**1. Introduction**

In the early stages of the development of stainless steels, the passivity of the material and, therefore, its "stainlessness" was the main scope of development [1,2]. Chemical passivity of steels in many environmental conditions is achieved by alloying at least about 11 wt% chromium to the base material. Due to an excellent combination of mechanical and technological properties, as well as corrosion resistance, austenitic stainless steels are the most prevalent group of stainless steels—widely used for components in nuclear power and chemical plants as well as a great variety of industrial, architectural and biological applications [3–6]. Since the chromium contents of typical austenitic stainless steels exceed 16 wt%, their equilibrium microstructure at room temperature would be fully ferritic, if no other austenite stabilizing alloying elements were added to the material. Elements most often used to obtain an austenitic microstructure are nickel, manganese, carbon and nitrogen. Because carbon has a very high affinity with chromium, chromium carbides are prone to develop particularly at

high temperatures. This can reduce the chromium solid solution content in the austenitic matrix to less than 11 wt% and, consequently, lead to localized loss of stainlessness, especially at, or close to, the grain boundaries, resulting—under certain conditions—in intercrystalline corrosion. Therefore, in order to assure the corrosion resistivity of austenitic stainless steels, a very low carbon content and/or alloying with elements of a higher affinity with carbon, (e.g. niobium or titanium) are required [4]. In some cases, the ferromagnetic body centered cubic (bcc) δ-ferrite can be obtained in the paramagnetic face centered cubic (fcc) γ-austenitic microstructure directly after the manufacturing or melting process [7–10]. Indeed, δ-ferrite is a stable phase and its volume fraction does not change during mechanical loading. Generally, the influence of the chemical composition of Cr-Ni stainless steels on the initial microstructure at ambient temperature (AT) obtained after solution annealing heat treatment can be roughly estimated from the Cr und Ni content using the Maurer diagram [1]. Furthermore, the Schaeffler diagram provides more detailed information based on Cr and Ni equivalents taking other alloying elements besides Cr and Ni into account and is generally used for determining welding microstructures in Cr-Ni stainless steels [11].

The change in chemical composition not only influences the passivity of austenitic stainless steel but also significantly affects the metastability of austenite [12–16], meaning it is susceptible to undergoing phase transformations. Hence, the paramagnetic γ-austenite can transform by plastic deformation to a more stable microstructure, i.e. paramagnetic hexagonal close-packed (hcp) ε-martensite and/or body cubic centered (bcc) α´-martensite [17–24]. Scheil, one of the earliest researchers in this field, investigated the γ-austenite to α´-martensite transformation by measuring magnetic properties [25]. The change in magnetic properties by phase transformation can be used for non-destructive detection of α´-martensite as well as for monitoring fatigue processes in metastable austenites [26]. However, δ-ferrite, in the initial state of metastable austenite, has to be clearly separated from deformation-induced α´-martensite because both phases are ferromagnetic [7–10]. Deformation-induced phase transformations in metastable austenite affect significantly the fatigue process and are influenced by chemical composition [12–16], temperature [14,27–30] (encompassed by stacking fault energy (SFE) [31–39]), as well as grain size [32,40–43] strain amplitude [29,44–47] strain rate [48–50] and strain/stress state [51]. Additionally, SFE in fcc materials influences the slip character of dislocation, which has been summarized in the cyclic deformation map as a function of SFE and plastic strain amplitude given in [52–54]. For low SFE, independent of strain (stress) amplitude, the planar slip character occurs but for materials with higher SFE, a dependency of strain (stress) amplitude on dislocation slip character exists. High strain (stress) amplitude in the low cycle fatigue (LCF) regime leads to the development of the cell dislocation structure, which correlates with the wavy slip character of dislocation. The decrease of strain (stress) amplitude results in the formation of persistent slip bands in the high cycle fatigue (HCF) regime. Between the LCF and HCF regimes and lower and higher SFE, mixed dislocation structures can be observed [52–54]. A cyclic dislocation structure map of fcc materials with different SFE is not currently available for the very high cycle fatigue (VHCF) regime. The relationship between dislocation slip character and SFE described above was found for stable fcc materials [52–54]. In the case of metastable fcc austenite, SFE influences not only the dislocation slip character but also the deformation-induced phase transformation in ε and/or α´-martensite [17–24] as well as the formation of twins [55–57]. Figure 1 summarizes the microstructural changes in metastable austenitic Cr-Ni stainless steels due to cyclic mechanical loading, supported by TEM micrographs, which influence the cyclic deformation behavior of metastable austenitic stainless steels and consequently fatigue life. In this context, the present paper focuses on microstructural changes in metastable austenitic stainless steels, their cyclic deformation and transformation behavior at ambient and elevated temperatures in the whole fatigue regime from LCF to VHCF.

**Figure 1.** TEM micrographs with deformation and transformation microstructures of cyclically loaded metastable austenitic stainless steels: (**a**) typical dislocation density of the initial state after solution annealing, AISI 348 [58]; (**b**) cell dislocation structure (wavy slip character) at Nf in AISI 348 fatigued with σ<sup>a</sup> = 280 MPa, R = −1 at AT with f = 5 Hz [58]; (**c**) dislocation accumulation in one direction (planar slip character) at Nf in AISI 348 fatigued with σ<sup>a</sup> = 260 MPa, R = −1 at AT with f = 5 Hz [58]; (**d**) stacking faults (SF) at Nf in AISI 304 fatigued with εa,t = 0.325%, R = -1 at AT with f = 5 Hz [58]; (**e**) twins in AISI 347 fatigued with <sup>σ</sup><sup>a</sup> <sup>=</sup> 160 MPa, R <sup>=</sup> <sup>−</sup>1 at T <sup>=</sup> <sup>300</sup> ◦C with f <sup>=</sup> 980 Hz at N <sup>=</sup> <sup>5</sup> <sup>×</sup> 108, (**f**) ε- and α´-martensite at Nf in AISI 321 fatigued with σ<sup>a</sup> = 330 MPa, R = −1 at AT with f = 5 Hz [59].

## **2. Materials**

The investigated material was metastable austenitic stainless steel AISI 347 (X10CrNiNb1810, 1.4550) in two batches (A and B). The chemical composition of both batches is given in Table 1, which corresponds to German and international standards [60,61]. However, it is important to note that these standards do not take into consideration the metastability of the austenitic microstructure, but focus on the stainlessness of the steel. It is known that the same type of austenitic stainless steel can exist in significantly different states of metastability [16] up to a fully stable state. The material's metastability can be characterized by experimentally estimated equations, which describe the martensitic start (MS) or deformation-induced transformation temperature (Md) as well as the stacking fault energy (SFE), according to the chemical composition of austenitic stainless steels. In the literature, several equations for MS [13], Md30 [14] and SFE [34] are given. Table 1 gives examples of these metastability parameters according to the following equations:

$$\text{M}\_{\text{d50,Nangel}} \text{ in } ^\circ \text{C} = 413 \text{ - } 462 \cdot (\text{C} + \text{N}) - 13.7 \cdot \text{C} \text{ r} - 9.5 \cdot \text{Ni} - 8.1 \cdot \text{Mn} - 18.5 \cdot \text{Mo} - 9.2 \cdot \text{Si} \tag{1}$$

$$\text{M}\_{\text{S,Eichelmann}} \text{ in } ^{\circ}\text{C}=1350 \text{ - } 166\text{S} \cdot (\text{C}+\text{N}) \text{ - } 42 \cdot \text{C}\text{r}-61 \cdot \text{Ni} \cdot \text{- } 33 \cdot \text{Mn} \cdot \text{- } 28 \cdot \text{Si} \tag{2}$$

$$\text{SFE in mJ/m}^2 = 25.7 + 2 \cdot \text{Ni} \cdot 0.9 \cdot \text{Cr} \cdot 1.2 \cdot \text{Mn} + 410 \cdot \text{C} \cdot 77 \cdot \text{N} \cdot 13 \cdot \text{Si} \tag{3}$$

The investigated austenitic stainless steel batches are in a metastable state (Md30 is in the range of ambient temperature). Md30 is the temperature at which 50 vol% of α´-martensite is developed by 30% of true plastic deformation [14] and was introduced for the comparison of the metastability of austenitic stainless steels. However, the deformation-induced phase transformation from γ-austenite in to α´-martensite can also take place at higher temperatures than Md30 [46,58,59,62,63]. The amount of deformation induced α´-martensite depends: (i) on the initial conditions, given by production process, such as chemical composition and initial microstructure e.g. the grain size of austenite, dislocation arrangements/density, precipitations and (ii) on loading parameters, like deformation temperature, amount of plastic deformation, as well as the stress and strain state/rate. Therefore, determining the true Md-temperature above which no α´-martensite formation takes place is not practically possible. In order to take into account both aspects specified above (i and ii) on the susceptibility of forming α´-martensite in metastable austenite, a method based on dynamically applied local plastic deformation and magnetic measurement was developed [16]. The parameter established by this method as I<sup>ξ</sup> correlates very well with the grade of α´-martensite formation during cyclic loading and allows to distinguish the susceptibility of austenitic stainless steels, which have the same chemical composition

and grain size, to undergo phase transformation. The Iξ parameter of the two investigated batches of AISI 347 is given in Table 1. Table 2 summarizes the mechanical properties of the investigated material at ambient temperature (AT) and T = 300 ◦C as well as α'-martensite content after specimen failure.


**Table 1.** Chemical composition in weight % and metastability parameters.



Shown in Figure 2 are light and electron microscopy micrographs of longitudinal sections of the initial microstructure of the investigated materials in the solution-annealed state and after plastic deformation. Specimens from batch A were extracted from an original nuclear power plant surge line pipe with an outside diameter of 333 mm and a wall thickness of 36 mm. The pipe was manufactured seamless, drilled from the inside, turned from the outside and delivered in a solution-annealed state (1050 ◦C / 10 min / H20), such that in the initial state no α'-martensite was detected. Note that the surge line pipe was investigated in the as-manufactured condition and has not been previously used in a nuclear power plant. The material of batch B was provided as rolled bars with a diameter of 25 mm in a solution-annealed state. A fully austenitic microstructure was obtained by additional annealing at 1050 ◦C for 35 minutes and quenching in helium atmosphere.

**Figure 2.** Optical micrographs of longitudinal sections using Bloech & Wedl I etching (**a**,**e**) initial state, (**b**,**f**) after plastic deformation as well as EBSD grain maps of (**c**,**g**) initial state and (**d**,**h**) after plastic deformation.

In Figure 2a the optical micrograph of the initial state of batch A is shown. This micrograph was taken after color etching using a Bloech & Wedl I etching agent, which is able to visualize local inhomogeneities in chemical composition [15]. A homogeneous distribution of the Cr and Ni content was detected in the microstructures of batch A. Furthermore, plastic deformation of batch A led to the homogeneous development of α´-martensite in the austenite matrix during plastic deformation (see Figure 2b,d). An electron backscatter diffraction (EBSD) micrograph of the initial state of both batches (Figure 2c,g) revealed a one-phase microstructure with annealing twins, typical for austenitic stainless steels. The same etching and observation techniques were used for characterizing the microstructure of batch B. In the case of batch B, the etching agent revealed local chemical inhomogeneities caused by slight variations of the Cr and Ni content as blue and brown bands (Figure 2e), which could not be removed during solution annealing. The blue band correlates with a lower Ni and higher Cr content, while the brown bands indicate higher Ni and lower Cr contents [15]. The band structure with a corresponding local metastability of austenitic microstructure led to a pronounced α´-martensite formation in regions with higher Cr content (Figure 2f). The local chemically induced band structure could not be observed in scanning electron micrographs using EBSD technique (Figure 2h). Instead, the EBSD image shows a homogeneous crystallographic microstructure in both cases, whereas the deformation-induced α´-martensite formation after plastic deformation can be clearly detected by EBSD images (Figure 2d,h). The comparison of EBSD grain maps (Figure 2c,g) of both batches presented a clear difference in the grain size. Quantitative evaluation yielded a mean grain size of 120 μm for batch A and of 17 μm for batch B, respectively.

#### **3. Methods**

To investigate the fatigue behavior of metastable austenitic stainless steels at ambient and elevated temperatures from the LCF to VHCF regime, servohydraulic and ultrasonic fatigue systems were used. The test temperature of T = 300 ◦C was achieved using an inductive heating system and control based on measurement by a type-K ribbon thermocouple in the center of the gauge length. The isothermal LCF and HCF tests at ambient temperature (AT) and T = 300 ◦C were performed with an MTS 100 kN servohydraulic testing system using load frequency of f = 0.01 Hz (LCF), 5 Hz and 20 Hz (HCF), see Figure 3a and b. The VHCF tests at T = 300 ◦C were performed with f = 980 Hz at an MTS 1 kHz servohydraulic testing system (Figure 3c). The VHCF tests at AT were realized in an ultrasonic fatigue testing system developed and built up at the authors' institute [64,65] (Figure 3d) with an operating frequency f = 20 kHz. In order to characterize the cyclic deformation behavior in the LCF and HCF regime, respectively, an extensometer (AT and T = 300 ◦C) and thermocouples (only AT) were used. The area of each hysteresis loop describes the cyclic plastic strain energy dissipated per unit volume during a given loading cycle, which is mainly dissipated into heat and, hence, results in a change in specimen temperature [66,67]. Temperature was measured with one thermocouple in the middle of the gauge length (T1) and two reference thermocouples at the elastically loaded specimen shafts (T2, T3). The temperature change induced by cyclic plastic deformation was calculated according to:

$$
\Delta \mathbf{T} = \mathbf{T}\_1 - 0.5 \mathbf{\cdot} (\mathbf{T}\_2 + \mathbf{T}\_3) \tag{4}
$$

The in situ detection of fatigue induced α´-martensite formation was done by magnetic FeritscopeTM (FISCHER, Windsor, CT, USA) measurements at AT (see Figure 3a). Due to the higher permeability of ferromagnetic ferrite compared to paramagnetic austenite, the response of the material to magnetic induction increases with the ferrite content. Using a non-destructive magnetic method, the FeritscopeTM measures the relative permeability of a material in the alternating magnetic field of its probe. This provides a ferrite content signal (FE%), which is also influenced by the curvature of the specimen's surface and stress-strain state. Furthermore, to determine the ferromagnetic α´-martensite content in vol%, the Feritscope™ signal (FE%) needs to be multiplied by a factor of 1.7 [68]. Because the calibration factor was determined only for α´-martensite contents below 55 FE%, in the following diagrams the magnetically determined α´-martensite is indicated as ξ in FE% without calculating the vol% of α´-martensite. Furthermore, within one load cycle, the magnetic properties of α´-martensite are influenced by stress/strain due to the Villari effect (inverse magnetostriction), which describes a change of the magnetic susceptibility of ferromagnetic material due to mechanical stresses [26]. Therefore, an arithmetic mean value per load cycle of the measured Feritscope™ signal is given in the diagrams. For specimens loaded in LCF, HCF and VHCF tests at T = 300 ◦C and in VHCF tests at AT, ex situ

Feritscope™ measurements were performed. The fatigue tests at AT and T = 300 ◦C were total strain controlled in LCF regime and stress controlled in the HCF regime. The VHCF tests at T = 300 ◦C were stress controlled and the ultrasonic VHCF tests at AT performed in displacement-control. All tests were performed in symmetric push-pull conditions with load ratio R = −1.

**Figure 3.** Schematic representation of the experimental setup for fatigue tests in the LCF and HCF regime at (**a**) AT and (**b**) at T = 300 ◦C, as well as in the VHCF regime at (**c**) T = 300 ◦C and (**d**) at AT.

VHCF testing of metastable austenitic stainless steels at ambient temperature using an ultrasonic fatigue system is more challenging than for stable metallic materials because of transient material behavior and significant self-heating of specimens. Due to the formation of high strength α'-martensite in softer austenite, less damping of the oscillation amplitude takes place, resulting in higher displacement amplitude. Therefore, an unstable displacement amplitude occurred. A representative pulse sequence from the VHCF fatigue test on a fully austenitic microstructure in its initial state and after cyclic loading up to N~2 <sup>×</sup> <sup>10</sup><sup>6</sup> clearly shows the challenge in performing the fatigue test with constant load amplitude (Figure 4). The first pulses were characterized by an oscillation plateau with a constant amplitude level during each pulse (Figure 4a). These results underline the necessity of a correct specimen design using FEM simulation to ensure fully reversed loading conditions with the maximum stress amplitude in the center of the gauge length and the maximum oscillation amplitude at the specimen´s end (see Figure 3d) [65]. However, due to fatigue-induced α'-martensite formation, the initial amplitude plateaus changed to pulses with an increasing displacement level (Figure 4b). This had to be leveled out by appropriate parameter adjustments during phase transformation. Further details can be found in further papers (see [65,69]).

Besides adjusting the proportional, integral and derivative (PID) parameters during VHCF tests, the deformation-induced specimen temperature increase has to be limited. Figure 5a shows the development of displacement for a pulse/pause ratio of 0.5 s/2.5 s, which is typically used for stable metallic materials [64], and which results in an effective load frequency feff = 3300 Hz. The progress of the specimen´s temperature is also plotted (Figure 5). It can be clearly seen that a pulse/pause ratio of 0.5 s/2.5 s cannot be used for fatigue testing of metastable austenite at ambient temperature because within two pulses the temperature increased to 200 ◦C (Figure 5a). To keep the specimen´s temperature below 50 ◦C, a change of temperature below 25 K and therefore a pulse/pause ratio of 0.06 s/2.94 s had to be used (Figure 5b). This led to an effective frequency of feff = 400 Hz. Theoretically, to achieve the limit of the number of cycles Nl = 2 <sup>×</sup> 10<sup>9</sup> for a fatigue test with feff = 400 Hz, about 58 days would be required. In reality, with the development of α'-martensite, cyclic hardening of materials takes

place, which reduces cyclic plasticity. Consequently, the development of the specimen's temperature decreases, and fatigue testing could be performed with a higher pulse/pause ratio with feff = 1650 Hz. The adjustment of PID parameters was also less critical given that saturation of α'-martensite was achieved in the cycle regime of N~108 (see Figure 10).

**Figure 4.** Displacement amplitude of batch A during VHCF testing at (**a**) the beginning of the fatigue test and (**b**) after fatigue-induced α'-martensite formation occurred without parameter adjustments.

**Figure 5.** Development of the specimen's temperature using a pulse/pause ratio of (**a**) 0.5 s/2.5 s and (**b**) 0.06 s/2.94 s for AISI 347 batch A.
