above the fracture stress ofthe ceramic shell.

1: (a) as-cast condition, (b) after solution heat treatment.

Fig. 21. Dislocation structures in as-cast CMSX 4: (a) dendritic region; (b) interdendritic region; (c) tensile plastic strain of 1.51% at 550 �C; (d) tensileplastic strain of 1.45% at 750 �C; (e) tensile plastic strain of 1.85% at 1050 �C; (d) tensile plastic strain of 1.30% at 1200 �C. A: dislocations at c/c0 interface;B: dislocation-free c; C: dislocation dipoles; D: dislocation pairs;, E: dislocation loop; F: stacking faults. The mottled appearance within c in (e) and (f) isdue to reprecipitation of c0 during cooling. The TEM foil normal is h001i – bright-field images under the ~0 �~g condition with ~g ¼ f200g.

Fig. 22. Critical strain data for recrystallization in as-cast tensile test pieces: “N” means no recrystallization and “Y” means that recrystallizationoccurred.


3.6. Critical plastic strain for recrystallization

As a final check of the conclusions drawn from this work,as-cast bars of CMSX-4 were cast and uniaxially strained, attemperatures between 1000 and 1200 �C. They were thensubjected to the standard solutioning heat treatment todetermine whether recrystallization did indeed occur. Notethat the test pieces were prepared with gauge length in theas-cast condition; consistent with the sense of stress expected

in practice, testing was carried out in tension. Fig. 22 sum-marizes the conditions of temperature and induced plasticstrain which were found to induce recrystallization. Ourresults indicate that the critical plastic strain needed toinduce recrystallization in CMSX-4 is in the range 1.5–2.0% when it is introduced at temperatures of 1000 �C orhigher. Further results of ours, which will be published else-where, indicate that substantially greater plastic strains areneeded to cause recrystallization when the deformation is


introduced in the range 550–750 �C and at ambient temper-ature. Thus, induced strain is appreciably more damagingwhen introduced at elevated temperatures.

One final point relates to the thermal–elastic–plastic lawthat is assumed for the modelling. One can see from thehigh-temperature mechanical testing data of Fig. 5a thatit is not easy to define the flow stress of the material pre-cisely at such high temperatures. Some scatter exists inour data – as can be seen from the tests at each temperaturewhich have been duplicated. Moreover, it is probable thatat least some of the decrease in apparent Young’s moduluswith increase in temperature is due to creep plasticity dur-ing tensile straining. Thus, our findings suggest that itwould be appropriate to check whether there is a substan-tial rate-dependence to the plasticity at high temperatures.Substantial creep testing would be required; no data for as-cast CMSX-4 have been reported as yet to the presentauthors. This is the topic of future research efforts of ours,which will be reported elsewhere.

4. Summary and conclusions

A model for the processing-induced plasticity duringinvestment casting has been presented. It is capable of pre-dicting the sites of localized plasticity needed for recrystal-lization to occur during heat treatment of single-crystalsuperalloy castings. The specific conclusions are:

� For typical casting conditions and materials, the analy-sis suggests that the plasticity needed for recrystalliza-tion is induced during the early stages of cooling,when the temperature has not yet fallen below 1000 �C.� Consistent with the modelling results, TEM microscopy

examination indicates that casting deformation isinduced at high temperatures close to the c0 solvus,which is between 1250 and 1310 �C for as-cast CMSX-4.� The modelling and supporting experimentation indicate

that recrystallization is exacerbated by stiffer and thickershells, by reduced metallic cross-sections and in particularby the presence of stress concentration features. Formany of the processing conditions considered – for exam-ple, thicker plain cylindrical geometries – the inducedplastic strain was insufficient to cause recrystallization.� Recrystallization was reproduced successfully in labora-

tory-scale cored castings of CMSX-4 of wall thickness1.5 mm, for which the modelling indicated that the totalplastic strain accumulated during cooling to ambienttemperature was �2.5%. Castings of greater wall thick-ness were not prone to recrystallization.� As-cast tensile test pieces were subjected to deformation

at elevated temperatures; a plastic strain of only 1.5%induced at temperatures between 1000 and 1300 �Cwas sufficient to cause recrystallization.

� Such modelling will aid in the assessment of castingstrains induced around intricate features, such as bladecooling holes and fillets, and thus to set design criteriato avoid recrystallization in investment castings.

Acknowledgments

C.P. and H.M. acknowledge support from the Engineer-ing & Physical Sciences Research Council (EPSRC) andRolls-Royce plc, in the form of Dorothy Hodgkin Post-graduate Awards (DHPAs). Helpful discussions with Dr.Hon Tong Pang, University of Cambridge, and PaulBrown and Dr. Neil Jones, Rolls-Royce plc, are acknowl-edged. The provision of the ProCAST software by theESI Group, and the help of Dr. Rajab Said in organizingthis, is acknowledged as part of the PRISM2 collaborationat the University of Birmingham.

References

[1] Cox DC, Roebuck B, Rae CMF, Reed RC. Mater Sci Technol2003;19:440–6.

[2] Xie G, Zhang J, Lou LH. Scr Mater 2008;59:858–61.[3] Eidel B. Acta Mater 2011;59:1761–71.[4] Zaafarani N, Raabe D, Roters F, Zaefferer S. Acta Mater

2008;56:31–42.[5] Zaafarani N, Raabe D, Singh RN, Roters F, Zaefferer S. Acta Mater

2006;54:1863–76.[6] Chen QZ, Jones N, Knowles DM. Acta Mater 2002;50:1095–112.[7] Meng J, Jin T, Sun X, Hu Z. Mater Sci Eng A 2010;527:6119–22.[8] Schaef W, Marx M. Acta Mater 2012;60:2425–36.[9] Schaef W, Marx M, Vehoff H, Heckl A, Randelzhofer P. Acta Mater

2011;59:1849–61.[10] Moverare JJ, Johansson S, Reed RC. Acta Mater 2009;57:2266–76.[11] Zambaldi C, Roters F, Raabe D, Glatzel U. Mater Sci Eng A

2007;454–455:434–40.[12] Goldschmidt D, Paul U, Sahm PR. In: Antolovich SD et al., editor.

Proceedings of “Superalloys 1992” conference. Seven Springs (PA):TMS; 1992. p. 155–64.

[13] Burgel R, Portella PD, Preuhs J. In: Pollock TM et al., editor.Proceedings of “Superalloys 2000” conference. Seven Springs (PA):TMS; 2000. p. 229–38.

[14] Wang L, Xie G, Zhang J, Lou LH. Scr Mater 2006;55:457–60.[15] Xie G, Wang L, Zhang J, Lou LH. Scr Mater 2012;66:378–81.[16] Wang L, Pyczak F, Zhang J, Lou LH, Singer RF. Mater Sci Eng A

2012;532:487–92.[17] Reed RC. The superalloys: fundamentals and applications. Cam-

bridge: Cambridge University Press; 2006.[18] Sieborger D, Knake H, Glatzel U. Mater Sci Eng A 2001;298:26–33.[19] Quested PN, Brooks RF, Chapman L, Morrell R, Youssel Y, Mills

KC. Mater Sci Technol 2009;25:154–62.[20] MacLachlan DW, Knowles DM. Mater Sci Eng A 2001;302:275–85.[21] Nair SV, Jakus K. High temperature mechanical behavior of ceramic

composites. Boston, MA: Butterworth-Heinemann; 1995.[22] Pabst W, Gregorova E, Ticha G, Tynova E. Ceramics – Silikaty

2004;48:165–74.[23] Green DJ. An introduction to the mechanical properties of ceram-

ics. Cambridge: Cambridge University Press; 1998.[24] Milligan WW, Antolovich SD. Metall Trans A 1987;18A:85–95.[25] Schubert F, Penkalla H, Singheiser L. Z Metall 2003;94:705–10.

prediction of recrystallization in investment cast single ... · prediction of recrystallization in...

Documents