Introduction

Heat-resistant steels with 9–12%Cr are widely used as structural materials for boilers, steam main tubes, and turbines of fossil power plants to increase thermal efficiency [1, 2]. The tempered martensite lath structure (TMLS) consisting of prior austenite grains (PAG), packets, blocks, and laths and containing a high density of separate dislocations and a dispersion of secondary-phase particles evolves after heat treatment [1–5]. The superior creep resistance of these steels is attributed to the stability of the TMLS under long-term aging and creep provided by the M23C6-type carbides and M(C,N) carbonitrides precipitated at boundaries and within the ferritic matrix, respectively, during tempering, and the boundary Laves phase particles precipitated during creep [1, 2, 4–12]. The main limiting factor for the increase in the service temperature of 9–12%Cr steels is the creep strength breakdown accompanied by premature fracture at a low stress due to the evolution of a dispersion of secondary phases and the transformation of the TMLS to a subgrain structure [7, 13–15].

Under creep the lattice mobile dislocations can interact with intrinsic dislocations of lath boundaries, which leads to the mutual annihilation of the dislocations with the opposite sign [5, 6, 16–19]. Dislocation climb is a necessary condition for the occurrence of this reaction, because annihilation events take place by climb of two dislocations with the opposite signs through critical annihilation distance [17–20]. Lath boundaries play a role of sinks for lattice dislocations [19]. Concurrently, climb of dislocations in the lath boundaries leads to the transformation of these boundaries, which are, in fact, irregular dislocation networks, to subboundaries. These processes are termed as the knitting reactions and relive the internal long-range strain fields [6, 7, 16–23]. Next, the migration of the lath boundaries leads to the formation of a well-defined subgrain structure instead of the TMLS [5, 7–9, 12]. Kostka et al. showed that a dispersion of carbides plays a key role in impeding the knitting reaction and hindering lath boundary migration by exerting Zener drag force [6, 22]. M(C,N) (where M—V or Nb) carbonitrides and boundary M23C6 carbides are highly effective in pinning the mobile lattice dislocations and preventing their interaction with sessile dislocations, which compose the lath boundaries [6, 7]. Boundary M23C6 carbides and Laves phase particles that exert a high Zener drag force hinder subgrain coarsening [7, 9–11]. Matrix M(C,N) carbonitrides provide a minor contribution to the overall pinning pressure [7, 9–11].

The dispersion of secondary-phase particles withstands short-term creep [1, 4–15]. Coarsening of the boundary M23C6 carbides and the Laves phase particles through Ostwald ripening and the replacement of nanoscale M(C,N) carbonitride particles by Z-phase (CrVN) micron particles [1, 7, 9–12, 24–29] diminish their efficiency as pinning agents and facilitate the knitting reaction and subboundary migration. The enhanced creep strength could be achieved through a pronounced stability of the dispersion of the secondary phase under long-term creep. An effective way to attain this goal is to slow down the diffusion using substitutional additives, such as Co and W, that decrease the rate of dislocation climb [1, 5, 7, 9, 30–32]. These additions significantly hinder the coarsening of M23C6 carbides and Laves phase particles, and the replacement of M(C,N) carbonitrides by Z-phase particles, which results in the superior creep resistance of martensitic steels [9, 13, 31, 32]. The efficiency of W as an alloying element in hindering diffusion is greater than that of Co [1]. However, no depletion of Co from the ferritic matrix occurs under creep conditions, whereas W and Mo have limited solubility within ferrite, and their excessive content is depleted from the solid solution leading to the precipitation of W/Mo-rich particles, such as Laves phase particles Fe2(W,Mo) or M6C carbides under creep conditions [1, 7, 9–11, 31, 33–42]. This depletion does not occur in 9%Cr steel containing no or <1 wt% W [1, 7, 42]. Depletion of the solid solution by these elements induces a significant coarsening of the M23C6 carbides and the Laves phase particles [1, 4, 7–11] that greatly deteriorates the creep resistance and correlates with the creep strength breakdown and the replacement of TMLS by well-defined subgrain structure [1, 4, 7, 9–15, 26, 29, 42].

It is worth noting that only a few limited examinations of the W-effect on creep behavior have been carried out for Co-free high-chromium martensitic steels [32–35, 42]. The aim of the present work is to examine the effect of a 1 wt% W addition on the creep behavior and microstructural evolution subjected to long-term aging and creep. To achieve this goal, a 0.1C–0.05N–9Cr–3Co–3W–0.5Mo–0.2V–0.05Nb steel is examined. The experimental data obtained are compared with data for a P92 steel [10, 43].

Materials and methods

A steel, which is denoted here as 9Cr3W, with the chemical composition (in wt%) Fe (bal.)–0.12C–9.5Cr–3.2Co–3.1W–0.45Mo–0.06Si–0.2Mn–0.2V–0.06Nb–0.05N–0.005B, was prepared by air melting 20 kg ingots. Square bars with a 13 × 13 mm2 cross section were cast and hot forged by the Central Research Institute for Machine-Building Technology, Moscow, Russia. This steel was solution treated at 1050 °C for 30 min, cooled in air, and subsequently tempered at 750 °C for 3 h. Flat specimens with a gage length of 25 mm and a cross section of 7 × 3 mm2, and cylindrical specimens with gage length of 100 mm and a 10 mm diameter were crept until rupture at 650 °C under an applied stress ranging from 100 to 220 MPa with a step of 20 MPa.

The structural characterization was carried out using a transmission electron microscope JEOL-2100 (TEM) with an INCA energy-dispersive X-ray spectrometer (EDS) and a Quanta 600FEG scanning electron microscope (SEM) on ruptured creep specimens. Identification of the precipitates was performed based on combination of EDS composition measurements of the metallic elements using the manufacturer’s library of internal reference standards and indexing of the electron diffraction patterns using TEM. The subgrain sizes were evaluated on TEM micrographs using the linear intercept method including all clearly visible subboundaries. The dislocation densities in the grain/subgrain interiors were estimated as a number of intersections of individual dislocations with upper/down foil surfaces per unit area on at least six arbitrarily selected typical TEM images for each data point [44]. The dislocation observation was carried out under multiple-beam conditions with large excitation vectors for several diffracted planes for each TEM image. M6C carbides and Laves phase particles were separated from each other using TEM EDS composition measurements and using the particle-size distribution. The volume fractions of the precipitated phases were calculated using the Thermo-Calc software with the TCFE6 database for the following steel composition (in wt%): Fe–0.1C–9.4Cr–0.5Mo–3.0W–3.0Co–0.2V–0.05Nb–0.05N–0.005B. The following phases were selected independently for calculation: BCC, FCC, M23C6 carbide, Laves phase (Fe2(W,Mo) (C14).

Experimental results

Initial structure

The structural characteristics of the TMLS of the 9Cr3W steel after normalizing and tempering at 750 °C are summarized in Table 1. The microstructure and the distributions of the secondary-phase particles were described in a recent work [45] in detail. Major portions of the M23C6 carbides were located on the high-angle boundaries of the PAGs/packets/blocks, whereas the M23C6 carbides along the lath boundaries were rarely observed (Fig. 1a, c). In addition, the W-rich M6C carbides (Fe3W3C) and the Laves phase (Fe2W) particles were found at the boundaries (Fig. 1d, e). The dimensions of the fine-boundary M23C6 carbides and the Laves phase particles were nearly the same (<100 nm) (Table 1), whereas the average size of the M6C carbides was ~350 nm (Fig. 1d, e). As a result, a wide size distribution of W-rich particles was observed (Fig. 1b). M(C,N) carbonitrides were uniformly distributed within the martensitic laths (Fig. 1c). Two-phase separation of these carbonitrides [1, 8, 45] into V-rich M(C,N), with a plate-like shape and a mean longitudinal size of 20 nm, and Nb-rich M(C,N) carbonitrides, with a round shape and an average size of ~40 nm, took place.

Table 1 Evolution of structural parameters after tempering at T = 750 °C, aging at T = 650 °C, and creep testing at T = 650 °C when subject to different stresses
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Figure 1
figure 1

Typical microstructure of the 9Cr3W steel after normalizing and tempering at 750 °C: TEM of foils (a) and replicas (c–e) and the size distribution of the W-rich precipitates (b)

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Creep behavior

Figure 2 shows the creep rupture data of the steels at a temperature of 650 °C. The variation in the rupture time with an applied stress for a P92-type steel [43] was also presented for comparison. The 3%Co and 3%W additions significantly increased the creep strength under the high applied stresses. Approximately 170-, 45-, and 40-fold differences in the creep rupture time were observed between the P92 [43] and the 9Cr3W steels at applied stresses of 160, 140, and 100 MPa, respectively. Under the low applied stress (less 140 MPa), the effect of the Co and W additives on the creep strength tends to diminish. Well-defined creep strength breakdown [1, 7, 13–15, 43] was observed at ~2000 h of creep for both steels. The 3%Co and 3%W additives increased the level of an applied stress, at which the creep strength breakdown was observed, from 110 to 160 MPa. It is worth noting that the high B and Mo-free 9Cr–3Co–3W steels developed at the National Institute for Materials Science (NIMS) exhibited creep strength breakdown at applied stress of 120 MPa with corresponding rupture time of ~104 h (MARBN10 steel with B content of 0.01 wt%) or no the creep strength breakdown appeared up to rupture times of ~4 × 104 h (MARBN12 steel with B content of 0.012 wt%) [46]. Superior creep strength of these steels was attributed to a strong effect of such elements as B, N, Mn, Ni on a dispersion of boundary M23C6 carbides [46–48].

Figure 2
figure 2

Time to rupture versus stress curve shows the creep strength breakdown for the 9Cr3W and P92 steels [36]

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The creep rate versus time and strain curves at 650 °C for the different nominal stresses (100–200 MPa) are shown in Fig. 3a, b. The creep behavior was typical for heat-resistant martensitic steels containing dispersed particles. The minimum creep rate decreased from approximately 10−7 to 10−10 s−1 with a decrease in the applied stress from 220 to 100 MPa. There was a linear dependence between the minimum creep rate and the applied stress (Fig. 3c). The experimental data obey a power law relationship throughout the whole range of the applied stress of the usual form [1, 7, 49, 50]:

Figure 3
figure 3

Creep rate versus time (a) and creep rate versus strain (b) curves at 650 °C and different stresses from 100 to 200 MPa, the stress dependence of the minimum creep rate (c) of the steel studied in comparison with data for P92 steel [36]

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$$ \dot{\varepsilon }_{\hbox{min} } = A \times \sigma^{n} \exp \left( {\frac{ - Q}{RT}} \right), $$
(1)

where \( \dot{\varepsilon }_{\hbox{min} } \) is the minimum creep rate, σ is the applied stress, Q is the activation energy for a plastic deformation, R is the gas constant, T is the absolute temperature, A is a constant, and n is the “apparent” stress exponent. This plot provides the best linear fit with a regression coefficient of 0.98 for n = 9 for the whole applied stress interval. This n value at all tested stress regimes remains constant. The steady-state stage of the 9Cr3 W steel was controlled using the same process for short- and long-term regions at a creep rate ranging from 10−6 to 10−10 s−1. This clearly indicates that there is no creep strength breakdown during the steady-state stage of creep of the 9Cr3 W steel [7, 13]. Abe showed [13] that the time to rupture correlates with the minimum creep rate, \( \dot{\varepsilon }_{\hbox{min} } \), in a Co-free 9% Cr steel (P91). However, no such correlation was observed in 9%Cr steels containing ≥2 wt% W [7, 21, 23]. At applied stress of ≥100 MPa, the creep strength breakdown was not accompanied by a decrease in the stress exponent, n, as in a P91 steel [13].

In contrast with the dependencies of the applied stress versus the rupture time (Fig. 2), the distinct inflection point for the transition from a short-term region to a long-term one by shapes of aforementioned curves was observed at an applied stress of 120 MPa. The elongation-to-failure increases with a decrease in the applied stresses to 140 MPa and then decreases further at 120 and 100 MPa (Fig. 4a). The 3- and 5-fold decreases in the ductility take place at 120 and 100 MPa, respectively, compared with the elongation-to-failure at an applied stress of 140 MPa. The off-set strain, εmin, which is the strain where the minimum creep rate is attained, exhibits linear dependence on the applied stress (Fig. 4b). The onset of acceleration creep occurs when the creep strain achieves 1.5–3% and less than 1% at high stresses and low stresses, respectively (Fig. 4b). The decrease in the off-set strain with a decrease in the applied stress supports the fact that the deformation in the transient creep stage becomes localized at low stresses [13]. Effect of an applied stress on the contribution to creep deformation incurred by the transient creep strain, ε T, creep strain accumulation at the minimum creep rate (ε min × t r, where t r is rupture time), and tertiary creep strain, ε 3, [13, 33, 34] is shown schematically in Fig. 4c. It is seen that at applied stress ≥140 MPa, the values of all these strain ranges (ε T, (ε min × t r) and ε 3) slightly depend on the applied stress. A decrease in the applied stress from 140 to 120 MPa leads to the 3- and 4-fold decreases in the ε T and ε 3 values, respectively, and a −22% decrease in the ε min × t r value.

Figure 4
figure 4

Effect of applied stress on the elongation-to-rupture (a), the off-set strain at which the minimum creep rate was attained for the 9Cr3W steel (b), and the contribution to creep deformation incurred by the transient creep strain, ε T, creep strain accumulation at the minimum creep rate, ε min × t r, and tertiary creep strain, ε 3 (c)

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It was recently shown that creep strength breakdown is a tertiary creep phenomenon [7, 13]. The Monkman–Grant relationship [51] relating the rupture time, τ r, to the minimum or steady-state creep rate is described as:

$$ \tau_{r} = (c'/\dot{\varepsilon }_{\hbox{min} } )^{m'} , $$
(2)

where c′ and m′ are constants. This relationship is used for the prediction of creep life of heat-resistant steels [1, 13]. Analysis of Eq. (2) for the studied steel (Fig. 5) shows that this approach is suitable for describing the relation of rupture time with the off-set strain rate, \( \dot{\varepsilon }_{\hbox{min} } \). For short-term conditions, which corresponds to a τ r less than approximately 3500 h, τ r is inversely proportional to \( \dot{\varepsilon }_{\hbox{min} } \) (Fig. 5) at m′ = 1. The constant c′ is 3.0 × 10−2. For long-term conditions, which corresponded to a τr greater than approximately 3500 h, the relationship between τr and \( \dot{\varepsilon }_{\hbox{min} } \) deviates downward. The transition from short-term creep to long-term creep appears as the deviation from the linear dependence described by Eq. (2), which indicates m′ < 1 [13], at an applied stress ≤120 MPa. In the 9Cr steels containing ≥2 wt% W, the creep strength breakdown is attributed to the strong acceleration of tertiary creep [7].

Figure 5
figure 5

Minimum creep rate as a function of time to rupture for the 9Cr3W steel

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Figure 6a demonstrates the change in the slope of the curves shown in Fig. 3b in creep acceleration region (dln \( \dot{\varepsilon }_{r} \)/dε) estimated using the method suggested in [13], where \( \dot{\varepsilon }_{r} \) and ε are the creep rate and the creep strain, respectively, at a time t. Value of dln \( \dot{\varepsilon }_{r} \)/dε increases with a decrease in the stress. The dependence of the strain rate on the strain in the acceleration region is described as [13]:

Figure 6
figure 6

Stress dependence of dln \( \dot{\varepsilon }_{r} \)/dε in the acceleration creep stage of the 9Cr3W steel

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$$ \dot{\varepsilon } = \dot{\varepsilon }_{0} \exp (n\varepsilon )\exp (m\varepsilon )\exp (d\varepsilon )\exp (i\varepsilon ) $$
(3)
$$ {\text{dln}}\dot{\varepsilon }{\text{ /d}}\varepsilon = n + m + d + i, $$
(4)

where \( \dot{\varepsilon }_{0} \) is the initial creep rate, n is the stress exponent from Eq. (1) and is 9 for the whole applied stress interval for the 9Cr3W steel, m is the microstructure degradation parameter, d is damage parameter due to the creep voids, and i describes the localized creep deformation [13]. As suggested in [13], parameter d is neglected because there is no evidence for cavitation in the 9Cr3W steel. Therefore, dln \( \dot{\varepsilon }_{r} \)/dε results from the parameters n, m, and i. At high stresses of 200–140 MPa, the dln \( \dot{\varepsilon }_{r} \)/dε ranges from 45 to 60. Therefore, when subject to stresses ranging from 200 to 140 MPa, the microstructural evolution has an insignificant effect on the tertiary creep behavior [13]. Conversely, at an applied stress of <120 MPa, dln \( \dot{\varepsilon }_{r} \)/dε increases to approximately 130 indicating a key role of microstructural changes in the softening of the 9Cr3W steel during tertiary creep. Therefore, creep strength breakdown does not coincide with the deviation from the linear dependence of the Monkman–Grant relationship that occurred at applied stresses less than 120 MPa, and during tertiary creep, the acceleration of the creep rate by the strain, dln \( \dot{\varepsilon }_{r} \)/dε, distinctly differs from that at greater applied stresses. Therefore, the present data are unambiguously indicative that the creep strength breakdown is a tertiary creep phenomenon [1, 7, 13], is distinguished by a strong decrease in the ε 3 value, and increased the rate of acceleration of tertiary creep characterized a high dln \( \dot{\varepsilon }_{r} \)/dε value at an applied stress ≤120 MPa.

Hardness behavior

In the grip portion of the creep specimens, the hardness remained virtually unchanged up to ~103 h and dropped at approximately 2000 h (Fig. 7a). This effect of long-term aging on hardness correlates with a breakdown in the creep strength curve (Fig. 2) and a depletion of the major portion of the W from the solid solution (Fig. 7b, c). It is worth noting that the Co content in the solid solution is independent of the exposure time for any creep conditions and under long-term aging. Strong strain-induced depletion of W and Mo from the solid solution took place at an exposure time of less than 103 h (Fig. 7c). Thermodynamic equilibrium of the elemental content in the solid solution was attained in specimens aged for 2000 h. Therefore, the depletion of W and Mo was complete in the short-term creep region. It is worth noting that, at rupture times of ≥2000 h, the Moeq = Σ(Mo + 0.5W) in the present steel and the 3%Co P92-type steel [7] became the same. Therefore, an increased W content provides additional solutes of this element in solid solution for only a limited time.

Figure 7
figure 7

Hardness decrease in the grip portion (a) was accompanied by the depletion of W from the solid solution in the grip (b) and the gage sections (c)

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Microstructures after long-term aging

Effect of long-term aging on microstructure and a dispersion of secondary phases was examined in the grip portion of samples, in which the thermally aged condition without stress occurred, compared to the gage section. No significant changes in the TMLS took place under long-term aging (Fig. 8; Table 1) even after 1.6 × 104 h. The lath thickness remained nearly unchanged, and the dislocation density decreased by a factor of more than 2 after 3.5 × 103 h (Figs. 8, 9a; Table 1). Concurrently, minor portions of the laths transformed to subgrains with approximately round shapes. However, the average size of subgrains and the lath thickness were nearly the same (Table 1). Therefore, this transformation occurred due to the subdivision of some laths by the transverse boundaries and was not accompanied by subgrain coarsening.

Figure 8
figure 8

Microstructure of the 9Cr3W steel in the grip portion after long-term aging at T = 650 °C for 50 (a), 1703 (b), and 15,998 h (c)

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Figure 9
figure 9

Mean size of the subgrain/lath and dislocation spacing (a) and the mean size of particles in the grip (b) and gage sections (c) of specimens as a function of time in the 9Cr3W steel during creep tests at 650 °C subject to stresses of 100–220 MPa

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Additional precipitation of the Laves phase particles at the PAG boundaries occurred during short-term aging. Precipitation of fine particles at the lath boundaries continuously appeared (Fig. 8). As a result, the lath boundaries became decorated by fine Laves phase particles even after 1.6 × 104 h. A strong acceleration of the coarsening took place after the depletion of a major part of W from the solid solution, which led to the formation of the chains of coarse Laves phase particles along the boundaries of the PAGs (Figs. 7, 8). Full replacement of M6C carbides, which is transition phase, by the Laves phase, which is the thermodynamical equilibrium phase [45, 52], occurred after 50 h of aging.

The mean size of the M23C6 carbides remained nearly unchanged during long-term aging up to ~3.5 × 103 h, because insignificant additional precipitation of these carbides occurred (Fig. 9b; Table 1). As it was shown by O. Prat et al. [29], the M23C6 carbides can reach their equilibrium volume fraction for 300 h of aging in the 12%Cr steels with a high content of W and Co. Additional precipitation of M23C6 carbides was detected during creep in the 3 wt% Co-modified 9/12%Cr steels containing ≥3wt % W. A +20% increase in the average dimension was observed after up to ~1.6 × 104 h due to the coarsening of these carbides located at the boundaries of the PAGs/packets/blocks. The average sizes of the M23C6 carbides and the Laves phase particles in the present steel after long-term aging for 3 × 103 h were smaller compared to a 9Cr–3Co–3W–0.014B steel [48].

Furthermore, 50 h of aging resulted in a + 150% increase in the size of V-rich M(C,N) carbonitrides and a +75% increase in the dimensions of the Nb-rich particles (Fig. 9b; Table 1). No remarkable effect of further long-term aging on the distribution of M(C,N) carbonitrides was found. It is worth noting that an insignificant increase in the volume fraction of V-rich M(C,N) carbonitrides occurred. All V-rich M(C,N) examined contained ≤20 at.% Cr, and therefore, no evidence for the formation of a Z-phase was observed [24].

Short-term creep microstructures

When subject to short-term creep conditions, the lath structure is nearly retained because the difference in the lath thickness and the dislocation density between the grip and gage lengths was less than 42% (Table 1). A minor part of laths transformed to subgrains in a manner similar to long-term aging of ≥3.5 × 103 h. An insignificant increase in the lath thickness occurred (Fig. 9a; Table 1).

A major portion of the W and Mo that was depleted from solid solution was consumed for the formation of new Laves phase particles. A major portion of the Laves phase particles precipitated at the lath boundaries. The precipitation of this phase at the boundaries of the PAGs/packets/blocks also took place (Fig. 10a, b). As a result, a strong increase in the density of fine particles along lath boundaries led to the appearance of almost continuous chains of Laves phase particles at some of these boundaries. No strain-induced coarsening was detected (Figs. 9c, 10a–d). The dimensions of the Laves phase particles were nearly the same after long-term aging and short-term creep (Table 1).

Figure 10
figure 10

Microstructure of the steel in the gage sections of the specimens after short-term and long-term creep tests at 650 °C and stresses of a, b 220 MPa (50 h), c, d 140 MPa (3489 h), and e, f 100 MPa (15,998 h)

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Insignificant additional precipitation of the M23C6 carbides could be observed. In general, the dimensions of the M23C6 carbides remained nearly unchanged for short-term conditions (Figs. 9c, 10a–d; Table 1). At an applied stress of 140 MPa, weak evidence for strain-induced coarsening of M23C6 carbides appeared (Table 1). The size of these carbides remained ~100 nm up to rupture times of ~5000 h. The Thermo-Calc calculation predicted the existence of a unified (V,Nb)N nitride with a very low C content [45], whereas thermodynamically unstable separation of M(C,N) carbonitrides to Nb-rich and V-rich particles remained during creep condition. The dispersion of M(C,N) carbonitrides changed insignificantly (Fig. 9c).

Long-term creep microstructures

Transformation of the TMLS to a subgrain structure occurred during long-term creep conditions in the same manner as during long-term aging, but a portion of the subgrain structure was significantly greater than after long-term aging (Fig. 10e–f). In contrast with steels containing less W [7, 9–11], this evolution was not followed by extensive subgrain coarsening (Fig. 9a; Table 1). The subgrain size increased insignificantly from 0.6 to 0.8 µm. Only a twofold difference in the lattice dislocation density between the grip and gage sections was observed at 100 MPa. It was obvious that the TMLS exhibited an increased stability during long-term creep conditions. This stability was provided by the dispersion of M23C6 carbides, because extensive coarsening of the Laves phase particles occurs during long-term creep conditions (Figs. 9c, 10e–f; Table 1). The average size of the Laves phase achieved ~550 nm after a creep test at 100 MPa (rupture time of ~1.6 × 104 h) due to the rapid strain-induced growth. Distinct strain-induced coarsening of the M23C6 carbides appeared after creep at an applied stress <140 MPa (life time is ~3.5 × 103 h), and the size of these carbides was >200 nm (Figs. 9c, 10e–f).

No strain-induced coarsening of the Nb-rich M(C,N) occurred during long-term creep conditions (Table 1). In contrast, at an applied stress of 100 MPa, strain-induced coarsening resulted in a +60% increase in the average size of the V-rich M(C,N) particles compared with long-term aging (Fig. 9b–c; Table 1). In some V-rich carbonitride particles, the portion of Cr exceeded 30 at.% and, therefore, the Z-phase (CrVN nitride) appeared [24]. However, the dimensions of the Z-phase and the V-rich M(C,N) carbonitrides were ~50 nm, and the portion of Z-phase among all the V-rich carbonitrides was less than 5%. More details of the formation of Z-phase in steel studied were reported in a previous work [53]. Therefore, the formation of the Z-phase was unimportant for the creep resistance of the 9Cr3W steel. In general, long-term creep leads to insignificant changes in the distribution of M(C,N) carbonitrides even at an applied stress of 100 MPa.

Discussion

Increased W content and creep strength breakdown

Inspection of the experimental data showed that the 9Cr3W steel exhibited a well-defined creep strength breakdown that had no well-defined relation with the formation of the Z-phase [24–26] or static recovery [15], because no significant evolution of the dispersion of the M(C,N) carbonitrides under any creep condition and no transformation of a major portion of the lath structure to a subgrain structure occurred during long-term aging. Increasing the W content from 2 to 3 wt% suppresses these processes [7, 9]. The difference in microstructures evolved after creep up to rupture correlates with distinct difference in tertiary creep behavior (Figs. 4a, c, 5, 6) and has no sense to inflection point for creep strength versus rupture time dependence (Fig. 2). The onset of the creep strength breakdown almost matches the complete depletion of the excess W from the solid solution. It is worth noting that the 3 wt% W addition is the most effective in decreasing the off-set strain, and this positive effect was retained after depleting this element and Mo from the solid solution. It is obvious that the precipitation of the fine Laves phase particles at lath boundaries provides this positive effect [27, 29, 42], stabilizing the TMLS and preventing the knitting reaction between the lattice dislocations and the sessile dislocations that compose the lath boundaries.

Effect of applied stress on the Zener drag pressure

The boundary Laves phase particles, M23C6 carbides, and matrix M(C,N) carbonitrides are known to exert different Zener drag forces. The Zener pinning force exerted by the M(C,N) carbonitrides can be evaluated as [7, 9, 10, 22]:

$$ P_{\text{Z}} = \frac{{3\gamma F_{\text{V}} }}{d}, $$
(5)

where γ is the boundary surface energy per unit area (0.153 J/m2), F v is the volume fraction of the particles calculated using Thermo-Calc, and d is the mean size of particles, m.

The Zener drag pressure exerted by the boundary particles of the M23C6 and Laves phases can be estimated as [7, 9, 10, 22]:

$$ P_{\text{B}} = \frac{{\gamma F_{\text{vB}} D}}{{d_{{}}^{2} }}, $$
(6)

where D is the subgrain size/lath width in µm, and F vB is the fraction of the particles located at the boundaries. The pinning pressures were calculated separately for the M23C6 carbides and the Laves phase:

$$ P_{\text{B}} = \frac{{\gamma F_{\text{vB}} D_{0} }}{{d_{0}^{2} }} \cdot \frac{{\beta_{\text{i}} }}{{\beta_{ 0} }}, $$
(7)

where ß 0 and ß i are the densities of the M23C6 carbides or the Laves phase particles that were located along boundaries for the initial state and for each applied stress. The procedure for calculation of the Zener drag pressure for different types of particles was considered in previous works [7, 9] in detail.

The effect of the applied stress on the Zener drag pressures by three types of precipitates is shown in Fig. 11. It is seen that M(C,N) carbonitrides give an insignificant contribution to the overall pinning pressure for almost all conditions except at an applied stress of 100 MPa at which PZ and PB force exerted by the Laves phase particles become nearly equal. The main feature of the present steel is the fact that the greatest Zener drag was exerted by the Laves phase particles at applied stresses greater than 100 MPa, and the M23C6 carbides gave the main contribution to the overall Zener drag force only at an applied stress of 100 MPa. Overall, the Zener drag was great enough at all creep conditions to suppress boundary migration. At applied stresses less than 120 MPa, the overall pinning pressure became equal or less than the critical value of 0.12 MPa, at which the lath structure transformed to a subgrain structure [7]. Therefore, at applied stress ≤120 MPa, the degradation of the Zener drag force below the critical value [7] corresponds to the transition to long-term creep associated with increased rate of acceleration of tertiary creep. However, even at an applied stress of 100 MPa, the overall Zener drag force was able to provide no onset of the extensive subgrain coarsening [7]. As a result, the blocks delimited by the boundaries decorated by the M23C6 and Laves phase particles retain stability during long-term creep, whereas a major part of laths within these blocks transformed to subgrains. Therefore, the transition from short-term creep to long-term creep in the 9Cr3W steel correlates with the strain-induced coarsening of the M23C6 carbides and the Laves phase particles, and leads to transformation of a major part of the lath structure to a subgrain structure and to a remarkable decrease in the lattice dislocation density due to the knitting reaction providing the transformation of lath boundaries to subgrain boundaries followed by their migration.

Figure 11
figure 11

Change in the pinning pressures from the M23C6 carbides, the Laves phase, and the MX carbonitrides in the gage section on the grain and lath boundaries of the steel during creep tests at 650 °C under stresses of 100–220 MPa. The critical value corresponds to the pinning pressure, which is the pressure at which the transformation of TMLS into subgrain structure occurs and is 0.12 MPa based on previous investigations [7]

Full size image

Role of strain-induced coarsening of boundary particles in creep resistance

In the 9Cr–3Cr–3W steel, the role of high densely distributed and fine particles of Laves phase precipitated at lath boundaries in impeding the knitting reaction between free dislocations and the lath boundaries and exerting Zener forces on the low-angle boundaries is the same as the role of the M23C6 carbides [6, 7, 9, 10, 54]. However, resistance of the Laves phase particles to coarsening is significantly lower than one of the M23C6 carbides, and transition to long-term creep correlates with the onset of extensive coarsening of these particles [29] which leads to the dissolution of the fine particles of Laves phase precipitated at lath boundaries in accordance with well-known Gibbs–Thomson schema [55].

Strain-induced coarsening of M23C6 carbides during creep in high-Cr martensitic steels has been reported in several studies [7, 16, 56, 57]. K. Maruyama et al. showed [56] that the transition to long-term creep was attributed to the coarsening of these carbides in grip sections and to the strain-induced coarsening of these carbides under steady-state and tertiary creep. The 1 wt% W additives highly accelerate the strain-induced coarsening of Laves phase under long-term creep [7]. At an applied stress >120 MPa, under the short-term creep, no pronounced coarsening of these particles takes place in the grip and gage sections of creep specimens. In the long-term creep region, the onset of the tertiary creep stage even at a low strain correlates with the strain-induced coarsening of the M23C6 carbides and the Laves phase particles and a loss of the pinning pressure from these particles.

Abe suggested that precipitation of the Laves phase particles may provide dispersion strengthening [42]. The mechanism of this strengthening is not obvious if a dislocation glides across a lath and does not cross the lath boundaries. A mean dislocation path is equal to the lath thickness. However, it was recently shown by direct TEM observations [19] that dislocation glide occurs along a lath. This glide occurs slowly bowing out because both ends of these dislocations are connected to the mutually opposite lath boundaries. Sessile dislocations that compose the lath boundaries exert a high pinning stress, which is inversely proportional to the lath thickness. Precipitation of the Laves phase particles at the lath boundaries further increases this pinning stress. Climb of dislocation segments is necessary to overcome the boundary M23C6 carbides and Laves phase particles. This is why the depletion of W and Mo from solid solution has a minor effect on the minimum creep rate. The facilitation of general dislocation climb is partially compensated by the pinning stress exerted by the lath boundary particles. In addition, these particles hinder the knitting reaction because local dislocation climb is necessary to bypass these particles, i.e., the role of W and Mo as pinning agents for the knitting reaction as substitutional solutes and in the form of lath boundary Laves phase particles is the same. As a result, the dislocation density is high enough except for the case of creep to rupture when subject to an applied stress of 100 MPa. Strain-induced dissolution of the fine M23C6 carbides and the Laves phase particles at the lath boundaries promotes the knitting reaction, decreases the pinning stress for the dislocation glide, and facilitates coarsening of the laths and their transformation to subgrains. In the 9Cr3W steel, the transition from short-term creep to long-term creep is primarily attributed to this process.

Conclusions

  1. 1.

    The 0.1C–9Cr–3Co–3W–0.5Mo–VNbBN martensitic steel exhibited a creep strength breakdown as a sudden drop in the rupture time at 650 °C under an applied stress of 160 MPa. However, transition from short-term creep to long-term creep was characterized by the deviation from the linear dependence of the Monkman–Grant relationship and an increased value of the creep rate by strain in the acceleration region (dln \( \dot{\varepsilon }_{r} \)/dε) for low applied stresses and appeared at 120 MPa. No effect of these transitions on the power law relationship between the steady-state creep rate and the applied stress was found. This unique creep behavior is associated with strain-induced precipitation of fine particles of Laves phase at lath boundaries.

  2. 2.

    The TMLS remains nearly unchanged during long-term aging up to ~1.6 × 104 h and short-term creep due to a very high Zener drag force exerted by the Laves phase particles and the M23C6 carbides. No strain-induced coarsening of these particles and M(C,N) carbonitrides occurred during short-term creep conditions, and coarsening of these particles during long-term aging and short-term creep was insignificant.

  3. 3.

    Creep strength breakdown at an applied stress of 160 MPa correlated with a depletion of excess W from the solid solution after 2000 h of long-term aging, and no evidence of any correlation between the creep strength breakdown appearance and the formation of the Z-phase particles was found. Transition from short-term creep to long-term creep associated with increased rate of acceleration of tertiary creep at an applied stress of 120 MPa was accompanied by the onset of strain-induced coarsening of the Laves phase particles and the M23C6 carbides, which facilitated the partial transformation of the TMLS. However, the Zener drag force exerted by the boundary particles remained high enough to suppress subgrain coarsening. The negative effect of the strain-induced particle coarsening on the creep resistance was attributed to the dissolution of the fine Laves phase particles located at the lath boundaries.