Detecting recrystallization in a single crystal Ni-base alloy using resonant ultrasound spectroscopy

NDT&E International 83 (2016) 68–77

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Detecting recrystallization in a single crystal Ni-base alloy using resonant ultrasound spectroscopy L.H. Rettberg n, B.R. Goodlet, T.M. Pollock Materials Department, University of California, Bldg. 503, Rm. 1355, Santa Barbara, CA 93106-5050, United States

art ic l e i nf o

a b s t r a c t

Article history: Received 1 February 2016 Received in revised form 23 May 2016 Accepted 24 May 2016 Available online 9 June 2016

The use of resonant ultrasound spectroscopy (RUS) as a nondestructive evaluation (NDE) technique for Ni-base single crystal superalloys has been investigated. Manufacture of single crystal superalloys can be challenging due to the prevalence of defects induced during single crystal growth or subsequent processing. Common defects involve the presence of misoriented (non-single crystal) material that change the bulk elastic properties and, as a result, are detectable by RUS. To control the extent of misoriented material, recrystallization induced by shot peening the surface of the single crystal has been studied. RUS was then used to determine the presence and depth of misoriented material due to recrystallization. Recrystallization of shot peened cylindrical single crystal specimens occurred to a depth of 80 μm and 178 μm during subsequent heat treatments. Experimental average resonance frequency shifts of 1.835% 71.704% and 2.380% 72.910%, respectively, were measured over a frequency range from 20–200 kHz when compared to the baseline shot peened condition. Finite element (FE) models using the ABAQUS Lanczos Eigen frequency solver assessed the influence of recrystallization as a function of depth from the surface and showed good agreement with the measured resonance frequency shifts. For the greatest NDE sensitivity on production-scale turbine blades and other gas turbine components, a coupled RUS measurement and FE modeling approach is essential, and has the potential to improve single crystal processing approaches and manufacturing yields. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Resonant inspection Ni-base superalloys Shot peening Recrystallization Finite element method (FEM) Resonant ultrasound spectroscopy (RUS) Nondestructive evaluation (NDE) Ultrasonics

1. Introduction For several decades, single crystal Ni-base superalloys have been the material of choice for high pressure turbine blades in gas turbine engines [1,2]. More recently, they have been implemented in land-based combined cycle power generation gas turbine engines to achieve efficiencies over 60%. The most advanced Ni-base superalloys may contain ten alloying elements, including significant amounts of refractory elements, and possess excellent mechanical properties (creep and fatigue), oxidation and corrosion resistance. A critical development in the processing of Ni-base superalloys was the use of high thermal gradient casting to create directionally solidified turbine blades and, with the use of a grain selector/seed crystal, single crystals [2]. By removing high angle grain boundaries, single crystal superalloys can tolerate thermomechanical loading at temperatures in excess of 85% of their melting point. Without the requirement for grain boundary strengtheners, microsegregation and eutectic content in single crystal superalloys can be significantly reduced during heat treatments without causing incipient melting, improving fatigue life [3,2]. n

Corresponding author. E-mail address: [email protected] (L.H. Rettberg).

http://dx.doi.org/10.1016/j.ndteint.2016.05.004 0963-8695/& 2016 Elsevier Ltd. All rights reserved.

A typical single crystal superalloy casting yield for aviation turbine blades may be as low as ∼70% due to defects such as misorentation, high-angle boundaries and recrystallization, with defect criteria being defined by a variety of manufacturer specifications [2]. By using nondestructive evaluation (NDE) techniques, superalloy castings with defects can be detected and subsequently repaired or reverted. Standard NDE techniques include: fluoroscopic inspection, liquid penetrant inspection, radiographic inspection, and eddy current inspection [4,5]. Research described in this paper demonstrates the utility of a novel NDE framework which employs nondestructive resonant ultrasound spectroscopy (RUS) measurements, informed by finite element (FE) models to evaluate grain structure defects in single-crystal superalloy specimens. Considering the anisotropic elastic properties of Ni-base materials and their influence on the mechanical resonance of a 3D body, RUS is employed for rapid NDE of surface recrystallization, using forward FE models of resonance, validated by experiments. 1.1. Resonant ultrasound spectroscopy In RUS, resonance modes are excited by a piezoelectric transducer(s) that provide a periodic displacement to the surface of the specimen. An elastic solid of any shape has normal modes and

L.H. Rettberg et al. / NDT&E International 83 (2016) 68–77

natural frequencies. If driven by the transducer(s) at a natural frequency, the amplitude of oscillation of the normal mode is enhanced by the quality factor (Q) of the sample, enabling experimental measurement [6–10]. These amplified deflections are then recorded across a range of frequencies by additional piezoelectric transducers contacting the specimen to yield a broadband resonance spectrum when plotted as a function of the excitation frequency [6–10]. From peaks in the broadband measurement, resonance frequencies are deduced that are characteristic of the geometry and material properties of the specimen [6–10].

Table 2 Directional elastic moduli for singlecrystal specimens, calculated with data from [13]. Directional Moduli Value (units)

2. Elasticity considerations Elastic waves excited in the specimen during RUS inspection are low-energy and generate very small sample deflections such that the assumption of linear elasticity is appropriate. The 3D constitutive law relating stresses (sij) and strains (ϵkl) is Hooke's law, given as:

σij = Cijkl ϵkl ,

(1)

where Cijkl is the rank-four stiffness tensor. Voigt shorthand maps the Cijkl of the rank-four tensor to a 6-by6 matrix ( Cijkl → Cpq ). The two constituent phases of Ni-base superalloy single crystals, γ, and γ′, possess cubic crystal structures, affording the material cubic elastic symmetry. Cubic symmetry materials are fully defined by 3 independent stiffness values, C11, C12, and C44 [8]. An important characteristic for RUS inspection of grain structure is the elastic anisotropy of the material, which is commonly defined for a cubic crystal by the Zener [11] anisotropy ratio:

A=

2C44 . C11 − C12

(2)

Metals with low elastic anisotropy include Al and W with AAl ≈ 1.2 and AW ≈ 1.0, while Ni, Fe, and Cu exhibit significant anisotropy with A values ranging from 2.4–3.2 [12]. Table 1 provides the stiffness values and calculated A for CMSX-4 [13], a Ni-base superalloy with similar composition and properties to the alloy employed in this study: René N5. 2.1. Engineering moduli of cubic single crystals Single crystal Ni-base superalloy castings are typically solidified along the 〈001〉 crystallographic direction since growth is preferred on the {100} family of planes, and the low modulus along this direction is favorable for strain-controlled fatigue [2]. The directionally-dependent Young's modulus ( E[hkl]) relates normal stresses to normal strains as applied parallel to a crystallographic direction [hkl], and is useful for comparisons to isotropic moduli. This constitutive behavior is in the same form as Eq. (1), whereby Cijkl is replaced by E[hkl] with the definition: Table 1 Single crystal stiffness values for CMSX-4, a 2nd generation single crystal Ni-base superalloy similar in composition to René N5, data from [13]. Stiffness

Value (units)

C11 C12 C44 A

252 GPa 161 GPa 131 GPa 2.88 unitless

69

E[hkl] =

E[100]

126 GPa

E[101]

231 GPa

E[111]

320 GPa

G{100} <⊥>

131 GPa

G(101)[110 ¯ ]

45.5 GPa

G(110)[001]

131 GPa

G{111} <⊥>

58.1 GPa

C44 (C11 − C12 )(C11 + 2C12 ) . C44 (C11 + C12 ) + (C11 + 2C12 ) αJhkl

(3)

The direction cosine (Jhkl) corresponds to the angle between the plane normal to the applied stress and the nearest 〈100〉 crystallographic direction; Jhkl is zero along 〈100〉, maximum when J111 = 1/3, and median for J110 = 1/4 . The anisotropy factor (α) is negative here and goes to zero as the material becomes isotropic ( A → 1), defined as: α = C11 − C12 − 2C44 [14,15]. From Eq. (3) it is clear that E[111] is the highest directionally-dependent Young's modulus and E[100] is the minimum modulus [13]. A directionally-dependent shear modulus ( G(mno)[hkl]) can be calculated in a similar manner, where (mno) is the plane normal and [hkl] is the direction of shear on (mno). G(mno)[hkl] has rotational symmetry on {100} and {111} planes allowing for the direction of shear to be expressed as an arbitrary perpendicular direction ([⊥]) contained in the plane, but loading on all other planes exhibit G(mno)[hkl] that vary with the direction of shear. G(mno)[hkl] and E[hkl] are calculated for key directions using Cpq from Table 1 and are summarized in Table 2 for subsequent discussion. 2.2. Isotropic moduli for polycrystalline aggregates When consisting of a large volume of randomly oriented grains, polycrystalline materials act as elastically isotropic bodies with no directional dependence of constitutive elastic behavior [16]. Through a series of FE models, Nygårds has demonstrated that the number of grains necessary for an isotropic response from an aggregate of cubic crystals depends on the anisotropy of the crystallites (A) and the preferred cut-off for an effectively isotropic response [17]. Considering the properties of René N5 specifically, an isotropic response would be expected from a aggregate volume containing 550 or more randomly oriented grains. With isotropy requiring that A ¼1 in Eq. (2), a degree of freedom is removed from the elastic body such that only two moduli fully define the response. The most common isotropic moduli being: Young's modulus (E), bulk modulus (K), shear modulus (G) or Poisson's ratio (ν) [12]; the specific pair of moduli selected is based on the context of their use. Isotropic moduli are determined through various averaging schemes (e.g. Voigt–Reuss–Hill [18], Hashin [19], Kröner [20], and Gairola–Kröner [21]), whereby all these schemes define K as:

K=

C11 + 2C12 . 3

(4)

The first polycrystalline average for the shear modulus was devised by Voigt ( GVo) and assumed uniform strain across all grains to yield:

GVo =

2C ′ + 3C44 , 5

(5)

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where C ′ = (C11 − C12 ) /2 is often referred to as the tetragonal shear modulus. However, a uniform strain assumption is not ideal for cubic materials with significant elastic anisotropy ( A > 2 as Ledbetter [15] and Kuhn and Sockel [22–24] have shown. For Ni-base superalloys specifically, Kuhn and Sockel suggest higher-order averaging schemes (e.g. [19–21]) be used, with the Gairola-Kröner average ( GGK ) [21] found to be superior. GGK is defined as:

GGK

⎡ ⎤ ⎛ C − C ′ ⎞2 ⎢ ⎥ 44 η ⎜ ⎟ ⎢ ⎥ G ⎛ ⎞ ⎝ ⎠ Vo 12 ⎥, ⎟ = GVo ⎢ 1 − ⎜ 2 ⎢ ⎥ ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎝ 125 ⎠ 2η ⎟ ⎜ C 44 − C ′ ⎟ ⎜ 24η2 ⎟ ⎛ C 44 − C ′ ⎞ ⎥ ⎢ ⎜ −⎜ ⎜ ⎟ 1−⎜ ⎟ ⎜ ⎟ ⎟ ⎢ ⎝ 25 ⎠ ⎝ GVo ⎠ ⎝ 625 ⎠ ⎝ GVo ⎠ ⎥⎦ ⎣

(6)

where η = (3K + 6GVo ) /(3K + 4GVo ). 2.3. Influence of recrystallization on resonance As a direct result of elastic anisotropy, a single crystal casting will exhibit different resonance characteristics as compared to a polycrystalline casting of the same material, with larger anisotropy leading to greater divergence of resonance characteristics. Conversely, a material with an A ¼1 would resonate irrespective of grain structure, and would not be a candidate material to detect recrystallization with RUS. René N5 single crystals will be the most compliant to normal stresses along 〈100〉 directions, and the least compliant to shear on {100} planes. As a [001] single crystal undergoes recrystallization, the recrystallized grains will have an orientation different than the parent material that is stiffer to normal loads, and will be more compliant to shear loading. The consequence of this is that resonance modes that are dominated by dilational or extensional motion will encounter a higher stiffness according to the following relation:

fR ∝

E ρ

(7)

whereby the resonance frequency (fR) increases, assuming everything else remains constant. Similarly, resonance modes dominated by shear or torsional motions will encounter a lower stiffness (G in place of E above), and should exhibit a decrease in fR. Ultimately, the goal of this research is to demonstrate the utility RUS measurements coupled with FE models to establish a NDE framework for characterizing and monitoring particular resonant modes of a geometrically complex single crystal specimen that contains grain defects, based on the fundamental principles outlined above.

Fig. 1. Schematic of the specimen design used in this study. This design is typically used for creep testing.

stress grinding technique to minimize surface damage and residual stresses. Typically used for creep testing, the specimen design has grooves for extensometer attachment and button-heads, as shown in Fig. 1. The machining variance between the specimen design dimensions and the actual dimensions of the gauge length and diameter of the creep specimens was less than 152 μm and 30 μm, respectively. The René N5 plate was solution treated below the full solvus temperature at 1215 °C and aged following standard procedures [26,27]. 3.2. Shot peening Shot peening was performed at GE Power & Water on the reduced gauge section and fillets using two different gas pressures. Full coverage was obtained using a custom fixture and rotating the specimen between passes as shown in Fig. 2. One specimen was shot peened using standard conditions and will be referred to henceforth as Specimen Low-Pressure (LP), while the other specimen was shot peened at double the typical pressure and will be referred to as Specimen High-Pressure (HP). There was a negligible change in the diameter of the specimens as a result of shot peening. To induce recrystallization, heat treatments were performed at the full γ′ solvus temperature for several hours in a reducing atmosphere to avoid surface oxidation and minimize mass change. 3.3. Crystal orientation of shot peened specimens The [001] crystal direction of Specimen LP and Specimen HP were misoriented from the primary specimen axis by 5.27° and 6.09°, respectively (Fig. 3). By using Eq. (3), the effective elastic moduli along the primary specimen axis of Specimen LP and Specimen HP were calculated to be 128 GPa and 129 GPa, respectively. This is 2.59% increase in the elastic modulus along the primary specimen axis when compared to the perfectly aligned [001] single crystal modulus of 126 MPa.

3. Methods 3.1. Material The single crystal Ni-base superalloy René N5 is a second generation turbine blade material with composition shown in Table 3. A René N5 single crystal plate measuring 13  24  1.5 cm, grown by the Bridgman process, was provided by GE Power & Water [25]. Shot peening was performed on two specimens of René N5 machined along the [001] growth direction using a lowTable 3 Composition, in weight percent, of the singe crystal (SX) gas turbine alloy investigated in this study, bal. Ni.

René N5(SX)

Cr

Co

Mo

W

Ta

Re

Al

Hf

C

B

Ref.

7

7.5

1.5

5

6.5

3.0

6.2

0.15

0.05

0.00

[49,50]

Fig. 2. Low magnification (a) and high magnification (b) images of a machined specimen after shot peening.

L.H. Rettberg et al. / NDT&E International 83 (2016) 68–77

Fig. 3. Inverse pole figure map of the directional elastic modulus of CMSX-4 with respect to the primary axis of the shot peened creep specimens. The values were calculated using Eq. (3) and the elastic constants reported by Seiborger, et al. and Zambaldi, et al. for CMSX-4 [13,40]. Image courtesy of W. Lenthe of the University of California, Santa Barbara.

3.4. Resonant ultrasound spectroscopy RUS measurements were collected using an apparatus manufactured by Vibrant NDT Corporation, shown in Fig. 4 and discussed in E2534–15. The setup consists of four omni-directional piezoelectric transducers (PTs), a transceiver unit, and a software control package developed by Magnaflux. A drive PT contacting the specimen is driven by a swept sinusoidal signal from the transceiver, exciting elastic waves in the specimen at a frequency of 20–200 kHz, with a sampling step-size of 3 Hz. Two PTs record the amplitude of the specimen deflection at their points of contact. A fourth “dummy” transducer is necessary to support the specimen but does not transmit or receive. High resolution broadband scans take approximately one hour to complete, while a rapid scan taking less than a minute can be implemented once modes diagnostic of recrystallization are identified. The transducers are arranged at the corners of a 42 mm  5 mm rectangle and are tilted to a 45° angle. The output drive voltage was continuously attenuated to prevent saturation of the amplitude readings. This RUS setup has a fR measurement repeatability of 0.02–0.05% after removing and replacing the specimen, which is similar to repeatability reported in previous studies [28]. RUS scans were collected from Specimen LP and Specimen HP in the as-machined (baseline), shot peened, and shot peened þsolution heat treated conditions. fR were measured for each condition, allowing for mode-specific resonance frequency shifts ( ΔfR ) to be determined as a result of shot peening and shot peening þsolution heat treatment. Three scans were collected and averaged for each condition. After collecting RUS spectra, Specimen LP and Specimen HP were sectioned longitudinally along the [001] growth direction and prepared for metallographic examination. Electron microscopy was performed using an FEI® XL30 field emission gun

71

scanning electron microscope (SEM). Detectors attached to this microscope include: standard secondary electron (SE), dedication back scattered electron (BSE) detector, an EDAX® Si-drift EDX detector for composition analysis and electron backscatter diffraction (EBSD) detector that provides crystallographic information. A 20 keV accelerating voltage and a spot size between 4–6 were used for BSE imaging. EBSD inverse pole figure maps showing individual point orientations with respect to the creep specimen longitudinal-axis were collected from near-surface regions with scan conditions involving a sample tilt of 70°, a working distance of 12 mm, beam voltage of 20 kV, and a step size of 2 μm to determine local crystal orientation and the presence of recrystallization. 3.5. Modeling resonance using finite elements Finite element methods are particularly useful for modeling resonance in samples with complex geometries such as the mechanical test specimen detailed in Fig. 1. Using ABAQUS CAE 6.12 [29], this specimen was discretized and the governing physics and material properties applied. The virgin specimen model was comprised of approximately 200,000 linear hexahedral (C3D8R) and wedge (C3D6) elements that were imparted single crystal elastic properties [29], Table 1, and a global material orientation such that the specimen long-axis was parallel to the [001] crystallographic direction. Compared to modeling the precise direction modulus values of the shot peened specimens mentioned in Section 3.3, using the [001] stiffness values will cause a negligible variation in the modeled resonant frequency shift on the order of a few hundredths of a percent. Once the modeled specimen was fully defined, the first 50 (lowest frequency) resonance modes were determined by the ABAQUS Lanczos Eigen frequency solver. The modeling was conducted on a 64-bit desktop computer with 3.4 GHz processor and 20 GB RAM. The model output provided exaggerated depictions of the resonance mode deflection character, Fig. 5, that allowed each mode to be classified as one of four distinct mode types: longitudinal bending, torsional, extensional, or transverse bending. Along with the deflection character, the model described above outputs a list of fR that establish the baseline response of a virgin specimen before shot peening or recrystallization. At this point in the model development process it is important to assure that the FE modeled and RUS measured fR agree to within approximately 71% for each mode [30]. Modeorder and periodicity should match well enough that measured and modeled modes can be matched over a majority of the broadband, herein considered the first 50 modes. While an eventual NDE protocol would likely focus on a subset of 10–15 modes from the broadband that are found to be the most diagnostic of the resonance-affecting mechanism of interest [30].

Fig. 4. Schematic (a) and image (b) of the RUS setup developed by Vibrant and modified for inspecting creep specimens. The specimen rests upon a cradle of four piezoelectric transducers (PT). One PT is driven with a swept sinusoidal signal with increasing frequency, from 1 to 200 kHz, to excite resonance in the specimen. As the specimen resonates it generates macroscopic deflections that are measured by two receive PT that translate the sample deflections into an electrical signal back to the transceiver. The fourth PT in the cradle is a dummy employed to support the specimen.

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Fig. 6. Creep specimen model depicting the (a) finite element mesh and (b) a cross sectional view of the sample with the red region along the surface of the gauge and fillets indicating a 200 μm layer of recrystallization.

Fig. 5. Depiction of the four distinct mode types that occur within in first 50 resonances predicted by the FE model. The shape of these modes, i.e. deflection character, is visualized by depicting the deflections in a highly exaggerated manner, while the actual deflections of a sample are minuscule.

3.5.1. Modeling recrystallization Due to the significant elastic anisotropy of René N5 (A¼ 2.88), Gairola and Kröner's third-order averaging scheme [21] is used to calculate self-consistent isotropic moduli for representing polycrystalline René N5, Eqs. (4) and (6). This homogenization procedure assumes: the recrystallized material will have a random grain orientation distribution consistent with Nygårds' analysis [17] addressed in Section 2.2. Table 4 summarizes the material properties used for modeling recrystallized René N5. These properties are applied to elements along the gauge and fillet sections of the creep specimen, Fig. 6, at depths of: 80, 100, 178, 200, and 1500þ μm, the latter corresponding to full recrystallization of the 3.06 mm diameter gauge and fillet regions. The finite element mesh in the recrystallized region of the gauge section was refined to have an average element dimension of 0.250 mm parallel to the length and 0.020 mm parallel to the diameter. Larger elements were used beyond the gauge section, with an average element dimension of 0.286 mm, and a maximum of 0.415 mm for the ends of the specimen. Additionally, a cylindrical sub-volume of René N5 was modeled with both a homogeneous and a discrete-grain representation of surface recrystallization to test the validity of applying homogenized properties. If valid, the discrete grain approach illustrated by Fig. 7(a) (for simplicity modeling cube-shaped grains) should predict similar shifts in fR as the homogeneous isotropic model Table 4 Material properties utilized in FE model to represent René N5. Isotropic polycrystalline moduli are calculated from the stiffness data detailed previously [13], while the density (ρ) reported in [2] is the same for both alloys. Property

Value (units)

K EGK GGK νGK ρ

191 GPa 226 GPa 86.8 GPa 0.303 8700 kg/m3

Fig. 7. Schematic of the two modeling approaches used to validate the assumption: representing surface recrystallization with discrete randomly-oriented anisotropic grains (a) yields similar results as a homogeneous layer of isotropic properties (b) when investigating the effect of recrystallization on low-order resonances. A unique grain color scheme was used in the discrete grain model (a) display and is not based on grain orientation.

L.H. Rettberg et al. / NDT&E International 83 (2016) 68–77

depicted in Fig. 7(b), particularly for the low-order resonance modes that involve deflections distributed broadly over large volumes of the cylinder. The rationale for the assumption of an isotropic elastic layer is discussed further in Section 4.2. Both approaches model a recrystallized layer thickness that is 5% of the cylinder radius, most comparable to the 80 μm of recrystallization observed in Specimen LP. The discrete-grain model has a layer of 128 single crystal grains in a 4 by 32 grid, with the orientation of each recrystallized grain assigned from a list of Euler angles representing a random orientation distribution; the color of each grain in Fig. 7(a) was arbitrarily assigned to aid viewing. Alternatively, Fig. 7(b) demonstrates the recrystallized layer modeled as a homogeneous volume with isotropic Gairola-Kröner average moduli.

4. Results 4.1. Resonant ultrasound spectroscopy measurements Baseline RUS scans were collected of both Specimen LP and Specimen HP in the as-machined condition. The fR measurements are repeatable for the same specimen condition, while the amplitudes are variable due to the fact that the specimen is free to deflect off the transducers. Fig. 8 depicts this with four offset broadband RUS measurements for Specimen LP in the as-machined condition. Thus, only the fR are monitored with a focus on the evolution of mode-specific changes in fR ( ΔfR ), defined as:

ΔfR =

f Rdamaged − f Rvirgin f Rvirgin

*100% (8)

73

Fig. 8. Four broadband resonance scans collected from 20–200 kHz for a single René N5 creep specimen (Specimen LP) in the as-machined condition. The measured amplitudes are not repeatable with the RUS setup as configured, so amplitudes are plotted in arbitrary units with the scans offset for clarity.

Using the baseline scans and the model-informed mode type information, 10–15 reliably-measured resonance modes were typically chosen to track and compare as the specimens were shot peened and heat treated. The mode number, mode type, and fR are listed in Table 5 for the shot peened specimens investigated here. The ΔfR after low pressure shot peening was negative across all mode numbers tracked with an average shift of 0.127% 70.046%. After high pressure shot peening (double the pressure) an average shift of  0.251% 7 0.089% was measured. While transmission electron microscopy studies were beyond the scope of this study, the ΔfR follows well with established theory that imparting dislocations into the material from processes such as shot peening will decreases the apparent modulus [31–33]. Following the solution heat treatment, an order of magnitude higher average shifts of 1.835% 71.704%, and 2.380% 72.910% were measured for Specimen LP and Specimen HP, respectively.

Table 5 Resonance frequencies (kHz) of the analyzed mode numbers for the low pressure (Specimen LP) and high pressure (Specimen HP) shot peened specimens in the asmachined, shot peened and heat treated condition. The mode type (torsional (T), longitudinal bending (B) or extensional (E)) of each resonance number and percent change relative to the prior condition as also listed. The modeled percent change used the experimentally measured recrystallization depth of 80.0 μm and 177.9 μm for Specimen LP and Specimen HP, respectively. Mode Number

Mode Type

Resonance frequency (kHz) As-Machined

Low Pressure Shot Peened

% Change

Solution Heat Treated

% Change

Modeled % Change

Specimen LP 13 14 27 28 29 30 33 34 32 38 41 22 26

B B B B B B B B T T T E E

35.82 35.93 91.69 91.80 108.87 108.99 126.22 126.33 120.95 148.44 166.64 68.77 85.62

35.79 – 91.53 91.63 108.70 108.81 126.03 126.13 120.80 148.32 166.47 68.74 85.55

 0.078 –  0.177  0.190  0.158  0.164  0.154  0.159  0.128  0.083  0.097  0.045  0.092

37.012 37.121 94.466 94.582 111.726 111.878 129.730 129.894 117.721 151.168 166.082 69.483 87.324

3.325 3.326 3.026 3.025 2.619 2.647 2.778 2.818  0.589  1.801  0.332 1.036 1.985

2.84 2.84 2.44 2.44 2.15 2.15 2.63 2.63  1.87  0.75  1.33 0.81 1.91

Specimen HP 13 14 27 28 29 30 33 34 32 38 41 22 26

B B B B B B B B T T T E E

35.61 35.69 91.26 91.33 108.50 108.57 125.79 125.86 121.33 154.53 166.50 68.68 85.37

35.51 35.57 90.99 91.08 108.18 108.24 125.42 125.47 120.91 154.32 166.20 68.63 85.25

 0.272  0.329  0.310  0.279  0.294  0.301  0.299  0.311  0.346  0.135  0.178  0.072  0.137

37.342 37.429 95.171 95.262 112.454 112.564 130.698 130.819 115.826 152.138 165.404 69.588 87.824

4.870 4.887 4.268 4.301 3.642 3.684 3.900 3.939  4.539  1.547  0.656 1.320 2.874

4.80 4.80 3.82 3.82 3.88 3.88 5.37 5.37  3.70  0.76  2.28 1.57 3.98

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Fig. 9. Backscattered electron (BSE) images (top row) of specimens subject to a heat treatment following shot penning at a low (a) and high pressure (b) show the varying depth of the recrystallized surface region. Electron backscatter diffraction (EBSD) (bottom row) was used to collect inverse pole figure (IPF) maps of the same location showing the orientation at every point with respect to the long axis of the creep specimens. The orientations of over 200 recrystallized grains are plotted on an inverse pole figure (c) to illustrate the approximately random texture of the recrystallized layer. The (d) color scale for the inverse pole figure maps (a) and (b), with respect to the primary specimen axis, is also included.

Fig. 10. BSE micrograph showing the boundary and the precipitate morphology in the recrystallized grains.

Microscopy revealed that both Specimen LP and Specimen HP recrystallized following solution heat treatment (Fig. 9). This recrystallization was responsible for the measured ΔfR following heat treatment. The depth of recrystallization was 80.0 μm 715.6 μm and 177.9 μm 727.2 μm for Specimen LP and Specimen HP, respectively. A minimum of 250 measurements of the recrystallized depth were taken, with each measurement spaced ∼20 μm along the surface of each specimen. Recrystallized grains contained cubodial γ′ precipitates that nucleated and grew during controlled cooling from the full solvus temperature, as shown in Fig. 10. Furthermore, the orientations of the recrystallized grains were uniformly distributed across the stereographic triangle, Fig. 9 (c), suggesting that the surface polycrystalline layer should be elastically isotropic. 4.2. Finite element model results The results from the cylindrical sub-volume modeling study comparing the discrete anisotropic grain representation of recrystallization to a homogenized isotropic approach are detailed in Fig. 11. The fact that the ΔfR predicted by the two representations are similar for the first 50 resonance modes validates the isotropic homogenization procedure. Essentially, the two modeling

Fig. 11. Modeled ΔfR for a single-crystal cylinder with recrystallization consuming 5% of the radius using two distinct modeling approaches. The agreement between the two model results illustrates that an isotropic homogeneous layer of recrystallized material sufficiently describes the ΔfR response of even coarse aggregates of (4  32) grains, and demonstrates that the isotropic representation is sufficient.

approaches depicted in Fig. 7 simulate the same sub-volume of material using two extreme representations. Experimentally observed ΔfR behavior would likely fall between the ΔfR predicted by the relatively coarse 128 discrete grain model and the ΔfR predicted by the isotropic model. Therefore, the disagreement between of the two model results indicates the maximum error introduced by the isotropic assumption for a recrystallization depth of 5% the cylinder radius. This error is very small compared to the magnitude of the ΔfR response resulting from recrystallization, and can therefore be neglected. Of the four distinct resonance mode types predicted by the FE model of the creep specimen over the frequency range of interest, illustrated in Fig. 5, 30 of the first 50 resonance modes are longitudinal bending. Due to the nature of bending deflections, longitudinal bending modes are more sensitive to mechanisms that affect stiffness near the surface of the specimen. Plotting the modeled ΔfR due to surface recrystallization for the first 50 resonance modes shows that, as expected, the longitudinal bending modes display a positive ΔfR that increases with the depth of the recrystallized layer, indicated in Fig. 12. This result agrees well with the expectation that the recrystallized grains on the surface will be oriented such that their directionally-dependent Young's

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Fig. 12. Model predicted mode-specific ΔfR for surface recrystallization of various depths along the gauge and fillet sections. The fully recrystallized model illustrates the most extreme case, and the 200 μm line has the resonance mode shape information overlaid. Because the modeled mode order is constant regardless of recrystallized depth, resonance mode shape is only included for the 200 μm line.

modulus is greater than the virgin E[100] material that exhibits the minimum E[hkl], with the recrystallized volume increasing the local stiffness by the ratio of EGK /E[100]. Extensional resonance modes behave similar to longitudinal bending modes because their deflection character is also dominated by the E of the specimen. The modeled transverse bending modes are not affected by the layer of recrystallized material due to fact that the deflection of these modes is concentrated at the ends of the specimen, effectively sampling the modulus of virgin single-crystal material; see Figs. 5 and 6. The resonance modes identified as torsional exhibited a negative ΔfR as a function of the recrystallized depth due to the fact that GGK is less than G{100}[⊥]. There is excellent agreement between the order-corrected measured ΔfR and the modeled ΔfR across the first 50 resonance modes, illustrated in Fig. 13, with the ΔfR listed in Table 4 for the reliably-measured resonance modes. Missing experimental data points indicate frequencies where the resonance modes could not be reliably recorded due to the low amplitude displacement character of the resonance mode in relation to transducer placement, or masking by a neighboring high-amplitude mode. Fig. 14 demonstrates there is a linear relationship between ΔfR and recrystallization depth up 200 μm for bending modes (resonance numbers 13,14,27–30,33,34). The linear relationship is a result of the linear dependence of the specimen modulus on volume fraction of recrystallized material (as one would expect from a rule of mixtures average), and the effectively linear relationship between volume fraction of recrystallized material and the recrystallization depth, assuming recrystallization consumes only a small fraction of the specimen radius. Models of a fully recrystallized specimen

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Fig. 13. Order-corrected measurements of ΔfR from the high gas pressure shot peened sample plotted with FE modeled ΔfR for recrystallized layer depths of 100 and 200 μm. There is good agreement between measurements and models for a majority of modes. Breaks in the measured data indicate where resonance modes were not reliably recorded and are likely due to the low amplitude displacement character of the resonance mode in relation to transducer placement, or masking by a neighboring high-amplitude mode.

indicate that the ΔfR trend with recrystallization depth becomes logarithmic due to the specimen's circular cross section, where for each incremental increase in recrystallization depth the volume of newly recrystallized material logarithmically approaches zero.

5. Discussion 5.1. The influence of recrystallization on mechanical properties Recrystallization is an important defect to be avoided during production or rejuvenation of directionally solidified and single crystal superalloy castings. Deformation induced though numerous potential sources of thermal and mechanical stress during directional solidification and post-casting mold removal can lead to recrystallization during subsequent solution heat treatments that are required for optimization of mechanical properties. Rejuvenation procedures to extend service life, receiving renewed interest of late due to economic benefits, also involve heat treatments but after components have operated in the service environment [34,26]. Previous studies have examined static surface recrystallization in Ni-base superalloys due to damage associated with shot peening, grit blasting, and cold working [35–41]. Besides static recrystallization, dynamic recrystallization has been recently reported in René N5 during creep testing [27]. The influence of recrystallization on mechanical properties in directionally solidified and single crystal superalloys appears to depend on the alloy

Fig. 14. Plot of ΔfR versus recrystallized depth for select bending modes with both measured and modeled points indicated at 80 and 178 μm. When recrystallization consumes small fractions of the specimen radius the ΔfR appears linear with recrystallization depth as the left plot indicates, however the trend becomes logarithmic at large fractions of the specimen radius as the right plot demonstrates.

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composition and the depth of the recrystallized layer [42–46]. In general, recrystallization increases the minimum creep rate and decreases the rupture life due to the introduction of high angle grain boundaries. There is a linear relationship between the fraction of recrystallized area and decrease in creep rupture life for both directionally solidified and single crystal alloys in the limited studies performed [43–45]. Other types of misoriented grains may also develop during the solidification process, resulting in bicrystal or tri-crystal structures. These often evolve from the grain nucleation process at the initiation of solidification, where neighboring dendrites with relatively low misorientation relative to one another persist due to similar growth rates. Such defects would also be detectable by RUS. Previous research on bicrystals of Ni-base superalloys GTD444 and René N4 concluded that GTD444 specimens with only 0.09 wt% carbon and 0.009 wt% boron were able to tolerate a misorientation greater than 20° while maintaining the same creep rupture life and a creep rupture ductility over 5% [47]. René N4, with approximately half the concentration of carbon and boron as GTD444, had a decrease in creep rupture life by a factor of 2 and a creep rupture ductility less than 1.5% in specimens with a misorientation greater than 20° between the two crystals [47]. Other alloys that do not have any additions of carbon or boron are even more prone to property degradation with the presence of high angle boundaries. For example, a bicrystal of CMSX-4 with a misorientation of 7° tested at similar creep conditions to the previous study lasted for 100 h while a perfect single crystal fails at over 10,000 h [2,48]. These studies illustrate the importance of being able to reliably detect high angle defects. 5.2. Advantages of RUS for detecting recrystallization The RUS technique used in this work was able to detect the presence of recrystallized material in shot peened and subsequently heat treated laboratory scale specimens. The primary advantages of using RUS when compared to other NDE techniques are the ease of use, short scan times, objective definitions for part acceptance/rejection, full component sampling with a single measurement, and the ability to configure of the piezoelectric transducers for NDE of various component geometries. While laboratory scans for developing this NDE framework were extremely conservative and required on the order of an hour to complete, optimized scan settings can reduce collection time to less than a minute per part without sacrificing diagnostic abilities. Accurate prediction of the recrystallized depth from experimentally measured ΔfR without requiring destructive microscopic examination was demonstrated with a specimen-specific FE based fR model. This capability has the potential to help improve single crystal processing approaches and manufacturing yields. Also, because the RUS technique samples bulk properties, internal recrystallization can also be detected. However, there is a poor understanding of how much recrystallization can be tolerated in directionally solidified and single crystal components, especially with regard to the influence of alloy chemistry. Alloy specific experimental studies are needed to determine the maximum tolerable recrystallization depth and volume fraction before RUS can be fully implemented to improve manufacturing yields. In the short term, however, there is a clear opportunity for improving current component inspection protocols for parts with sub-surface recrystallization. 5.3. A RUS framework for accurately detecting recrystallization or grain defects Given the demonstrated capability for detecting grain defects it is worthwhile to outline a RUS for NDE framework for generally

applying this approach to a new alloy and/or component geometry. Starting with a new specimen geometry or new material requires an overview scan of a virgin specimen covering a large frequency range, such that upwards of 50 individual resonance peaks from the broadband are recorded. All efforts should be made to collect the lowest-frequency modes for two reasons. First, the model results in Fig. 13 clearly indicate that the lowest-frequency resonance modes exhibit the greatest sensitivity to recrystallization, which is also reported for creep damage associated with changes in specimen geometry [30]. Second, low-frequency resonances have the greatest separation between nearest-neighbors, making them far easier to identify and track as damage evolves. Broadband scans should be collected from multiple virgin specimens such that a typical baseline resonance profile can be established for a given specimen or component, as any one specimen may contain an unintentional defect or abnormality. Next is the development of a FE model, as discussed previously, that is capable of predicting the baseline response of a typical virgin specimen that has been measured. It is not necessary to perfectly match the FE model to any specific virgin sample, but mode order and periodicity should agree with an average virgin specimen such that measured and modeled modes can be matched over a majority of the 50-mode broadband. This process of matching measured and modeled resonances is important for correlating mode type information to the broadband measurements, distinguishing this NDE framework from others based on population statistics. Instances of mode order switching between measurements and models can be identified using procedures discussed in previous work [30], but ultimately only a subset of the 50 modes will be necessary for establishing a robust NDE framework, while segments of the broadband containing multiple resonances in close proximity can be avoided. It is common to find that “identical” complex geometry parts exhibit a natural variability in fR on the order of 1–2% for each individual resonance. For this reason it has been pointed out by others that NDE efforts seeking to identify damaged parts as outliers from a population of peers requires damage causing a ΔfR exceeding the natural variability of the part population. This is true for identifying defects present at the time of the first RUS measurement, e.g. a stray-grain casting defect in a turbine blade. However, this constraint is removed for efforts to identify damage such as recrystallization that arises during subsequent processing or heat treatments. Scanning individual parts before and after these heat treatments allows determination of the ΔfR resulting only from microstructural evolution during the heat treatment. The final step to developing a generalized RUS for NDE framework of recrystallization is to take the FE model that represents the virgin single crystal specimen, and impart various levels of recrystallization to the model consistent with what is observed or suspected to occur. Recrystallized regions can be defined with homogenized isotropic elastic properties calculated for polycrystalline aggregates. This model containing recrystallization can then be evaluated with an Eigen frequency solver to determine the ΔfR response as compared to the virgin specimen model [29]. fR isolated from others in the frequency regime that are both consistently measured and sensitive to recrystallization according to the FE model are the diagnostic modes useful for NDE. These diagnostic modes can be selectively measured from the broadband to significantly decrease scan time, with the magnitude of the measured ΔfR correlated to the recrystallized volume determined by FE models. This process can be established for a turbine blade just as it was established for a complex geometry creep specimen, while a component-specific trial should be conducted with concomitant destructive analysis to validate the fidelity of any new FE models.

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6. Conclusions Based on the results of detailed RUS and FE modeling, the following conclusions are made with regards to the capability of detecting grain defects in elastically anisotropic Ni-base single crystals:

 A finite element model of a superalloy specimen with a thin







layer of material with isotropic elastic properties showed good agreement with the experimentally measured frequency shifts after heat treatment, confirming that recrystallization caused the frequency shifts. Surface recrystallization can be detected nondestructively by using resonant ultrasound spectroscopy equipment similar to that utilized in this study. Shifts in resonance frequency have a linear relationship to the volume of recrystallized material for resonance frequencies with a bending mode type. Transitioning from resonant ultrasound spectroscopy on labscale specimens to production-scale components requires a coupled experimental and modeling approach to correctly attribute the dominant mechanism affecting resonance and identify diagnostic resonance modes for NDE. The mechanistic underpinning of evaluating abnormalities in grain structure with RUS relies on significant elastic anisotropy, a requirement met by Ni-base alloys.

Acknowledgements The authors would like to thank GE Power & Water, specifically Jesse Keller, Art Peck and Jon Schaeffer, for shot peening the specimens examined in this work, providing financial support, and technical guidance. The RUS measurements were collected using a setup provided by Vibrant NDT Corporation. This work was also supported by the U.S. Air Force Research Laboratory (AFRL) through Research Initiatives for Materials State Sensing (RIMSS) Contract FA8650-15-C-5208, through Universal Technology Corporation. Support of the microscopy equipment is provided by the MRSEC program of the National Science Foundation under award No. DMR 1121053.

References [1] Pollock TM, Tin S. J Propul Power 2006;22:361–74. [2] Reed RC. The superalloys: fundamentals and applications. New York: Cambridge University Press; 2006. [3] Kear B, Piearcey B. AIME Trans 1967;239:1209–15. [4] Nondestructive evaluation and quality control. ASM handbook, ASM International 17; 1989.

77

[5] Marder J, Kortovich C. Characterization of casting defects in typical castings of a directionally solidified superalloy. Technical Report, DTIC Document; 1979. [6] Migliori A, Sarrao J, Visscher WM, Bell T, Lei M, Fisk Z, Leisure R. Phys B Condens Matter 1993;183:1–24. [7] Migliori A, Sarrao J. resonant ultrasound spectroscopy: applications to physics, materials measurements, and nondestructive evaluation.New York: WileyInterscience; 1997. [8] Leisure RG, Willis FA. J Phys Condens Matter 1997;9:6001–29. [9] Heyliger P, Jilani A, Ledbetter H, Leisure RG, Wang C-L. J Acoust Soc Am 1993;94:1482–7. [10] Zadler BJ, Le Rousseau JHL, Scales JA, Smith ML. Geophys J Int 2004;156:154– 69. [11] Zener C. Phys Rev 1947;71:846–51. [12] Bower A. Applied mechanics of solids.Boca Ratton: CRC Press; 2010. [13] Siebörger D, Knake H, Glatzel U. Mater Sci Eng A 2001;298:26–33. [14] Stanke FE. J Acoust Soc Am 1984;75:665. [15] Ledbetter H. In: Wolfenden A, editor, Dynamic elastic modulus measurements in materials, ASTM STP 1045, Philadelphia; 1990. p. 135–48. [16] Musgrave MJP. Reports Prog Phys 1959;22:303. [17] Nygårds M. Mech Mater 2003;35:1049–57. [18] Hill R. Proc Phys Soc Sect A 1952;65:349–54. [19] Hashin Z, Shtrikman S. J Mech Phys Solids 1962;10:343–52. [20] Kröner E. J Mech Phys Solids 1967;15:319–29. [21] Gairola B, Kröner E. Int J Eng Sci 1981;19:865–9. [22] Kuhn HA, Sockel HG. Phys Status Solidi 1988;110:449–58. [23] Kuhn HA, Sockel HG. Mater Sci Eng A 1989;112:117–26. [24] Kuhn HA, Sockel HG. Phys Status Solidi 1990;119:93–105. [25] Elliott A, Pollock T, Tin S, King W, Huang S-C, Gigliotti M. Metall Mater Trans A 2004;35:3221–31. [26] Rettberg L, Tsunekane M, Pollock T. In: Superalloys 2012. Warrendale, PA, USA: TMS; 2012. p. 341–9. [27] Rettberg L, Pollock T. Acta Mater 2014;73:287–97. [28] Aldrin JC, Jauriqui L, Hunter L. In: Proceedings of the 39th annual review of progress in quantitative nondestructive evaluation; 2013. p. 1393–400. [29] Abaqus/CAE Version 6.12–1 User manual. Providence, RI: Dassault Systèmes Simulia Corp.; 2012. [30] Goodlet B, Torbet C, Jauriqui L, Aldrin C, Pollock T. Ultrasonics 2016 (submitted for publication). [31] Granato A, Lücke K. J Appl Phys 1956;27:583. [32] De Kock A, Crans W, Druyvesteyn M. Physica 1965;31:866–76. [33] Granato A, Hikata A, Lücke K. Acta Metall 1958;6:470–80. [34] Baldan A. J Mater Sci 1991;26:3409–21. [35] Porter A, Ralph B. J Mater Sci 1981;16:707–13. [36] Porter A, Ralph B. Mater Sci Eng 1983;59:69–78. [37] Bürgel R, Portella PD, Preuhs J. Superalloys 2000;2000:229–38. [38] Cox DC, Roebuck B, Rae C, Reed RC. Mater Sci Technol 2003;19:440–6. [39] Wang L, Xie G, Zhange J, Lou LH. Acta Mater 2006;55:457–60. [40] Zambaldi C, Roters F, Raabe D, Glatzel U. Mater Sci Eng A 2007:433–40. [41] Bond S, Martin J. J Mater Sci 1984;19:3867–72. [42] Jo C-Y, Kim H-M. Mater Sci Technol 2003;19:1671–6. [43] Xie G, Wang L, Zhang J, Lou L. Metall Mater Trans A 2008;39:206–10. [44] Meng J, Jin T, Sun X, Hu Z. Mat Sci Eng A 2010;527:6119–22. [45] Zhang B, Lu X, Liu D, Tao C. Mat Sci Eng A 2012;551:149–53. [46] Khan T, Caron P, Nakagawa Y. JOM 1986;38:16–9. [47] Stinville J, Gallup K, Pollock T. Metall Mater Trans A 2015;46:2516–29. [48] Harris K, Erickson G, Sikkenga S, Brentnall W, Aurrecoechea J, Kubarych K. Superalloys 1992;1992:297. [49] Ross EW, Wukusick CS, King WT. US Patent 5,399,313 Nickel-based superalloys for producing single crystal articles having improved tolerance to low angle grain boundaries; 1995. [50] Wukusick CS, Buchakjian L Jr., UK Patent Appl. GE2235697 improved property balanced nickel-base superalloys for producing single crystal articles - René N5; 1991.