The influence of temperature on the deformation behavior, strength and fracture mechanism of the heat-resistant Nickel-based alloy EI698-VD

Components produced from heat-resistant nickel alloys are exposed to monotonic or cyclic loading. Concurrently, the material is subjected to damaging external factors, including elevated and cyclically changing temperatures. The behaviour of materials under these conditions is subject to variation, with the potential to significantly impact performance and service life. In order to design components and structures correctly, and to determine stress-strain states and predict durability, it is necessary to obtain complete and accurate data on the behaviour of the material under the relevant operating conditions.
The nickel-based polycrystalline alloy XH73MBTU-VD (EI698-VD) is used in the power industry and aviation at temperatures of up to ${750}^{\circ }\mathrm{C}$${750}^{\circ }\mathrm{C}$750^(@)C750^{\circ} \mathrm{C}${750}^{\circ }\mathrm{C}$. GTE turbine discs are made from the EI698-VD alloy. There have been documented cases of surface cracks and failure in service of GTE turbine components made from the EI698-VD alloy [1]. Furthermore, it was observed that when the EI698-VD alloy was maintained at elevated temperatures (in excess of ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$ ) for extended periods without the action of an external load, inelastic shrinkage and swelling strain occurred [2]. These phenomena were accompanied by strain oscillations.
In [3], an overview of the characteristics of the EI698-VD alloy structure and the features of its behaviour in operation was previously presented. In this section, the primary characteristics of the alloy under consideration are outlined. The heatresistant nickel-based alloy EI698-VD is dispersion-strengthened. During the process of cooling, a strengthening ${\gamma }^{\prime }$${\gamma }^{\prime }$gamma^(')\gamma^{\prime}${\gamma }^{\prime }$-phase is released from the nickel-based $\gamma$$\gamma$gamma\gamma$\gamma$ matrix with a BCC lattice [4, 5]. According to [6], the grain size is approximately 30-60 $\mu \mathrm{m}$$\mu \mathrm{m}$mum\mu \mathrm{m}$\mu \mathrm{m}$. Large MC carbides are embedded inside the grain, and small ${\mathrm{M}}_{23}{\mathrm{C}}_6$${\mathrm{M}}_{23}{\mathrm{C}}_6$M_(23)C_(6)\mathrm{M}_{23} \mathrm{C}_{6}${\mathrm{M}}_{23}{\mathrm{C}}_6$ carbides are located at the grain boundaries [7]. The ${\gamma }^{\prime }$${\gamma }^{\prime }$gamma^(')\gamma^{\prime}${\gamma }^{\prime }$-phase particles are spherical in shape, with a large particle size of $0.2-0.6\mu \mathrm{m}[6,7,8]$$0.2-0.6\mu \mathrm{m}[6,7,8]$0.2-0.6 mum[6,7,8]0.2-0.6 \mu \mathrm{~m}[6,7,8]$0.2-0.6\mu \mathrm{m}[6,7,8]$. The mass fraction of the ${\gamma }^{\prime }$${\gamma }^{\prime }$gamma^(')\gamma^{\prime}${\gamma }^{\prime }$-phase in the alloy is $20.5\mathrm{\%}$$20.5\mathrm{\%}$20.5%20.5 \%$20.5\mathrm{\%}$ [9]. According to the measurements reported in [10], the primary spherical ${\gamma }^{\prime }$${\gamma }^{\prime }$gamma^(')\gamma^{\prime}${\gamma }^{\prime }$ particles have a size of approximately $0.06\mu \mathrm{m}$$0.06\mu \mathrm{m}$0.06 mum0.06 \mu \mathrm{~m}$0.06\mu \mathrm{m}$, and their volume fraction was estimated to be around $35\mathrm{\%}$$35\mathrm{\%}$35%35 \%$35\mathrm{\%}$.
In the preceding studies on fatigue crack growth rate in the temperature range of $25-{650}^{\circ }\mathrm{C}$$25-{650}^{\circ }\mathrm{C}$25-650^(@)C25-650^{\circ} \mathrm{C}$25-{650}^{\circ }\mathrm{C}$ and under thermomechanical conditions, a change in the fracture mechanism was observed from transgranular to intergranular at temperatures above ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$ [11]. An attempt to numerically reproduce this process within the frame of the finite element method was made in [12]. Furthermore, when this temperature threshold was exceeded, the fatigue crack growth rate increased significantly [3]. It is important to note that the model based on the energy fracture resistance parameter, the damage impact parameter A introduced by Sulamanidze [3], demonstrated the capacity to predict fatigue crack growth, taking into account the rapid degradation of properties as the temperature rises, as well as under thermomechanical conditions of cyclic loading. The input data for numerical finite element analysis [13, 14], on the basis of which the values of the damage impact parameter A were determined, were the results of tests on uniaxial monotonic tension in the temperature range of fatigue crack growth. Consequently, it can be assumed that the mechanisms controlling the degradation of fatigue crack growth characteristics with increasing temperature are related to the mechanisms controlling the decrease in strength and plasticity characteristics under uniaxial monotonic loading. The present study aims to analyse the deformation behaviour and microstructure of specimens made of the nickel-based alloy EI698-VD, with a view to proposing possible causes for the rapid decrease in characteristics and the change in the fracture mechanism with increasing temperature.

The behaviour of the EI698-VD alloy was studied under elevated temperatures in the range of $25-{700}^{\circ }\mathrm{C}$$25-{700}^{\circ }\mathrm{C}$25-700^(@)C25-700^{\circ} \mathrm{C}$25-{700}^{\circ }\mathrm{C}$. Cylindrical specimens (Fig. 1) were cut from hot-rolled bar. The nominal composition of the EI698-VD alloy is given in Tab. 1. The specimens were tested using the UTS111 testing setup (Fig. 1), which is equipped with an Epsilon hightemperature extensometer and a high-temperature furnace.

The objective of this study is to conduct a series of short-term tests at temperatures ranging from 25 to ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$. In monotonic tensile tests until fracture, the specimen was fixed in the upper and lower rods of the UTS111 test frame. The specimen was heated to a temperature T and maintained for 1.5 h at a load of 200 N before the main load was applied. The load was applied in a displacement control mode with a constant displacement rate of $1\mathrm{mm}/\min$$1\mathrm{mm}/\min$1mm//min1 \mathrm{~mm} / \mathrm{min}$1\mathrm{mm}/\min$ (Fig. 2).

The UTS111 test setup is equipped with a three-zone high-temperature furnace that can maintain a constant temperature of up to ${1200}^{\circ }\mathrm{C}$${1200}^{\circ }\mathrm{C}$1200^(@)C1200^{\circ} \mathrm{C}${1200}^{\circ }\mathrm{C}$. The air temperature was measured by three N -type thermocouples positioned within the specimen area. The surface temperature of the specimen in the furnace was measured with a K-type thermocouple (Fig. 1). The axial ${\epsilon }_Y$${\epsilon }_Y$epsi_(Y)\varepsilon_{Y}${\epsilon }_Y$
strains were measured using a high-temperature Epsilon extensometer with a 25 mm gauge length (Fig. 1). The experimental data, which included strain, force, traverse displacement, and T , were recorded from the beginning of the test until fracture. The fractured specimen images were analysed in CAE applications to measure the slip plane angle. In the CAE application, the specimen axis was defined as the midline between the cylindrical surface contours. The mean-square deviation is calculated based on measurements of the slope angles of five slip planes.
The microstructure of the alloy was characterised using a Zeiss Merlin scanning electron microscope (SEM), which was equipped with an Oxford X-max 80 energy-dispersive X-ray (EDX) detector for elemental analysis. Discs with a thickness of 3 mm and a diameter of 11 mm were cut from the specimens, as was previously described in [15]. For the SEM, the cut discs were polished to $0.1\mu \mathrm{m}$$0.1\mu \mathrm{m}$0.1 mum0.1 \mu \mathrm{~m}$0.1\mu \mathrm{m}$.

The properties of alloy EI698-VD are outlined in Tab. 2 [13, 14]. In this table, E is the Young's modulus, ${\sigma }_{\mathrm{y}}$${\sigma }_{\mathrm{y}}$sigma_(y)\sigma_{\mathrm{y}}${\sigma }_{\mathrm{y}}$ is the yield stress, ${\sigma }_{\mathrm{u}}$${\sigma }_{\mathrm{u}}$sigma_(u)\sigma_{\mathrm{u}}${\sigma }_{\mathrm{u}}$ is the ultimate tensile strength, ${\sigma }_{\mathrm{f}}$${\sigma }_{\mathrm{f}}$sigma_(f)\sigma_{\mathrm{f}}${\sigma }_{\mathrm{f}}$ is the true rupture strength (see Eqn. 1), ${\epsilon }_{\mathrm{f}}$${\epsilon }_{\mathrm{f}}$epsi_(f)\varepsilon_{\mathrm{f}}${\epsilon }_{\mathrm{f}}$ (see Eqn. 2) and ${\epsilon }_{\mathrm{fe}}$${\epsilon }_{\mathrm{fe}}$epsi_(fe)\varepsilon_{\mathrm{fe}}${\epsilon }_{\mathrm{fe}}$ are true and engineering rupture strains, and ${\psi }_{\mathrm{en}}$${\psi }_{\mathrm{en}}$psi_(en)\psi_{\mathrm{en}}${\psi }_{\mathrm{en}}$ (see Eqn. 3) is relative reduction. ${\omega }_{\mathrm{f}}$${\omega }_{\mathrm{f}}$omega_(f)\omega_{\mathrm{f}}${\omega }_{\mathrm{f}}$ and ${\omega }_{\mathrm{fe}}$${\omega }_{\mathrm{fe}}$omega_(fe)\omega_{\mathrm{fe}}${\omega }_{\mathrm{fe}}$ are the critical strain energy density, which are obtained as the area under the true and engineering stress-strain curve [3].

where ${\mathrm{F}}_0,{\mathrm{F}}_{\mathrm{f}}$${\mathrm{F}}_0,{\mathrm{F}}_{\mathrm{f}}$F_(0),F_(f)\mathrm{F}_{0}, \mathrm{~F}_{\mathrm{f}}${\mathrm{F}}_0,{\mathrm{F}}_{\mathrm{f}}$ are the cross-sectional areas of the specimen before and after the test, and ${\mathrm{P}}_{\mathrm{f}}$${\mathrm{P}}_{\mathrm{f}}$P_(f)\mathrm{P}_{\mathrm{f}}${\mathrm{P}}_{\mathrm{f}}$ is the force at the moment of rupture [16].
The data presented in Fig. 3 [13] and Tab. 2 demonstrate that an increase in temperature results in a decrease in the strength and plasticity of the alloy, specifically the critical strain energy density, ultimate tensile strength, and rupture strain. When the temperature exceeds ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$, the values of rupture strain decrease sharply. However, for the nominal characteristics of alloy EI698-VD [17], the rupture strain for temperatures of $20,500,600,650$$20,500,600,650$20,500,600,65020,500,600,650$20,500,600,650$, and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ is $31,31,28,28$$31,31,28,28$31,31,28,2831,31,28,28$31,31,28,28$, and $24\mathrm{\%}$$24\mathrm{\%}$24%24 \%$24\mathrm{\%}$, respectively.

As demonstrated in Fig. 3a, the "serrated flow" effect, also referred to as the Savatry-Masson or Porteven-Le Chatelier (PLC) effect, occurred at a temperature of ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$. The serrated flow effect has been observed to be associated with negative strain-rate sensitivity and the interaction of dislocations with impurity atoms [18,19,20]. Impurity atoms are fixed on dislocations, thereby limiting their movement due to the slower diffusion mechanism of atom movement. The increase in yield stress that was observed with rising temperature ( $400-{700}^{\circ }\mathrm{C}$$400-{700}^{\circ }\mathrm{C}$400-700^(@)C400-700^{\circ} \mathrm{C}$400-{700}^{\circ }\mathrm{C}$, see Tab .2 ) had previously been attributed by the authors [21] to the PLC effect. The behavior of the material at temperatures of 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ corresponds to serrated flow type C [22,23], since stress drops do not appear at the initial stage of the elastic-plastic section of the tensile curve. Type C is also often observed at higher temperatures. In this case, localized strain bands originate with high stress drop values. At a temperature of ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$, serrated flow occurs throughout the entire elastic-plastic deformation, which corresponds to type B.

It can be seen that during serrated flow, in sections where the load increases between stress drops, the strain rate rapidly increases (Fig. 4). The strain rate for 400 and ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$ at the moment of stress drops is approximately constant throughout the entire tensile curve and is equal to about $(5...9)\cdot {10}^{-4}{\sec }^{-1}$$(5...9)\cdot {10}^{-4}{\sec }^{-1}$(5...9)*10^(-4)sec^(-1)(5 . . .9) \cdot 10^{-4} \mathrm{sec}^{-1}$(5...9)\cdot {10}^{-4}{\sec }^{-1}$ (Fig. 4). For 23, 650 , and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$, the strain rate was about $(4...5)\cdot {10}^{-4}{\sec }^{-1}$$(4...5)\cdot {10}^{-4}{\sec }^{-1}$(4...5)*10^(-4)sec^(-1)(4 . . .5) \cdot 10^{-4} \mathrm{sec}^{-1}$(4...5)\cdot {10}^{-4}{\sec }^{-1}$ (Fig. 5) without serrated flow. As is known, the diffusion rate of atoms increases with temperature. It can be seen that for 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$, serrated flow appears under conditions of increased strain rate values. At a temperature of ${650}^{\circ }\mathrm{C}$${650}^{\circ }\mathrm{C}$650^(@)C650^{\circ} \mathrm{C}${650}^{\circ }\mathrm{C}$, the strain rate at the onset of serrated flow was $6\cdot {10}^{-4}{\sec }^{-1}(\epsilon =8.5\mathrm{\%})$$6\cdot {10}^{-4}{\sec }^{-1}(\epsilon =8.5\mathrm{\%})$6*10^(-4)sec^(-1)(epsi=8.5%)6 \cdot 10^{-4} \sec ^{-1}(\varepsilon=8.5 \%)$6\cdot {10}^{-4}{\sec }^{-1}(\epsilon =8.5\mathrm{\%})$, and at a temperature of ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$, it was $7\cdot {10}^{-}{}^4{\sec }^{-1}(\epsilon =6\mathrm{\%})$$7\cdot {10}^{-}{}^4{\sec }^{-1}(\epsilon =6\mathrm{\%})$7*10^(-)^(4)sec^(-1)(epsi=6%)7 \cdot 10^{-} { }^{4} \sec ^{-1}(\varepsilon=6 \%)$7\cdot {10}^{-}{}^4{\sec }^{-1}(\epsilon =6\mathrm{\%})$. Therefore, based on the concept of the PLC effect mechanism, it can be assumed that strain at a strain rate of $(4...5)\cdot {10}^{-4}{\sec }^{-1}$$(4...5)\cdot {10}^{-4}{\sec }^{-1}$(4...5)*10^(-4)sec^(-1)(4 . . .5) \cdot 10^{-4} \mathrm{sec}^{-1}$(4...5)\cdot {10}^{-4}{\sec }^{-1}$ for temperatures of 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ enabled impurity atoms to move together with dislocations until the strain rate increased further. It can then be supposed that at 400 and ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$, the strain rate at which the stress drop occurred $(5\dots 9)\cdot {10}^{-4}{\sec }^{-1}$$(5\dots 9)\cdot {10}^{-4}{\sec }^{-1}$(5dots9)*10^(-4)sec^(-1)(5 \ldots 9) \cdot 10^{-4} \sec ^{-1}$(5\dots 9)\cdot {10}^{-4}{\sec }^{-1}$ is the upper limit for the movement of impurity atoms fixed on dislocations.

In a hypothetical scenario, the serrated flow phenomenon observed in the tests may be attributed to the pinning of dislocations on ordered regions, followed by the subsequent cluster breaking free. The phenomenon of local reorganization (ordering) of the short-range ordering (SRO) [24,25] Ni-Cr lattice regions, which are present in all Ni-Cr alloys, and the transition to the long-range rhombic ( ${\mathrm{Ni}}_2\mathrm{Cr}$${\mathrm{Ni}}_2\mathrm{Cr}$Ni_(2)Cr\mathrm{Ni}_{2} \mathrm{Cr}${\mathrm{Ni}}_2\mathrm{Cr}$ ) order (LRO) [26,27] are of particular interest. The ordering of SRO is consistent with interatomic distances, while LRO is characterised by the presence of ordering repetition at distances that are not constrained in size. This phenomenon can be attributed to the stronger attraction exhibited by different types of atoms in comparison to identical atoms, within a specific temperature range. This temperature range persists up to the critical temperature, which is situated between 530 and ${600}^{\circ }\mathrm{C}$${600}^{\circ }\mathrm{C}$600^(@)C600^{\circ} \mathrm{C}${600}^{\circ }\mathrm{C}$ [28,29]. It is noteworthy that SRO and LRO, as suggested in a number of studies, may be the cause of the previously observed phenomenon of abnormal shrinkage without load application, and "instantaneous elongation" or "strain burst" in nickel-based alloys and EI698-VD in particular [30,31,32]. Moreover, it is known that the temperature-dependent changes in characteristics observed in the tests, namely an increase in the yield stress and a decrease in rupture strain, also occur in LRO. LRO induces a change in the fracture mechanism
from ductile, with coalescence of microvoids in a disordered alloy, to brittle, intergranular fracture in an ordered material. However, additional studies using transmission electron microscopy and X-ray diffraction methods are required to correctly establish the effect of ordering processes in the EI698-VD alloy.

Within the elastic-plastic range of the tensile curve, strain and load drop in alternation with subsequent monotonic loading sections. Subsequent to a drop in load, the tensile curve reveals a slope that is similar to that of the elastic mode. Thus, for low values of accumulated plastic strain, the tangent modulus ${\mathrm{E}}_{\tan }=\mathrm{d}\sigma /\mathrm{d}\epsilon$${\mathrm{E}}_{\tan }=\mathrm{d}\sigma /\mathrm{d}\epsilon$E_(tan)=dsigma//depsi\mathrm{E}_{\mathrm{tan}}=\mathrm{d} \sigma / \mathrm{d} \varepsilon${\mathrm{E}}_{\tan }=\mathrm{d}\sigma /\mathrm{d}\epsilon$ (Figs. 6 and 7) when loading after a load drop is similar in value to the E (Tab. 2) for a given temperature. Then, ${\mathrm{E}}_{\tan }$${\mathrm{E}}_{\tan }$E_(tan)\mathrm{E}_{\tan }${\mathrm{E}}_{\tan }$ decreases as the strain $\epsilon$$\epsilon$epsi\varepsilon$\epsilon$ increases during monotonic tension. The relationship between ${\mathrm{E}}_{\tan }$${\mathrm{E}}_{\tan }$E_(tan)\mathrm{E}_{\tan }${\mathrm{E}}_{\tan }$ values and $\epsilon$$\epsilon$epsi\varepsilon$\epsilon$ can be approximated by a logarithmic function (Fig. 7, Eqn. 4).

where ${\mathrm{B}}_1=-3.071\cdot {10}^4\mathrm{MPa},{\mathrm{B}}_2=6.626\cdot {10}^4\mathrm{MPa}$${\mathrm{B}}_1=-3.071\cdot {10}^4\mathrm{MPa},{\mathrm{B}}_2=6.626\cdot {10}^4\mathrm{MPa}$B_(1)=-3.071*10^(4)MPa,B_(2)=6.626*10^(4)MPa\mathrm{B}_{1}=-3.071 \cdot 10^{4} \mathrm{MPa}, \mathrm{B}_{2}=6.626 \cdot 10^{4} \mathrm{MPa}${\mathrm{B}}_1=-3.071\cdot {10}^4\mathrm{MPa},{\mathrm{B}}_2=6.626\cdot {10}^4\mathrm{MPa}$ for ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$ and ${\mathrm{B}}_1=-3.124\cdot {10}^4\mathrm{MPa},{\mathrm{B}}_2=5.132\cdot {10}^4\mathrm{MPa}$${\mathrm{B}}_1=-3.124\cdot {10}^4\mathrm{MPa},{\mathrm{B}}_2=5.132\cdot {10}^4\mathrm{MPa}$B_(1)=-3.124*10^(4)MPa,B_(2)=5.132*10^(4)MPa\mathrm{B}_{1}=-3.124 \cdot 10^{4} \mathrm{MPa}, \mathrm{B}_{2}=5.132 \cdot 10^{4} \mathrm{MPa}${\mathrm{B}}_1=-3.124\cdot {10}^4\mathrm{MPa},{\mathrm{B}}_2=5.132\cdot {10}^4\mathrm{MPa}$ for ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$ are the temperature characteristics. It is a well-known fact that plastic strain is directly implicated in the generation of defects, pores, and cracks in materials. A substantial number of concepts for the evaluation of material degradation (damage) are predicated on alterations in the Young's modulus during fatigue tests or in operational conditions [33]. The tangent modulus is sensitive to the mobility of defects, primarily dislocations, as well as dislocation clusters and structures (cells, walls), grain
boundaries, vacancies, microcracks, and pores (at large strains) [34,35]. The observed change in the values of the tangent modulus ${\mathrm{E}}_{\text{tan}}$${\mathrm{E}}_{\text{tan }}$E_("tan ")\mathrm{E}_{\text {tan }}${\mathrm{E}}_{\text{tan }}$ (Fig. 7) as the accumulated plastic strain increases can be attributed to the coupled effect of the generation of macro and micro-defects. The tangent modulus decreases in accordance with the principle that, as plastic strain accumulates, the increase in strain is achieved by increasingly easier dislocation movement rather than elastic stretching of the lattice [36,37]. Subsequent to unloading, the material exhibits a high density of mobile dislocations and back stresses. Upon reloading, plastic deformation occurs almost instantaneously. The movement of dislocations is facilitated by internal stresses, thereby reducing the necessary increase in external stress. This results in the same dɛ requiring less do.

For 400 and ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$, the stress drop $\mathrm{\Delta }\sigma$$\mathrm{\Delta }\sigma$Delta sigma\Delta \sigma$\mathrm{\Delta }\sigma$ (see Fig. 8) on the tensile curve shows three regions with different behavior. At the initial regime of elastic-plastic strain (A regime, Fig. 8), the stress drop $\mathrm{\Delta }\sigma$$\mathrm{\Delta }\sigma$Delta sigma\Delta \sigma$\mathrm{\Delta }\sigma$ increases rapidly from initial values of 6 and 20 MPa for 400 and ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$ to 20 and 40 MPa ( $\epsilon \approx 0.04$$\epsilon \approx 0.04$epsi~~0.04\varepsilon \approx 0.04$\epsilon \approx 0.04$, see Fig. 8) at the beginning of the regime of stable $\mathrm{\Delta }\sigma$$\mathrm{\Delta }\sigma$Delta sigma\Delta \sigma$\mathrm{\Delta }\sigma$ growth (B regime, Fig. 8). When strain values of approximately 0.25 and $\mathrm{\Delta }\sigma =50$$\mathrm{\Delta }\sigma =50$Delta sigma=50\Delta \sigma=50$\mathrm{\Delta }\sigma =50$ and 80 MPa are reached for 400 and ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$, a period of unstable $\mathrm{\Delta }\sigma$$\mathrm{\Delta }\sigma$Delta sigma\Delta \sigma$\mathrm{\Delta }\sigma$ begins (C regime, Fig. 8) before the specimen ruptures. Actually, during high-temperature testing procedure, the specimen was exposed to cyclic loading with a $\mathrm{\Delta }\sigma$$\mathrm{\Delta }\sigma$Delta sigma\Delta \sigma$\mathrm{\Delta }\sigma$ stress amplitude at mean stress at the level of the ultimate strength. It should be noted that at a temperature of ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$, the summary contribution of all $\mathrm{\Delta }{\omega }_{\text{unload}}$$\mathrm{\Delta }{\omega }_{\text{unload }}$Deltaomega_("unload ")\Delta \omega_{\text {unload }}$\mathrm{\Delta }{\omega }_{\text{unload }}$ (see Fig. 6) ( $0.0002422\dots 0.1173\mathrm{MJ}\cdot {\mathrm{m}}^{-3}$$0.0002422\dots 0.1173\mathrm{MJ}\cdot {\mathrm{m}}^{-3}$0.0002422 dots0.1173MJ*m^(-3)0.0002422 \ldots 0.1173 \mathrm{MJ} \cdot \mathrm{m}^{-3}$0.0002422\dots 0.1173\mathrm{MJ}\cdot {\mathrm{m}}^{-3}$ ) and $\mathrm{\Delta }{\omega }_{\text{load}}(0.0004617\dots 0.04133\mathrm{MJ}\cdot {\mathrm{m}}^{-3})$$\mathrm{\Delta }{\omega }_{\text{load }}\left(0.0004617\dots 0.04133\mathrm{MJ}\cdot {\mathrm{m}}^{-3}\right)$Deltaomega_("load ")(0.0004617 dots0.04133MJ*m^(-3))\Delta \omega_{\text {load }}\left(0.0004617 \ldots 0.04133 \mathrm{MJ} \cdot \mathrm{m}^{-3}\right)$\mathrm{\Delta }{\omega }_{\text{load }}(0.0004617\dots 0.04133\mathrm{MJ}\cdot {\mathrm{m}}^{-3})$ to the total fracture energy ${\omega }_{\mathrm{fe}}=351.91\mathrm{MJ}\cdot {\mathrm{m}}^{-3}($${\omega }_{\mathrm{fe}}=351.91\mathrm{MJ}\cdot {\mathrm{m}}^{-3}($omega_(fe)=351.91MJ*m^(-3)(\omega_{\mathrm{fe}}=351.91 \mathrm{MJ} \cdot \mathrm{m}^{-3}(${\omega }_{\mathrm{fe}}=351.91\mathrm{MJ}\cdot {\mathrm{m}}^{-3}($ see Tab. 2) is only 9.168 $\mathrm{MJ}\cdot {\mathrm{m}}^{-3}$$\mathrm{MJ}\cdot {\mathrm{m}}^{-3}$MJ*m^(-3)\mathrm{MJ} \cdot \mathrm{m}^{-3}$\mathrm{MJ}\cdot {\mathrm{m}}^{-3}$ or $2.54\mathrm{\%}$$2.54\mathrm{\%}$2.54%2.54 \%$2.54\mathrm{\%}$.

The fracture of the specimens was accompanied by the formation of a neck at temperatures between 25 and ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$ (Figs. 9-11). At temperatures of 25 and ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$, two typical zones can be observed in the neck region: the central fibrous zone, where the pores coalesced as they expanded, and the ring-shaped shear lip zone (Figs. 9, 10). In contrast, fracture at higher temperatures of 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ occurred in the absence of localized plastic strain in the neck region, as evidenced in Figs. 12 and 13. Increasing the test temperature of the specimens to 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ resulted in more uniform transverse strain along the gauge length of the specimens.
The ${25}^{\circ }\mathrm{C}$${25}^{\circ }\mathrm{C}$25^(@)C25^{\circ} \mathrm{C}${25}^{\circ }\mathrm{C}$ specimen achieved high strain values (see Tab. 2 and Fig. 3) during tensile testing, causing the appearance of intersecting slip lines (Fig. 9). The angle of orientation of the slip lines to the loading axis was found to be ${43}^{\circ }{7}^{\prime }$${43}^{\circ }{7}^{\prime }$43^(@)7^(')43^{\circ} 7^{\prime}${43}^{\circ }{7}^{\prime }$ (Fig. 9, Tab. 3), which corresponded to the plane of maximum shear stress. The fracture surface is typical of the mechanism of ductile generation and coalescence of pores. The circular area in the center of the failure surface is the site of an internal crack formed from a multitude of pores. Multiple surface defects were identified on the cylindrical surfaces of the fractured specimens, located primarily normal to the loading axis or at a small angle above and below the rupture plane.

A small decrease in plasticity was observed at a temperature of ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$ (Tab. 2 and Fig. 10). The presence of surface defects became more consistent. However, the fracture mechanism remained ductile. Deformations in the neck occurred in different slip planes at an angle of ${43}^{\circ }{21}^{\prime }$${43}^{\circ }{21}^{\prime }$43^(@)21^(')43^{\circ} 21^{\prime}${43}^{\circ }{21}^{\prime }$ (see Fig. 10, Tab. 3), in the plane of maximum tangential stresses.

The behaviour of the alloy at a temperature of ${550}^{\circ }\mathrm{C}$${550}^{\circ }\mathrm{C}$550^(@)C550^{\circ} \mathrm{C}${550}^{\circ }\mathrm{C}$ was found to be qualitatively and quantitatively similar to that at ${400}^{\circ }\mathrm{C}$${400}^{\circ }\mathrm{C}$400^(@)C400^{\circ} \mathrm{C}${400}^{\circ }\mathrm{C}$, with a continuing trend toward a moderate decrease in strength and plasticity (Fig. 3, Tab. 2). A ductile mechanism of deformation and fracture was observed. The deformation proceeded at an angle of ${49}^{\circ }{30}^{\prime }$${49}^{\circ }{30}^{\prime }$49^(@)30^(')49^{\circ} 30^{\prime}${49}^{\circ }{30}^{\prime }$ (Fig. 11, Tab. 3) to the loading axis, occurring in two planes. A minor portion of the fracture surface in the central region was found to correspond to the fibrous zone of the ductile formation and coalescence of pores, as observed at lower temperatures. However, the majority of the failure surface was formed by ductile shearing.
At temperatures of 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$, numerous semi-elliptical microcracks and discrete crack fronts marks are observed in the rupture surface. The Figs 12 and 13 show that large cracks at temperatures of 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ are predominantly located at the boundaries of localized slip bands. Additionally, at ${650}^{\circ }\mathrm{C}$${650}^{\circ }\mathrm{C}$650^(@)C650^{\circ} \mathrm{C}${650}^{\circ }\mathrm{C}$, the presence of smaller cracks on the specimen surface oriented perpendicularly to the loading axis is indicative of fracture at the grain boundary [38]. The cause of the transition from transgranular fracture to intergranular fracture [11] in nickel alloys, as is widely attributed to the degradation of cohesive bonds at the grain boundary as a result of the intensification of diffusion and phase changes with increasing temperature. It is also known that non-crystallographic slip bands intensify the formation of macro-cracks and intergranular fracture [39]. Observations made at temperatures of 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ reveal the interaction and coalescence of multiple minor cracks on the surface of the specimens (see Figs. 12 and 13). Thus, at ${650}^{\circ }\mathrm{C}$${650}^{\circ }\mathrm{C}$650^(@)C650^{\circ} \mathrm{C}${650}^{\circ }\mathrm{C}$, the fracture of the specimen occurred by a shear in the plane at an angle of ${40}^{\circ }{1}^{\prime }$${40}^{\circ }{1}^{\prime }$40^(@)1^(')40^{\circ} 1^{\prime}${40}^{\circ }{1}^{\prime }$, between surfaces approximately normal to the loading axis of the preceding crack growth, which is an indicator of the action of a mixed mode.
In turn, a rapid decrease in rupture strain at elevated temperatures may be caused by the occurrence of areas of localized elevated strain in the neighborhood of crack fronts, as well as strain bands [40]. Moreover, the true stresses in the neighborhood of such cracks at the moment of rupture are obviously significantly higher than the nominal engineering stresses and true stresses calculated taking into account the area of the specimen diameter in the rupture plane. This can be confirmed by the presence of clearly visible areas of localised intense plastic strain ahead of the fronts of semi-elliptical cracks on the surface of the specimens (Fig. 12). Concurrently, energy parameters, including fracture toughness, may be less influenced by the revealed features due to the comprehensive evaluation of the fracture process. Specimens tested at a temperature of ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$ fractured either in a similar behavior to specimens tested at ${650}^{\circ }\mathrm{C}$${650}^{\circ }\mathrm{C}$650^(@)C650^{\circ} \mathrm{C}${650}^{\circ }\mathrm{C}$, or, in some cases, crack growth was followed by quasi-brittle fracture (Fig. 12 and 13). The bifurcation in this process was controlled by the presence or relative orientation of surface cracks in the neighbourhood of the rupture initiation site.
The slip lines are less visible, which is typical of brittle fracture and comparatively low strain. As illustrated in Figs. 12 and 13, some of the observed cracks are formed from slip bands. The orientation of the shear stresses and slip plane under tension is typically at an angle of ${45}^{\circ }$${45}^{\circ }$45^(@)45^{\circ}${45}^{\circ }$ to the loading axis. As demonstrated in Tab. 3, a propensity for an increase in the slip angle values was observed as the temperature increased. It is evident that the slip angle exhibited a sensitivity to variations in temperature, concomitant with a decline in plasticity and strength characteristics. For 650 and ${700}^{\circ }\mathrm{C}$${700}^{\circ }\mathrm{C}$700^(@)C700^{\circ} \mathrm{C}${700}^{\circ }\mathrm{C}$, as illustrated in

Tab. 3, the minimum values for angle measurements are shown, given the variability of these values up to approximately a right angle.

The slip mode in nickel-base alloys is influenced by the composition and the process of heat treatment [38]. In order to identify the factors that may have an effect on the strength, plasticity, and changes in the fracture mechanism of the EI698VD alloy, the microstructure of the alloy must be analysed. SEM observations of the polished surface of a cut section from the initial state specimen revealed the presence of structural defects not only on the fracture surface, but also in the volume of the primary specimen. The surface in Fig. 14 is oriented perpendicular to the direction of the load.

The polished surface of the alloy was found to have pores (blue arrow) and microcracks (yellow arrow). The specimen was not subjected to mechanical loading. Therefore, the cracks found can be attributed to solidification cracks and liquation cracks. These cracks typically occur in zones exhibiting the presence of detrimental impurities with a low melting point. EDX analysis revealed a deviation in the chemical composition (Tab. 4) [2] of the surface observed in Fig. 14 from the nominal composition (Tab. 1). The most pronounced disparities are observed in Pb , where the mass fraction was found to be $0.09\mathrm{\%}$$0.09\mathrm{\%}$0.09%0.09 \%$0.09\mathrm{\%}$ (Tab. 4) compared to $<0.001\mathrm{\%}$$<0.001\mathrm{\%}$< 0.001%<0.001 \%$<0.001\mathrm{\%}$ (Tab. 1). Large Pb -rich particles have been observed in Fig. 15. The yellow arrows in Fig. 15 indicate an area characterised by a relative depletion of Ni and an enrichment of $\mathrm{Pb},\mathrm{P},\mathrm{Nb},\mathrm{Mo}$$\mathrm{Pb},\mathrm{P},\mathrm{Nb},\mathrm{Mo}$Pb,P,Nb,Mo\mathrm{Pb}, \mathrm{P}, \mathrm{Nb}, \mathrm{Mo}$\mathrm{Pb},\mathrm{P},\mathrm{Nb},\mathrm{Mo}$, and $\mathrm{Ti}.\mathrm{Pb}$$\mathrm{Ti}.\mathrm{Pb}$Ti.Pb\mathrm{Ti} . \mathrm{Pb}$\mathrm{Ti}.\mathrm{Pb}$ content is incompatible with the heat resistance characteristics. The presence of low-melting-point metals $(\mathrm{Pb})$$(\mathrm{Pb})$(Pb)(\mathrm{Pb})$(\mathrm{Pb})$ in alloys has been shown to result in a significant decrease in strength characteristics at temperatures exceeding $400-{600}^{\circ }\mathrm{C}$$400-{600}^{\circ }\mathrm{C}$400-600^(@)C400-600^{\circ} \mathrm{C}$400-{600}^{\circ }\mathrm{C}$ [41,42]. Cracks during the forging, rolling, and welding processes are frequently attributable to the influence of $\mathrm{Pb}.\mathrm{Pb}$$\mathrm{Pb}.\mathrm{Pb}$Pb.Pb\mathrm{Pb} . \mathrm{Pb}$\mathrm{Pb}.\mathrm{Pb}$ is not soluble in Ni and is prone to segregation at grain boundaries, which prevents the normal movement of dislocations and initiates intergranular fracture [43]. This may provide a valid explanation for the previously observed steep drop in fracture resistance and the change in fracture mechanism when the temperature increases above ${550}^{\circ }\mathrm{C}[3,11]$${550}^{\circ }\mathrm{C}[3,11]$550^(@)C[3,11]550^{\circ} \mathrm{C}[3,11]${550}^{\circ }\mathrm{C}[3,11]$.

EDX mapping in Fig. 15 reveals depleted Ni and enriched O , Si, C bands (red dashed lines) along the chains. In nickel alloys, carbides occur on slip bands [38,44], blocking dislocations, which additionally affects oxidation and increases internal stresses, causing microcracks to appear. In addition, an elevated Si content was identified in the composition of the alloy ( $0.61\mathrm{\%}$$0.61\mathrm{\%}$0.61%0.61 \%$0.61\mathrm{\%}$ instead of $\le 0.5\mathrm{\%}$$\le 0.5\mathrm{\%}$<= 0.5%\leq 0.5 \%$\le 0.5\mathrm{\%}$ ), accompanied by the presence of Si-rich particles (Fig. 15). SEM analysis of the etched surface of the alloy revealed the presence of spherical, cubic, prismatic, and polygonal particles (Fig. 16). As demonstrated in Fig.15, the spherical and triangular particles $(100-200\mathrm{nm})$$(100-200\mathrm{nm})$(100-200nm)(100-200 \mathrm{~nm})$(100-200\mathrm{nm})$ are enriched in Si and correspond to ${\mathrm{NiSi}}^{\circ },{\mathrm{NiSi}}_2[2,45,46]$${\mathrm{NiSi}}^{\circ },{\mathrm{NiSi}}_2[2,45,46]$NiSi^(@),NiSi_(2)[2,45,46]\mathrm{NiSi}^{\circ}, \mathrm{NiSi}_{2}[2,45,46]${\mathrm{NiSi}}^{\circ },{\mathrm{NiSi}}_2[2,45,46]$.

It is frequently postulated that methodologies which consider phase change and diffusion processes occurring at the nanoand micro-scale of the material should be utilised to predict the fatigue crack growth rate at elevated temperatures and under thermomechanical loading, as opposed to employing generalised fracture resistance parameters. This study demonstrates that the impact of temperature on fracture mechanisms, as well as the decline in strength and ductility, is qualitatively similar to the previously identified effect of temperature on increasing the fatigue crack growth rate in the EI698-VD alloy [3,11]. Consequently, the damage impact parameter A, determined using a uniaxial monotonic tensile curve, has been demonstrated to predict fatigue crack growth characteristics over a broad range of temperature conditions [3]. The temperature effect on the change in fatigue crack growth resistance under isothermal and thermo-mechanical loading conditions can be characterised using monotonic uniaxial tensile characteristics. This method is less costly compared to data obtained from transmission and scanning electron microscopy, as well as other methods of investigating material structure. Nevertheless, data on the microstructure of alloys is of obvious importance for understanding the mechanisms of the processes involved and improving the characteristics of alloys.

Adetailed investigation was performed into the fracture mechanisms of smooth cylindrical specimens made of polycrystalline heat-resistant nickel-based alloy XH73MBTU-VD (EI698-VD) under uniaxial tension in the temperature range of $25-{700}^{\circ }\mathrm{C}$$25-{700}^{\circ }\mathrm{C}$25-700^(@)C25-700^{\circ} \mathrm{C}$25-{700}^{\circ }\mathrm{C}$. Both external and internal defects in the alloy structure were identified and described. Observations of the morphology and topology of the alloy microstructure were carried out using SEM and EDX methods. A relationship was established between the features of the deformation process, the fracture mechanism, and the strength and plasticity characteristics. The deviation of the composition of the alloy batch under consideration in this study from the nominal values does not extend the results obtained to specimens and parts of the correct composition.
The high-temperature behaviour characteristics of the alloy with an increased level of detrimental impurities, as identified in the paper, can lead to the unexpected formation of surface defects and cracks, as well as a loss of efficiency and failure of the gas turbine engine.
Below are the summarised results and conclusions of this work.

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