# On the Dwell-Fatigue Crack Propagation Behavior of a High-Strength Ni-Base Superalloy Manufactured by Selective Laser Melting

- 114 Downloads

## Abstract

This study focuses on the dwell-fatigue crack propagation behavior of IN718 manufactured *via* selective laser melting (SLM). The dwell-fatigue test condition is 823 K (550 \(^{\circ }\)C) with a long 2160-s dwell-holding period. Effects of heat treatment and loading direction on dwell-fatigue crack propagation rates are studied. A grain boundary \(\delta \) precipitate seems to be slightly beneficial to the dwell-fatigue cracking resistance of SLM IN718. A comparison has been made between SLM IN718 and forged counterparts at different temperatures, indicating that a creep damage mechanism is likely dominant for SLM IN718 under the present test condition. A general discussion of the inferior creep resistance of SLM IN718 is also included. The anisotropic dwell-fatigue cracking resistance has also been studied and rationalized with the effective stress intensity factor calculated from finite element modeling.

## 1 Introduction

Selective laser melting (SLM) is one of the most widely used additive manufacturing (AM) techniques for metallic materials. The extremely rapid and localized solidification during the SLM process results in quite different as-built microstructures compared with conventional cast or hot-worked ones. For critical Ni-base superalloy engine components, SLM shows overwhelming advantages over other non-AM processes for geometric complexities.[1] The attempts to manufacture Ni-base superalloy (IN718,[2, 3, 4] IN738LC,[5,6] Hastelloy X,[7, 8, 9] CM247LC[10, 11, 12] and IN625[13, 14, 15] components) *via* SLM have attracted much attention in the AM field in the past years. Most of these studies focused on microstructural studies, process parameter optimizations and monotonic mechanical properties (tensile test and hardness). Though promising, the reliability of these SLM Ni-base superalloys under dynamic and complicated service conditions still needs to be demonstrated.

IN718 is a \(\gamma ''\) strengthened Ni-base superalloy, and it is widely used for turbine disk materials. Turbine disk materials are usually subjected to dwell-fatigue loading during real engine operation, *i.e.*, there is a dwell period at peak loading, in addition to the cyclic ramping up and down. By prolonging the dwell period and/or increasing the test temperature, the fatigue crack propagation in conventional IN718 has been largely accelerated and becomes time-dependently intergranular[16, 17, 18, 19, 20, 21, 22, 23, 24, 25] compared with the pure-cyclic fatigue condition. Two possible theories regarding environmentally assisted grain boundary attack, namely dynamic embrittlement (DE)[26] and stress-assisted grain boundary oxidation (SAGBO),[27] are suggested to explain this dwell effect, but there is still debate about which of these two theories is the actual one. On the other hand, it is also possible that creep happens during the dwell-fatigue test, depending on the relative resistance of creep and environmentally assisted grain boundary degradation for the specific microstructure under the test condition.

IN718 has been intensively studied in the AM field because of its excellent weldability. The typical SLM microstructure is very different from that of the hot-worked counterpart; please see the detailed microstructural study of SLM IN718 reported in our previous work.[3] This motivated the authors to study the dwell-fatigue cracking behaviors in the present study and demonstrate the reliability of SLM components in service conditions, which is important but has rarely been reported so far. Specific focuses will be on (1) the damage mechanism, (2) effects of heat treatments and (3) effect of anisotropy (loading parallel and perpendicular to the building direction). Comparison will also be made with the conventional counterparts reported in References 19, 24 and 28. The present study will contribute to the understanding of the dwell damage mechanism and the general inferior creep resistance of the typical SLM microstructure.

## 2 Experimental

### 2.1 Material and Heat Treatments

Nominal Chemical Composition of the Gas Atomized IN718 Powder

Element | Ni | Cr | Fe | Nb | Mo | Co | Ti | Al |
---|---|---|---|---|---|---|---|---|

Wt Pct | 50–55 | 17.0–21.0 | bal. | 4.75–5.5 | 2.8–3.3 | \(<1.0\) | 0.65–1.15 | 0.20–0.80 |

Element | Mn | Si | Cu | C | P | S | B |
---|---|---|---|---|---|---|---|

Wt Pct | \(<0.35\) | \(<0.35\) | \(<0.3\) | \(<0.08\) | \(<0.015\) | \(<0.0015\) | \(<0.006\) |

Designations of Specimens and the Corresponding Heat Treatment Details

Homogenization | Solution | Aging | |
---|---|---|---|

SA | None | 1253 K (980 °C)/1 h/WC | 993 K (720 °C)/8 h 50 K/h FC to 893 K (620 °C) 893 K (620 °C)/8 h/AC |

HA | 1353 K (1080 °C)/1 h/WC | None | |

HSA | 1353 K (1080 °C)/1 h/WC | 1253 K (980 °C)/1 h/WC |

### 2.2 Dwell Fatigue Crack Propagation Tests

Compact tension (CT) geometry was adopted in the present study to investigate the crack propagation behaviors. Two sample orientations were tested to investigate the anisotropic cracking resistance: the N-type has the machined notch normal to the building direction, while the P-type has the machined notch parallel to the building direction, as shown in Figures 1(b) and (c). These CT specimens were first pre-cracked at room temperature under the pure-fatigue condition to generate a pre-crack of about 1.5 mm in length from the electrical discharge machined (EDM) notch tip. The pure-fatigue loading was under the load ratio of \(R = P_{\min }/P_{\max } = 0.05,\) load range of \(\Updelta P = P_{\max } - P_{\min } = 2500\) N and cyclic frequency of 10 Hz.

Summary of Dwell-Fatigue Crack Propagation Tests at 823 K (550 \(^{\circ }\)C), Load Ratio \(R = 0.05,\) 2160 s Dwell Period

Heat Treatment Condition | Direction | \(\Updelta P\) (N) | \(P_{\max}\) (N) | \(P_{\min}\) (N) |
---|---|---|---|---|

SA | N type | 4500 | 4737 | 237 |

HSA | ||||

SA | P type | 3000 | 3157 | 157 |

HA | ||||

HSA |

### 2.3 Microscopy Analysis

The tested specimens were first cut into two halves along the planes perpendicular to the crack surface: one half was then forced open by a tensile load to reveal the dwell-fatigue crack surface, and the other half was polished to reveal the crack cross section. The crack cross sections were mechanically ground successively from 500 to 4000 grit and polished with a diamond suspension from 3 to 1/4 \(\mu \)m and finally with Struers OP-U colloidal silica suspension. A Hitachi SU70 FEG scanning electron microscope, equipped with energy-dispersive X-ray spectroscopy and an electron backscatter diffraction (EBSD) system from Oxford Instruments, was employed to detail the microstructural features. Texture and grain misorientation measurements were performed with a scanning step size of 1 \(\mu \)m and analyzed with HKL Channel 5 software.

### 2.4 Finite Element Modeling

*i.e.*, for cracks deviating from the pre-cracking plane), the stress intensity factor was calculated using the Abaqus 6.12 commercial finite element code. The CT specimen was modeled in 2D plane strain using six-node quadratic elements. Around the crack tip, several measures were taken to more accurately capture the stress singularity: (1) the mesh was refined, (2) collapsed node elements were used, and (3) the location of the midside nodes was shifted toward the crack tip. Loads were applied as pressure on the half of the pin hole in contact with the pin during loading. The specimen was constrained vertically at the symmetry line and horizontally at the pin holes. Figure 3 shows the mesh and illustrates the applied boundary condition. The stress intensity factors in modes I and II, \(K_{\text {I}}\) and \(K_{\text {II}},\) were calculated using elastic constants of \(E = 210\) GPa and \(\nu = 0.3\) and by using Abaqus’ built-in interaction integral method. The stress intensity factors were calculated along a pre-defined crack path chosen to correspond to experimental observations.

## 3 Results

### 3.1 Crack Path and Fracture Morphology

Comparisons of the crack paths and fracture surface morphologies have been made on different heat-treated conditions of both P- and N-type specimens. However, the general dwell crack propagation direction and fracture surface feature depend more on specimen orientation than heat treatment condition. For brevity, crack paths and fracture surfaces are only compared between the P- and N-type orientations, but not between different heat treatment conditions.

The crack path of a P-type specimen is shown in Figure 4(a). The dwell crack generally propagates on the same plane as the pre-crack (in-plane cracking), and the propagation direction is perpendicular to the loading direction and parallel to the building direction. The P-type fracture surface (see Figure 4(b)) shows that, as the dwell crack propagates, the fracture mode changes gradually from intergranular to transgranular, accompanied by the fracture surface color changing from green-blue to dark blue and finally to dark brown.

### 3.2 Validity of Crack Length Measurement and Correlation with \(\Updelta K\)

It is worth briefly discussing the validity of crack length measurement/correction and \(\Updelta K\) in both the P- and N-type cases before the crack growth rate data are presented.

For P-type specimens, the fracture is under the typical mode I as the dwell crack plane is perpendicular to the loading direction, and the crack length monitored by DCPD during testing can be simply corrected with fracture surface measurements after the test. However, for N-type specimens, such a large deviation angle from the pre-crack plane invalidates the pure mode I fracture per ASTM E647. In addition, DCPD might not even be able to roughly monitor the out-of-plane crack growth during testing per ASTM E647, especially when two dwell cracks propagate simultaneously. Therefore, for these N-type cases, calculation of the stress intensity factor range \(\Updelta K\) with the DCPD data is less reliable.

Instead of accurately quantifying the crack growth rate \({\text {d}}a/{\text {d}}N\) as a function of the stress intensity factor range \(\Updelta K\) for the N-type specimens, it would be more interesting to show the anisotropic dwell cracking resistance, if any, between N- and P-type orientations.

The dwell fatigue test on the SA N-type specimen was started with a \(\Updelta P\) of 3000 N, exactly as for P-type specimens. However, it did not result in noticeable crack growth even after about a week of test time. Increasing the load range to \(\Updelta P\) to 3500 N and further to 4000 N still did not really propagate the crack. Crack growth was not noticeable until the \(\Updelta P\) was increased to 4500 N. Although these 0 mm/cycle data were not shown here for brevity, they do suggest that the N-type orientation has better dwell cracking resistance than the P-type orientation at a similar \(\Updelta K.\)

### 3.3 Crack Growth Rate

*vs*the stress intensity factor range \(\Updelta K\) in Figure 6 for both N- and P-type specimens of different heat-treated conditions. The P-type crack growth rate is calculated per ASTM E647 and is reliable. For the N-type specimens, due to the aforementioned invalidities per ASTM E647, no quantitative crack growth rate data are achieved in the present study; instead, the present authors would simply adapt the crack length measured from DCPD and apply the Mode I configuration to calculate the crack growth rate. Such a simplification is, at least, able to indicate the reliable anisotropic dwell cracking resistance between N- and P-type specimens.

As shown in Figure 6, the N-type orientation has noticeably better cracking resistance than the P-type orientation. Among the heat treatments of P-type specimens, it shows that the HA treatment (without grain boundary \(\delta \)) gives a faster crack propagation rate than the SA and HSA treatments (with grain boundary \(\delta \)). The SA and HSA conditions show very similar cracking resistance.

## 4 Discussion

### 4.1 Damage Mechanism: Creep or Environmentally Assisted Grain Boundary Attack?

- (1)
Discontinuous and almost perpendicular to the loading direction.

- (2)
Not branched or originating from the main crack.

- (3)
Associated with high-angle (\(>15\) degrees, confirmed with EBSD) grain boundaries.

- (4)
Associated with plastic deformation as evident from the backscatter contrast.

*via*lattice diffusion seems less likely considering the relatively low test temperature of 823 K (550 \(^{\circ }\)C). Furthermore, some random grain boundaries are crossed during this long-range transportation but are not cracked, which might also violate the DE or SAGBO mechanism. With this in mind, environmentally assisted grain boundary attack is not believed to be the principle damage mechanism.

*vs*

*K*(or \(K_{\max }\)) behaviors with the conventionally manufactured counterparts that are tested under the creep (sustained loading) crack growth condition at different temperatures. The comparison shown in Figure 8 is made on a forged IN718 (from Reference 19), an alloy 718 (from Reference 28) and HA P-type specimen in the present study. The \({\text {d}}a/{\text {d}}t\)

*vs*

*K*(or \(K_{\max }\)) relationships can be established by a Paris’ law type equation for all cases shown:

*A*is a temperature- and microstructure-dependent term, and the stress intensity exponent

*m*is similar but not identical to the power-law creep stress exponent.[30] Interestingly, for the forged IN718 counterpart, the exponent

*m*is almost identical at temperatures of 823 K, 873 K and 923 K (550 \(^{\circ }\)C, 600 \(^{\circ }\)C and 650 \(^{\circ }\)C, respectively), which might indicate that the time-dependent crack propagation mechanism is identical in these three cases. Metallographic cross sections of the aforementioned forged IN718 specimens are not available for detailed damage examination in the present study. However, a rough speculation can be made by comparing the crack paths from long dwell-time tests reported in [24,31] for the same batch of forged IN718 as in Figure 8: environmentally assisted grain boundary attack, instead of creep damage, is the dominant damage mechanism under 2160 seconds dwell condition at both 823 K and 923 K (550 \(^{\circ }\)C and 650 \(^{\circ }\)C) for the forged counterpart.

Actually, this indicates that mechanically sustained load alone does not necessarily result in creep damage, since temperature and microstructure (intrinsic creep/deformation and oxidation resistances) are also important factors affecting whether creep damage occurs. Generally, for IN718, at the temperature of 1033 K (760 \(^{\circ }\)C) creep surely happens. Reference 32 suggests that for standard aged IN718 with an average grain size of 150 \(\mu \)m, the onset of tertiary creep occurs rather early at 1033 K (760 \(^{\circ }\)C), during which regime creep strain/damage dramatically accumulates with time. The creep crack growth at 1033 K (760 \(^{\circ }\)C) reported by Sadananda and Shahinian[28] shows that the time-dependent crack growth rate significantly increases with *K*, as shown in Figure 8 with a stress intensity exponent *m* of 8.45. Therefore, such a high value of the stress intensity exponent *m* possibly indicates that creep, specifically tertiary creep, is responsible for the time-dependent cracking behavior in Sadananda’s case. Similarly, it is quite convincing that creep (specifically in the tertiary creep regime) is the dominant cracking mechanism for the SLM HA P-type case in the present study, which has an even larger *m* of 12.18. To the best of our knowledge, creep tests on SLM IN718 reported in the literature have been conducted at 903 K (630 \(^{\circ }\)C)[33] and 923 K (650 \(^{\circ }\)C).[34,35] Specifically, in Reference 35, under 923 K (650 \(^{\circ }\)C)/550 MPa, the creep properties of SLM IN718 are noticeably inferior to the cast&wrought (C&W) counterpart: the steady creep regime is almost absent, and the onset of tertiary creep occurs quite early for both the as-built and heat-treated conditions. The early onset of tertiary creep[35] is believed to be consistent with the relatively fast crack growth rate in the present SLM cases, which is associated with the high-stress intensity exponent *m* in Figure 8.

### 4.2 Effects of Grain Boundary \(\delta \) and Grain Boundary Sliding

Another proof of creep damage, instead of environmentally assisted grain boundary attack, can be presented by the effects of grain boundary \(\delta \) on the crack propagation rate. If environmentally assisted grain boundary attack was the case, the crack propagation rate of the HA condition without grain boundary \(\delta \) would be the lowest among these three conditions, since the grain boundary \(\delta \) has been reported as susceptible to forming brittle \({\hbox {Nb}}_{2} {\hbox {O}}_{5}\)[36,37] and accelerates oxygen-related crack propagation. However, as shown in Figure 6, grain boundary \(\delta \) slightly reduces the crack propagation rate, and the HA P-type condition without grain boundary \(\delta \) has the highest crack propagation rate.

### 4.3 Creep at 823 K (550 \(^{\circ }\)C)? A General Discussion on Inferior Creep Resistance of SLM IN718

Creep was discussed in the previous subsections as the dwell-fatigue cracking mechanism for the SLM specimens in the present study. However, one question might arise: is the test temperature of 823 K (550 \(^{\circ }\)C) too low for creep to happen?

The creep mechanisms of C&W IN718 have been systematically studied, with emphasis on the steady-state creep at over 873 K (600 \(^{\circ }\)C), in References 38, 39, 40 and 41. However, limited creep data are available for SLM materials, and their creep mechanisms are not well understood compared with the conventional counterparts. Kuo *et al*.[42] suggested that the high dislocation density and subgrain boundaries prohibit dislocation motions and cause stress concentrations in the SLM IN718 materials, which lead to inferior creep resistance. This sounds plausible in the first place, but becomes questionable if considering a ‘work-hardening’ effect of the aforementioned high dislocation density and subgrain boundaries on the primary creep rate. Reference 34 clearly shows that SLM IN718 has an at least four orders of magnitude higher primary creep rate than the C&W counterpart. This indicates that the high dislocation density and subgrain boundary do not actually ‘work-harden’ the SLM material or provide better creep resistance from the very beginning.

*G*is the shear modulus,

*b*is the Burgers vector,

*k*is the Boltzmann constant,

*T*is temperature in K,

*R*is the gas constant, \(\sigma _{\text {a}}\) is the applied stress, \(\sigma _{0}\) is the back stress inhibiting dislocation movement, \(Q_{\text {e}}\) is the effective activation energy, and \(n_{\text {e}}\) is the effective stress exponent. The main creep parameters of SLM and C&W IN718 are listed in Table IV. As seen, the minimum creep rate of SLM is at least three orders of magnitude higher than that of the C&W counterpart. The back stress \(\sigma _{0},\) effective stress component \(n_{\text {e}}\) and effective activation energy \(Q_{\text {e}}\) for the C&W counterpart are adapted from Reference 41, while they remain unknown for the SLM material.

| \(\dot{\varepsilon _{\text {ss}}}\) (\({\hbox {s}}^{-1}\))* | \(\sigma _{\text {a}}\) (MPa)* | \(\sigma _{0}\) (MPa) | \(n_{\text {e}}\) | \(Q_{\text {e}}\) (kJ/mol) | |
---|---|---|---|---|---|---|

SLM | 923 | \(\sim 10^{-7}\) | 550 | ? | ? | ? |

C&W | \(\sim 10^{-10}\) | 510** | \(\sim 1.2\)** | \(\sim 250\)** |

Effective activation energy \(Q_{\text {e}}\) should be about 197 kJ/mol, which is much less than the creep activation energy of 265 to 295 for pure Ni and Ni-Cr alloys quoted in Reference 43 and might be unreasonable.

The back stress \(\sigma _{0}\) and effective stress component \(n_{\text {e}}\): mathematically, for instance, with a slightly smaller back stress \(\sigma _{0}\) of 480 MPa and a slightly lower stress exponent \(n_{\text {e}}\) of 1.1, would give such a two to three orders of magnitude higher minimum creep rate.

The grain boundary diffusivity \(D_{\text {gb}}\) contribution in the material constant \(A^{*}\) should also be three orders of magnitude higher than that of the C&W counterpart, which might be less likely to have random high-angle grain boundaries at the same temperature.

*et al*.[34,35] Here, we construct recrystallization fraction maps on a forged IN718 and SLM HA specimen, of which the forged IN718 is the same batch as in Gustafsson and Lundström[19] and is in as-received heat-treated condition, and the SLM HA is the one studied in the present study and is in as-heat-treated condition. As shown in Figure 10, the forged counterpart has a 69.79 pct recrystallization fraction, which is much higher than the 3.02 pct of the SLM HA condition. Surprisingly, about 25.51 pct of the microstructure in the SLM HA condition is indexed as deformed. The 71.47 pct substructured fraction in Figure 10 is consistent with the very typical cell/subgrain microstructure in the as-built, short-time or low-temperature heat-treated SLM microstructure. Generally, the lower fraction of recrystallization indicates a less perfect or less well-annealed material and possibly a greater degradation or deformation of the microstructure. The comparison in Figure 10 clearly suggests that the SLM IN718 after the conventional heat treatment routine is in a degraded or deformed condition, even though it has not physically been through any mechanical deformation process.

This degradation speculation is tenable, and it is consistent with the early onset of tertiary creep observed in Reference 34. The microstructural degradation possibly resulted from the rapid solidification during the SLM process. From the point of view of rapid solidification, welding is similar to the SLM process. The stress rupture properties of welded IN718 compared with the base/parent IN718 also show inferiority and early onset of tertiary creep.[44, 45, 46] If this is the case, creep damage at 823 K (550 \(^{\circ }\)C) during the present dwell-fatigue tests might become possible, because creeping a largely pre-deformed specimen can be much easier. The detailed creep mechanism for the SLM material is still open to further investigation with more experimental data.

### 4.4 Effects of Notch Orientation

In the present FEA modeling, the kinked dwell crack is simplified as inclining at a constant angle, while in reality the kinked dwell crack might branch and zag, depending on how the cracked grain boundary aligns at the crack tip. This means in real cases it might be very difficult to predict the local stress intensity factors as the crack tip propagates. The lower effective stress intensity factor is caused by the large deviation of the dwell crack from the pre-crack plane, which is believed to be the main reason for the better dwell cracking resistance of the N- than P-type specimens.

## 5 Conclusions

The main damage mechanism during the dwell-fatigue crack propagation of SLM IN718 at 823 K (550 \(^{\circ }\)C) is creep, while at the same temperature it is the environmentally assisted grain boundary attack for forged IN718. Therefore, SLM IN718 shows inferior dwell-fatigue cracking resistance to the forged counterpart.

Grain boundary \(\delta \) inhibits grain boundary sliding and reduces the crack propagation rate in the intergranular fracture regime.

In the N-type specimens the columnar grain boundaries mostly deviate at a small angle or even parallel to the loading direction, resulting in a lower effective stress intensity for this kinked crack path. The cracking mechanism is the same in N- and P-type specimens for the same heat-treated condition.

## Notes

### Acknowledgments

Open access funding provided by Linköping University. This research was sponsored by Siemens AG in Berlin, Germany, who provided selective laser-melted IN718 for this research. Faculty grant SFO-MAT-LiU#2009-00971 at Linköping University, the Chinese Scholarship Council, Agora Materiae and Swedish Governmental Agency for Innovation Systems (Vinnova grant 2016-05175) are also acknowledged for their financial support.

## References

- 1.Gasser, A., G. Backes, I. Kelbassa, A. Weisheit, and K. Wissenbach:
*Laser Tech. J*., 2010, vol. 7, pp. 58–63.CrossRefGoogle Scholar - 2.Chlebus, E., K. Gruber, B. Kuźnicka, J. Kurzac, and T. Kurzynowski:
*Mater. Sci. Eng. A*, 2015, vol. 639, pp. 647–55.CrossRefGoogle Scholar - 3.Deng, D., R.L. Peng, H. Brodin, and J. Moverare:
*Mater. Sci. Eng. A*, 2018, vol. 713, pp. 294–306.CrossRefGoogle Scholar - 4.Trosch, T., J. Strößner, R. Völkl, and U. Glatzel:
*Mater. Lett*., 2016, vol. 164, pp. 428–31.CrossRefGoogle Scholar - 5.Rickenbacher, L., T. Etter, S. Hövel, and K. Wegener:
*Rapid Prototyp. J*., 2013, vol. 19, pp. 282–90.CrossRefGoogle Scholar - 6.Xu, J., H. Gruber, D. Deng, R.L. Peng, and J.J. Moverare:
*Acta Mater*., 2019, vol. 179, pp. 142–57.CrossRefGoogle Scholar - 7.Montero-Sistiaga, M.L., S. Pourbabak, J. Van Humbeeck, D. Schryvers, and K. Vanmeensel:
*Mater. Des*., 2019, vol. 165, p. 107598.CrossRefGoogle Scholar - 8.Tomus, D., Y. Tian, P.A. Rometsch, M. Heilmaier, and X. Wu:
*Mater. Sci. Eng. A*, 2016, vol. 667, pp. 42–53.CrossRefGoogle Scholar - 9.Tomus, D., P.A. Rometsch, M. Heilmaier, and X. Wu:
*Addit. Manuf*., 2017, vol. 16, pp. 65–72.CrossRefGoogle Scholar - 10.Carter, L.N., C. Martin, P.J. Withers, and M.M. Attallah:
*J. Alloys Compd*., 2014, vol. 615, pp. 338–47.CrossRefGoogle Scholar - 11.Messé, O., R. Muñoz-Moreno, T. Illston, S. Baker, and H. Stone:
*Addit. Manuf*., 2018, vol. 22, pp. 394–404.CrossRefGoogle Scholar - 12.Wang, X., L.N. Carter, B. Pang, M.M. Attallah, and M.H. Loretto:
*Acta Mater*., 2017, vol. 128, pp. 87–95.CrossRefGoogle Scholar - 13.Koutiri, I., E. Pessard, P. Peyre, O. Amlou, and T. De Terris:
*J. Mater. Process. Technol*., 2018, vol. 255, pp. 536–46.CrossRefGoogle Scholar - 14.Leary, M., M. Mazur, H. Williams, E. Yang, A. Alghamdi, B. Lozanovski, X. Zhang, D. Shidid, L. Farahbod-Sternahl, G. Witt, et al.:
*Mater. Des*., 2018, vol. 157, pp. 179–99.CrossRefGoogle Scholar - 15.Li, H., J. Sun, M. Hardy, H. Evans, S. Williams, T. Doel, and P. Bowen:
*Acta Mater*., 2015, vol. 90, pp. 355–69.CrossRefGoogle Scholar - 16.Andersson, H., C. Persson, and T. Hansson:
*Int. J. Fatigue*, 2001, vol. 23, pp. 817–27.CrossRefGoogle Scholar - 17.Antunes, F., J. Ferreira, and C. Branco:
*Mater. High Temp*., 2000, vol. 17, pp. 439–48.CrossRefGoogle Scholar - 18.Bache, M., W. Evans, and M. Hardy:
*Int. J. Fatigue*, 1999, vol. 21, pp. S69–77.CrossRefGoogle Scholar - 19.Gustafsson, D. and E. Lundström:
*Int. J. Fatigue*, 2013, vol. 48, pp. 178–86.CrossRefGoogle Scholar - 20.Gustafsson, D., J. Moverare, S. Johansson, K. Simonsson, M. Hörnqvist, T. Månsson, and S. Sjöström:
*Int. J. Fatigue*, 2011, vol. 33, pp. 1461–69.CrossRefGoogle Scholar - 21.Gustafsson, D., E. Lundström, and K. Simonsson:
*Int. J. Fatigue*, 2013, vol. 52, pp. 124–30.CrossRefGoogle Scholar - 22.Osinkolu, G., G. Onofrio, and M. Marchionni:
*Mater. Sci. Eng. A*, 2003, vol. 356, pp. 425–33.CrossRefGoogle Scholar - 23.Pedron, J.P. and A. Pineau:
*Mater. Sci. Eng*., 1982, vol. 56, pp. 143–56.CrossRefGoogle Scholar - 24.Saarimäki, J., J. Moverare, R. Eriksson, and S. Johansson:
*Mater. Sci. Eng. A*, 2014, vol. 612, pp. 398–405.CrossRefGoogle Scholar - 25.Saarimäki, J., M.H. Colliander, and J.J. Moverare:
*Mater. Sci. Eng. A*, 2017, vol. 692, pp. 174–81.CrossRefGoogle Scholar - 26.Krupp, U. and C. McMahon Jr.:
*J. Alloys Compd*., 2004, vol. 378, pp. 79–84.CrossRefGoogle Scholar - 27.Bricknell, R. and D. Woodford:
*Metall. Trans. A*, 1981, vol. 12, pp. 1673–80.CrossRefGoogle Scholar - 28.Sadananda, K. and P. Shahinian:
*Metall. Trans. A*, 1977, vol. 8, pp. 439–49.CrossRefGoogle Scholar - 29.Johnson, H.:
*Mater. Res. Stand*., 1965, vol. 5, pp. 442–45.Google Scholar - 30.Xu, S., X.J. Wu, A. Koul, and J. Dickson:
*Metall. Mater. Trans. A*, 1999, vol. 30A, pp. 1039–45.CrossRefGoogle Scholar - 31.Gustafsson, D., J. Moverare, S. Johansson, M. Hörnqvist, K. Simonsson, S. Sjöström, and B. Sharifimajda:
*Procedia Eng*., 2010, vol. 2, pp. 1095–1104.CrossRefGoogle Scholar - 32.Hayes, R.:
*Superalloys 718, 625 and Various Derivatives*, TMS, 1991, pp. 549–62.Google Scholar - 33.Pröbstle, M., S. Neumeier, J. Hopfenmüller, L. Freund, T. Niendorf, D. Schwarze, and M. Göken:
*Mater. Sci. Eng. A*, 2016, vol. 674, pp. 299–307.CrossRefGoogle Scholar - 34.Kuo, Y.L., A. Kamigaichi, and K. Kakehi:
*Metall. Mater. Trans. A*, 2018a, vol. 49A, pp. 3831–37.CrossRefGoogle Scholar - 35.Kuo, Y.L., T. Nagahari, and K. Kakehi:
*Materials*, 2018b, vol. 11, p. 996.CrossRefGoogle Scholar - 36.Hayes, R.:
*Metall. Mater. Trans. A*, 2008, vol. 39A, pp. 2596–2606.CrossRefGoogle Scholar - 37.Miller, C.F., G.W. Simmons, and R.P. Wei:
*Scripta Mater*., 2000, vol. 42, pp. 227–32.CrossRefGoogle Scholar - 38.Boehlert, C., D. Dickmann, and N.N. Eisinger:
*Metall. Mater. Trans. A*, 2006, vol. 37A, pp. 27–40.CrossRefGoogle Scholar - 39.M. Chaturvedi and Y. Han: https://doi.org/10.7449/1989/Superalloys_1989_489_498, 1989.
- 40.Chen, W. and M. Chaturvedi:
*Acta mater*., 1997, vol. 45, pp. 2735–46.CrossRefGoogle Scholar - 41.Han, Y. and M. Chaturvedi:
*Mater. Sci. Eng*., 1987, vol. 89, pp. 25–33.CrossRefGoogle Scholar - 42.Kuo, Y.L., S. Horikawa, and K. Kakehi:
*Scripta Mater*., 2017, vol. 129, pp. 74–78.CrossRefGoogle Scholar - 43.Chen, W. and M. Chaturvedi:
*Mater. Sci. Eng. A*, 1994, vol. 183, pp. 81–89.CrossRefGoogle Scholar - 44.Hyde, T., A. Becker, Y. Song, and W. Sun:
*Comput. Mater. Sci*., 2006, vol. 35, pp. 35–41.CrossRefGoogle Scholar - 45.Radhakrishna, C. and K.P. Rao:
*Mater. High Temp*., 1994, vol. 12, pp. 323–27.CrossRefGoogle Scholar - 46.Reddy, G.M., C. Murthy, N. Viswanathan, and K.P. Rao:
*Sci. Technol. Weld. Join*., 2007, vol. 12, pp. 106–14.CrossRefGoogle Scholar

## Copyright information

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.