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Copper precipitates in 15 NiCuMoNb 5 (WB 36) steel: material properties and microstructure, atomistic simulation, and micromagnetic NDE techniques
Nuclear Engineering and Design 206 (2001) 337– 350 www.elsevier.com/locate/nucengdes
Copper precipitates in 15 NiCuMoNb 5 (WB 36) steel: material properties and microstructure, atomistic simulation, and micromagnetic NDE techniques I. Altpeter a,*, G. Dobmann a, K.-H. Katerbau b, M. Schick b, P. Binkele b, P. Kizler b, S. Schmauder b a
Fraunhofer-Institut fu¨r Zersto¨rungsfreie Pru¨f6erfahren IZFP, Uni6ersita¨t, Geb. 37, 66123 Saarbru¨cken, Germany b MPA Stuttgart, Germany Accepted 24 November 2000
Abstract The material investigations presented confirm the results of earlier MPA investigations that the service-induced hardening and decrease in toughness in WB 36 materials are caused by the precipitation of copper. In the initial state of the material, generally only a part of the alloyed copper is precipitated. The other part is still in solution and can be precipitated during long-term operation at temperatures above 320– 350°C. The copper precipitation leads to a distortion of the crystal lattice surrounding the copper precipitates and yields internal micro-stresses. If the number and size of the copper precipitates change during operation of a component, a change of the residual-stress level occurs. Formation and growth of copper precipitates was simulated using atomistic calculations. In addition, it was possible to mathematically follow the movement of dislocations and their attachment to precipitates. In this way the nano-simulation was established as a scientific method for the numerically based understanding of precipitation hardening. The results obtained from load stress-related Barkhausen noise measurements demonstrated that these micro-magnetic procedures are generally suitable for the verification of copper precipitation. The goal of current research is to establish these findings statistically through further experimental measurements. In addition, the influence of different deformation states, macro residual stress, and thermal-induced residual stress have to be researched. This is important for future developments of non-destructive inspection techniques applied to inservice components. © 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The low-alloy, heat-resistant steel 15 NiCuMoNb 5 (WB 36, material number 1.6368) is used * Corresponding author. Tel.: +49-681-93023827; fax: + 49-681-93025920.
as piping and vessel material in boiling water reactor (BWR) and pressurized water reactor (PWR) nuclear power plants in Germany. One reason for its wide application is the improved 0.2% yield strength at elevated temperatures. In addition, heat treatment is economical because a ferrite –bainite structure with relatively high
0029-5493/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 0 0 ) 0 0 4 2 0 - 9
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bainite content and without any pearlite also results from air cooling after austenitizing. This is possible due to the nickel and molybdenum contents of the steel. Conventional power plants use this material at operating temperatures of up to 450°C, whereas German nuclear power plants use the material mainly for pipelines at operating temperatures below 300°C and in some rare cases in pressure vessels up to 340°C (e.g. a pressurizer in a PWR). Following long hours of operation (90 000 –160 000) some damage was seen in piping systems and in one pressure vessel of conventional power plants during 1987 –1992 (Adamsky et al., 1991, 1996; Rau et al., 1991; Jansky et al., 1993), which occurred during operation and in one case during in service hydrotesting. In all damage situations, the operating temperature was between 320 and 350°C. Even though different factors played a role in causing the damage, an operation-induced hardening associated with a decrease in toughness was seen in all cases. The latter is mainly a shift in the transition temperature of the notched-bar impact test to higher temperatures. According to Adamsky et al. (1996), the processes that lead to the shift in the transition temperature of the notched-bar impact test in WB 36 are unknown. Since the beginning of the 1990s, the Materials Testing Institute (MPA) Stuttgart has performed several projects to shed light upon the operation-induced hardening and decrease in toughness of WB 36 (Ruoff and Katerbau, 1992; Schick and Wiedemann, 1995; Willer and Katerbau, 1995; Schick, 1996; Schick et al., 1998). This resulted in obvious indications that these processes are caused by the copper precipitation that occurs during long-term operation at temperatures from 320°C upwards. Based on this level of information, a government-supported project was started (BMWi-Vorhaben, 1997). The objectives of this project are to describe quantitatively the alterations of the mechanical properties of WB 36 which are possible under light water reactor conditions, and to understand the underlying microstructural processes. In parallel to the above activities, MPA Stuttgart executed calculations using a mesoscopic
theory of precipitation hardening and electronmicroscope data, which showed a quantitative correlation between the number and size of the service-related generation of copper precipitates and the service-related increase of the elastic limit of WB 36 (Kizler et al., 1998, 2000; Uhlmann et al., 1998). The current project includes an in-depth, theoretically improved, understanding of the mechanical behavior of WB 36. The goal is to determine the mechanical properties of the material starting from its atomic structure, i.e. starting from model calculations using the atomic length scale (‘nano-simulation’). The following points are particularly important: Simulation of the formation and growth of copper precipitates in steel; Simulation of the movement of dislocations and their pinning at precipitates. At IZFP Saarbru¨cken, projects have been and are being pursued with the goal to detect the generation of service-induced copper precipitation in WB 36 using micro-magnetic test procedures (Altpeter et al., 1998; BMWi-Vorhaben, 1998). A process is being used for the determination of the high degree of higher-order internal stresses that was developed and patented within the framework of a DFG-research project for steel containing cementite (Altpeter et al., 1995). The feasibility study (Altpeter et al., 1998) showed that this process could generally be extended to the determination of high degree internal stress for copper precipitates. This project (BMWi-Vorhaben, 1998) included the statistical determination of the usability of the procedure to verify copper precipitates and to provide requirements for non-destructive determination and (possible) quantification of WB 36 material alterations such as service-induced hardening and decrease in toughness. This paper outlines the current understanding of copper precipitation in WB 36. The three topics mentioned above will be included, as follows: Material properties and microstructure; Results of the atomistic simulation; Non-destructive testing using micro-magnetic techniques.
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2. Material properties and microstructure Tables 1 and 2 show the specified data (status 1965) for the chemical composition and tensile tests of the WB 36 material in comparison to two other typical steel types used for vessel construction, 15 Mo 3 and 13 CrMo 44. The copper, nickel, and niobium contents, as well as the increased values of manganese along with decreased chromium content are typical for WB 36 material. In the meantime, also the contents of aluminum (0.015 –0.050%) and nitrogen (max. 0.02%) were specified. There are significant differences with respect to the strength values: the yield strength at 350°C for WB 36 is almost twice the value of the other two steels. This, in addition to the economical heat treatment, explains the extensive application of the WB 36 material in the medium temperature range. Table 3 shows data on the change of material properties of WB 36 material components after long-term service temperatures ranging from 330 to 350°C. The first three components listed in Table 3 have shown damages (Adamsky et al., 1991, 1996; Rau et al., 1991; Jansky et al., 1993). The strength parameters increased up to 140 MPa during operation, with a corresponding increase in hardness, and the transition temperature for the notched-bar impact energy was elevated up to 70 K. Fig. 1 shows the respective notched-bar impact energy versus temperature curve (KV –T curve) for the initial state and after service at 350°C for 57 000 h. In addition to the shift of the transition temperature a reduction of the upper shelf energy, although less relevant, of approximately 20% can be observed. Similar changes are
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found for the other components shown in Table 3. It is interesting that the KV –T curve of the initial state can, for the most part, be restored by recovery annealing at 550°C for 3 h of the material state after long-term service, as shown in Fig. 1. Further investigations have demonstrated that the difference between the initial state and the recovery annealed condition, which is still visible here, is virtually lost when recovery annealing is performed at the temperature of the last stress-relief heat treatment of the component (in the present case at 580°C). The dependence of the stress intensity factor KIJ for crack initiation on the test temperature is shown in Fig. 2. A comparison is made between the initial state and the material condition after service (350°C, 57 000 h). The service exposure results in a shift of the transition temperature of approximately 100 K, which is significantly larger than the shift of 58 K measured by the notchedbar impact tests in this case. The upper shelf value also shows a noticeable reduction of the values of KIJ. Further investigations are being made in order to verify these results. The explanation of the service-induced changes of the properties of the WB 36 material can be derived from the currently available knowledge on the iron –copper-phase diagram depicted in Fig. 3. The solubility of copper in steel at temperatures below approximately 650°C was unknown until the 1980s (Hansen and Anderko, 1958; Kubaschewski, 1982), and it was assumed, obviously, that steel heat-treated at temperatures between 650 and 550°C would not contain any dissolved copper (Haarmann and Kalwa, 1986). It
Table 1 Chemical composition of vessel steels (status 1965)a Material 15 Mo 3 (TH 31) 13 CrMo 4 4 (TH 32) 15 NiCuMoNb 5 (WB 36)
a
All values in mass %.
Min. Max. Min. Max. Min. Max.
C
Si
Mn
0.12 0.20 0.10 0.18
0.15 0.35 0.15 0.35 0.25 0.50
0.50 0.70 0.40 0.70 0.80 1.20
0.17
Cr
Mo
Ni
Nb
Cu
0.70 1.00
0.25 0.35 0.40 0.50 0.25 0.40
1.00 1.30
:0.20
0.50 0.80
0.30
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Table 2 Mechanical properties of vessel steels (status 1965) Material
15 Mo 3 (TH 31) 13 CrMo 4 4 (TH 32) 15 NiCuMoNb 5 (WB 36)
Yield strength, ReH (MPa) at
Ultimate tensile strength, Rm (RT) (MPa)
Uniform elongation, A5 (%)
RT
350°C
]265 ]295
]175 ]215
430–520 430–550
]19 ]18
]430
]353
610–760
]16
is now known, however, that WB 36 materials annealed in this temperature range still contain noticeable amounts of copper in solid solution (Sundman et al., 1985). Therefore, the desired increase in strength of the WB 36 material is caused by only a part of the alloyed copper. The other part of the copper, which is still in solid solution in the initial state of the material, slowly precipitates during long-term operation at temperatures above 320°C and may lead to an undesirable increase in hardness and decrease in toughness. These precipitation processes have long been described, by the way, but not for steels, but rather for iron – copper model alloys only (Hornbogen and Glenn, 1960; Hornbogen et al., 1966; Goodman et al., 1973; Othen et al., 1991, 1994). First results of service-related copper precipitation in WB 36 materials were outlined by Ruoff and Katerbau (1992). Further investigations were carried out by Willer and Katerbau (1995) and Schick et al. (1998). Fig. 4 shows an example of a transmission electron-microscope (TEM) image of service-exposed WB 36 material. Copper particles ranging from 2 to 20 nm in size are present. Some of the particles have a twin structure recognizable by a typical striping. With the TEM investigations, it was furthermore shown that the copper particles have three differing crystal structures depending on their size: up to 6 nm, body-centered cubic, the same as the surrounding matrix, above 20 nm, face-centered cubic like pure copper, and between about 6 and 20 nm size, a transition structure. Particles of the latter group make up about 50% of all particles visible by
TEM and lead to a pronounced distortion of the crystal matrix in the regions around the particles, visible under suitable TEM conditions. Therefore, well defined internal micro-stresses are present. Fig. 5 shows the number and size distribution of the precipitated copper particles visible in the TEM. The initial state of a WB 36 material is shown on top, the material after service at the bottom. Approximately the same volume of material was analyzed in both cases. The location of the maximum of the size distribution and the average diameter do not differ significantly. In contrast, the total number of particles after service is approximately twice as high as in the initial state. The results of the TEM investigations show that the number of particles increases during service for all of the three size groups. In comple-
Fig. 1. WB 36 — absorbed energy versus temperature curve.
Lignite (1987) Oil-fired (1990) Lignite (Greece, 1992) NPP (1993) Coal-fired (1995)
T-Component Boiler drum Piping
Pressurizer Boiler drum
Power plant
Component
Yield strength, DRp0,2 (MPa)
339°C/160 000 h 110 350°C/57 000 h 140
330°C/91 600 h 48 330°C/163 000 h 110 338°C/128 000 h –
Service conditions
Table 3 WB 36-alteration of material properties during service
110 125
84 82 –
Ultimate tensile strength, DRm (MPa)
– 55
– 28 –
Vickers hardness, DHV
45 70
55 40 50–60
Transition temperature, DT (K)
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Fig. 4. WB 36 — precipitations after long-term service. Fig. 2. WB 36 — fracture toughness at crack initiation.
mentary investigations using SANS (Small Angle Neutron Scattering) technique it was additionally found that the number of particles (not detectable in TEM) having a size of approximately 1 nm also increases significantly. Furthermore, it was demonstrated by TEM that the number and size
Fig. 3. Iron–copper phase diagram.
distribution of the copper precipitates are virtually the same for a material in the initial state and the material after service and an additional recovery annealing (at the temperature of the last stress-relief heat treatment).
Fig. 5. WB 36 — size distribution of the copper precipitates.
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Fig. 6. Results of a Monte Carlo simulation on formation and growth of copper precipitates; only the copper, not the iron atoms are shown.
3. Atomistic simulation (nanosimulation) of WB 36 material
3.1. Simulation of formation and growth of copper precipitates in steel The objective of these investigations was to describe the formation and growth of copper precipitates on the atomic level. Results concerning the thermal-induced hardening of copper alloyed steel and the possibility to pre-calculate this quantity were expected. Calculations were done using the Monte-Carlo simulation program (Soisson et al., 1996), which was modified for the current investigation. The simulation uses a body centered cubic crystal lattice. The model volume used was a cube having an edge length of 32 lattice constants and periodic boundary conditions. Therefore, the lattice contains 2×323 =65 536 lattice points. In the original state the lattice has 0.6 at.%= 393 randomly distributed copper atoms, a vacancy and 65 142 iron atoms. The simulation has a vacancy concentration of CSIM =1.526 × 10 − 5 but in reality, at 350°C, the concentration is CREAL = 1.14× 10 − 13. Therefore, the time scale of the simulation is multiplied by the appropriate factor. The diffusion of the atoms proceeds via vacancy jumps towards nearest neighbor atoms. This type of position exchange is thermally activated and the jump frequency Y is given by: Gi6 = wi exp
−DEi6 kT
with k the Boltzmann’s constant and T, temperature. The attempt frequencies (wi ) to change the lattice location is dependent on the lattice constant a and the diffusion coefficient DO,i of iron or copper via wi = DO,i /a 2. The activation energy DEiw is the difference in energy between the stable state and the saddle point position of a diffusing atom, which is located next to a vacancy. The activation energy depends on the local short-range-order and is determined separately for each position exchange. The following illustration shows the results of a simulation at a temperature of T= 350°C (=623 K) as displayed in Fig. 6. After t= 2.2 years, small precipitates (approximately 1 nm in diameter) have formed from the originally randomly distributed copper atoms. After t=12.1 years these have merged into four larger precipitates (approximately 2 nm in diameter).
3.2. Simulation of the mo6ement of dislocations and their pinning at precipitates The pinning of dislocations at obstacles is the basic mechanism of precipitation strengthening (Nembach, 1997). In the case of precipitates that can be cut, for example copper precipitates in WB 36 material, the movement of dislocations is not completely blocked, just hindered (Russell and Brown, 1972). During cutting of the precipitate by the moving dislocation, a characteristic angle is found between the dislocation segments at the moment of maximum stress, called the critical
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Fig. 7. Cross-section through the iron structure model used for the nano-simulation of the dislocation movement; scale in 1 A, (0.1 nm).
angle. This is a key parameter for the understanding of precipitation hardening. If it can be determined using the nano-simulation, it then provides the possibility to understand and pre-calculate the precipitation hardening starting from the atomistic properties (Russell and Brown, 1972; Nembach, 1997). The model for the present simulation was a cuboid-shaped iron mono-crystal, consisting of 82 600 atoms, measuring 7.5×7.6 × 17.0 nm3. A cross-section is shown in Fig. 7. Further details are published separately (Nedelcu et al., 1999a,b, 2000). Two edge dislocations were introduced into the model, located at the right and left of Fig. 7. Gliding plane and Burgers vector (b) have the crystallographic label (1 – 10) and b = 91 1 1. Iron atoms were replaced with copper atoms in a spherical area representing a coherent precipitate. In the present case, the copper precipitate has a diameter of 3.0 nm and consists of 1254 copper atoms. Fig. 7 shows a cross-section through the center of the model; the copper precipitate is indicated in light gray. The model has internal stress due to the dislocation and it must relieve this stress using a relaxation algorithm. It turned out that the internal stress was sufficient to initiate movement of the dislocations. This model was retained since the current simulation calculations are the first of this kind. In addition to the movement of the dislocations, the lattice also relaxes slightly around the precipitate to account for the differing atomic diameters of iron and copper. This stress is negligible compared to the stress caused by the dislocation. The molecular dynamics program FEAt was used for the relaxation of the model (Kohlhoff and Schmauder, 1989). The inter-atomic forces
are represented by the current Embedded-AtomModel, EAM. The EAM potentials for iron and copper can be found in the literature. A potential developed by MPA Stuttgart was used for the iron –copper (Fe –Cu) interaction (Ludwig et al., 1998). Using this relaxation algorithm, the movement of the dislocation is initiated without external force. To investigate this, an algorithm was developed that recognized the changing position of the dislocation in the relaxing model, by calculating the Burgers vector density distribution (Nedelcu et al., 1999a,b, 2000). The positions of the dislocation lines represent the maxima of the distribution.
Fig. 8. Dislocation movement: movement to a precipitate (grey circle) and cutting of the precipitate.
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Fig. 8 shows six different stages of the dislocation movement relative to a precipitate. The dislocations are perpendicular to the cross-section of the simulation model depicted in Fig. 7. The first partial illustration shows the dislocation at a large distance from the precipitate (gray circle). The second illustration shows the protuberance of the dislocation line indicating the attraction between the dislocation and the precipitate. The last illustration shows the state of maximum stress. The angle between the dislocation segments, the critical angle, is approximately 140°. This value corresponds to the value that can be calculated for copper precipitates of this size and is confirmed by continuum mechanics theory (Russell and Brown, 1972; Nedelcu et al., 1999a,b, 2000). While various theoretical approximations and parameters (that must be developed through experiments) are required for continuum mechanics theory, the current calculations are based on nothing more than the elastic properties on the atomic length scale as represented by the EAM potentials. The hardening of the investigated iron –copper system is therefore based on the modulus of transverse elasticity of matrix and precipitate. The nano-simulation could therefore be established as a scientific method for the numerically based understanding of precipitation hardening using the performed calculations.
4. NDT using micro-magnetic techniques
4.1. Principles The micro-magnetic concept used is based on load –stress dependent Barkhausen noise measurements. The maximum of the Barkhausen noise amplitude is recorded as a function of the increasing load stress. This curve runs through a magnetostrictive-related maximum. The shift of this maximum along the stress axis is a measurement of the change of the micro (or macro) residual stress condition. This technique permits the collection of quantitative data of residual stress variations without the use of a reference method such as X-ray diffraction.
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4.2. Experimental set-up 4.2.1. Recording of hysteresis cur6es Cylindrical samples are inserted into the Hystrometer (manufactured by List) for magnetization. The magnetizing frequency ( fE) is 1 Hz and the energized field amplitude (HMAX) is 50 A cm − 1. These magnetized samples are then used for the recording of ferro-magnetic hysteresis curves. The voltage induced in an encircling coil is used to calculate the respective induction B(t) by integration. Previous investigations, jointly performed with PTB in Braunschweig, have demonstrated the comparability of the magnetizing curves using the apparatus with a tolerance of B 10% of PTP’s calibration standard, which is sufficient for these materials. 4.2.2. Integral load-stress related Barkhausen noise measurements To establish load –stress related Barkhausen noise measurements, a measurement system was installed to record micromagnetic test values during concurrent tensile loading. The samples are magnetized in the longitudinal direction. The Barkhausen noise signal is recorded using two differential air-core coils to separate the influence of the energizing magnetic field. The magnetic Barkhausen noise is triggered by an alternating magnetic field applied to the sample using an electromagnet. The noise signal is recorded as inducted voltage, appropriately filtered, rectified, amplified, and displayed as function of the tangential field strength. The resulting so called Barkhausen noise profile is evaluated with respect to their maxima and their respective magnetic field positions by a computer (Altpeter et al., 1998). 4.2.3. Recording of the longitudinal magnetostriction cur6es All dimensional changes in the ferromagnetic material that result from changes in the magnetization state are called magnetostriction. A differentiation is made between the longitudinal magnetostriction (uL) and the transverse magnetostriction (uT), length variations parallel or perpendicular to the field direction, and volumetric
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Fig. 9. Ferromagnetic hysteresis curve for the service-exposed material state, measured without load stress. The material state after recovery annealing showing the same hysteresis curve.
magnetostriction. The value recorded in the area of magnetic saturation is called saturation magnetostriction (uS). This is a combination of longitudinal and transverse magnetostriction (Bozorth, 1951). A positive magnetostrictive material, like ironbased materials, under the influence of external stresses shows the following behavior: tensile stress results in the alignment of the magnetizing vectors of the individual domains in the direction of tension (Bozorth, 1951). The measurement of the longitudinal magnetostriction under load stress is performed in a standard way using a strain gauge affixed to the samples and an amplifier (manufactured by HBM). The load stress applied to the sample is measured using a second amplifier connected to a load cell mounted on the tensile test machine.
The hysteresis curves of the service-exposed and recovery-annealed states are identical (Fig. 9). A difference of 140 MPa change in yield strength is not reflected in the B–H-loop. The coercive strength (Hc) is 6.59 0.1 A cm − 1 in both microstructure states (service-exposed material state and recovery annealed state). The strong localized residual stress of higher order, due to copper precipitation, is not reflected in the macroscopic hysteresis curve since this is averaged over volume. The magnetic Barkhausen noise profile and the hysteresis curves were recorded using the encircling coil technique (Fig. 10). Both material conditions can be differentiated in the unstressed condition using the maximum Barkhausen noise amplitude MMAX. This can be explained by the fact that the tension stress sensitivity (load and internal stress) of the test value MMAX (Altpeter et al., 1995) is much larger than the coercive field strength of the hysteresis curve. The change in the magnetic Barkhausen noise peak position between the service exposed and recovery annealed sample is within the error tolerance. The longitudinal magnetostriction behavior of the two different material conditions was investigated in addition to the Barkhausen noise profile. The dependence of the longitudinal magnetostriction uL on the tangential component Ht of the exciting magnetic field is shown in Fig. 11 without additional load. An obvious difference can be
4.3. In6estigation results Measurements were taken on two material states of WB 36 from the same melt, the serviceexposed state (‘B’) and the recovery annealed state (‘E’). The investigated samples consisted of rods with 8 mm diameter and 160 mm length. TEM investigations have shown that in both conditions, three groups of copper precipitates are present whereby state B has more copper precipitates than state E in every group.
Fig. 10. Barkhausen noise profile curves for the service-exposed material state and after recovery annealing, measured without load stress.
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Fig. 11. Variation of longitudinal magnetostriction uL with magnetic field Ht for the service-exposed material state and after recovery annealing, measured without load stress.
observed in the two material conditions, uLMAX,E (4.249 0.06 mm m − 1) and is much larger than uLMAX,B (3.48 90.05 mm m − 1), where uLMAX is the maximum of the longitudinal magnetostriction. The copper-dependent residual stress reduced by recovery annealing leads to a change in the uL (Ht) curve for the no-load stress condition. To quantify the degradation of the residual stress of a higher order, load stress-related micro-magnetic tests were carried out. Both material conditions ‘B’ and ‘E’ can be clearly differentiated in the load stress dependency of the magnetic Barkhausen noise profile, as shown in Fig. 12. The maximum of the MMAX(|) curve is shifted by approximately D| : 20 MPa, from |B : 50 MPa to |E :67 MPa. The curves were approximated using polynomials of the 6th order and the maxima of the respective approximation curves were determined analytically. The magnetic Barkhausen noise profile is influenced by the total stress state of the material, i.e. the superposition of macro stress and stress of a higher degree. If internal stresses, due to copper precipitates, are reduced by recovery annealing, then a higher load must be applied to arrive at the same total stress condition. The stress difference of D| :20 MPa indicates an integral value for the total sample volume. Local stress concentrations can be much higher at the phase boundaries of copper and matrix.
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Fig. 12 shows that the longitudinal magnetostrictive curve shifts to smaller values under increasing tensile load, since the density of movements at the [100]-90° domain wall decreases in the direction of magnetization. With increasing tensile loads, the magnetic reversal process transforms into magnetostrictive negative rotation (Bozorth, 1951). Above the tensile stress limit, the total longitudinal magnetostrictive curve is in the negative area, a characteristic for every type of steel. This stress corresponds to the value on the MMAX(|) curve where the maximum occurs. This is the case for the service-exposed material states starting at |B : 55 MPa (top right in Fig. 12) for the recovery annealed material state, but starting at |E : 70 MPa, bottom right of Fig. 12, where the stress difference is also D| : 20 MPa. The evaluation of the longitudinal magnetostriction curves therefore yield qualitatively and quantitatively the same result as the magnetic Barkhausen noise profile curves.
5. Conclusion The material investigations presented confirm the results of earlier MPA investigations that the service-induced hardening and decrease in toughness in WB 36 materials are caused by the precipitation of copper. In the initial state of the material, generally only a part of the alloyed copper is precipitated. The other part is still in solution and can be precipitated during long-term operation at temperatures above 320°C. The copper precipitation leads to a distortion of the crystal lattice surrounding the copper precipitates and yields internal micro-stresses. If the number and size of the copper precipitates change during operation of a component, a change of the residual-stress level occurs. Formation and growth of copper precipitates was simulated using atomistic calculations. In addition, it was possible to mathematically follow the movement of dislocations and their attachment to precipitates. In this way the nano-simulation was established as a scientific method for the numerically based understanding of precipitation hardening.
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The results obtained from load stress-related Barkhausen noise measurements demonstrated that these micro-magnetic procedures are generally suitable for the verification of copper precipitation. The goal of current research is to establish
these findings statistically through further experimental measurements. In addition, the influence of different deformation states, macro residual stress, and thermal-induced residual stress has to be researched. This is important for future devel-
Fig. 12. Variation of the maximum MMAX of the Barkhausen noise amplitude and of longitudinal magnetostriction uL with applied load, for material states after service (upper row) and after recovery annealing (lower row).
I. Altpeter et al. / Nuclear Engineering and Design 206 (2001) 337–350
opments of non-destructive inspection techniques applied to inservice components.
Acknowledgements The authors would like to thank the (German) Federal Ministry of Education and Research (BMBF), for Economic Affairs (BMWi) and for Environmental Protection, Nature Conservation, and Reactor Safety (BMU) for the promotion and sponsorship of the research work. In addition, we thank Dr F. Soisson and Professor Dr G. Martin (both CEA Saclay) for providing the MonteCarlo software and their support during the further development of the software.
References Adamsky, F.-J., To¨nnes, F.-G., Teichmann, H.-D., 1991. Schaden an der Eco-Falleitung eines 600 MW-Blocks bei der wiederkehrenden Wasserdruckpru¨fung, VGB-Konferenz ‘Werkstoffe und Schweißtechnik im Kraftwerk 1991’, 9 – 10 Jan. 1991, Essen. Adamsky, F.-J., Teichmann, H., Tolksdorf, E., 1996. Betriebserfahrungen mit dem warmfesten Werkstoff 15 NiCuMoNb 5 in konventionellen Kraftwerksanlagen, 22. MPA-Seminar, 10–11 Oct. 1996, Stuttgart, Beitrag Nr. 12, and VGB Kraftwerkstechnik 77 H. 8 (1997) 667– 675. Altpeter, I., Detemple, I., Faßbender, S., Hartmann, S., Kern, R., Raab F., 1995. Untersuchung von thermisch induzierten phasenspezifischen Eigenspannungen in weißem Gußeisen und in Sta¨hlen mit unterschiedlicher Zementitmorphologie, Berichts-Nr. 950534-TW, IZFP Saarbru¨cken, 1995. Altpeter, I., Kern, R., Lang, M., Ro¨sner, H., 1998. Nachweis von Cu-Ausscheidungen mittels mikromagnetischer Pru¨fverfahren, BMBF-Vorhaben 150 1078, Abschlußbericht, Berichts-Nr. 980232-TW, IZFP Saarbru¨cken, 1998. BMWi-Vorhaben 150 1087, Betriebsbedingte Eigenschaftsa¨nderungen kupferhaltiger ferritischer Beha¨lter- und Rohrleitungsbausta¨hle, MPA Stuttgart, Laufzeit 1997 bis 2000. BMWi-Vorhaben 150 1219: Nachweis von Cu-Ausscheidungen mittels mikromagnetischer Pru¨fverfahren, IZFP Saarbru¨cken, Laufzeit 1998 bis 2001. Bozorth, R.M., 1951. Ferromagnetism. van Nostrand, New York, p. 632. Goodman, S.R., Brenner, S.S., Low, J.R., 1973. An FIMatom probe study of the precipitation of copper from iron-1.4 at pct copper, Part I: Field-iron microscopy, Part
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II: Atom probe analyses, Metall. Trans. 4, 2363–2369, 2372– 2378. Haarmann, K., Kalwa, G., 1986. Fu¨nf Jahrzehnte warmfeste Kupfer-Nickel-(Molybda¨n-)Sta¨hle. VGB Kraftwerkstechnik 66, 588– 598. Hansen, M., Anderko, K., 1958. Constitution of Binary Alloys. McGraw-Hill, New York. Hornbogen, E., Glenn, R.C., 1960. A metallographic study of precipitation of copper from a-iron. Trans. Metall. Soc. AIME 218, 1064– 1070. Hornbogen, E., Lu¨tjering, G., Roth, M., 1966. Koha¨rente Ausscheidung in Substitutionsmischkristallen des a-Eisens. Arch. Eisenhu¨ttenwes. 37, 523– 532. Jansky, J., Andra¨, T., Albrecht, K., 1993. Feedwater piping guillotine breaks at 340°C operation temperature. In: Kussmaul, K. (Ed.), Transactions of the 12th International Conference on Structural Mechanics in Reactor Technology, vol. F. North-Holland, Amsterdam, pp. 207– 214. Kizler, P., Uhlmann, D., Schmauder, S. 1998. Linking nanoscale and macroscale: Calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress– strain curves owing to dislocation theory, 24th MPA-Seminar, 8 – 9 Oktober 1998, Stuttgart, Beitrag Nr. 50. Kizler, P., Uhlmann, D., Schmauder, S., 2000. Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress– strain curves owing to dislocation theory. Nucl. Eng. Des. 196, S175– S183. Kohlhoff, S., Schmauder, S., 1989. A new method for coupled elastic-atomistic modelling. In: Vitek, V., Srolovitz, D.J. (Eds.), Atomistic Simulation of Materials: Beyond Pair Potentials, New York. Kubaschewski, O., 1982. Iron — Binary Phase Diagrams. Springer, Berlin. Ludwig, M., Farkas, D., Pedraza, D., Schmauder, S., 1998. Embedded atom potential for Fe – Cu interactions and simulations of precipitate– matrix interfaces. Model. Simul. Mater. Sci. Eng. 6, 19. Nedelcu, S., Kizler, P., Schmauder, S., Moldovan, N., 1999a. Atomic scale modelling of edge dislocation movement in the a-Fe-Cu system, Modelling and Simulation in Materials Science and Technology, eingereicht. Nedelcu, S., Kizler, P., Schmauder, S., Moldovan, N., 1999b. Modellierung der Versetzungsbewegung im a-Fe– Cu System auf atomarer La¨ngenskala, Technischer Bericht, MPA Stuttgart. Nedelcu, S., Kizler, P., Schmauder, S., Moldovan, N., 2000. Modelling simulation. Mater. Sci. Eng. 8, S181– 191. Nembach, E., 1997. Particle Strengthening of Metals and Alloys. Wiley, New York. Othen, P.J., Jenkins, M.L., Smith, G.D.W., Pythian, W.J., 1991. Transmission electron microscope investigation of the structure of copper precipitates in thermally-aged Fe– Cu and Fe– Cu– Ni. Phil. Mag. Lett. 64, 383– 391.
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Othen, P.J., Jenkins, M.L., Smith, G.D.W., 1994. High-resolution electron microscopy studies of the structure of Cu precipitates in a-Fe. Phil. Mag. 70, 1–14. Rau, P., Schick, M., Albert, F., Helmrich, A., 1991. Schaden und Reparatur an einer Kesseltrommel aus 15 NiCuMoNb 5 (WSB 62), VGB-Konferenz ‘Werkstoffe und Schweißtechnik im Kraftwerk 1991’, 9–10 Jan. 1991, Essen, and VGB Kraftwerkstechnik 72 H. 5 (1992) 444– 454. Ruoff, H., Katerbau, K.-H., 1992. Orientierende TEM-Untersuchungen zur betrieblichen Za¨higkeitsabnahme des Werkstoffs WB 36, BMU-Vorhaben SR 471, 24. Technischer Bericht, MPA Stuttgart. Russell, K., Brown, L., 1972. A dispersion strengthening model based on differing elastic moduli applied to the iron– copper system. Acta Metall. 20, 969. Schick, M., Wiedemann, J., 1995. Langzeit-Glu¨hversuche an unterschiedlichen Schmelzen und Wa¨rmebehandlungszusta¨nden des Werkstoffs 15 NiCuMoNb 5, BMU-Vorhaben SR 2065, Technischer Bericht 2.1, MPA Stuttgart. Schick, M., 1996. Unvero¨ffentlichte Untersuchungen zum Werkstoff WB 36, MPA Stuttgart, 1990 bis 1996. Schick, M., Wiedemann, J., Willer, D., 1998. Untersuchungen zur sicherheitstechnischen Bewertung von geschweißten
.
Komponenten aus Werkstoff 15 NiCuMoNb 5 (WB 36) im Hinblick auf die Za¨higkeitsabnahme unter Betriebsbeanspruchung, BMU-Vorhaben SR 2239, Technischer Bericht, MPA Stuttgart. Soisson, F., Barbu, A., Martin, G., 1996. Monte Carlo simulations of copper precipitates in dilute iron– copper alloys during thermal ageing and under electron irradiation. Acta Mater. 44, 3898. Sundman, B., Jansson, B., Andersson, J.-O., 1985. The Thermo-Calc databank system. Calphad 9, 153– 190. Uhlmann, D., Kizler, P., Schmauder, S., 1998. From nanoscale to macroscale: Study of damage in steels with Cu precipitates using micromechanically based stress– strain curves. In: Christensen, J.V., et al. (Eds.), Proceedings of the 19th Risø International Symposium on Materials Science: Modelling of Structure and Mechanics of Materials from Microscale to Product. Risø National Laboratory, Roskilde, Denmark, pp. 529– 534. Willer, D., Katerbau, K.-H., 1995. Auswertungen und Untersuchungen zur betriebsbedingten Za¨higkeitsabnahme des Werkstoffs 15 NiCuMoNb 5, BMU-Vorhaben SR 2065, Technischer Bericht 2.2, MPA Stuttgart.
Copper precipitates in 15 NiCuMoNb 5 (WB 36) steel: material properties and microstructure, atomistic simulation, and micromagnetic NDE techniques I. Altpeter a,*, G. Dobmann a, K.-H. Katerbau b, M. Schick b, P. Binkele b, P. Kizler b, S. Schmauder b a
Fraunhofer-Institut fu¨r Zersto¨rungsfreie Pru¨f6erfahren IZFP, Uni6ersita¨t, Geb. 37, 66123 Saarbru¨cken, Germany b MPA Stuttgart, Germany Accepted 24 November 2000
Abstract The material investigations presented confirm the results of earlier MPA investigations that the service-induced hardening and decrease in toughness in WB 36 materials are caused by the precipitation of copper. In the initial state of the material, generally only a part of the alloyed copper is precipitated. The other part is still in solution and can be precipitated during long-term operation at temperatures above 320– 350°C. The copper precipitation leads to a distortion of the crystal lattice surrounding the copper precipitates and yields internal micro-stresses. If the number and size of the copper precipitates change during operation of a component, a change of the residual-stress level occurs. Formation and growth of copper precipitates was simulated using atomistic calculations. In addition, it was possible to mathematically follow the movement of dislocations and their attachment to precipitates. In this way the nano-simulation was established as a scientific method for the numerically based understanding of precipitation hardening. The results obtained from load stress-related Barkhausen noise measurements demonstrated that these micro-magnetic procedures are generally suitable for the verification of copper precipitation. The goal of current research is to establish these findings statistically through further experimental measurements. In addition, the influence of different deformation states, macro residual stress, and thermal-induced residual stress have to be researched. This is important for future developments of non-destructive inspection techniques applied to inservice components. © 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The low-alloy, heat-resistant steel 15 NiCuMoNb 5 (WB 36, material number 1.6368) is used * Corresponding author. Tel.: +49-681-93023827; fax: + 49-681-93025920.
as piping and vessel material in boiling water reactor (BWR) and pressurized water reactor (PWR) nuclear power plants in Germany. One reason for its wide application is the improved 0.2% yield strength at elevated temperatures. In addition, heat treatment is economical because a ferrite –bainite structure with relatively high
0029-5493/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 9 - 5 4 9 3 ( 0 0 ) 0 0 4 2 0 - 9
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bainite content and without any pearlite also results from air cooling after austenitizing. This is possible due to the nickel and molybdenum contents of the steel. Conventional power plants use this material at operating temperatures of up to 450°C, whereas German nuclear power plants use the material mainly for pipelines at operating temperatures below 300°C and in some rare cases in pressure vessels up to 340°C (e.g. a pressurizer in a PWR). Following long hours of operation (90 000 –160 000) some damage was seen in piping systems and in one pressure vessel of conventional power plants during 1987 –1992 (Adamsky et al., 1991, 1996; Rau et al., 1991; Jansky et al., 1993), which occurred during operation and in one case during in service hydrotesting. In all damage situations, the operating temperature was between 320 and 350°C. Even though different factors played a role in causing the damage, an operation-induced hardening associated with a decrease in toughness was seen in all cases. The latter is mainly a shift in the transition temperature of the notched-bar impact test to higher temperatures. According to Adamsky et al. (1996), the processes that lead to the shift in the transition temperature of the notched-bar impact test in WB 36 are unknown. Since the beginning of the 1990s, the Materials Testing Institute (MPA) Stuttgart has performed several projects to shed light upon the operation-induced hardening and decrease in toughness of WB 36 (Ruoff and Katerbau, 1992; Schick and Wiedemann, 1995; Willer and Katerbau, 1995; Schick, 1996; Schick et al., 1998). This resulted in obvious indications that these processes are caused by the copper precipitation that occurs during long-term operation at temperatures from 320°C upwards. Based on this level of information, a government-supported project was started (BMWi-Vorhaben, 1997). The objectives of this project are to describe quantitatively the alterations of the mechanical properties of WB 36 which are possible under light water reactor conditions, and to understand the underlying microstructural processes. In parallel to the above activities, MPA Stuttgart executed calculations using a mesoscopic
theory of precipitation hardening and electronmicroscope data, which showed a quantitative correlation between the number and size of the service-related generation of copper precipitates and the service-related increase of the elastic limit of WB 36 (Kizler et al., 1998, 2000; Uhlmann et al., 1998). The current project includes an in-depth, theoretically improved, understanding of the mechanical behavior of WB 36. The goal is to determine the mechanical properties of the material starting from its atomic structure, i.e. starting from model calculations using the atomic length scale (‘nano-simulation’). The following points are particularly important: Simulation of the formation and growth of copper precipitates in steel; Simulation of the movement of dislocations and their pinning at precipitates. At IZFP Saarbru¨cken, projects have been and are being pursued with the goal to detect the generation of service-induced copper precipitation in WB 36 using micro-magnetic test procedures (Altpeter et al., 1998; BMWi-Vorhaben, 1998). A process is being used for the determination of the high degree of higher-order internal stresses that was developed and patented within the framework of a DFG-research project for steel containing cementite (Altpeter et al., 1995). The feasibility study (Altpeter et al., 1998) showed that this process could generally be extended to the determination of high degree internal stress for copper precipitates. This project (BMWi-Vorhaben, 1998) included the statistical determination of the usability of the procedure to verify copper precipitates and to provide requirements for non-destructive determination and (possible) quantification of WB 36 material alterations such as service-induced hardening and decrease in toughness. This paper outlines the current understanding of copper precipitation in WB 36. The three topics mentioned above will be included, as follows: Material properties and microstructure; Results of the atomistic simulation; Non-destructive testing using micro-magnetic techniques.
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2. Material properties and microstructure Tables 1 and 2 show the specified data (status 1965) for the chemical composition and tensile tests of the WB 36 material in comparison to two other typical steel types used for vessel construction, 15 Mo 3 and 13 CrMo 44. The copper, nickel, and niobium contents, as well as the increased values of manganese along with decreased chromium content are typical for WB 36 material. In the meantime, also the contents of aluminum (0.015 –0.050%) and nitrogen (max. 0.02%) were specified. There are significant differences with respect to the strength values: the yield strength at 350°C for WB 36 is almost twice the value of the other two steels. This, in addition to the economical heat treatment, explains the extensive application of the WB 36 material in the medium temperature range. Table 3 shows data on the change of material properties of WB 36 material components after long-term service temperatures ranging from 330 to 350°C. The first three components listed in Table 3 have shown damages (Adamsky et al., 1991, 1996; Rau et al., 1991; Jansky et al., 1993). The strength parameters increased up to 140 MPa during operation, with a corresponding increase in hardness, and the transition temperature for the notched-bar impact energy was elevated up to 70 K. Fig. 1 shows the respective notched-bar impact energy versus temperature curve (KV –T curve) for the initial state and after service at 350°C for 57 000 h. In addition to the shift of the transition temperature a reduction of the upper shelf energy, although less relevant, of approximately 20% can be observed. Similar changes are
339
found for the other components shown in Table 3. It is interesting that the KV –T curve of the initial state can, for the most part, be restored by recovery annealing at 550°C for 3 h of the material state after long-term service, as shown in Fig. 1. Further investigations have demonstrated that the difference between the initial state and the recovery annealed condition, which is still visible here, is virtually lost when recovery annealing is performed at the temperature of the last stress-relief heat treatment of the component (in the present case at 580°C). The dependence of the stress intensity factor KIJ for crack initiation on the test temperature is shown in Fig. 2. A comparison is made between the initial state and the material condition after service (350°C, 57 000 h). The service exposure results in a shift of the transition temperature of approximately 100 K, which is significantly larger than the shift of 58 K measured by the notchedbar impact tests in this case. The upper shelf value also shows a noticeable reduction of the values of KIJ. Further investigations are being made in order to verify these results. The explanation of the service-induced changes of the properties of the WB 36 material can be derived from the currently available knowledge on the iron –copper-phase diagram depicted in Fig. 3. The solubility of copper in steel at temperatures below approximately 650°C was unknown until the 1980s (Hansen and Anderko, 1958; Kubaschewski, 1982), and it was assumed, obviously, that steel heat-treated at temperatures between 650 and 550°C would not contain any dissolved copper (Haarmann and Kalwa, 1986). It
Table 1 Chemical composition of vessel steels (status 1965)a Material 15 Mo 3 (TH 31) 13 CrMo 4 4 (TH 32) 15 NiCuMoNb 5 (WB 36)
a
All values in mass %.
Min. Max. Min. Max. Min. Max.
C
Si
Mn
0.12 0.20 0.10 0.18
0.15 0.35 0.15 0.35 0.25 0.50
0.50 0.70 0.40 0.70 0.80 1.20
0.17
Cr
Mo
Ni
Nb
Cu
0.70 1.00
0.25 0.35 0.40 0.50 0.25 0.40
1.00 1.30
:0.20
0.50 0.80
0.30
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Table 2 Mechanical properties of vessel steels (status 1965) Material
15 Mo 3 (TH 31) 13 CrMo 4 4 (TH 32) 15 NiCuMoNb 5 (WB 36)
Yield strength, ReH (MPa) at
Ultimate tensile strength, Rm (RT) (MPa)
Uniform elongation, A5 (%)
RT
350°C
]265 ]295
]175 ]215
430–520 430–550
]19 ]18
]430
]353
610–760
]16
is now known, however, that WB 36 materials annealed in this temperature range still contain noticeable amounts of copper in solid solution (Sundman et al., 1985). Therefore, the desired increase in strength of the WB 36 material is caused by only a part of the alloyed copper. The other part of the copper, which is still in solid solution in the initial state of the material, slowly precipitates during long-term operation at temperatures above 320°C and may lead to an undesirable increase in hardness and decrease in toughness. These precipitation processes have long been described, by the way, but not for steels, but rather for iron – copper model alloys only (Hornbogen and Glenn, 1960; Hornbogen et al., 1966; Goodman et al., 1973; Othen et al., 1991, 1994). First results of service-related copper precipitation in WB 36 materials were outlined by Ruoff and Katerbau (1992). Further investigations were carried out by Willer and Katerbau (1995) and Schick et al. (1998). Fig. 4 shows an example of a transmission electron-microscope (TEM) image of service-exposed WB 36 material. Copper particles ranging from 2 to 20 nm in size are present. Some of the particles have a twin structure recognizable by a typical striping. With the TEM investigations, it was furthermore shown that the copper particles have three differing crystal structures depending on their size: up to 6 nm, body-centered cubic, the same as the surrounding matrix, above 20 nm, face-centered cubic like pure copper, and between about 6 and 20 nm size, a transition structure. Particles of the latter group make up about 50% of all particles visible by
TEM and lead to a pronounced distortion of the crystal matrix in the regions around the particles, visible under suitable TEM conditions. Therefore, well defined internal micro-stresses are present. Fig. 5 shows the number and size distribution of the precipitated copper particles visible in the TEM. The initial state of a WB 36 material is shown on top, the material after service at the bottom. Approximately the same volume of material was analyzed in both cases. The location of the maximum of the size distribution and the average diameter do not differ significantly. In contrast, the total number of particles after service is approximately twice as high as in the initial state. The results of the TEM investigations show that the number of particles increases during service for all of the three size groups. In comple-
Fig. 1. WB 36 — absorbed energy versus temperature curve.
Lignite (1987) Oil-fired (1990) Lignite (Greece, 1992) NPP (1993) Coal-fired (1995)
T-Component Boiler drum Piping
Pressurizer Boiler drum
Power plant
Component
Yield strength, DRp0,2 (MPa)
339°C/160 000 h 110 350°C/57 000 h 140
330°C/91 600 h 48 330°C/163 000 h 110 338°C/128 000 h –
Service conditions
Table 3 WB 36-alteration of material properties during service
110 125
84 82 –
Ultimate tensile strength, DRm (MPa)
– 55
– 28 –
Vickers hardness, DHV
45 70
55 40 50–60
Transition temperature, DT (K)
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Fig. 4. WB 36 — precipitations after long-term service. Fig. 2. WB 36 — fracture toughness at crack initiation.
mentary investigations using SANS (Small Angle Neutron Scattering) technique it was additionally found that the number of particles (not detectable in TEM) having a size of approximately 1 nm also increases significantly. Furthermore, it was demonstrated by TEM that the number and size
Fig. 3. Iron–copper phase diagram.
distribution of the copper precipitates are virtually the same for a material in the initial state and the material after service and an additional recovery annealing (at the temperature of the last stress-relief heat treatment).
Fig. 5. WB 36 — size distribution of the copper precipitates.
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Fig. 6. Results of a Monte Carlo simulation on formation and growth of copper precipitates; only the copper, not the iron atoms are shown.
3. Atomistic simulation (nanosimulation) of WB 36 material
3.1. Simulation of formation and growth of copper precipitates in steel The objective of these investigations was to describe the formation and growth of copper precipitates on the atomic level. Results concerning the thermal-induced hardening of copper alloyed steel and the possibility to pre-calculate this quantity were expected. Calculations were done using the Monte-Carlo simulation program (Soisson et al., 1996), which was modified for the current investigation. The simulation uses a body centered cubic crystal lattice. The model volume used was a cube having an edge length of 32 lattice constants and periodic boundary conditions. Therefore, the lattice contains 2×323 =65 536 lattice points. In the original state the lattice has 0.6 at.%= 393 randomly distributed copper atoms, a vacancy and 65 142 iron atoms. The simulation has a vacancy concentration of CSIM =1.526 × 10 − 5 but in reality, at 350°C, the concentration is CREAL = 1.14× 10 − 13. Therefore, the time scale of the simulation is multiplied by the appropriate factor. The diffusion of the atoms proceeds via vacancy jumps towards nearest neighbor atoms. This type of position exchange is thermally activated and the jump frequency Y is given by: Gi6 = wi exp
−DEi6 kT
with k the Boltzmann’s constant and T, temperature. The attempt frequencies (wi ) to change the lattice location is dependent on the lattice constant a and the diffusion coefficient DO,i of iron or copper via wi = DO,i /a 2. The activation energy DEiw is the difference in energy between the stable state and the saddle point position of a diffusing atom, which is located next to a vacancy. The activation energy depends on the local short-range-order and is determined separately for each position exchange. The following illustration shows the results of a simulation at a temperature of T= 350°C (=623 K) as displayed in Fig. 6. After t= 2.2 years, small precipitates (approximately 1 nm in diameter) have formed from the originally randomly distributed copper atoms. After t=12.1 years these have merged into four larger precipitates (approximately 2 nm in diameter).
3.2. Simulation of the mo6ement of dislocations and their pinning at precipitates The pinning of dislocations at obstacles is the basic mechanism of precipitation strengthening (Nembach, 1997). In the case of precipitates that can be cut, for example copper precipitates in WB 36 material, the movement of dislocations is not completely blocked, just hindered (Russell and Brown, 1972). During cutting of the precipitate by the moving dislocation, a characteristic angle is found between the dislocation segments at the moment of maximum stress, called the critical
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Fig. 7. Cross-section through the iron structure model used for the nano-simulation of the dislocation movement; scale in 1 A, (0.1 nm).
angle. This is a key parameter for the understanding of precipitation hardening. If it can be determined using the nano-simulation, it then provides the possibility to understand and pre-calculate the precipitation hardening starting from the atomistic properties (Russell and Brown, 1972; Nembach, 1997). The model for the present simulation was a cuboid-shaped iron mono-crystal, consisting of 82 600 atoms, measuring 7.5×7.6 × 17.0 nm3. A cross-section is shown in Fig. 7. Further details are published separately (Nedelcu et al., 1999a,b, 2000). Two edge dislocations were introduced into the model, located at the right and left of Fig. 7. Gliding plane and Burgers vector (b) have the crystallographic label (1 – 10) and b = 91 1 1. Iron atoms were replaced with copper atoms in a spherical area representing a coherent precipitate. In the present case, the copper precipitate has a diameter of 3.0 nm and consists of 1254 copper atoms. Fig. 7 shows a cross-section through the center of the model; the copper precipitate is indicated in light gray. The model has internal stress due to the dislocation and it must relieve this stress using a relaxation algorithm. It turned out that the internal stress was sufficient to initiate movement of the dislocations. This model was retained since the current simulation calculations are the first of this kind. In addition to the movement of the dislocations, the lattice also relaxes slightly around the precipitate to account for the differing atomic diameters of iron and copper. This stress is negligible compared to the stress caused by the dislocation. The molecular dynamics program FEAt was used for the relaxation of the model (Kohlhoff and Schmauder, 1989). The inter-atomic forces
are represented by the current Embedded-AtomModel, EAM. The EAM potentials for iron and copper can be found in the literature. A potential developed by MPA Stuttgart was used for the iron –copper (Fe –Cu) interaction (Ludwig et al., 1998). Using this relaxation algorithm, the movement of the dislocation is initiated without external force. To investigate this, an algorithm was developed that recognized the changing position of the dislocation in the relaxing model, by calculating the Burgers vector density distribution (Nedelcu et al., 1999a,b, 2000). The positions of the dislocation lines represent the maxima of the distribution.
Fig. 8. Dislocation movement: movement to a precipitate (grey circle) and cutting of the precipitate.
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Fig. 8 shows six different stages of the dislocation movement relative to a precipitate. The dislocations are perpendicular to the cross-section of the simulation model depicted in Fig. 7. The first partial illustration shows the dislocation at a large distance from the precipitate (gray circle). The second illustration shows the protuberance of the dislocation line indicating the attraction between the dislocation and the precipitate. The last illustration shows the state of maximum stress. The angle between the dislocation segments, the critical angle, is approximately 140°. This value corresponds to the value that can be calculated for copper precipitates of this size and is confirmed by continuum mechanics theory (Russell and Brown, 1972; Nedelcu et al., 1999a,b, 2000). While various theoretical approximations and parameters (that must be developed through experiments) are required for continuum mechanics theory, the current calculations are based on nothing more than the elastic properties on the atomic length scale as represented by the EAM potentials. The hardening of the investigated iron –copper system is therefore based on the modulus of transverse elasticity of matrix and precipitate. The nano-simulation could therefore be established as a scientific method for the numerically based understanding of precipitation hardening using the performed calculations.
4. NDT using micro-magnetic techniques
4.1. Principles The micro-magnetic concept used is based on load –stress dependent Barkhausen noise measurements. The maximum of the Barkhausen noise amplitude is recorded as a function of the increasing load stress. This curve runs through a magnetostrictive-related maximum. The shift of this maximum along the stress axis is a measurement of the change of the micro (or macro) residual stress condition. This technique permits the collection of quantitative data of residual stress variations without the use of a reference method such as X-ray diffraction.
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4.2. Experimental set-up 4.2.1. Recording of hysteresis cur6es Cylindrical samples are inserted into the Hystrometer (manufactured by List) for magnetization. The magnetizing frequency ( fE) is 1 Hz and the energized field amplitude (HMAX) is 50 A cm − 1. These magnetized samples are then used for the recording of ferro-magnetic hysteresis curves. The voltage induced in an encircling coil is used to calculate the respective induction B(t) by integration. Previous investigations, jointly performed with PTB in Braunschweig, have demonstrated the comparability of the magnetizing curves using the apparatus with a tolerance of B 10% of PTP’s calibration standard, which is sufficient for these materials. 4.2.2. Integral load-stress related Barkhausen noise measurements To establish load –stress related Barkhausen noise measurements, a measurement system was installed to record micromagnetic test values during concurrent tensile loading. The samples are magnetized in the longitudinal direction. The Barkhausen noise signal is recorded using two differential air-core coils to separate the influence of the energizing magnetic field. The magnetic Barkhausen noise is triggered by an alternating magnetic field applied to the sample using an electromagnet. The noise signal is recorded as inducted voltage, appropriately filtered, rectified, amplified, and displayed as function of the tangential field strength. The resulting so called Barkhausen noise profile is evaluated with respect to their maxima and their respective magnetic field positions by a computer (Altpeter et al., 1998). 4.2.3. Recording of the longitudinal magnetostriction cur6es All dimensional changes in the ferromagnetic material that result from changes in the magnetization state are called magnetostriction. A differentiation is made between the longitudinal magnetostriction (uL) and the transverse magnetostriction (uT), length variations parallel or perpendicular to the field direction, and volumetric
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Fig. 9. Ferromagnetic hysteresis curve for the service-exposed material state, measured without load stress. The material state after recovery annealing showing the same hysteresis curve.
magnetostriction. The value recorded in the area of magnetic saturation is called saturation magnetostriction (uS). This is a combination of longitudinal and transverse magnetostriction (Bozorth, 1951). A positive magnetostrictive material, like ironbased materials, under the influence of external stresses shows the following behavior: tensile stress results in the alignment of the magnetizing vectors of the individual domains in the direction of tension (Bozorth, 1951). The measurement of the longitudinal magnetostriction under load stress is performed in a standard way using a strain gauge affixed to the samples and an amplifier (manufactured by HBM). The load stress applied to the sample is measured using a second amplifier connected to a load cell mounted on the tensile test machine.
The hysteresis curves of the service-exposed and recovery-annealed states are identical (Fig. 9). A difference of 140 MPa change in yield strength is not reflected in the B–H-loop. The coercive strength (Hc) is 6.59 0.1 A cm − 1 in both microstructure states (service-exposed material state and recovery annealed state). The strong localized residual stress of higher order, due to copper precipitation, is not reflected in the macroscopic hysteresis curve since this is averaged over volume. The magnetic Barkhausen noise profile and the hysteresis curves were recorded using the encircling coil technique (Fig. 10). Both material conditions can be differentiated in the unstressed condition using the maximum Barkhausen noise amplitude MMAX. This can be explained by the fact that the tension stress sensitivity (load and internal stress) of the test value MMAX (Altpeter et al., 1995) is much larger than the coercive field strength of the hysteresis curve. The change in the magnetic Barkhausen noise peak position between the service exposed and recovery annealed sample is within the error tolerance. The longitudinal magnetostriction behavior of the two different material conditions was investigated in addition to the Barkhausen noise profile. The dependence of the longitudinal magnetostriction uL on the tangential component Ht of the exciting magnetic field is shown in Fig. 11 without additional load. An obvious difference can be
4.3. In6estigation results Measurements were taken on two material states of WB 36 from the same melt, the serviceexposed state (‘B’) and the recovery annealed state (‘E’). The investigated samples consisted of rods with 8 mm diameter and 160 mm length. TEM investigations have shown that in both conditions, three groups of copper precipitates are present whereby state B has more copper precipitates than state E in every group.
Fig. 10. Barkhausen noise profile curves for the service-exposed material state and after recovery annealing, measured without load stress.
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Fig. 11. Variation of longitudinal magnetostriction uL with magnetic field Ht for the service-exposed material state and after recovery annealing, measured without load stress.
observed in the two material conditions, uLMAX,E (4.249 0.06 mm m − 1) and is much larger than uLMAX,B (3.48 90.05 mm m − 1), where uLMAX is the maximum of the longitudinal magnetostriction. The copper-dependent residual stress reduced by recovery annealing leads to a change in the uL (Ht) curve for the no-load stress condition. To quantify the degradation of the residual stress of a higher order, load stress-related micro-magnetic tests were carried out. Both material conditions ‘B’ and ‘E’ can be clearly differentiated in the load stress dependency of the magnetic Barkhausen noise profile, as shown in Fig. 12. The maximum of the MMAX(|) curve is shifted by approximately D| : 20 MPa, from |B : 50 MPa to |E :67 MPa. The curves were approximated using polynomials of the 6th order and the maxima of the respective approximation curves were determined analytically. The magnetic Barkhausen noise profile is influenced by the total stress state of the material, i.e. the superposition of macro stress and stress of a higher degree. If internal stresses, due to copper precipitates, are reduced by recovery annealing, then a higher load must be applied to arrive at the same total stress condition. The stress difference of D| :20 MPa indicates an integral value for the total sample volume. Local stress concentrations can be much higher at the phase boundaries of copper and matrix.
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Fig. 12 shows that the longitudinal magnetostrictive curve shifts to smaller values under increasing tensile load, since the density of movements at the [100]-90° domain wall decreases in the direction of magnetization. With increasing tensile loads, the magnetic reversal process transforms into magnetostrictive negative rotation (Bozorth, 1951). Above the tensile stress limit, the total longitudinal magnetostrictive curve is in the negative area, a characteristic for every type of steel. This stress corresponds to the value on the MMAX(|) curve where the maximum occurs. This is the case for the service-exposed material states starting at |B : 55 MPa (top right in Fig. 12) for the recovery annealed material state, but starting at |E : 70 MPa, bottom right of Fig. 12, where the stress difference is also D| : 20 MPa. The evaluation of the longitudinal magnetostriction curves therefore yield qualitatively and quantitatively the same result as the magnetic Barkhausen noise profile curves.
5. Conclusion The material investigations presented confirm the results of earlier MPA investigations that the service-induced hardening and decrease in toughness in WB 36 materials are caused by the precipitation of copper. In the initial state of the material, generally only a part of the alloyed copper is precipitated. The other part is still in solution and can be precipitated during long-term operation at temperatures above 320°C. The copper precipitation leads to a distortion of the crystal lattice surrounding the copper precipitates and yields internal micro-stresses. If the number and size of the copper precipitates change during operation of a component, a change of the residual-stress level occurs. Formation and growth of copper precipitates was simulated using atomistic calculations. In addition, it was possible to mathematically follow the movement of dislocations and their attachment to precipitates. In this way the nano-simulation was established as a scientific method for the numerically based understanding of precipitation hardening.
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The results obtained from load stress-related Barkhausen noise measurements demonstrated that these micro-magnetic procedures are generally suitable for the verification of copper precipitation. The goal of current research is to establish
these findings statistically through further experimental measurements. In addition, the influence of different deformation states, macro residual stress, and thermal-induced residual stress has to be researched. This is important for future devel-
Fig. 12. Variation of the maximum MMAX of the Barkhausen noise amplitude and of longitudinal magnetostriction uL with applied load, for material states after service (upper row) and after recovery annealing (lower row).
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opments of non-destructive inspection techniques applied to inservice components.
Acknowledgements The authors would like to thank the (German) Federal Ministry of Education and Research (BMBF), for Economic Affairs (BMWi) and for Environmental Protection, Nature Conservation, and Reactor Safety (BMU) for the promotion and sponsorship of the research work. In addition, we thank Dr F. Soisson and Professor Dr G. Martin (both CEA Saclay) for providing the MonteCarlo software and their support during the further development of the software.
References Adamsky, F.-J., To¨nnes, F.-G., Teichmann, H.-D., 1991. Schaden an der Eco-Falleitung eines 600 MW-Blocks bei der wiederkehrenden Wasserdruckpru¨fung, VGB-Konferenz ‘Werkstoffe und Schweißtechnik im Kraftwerk 1991’, 9 – 10 Jan. 1991, Essen. Adamsky, F.-J., Teichmann, H., Tolksdorf, E., 1996. Betriebserfahrungen mit dem warmfesten Werkstoff 15 NiCuMoNb 5 in konventionellen Kraftwerksanlagen, 22. MPA-Seminar, 10–11 Oct. 1996, Stuttgart, Beitrag Nr. 12, and VGB Kraftwerkstechnik 77 H. 8 (1997) 667– 675. Altpeter, I., Detemple, I., Faßbender, S., Hartmann, S., Kern, R., Raab F., 1995. Untersuchung von thermisch induzierten phasenspezifischen Eigenspannungen in weißem Gußeisen und in Sta¨hlen mit unterschiedlicher Zementitmorphologie, Berichts-Nr. 950534-TW, IZFP Saarbru¨cken, 1995. Altpeter, I., Kern, R., Lang, M., Ro¨sner, H., 1998. Nachweis von Cu-Ausscheidungen mittels mikromagnetischer Pru¨fverfahren, BMBF-Vorhaben 150 1078, Abschlußbericht, Berichts-Nr. 980232-TW, IZFP Saarbru¨cken, 1998. BMWi-Vorhaben 150 1087, Betriebsbedingte Eigenschaftsa¨nderungen kupferhaltiger ferritischer Beha¨lter- und Rohrleitungsbausta¨hle, MPA Stuttgart, Laufzeit 1997 bis 2000. BMWi-Vorhaben 150 1219: Nachweis von Cu-Ausscheidungen mittels mikromagnetischer Pru¨fverfahren, IZFP Saarbru¨cken, Laufzeit 1998 bis 2001. Bozorth, R.M., 1951. Ferromagnetism. van Nostrand, New York, p. 632. Goodman, S.R., Brenner, S.S., Low, J.R., 1973. An FIMatom probe study of the precipitation of copper from iron-1.4 at pct copper, Part I: Field-iron microscopy, Part
349
II: Atom probe analyses, Metall. Trans. 4, 2363–2369, 2372– 2378. Haarmann, K., Kalwa, G., 1986. Fu¨nf Jahrzehnte warmfeste Kupfer-Nickel-(Molybda¨n-)Sta¨hle. VGB Kraftwerkstechnik 66, 588– 598. Hansen, M., Anderko, K., 1958. Constitution of Binary Alloys. McGraw-Hill, New York. Hornbogen, E., Glenn, R.C., 1960. A metallographic study of precipitation of copper from a-iron. Trans. Metall. Soc. AIME 218, 1064– 1070. Hornbogen, E., Lu¨tjering, G., Roth, M., 1966. Koha¨rente Ausscheidung in Substitutionsmischkristallen des a-Eisens. Arch. Eisenhu¨ttenwes. 37, 523– 532. Jansky, J., Andra¨, T., Albrecht, K., 1993. Feedwater piping guillotine breaks at 340°C operation temperature. In: Kussmaul, K. (Ed.), Transactions of the 12th International Conference on Structural Mechanics in Reactor Technology, vol. F. North-Holland, Amsterdam, pp. 207– 214. Kizler, P., Uhlmann, D., Schmauder, S. 1998. Linking nanoscale and macroscale: Calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress– strain curves owing to dislocation theory, 24th MPA-Seminar, 8 – 9 Oktober 1998, Stuttgart, Beitrag Nr. 50. Kizler, P., Uhlmann, D., Schmauder, S., 2000. Linking nanoscale and macroscale: calculation of the change in crack growth resistance of steels with different states of Cu precipitation using a modification of stress– strain curves owing to dislocation theory. Nucl. Eng. Des. 196, S175– S183. Kohlhoff, S., Schmauder, S., 1989. A new method for coupled elastic-atomistic modelling. In: Vitek, V., Srolovitz, D.J. (Eds.), Atomistic Simulation of Materials: Beyond Pair Potentials, New York. Kubaschewski, O., 1982. Iron — Binary Phase Diagrams. Springer, Berlin. Ludwig, M., Farkas, D., Pedraza, D., Schmauder, S., 1998. Embedded atom potential for Fe – Cu interactions and simulations of precipitate– matrix interfaces. Model. Simul. Mater. Sci. Eng. 6, 19. Nedelcu, S., Kizler, P., Schmauder, S., Moldovan, N., 1999a. Atomic scale modelling of edge dislocation movement in the a-Fe-Cu system, Modelling and Simulation in Materials Science and Technology, eingereicht. Nedelcu, S., Kizler, P., Schmauder, S., Moldovan, N., 1999b. Modellierung der Versetzungsbewegung im a-Fe– Cu System auf atomarer La¨ngenskala, Technischer Bericht, MPA Stuttgart. Nedelcu, S., Kizler, P., Schmauder, S., Moldovan, N., 2000. Modelling simulation. Mater. Sci. Eng. 8, S181– 191. Nembach, E., 1997. Particle Strengthening of Metals and Alloys. Wiley, New York. Othen, P.J., Jenkins, M.L., Smith, G.D.W., Pythian, W.J., 1991. Transmission electron microscope investigation of the structure of copper precipitates in thermally-aged Fe– Cu and Fe– Cu– Ni. Phil. Mag. Lett. 64, 383– 391.
350
I. Altpeter et al. / Nuclear Engineering and Design 206 (2001) 337–350
Othen, P.J., Jenkins, M.L., Smith, G.D.W., 1994. High-resolution electron microscopy studies of the structure of Cu precipitates in a-Fe. Phil. Mag. 70, 1–14. Rau, P., Schick, M., Albert, F., Helmrich, A., 1991. Schaden und Reparatur an einer Kesseltrommel aus 15 NiCuMoNb 5 (WSB 62), VGB-Konferenz ‘Werkstoffe und Schweißtechnik im Kraftwerk 1991’, 9–10 Jan. 1991, Essen, and VGB Kraftwerkstechnik 72 H. 5 (1992) 444– 454. Ruoff, H., Katerbau, K.-H., 1992. Orientierende TEM-Untersuchungen zur betrieblichen Za¨higkeitsabnahme des Werkstoffs WB 36, BMU-Vorhaben SR 471, 24. Technischer Bericht, MPA Stuttgart. Russell, K., Brown, L., 1972. A dispersion strengthening model based on differing elastic moduli applied to the iron– copper system. Acta Metall. 20, 969. Schick, M., Wiedemann, J., 1995. Langzeit-Glu¨hversuche an unterschiedlichen Schmelzen und Wa¨rmebehandlungszusta¨nden des Werkstoffs 15 NiCuMoNb 5, BMU-Vorhaben SR 2065, Technischer Bericht 2.1, MPA Stuttgart. Schick, M., 1996. Unvero¨ffentlichte Untersuchungen zum Werkstoff WB 36, MPA Stuttgart, 1990 bis 1996. Schick, M., Wiedemann, J., Willer, D., 1998. Untersuchungen zur sicherheitstechnischen Bewertung von geschweißten
.
Komponenten aus Werkstoff 15 NiCuMoNb 5 (WB 36) im Hinblick auf die Za¨higkeitsabnahme unter Betriebsbeanspruchung, BMU-Vorhaben SR 2239, Technischer Bericht, MPA Stuttgart. Soisson, F., Barbu, A., Martin, G., 1996. Monte Carlo simulations of copper precipitates in dilute iron– copper alloys during thermal ageing and under electron irradiation. Acta Mater. 44, 3898. Sundman, B., Jansson, B., Andersson, J.-O., 1985. The Thermo-Calc databank system. Calphad 9, 153– 190. Uhlmann, D., Kizler, P., Schmauder, S., 1998. From nanoscale to macroscale: Study of damage in steels with Cu precipitates using micromechanically based stress– strain curves. In: Christensen, J.V., et al. (Eds.), Proceedings of the 19th Risø International Symposium on Materials Science: Modelling of Structure and Mechanics of Materials from Microscale to Product. Risø National Laboratory, Roskilde, Denmark, pp. 529– 534. Willer, D., Katerbau, K.-H., 1995. Auswertungen und Untersuchungen zur betriebsbedingten Za¨higkeitsabnahme des Werkstoffs 15 NiCuMoNb 5, BMU-Vorhaben SR 2065, Technischer Bericht 2.2, MPA Stuttgart.