Extrapolation of short-term creep rupture data—The potential risk of over-estimation

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International Journal of Pressure Vessels and Piping 85 (2008) 55–62 www.elsevier.com/locate/ijpvp

Extrapolation of short-term creep rupture data—The potential risk of over-estimation$ G. Dimmler, P. Weinert, H. Cerjak Institute for Materials Science, Welding and Forming, Graz University of Technology, Austria

Abstract This work deals with the creep behaviour of 9–12% Cr steels in the steady-state (secondary) creep regime in order to enable a more detailed and exact description of the creep rupture strength on the basis of the Monkman–Grant relation. The stationary creep behaviour has been investigated by evaluating the creep rate and the change of stress exponent of established grades of high temperature creep resistant steels using the so-called back-stress concept. A change in creep mechanism with applied stress is clearly identified in the creep rupture curves. The impact of this change is discussed and the huge potential for over-estimation of creep strengths from extrapolated short-term creep rupture data is emphasized. r 2007 Elsevier Ltd. All rights reserved. Keywords: Creep behaviour; Back-stress concept; Stationary creep rate; Extrapolation of creep rupture time; 9–12% Cr steels

1. Introduction Extrapolation of creep rupture times based on the results of short time creep tests is an important aspect for the design of new heat resistant steels. The stress dependence of the creep rate and the time to rupture as a basis for extrapolation of the rupture time have been frequently investigated in the case of precipitation strengthened 9–12% Cr steels especially for the steel grade NF616 by Ennis et al. [1] and for the steel grade P91 (X10CrMoVNb 9 1) by Kloc and Sklenicka [4]. The chemical composition of these steels is given in Table 1. It was shown that the creep rate shows different stress dependences at high and low stress regimes. The transition in the stress dependence indicates a change in the creep mechanism from a higher stress dependence of the secondary creep rate at higher stresses to a lower one at lower stresses. When estimating component life times from these data, based on short-term creep experiments using high stresses, extrapolation meth$ This article appeared in its original form in Creep; Fracture in High Temperature Components: Design; Life Assessment Issues, 2005. Lancaster, PA: DEStech Publications, Inc. Corresponding author. E-mail address: [email protected] (G. Dimmler).

0308-0161/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijpvp.2007.06.003

ods which are based on creep rates from stress regions of ‘‘power-law breakdown’’ (see Fig. 2) to stress levels in the range of designing limits, would lead to clearly underestimated creep rates and overestimated creep rupture strengths. In this content, creep rupture times of typical 9–12% Cr steels at 650 1C are shown in Fig. 1 (left). Significant differences in the time to rupture within this steel group with similar chemical composition can be observed. Exemplarily, the stationary creep rate (creep strength) in Fig. 1 (right) of the new co-modified cast alloy CB8 (chemical composition listed in Table 1) was found in the range of the forged steel B2 or the pipe steel NF616. On the other hand, a dramatic difference of the time to rupture (creep strength) between these steels, especially in the stress range of 80 MPa was observed. These inconsistencies between mean creep strength versus lower secondary creep rate relationships and mean creep rupture strength versus time behaviour was expected as a consequence of the differences in the microstructures of these steels. Different creep rupture times could not be explained by significant observable differences of single secondary phases of these broken specimens. However, strong interactions between large secondary phases have been investigated. Now, the stationary creep behaviour of

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56

Table 1 Chemical composition of validated heat-resistant steels

P91 GX12 NF616 X20 B2

C

Mn

Cr

Ni

Mo

V

Nb

W

B

N

Si

0.1 0.13 0.124 0.17–0.23 0.17

0.45 0.52 0.47 Max. 1.0 0.06

8.75 10.5 9.0 10.0–12.5 9.34

0.4 0.86 0.06 0.3–0.8 0.12

0.95 1.03 0.46 0.8–1.2 1.55

0.215 0.23 0.19 0.25–0.35 0.27

0.08 0.066 0.063 y 0.064

y 1.01 1.8 y y

y y 0.003 y 0.01

0.05 0.049 0.043 y 0.015

0.35 0.33 0.02 Max. 0.5 0.07

150

150 B2

125

B2

NF616

650°C

NF616

650°C CB8

125

GX12

100

stress [MPa]

stress [MPa]

P91

P91

75

NF616

100

B2 P91

75

50

50

P91

25 100

1000

10000

100000

25 1.E-07

1.E-08

time [h]

1.E-09

1.E-10

1.E-11

stationary cree prate [1/s]

Fig. 1. Comparison of creep rupture strength and creep strength of 9–12% Cr-steels at 650 1C.

log (ε) Diffusional or “Harper-Dorn”creep

At low stresses, creep is controlled by diffusion (diffusional creep). At higher stresses, creep is dominated by a dislocation movement (dislocation creep) [2], which can be described by power laws [3,4] such as the well-known Norton relationship (1)

where A0 is a constant, s is the applied stress and _ss is the steady-state creep rate. The stress exponent n is typically between 3 and 5 in the ‘‘power-law’’ regime for pure metals and mono-phase materials [5]. At low stresses, a stress exponent of n1 is observed [6]. This behaviour is denoted as ‘‘Harper–Dorn’’ (H–D) creep [7], which is explained in more detail below. At high stresses, values for the stress exponent up to nX20 have been measured [8]. This behaviour is understood as the ‘‘power-law breakdown’’ or exponential creep [9,10] (see Fig. 2). In the range of a constant exponential relationship between the stationary creep rate _ ss and the applied stress

technical t chnical operating operating region region

n

n1

stress exponent n1< n < n2

experimental creep tests

n2

2. Stress dependence of steady-state creep rate

_ ss ¼ A0  sn ,

“Power-lawBreakdown

“Viscous glide”

extraextrapolation polation

these alloys should be understood in more detail by understanding the time dependent interactions of secondary phases. Different approaches are used to describe the dependency of the stationary creep rate on stress. The following section will deal with the modelling approach for the description of the stationary creep rate.

log (σ)

Fig. 2. Schematic illustration of stress dependence of the steady-state creep rate _SS (after Ref. [11]).

s, an extrapolation of the creep rate to lower stress levels is acceptable (see Figs. 1–3). Consequently, extrapolation of the time to rupture tB based on the well-known Monkman–Grant relation [12] log tB þ log _ SS ¼ const

or

_SS  tB ¼ C MG

(2)

is possible. The Monkman–Grant constant CMG can be evaluated from short time creep tests. The results of Kloc and Sklenicka [35] illustrate that a change in the creep exponent takes place at 100 MPa for

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Climb

where M is the Taylor factor. In the following calculations, a typical Taylor factor of anisotropic materials of M ¼ 3 is used. When incorporating the internal stress si into the Norton approach, Eq. (1) can be adapted to

Orowan

inner stress σiM-1

H.D. Creep

_ ¼ AðSÞ  ðs  si Þn

dislocations: disl

o

applied - stress σ

Fig. 3. Scheme of internal stress si as a function of the back stress of particles tpart and the dislocations tdsil [23].

the steel P91. Ennis et al. [1] investigated the stationary creep behaviour of the steel NF616 and distinguished also between two regions with a stress exponent n ¼ 16 at high stresses and n ¼ 6 at lower stresses. In contrast to the evaluations on P91, creep data at stress regions with predominantly diffusional creep behaviour (low stress regions with an exponent n1) have not been investigated for the steel NF616. Only a small amount of data on the stationary creep rates within the stress range of 10–100 MPa has been published. When combining these results, three clearly separable stress regions characterized by different stress exponents can be observed (see Fig. 2). Because of their favourable short testing time, most of the creep tests are conducted at typical stress levels within the ‘‘power-law breakdown’’ regime. The operating stress levels of real components are generally below these creep test levels and a change in creep mechanism occurs between these stress levels. To guarantee reliable results, extrapolation is valid only at stress levels without a change of creep mechanism. One way to find these thresholds is to carry out large numbers of creep tests, which are time consuming and costly. Alternatively, it is shown that the transition from one creep mechanism to the other can be estimated based on physical reasoning. A corresponding model is known from literature as ‘‘back-stress concept’’. This model will be explained in detail in the following section. 2.1. Back-stress concept 2.1.1. Internal stress Alloys with enhanced creep resistance get their strength partly from precipitation hardening. These materials often exhibit values for the stress exponent nX20 [13] in the stress regions of power-law breakdown. Nowick and Machlin [14] and Cotrell and Aytekin [15] explained these high values by an enhanced internal stress si compared with pure materials. This internal stress si consists of shear–stress contributions from secondary phases tpart [16,17] and from dislocations tdisl [18]: si ¼ Mðtdisl þ tpart Þ,

(4)

with a modified stress exponent n. According to Taylor [19], the back stress from dislocations can be calculated by pffiffiffiffiffiffiffiffiffi (5) tdisl ¼ a  G  b  rf;1

particles: part

∼ 0.36..0.70* o

57

(3)

with the elastic interaction-constant a, the shear modulus G, the Burgers vector b and the stationary mobile dislocation density rf,N. To measure the dislocation density, expensive and time consuming TEM-investigations are necessary and the resulting scatterband of these data leads to very uncertain results. On the other hand, investigations [20] on the microstructure in 9–12% Cr steels have shown that the dislocation spacing approaches steady-state values during creep exposure, as a function of the applied stress s with increasing strain e. This value is given by the dislocation density rf,N that reaches a steadystate value over a wide range of alloy compositions of [23] 1  s 2  rf;1 ¼ (6) 3; 9 G  b with the applied stress s. The back stress from particles for precipitation hardened materials can be derived by using the approach of Ashby [21] for the Orowan stress qffiffiffiffiffiffiffiffiffi   G  b  f part 2  rpart v tO ¼ C   ln , (7) rpart r0 where constant C ¼ 0.14 is for screw dislocations or C ¼ 0.093 for edge dislocations. f part is the volume fraction v of precipitates, rpart the radius of precipitates and r0 the ‘‘cut-off’’ radius of the dislocations (r030b). With this approach, the internal stress si can be calculated using Eq. (3). However, how does the internal stress change with increased applied stress s ? This issue is discussed below. 2.1.2. Stress dependence of internal stress si In the region of low applied stresses, the operative creep mechanism is given by the diffusional creep (Newtonian viscous behaviour). This linear relationship between stress and strain rate (stress exponent n1) is known as H–D creep and has been confirmed in aluminium and its alloys [21,22]. The scarcity of data at the low stress of the H–D creep regime has limited the number of detailed analyses of this mode of creep. It is well established, however, that the mechanism of deformation in the H–D creep regime is diffusion-controlled dislocation motion. Thus, dislocation substructure, grain size and density are important microstructural variables influencing the H–D creep [22,23]. Several dislocation movement mechanisms have been proposed for H–D creep, which are described in the literature [6,19]. With increasing (applied) stress levels, dislocations can by-pass particles by climb process. This climb process is proportional to the applied stress. Up to a

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G. Dimmler et al. / International Journal of Pressure Vessels and Piping 85 (2008) 55–62

‘‘critical’’ applied stress, changing parameters of precipitate populations have a less detrimental effect on the inner stress. Above this ‘‘critical’’ stress, the Orowan process becomes stress independent (Fig. 3). This means that the Orowan stress to represents a threshold stress (back stress) of the particles tpart to the dislocation movement. Below the Orowan stress to, dislocations can by-pass a group of particles by a local climb or general climb [16,24,25]. The threshold stress follows from the requirement to create a new length of dislocation during the intersection between particles and dislocations. Particles can be climb by-passed with a smaller increase in dislocation length compared to general climb. Thus, a general climb is associated with much smaller threshold stresses. This has been estimated by Blum and Reppich [26] depending on the volume fraction range of precipitates (from 1% to 10%) as a function of the Orowan stress to [25,27] tcl;gen ffi 0:03; . . . ; 0:08  to .

(8)

A statistical based approach to describe the threshold of local climb is also given by Blum and Reppich as a function of the Orowan stress tO [23,26,28]. Further refinements alter the results of tcl;loc ffi 0:36  tO by less than a factor of two, so that the threshold is given by tcl;loc ffi 0:36; . . . ; 0:7  tO .

(9)

The scatter in experimental data is usually larger than this [26]. Therefore, this approximate equation describes the local climb behaviour with sufficient accuracy. For more detailed information concerning the climb threshold see Ref. [20]. 2.2. Validation of the back-stress concept Above, the main contributors to the internal stress si are discussed. It is shown that changes in the kind of interaction between dislocations and secondary phases are reflected in different characteristic threshold stresses. Spinning the wheel further, the principal question arises: Are the macroscopic transition stresses in the steady-state (minimum) creep rate versus stress curves controlled mainly by the distributions of precipitates? This question is explored below using experimental data of established representatives of heat resistant steels listed in Table 1. 2.2.1. Experimental quantifications as basis for back-stress calculations Using the energy filtering transmission electron microscopy (EFTEM) method to examine 10% Cr steels, Hofer et al. [29,30] made it possible to investigate and quantify microstructure and precipitates comprehensively. In addition to a change in dislocation density during creep exposure, a change of the radius and the volume fraction of the precipitates could also be observed. These investigations have further shown that there are several different types of precipitates present. They differ in

Table 2 Sources of published data used for evaluation of the back-stress concept Main precipitates

Microstructure

Creep data

NF616

M23C6 MX Laves-phase

Ha¨ttestrand [31]

Ennis et al. [16] Data package [32] Minura H. (1994) Wachter O. (1996)

P91

M23C6 MX

Polcik [39]

Spigarelli [33] Taylor [34] Sklenicka [35] Polcik [36]

GX12

M23C6 MX Laves-phase Z-phasea

Hofer [32,33] Polcik [39] Dimmler [37]

Hofer [33] Dimmler (Fig. 8) Polcik [36]

a

Was not considered for the calculations.

their time of occurrence, position within the microstructure, size and/or growth rate and cause different softening effects under creep exposure. It has also been found that the precipitates positioned on dislocations, delay microstructural development during creep exposure and thereby the development of strain in time, by blocking the movement of dislocations. Detailed microstructural investigations on the steel G-X12CrMoWVNbN 10 1 1 (GX12) [33] have shown that the Laves phase can decrease the solid solution strengthening effect of the matrix by depleting the matrix of Mo and W. Moreover, the appearance of the Z-phase coincided clearly with a decrease in the number of substructures stabilizing M23C6 and VN precipitates and a reduction in creep resistance. The main sources of the data, which are used in the following calculations, are summarized in Table 2. 2.2.2. NF616 (P92) As a first example, the back-stress concept is applied to the steel NF616 (P92 after ASME Code Case 2179). For this steel, creep rate data in the stress regime of the expected mechanism change have been published by Ennis et al. [1] and extensive microstructural investigations of precipitate size and volume fraction for the temperatures 873 and 923 K have been conducted by Ha¨ttestrand et al. [31]. The contribution of each population of precipitate to the total Orowan stress of this steel is calculated using Eq. (7). Fig. 4 shows the back stress of the main precipitate populations (in order of their contribution to the Orowan stress: M23C6, MX, Laves-phase) as a function of creep exposure time. Since there are no microstructure quantifications of specimens with very long creep exposure times available (e.g. 1  105 h), it is assumed that the volume fraction of precipitates approaches the value from equilibrium calculations, e.g. [37]. The equivalent diameters are assumed to be constant after several thousand hours. As a result of the microstructural changes during creep, the total Orowan stress of the steel NF616 at 873 K starts

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possible because of the strong scatter of the experimental creep rates of different authors. Nevertheless, the transition in the experimental creep rates and the ‘‘calculated’’ threshold stress correlate well and indicate the expected change in the deformation mechanism visible by different slopes in Fig. 5. For a further check of this correlation, calculations and validations for typical representatives of 9–12% Cr-steels such as grades G-X12CrMoWVNbN10 1 1 (GX12), X10-CrMoVNb 9 1 (P91) and X20CrMo-V 12 1 (X20) have been carried out (for chemical compositions see Table 1). The results are discussed below.

150 Laves Laves

NF616 (873K)

MX MX M23C6 M23C6

back stress [MPa]

125

59

100 75 50 25 0 20

40

60

time [10

80

100

3 h]

Fig. 4. Calculated back stress of precipitates (tp ¼ to) in steel NF616 versus creep exposure at 873 K. 1.E-04 NF616

1.E-05

923K

creep rate [1/s]

1.E-06

n=14.3

873K

1.E-07 1.E-08 n=14.8

1.E-09 1.E-10

n=6.2

1.E-11

n=8.3

Threshold scatterband

1.E-12 75

100

125

150

175

stress σ [MPa]

Fig. 5. Creep rate versus applied stress s for steel NF616 at 873 and 923 K in comparison with calculated threshold scatterband.

at 110 MPa after a short time and decreases to 100 MPa with increasing creep exposure time owing to softening effects. Knowing the total back stress of precipitates at different creep times (see symbols in Fig. 4), the corresponding internal stress si can be calculated using Eq. (3). The threshold scatterband of the applied stress, where the dominant moving dislocations can by-pass the particles mainly by Orowan mechanism, is the range between the minimum and maximum value of the calculated internal stress si at different creep times. A small threshold scatterband means a steady back stress of secondary phases, which indicates the long-term stability of the microstructure. For steel NF616, this threshold-stress scatterband has been calculated for the temperatures 923 and 873 K (see Fig. 5). In addition to the threshold-stress scatterband, the creep rates of the steel NF616 are plotted over a wide stress range. According to Ennis et al. [1], a change in the deformation mechanism is indicated by a different stress exponent n in the Norton equation. The stress exponent n has been evaluated from a power-law regression model on the creep rate data in Fig. 5. A better correlation of the stress exponent to the creep rates is not

2.2.3. X10CrMoV 12 1 (P91) The steel P91 is an interesting candidate for validating the back-stress concept, because creep rate data is available even for very low stresses. To evaluate creep rates in this low stress region, Kloc and Sklenicka [38] used a special testing method known as the ‘‘helicoidal-spring technique’’ [39–41]. At these low stress levels, diffusional or ‘‘H–D’’creep with a stress exponent of n1 is expected, further supporting the assumption that there are three stress regions with roughly constant stress exponents. The first mechanism change at higher stresses has been described with a threshold stress based on the total Orowan mechanism (M23C6- and MX-precipitates) under the contribution of the dislocation barrier behaviour (see Fig. 6). In this steel, Laves phase is not observed. Below the Orowan stress, dislocations can bypass particles via a climb mechanism. Due to surface energy effects, local-climb behaviour can be expected for incoherent or semicoherent precipitates, such as M23C6 in the steel P91. The coherent particles (very small MX precipitates in the steel P91) lead to general-climb behaviour. This contribution can be neglected because of less interaction with the dislocations, see Eq. (8). The climb threshold depends on the barrier behaviour of incoherent precipitates and can be calculated using Eq. (9). The calculated climb threshold for the steel P91 and the Orowan threshold is shown in Fig. 7.

150 P91 (873K)

MX

125 back stress [MPa]

0

M23C6

100 75 50 25 0 0

20

40

60

80

100

time [103 h]

Fig. 6. Calculated back stress of precipitates (tp ¼ to) in the steel P91 versus creep exposure at 873 K.

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60 1.E-04

1.0E-04 P91 (873K)

1.E-05

creep rate [1/s]

creep rate [1/s]

Dimmler Polcik etal. al. Polcik et

1.0E-06

1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 n=0.99

1.0E-08 1.0E-09

n=2.75 n=0.61

1.0E-11

Threshold scatterband

Threshold scatt Threshold scatterband erband

1.0E-12

1.E-12 1

10

100

n=15.39

1.0E-07

1.0E-10

n=1.94

1.E-11

0

1000

25

50

75 100 125 150 175 200 225

stress σ [MPa]

stress σ [MPa]

Fig. 7. Creep rate versus applied stress s of steel P91 at 873 K in comparison with calculated threshold scatterband.

Fig. 9. Creep rate versus applied stress s of steel GX12 at 873 K in comparison to the calculated threshold scatterband. 150

150 125

Orowan threshold [MPa]

Laves MX M23C6

GX12 (873K)

back stress [MPa]

GX12(873K) GX12 (873K)

1.0E-05

n=10.15

100 75 50 25

140

873K

130

B2 B2

120

NF616 NF616

110

P91 P91

100

GX12 GX12

90

X20 X20

80 70 60 50

0 0

5

10

15

20

25

30

35

time [103 h]

Fig. 8. Calculated back stress of precipitates (tp ¼ to) in steel GX12 versus creep exposure at 873 K.

2.2.4. G-X12CrMoWVNbN 10 1 1 (GX12) Fig. 8 shows the calculated individual back stress of the secondary phases in the steel GX12. For the steels GX12 and NF616, some controversy exists with regard to the influence of Laves phase coarsening on the creep strengths. Accordingly, a decreasing back stress of this type of precipitate in combination with decreasing solid solution hardening of the ferritic/martensitic matrix was expected [42]. Nevertheless, comparison of the contributions of Laves phase to the total Orowan threshold of these two steels (Figs. 4 and 8) does not confirm this explanation. In contrast, a significant contribution of Laves phase is observed in Fig. 9. A more detailed validation of the Laves phase coarsening and its contribution to the Orowan threshold is given in [40]. The calculated threshold scatterband for the steel GX12 is shown in Fig. 9. The differences in the scatterband of the calculated threshold stresses between these three heat resistant steels are due to a number of reasons: On the one hand, different phases have different total back stresses. On the other hand, these precipitates show different long-term stabilities. Both aspects strongly affect the threshold scatterband.

0

10 20 30 40 50 60 70 80 90 100 time [103 h]

Fig. 10. The evolution of the total back stress of precipitates of typical heat resistant steels under creep exposure.

2.3. Correlation between Orowan stress and creep strength Fig. 10 gives an overview of the calculated total back stress of secondary phases of all heat resistant steels listed in Table 1. The direct comparison of the calculated Orowan thresholds shows that the steels with higher creep strength also show a tendency to higher total Orowan threshold. The steels are listed in order of their creep strength. 3. Temperature dependence of stationary creep rate In fracture mechanism maps, the dependence of stress on the creep and fracture behaviour and also the influence of temperature are considered. Thereby, fields of dominated micromechanisms for fracture such as cleavage, ductile fractures and so on, can be defined, and the principle deformation behaviour can be estimated over a wider temperature range. So far, the creep rates and threshold stresses for only one temperature have been evaluated. The influence of the temperature on the breakpoints in creep rate versus stress curves is still not elucidated because of scarce experimental data.

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Fo¨rderung der wissenschaftlichen Forschung’’—Contract FWF P13802 TEC.

1.E-05

NF616

creep rate [1/s]

1.E-06

61

600°C 600°C 65 650°C

1.E-07

70 700°C 1.E-08

References

75 0°C

1.E-09 1.E-10 Extrapolation of the Orowanthreshold Orowan threshold

1.E-11 1.E-12 10

100

1000

stress σ [MPa]

Fig. 11. Creep rate of the steel NF616 at different temperatures.

A collection of published data of creep rates for steel NF616 at various temperatures is shown in Fig. 11 (sources are given in Table 2). Will the number of different creep mechanisms be reduced with increasing temperature or are the three regimes of different stress exponents n still active at higher temperatures and what does the tendency of changing breakpoints look like? Questions like this, which consider the influence of the temperature to the creep behaviour, are still not answered. 4. Conclusions Hofer et al. [29] introduced a method for the quantification of the microstructural changes such as the diameter of precipitates and the volume fraction of a precipitate population during creep exposure. Based on these microstructural data, a new approach is presented for the estimation of microstructurally determined threshold stresses (back-stress concept). Although a scatterband has to be considered, these threshold stresses show a good correlation with the stress levels of expected changes of creep mechanism based on the experimental creep data. As well as confirming the apparent mechanism changes, this method can help to support the quantification of creep rates based on rupture time extrapolation methods such as the Monkman–Grant relationship. Knowledge of these threshold stresses limits the range of experimentally based extrapolations of the creep rate. Because these thresholds are possible to calculate, the stress levels for creep tests can be optimized and the effectiveness of creep experiments can be increased. However, for a more quantified evaluation of the backstress approach for 9–12% Cr steels, further experiments, especially at low stress levels and several different temperatures are necessary. Acknowledgements The authors gratefully acknowledge the funding of this work by the Austrian research fund FWF-‘‘Fonds zur

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