Age-hardening Behavior in γ′-phase Precipitation-hardening Ni-based Superalloy

Abstract

Dislocations are often introduced in Ni-based superalloys to impart sufficient strength at both room temperature and high temperatures prior to their use in automobile exhaust gaskets. However, the interaction between the representative γ′ (Ni₃(Al, Ti))-phase precipitates and dislocations in high temperature remains unclear. Therefore, this study examined the effect of cold rolling on age-hardening behavior and microstructure evolution, focusing on the formation of γ′-phase Ni₃Ti during aging at 700°C for up to 400 h after 60% cold rolling of solution-treated specimens. During the early stage of aging, at 0.03 h, the hardness rapidly increased from 401 HV to 496 HV. Age-hardening continued until 3 h and reached its peak of 536 HV, followed by gradual decrease with aging time. 3D atom probe investigation revealed that the γ′-phase was confirmed after 0.3 h of aging. However, the composition-modulated structure speculated to be caused by spinodal decomposition was observed in the 0.03 h aged specimen. The change in strength with aging time was considered by calculating the contribution of each strengthening mechanism. In the initial stage of aging (0–3 h), dislocation and solid-solution strengthening dominated along with spinodal strengthening. Strengthening by spinodal decomposition in the 0.03 h aged specimen is presumptively accelerated by the introduced dislocations, which is followed by further precipitation strengthening caused by γ′-phase precipitates. In the later stage of aging (3–400 h), precipitation strengthening became dominant and reached its peak at 20 h aging, while dislocation strengthening decreased with aging time.

1. Introduction

There are many components in automobiles powered by petrol engines that require a heat resistant ability, such as high temperature strength. In particular, components used in exhaust systems are exposed to a thermally harsh environment in which materials used in components experience repeated thermal expansion and contraction, which cause a leakage of exhaust gases from the chasm of the joint. Therefore, gaskets are used in joints of exhaust components to prevent leakages.¹⁾ Materials that utilize solid solution or precipitation strengthening, such as heat-resistant stainless steels and Ni-based alloys, are often used for gaskets exposed to severely high temperatures.^2,3) However, when strength is required at not only high temperatures but also at room temperature, dislocation strengthening is often also utilized.^1,4,5)

Many assume that there are few contributions from dislocations to strength because dislocations are reduced by the progress of recovery and recrystallization at elevated temperatures.⁶⁾ Dislocations may also cause a rapid decrease in strength at high temperatures due to accelerated atomic diffusion, which leads to coarsening precipitates.

Conversely, Saito and Komai⁷⁾ studied the effect of prestrain in a creep rupture test of austenitic heat resistant steel and reported that creep life was improved by the prestrain. Prestrain caused strengthening phases such as M₂₃C₆ precipitate on grain boundaries and dislocations in grains, which more uniformly distributed the precipitates. The results showed that dislocations may play an important role in strengthening heat resistant metallic materials that utilize precipitation strengthening.

Ni-based heat resistant superalloys often apply the γ′-phase (Ni₃Al, L1₂ crystal structure) as the strengthening phase at high temperatures.²⁾ There are few studies into the effect of dislocations on γ′ precipitation because dislocations are considered to have little influence on γ′ precipitation for high interfacial coherence between the matrix and γ′ which makes the boundary energy low.

However, there are some studies that show that spinodal decomposition occurs as a preliminary step in the formation of γ′ in an alloy with a high Ti/Al composition ratio in which γ′ has an Ni₃Ti composition.^2,8,9,10) There are also several research on the effect of dislocations on the spinodal modulated structure that take the phase field approach into account,^11,12,13) some of these report that the stress field around dislocations accelerates spinodal decomposition.¹³⁾ Thus, dislocations in the alloy in which spinodal decomposition occurs prior to the precipitation of γ′ accelerate the formation of the modulated structure, which may have some effect to the subsequent precipitation behavior and mechanical properties. Incidentally, such spinodal decomposition does not occur prior to the formation of γ′ in the Ni–Al binary alloy¹⁴⁾ and has only been confirmed in the Ni–Ti alloy.^8,9,10)

From the above, the objective of this study is to investigate the precipitation behavior of γ′ during heat treatment in an Ni-based alloy in which γ′ with a near Ni₃Ti composition precipitates introduced dislocations by cold working. That is, the age hardening behavior of the Ni-based alloy introduced dislocations by cold rolling, composition modulated structure as a preliminary step to the formation of γ′, and the precipitation behavior of γ′ are carefully investigated. Additionally, from the investigated data, we measure the contribution of each strengthening mechanism to the age hardening behavior of the dislocation introduced Ni-based superalloy and considered its strengthening mechanism.

2. Experimental Procedure

Table 1 shows the chemical composition of the alloy used in this study. The alloy contains 4 mass% of Ti to precipitate γ′ contained Ti instead of Al.

Table 1. Chemical composition of the Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy (mass%).

C	Mn	Cr	Fe	Mo	Ti	Al	Nb	Ni
0.04	0.21	15.0	36.9	1.2	4.0	0.05	2.1	Bal.

The alloy was smelted in a vacuum induction melting furnace and formed into an ingot. This ingot was heated to 1080°C, which is higher than the solution temperature of γ′, formed into a 5.0 mm thick alloy plate by hot forging and rolling, and subsequently water quenched to room temperature. The plate was annealed at 1080°C and pickled. Then, cold rolling and intermediate annealing at 1080°C were repeated to obtain an alloy sheet with a thickness of 0.2 mm. The temperature just before finish rolling was 1080°C and the reduction rate in the finish rolling was 60%.

To investigate the age hardening behavior of the alloy sheet, aging heat treatment was carried out at 700°C for up to 400 h with a heating rate of 6.8°C/s and then air cooled to room temperature. These specimens including the specimen as cold rolled were measured its Vickers hardness at room temperature and observed its microstructure on the transverse direction (TD) surface which is perpendicular to the sheet width direction. The hardness was measured using five indentations with a load of 4.9 N (0.5 kgf). The microstructures of the specimens were observed using optical microscopy and transmission electron microscopy (TEM). Additionally, the three-dimensional atomic distribution of each specimen was investigated using a three-dimensional atom probe (3DAP) method with a resolution of less than 0.5 nm for detailed observations of γ′ precipitation behavior.

The property diagram of the alloy obtained using thermodynamic calculation (Thermo-Calc ver. 2019a, Database: Ni8)^15,16) is shown in Fig. 1. According to the diagram, γ′ will be solutionized by solution heat treatment at 1080°C. Additionally, the diagram also suggests that the precipitate phases are mainly γ′ and a small amount of the σ-phase (FeCr) in the equilibrium state at 700°C. The composition of γ′ obtained by the calculation consisted mainly of 70 mass% Ni and 16 mass% Ti. A small amount of Nb of about 7 mass% was also considered to be dissolved.

Fig. 1.

Calculated property diagram showing the variation of volume fraction of each phase in the Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy. (Software: Thermo-Calc ver. 2019a, Database: Ni8).^15,16)

3. Results

3.1. Age Hardening Behavior

Figure 2 shows the age hardening behavior of the cold rolled alloy sheet after 60% reduction at 700°C. The specimen after cold rolling (shown by as CR in the figure) has a much higher hardness (401 HV) than the alloy before cold rolling (174 HV) due to dislocation hardening. The cold rolled specimen also shows rapid hardening from 401 HV to 496 HV after aging at 700°C for 0.03 h (108 s). The hardness of the specimen reaches its peak of 536 HV after 3 h aging. Subsequently, the hardness begins to decrease as aging progress, and reaches 437 HV after 400 h aging. However, this hardness value is higher than that of the specimen before cold rolling and that as cold rolled.

Fig. 2.

Change in Vickers hardness with aging time at 700°C of the Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy after cold rolling by 60%.

3.2. Microstructure Observation (Optical Microscopy, TEM)

Figure 3 shows optical micrographs on the TD surfaces of the 60% cold rolled specimen and specimens subsequently aged at 700°C. Crystal grains of the austenite matrix in the as cold rolled sample, shown in Fig. 3(a), have a compressed shape due to the cold rolling. Recrystallization grains are not observed and the grain size and shape do not change in the aged specimens as shown in Figs. 3(b) to 3(e). However, the optical micrograph of the 400 h aged specimen shown in Fig. 3(f) has a different contrast compared to other specimens and a mottled pattern can be seen over the entire surface.

Fig. 3.

Optical micrographs from transverse direction of Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy: a) 60% cold rolled specimen, b) to f) subsequently aged specimens at 700°C for up to 400 h.

In the optical micrograph of the cold rolled sample, there is nothing to be visible except for grain boundaries and a nonuniform deformation structure in each grain. On the other hand, there are some clear black etched sections, which appeared to correspond to a nonuniform deformation structure such as grain boundaries and intragranular slip lines in the optical micrograph of the aged specimens at 700°C as indicated by white arrows on Figs. 3(b) to 3(e). It is possible that some factor included coarse precipitates other than γ′ such as σ on the grain boundaries and dislocations that affected the etching process, however, the mechanism is unclear. Regardless, an intragranular nonuniform deformation structure is clearly observed in specimens aged up to 20 h, which suggested a certain amount of dislocations in the crystal grains until 20 h of aging. Incidentally, a mottled pattern is observed over the entire surface of the specimen aged for 400 h, and it is possible that this mottling reflects the recrystallized structure with densely packed, fine precipitates.

Next, TEM observations of the thin film samples made from specimens aged at 700°C for 1 h and 400 h were taken place in order to investigate the precipitation of γ′ and the presence of dislocations.

Figure 4(a) shows the TEM bright field image in low magnification on the specimen aged at 700°C for 1 h. The dense dislocation structure still remains after 1 h aging. No distinct pattern of γ′ precipitate is observed in the area, as shown in the high magnification images in Figs. 4(b) and 4(c). Figure 5(a) shows the enlarged TEM bright field image of the inside of a grain in the specimen aged at 700°C for 400 h. A selected area electron diffraction pattern that indicates the existence of γ′ appeared in two areas indicated by white circles in Fig. 5(a) as showed in Fig. 5(b). However, comparing these two areas in the bright field image, a linear pattern of the shading is seen in area 1, whereas a similar pattern is not observed in area 2. In both areas, streaks are observed at the diffraction spots of the austenite matrix, but no streaks are observed at the diffraction spots relating to γ′. From these results, we can not determine the morphology of γ′ using TEM in the area observed, and another method of observation is required to determine that. Additionally, a small amount of coarse precipitates such as the η-phase (Ni₃Ti) and σ with diameters of about 200 nm and 500 nm, respectively, are found at the grain boundaries, as shown in Fig. 6. These precipitates appear to contribute little to strengthening. Incidentally, the dislocation density of the specimen aged at 700°C for 400 h appears to be lower than that of the specimen aged for 1 h.

Fig. 4.

a) TEM bright field image of Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy after aging at 700°C for 1 h following 60% cold rolling and b) selected area electron diffraction pattern from the observed area which shows the existence of austenite (γ) phase.

Fig. 5.

a) TEM bright field image of Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy after aging at 700°C for 400 h following 60% cold rolling and b) selected area electron diffraction pattern from the observed circled area which shows the existence of γ′-phase (Ni₃Ti).

Fig. 6.

a) TEM bright field image at the grain boundary area of Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy after aging at 700°C for 400 h following 60% cold rolling and b) selected area electron diffraction pattern from the observed circled area which shows the existence of σ-phase (FeCr) and η-phase (Ni₃Ti).

3.3. Precipitation Analysis by 3DAP

The TEM observation revealed that there are some amounts of γ′ in crystal grains of the specimens aged at 700°C. However, the distribution and shape of γ′ remained unclear. Therefore, we attempted atomic mapping using 3DAP to observe γ′. Figure 7 shows the atomic mapping results by 3DAP of the specimen as cold rolled and the specimens aged at 700°C. Thermodynamic calculation suggests that γ′ mainly consists of Ni and Ti, therefore, we assumed the region with a high chemical composition of Ti in the three-dimensional atomic mapping as the γ′ precipitation site in this study. We postulated the plane which Ti concentration is 12.0 at%, which is the middle of the measured average Ti concentration of the center of γ′ in the specimen aged for 400 h, 24.0 at%, and the measured average Ti concentration of austenite matrix in the specimen aged for 400 h, 0.3 at%, as the boundary between γ′ and austenite matrix and indicated that as a purple plane in Fig. 7. No Ti concentrated regions corresponding to γ′ are observed in the specimen as cold rolled as shown in Fig. 7(a). There are also no Ti concentrated regions above 12.0 at% observed in the specimen aged for 0.03 h as shown in Fig. 7(b). However, in the specimen aged for 0.3 h, some Ti concentrated regions above 12.0 at% corresponding to γ′ are observed as shown by the nearly sphere-shaped regions in Fig. 7(c). The size of γ′ become larger as the aging time passes. The distribution of γ′ is uniform and fine in the specimen aged for 0.3 h, however, the density of γ′ decrease as the aging time progress.

Fig. 7.

3D atom probe images of Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy: a) 60% cold rolled specimen, b) to e) subsequently aged specimens for up to 400 h at 700°C. Needle-shaped specimen was aligned to rolling direction. A purple surface in the image represents the area in which the chemical composition of Ti is more than 12 at%.

The linear pattern of shading seen in TEM image of Fig. 5 does not appear to correspond to the shape of γ′ due to the lack of supporting evidence which suggests the shape of γ′ as mentioned earlier and the result of three-dimensional atomic mapping by 3DAP showed in Fig. 7 although the mapped area is small. However, there are some regions in which both the streaked diffraction spots of the austenite matrix and diffraction spots peculiar to γ′ can be seen in the selected area electron diffraction pattern. The introduction of strain by cold rolling may cause changes to the structure of the austenite matrix and have an effect on the precipitation behavior of γ′ although this is speculation because the causes of the linear shading pattern in the TEM bright field image and streaked diffraction spots in the austenite matrix are still unclear. This should be investigated in future studies.

The precipitation of γ′ could not be clearly observed in the specimen aged at 700°C for 0.03 h despite rapidly hardening due to aging. Figure 8 shows the linear distributions of Ni, Fe, Cr, Ti and Nb, which are the main elements composing the alloy, using a part of the 3DAP data of the specimen aged at 700°C for 0.03 h. The linear distribution of each element composition shows a composition-modulated distribution in which locally high and locally low compositions are periodically repeated. The composition modulation has a structure in which a region where Ni, which is contained within γ′, is enriched and Fe, which is not contained in γ′, is reduced and the region where Ni is reduced and Fe is enriched are periodically repeated. Some of the Ni enriched region are overlapped by Ti- and Nb-enriched regions. This led us to speculate that the composition-modulated structure is formed as a result of spinodal decomposition followed by the precipitation of γ′ which mainly consists of Ni and Ti.

Fig. 8.

3D atom probe elemental distribution profiles of Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy aged at 700°C for 0.03 h following 60% cold rolling (ROI: 5nm diameter cylinder).

4. Discussion

The cold rolled specimen used in this study significantly hardened from 401 HV to 496 HV after aging for only 0.03 h. However, the precipitation of γ′, which was assumed to be the main strengthening mechanism of the alloy, was only confirmed in specimens aged for over 0.3 h. Conversely, the composition-modulated structure formed by spinodal decomposition that speculated to be a preliminary step in the precipitation of γ′ was observed and that suggested to affect the hardness of the specimen aged for 0.03 h. Therefore, the amount of strengthening by the composition-modulated structure supposed to be formed by spinodal decomposition in the 0.03 h aged specimen and the overall change in the age-hardening behavior of the specimen used in this study at 700°C by aging time were evaluated quantitatively based on each strengthening mechanism.

4.1. Strengthening Mechanisms during Aging

The amount of strengthening produced by each strengthening mechanism in the age-hardening behavior of the specimens was evaluated from results of microstructure observations by the optical microscope and 3DAP. The amount of strengthening from spinodal decomposition in the early stage of aging, and precipitation, solid solution, and grain boundary strengthening were calculated based on each theoretical model. Any remaining amount of strengthening was assumed to be mainly due to dislocation strengthening after considering the fabrication procedure of the specimen and results of the microstructure observations as described later. Each strengthening mechanism is considered below.

4.1.1. Spinodal Decomposition Strengthening

No γ′ precipitation was observed in the specimen aged at 700°C for 0.03 h, however, the composition-modulated structure assumed to be formed by spinodal decomposition was observed. Therefore, the amount of strengthening by spinodal decomposition was calculated. The amount of spinodal decomposition strengthening Δσ_ms is known to be expressed as.¹⁷⁾   

$$\Delta {\sigma }_{\mathrm{m}\mathrm{s}}=\frac{A\eta Y}{\sqrt{6}}$$(1)

where A is the amplitude of the atomic composition modulation, and η is a misfit parameter expressed as   

$$\eta =\frac{1}{a}\cdot \frac{\partial a}{\partial c}$$(2)

where a is the lattice parameter of the austenite matrix, c is the atomic concentration of the solid solution element, and ∂a/∂c is the increment of lattice parameter per unit composition of the solid solution element. Y is a constant expressed as   

$$Y=\frac{\left(C_{11}-C_{12}\right)\left(C_{11}+2C_{12}\right)}{C_{11}}$$(3)

where C₁₁ and C₁₂ are elastic constants.

The specimen was a multinary alloy, and composition modulations were observed in the five elements, Ni, Fe, Cr, Ti and Nb. However, it is difficult to investigate the amount of strengthening while considering multiple composition-modulated structures. Therefore, only the composition modulation between the two elements Ni and Fe, which have the largest composition amplitude, was taken into consideration in the calculation for simplicity in this study. The composition amplitude of Fe in the austenite matrix, A, was 6.0 at% from the result of 3DAP observation. The misfit parameter, η, was 0.034 when Fe atoms were dissolved in Ni (austenite phase).¹⁸⁾ Y was calculated as 167 GPa when the elastic constants of the value of type 316 stable austenitic stainless steel, which value is C₁₁ = 206 GPa and C₁₂ = 133 GPa,¹⁹⁾ were substituted for the values of the specimen because the elastic constants of the actual specimen are unknown. From these values, Δσ_ms was calculated as 139 MPa. The actual amount of spinodal decomposition strengthening is suggested to be larger than calculated considering that composition-modulated structures of other elements were also observed. The comprehensive change in strengthening amount during aging considering each strengthening mechanism will be discussed in Section 4.2.

Kusabiraki et al.²⁰⁾ studied the age-hardening behavior at 720°C of A286 alloy (Fe-26Ni-15Cr-1.2Mo-2Ti) known to be hardened by γ′ (Ni₃Ti) precipitation, and the specimen appeared to have almost no dislocations caused by the solution heat treatment. However, even in the specimen aged for 0.1 h, which was the shortest aging time in the study, almost no increase in hardness was observed. The details of the microstructure and the existence of the composition-modulation structure were not described in the study, and the chemical composition of the specimen were also different to that in the present study. However, the existence of dislocations may affect the change in hardness for a short aging period of several hundreds of seconds in in γ′ (Ni₃Ti) precipitation hardening alloys although it remains purely speculative. We supposed that the existence of dislocations encourages atomic diffusion and accelerates spinodal decomposition.

4.1.2. Precipitation Hardening

It is known that there are two types of strengthening mechanisms caused by precipitates in the matrix. When the precipitates are small, the cutting mechanism in which dislocations shear the precipitates is exhibited. When precipitates are too large and strong to shear, the Orowan mechanism in which dislocations bypass precipitates while forming a dislocation loop around the precipitate is exhibited.

Anti-phase boundaries (APB) which are formed by shearing γ′ particles and hinder dislocation movement needed to be taken into consideration when dealing with the cutting mechanism in this study.²⁾ The amount of precipitation strengthening caused by the cutting mechanism and considering APB Δσ_apb can be expressed as²¹⁾   

$$\Delta {\sigma }_{\text{apb}}=\frac{M{E}_{\text{apb}}}{2b}\left(\frac{l}{\lambda +2r}\right)$$(4)

where M is the Taylor factor and b is the magnitude of the Burgers vector, set to 3 and 0.25 nm, respectively. E_apb is the APB energy per unit area. There are various derivations of E_apb ranging from 0.1 to 0.6 J/mm² depending on the reference.^{22,23,24,25,26,27,28,29,30)} Additionally, there are some studies reporting that Ti dissolved γ′ has a higher E_apb than the basic composition Ni₃Al.^28,29,30) We assumed that γ′ had the composition Ni₃Ti and E_apb was set to 0.55 J/mm², as calculated by Chandran et al.^28,30) in this study. The segment length of the leading dislocation that shears the precipitate particle l, and the average distance between precipitates λ were calculated using the volume fraction of γ′ f_γ′ and average radius of γ′ r referring to a previous study.²¹⁾ The shear modulus μ was set to 80 GPa for this calculation. For the specimen aged for 20 h, which did not have parameters measured using 3DAP, the mean values of the 3 h and 400 h aged specimens were used. Table 2 shows the values used in the calculation, f_γ′, r, l, and λ.

Table 2. Changes in necessary parameters for calculating precipitation strengthening with aging time at 700°C together with the amount of precipitation strengthening (Δσ_p). Parameters were obtained by 3D atom probe method.

Aging time (h)	γ′ phase fraction (fmat)	Mean radius of γ′ (r, nm)	Segment length of the dislocation acting in the cutting of γ′ (l, nm)	mean γ′ particle spacing (λ, nm)	Δσapb (MPa)	Δσoro (MPa)	Δσp (MPa)
0	–	–	–	–	–	–	–
0.3	0.02	1.5	3.0	28.9	333	3599	333
3	0.12	2.7	1.3	15.8	890	5036	890
20	(0.16)	(14)	22.0	31.2	1175	1921	1175
400	0.2	30	34.1	62.9	836	1203	836

On the other hand, the amount of precipitation hardening considering the Orowan mechanism Δσ_oro was calculated using the Ashby-Orowan equation^31,32,33,34) expressed as   

$$\Delta {\sigma }_{\text{oro}}= \sqrt{\frac{3}{2}}\cdot \frac{0.8M\mu b}{2\pi r\sqrt{1-\nu }}{\left(\frac{\pi }{f}-2\right)}^{-1}ln\left(\sqrt{\frac{2}{3}}\cdot \frac{r}{b}\right)$$(5)

where ν is the Poisson coefficient which was set to 0.28 in this calculation. Of the two parameters, Δσ_apb and Δσ_oro, the one with the lower calculated amount was defined as the precipitation strengthening amount Δσ_p. Table 2 shows the calculated values of Δσ_p.

This data suggests that the precipitation strengthening amount Δσ_p increased from 333 MPa (0.3 h) to 1175 MPa (20 h) as aging time increased, then started to decrease and became 836 MPa at 400 h aging. From these calculations, it is also speculated that the cutting mechanism, but not the Orowan mechanism, operates from 0.3 h aging when precipitation of γ′ begins to 400 h aging in this result of calculation.

4.1.3. Solid Solution Hardening

The amount of solid solution hardening Δσ_s was calculated based on the Labusch model which is expressed as   

$$\Delta {\sigma }_{\text{s}}=f_{\text{mat}}{\left({\sum }_i{k}_{\mathrm{s},\mathrm{i}}^{3/2}{x}_{\mathrm{i}}\right)}^{2/3}$$(6)

where k_s,i is the solid solution strengthening coefficient for element i and x_i is the concentration of element i in the matrix.^35,36,37,38) From the results of the thermodynamic calculation and 3DAP observation, we considered that the change in the volume fraction of γ′ during aging could not be ignored in this study. Therefore, an additional term for the effect of the volume fraction of the austenite matrix, f_mat, was incorporated into the equation. The values in Table 3 were used as k_s,i that calculated from the atomic size and shear modulus of each element³⁹⁾ with reference to a previous study.⁴⁰⁾ The values of f_mat and x_i were derived from the result of 3DAP observation. For the specimen aged for 20 h, which did not have parameters measured by 3DAP, the mean values of the 3 h and 400 h aged specimens were used. Table 4 shows f_mat and x_i which were used in the calculation and figured results of Δσ_s. The amount of solid solution hardening, Δσ_s, was predicted to decrease from 306 MPa to 127 MPa as the aging time progressed. The chemical composition of Ni, Ti, Nb and Al decreased and Fe and Cr increased as aging time progressed in the matrix. This change was assumed to be mainly due to the precipitation and growth of γ′ and η because these have Ni, Ti, Nb and Al as components.

Table 3. Solid solution strengthening coefficient k_s,i/MPa calculated from shear modulus and atomic size of each element.^1,39,40)

i	Ni	Cr	Mo	Al	Ti	Nb
ks,i	112	102	637	43	720	1106

Table 4. Changes in necessary parameters for calculation solid solution strengthening 700°C together with the amount of solid solution strengthening (Δσ_s). Parameters were obtained by 3D atom probe.

Aging time (h)	Austenite phase fraction (fmat)	Chemical composition of austenite phase (at%)							Δσs (MPa)
		Fe	Ni	Cr	Mo	Al	Ti	Nb
0	1	39.33	38.43	16.31	0.70	0.11	4.32	0.80	306
0.3	0.98	40.97	37.38	16.57	0.76	0.06	3.55	0.72	278
3	0.88	45.61	31.68	19.66	0.85	0.05	1.62	0.52	195
20	(0.84)	(47.21)	(29.58)	(21.09)	(0.81)	(0.03)	(0.94)	(0.33)	160
400	0.8	48.81	27.49	22.51	0.77	0.02	0.27	0.14	127

4.1.4. Grain Boundary Strengthening

The amount of strengthening by grain boundaries in matrix Δσ_gb was derived from the Hall-Petch relationship⁴¹⁾ expressed as   

$$\Delta {\sigma }_{\mathrm{g}\mathrm{b}}={\sigma }_0+k_{\mathrm{g}\mathrm{b}}{D}^{-1/2}$$(7)

where σ₀ is the friction or lattice stress, k_gb is the Hall-Petch coefficient, and D is the mean grain diameter. For σ₀ and k_gb, we used 100 MPa and 600 MPa/mm^1/2, respectively, which are generally used for austenitic stainless steels.⁴²⁾ The mean grain diameter of the matrix was measured and found to be 60 μm regardless of the aging time from the results of optical microscope observation shown in Fig. 3. The average of the major and minor diameters of the crystal grains was taken as the particle size, because the crystal grain shape of the matrix was flat. Although the grain boundaries of the specimen aged for 400 h were unclear, its mean grain size was assumed to 60 μm because the mean grain size of the specimens aged from 0 h to 20 h remained unchanged at 60 μm. Using this value, the amount of strengthening, Δσ_gb, was calculated as 177 MPa regardless of aging time.

4.1.5. Dislocation Strengthening

A 60% cold rolled specimen was used as the starting material in this study. Therefore, we assumed that the dislocation structure also contributed significantly to the strengthening of specimens. However, although we attempted to measure the dislocation density of the austenite matrix using X-ray diffraction for 700°C aged specimens, the peak positions of γ′ overlapped to these of the matrix. The crystal structure of γ′ is close to that of the austenite matrix, and the peaks could not be separated to measure the dislocation density of the matrix. This made it impossible to determine quantitatively the amount of strengthening by dislocations. However, it is appropriate to assume that the strengthening mechanism of the specimen used in this study is the total effect of dislocation, spinodal decomposition, γ′ precipitation, solid solution, and grain boundary strengthening. Thus, we assumed that the residual amount obtained after subtracting the contributions of the spinodal decomposition, γ′ precipitation, solid solution, and grain boundary strengthening from the total strengthening amount is the strengthening amount by dislocations in this study.

4.2. Change of Hardness during Aging and Its Quantitative Evaluation

In order to quantitatively evaluate the overall change in the age-hardening behavior at 700°C of the specimen based on each strengthening mechanism, the actual measured hardness (HV) of the cold rolled specimen and aged specimens at 700°C was converted into yield strength (YS) using the following equation.⁴³⁾   

$$YS=3.053\mathrm{\hspace{0.17em} } HV+22.0$$(8)

Although the original is an empirical equation that describes the relationship between HV and tensile strength, the difference between yield strength and tensile strength was assumed to be small because the specimen used in this study was cold rolled and then subjected to aging. Therefore, the tensile strength term was directly replaced with the yield strength in Eq. (8).

Figure 9 shows the results of quantitative estimation of the yield strength changing behavior of the specimen used in the study during aging at 700°C based on each strengthening mechanism.

Fig. 9.

Change in yield strength as a function of aging time at 700°C together with the predicted amount of contribution to strength from each strengthening mechanism. Ni-37Fe-15Cr-1.2Mo-4Ti-2Nb superalloy was cold rolled by 60% and subsequently aged.

Strengthening by the composition-modulated structure that was speculated to be caused by spinodal decomposition was assumed to contribute the rapid strengthening in the early stage of aging (0.3 h). The amount of spinodal strengthening for the 0.03 h aged specimen estimated in Sec. 4.1.1, 139 MPa, is lower than the actual strengthening amount of the same, 290 MPa. However, the actual composition-modulated structure was confirmed for not only Fe and Ni but also Ti, Cr and Nb as shown in Fig. 8. The actual amount of strengthening contributed by the composition-modulated structure appears to be higher than the calculated amount. Additionally, although the crystal orientations of the specimens were not measured in this study, the value of constant Y that is determined by elastic constants that was considered to be anisotropic. The effect of crystal orientation was not taken into consideration in the study for simplicity, however, these points should be considered in order to calculate the amount of strengthening more accurately in future studies.

A certain amount of solid solution elements remained in the initial stage of aging (~0.3 h), therefore, the contribution of solid solution strengthening can not be ignored. In addition, the contribution of the dislocations introduced by cold rolling, which was assumed to the amount subtracted the sum of each strengthening mechanism from the whole, was expected to be similar to that of the cold rolled specimen and a major contributor to strengthening at the initial stage of aging.

The contribution of γ′ precipitation strengthening increased significantly from 0.3 h to about 20 h, as shown in Fig. 9. The amount of precipitation strengthening reached a maximum of 1175 MPa after 20 h aging, and then decreased to 836 MPa when the aging time reached 400 h. It was considered that the specimen was overaged and precipitates were coarsened in the specimen. The amount of strengthening by solid solution gradually decreased with the progress of aging, which was mainly due to the decrease of solid solution strengthening elements by the precipitation of γ′ and η. The amount of dislocation strengthening had little change from 0.3 h to 3 h, but decreased significantly from 3 h to 20 h. We considered that there was very little contribution to strength by dislocations in specimens aged 20 h and 400 h. On the other hand, the contribution of grain boundary strengthening was presumed to be constant regardless of the aging time because recrystallization and grain growth were not observed during aging which makes the average particle size of the matrix constant.

Overall, the age-hardening behavior of the specimen at 700°C can be summarized as follows. The grain boundary strengthening contributes an almost constant amount regardless of the aging time. In the early stage of aging (0 to 3 h), spinodal decomposition which is presumed to occur as a precursor of γ′ precipitation takes place. The formation of a composition-modulated structure affects the strength of the specimen alongside dislocation and solid solution strengthening. In the late stage (3 to 400 h), the contribution of dislocation strengthening decreases and the contribution of γ′ precipitation strengthening increases in parallel with aging time. Then, the strength of the specimen is assumed to decrease as aging time progresses because the amount of precipitation strengthening begins to decrease after peaking at an aging time of 20 h due to the coarsening of γ′, coupled with the decrease of dislocation strengthening and solid solution strengthening contributions.

However, there remain issues regarding the validity of simply adding the amount of precipitation and dislocation strengthenings and the method for evaluating the actual effect of dislocation strengthening. The residual amount of strengthening after removing the other strengthening mechanisms was tentatively used as the amount of dislocation strengthening in this study because it was not possible to accurately quantify the dislocation density of the specimen. However, previous studies^31,44) indicate that the amount of precipitation and dislocation strengthenings can not be accurately predicted by simple addition when the strengthening phase precipitation and dislocations are present simultaneously in the matrix.³¹⁾ It is concerned that the amount of dislocation strengthening might have been underestimated because a certain amount of dislocations were still assumed to exist in the specimen aged for up to 20 h from the result of microstructure observations by optical microscope and TEM. Still, we consider the amount of dislocation strengthening to be negligibly small in the specimen aged for 400 h because almost no dislocation was observed using TEM, and this supposed to make the sum of the amount of precipitation, solid solution and grain boundary strengthening relatively correspond to the experimental value. In addition, strengthening by the fine subgrain boundaries (low-angle boundaries) that is assumed to exist in a specimen aged for 400 h was investigated by Bowen et al.⁴⁵⁾ However, its amount is supposed to be sufficiently small compared to that of other strengthening mechanisms. Therefore, the effect of subgrain boundaries was not considered in this study.

5. Conclusions

To investigate the effect of dislocations on the age-hardening behavior of γ′-phase (Ni₃Ti) precipitation-hardening Ni-based superalloy, specimens which solution heat treated and introduced dislocations by 60% cold rolling were aged at 700°C for up to 400 h and measured the change in hardness at room temperature. The changes in the microstructure during aging were also specifically observed using an optical microscope, TEM, and 3DAP. We evaluated the contribution of each strengthening mechanism at each stage of aging based on each theoretical model from these results. The following conclusions were obtained:

(1) The hardness of the specimens which were solution heat treated and 60% cold rolled (401 HV) rapidly increases to 496 HV after aging at 700°C for 0.03 h (108 s). The hardness reaches a peak of 536 HV after 3 h aging and then gradually decreases. The specimen hardness is 437 HV after 400 h aging.

(2) The rapid increase in hardness at the initial stage of aging (~0.3 h) is assumed to be caused by the composition-modulated structure observed using 3DAP which we presume to be formed by spinodal decomposition. We speculate that the dislocations introduced before aging contribute to rapid occurrence of spinodal decomposition.

(3) The precipitation of γ′ is observed after aging for 0.3 h and the amount of precipitation hardening increase as aging time progresses. However, precipitation hardening peaks at 20 h aging and then decrease as aging time passes.

Acknowledgement

We would like to thank Dr. Kohsaku Ushioda for his useful advices regarding this study.

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