Creep data obtained from creep curves and for the G variant are depicted in Figures 9a and 9b In Figure 9a, the minimum creep rates ${\dot{\epsilon}}_{\mathrm{min}}$are plotted against the applied stress *σ* on a bilogarithmic scale. This figure shows that the stress dependences of ${\dot{\epsilon}}_{\mathrm{min}}$for all temperatures have the same trend. However, the slopes and therefore the values of the apparent stress exponent of the creep rate *n* (Eq. ()) for individual temperatures are slightly different. The exponent *n* can be written as follows [13].

Figure 9 Stress dependences of a) minimum creep rate, and b) time to fracture for superalloys MAR-M247 (variant G).

$$n={\left(\frac{\partial \mathrm{ln}{\dot{\epsilon}}_{\mathrm{min}}}{\partial \mathrm{ln}\sigma}\right)}_{T}.$$(1)The decrease in *n* at the lower stresses indicates changes in the rate-controlling creep deformation mechanism(s) and/or microstructural instability. The determined values of *n* ( correspond to the power-law dislocation creep regime [12–14]. Figure 9b shows the variation of the time to fracture *t*_{f} with the applied stress. It is clear from this plot that values of stress exponent *m* of creep life (see Eq. ()) are very similar to the values for the stress exponent *n* indicating that both the creep deformation and fracture could be controlled by the same mechanism(s) [12]:

Table 2 Values of the stress exponent of the creep rate *n* and the stress exponent of the creep life *m* for superalloy MAR-247 of G variant for different testing temperatures within the used intervals of applied stress.

$${t}_{f}\approx B\cdot {\sigma}^{-m},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{where}m=-{\left(\frac{\partial \mathrm{ln}{t}_{f}}{\partial \mathrm{ln}\sigma}\right)}_{T}.$$(2)The values of exponents *n* and *m* are presented in . With respect to non-linear curves in bilogarithmic plots the values of *n* and *m* were determined as local slopes of the relevant part of creep curves.

The values of the minimum creep rate and the time to fracture for the alloy G1 were nearly the same for the corresponding loading conditions (Figures 10a, b and ). Thus, it is reasonable to perform the following analysis of the creep deformation behaviour only from data corresponding to the G alloy.

Figure 10 Comparison of the stress dependence of a) minimum creep rate, and b) time to fracture for superalloys MAR-M247 of G variant (solid line) and of G1 variant (dashed line).

The results for creep plastic deformation of superalloy specimens are presented in Figure 11. The creep testing revealed very low values of creep plasticity characterized by values of the fracture elongations. However, while fracture elongation was about 3% at 800^{∘}C, increasing the testing temperature slightly increased the creep ductility to about 5 to 8%. The increasing creep plasticity (elongation) of superalloy MAR-M247 may be explained by the course of its tertiary creep behaviour (Figure 1) and/or creep fracture type.

Figure 11 Stress dependence of fracture strain for superalloy MAR-M247 G and G1 alloys at different temperatures and applied stresses.

The minimum creep rates for each test were determined during very early stage of deformation, where the value of creep deformation is rather small. The apparent activation energy of creep *ΔQ*_{c} can be obtained from the creep test with constant loading according to the Dorn´s relationship

$${\dot{\epsilon}}_{\mathrm{min}}=A{\sigma}^{n}\mathrm{exp}\left(-\frac{\Delta {Q}_{c}}{RT}\right)$$(3)where *A* is a constant, *R* is the gas constant and *T* is temperature. So that

$$\Delta {Q}_{c}=-{\left(\frac{\partial \mathrm{ln}{\dot{\epsilon}}_{\mathrm{min}}}{\partial \left(1\text{/}Rt\right)}\right)}_{\sigma}$$(4)The results of an activation analysis are presented in Figure 12.

Figure 12 Determination of the activation energy of creep of the MAR-M247 alloy at different levels of applied stress.

Experimentally obtained values of the apparent activation energy of creep for MAR-M247 (560-660 kJ/mol) are much higher in comparison with the energy of volume self-diffusion of the Ni species (284kJ/mol) [15].Nevertheless, the precipitation-strengthened alloys typically exhibit such high and temperature-dependent values of the apparent creep activation energy [13], which corresponds to a model of diffusion-controlled dislocation movement by glide and climb. Moreover, the increased value of the apparent creep activation energy can be explained by a presence of back stress induced by precipitated particles [13, 16, 17].

The other important field of interest about nickel-based superalloy MAR-M247 (especially for its use in industry) is the life assessment *i.e*. prediction of the lifetime. There are several empirical formulas that, on different levels of sophistication, describe the dependence of the creep life on stress and on temperature. One such relationship proposed by Monkman and Grant [18] seems to have wider applicability than might be reasonably expected. The Monkman-Grant relationship

$${t}_{f}={\left(C\text{/}{\dot{\epsilon}}_{\mathrm{min}}\right)}^{\alpha},$$(5)where *C* and *α* are constants, has frequently been used for the prediction of creep life of creep-resistant materials.

It was found (Figure 13) that the experimental data obey the Monkman-Grant relationship with surprising accuracy, as exhibited by the nearly identical values of the constant *α* for different temperatures (*α* = 0.83 for 800^{∘}C and *α* = 0.85 for 950^{∘}C).

Figure 13 Monkman-Grant relationship for different temperatures for the G alloy.

The Monkman-Grant relationship can be modified [19] for the creep data in terms of normalized creep fracture strains *ε*_{f}/*t*_{f} and the minimum creep rates ${\dot{\epsilon}}_{\mathrm{min}}$as shown in Figure 14.Nearly all experimental points fall on one master solid line. The double logarithmic plot in Figure 14 indicates that the experimental data can be represented by a line with exponent *a* $\cong $1.0. This suggests that fracture process is controlled by a dislocation mechanism as similar to that in creep deformation.

Figure 14 Normalized Monkman-Grant relationship for different temperatures for the G alloy.

In summary, based on the results of creep testing of two grain-sized variants of the nickel-based MAR-M247 superalloy, the difference in the creep behaviour of variants G and G1 is nearly negligible. It was suggested that under creep testing conditions used in this study, the creep behaviour of the alloys corresponds to power-law or dislocation creep. It should be noted that no proposed formula for the minimum creep rate (*e.g*. Eq. 3) in the region of dislocation creep complied with explicit dependence on grain size [13, 14, 20]. Furthermore, creep deformation in this class of superalloys occurs predominantly in the matrix phase. One possible deformation mechanism is grain boundary sliding, which could be minimized by a coarser grain size [13].However, creep in superalloys is very dependent on a number of microstructural parameters. Those of primary importance are the *𝛾*^{′} precipitate volume fraction, lattice mismatch and morphology. It was reported [21] that creep life roughly linearly increases with the *𝛾*^{′} volume fraction. The lattice mismatch between the matrix and *𝛾*^{′} also influences the creep strength [22, 23]. For the best creep strength, the *𝛾′* particles should be very small, but this may cause undesirable losses in ductility. Coarse primary *𝛾′* phase particles with an average size of ~2 μm were observed (see Section 3.2.) in both variants G and G1. These large particles could be caused by the microsegregation of alloying elements during the solidification process and were difficult to refine or even dissolve during heat treatment. Carbides play an important role in the creep strengthening mainly by pinning the grain boundaries and subsequently prevent the grain boundaries from sliding and migrating.

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