Fatigue mechanisms in an austenitic steel under cyclic loading: Experiments and atomistic simulations

Materials Science & Engineering A 597 (2014) 128–138

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Fatigue mechanisms in an austenitic steel under cyclic loading: Experiments and atomistic simulations E.A. Soppa n, C. Kohler, E. Roos Materialprüfungsanstalt (MPA) Universität Stuttgart, Pfaffenwaldring 32, 70569 Stuttgart, Germany

ar t ic l e i nf o

a b s t r a c t

Article history: Received 5 September 2013 Received in revised form 10 December 2013 Accepted 11 December 2013 Available online 18 December 2013

Experimental investigations on the austenitic stainless steel X6CrNiNb18-10 (AISI – 347) and concomitant atomistic simulations of a FeNi nanocrystalline model system have been performed in order to understand the basic mechanisms of fatigue damage under cyclic loading. Using electron backscatter diffraction (EBSD) the influence of deformation induced martensitic transformation and NbC size distribution on the fatigue crack formation has been demonstrated. The martensite nucleates prevalently at grain boundaries, triple points and at the specimen free surface and forms small (
1 mm sized) differently oriented grains. The atomistic simulations show the role of regions of a high density of stacking faults for the martensitic transformation. & 2013 Elsevier B.V. All rights reserved.

Keywords: Fatigue Steel Austenite Martensitic transformation EBSD

1. Introduction Strong and ductile steels with excellent corrosion resistance are of particular interest for various applications. Deformation induced martensitic transformation of fcc austenite into bcc α0 martensite offers a unique possibility to enhance significantly the yield stress and the tensile strength of the material at a remaining good toughness [30]. This is the reason for the great research interest in metastable austenitic steels [1,7,8,20,28,29,37]. Nevertheless, despite an intensive research work, reliable models of martensitic transformation suitable for practical assessment of the specimen/component lifetime are missing up to now [32]. The interaction between microstructure and nucleation of martensite and its impact on crack initiation and crack growth is a key factor in this respect. Idrissi et al. [10] investigated, by transmission electron microscopy, a relationship between the stacking fault character and plasticity mode active during loading: ε-martensite transformation or mechanical twin formation in Fe–Mn–Al–Si austenitic steels. Raabe [25] is exploring the influence of carbon content on martensitic transformation (TRIP) or twinning (TWIP) in austenitic steels using ab initio methods. Two variants of deformation induced martensite are mentioned in the literature: ε-martensite (hcp) and α0 -martensite (bcc) for which different opinions concerning their nucleation sites in the microstructure n

Corresponding author. E-mail addresses: [email protected] (E.A. Soppa), [email protected] (C. Kohler), [email protected] (E. Roos). 0921-5093/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.12.036

exist. According to Nishiyama [21] ε-martensite forms in the areas with a beneficial but irregular distribution of stacking faults. The formation of α0 -martensite is, according to Poulon et al. [24], connected with dislocation pileups on the active slip planes. Peralta et al. [22] found martensite nucleation sites at crossing points of shear bands. A certain amount of accumulated plastic strain [13,32] and a threshold value of plastic strain Δεpl/2 ¼0.3% [1,8] must be reached in order to trigger martensite formation. A modified version of the Olson–Cohen model presented by Lehnhoff and Findley [15] shows the dependence of transformed martensite on the local strain amplitude in the microstructure and its impact on mechanical behaviour of the material and its fatigue resistance [8]. It is known that the growth of microstructurally “short” cracks can last until 90% of the specimen’s total lifetime in the HCF regime. The proper description of short cracks requires the consideration of the anisotropic material behaviour on the microscopic scale [12,19,22,26]. According to [17] cracks initiate in an austenitic steel AISI 316L under LCF-loading in persistent shear bands. Chauvot and Sester [5] examined the crack growth in X6CrNiNb18-10 at room temperature by replica. Unlike the authors of this paper they did not find the deformation induced martensitic transformation in any stage of the specimen lifetime. Roth et al. [27] performed in situ and ex situ cyclic deformation experiments in the HCF-regime on a metastable austenitic steel in combination with electron backscatter diffraction. They found that the majority of cracks initiate at twin boundaries in the absence of a martensitic phase. At the tip of a propagating short crack martensitic transformation first takes place. The instability of retained austenite in the plastic zone at the crack tip leads to the

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Table 1 Chemical composition of the X6CrNiNb18-10 steel (in weight %) [6]. C

Si

0.043 0.410 Balance Fe

Mn

P

S

Cr

Ni

Nb

Ta

1.900

0.019

0.002

17.150

10.300

0.660

0.008

formation of martensite [9]. Stolarz et al. [36] observed in a high purity Fe–17Cr–13Ni alloy loaded with a strain amplitude of 70.4% that cracks nucleate in transformed α0 -regions irrespective of the grain size and martensite content. All authors share the opinion that the growth rate of short cracks decreases rapidly due to their interaction with microstructural barriers (e.g. [14]). This process is connected with crack closure and a reduction of the propagation rate. The crack closure is enforced by a volume expansion of about 2% during the martensite formation [27,41].

Fig. 1. Microstructure of the X6CrNiNb18-10 after heat treatment and before mechanical loading.

Austenitic stainless steel X6CrNiNb18-10 with the chemical composition as presented in Table 1 was used in this study. This material delivered by DMV STAINLESS Deutschland GmbH was manufactured by melting metallurgy and casting with subsequent plastic forming and solution heat treatment at 1050 1C for 10 min and was water-quenched to room temperature [6].

that it is not exhausted to chromium carbides. The addition of 0.66% of Nb (Table 1) bound the entire C to niobium carbides (NbC) and thus stabilized the chemical resistance of the steel. The resulting microstructure after heat treatment (homogenization) consisted of austenitic grains with several twins and finely distributed NbC located along the sub-grain boundaries or lattice imperfections and forming structures similar to ropes of pearls in the grains (Fig. 1). Two classes of NbC size distribution, with average values of 33 nm and 410 nm, were found by using replica. In addition to fine NbC, isolated large NbC particles (
30 mm) were found. They are primary carbides formed during casting and not dissolved during the short homogenization time of 10 min only.

2.2. Low cycle fatigue test and electron backscatter diffraction

3.2. Combination of interrupted LCF tests with EBSD measurements

Smooth cylindrical specimens [33] were uniaxially loaded in air at room temperature with different strain amplitudes between 0.25% and 1.5%, R¼  1 with a strain rate of 0.1% s  1 until initiation of macroscopic crack. For an interrupted LCF test combined with the electron backscatter diffraction (EBSD) technique, a strain amplitude of 1.5%, R ¼ 1 was chosen. This relatively great loading amplitude should ensure a moderate number of loading cycles until break. The total length of the specimen of 60 mm allowed a non-destructive analysis in the scanning electron microscope after a defined number of cycles and a new loading after breaks. For the observation of the microstructure alteration and crack development at different stages of the specimen lifetime, two narrow flat bands (3 mm  20 mm), symmetrically placed on the specimen lateral surface, were grounded and electrolytically polished before loading. EBSD was used to study the distribution of grain orientations on the specimen surface and to identify deformation induced α0 -martensite in the austenitic matrix. The phase identification – austenite or α0 -martensite – was based on the comparison of the measured diffraction patterns with the data stored in the ICCD database [11] for the assumed phase. Five overlapping measuring fields of 350  350 mm2 localized on the flat polished area on the specimen surface were chosen for the EBSD measurements. The resolution of the standard scans was 1 mm; additional scans of interesting details were recorded with higher resolution.

Changes in the microstructure and fatigue crack formation in the specimen under cyclic loading were observed by a combination of interrupted LCF tests and EBSD analysis in SEM. The first EBSD scans were recorded on the undeformed specimen in the previously marked areas and served as a reference for further measurements. The subsequent scans were taken after 10, 50, 100, 130, 180, 230 and 300 cycles. The crystallographic orientation of grains and twins in the reference state was randomly distributed. In this state no α0 -martensite was found. A small amount (less than 1%) of the bcc-phase was detected as delta-ferrite and was also partially caused by etching pits after electrolytic polishing. These small and flat etching pits had no influence on the crack formation. On the contrary, they were very helpful as identification marks making the mapping of the grain boundary contours to the SEM images easy and reliable [33].

2. Material and experimental methods 2.1. Material

3. Experimental results 3.1. Microstructure Ni forms with Fe a solid solution, extends the γ-Fe field and stabilizes (partially) the austenitic phase until room temperature or even below it. Cr enhances the corrosion resistance, provided

3.2.1. Work hardening behaviour of the material under cyclic loading Deformation and hardening behaviour of X6CrNiNb18-10 under cyclic loading depends on the strain amplitude (Fig. 2(a)). At the smaller amplitude of 0.25% a minor softening occurs, caused probably by arrangement of dislocations into energetically beneficial patterns. For the medium sized amplitudes until 0.75% the ultimate stress reaches the saturation stadium from the very beginning. For the strain amplitudes greater than 0.75% a pronounced work hardening caused by martensitic transformation was observed. The higher the loading amplitude the greater the volume fraction of α0 -martensite in the microstructure. The curves of minimum and maximum stresses recorded during the LCF-tests performed with a strain amplitude between 0.25%–1.5% and separately for the interrupted LCF-tests (strain amplitude of 1.5%, R¼  1) are shown in Fig. 2(a, b). The development of the volume fraction of α0 -martensite as a function of loading cycles is presented in Fig. 2(c). The volume

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Stress [MPa]

500 250 0 -250 -500 0

50

100

150

200

250

300

Volume % of martensite

Number of cycles 10 9 8 7 6 5 4 3 2 1 0

area_1 area_2 area_5 area_4 area_3

0

50

100

150

200

250

300

Number of cycles Fig. 2. Stress curves (minimum, maximum) recorded during the LCF-tests for: (a) strain amplitudes between 0.25% and 1.5%, (b) the strain amplitude 1.5% in the interrupted LCF test combined with EBSD measurements, (c) volume fraction of α0 -martensite after different numbers of cycles.

increased up to 6%–9% respectively after 300 cycles, apart from a partial back-transformation between 180 and 230 cycles. In this interval the loading parameters were changed from symmetric tensile/compression to pure tensile loading and subsequent unloading without a compression part (Fig. 2(b)). The resumption (restoration) of the initial symmetrical tensile–compression loading caused a partial back-formation of α0 -martensite to austenite.

3.2.2. Alteration of the microstructure during cyclic loading, formation of α0 -martensite The first “spots” in grains with slightly different crystallographic orientations as the parent grain appeared in the EBSD scans after 50 cycles. These “spots” enlarged under subsequent loading and formed regions with significantly different orientations from the original grains (Fig. 3). The first indication of the martensitic phase was found as well after 50 cycles. After 100 cycles there were already several locations of α0 -martensite detectable by EBSD. Fig. 3 shows the distribution of α0 -martensite in the austenitic matrix after 180 and 300 cycles in comparison to the undeformed state. α0 -martensite forms mainly at grain boundaries and triple points. In addition to grain boundaries as preferential sites for martensitic nucleation, there were grains without any visible substructure in which α0 -martensite formed in the inner part and filled step by step the whole grain area. Not only the α0 -martensite volume fraction but also the amount of defects grew with the number of cycles (Fig. 3). The evaluation of the EBSD scans was carried out with the Software EDAX-TSL OIM Analysis 5. The clean-up procedure with a minimum confidence index CI¼0.1 was used only once. Pixels with the confidence-index CIo0.1 were replaced by neighbour pixels. Using a “minimum confidence index” only these measuring points were assigned to the martensitic phase for which diffraction patterns showed a high accordance to the data for the bcc lattice of α-ferrite stored in the ICCD database [11]. On the specimen lateral surface parallel to the loading axis, α0 -martensite occurs as small

(
1 mm) “islands” with different orientations (Fig. 4(a, b)), which gradually fill the grain interior.

3.2.3. Crack formation mechanisms Most of the cracks in the specimen loaded with the strain amplitude of 1.5%, R¼  1 were oriented almost normal to the loading axis right from the beginning. This fact and the absence of extrusions and intrusions excluded the observed cracks as “crystallographic cracks” growing along the slip planes. Two main crack initiation scenarios were observed in the LCF regime: cracks at the phase boundaries between austenite and α0 -martensite or in fully martensitic areas (Fig. 5(a), (b)) and coarse NbC particles broken or/and separated from the matrix (Fig. 5(c)). The formation of α0 -martensite in the specimen was observed before first fatigue cracks emerged. Formation of a hard α0 -martensite in the soft austenite intensifies the heterogeneous stress and strain distribution in the microstructure and can cause the premature crack initiation. The phase boundary between α0 -martensite and austenite corresponds in most cases with the course of the grain boundaries in the parent austenite. Assuming that the phase boundary is a “weak link” in the microstructure, it is understandable that such an interface will be cracked and even very short cracks are oriented almost normal to the loading axis. The normal stress component is maximal for this orientation. Some parts of the crack with martensite at one crack edge only are visible in Fig. 5(b). It seems to be likely that these parts of the crack result from decohesion of highly stressed phase boundaries. Once the crack was present in the microstructure, the area around its sharp tip with significant stress and strain concentrations and stress triaxialities was a preferable site for further martensitic transformation. Another possible scenario is the crack initiation in fully martensitic area which consists of a great number of small grains in α0 -martensite corresponding to the areas with high dislocation

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Fig. 3. Formation of deformation induced α0 -martensite (black) in the austenitic matrix after (a) 0 cycles; (b) 180 cycles; (c) 300 cycles (LCF, strain amplitude 1.5%, R ¼  1); (d) standard orientation triangles valid for all EBSD-images in the text.

Fig. 4. Microstructure of the martensitic area: (a) EBSD: grain orientations in austenite, α0 -martensite is black; (b) EBSD: grain orientations in α0 -martensite, austenite is black.

density. Also in austenite surrounding the transformed martensite a high density of interfaces forming substructures with small orientation misfit were found [33,34]. The genesis of their formation is not fully understood, but it is known that during a symmetric tensile–compression loading a partial back-transformation of α0 -martensite under compression stress takes place (Fig. 2(c)). It can thus be assumed that the back-transformation of the single “martensite domains” leaves behind a lot of interfaces which make the repeated martensite nucleation under tensile loading easier.

Stress and strain fields in the microstructure with and without cracks are significantly different. Martensitic transformation, however, occurs in undamaged as well as in cracked regions. The coarse and elongated NbC (10 mm–30 mm long) break or separate from the matrix more easily than small and globular carbides and build short cracks that can grow further into the matrix phase. It is also possible that large NbC particles which are located accidentally at the crack path modify it through the interaction with the stress field around the crack and could thus be damaged.

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Fig. 5. Crack path along the phase boundary between α0 -martensite and austenite: (a) SEM image of the crack; (b) EBSD: grain orientation in austenite, martensite – black, crack – white and (c) Crack initiation at broken and debonded coarse NbC.

ε

X-ray diffraction measurements (XRD) confirmed the existence of 80–90% of α0 -martensite in the fatigue surface whereas in the residual fracture area only about 10–20% of α0 -martensite was found [33]. This indicates that the propagation of fatigue cracks in X6CrNiNb18-10 at room temperature is controlled mostly by the martensitic phase.

NPT Free Surface

NVT 4. Molecular Dynamics (MD) simulations In order to investigate the mechanisms of the martensitic transformations of a polycrystalline sample of steel under loading conditions we used Molecular Dynamics (MD) simulations.

z y

NVT

x

ε Fig. 6. Schematic set-up of the simulation box.

4.1. Methods For the simulations we employed classical MD simulations with EAM potentials. The simulations have been performed with the MD code IMD [35]. Since available interatomic potentials for Fesystems have the bcc structure as the structure of lowest energy, we used a Fe–Ni random alloy in order to stabilize the austenitic fcc structure by adding Ni atoms while still allowing a transition into the bcc structure under deformation. For the Fe–Fe interaction we used the potential by Simonelli et al. [31], for the Ni–Ni interaction the potential by Voter [39], and for the Fe–Ni interaction the potential by Vailhe et al. [38]. In this work, the chemical composition Fe50Ni50 has been chosen. Simulations with different Ni concentrations have shown that this is a good compromise between the aim to model a system of austenitic steel (high Fe concentration) and a high stability of the austenitic phase (high Ni concentration), i.e. a small tendency to undergo a martensitic transformation. The stacking fault energy in the composition Fe50Ni50 is 1.6 mJ/m2.

Polycrystalline austenitic structures have been generated using a Voronoi construction where the centres of the grains and the grain orientations are chosen randomly. Periodic boundary conditions are applied in two spatial dimensions while in the third spatial dimension free boundary conditions are chosen in order to study the effect of free surfaces. The simulations are performed at a temperature of 300 K with a time step of 1 fs. The sample is shown schematically in Fig. 6. A strain controlled uniaxial tensile test is simulated by rescaling the simulation box in the loading direction every 10 time steps corresponding to a strain rate of 108 s  1. In y direction a stress control has been applied in such a way that the stress in this direction is always zero thus allowing a contraction of the simulation box. Two types of geometry of a polycrystalline model have been studied. First a full three dimensional geometry with a cubic simulation box and, secondly, a quasi three dimensional geometry where the width of the simulation box in y direction is about

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2 nm. The grains in the latter models have a columnar shape where the o110 4 direction of the initial fcc structure has been used in the direction of the columns. By choosing the quasi three dimensional geometry a much bigger extension of the simulation box in the direction perpendicular to the columns than in the cubic geometry can be achieved using the same number of atoms as in the full three dimensional simulations. However, the degrees of freedom of the system are restricted. For the analysis of the defect structures that are generated during the deformation simulations the Common-Neighbour analysis has been employed. Using this method, the crystallinity of the atoms has been determined differentiating whether the atoms are in the fcc structure, the hcp structure (stacking faults), in another 12-fold coordinated structure or in a not 12-fold coordinated structure. This method has been extended to detect the bcc structure by selecting atoms having in the two nearest neighbour shells the coordination number 14. 4.2. Simulation results 4.2.1. Deformation of cubic nanocrystals The deformation behaviour of three dimensional polycrystalline models of austenitic steel has been simulated with systems of three different sizes: a small model with box lengths of 12.5 nm, a medium-sized model of size 25 nm and a large model of size 50 nm. All models contain 16 grains thus allowing to study the effect of different grain sizes. The small and the medium-sized model have been deformed cyclically with a strain amplitude of 10% for 15 and 12 cycles, respectively, while the large model has been deformed uniformly with a maximum strain of 20%. 4.2.1.1. Cyclic deformation of the small model. The stress history of the cyclic deformation of the small model is shown in Fig. 7(a). It can be seen that during the first five cycles a large strengthening arises. Then a sudden softening occurs with nearly constant stress amplitude during the next five cycles. After this, an unsteady behaviour of the stress can be seen. The large fluctuations in the stress values during the cycles can be traced back to single deformation processes (generation of dislocations, displacement of grain boundaries, martensitic transformations) which are more pronounced for smaller models. The deformation processes which occur during the cycles shall now be considered in more detail using the development of the crystal defects. Fig. 7(b) shows the time development of the crystallinity of the atoms.

During the first cycles, a large oscillation of the number of atoms in fcc, hcp, and bcc structure can be seen while there is an overall increase in the fraction of bcc atoms. After the fourth cycle, there is an intermediate decrease of the number of bcc atoms while the fraction of hcp atoms increases. After the fifth cycle, there is a long period of almost constant crystallinities which is followed by a period of unsteady behaviour. Comparing the time development of the stress and the crystallinities in Fig. 7(a) and (b), it can be concluded that the increase in the fraction of atoms in the bcc structure, that is, α0 -martensite, leads to strengthening. However, to understand the softening of the model during the period of constant α0 -martensite content the spatial distribution of the phases has to be considered. Fig. 8 shows the crystallinities of the atoms at different times during the cyclic deformation. Fig. 8(a) depicts the state of the model after equilibration. The austenitic structure of the grains is widely free of defects while at the grain boundaries small regions of α0 -martensite have formed. Fig. 8(b) shows the state of the model after the first cycle of deformation. Extended regions of α0 -martensite have formed and partial dislocations have moved through the grains leaving stacking faults behind. After the third cycle, the transformation into α0 -martensite is almost completed (Fig. 8(c)). The original structure of the grains has almost vanished and larger grains of α0 -martensite have formed. During the following deformation up to a strain of 10% the structure changes again completely (Fig. 8(d)). The fraction of fcc atoms has vanished and except for a slant layer which consists of a twin the model consists of a single crystal of α0 -martensite. A further change of the structure occurs during the fifth cycle (Fig. 8(e)) in the form of an almost complete transformation of the model into the hcp structure (ε-phase). This intermediate structure transforms again into a layered structure (Fig. 8(f)) with a high activity of dislocation motion in the boundaries leading to the softening of the model. It can also be seen in Fig. 8 that the roughness of the free surfaces of the model increases during the cyclic deformation. 4.2.1.2. Cyclic deformation of the medium-sized model. The time development of the stress during the cyclic deformation of the medium-sized model is shown in Fig. 9(a). During the first 8 cycles, a strengthening can be seen which is followed by a period of unsteady behaviour. The time development of the crystallinity (Fig. 9(b)) shows an increase of the fraction of atoms in the bcc structure with increasing time. The structure of the model at different times is shown in Fig. 10(a–c). Starting with grains almost free of defects (Fig. 10(a)) extended regions of

5000 4000

σ [MPa]

Percentage of atoms

σ ε *100

3000 2000 1000 0 −1000 −2000 −3000

0

10

20

30 40 Time [ns]

50

60

133

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1

fcc hcp bcc other

0

10

20

30 Time [ns]

40

50

60

Fig. 7. (a) Stress as a function of time during 15 cycles of the uniaxial deformation of the small model. (b) Time development of the percentage of atoms with a given crystallinity in the small model.

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Fig. 8. Structure of the small model at several states during the cyclic deformation. (a) t¼ 0, ε ¼ 0, (b) t ¼4 ns, ε¼ 0, (c) t ¼12 ns, ε ¼0, (d) t ¼13 ns, ε¼ 10%, (e) t¼ 16.5 ns, ε ¼5%, (f) t ¼18 ns, ε ¼0. The colour encoding is: grey (fcc), red (hcp), yellow (bcc), green (other 12 fold coordinated) and blue (other).

α0 -martensite have formed after the first cycle of deformation (Fig. 10(b)). Fig. 10(c) shows the model after 7 cycles of deformation. The model has been transformed into large grains of α0 -martensite which form a quasi two dimensional structure. 4.2.1.3. Uniform deformation of the large model. Fig. 10(d–f) shows the structure of the large model during uniaxial deformation up to a strain of 20%. The structure exhibits the same phenomena as in the smaller models. Additionally, a substructure within the α0 -martensite grains is visible which consists of different variants of α0 -martensite forming a domain like structure. Furthermore, in the shrinking austenitic grains a large density of stacking faults has formed in such a way that the resulting structure can be considered as a new crystalline phase in between the fcc and the hcp structure (referred to as quasi ε-phase in the following). 4.2.1.4. Deformation of quasi three-dimensional nanocrystals. Simulations of quasi three-dimensional nanocrystals have been performed in order to determine the nanostructure during deformation in dependence of the model size and the number of grains. Eight different models have been considered with model sizes of 50 nm, 100 nm, 200 nm and 250 nm. For all sizes, models containing 8 grains have been simulated. In the case of the models of sizes 100 nm and 200 nm, also variants composed of 16 and 32 grains have been considered. All systems have been uniaxially deformed up to a strain of 20%. The fraction of atoms in bcc structure (α0 -martensite) as a function of the strain is shown in Fig. 11 for all models. It can be seen that the dependence of the martensitic transformation on the model size is stronger than the dependence on the number of grains for a given model size. In the case of the model of width 50 nm, the percentage of α0 -martensite has a maximum for a strain of about 7.5% and then

decreases with increasing strain. The reason for this behaviour can be seen in the development of the plastic deformation as can be inferred from Fig. 12(a, b) where the structure of the model is shown for two different strain values. The small size of the grains as well as the large free surface (compared to the model size) lead to a stress reduction due to the plastic deformations which results in a back formation of α0 martensite into austenite. For the models of size 100 nm, the percentage of α0 -martensite attains values up to 75–85% at the end of the deformation where the increase of the fraction of α0 -martensite is larger for smaller grains. The reason for this behaviour can be seen in the stress reduction due to the larger number of grains. In the case of the models of size 200 nm the percentage of martensite in the strain range up to 20% attains only a value of about 10%. Fig. 12(c, d) shows the structure of the model for two strain values. A special feature in the larger models which is not clearly visible in smaller models is the formation of extended regions with high densities of stacking faults. These are generated by the collective emission of partial dislocations from grain boundaries and form subgrains. As can be seen in Fig. 12(d) the martensitic transformations preferentially take place in these subgrains where the grain boundaries are the seeds of the transformation. Accordingly, the transformation from austenite to α0 -martensite seems partly to proceed via the quasi ε-phase. The model of size 250 nm shows a higher content of α0 martensite than the models of size 200 nm. However, for high strain values there is a slight decrease of the percentage of α0 martensite which may be due to the stress release because of the necking of the model. Fig. 12(e, f) shows the structure of the model for two strain values. It can be seen in the lower right of Fig. 12 (f) that the back transformation of α0 -martensite proceeds into the quasi ε-phase.

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3000

Percentage of atoms

2000

σ [MPa]

1000 0 −1000 −2000 −3000

σ ε *100 0

5

10

15

20 25 30 Time [ns]

35

40

45

50

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1

135

fcc hcp bcc other

0

5

10

15

20 25 30 Time [ns]

35

40

45

50

Fig. 9. (a) Stress as a function of time during 12 cycles of the uniaxial deformation of the medium-sized model. (b) Time development of the percentage of atoms with a given crystallinity in the medium-sized model.

Fig. 10. Structure of the medium-sized (a–c) and large (d–f) model at several states during the cyclic deformation. (a) t¼ 0, ε ¼0, (b) t¼ 4 ns, ε¼ 0, (c) t¼ 28 ns, ε¼ 0, (d) t ¼0, ε¼ 0, (e) t¼ 10 ns, ε¼ 10%, (f) t¼ 20 ns, ε ¼20%. The colour encoding is: grey (fcc), red (hcp), yellow (bcc), green (other 12 fold coordinated) and blue (other).

5. Discussion The aim of this work was to study the phenomena which are essential for fatigue crack initiation and growth in the austenitic stainless steel X6CrNiNb18-10 under low cyclic loading at room temperature in air. The permanent delivery of mechanical energy during cyclic loading affects the microstructure and evokes changes on nano- and micro-levels which help to dissipate the energy in the material for a certain time. A close combination of experiment and Molecular Dynamics simulations was used to study the impact of cyclic loading on the microstructural changes and crack initiation in X6CrNiNb18-10 at room temperature.

Both in experiment and in the atomistic simulations a deformation induced transformation of a fcc austenite into a bcc α0 -martensite was found. In the conventional carbon steels, the carbon atoms are located at the octahedral interstitial sites preferentially in the c-direction and form a tetragonal lattice. The tetragonal variant of martensite is hard and brittle. In the X6CrNiNb18-10 there is only a small content of carbon that is totally bonded to NbC. For the resulting bcc lattice of α0 -martensite there is no reason for the tetragonal distortion. A cubic shape with the lattice parameters similar to that of ferrite was detected by electron diffraction on thin foils in TEM [11,34]. This fact has wide-ranging consequences for mechanical properties of the formed martensite and for the initiation mechanisms of fatigue cracks.

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α0 -martensite nucleates prevalently at grain boundaries, triple points and on the specimen surface and forms small (
1 mm sized) differently oriented grains (even in the same parent austenitic grain (Fig. 3)). Also in the atomistic simulations the grain boundaries and the specimen surface were preferred as nucleation sites for the martensitic phase. In the simulation of the “large model” the domain like substructure of martensitic areas similar to the small martensitic grains detected in experiment was

Fraction of atoms with bcc structure

1 w=50, g=8 w=100, g=8 w=100, g=16 w=100, g=32 w=200, g=8 w=200, g=16 w=200, g=32 w=250, g=8

0.8

0.6

0.4

0.2

0

0

5

10

15

20

ε [%] Fig. 11. Fraction of atoms with bcc structure (α0 -martensite) in quasi threedimensional models of width w (in nm) and with g grains.

observed. The interfaces with their “defected structure” compared to the grain interior offer suitable sites for the martensitic transformation. Moreover, elevated stress and strain concentrations caused by crystallographic anisotropy can be found very often in the vicinity of grain boundaries. Such places facilitate the martensitic transformation. The volume fraction of α0 -martensite measured by EBSD and Xray diffraction (XRD) on the same specimen gave similar results. The average volume fraction of α0 -martensite measured on the lateral surface in the LCF-specimen after 300 cycles (almost 100% lifetime) by the strain amplitude of 1.5%, R ¼ 1 varied from 6–9% in dependence of the local microstructure. The amount of α0 martensite in the microstructure depends on the loading amplitude. A higher strain amplitude leads to a larger volume fraction of the formed martensite. It is visible in the increase of the materials work hardening and connected with the more pronounced hardening behaviour of α0 -martensite compared to austenite. The following conditions must be fulfilled in order to start martensitic transformation: The threshold value of the equivalent plastic strain εpl ¼ 0.3% must be reached locally in the microstructure [1,4,18] and a certain amount of the accumulated plastic strain must be present. According to our observations even at the great strain amplitude of 1.5% the martensitic transformation needed at least 50 cycles to start. It seems to be obvious that changes of the microstructure on the nano-level are required to initiate the transformation. In the atomistic simulations, it was seen that the formation of α0 -martensite proceeds preferentially through the intermediate

Fig. 12. Quasi three-dimensional models of width 50 nm (a, b), 200 nm (c, d), and 250 nm (e, f) during uniaxial deformation. (a) ε¼ 10%, (b) ε ¼20%, (c) ε ¼2.4%, (d) ε ¼ 5%, (e) ε¼ 10%, (f) ε ¼15%. The colour encoding is: grey (fcc), red (hcp), yellow (bcc), green (other 12 fold coordinated) and blue (other).

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quasi ε-phase consisting of a high density of stacking faults in the fcc phase (or, equivalently, of a high density of stacking faults in the hcp phase). The occurrence of this phase can be attributed to the low stacking fault energy. Also the backformation of the martensite yields the quasi ε-phase. The quasi ε-phase could not be seen in the experiments. The reason for this could be the low resolution of the EBSD measurements or the higher stacking fault energy in X6CrNiNb18-10. The formation of the α0 -martensite leads to a strengthening which can be attributed to the lower susceptibility to deform plastically which means that less dislocations are emitted from the grain boundaries. However, it could be seen that this can partially be circumvented by the formation of twins in the α0 martensite with a high activity of dislocation motion in the twin boundaries which can be seen as the equivalent of shear bands at the nanoscale. Despite intensive efforts using SEM neither extrusions nor intrusions were found at the specimen surface at any stage of the specimen lifetime. This confirms the observations that short cracks in X6CrNiNb18-10 do not propagate transcrystalline which is characteristic for crystallographic cracks starting to grow in the intrusions. On the contrary, the cracks were often oriented almost normal to the loading axis from the very beginning. The EBSD measurements showed that cracks started at the phase boundary between austenite and α0 -martensite or inside fully martensitic areas in the austenitic matrix. This process is controlled by normal stress which is maximal for the perpendicular orientation to the phase boundary. From the point of view of the micromechanics it is obvious that formation of a hard bcc-α0 -martensite in a ductile and relatively soft austenite causes a heterogeneous stress and strain distribution on the microscopic level. α0 -martensite enhances locally the stress amplitude whereas in a soft austenite the plastic strain amplitude increases. Strain concentration in the austenite along the phase boundary is connected with a stress increase along the interface and can initiate fatigue crack there. The XRD measurements of the austenite and α0 -martensite in the LCF-specimens showed more than 80% martensite in the fatigue surface and only about 20% in the residual fracture area. Not only the crack formation but also its growth under low cyclic loading seems to be controlled by the martensitic phase. The remaining 20% of nonmartensitic area in the fatigue surface are probably partially connected with the crack path along the phase boundary between martensite and austenite and debonded or broken coarse NbC as crack initiation sites. An interesting fact is that crack in the residual fracture area caused by overload breakage exhibited only
20% of martensite. This fact confirms the supposition that martensitic transformation needs a certain amount of accumulated strain, in this case at the crack tip, in order to come about. In the residual fracture area this requirement is not fulfilled. In the X6CrNiNb18-10 under cyclic loading plastic zones develop at the crack tips, in which stress and strain amplitudes are much higher than nominal loading, and enable martensitic transformation in the surrounding of the crack tip. The consequence of this is that cracks grow in the “martensitic tunnels”. As already said martensitic transformation requires a threshold value of strain amplitude
0.3% and a certain amount of accumulated plastic strain. This fact indicates that the crack propagation in the residual area is controlled by another mechanism than in the fatigue areas.

6. Outlook There are a great number of factors that influence the microstructure alterations in X6CrNiNb18-10 steel under cyclic loading.

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Some of them can probably cause crack growth retardation and are therefore beneficial for the specimen0 s lifetime. It is currently unclear whether the fine size distribution of NbC could partially suppress the martensitic transformation and generally improve the fatigue resistance of the studied austenitic steel. It was always observed by the authors that coarse NbC are crack initiation sites next to the martensite/austenite interfaces. The elimination of these large particles through plastic deformation and subsequent homogenization above T ¼1000 1C for a longer time should result in refinement of NbC. Moreover, the appearance of ε-martensite as precursor of α0 -martensite in the atomistic simulations could not be confirmed experimentally up to now. Narrow bands, similar to twins, with small areas of transformed α0 -martensite were visible in TEM. The crystallographic structure of these bands, however, known from simulations as a mixture of fcc and hcp phases, could not be determined by electron diffraction. Nevertheless, the authors are confident that the simulation tools combined with improved experimental techniques might enable clarifying these problems in the future work.

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