Modeling the Electrical Response of Waspaloy due to the Nucleation,

Growth, and Coarsening of γγγγ’

Ricky L. Whelchel1,a , Rosario A. Gerhardt1,b and Ken C. Littrell2,c

1School of Materials Science and Engineering Georgia Institute of Technology

Atlanta, GA, 30332, USA

2High Flux Isotope Reactor Oak Ridge National Laboratory Oak Ridge, TN, 37831, USA

arwhelchel@gatech.edu, brosario.gerhardt@mse.gatech.edu, clittrellkc@ornl.gov

Keywords: Nickel-base Superalloy, Electrical Resistivity, Non-Destructive Testing, Small Angle Scattering

Abstract. Waspaloy is a polycrystalline nickel-base superalloy used in disc rotors for gas turbine engines. Waspaloy, like other superalloys, is strengthened through the formation of the γ’ precipitate phase. As this precipitate phase evolves with processing and thermal exposure, it is desirable to non-destructively monitor the precipitate microstructural evolution. Electrical resistivity was used as such a non-destructive monitoring technique for aging temperatures ranging from 600°C to 800°C and aging times ranging between 2min and 263.5h. In the nucleation regime, a Johnson-Mehl-Avrami type equation was fit to the electrical response. For the growth and coarsening regimes, a volume distribution of precipitates was fit to the measured electrical resistivity. These fitting techniques were facilitated by microstructural data obtained from SEM imaging, X-ray diffraction, and small angle neutron scattering (SANS) measurements. For both cases, the models showed an excellent fit to the measured electrical data, implying that electrical resistivity is a viable technique for non-destructively monitoring the precipitate phase in Waspaloy. Introduction

Nickel-base superalloys are used in both land and air-based gas turbine engines, due to their superior high temperature mechanical properties. These materials have enhanced high temperature strength and creep resistance due to the formation of nanometer-scale precipitate phases within the matrix phase. The distribution of precipitates will evolve with processing or with thermal exposure in the gas turbine engine, resulting in corresponding changes to the alloy mechanical properties. It is therefore desirable to non-destructively monitor this evolution in the precipitate phase, so that the mechanical properties of gas turbine engine components might also be monitored in the future. Electrical resistivity testing has shown promise for non-destructively monitoring the precipitate phases in superalloys [1-5]. The typical electrical response involves a fast increase to a resistivity maximum due to the initial nucleation of the precipitates, followed by a much slower decrease with growth and coarsening. The main mechanisms that affect these resistivity changes are the extent of conduction electron scattering from the precipitates and solute atoms in the matrix phase – both of which will evolve with the nucleation growth and coarsening of the precipitate phase. Empirical models for the electrical response due to growth and coarsening of precipitates have already been proposed for superalloy samples [2-5]. For the nucleation regime, a Johnson-Mehl-Avrami (JMA) type equation has been previously used to fit to the electrical response of several aluminum alloys [6, 7]. In this paper, the electrical response of Waspaloy due to the formation of γ’ Ni3(Al,Ti) precipitates for samples aged from 600ΕC up to 800ΕC was fit with microstructural models throughout the nucleation, growth, and coarsening stages of precipitation. For the nucleation regime, the JMA type fit was used. For the growth and coarsening regimes, the previous models

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previously presented[2-5] by our group were modified to include a volume distribution of precipitates. In order to characterize the superalloy microstructure both scanning electron microscopy (SEM) and scattering experiments were performed. In the case of the nucleation regime, X-ray diffraction (XRD) was used, and for the later precipitation regimes, volumetric small angle neutron scattering (SANS) experiments were performed. Procedure

Material and Heat Treatments. Bulk 13mm diameter Waspaloy bars were obtained from Fry Steel with an approximate composition as follows: (in at%: Ni 56.1, Cr 21.2, Co 12.3, Ti 3.6, Al 2.7, Mo 2.5 and Fe 1.3). The bars were first solution treated at 1145°C for four hours followed by a rapid quench in a ~5wt% brine solution. The bars were then cut into approximately 8mm sections for aging. For the nucleation experiments, aging was performed at 600, 625, and 650°C for times ranging between 18min and 263.5h. For the growth and coarsening experiments, aging was performed at 725°C and 800°C for times ranging between 2min and 263.5h. After each aging treatment the sections were quenched again, and sectioned into 2mm thick samples for characterization studies.

For the resistivity and microscopy specimens, the samples were first flattened using 400 US grit grinding papers, followed by polishing with 9µm and 3µm diamond suspensions. Fine polishing was performed using a solution of 0.05µm colloidal silica mixed with 1 part 30% H2O2 followed by polishing with a suspension of 0.05µm alumina. For the scattering experiments (both X-ray diffraction and small angle scattering), the specimens were polished with a series of 400, 800, and 1200 US grit grinding papers. Electrical Resistivity. DC four-point probe resistivity testing was performed at the center of the cylindrical disc specimens along different diameters. The experimental setup for the resistivity measurements involved a Signatone S301-6 probe station attached to a Signatone SP4-40045TFS four probe head. Current was applied to the outer two probes using the delta mode setting of a Keithley 6221 AC/DC current source, and the voltage drop was measured across the inner two probes using a Keithley 2182A nanovoltmeter. The geometric correction factors used to convert the resistance values to resistivity are described elsewhere [8]. Microscopy. The polished microscopy specimens were given a preferential matrix etchant consisting of 2 parts methanol and 1 part HNO3 at room temperature. The specimens were etched for approximately 30s along with the application of 50V DC from a Keithley 228A voltage/current source. SEM images were obtained using a Zeiss SEM Ultra60. X-ray Diffraction. X-ray diffraction (XRD) measurements were obtained with a PANalytical X’Pert PRO Alpha-1 diffractometer with Cu Kα1 radiation and a Bragg-Brentano parafocusing setup. The diffracted intensity was measured for scattering angles between 42.981° to 100.000° with a step size of 0.0334225° and a scan rate of 0.005655°/s. All background removal and data analysis was performed using the JADE 9 software from Materials Data, Inc. Small Angle Neutron Scattering. All small angle neutron scattering (SANS) experiments were performed at the CG-2 beamline at Oak Ridge National Laboratory’s High Flux Isotope Reactor. The data were obtained using three different instrument configurations for each sample, yielding SANS data for a scattering vector (Q) range of approximately 10-3Ǻ-1 to 1Ǻ-1. The high and medium Q ranges were both obtained using a source to sample distance of 9.229m and a wavelength of 4.75Ǻ. The sample to detector distances for the high and medium Q ranges were 1.161m and 8.861m respectively. The low Q region was obtained with a source to sample distance of 17.275m, a sample to detector distance of 19.361m, and a wavelength of 12Ǻ. The scattering intensity was azimuthally averaged as a function of Q using the SPICE SANS reduction package [9], which operates within the Igor Pro software from Wavemetrics, Inc.

Materials Science Forum Vols. 706-709 2407

Subsequent analysis of the SANS data was performed using the Irena package [10], which also operates within the Igor Pro software. Volume distributions of the γ’ phase were fit to the measured SANS intensity by assuming spherical particles and a hard sphere model for the structure factor. More in-depth descriptions of the models used for fitting of the SANS data are given by other publications for similarly treated but different Waspaloy specimens [2, 3, 5]. Results and Discussion

Resistivity due to Nucleation. The relative resistivity (ρrel) has been successfully fit with a JMA type model for several aluminum alloys[6,7]. Both the equation for ρrel and the JMA fit are given by Eq. 1.

ρrel =ρi − ρST

ρmax − ρST

=1− exp − kt( )n[ ]. (1)

The subscripts i, ST, and max represent the resistivities of each specimen, the solution treated specimen, and the maximum in resistivity, respectively. For the JMA fit, t is the aging time, and k is a rate constant and n is a fitting constant related to the material. The measured electrical resistivity data and the corresponding JMA fits are given in Fig. 1. In all cases, the electrical resistivity shows a fast increase to a maximum. Evidence for γ’ nucleation was seen through the formation of small intensity peaks in the XRD spectra at similar scattering angles to the matrix peaks. Such peaks are common for nickel-base superalloys, such as Waspaloy, due to the similar lattice parameter between the two phases [11]. It is obvious from Fig. 1 that the JMA model shows an excellent fit to the measured electrical data prior to the resistivity peak, making this model a good indicator of the electrical response due to γ’ nucleation.

Fig. 1. Measured relative electrical resistivity with JMA type fits for Waspaloy specimens heat treated at 600, 625, and 650°C

The ratios in the peak intensities were used as an indicator of the relative γ’ volume fraction (fV, rel), as described by Jenkins and Snyder [12]. Both the volume fraction and resistivity displayed similar increasing trends with aging time up to the maximum in resistivity; however, the resistivity

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was larger than the volume fraction data throughout all measured aging times. Lendvai et. al [13] observed an fV

2/3 dependence of the resistivity for nucleation of GP zones in an aluminum alloy, which would account for this behavior. Resistivity due to Growth and Coarsening. The JMA model is useful for fitting the electrical response prior to the resistivity maximum, when the precipitates initially nucleate, but this model fails to describe the electrical response after the peak, whereby the resistivity shows a slow decrease with aging time. In this region, growth and coarsening are the dominant mechanisms. Derivation of Model. A model for the electrical response in this region has been proposed previously, and has shown excellent fits to the measured electrical data [2-5]. The theory behind this model is explained in much greater detail in these previous papers than is possible to describe in this publication, so the reader is referred to them for a better understanding of this model. The previous model for the electrical response due to growth and coarsening (η’) is given by Eq. 2 and involves the competing mechanisms of conduction electron scattering from precipitates (given by ηg) and conduction electron scattering from solute atoms (given by ηc)[3]. The η’ model has been normalized by dividing by (ηmax), so that it is unitless, and be able to be compared to the relative resistivity[5]. The microstructural features of interest are the precipitate volume fraction, fV, and the average precipitate radius, <r>. The variables, C and n, are positive non-zero fitting constants that relate the effects of increasing volume fraction to the change in solute content at a given aging temperature.

η'≡ηg + ηc

ηmax

=3.33

fV4 / 3

< r >2 −CfVn

ηmax

. (2)

The ηg term is meant to approximate the extent of conduction electron scattering from precipitates[2]. It is therefore directly proportional to the precipitate surface area per unit volume and indirectly proportional to the precipitate spacing. The original formulation for ηg relies on several assumptions: that the precipitates are spherical, that the microstructure can be modeled as a distribution of point particles, and that the precipitates are all assumed to be of the average size. For Waspaloy the precipitates are known to be spherical [2-5]; however, the last two assumptions are not an accurate description of the true Waspaloy microstructure. This section will discuss modifications toηg to fit the electrical response with a more realistic distribution of precipitates. The new formulation for ηg is given by Eq. 3, where SV, λ, and NV are the surface area per unit volume, the mean free path, and the number density of the precipitates respectively. Eq. 3 is superior to the previous model in that the formulation for SV does not assume that all precipitates have the average size and λ does not involve the point particle assumption. Therefore, the effects of a distribution of finite precipitate sizes can be modeled to the electrical response using Eq. 3, and the total electrical response due to precipitate growth and coarsening is given by Eq. 4.

ηg =SV

λ=

4πNV r2

4 1− fV( ) SV=

9 fV2

4 1− fV( )r2

r3

2

(3)

η'≡ηg + ηc

ηmax

=

9 fV2

4 1− fV( )r2

r3

2

−CfVn

ηmax

(4)

Modeling Results. The microstructure due to aging at 800°C under increasing aging time is given by Fig. 2. The precipitates increased in size with aging time in all cases. The precipitate microstructure was quantified via small angle neutron scattering (SANS), whereby the SANS

Materials Science Forum Vols. 706-709 2409

spectra were fit with a volume distribution of spherical particles. The data showed that the precipitate radii increased smoothly with both aging time and temperature in all cases, as would be expected. A plot of the natural logarithm of the radius against the natural logarithm of the aging time revealed a t0.33 and t0.39 dependence for the increase in the radius at 800°C and 725°C respectively. This suggests that the precipitates were in the diffusion controlled coarsening regime for aging at 800°C and in a mixed mode of growth and coarsening upon aging at 725°C.

Fig. 2. SEM images of the evolving precipitate microstructure in Waspaloy upon aging at 800°C under increasing aging time

The microstructural data needed for Eq. 4 was obtained from the volume distributions fitted to the SANS data. The measured relative resistivities upon aging at 725°C and 800°C, along with the η’ fits, are given in Fig. 3. The η’ model shows excellent agreement with the measured electrical response, implying that a distribution of precipitates may be fit to the resistivity in this manner.

Fig. 3. Relative resistivities with η’ fits for Waspaloy specimens heat treated at (a) 725°C and (b) 800°C

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Conclusions

The electrical response of aged Waspaloy specimens has been modeled throughout the nucleation, growth, and coarsening stages of γ’ precipitation. The nucleation regime (which showed a characteristic fast increase to a maximum) was modeled with a JMA type model, which is related to the increase in volume fraction of the initially nucleated phase. The region after the maximum in resistivity showed a slower decrease to a minimum, and is due to precipitate growth and coarsening. This region was fit with a model that accounts for conduction electron scattering from both precipitates and solute atoms, whereby a volume distribution of precipitates was fit to the measured electrical resistivity. Both models showed excellent fits to the electrical data in their respective regions and show promise for using electrical resistivity testing as a non-destructive testing method for monitoring the γ’ phase in Waspaloy. Acknowledgements

The authors wish to acknowledge the funding for this work provided by the U.S. Department of Energy under grant number DE-FG 02-03-ER 46035. All SANS data was obtained at Oak Ridge National Laboratory's High Flux Isotope Reactor, sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. References

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Materials Science Forum Vols. 706-709 2411

THERMEC 2011 10.4028/www.scientific.net/MSF.706-709 Modeling the Electrical Response of Waspaloy due to the Nucleation, Growth, and Coarsening of γ′ 10.4028/www.scientific.net/MSF.706-709.2406

DOI References

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http://dx.doi.org/10.1016/j.actamat.2009.06.019 [6] W. Oettel, C. Radomsky and H. Loffler: Krist. Tech. Vol. 15 (1980), p.713.

http://dx.doi.org/10.1002/crat.19800150613 [7] R. Ferragut, A. Somoza and I. Torriani: Mat. Sci. Eng. A Vol. 334 (2002), p.1.

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Mater. Sci. Forum Vol. 426-432 (2003), p.821.

http://dx.doi.org/10.4028/www.scientific.net/MSF.426-432.821 [13] J. Lendvai, T. Ungar, I. Kovacs and G. Groma: Philos. Mag. Vol. 33 (1976), p.209.

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