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TWIP steels at room and elevated temperature investigated by acoustic emission and scanning electron microscopy
Materials Science & Engineering A 597 (2014) 183–193
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation mechanisms in austenitic TRIP/TWIP steels at room and elevated temperature investigated by acoustic emission and scanning electron microscopy M. Linderov a, C. Segel b, A. Weidner b, H. Biermann b, A. Vinogradov a,n a b
Laboratory of Physics of Strength of Materials and Intelligent Diagnostic Systems, Togliatti State University, Togliatti 445667, Russia Institute of Materials Engineering, Technische Universität Bergakademie Freiberg, 09599 Freiberg, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 9 November 2013 Received in revised form 23 December 2013 Accepted 28 December 2013 Available online 7 January 2014
The modern austenitic stainless TRIP/TWIP steels have an outstanding combination of strength and ductility, depending on their chemical composition and loading conditions. A critical factor, which strongly affects all deformation-induced processes in metastable austenitic steels, is the temperature. To get a better insight into the effect of temperature on the deformation kinetics and transformation processes in high-alloy CrMnNi TRIP/TWIP steels with different austenite stability due to a varied content of Ni (3, 6 and 9 wt%), an acoustic emission (AE) technique was used during uniaxial tension at two different temperatures – ambient and 373 K. The in-situ AE results were paired with detailed SEM investigations using the electron backscattered diffraction (EBSD) technique to identify the deformationinduced phase transformations and mechnical twinning. The cluster analysis of the AE signals has revealed an excellent correlation of AE features with synergistic complexity of deformation mechanisms involved in various combinations: dislocation glide, stacking faults, martensitic phase transformation and twinning. & 2014 Elsevier B.V. All rights reserved.
Keywords: Ferrous alloy Phase transformation Electron microscopy EBSD Mechanical characterization
1. Introduction Strength and ductility are primary characteristics of virtually any engineering material, which largely affect the other properties of interest, e.g. fatigue resistance and toughness. The ideal structural material should combine high strength with sufficient ductility along with other functional properties. However, high strength and good ductility are often mutually exclusive, and improving both at the same time is a very challenging task, which can be hardly accomplished by conventional strain hardening techniques aiming at limiting dislocation mobility. The improved ductility can be associated with “delayed necking”, which can be achieved by activating deformation mechanisms other than dislocation-based ones, cf. phase transformations or twinning. These well-known mechanisms, which are broadly utilized in modern austenitic steels, are referred to as transformation induced plasticity (TRIP) [1] and twinning induced plasticity (TWIP) [2]. Since recently the high-alloy steels enjoy increasing popularity due to their outstanding combination of functional properties including excellent strength and ductility, extended strain hardening and high deformation energy absorption [3]. These properties result from a specific combination of multiple microstructural processes activated
n
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during plastic deformation. These processes include primarily (i) dislocation glide, (ii) formation of stacking faults, (iii) mechanical twinning and (iv) martensitic phase transformation. Occurring in a variety of combinations and/or almost always largely overlapping, these mechanisms govern the overall mechanical response of this class of austenitic steels. The root cause of the TRIP effect is a diffusionless deformationinduced martensitic phase transformation. This transformation from the metastable austenitic γ phase (f.c.c.) into the α0 -martensite (b.c.c.) often occurs via the intermediate so-called ε-martensite, which appears as a result of dense arrangement of significantly extended and overlapping stacking faults forming a specific h.c.p. atomic structure [4–7]. Steels exhibiting the TRIP effect are characterized by concurrently high strength and high ductility. The dominating deformation process substantiating the TWIP effect is mechanical twinning. The boundaries of microtwin bundles act as strong barriers for gliding dislocations, thus leading to a dynamic Hall–Petch effect promoting strain hardening and delaying necking [8]. It has long been recognized that dominating deformation mechanisms in TRIP and TWIP steels are controlled by the chemical composition and the deformation temperature since both these factors strongly affect the stacking fault energy (SFE) and the austenite stability [9–12]. Both the SFE and the austenite stability increase with increasing temperature. Krüger et al. [9] and Martin et al. [10] showed that the preferred deformation mechanism in the
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cast high alloyed CrMnNi steels at room temperature is associated with the deformation-induced α0 -martensite transformation due to low austenite stability as well as low SFE. Increasing temperature leads to reduction in the stacking faults formation rate due to the increasing austenite stability and SFE. In conjunction with evidence for the increased microstructural stability, the increased activation stress for the martensitic phase transformation, reduction of the overall amount of the α0 -martensite and preponderance for other deformation modes such as twinning and dislocation glide is observed at elevated temperatures [13]. It has been demonstrated in Refs. [14–16] that the desired control over the austenite stability and, therefore over the deformation mechanisms of high-alloy CrMnNi cast TRIP/TWIP steels can be achieved through a judicious variation of the nickel content. Deformation twinning, formation of stacking faults and deformation-induced martensitic phase transformation are similar microstructural processes in that they all involve fast diffusionless cooperative motion of large groups of atoms resulting in shear of a constrained plate-shaped region of a parent crystal [17]. To tailor deformation microstructures and develop materials with novel enhanced properties it is essential to know the details of the kinetics of different deformation processes. However, despite the significant amount of experimental data collected to date, we are still far from comprehensive understanding of the synergistic interplay between the primary mechanisms involved into complexity of plastic deformation – dislocation glide, formation of stacking faults, twinning and martensitic phase transformation, particularly at higher temperatures. Therefore, the aim of the present investigation is to get a better insight into the evolution of different deformation processes in TRIP/TWIP steels at ambient and elevated temperatures. A powerful means which can shed light on the development of deformation microstructures in real time scale is the acoustic emission (AE) technique complementing conventional mechanical testing. The AE method provides highly time-resolved information on the microstructural processes in the bulk of the material because it is fundamentally based on recording of surface displacements caused by local stress relaxations associated with different sources (deformation mechanisms) during plastic deformation and fracture. The present investigation is focused on the effect of temperature on the deformation behaviour of metastable austenitic stainless steels. To attain the goal, the quantitative AE analysis is coupled with the detailed microstructural characterization. The general methodology based on the statistical and cluster analysis of the AE time-series in real time scale in this work was borrowed from an earlier paper [18].
2. Experimental details A chemical design of high-alloy CrMnNi steels promoted by Weiß et al. [14] with a low carbon content of 0.05–0.08, Cr – 16%, Mn 6% and the varied nickel amount to be of 3%, 6% and 9% (all in wt%), respectively, was used for the present study. Details of the chemical composition and other relevant characteristics including Cr and Ni equivalents, martensitic start temperature and stacking fault energy are given in Ref. [18]. Flat tensile specimens with a rectangular cross section of 8 4 mm2 and a gauge length of 35 mm were machined from cast plates of 20 mm thickness. The cast plates were solution annealed at 1273 K for 0.5 h followed by N2-gas quenching. Tensile deformation of the specimens was performed at room temperature (RT) and 373 K under crosshead displacement control with a nominal initial strain rate of 3 10 3 s 1 on a screw-driven testing frame (Zwick 1476, Germany). The experimental setup for AE measurements based on the 18 bit PCI-2 data acquisition board
(Physical Acoustic Corporation, USA) operating in a continuous mode with 2 M Samples/s data rate has been described in Ref. [18]. The WDFS63 (Physical Acoustic Corporation, USA) AE sensor was fixed at the shoulder part of the specimen using machine oil as a coupling media ensuring a good acoustic contact between the surface and the sensor. The actual frequency response of the sensor verified by a primary calibration technique [19] revealed two strong resonant peaks at 260 kHz and 700 kHz. Because of this resonant nature of the sensor, the application of the recently developed so-called adaptive sequential k-means (ASK) technique [20] has become a challenging task: aiming at distinction between underlying deformation mechanisms we applied the categorization procedure to a set of AE power spectral densities (PSD), which inevitably inherited the sensor resonances having little to do with the actual microstructural development. The ASK algorithm, which has been tested successfully in several studies [18,21], is a nonsupervised version of the conventional k-means procedure, which does not require to specify the number of clusters to be extracted in advance and which is capable of working in real time. The AE signal from the sensor output was amplified by 60 dB using a lownoise PAC 2/4/6 preamplifier and passed through the 30–1000 kHz band-pass filter before acquisition. A thermocouple was fixed on the gauge part of the specimen to control the deformation temperature during tensile testing at 373 K. The continuously streamed data were sectioned into consecutive individual realizations of 4096 readings. After Fast Fourier Transformation (FFT) of the AE data stream the power spectral density (PSD) function Gðf Þ was calculated using a Welch technique. The average AE energy (or average power related to the duration of the realization) and the median frequency fm of the PSD Rf R fm function were computed by definition as E ¼ f max Gðf Þdf ; 0 R1 min Gðf Þdf ¼ f Gðf Þdf , respectively. Further details of the procedures m employed for AE signal processing can be found in Ref. [22]. The time duration of the deformation tests was depending on the material, the deformation temperature and mostly on the nominal strain rate of 1 10 3 s 1 in a range between 110 and 240 s. Because of the relatively high data acquisition rate, the amount of data received in a single continuously recorded AE stream was in the range of 0.5–1 Gb resulting in time consuming calculations involving millions of Fourier transforms and data manipulation during clustering. Therefore, the above described ASK procedure was applied only to the first 60 s of the test. Actually, this region is of greatest interest since all major structural transformations occur during this time. The results of the AE cluster analysis were corroborated by post-mortem SEM investigations with backscattered electron (BSE) imaging and electron backscattered diffraction (EBSD). In order to avoid any preparation influence on the material state, the gauge parts of the specimens were vibration-polished for 24 h with 0.02 μm grade colloidal silica. The SEM investigations were performed using the field emission scanning electron microscope (MIRA 3 XMU, TESCAN, Czech Republic) equipped with the OIMTMtechnology from EDAX/TSL.
3. Results and discussion 3.1. Mechanical testing and acoustic emission behaviour The AE events in all steel variants appear as a random timeseries consisting of high-amplitude bursts overlapping with a lowamplitude continuous signal, which is very similar to a background noise in visual appearance but is different in amplitude and spectral features, thus making it possible to separable one from the other as shown in Ref. [18] for the same steel variants at room temperature. Typically for pure f.c.c. metals and alloys,
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Fig. 1. Stress–strain (time) curves plotted together with the average AE energy E and the median frequency fm measured during tensile straining of high-alloy CrMnNi cast TRIP/TWIP steels with varying Ni content of 9% (a, b), 6% (c, d) and 3% (e, f), tested at room temperature (a, c, e) and at 373 K (b, d, f) at a nominal strain rate of 3 10 3 s–1.
the AE level rapidly increases after the beginning of loading around the yield stress and then reduces smoothly until fracture. Fig. 1 shows the AE diagrams synchronized with the loading curves, revealing noticeable differences in the mechanical behaviour as well as in the AE history of the studied steels with 3%, 6% and 9% of nickel at both temperatures (RT and 373 K). The steel with 9% Ni shows the highest elongation to failure but the lowest tensile strength at room temperature. In contrast, the steel with 3% Ni shows a pronounced secondary hardening resulting in the highest tensile strength and the shortest elongation to failure at RT; its stress–strain curve is sigmoidal, which is indicative of the martensitic phase transformation. A temperature increase up to 373 K exerts a very strong effect on the hardening mechanisms altering the stress–strain curves of all steels under investigation. However, this influence is most significant in the steels with 3% and 6% of nickel. Considering the AE diagrams, it is important to notice that the behaviour of the spectrum median frequency fm is quite specific in the investigated steels and is different from what is typically observed during hardening of pure f.c.c. metals. The fm vs. time (strain) curve exhibits a clearly pronounced maximum on the early deformation stage of the steels with 9% and 6% Ni, respectively, at
both testing temperatures as shown in Fig. 1a–d. The opposite trend is observed in pure f.c.c. metals such as Cu [23,24] where the AE spectrum commonly shifts to higher frequencies due to the reduction of the dislocation mean free path during uniform deformation hardening stage mediated by dislocation slip and interaction between dislocations. The specific behaviour of the AE PSD function in the investigated steel variants is a clear indicator of the active deformation mechanisms (dominating AE sources) other than dislocation glide. The most obvious candidates for those sources are mechanical twins and martensitic phase transformations. The distinction between active deformation mechanisms has been done with an aid from the AE cluster analysis using the ASK algorithm. In the steel variant with 3% Ni, the trends in the fm behaviour at RT and 373 K appear to be opposite to those seen in the other two steels. As shown in Fig. 1e and f, a pronounced fm maximum at the onset of deformation is followed by graduate reduction in fm at RT, whereas at 373 K the fm value shifts to a higher frequency domain before dropping when strain localization sets in on the late deformation stage. Thus, it is evident that the deformation mechanism changes substantially at the elevated temperature and this will be demonstrated below by direct microstructural observations. Furthermore, the AE energy
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reflecting the dynamics at the source is by order of magnitude higher at RT than at 373 K in the steel variant with 3% Ni content. This is associated with the massive diffusionless martensitic phase transformation, which is obviously more pronounced at ambient than at elevated temperature. The issue regarding the role of the other possible mechanisms involved into the deformation process has yet to be addressed.
3.2. Acoustic emission cluster analysis and microstructural observations A generally reasonable assumption based on fundamental theoretical considerations is that different sources produce AE signals with different waveforms and, therefore, PSDs. Since AE is
actually a random process with inevitable scatter in descriptive variables, it is difficult, or impossible, to distinguish between different sources by visual comparison of waveforms and PSDs. However, such distinction can become possible through the quantitative grouping of signals of a similar kind if a certain statistical criterion of similarity/dissimilarity is met. Using a data processing methodology described in early works in detail [20,21], the ASK clustering procedure, comparing individual PSD functions in order of their appearance in time, returned the indexed AE series with the clustered AE patterns shown in Fig. 2 in terms of bi-variant E vs. fm distributions for different steels and temperatures. Two different clusters were identified in the steels with 9% and 3% nickel, respectively, whereas in the steel with 6% nickel four different clusters were distinguishable at room temperature. In the steel with 9% nickel, no significant change in the
Fig. 2. Scatter-plots showing bi-variate distributions of AE descriptive variables – average energy E and median frequency fm – for austenitic stainless steels with different Ni content tested at room temperature and at 373 K. Parameters related to individual realizations assigned to different AE clusters (i.e. to different deformation mechanisms) are shown in different colours, corresponding to those in Figs. 3, 5 and 7: (a, b) 9% Ni, (c, d) 6% Ni and (e, f) 3% Ni.
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identified clusters was observed at higher temperature (373 K). However, significant changes occurred in the steel variants with 6% and 3% nickel, respectively. This indicates that the identified clusters as well as their changes depending on temperature correlate well with the underlying microstructural processes. In what follows, the time evolution of the identified AE clusters in each steel variant at two temperatures (RT and 373 K) will be highlighted with support from detailed microstructure analysis.
3.2.1. Steel variant with 9% nickel Fig. 3a–d shows the evolution of two AE clusters (shown in green and red, respectively) in terms of their cumulative energy (a, b) and the number of cluster members (c, d) at RT (a, c) and 373 K (b, d). As has been shown in previous investigations [5], no martensitic phase transformation is observed in this steel variant. However, profuse mechanical twinning does occur leading to the TWIP effect. At room temperature the first cluster (red), starts at the very beginning of deformation and is characterized by a low AE energy, cf. Figs. 2 and 3a. The large body of investigations shows that the low amplitude AE in pure iron or stable steels [25–27] is typical for materials without any phase transformations or mechanical twinning. This type of low amplitude and relatively low frequency cluster is correlated with the ordinary dislocation slip. The second identified cluster (green) starts later on the deformation history. The high-energy burst type AE with reasonably high frequency content (see Fig. 2a) is specific to this cluster. The number of AE cluster elements is increasing over the whole deformation range up to failure, however the rate of AE signal accumulation is more pronounced at the beginning of deformation. Signals of this kind are commonly associated with mechanical twinning [21].
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The same primary deformation mechanisms – dislocation slip and mechanical twinning – were identified by means of the AE cluster analysis at 373 K. However, at this temperature the intensity of twinning decreased and regularly dislocation slip becomes more pronounced. This is reflected by the relative number of AE cluster elements were a significant increase in the “dislocation” cluster members is observed clearly. In contrast, the cluster corresponding to mechanical twinning loses its members significantly and the cumulative AE energy reduces concurrently. These findings agree nicely with the direct, but post-mortem, microstructural observations. Fig. 4 shows the results of EBSD investigations performed after specimen failure on the steel with 9% nickel at RT (a–c) and 373 K (d–f). As expected, no martensitic phase transformation was detected in this steel variant at both temperatures. However, intensive mechanical twinning becomes evident on OIM maps. Both, the image quality map with indicated twin boundaries in red (601 〈111〉 misorientation) (a, d) as well as the surface normal-projected inverse pole figure orientation map (b, e) reveal the dense populations of mechanical twins on two different twin systems. Individual twin lamellae can have a thickness of few nanometres. Due to the limited resolution of EBSD measurements (step size is 100 nm), the nanometre thick twin lamellae cannot be resolved. Twin bundles on the primary twin system were identified as large areas consisting of many individual twins and extending over a whole grain. Shorter and thinner twins on a secondary twin system were observed in between the primary twin bundles. The length and thickness of these secondary twin bands were much less than on the primary system. At higher temperature (373 K), significant changes in the twinning activity are observed: the density of twins decreases remarkably with increasing temperature. Nevertheless, the thicker twins on the primary twin system are characterized by a higher strain level both at RT and at 373 K, which is evident from the kernel
Fig. 3. Results of the AE cluster analysis for the steel variant with 9% nickel tested in tension at RT (a, c) and 373 K (b, d): (a, b) time-evolution of the cumulative AE energy and (c, d) time-evolution of the number of AE cluster elements.
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Fig. 4. Summary of microstructure observations and EBSD measurements on the steel variant with 9% nickel after tensile test at RT (a–c) and 373 K (d–f): (a, d) band contrast images with twin boundaries indicated in red; (b, e) crystallographic orientation map in the inverse pole figure colouring code according to the surface normal direction; and (e, f) kernel average misorientation. Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Twin fraction of the steel variant with 9% nickel after tensile tests at RT and 373 K calculated using the primary and secondary twin orientation from the inverse pole figure colouring of the EBSD orientation maps. 16% Cr–6% Mn–9% Ni
RT 373 K
Therefore, the large scatter in the results obtained on the specimen deformed at 373 K is reasonable. In spite of these limitations, the determined values show favourable agreement with the AE findings.
Twin fraction [%] from EBSD orientation maps AOI 1
AOI 2
AOI 3
average
37 35
29 2
29 9
31.7 15.3
average misorientation shown in Fig. 4c and f. In order to quantify the volume fraction of mechanical twins, the area fraction of twinned regions was determined from the crystallographic orientation map. The twin orientation relationship between adjacent crystal domains is described by a misorientation angle/axis pair of 601 around a 〈111〉 direction. In the inverse pole figure crystallographic orientation map this relation is seen in different specific colours for the matrix and the twinned areas. Performing EBSD measurements on three commensurable and randomly chosen areas of interest (AOI) at RT and 373 K, respectively, it was found that the area fraction of mechanical twins decreased from of 31% at RT to 15% at 373 K on average. Results of three individual measurements at both temperatures are summarized in Table 1. We should notice that this is a lower-bound estimate due to the fact that nano-twins are not detectable by EBSD measurements and are not included into statistics. On the other hand, it is well known that the crystallographic orientation of the grains is decisive for the appearance of mechanical twins. The large grain size of the as-cast material is another limiting factor for the estimation of the area fraction of mechanically twinned regions.
3.2.2. Steel variant with 6% nickel Fig. 5 shows the results of the AE cluster analysis at RT (a, c) and 373 K (b, d) obtained for the steel containing 6% of nickel. Fig. 5a and b demonstrates the evolution of the cumulative AE energy, whereas Fig. 5c and d represents the kinetics of AE cluster members accumulation. The steel variant with 6% nickel is a metastable austenitic steel, which exhibits a pronounced deformation-induced martensitic phase transformation at room temperature [11]. The phase transformation occurs from the metastable austenitic phase (f.c.c.) via the intermediate state termed commonly “ε-martensite” (h.c.p.) into the α0 -martensite (b.c.c.) [4]. The hexagonal structure of the ε-martensite results from the stacking faults, which are densely packed in deformation bands [8]. The AE cluster analysis revealed at least four different microstructural processes operating more or less at the same time at RT. The first cluster (shown in red) is pretty much the same as the corresponding cluster in the steel with 9% nickel. It is attributed to the conventional dislocation slip and its behaviour is quite similar to what we have discussed in the preceding section. The second cluster (shown in green) is also similar to that in the steel with 9% Ni and is attributed to mechanical twinning starting around the yield point. However, the smaller number of cluster elements was detected (N o500) in this steel variant. This means that mechanical twinning is observed only occasionally and locally due to chemical inhomogeneity, but it is not the dominating deformation mechanism. To the contrast with the steel containing 9% nickel, a
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Fig. 5. Results of the AE cluster analysis for the steel variant with 6% nickel tested in tension at RT (a, c) and 373 K (b, d): (a, b) time-evolution of the cumulative AE energy and (c, d) time-evolution of the number of AE cluster elements.
third cluster (shown in blue) was distinguished its features appear to be similar to those of the cluster caused by mechanical twinning in terms of AE energy and median frequency, Fig. 2c. This cluster is also composed of high-energy pulses with a broad frequency range from 250 kHz up to 700 kHz. However, according to the basics of the categorization procedure, these classes should be regarded as statistically different and thus they describe populations of different AE sources. Therefore, the latter cluster is most likely associated with the motion of Shockley-partial dislocations forming stacking faults. This cluster starts to develop immediately as the yield point is reached; it then increases significantly before saturation already on the early deformation stage. This finding is in good agreement with microstructural investigations performed in situ or during interrupted tests reported in Refs. [5,28], where it was shown that the hexagonal phase inside the deformation bands composed of densely packed stacking faults (ε-martensite) transforms into the α0 -martensite during deformation. The fourth identified cluster (shown in pink) is obviously related to the dominant deformation mechanism in this steel variant – the martensitic phase transformation. It comes into force at the same moment as the so-called ε-martensite starts to form by motion of partial dislocations. The number of elements contributing to this type of cluster increases significantly over the whole deformation range. A significant change in the kinetics of the identified clusters is observed at the elevated temperature. As has been reported in Ref. [8], a transition from the martensitic phase transformation to mechanical twinning occurs in the steel variant with 6% nickel around deformation temperature of 353 K. Pronounced mechanical twinning becomes evident from the AE cluster analysis at 373 K as shown by the well developed cluster corresponding to twins (shown in green, Fig. 5b and d). This cluster starts around the yield point of the material. The number of elements contributing to this cluster increases
progressively with deformation. The third cluster composed of the signals originated from martensitic phase transformation (shown in pink) was identified too. In view of the two-step γ 4 ε 4 α0 nature of the martensitic transformation, the stacking faults should be present in the microstructure since they serve as the prerequisites for the α0 -martensite. However, only few signals related to the possible stacking faults were identified by the AE analysis, because they were hardly separable from the twin cluster. In order to achieve a better discrimination between the twins and stacking faults, a signal acquisition chain with a substantially improved wideband sensor response should be helpful. The microstructural observations corroborate the deformation scenario proposed by the AE analysis. Fig. 6a–f shows the results of EBSD-measurements at RT (a–c) and 373 K (d–f), where a and d visualize the phase transformation in the respective EBSD maps, b and e show the crystallographic orientation of the f.c.c. phase and c and f illustrate the appearance of twin boundaries in the microstructure. The change in the operating deformation mechanisms becomes clearly evident. Whereas the martensitic phase transformation, which occurs through the intermediate ε-martensite, dominates in the deformation patterns at RT, mechanical twinning substitutes for it at 373 K to a large extent. Fig. 6a illustrates clearly the formation of deformation bands, which were indexed as a hexagonal phase (yellow) due to the high density of stacking faults. Inside these bands, the α0 -martensite nuclei form. The mechanical twins were observed sporadically near the stacking faults, Fig. 6b and c, cf. Ref. [5]. No massive martensitic phase transformation occurred at 373 K. Nevertheless, small areas of ε- and α0 -martensite were detected very locally by the EBSD measurements as shown in Fig. 6d, while Fig. 6e and f demonstrates clearly the prevalence of mechanical twinning at this temperature.
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Fig. 6. Summary of microstructure observations and EBSD measurements on the steel variant with 6% nickel after tensile test at RT (a–c) and 373 K (d–f). (a, d) Phase map with austenitic phase (f.c.c.) in red, ε-martensite (h.c.p.) in yellow and α0 -martensite (b.c.c.) in blue colour (b, e). Crystallographic orientation map in the inverse pole figure colouring code according to the surface normal direction; (e, f) band contrast images with indicated twin boundaries (red). Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3.2.3. Steel variant with 3% nickel Main results of the AE cluster analysis are summarized in Fig. 7 for the steel variant with 3% nickel. The deformation process in this steel is mediated entirely by intensive deformation-induced and/or stress-assisted martensitic phase transformation [11]. Two major types of AE signals were distinguished at room temperature by the ASK procedure. At the onset of straining, the first cluster (shown in blue) of AE signals emerge. The signals belonging to this cluster possess a remarkably high energy. This cluster has boosted its membership significantly in the first fifth part of the deformation process. This cluster, as discussed above, is originated from the motion of partial dislocations and, consequently, is related to the formation of ε-martensite within the deformation bands, which shows a progressive development during deformation. This agrees well with results reported by Jahn et al. [11] who showed that the formation of ε-martensite goes through an intermediate concentration maximum. The second massive cluster (shown in pink) correlates obviously with the martensitic phase transformation. This cluster appears reasonably and starts to grow after the sharp accumulation of the stacking faults signified by a respective AE cluster. AS signals originated from the formation of α0 -martensite are characterized by the high energy and steep increase in membership during deformation. The increase in the testing temperature exerts a significant effect on the behaviour of this steel with unstable microstructure. Although, this steel shows signatures of the two-stage γ 4 ε 4 α0 martensitic transformation even at 373 K, the activity of the underlying AE sources drops substantially, leading to significant reduction in the cumulative energy of corresponding AE clusters; notice the different scales in Fig. 7a and b. On the other hand, the contribution of the dislocation glide to the resultant strain and corresponding AE increases sharply with increasing temperature.
The steel variant with 3% nickel exhibits the lowest austenite stability. The initial microstructure of this steel variant consists of three phases: (i) austenite, (ii) roughly 12 vol% δ-ferrite inherited from processing and (iii) a small volume fraction of athermal martensite resulting from rapid cooling. The δ-ferrite has the same b.c.c. crystallographic structure as the α0 -martensite. Therefore, distinction between these two phases by EBSD analyses is not straightforward. The specific morphology as well as the better band contrast of Kikuchi patterns originated from the δ-ferrite are the main microstructural features essential for a good separation between the δ-ferrite and α0 -martensite. Fig. 8 shows the microstructure (a) and the phase distribution (b) in the steel with 3% nickel after tensile test at RT interrupted at 33% elongation. The SEM micrograph taken in the BSE contrast (a) reveals clearly an arrangement of numerous deformation bands along different activated slip systems; the α0 -martensite nuclei appear in dark contrast. The EBSD-analysis clarifies the phase distribution in the deformation bands as illustrated in Fig. 8b. The deformationinduced α0 -martensite (blue) originates inside deformation bands with a hexagonal lattice structure (yellow) as well as at the band intersections. The high strain level in the material caused some amount of non-indexed Kikuchi patterns (zero solutions coloured in black) during EBSD measurement. The influence of temperature on the martensitic phase transformation in the steel with 3% nickel is convincingly demonstrated by results of SEM investigations summarized in Fig. 9a–c at RT and d–e at 373 K. The blue coloured b.c.c. phase fraction is constituted by two major phases: the δ-ferrite and deformation induced α0 -martensite. Using the BSE contrast images (a, d) the clear identification of the δ-ferrite is possible. The EBSD measurements reveal a significant decrease in the total b.c.c. phase fraction from 65% to 30% with increasing temperature
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Fig. 7. Results of the AE cluster analysis for the steel variant with 3% nickel tested in tension at RT (a, c) and 373 K (b, d): (a, b) time-evolution of the cumulative AE energy and (c, d) time-evolution of the number of AE cluster elements. Please, note the different scales in Fig. 7a and b for the cumulative AE energy.
Fig. 8. SEM mages showing a deformation microstructure of the steel variant with 3% nickel strianed in tension at RT up to 33% elongation: (a) BSE contrast image showing formation of deformation bands on two different activated slip systems and (b) EBSD phase map with austenitic phase (f.c.c.) in red, ε-martensite (h.c.p.) in yellow and α0 -martensite (b.c.c.) in blue colour. Black colour corresponds to zero solutions. Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from RT to 373 K. With account to the amount of δ-ferrite, this means that the fraction of the deformation-induced α0 -martensite reduced from 28.7% after deformation at RT (cf. data obtained by FerritscopeTM [18]; an excellent quantitative agreement has been found for the α0 -martensite volume fraction assessed by AE and by magnetic measurements) to 8.8% at 373 K. The orientation map of the b.c.c. phases is displayed in the inverse pole figure (IPF) colours (Fig. 9c and f), confirming the reduction in the α0 -martensite phase fraction with increasing temperature.
4. Summary and conclusions Motivated by the need for better understanding of the deformation mechanisms underlying complex mechanical behaviour of metastable austenitic stainless steels with TRIP/TWIP effects facilitating their strength and ductility, the relative roles of primary deformation mechanisms were investigated at ambient and elevated temperature. The advanced AE technique employed was shown to be well suited for discrimination in between mechanical twinning, stacking fault formation, martensitic phase
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Fig. 9. Summary of microstructure observations and EBSD investigations for the steel variant with 3% nickel after tensile test at RT (a–c) and 373 K (d–f): (a, d) SEM images in BSE contrast showing formation of deformation bands on different slip systems; δ-ferrite in dark contrast is clearly distinguished within the microstructure (see arrows); (b, e) EBSD phase maps with austenitic phase (f.c.c.) in red, ε-martensite (h.c.p.) in yellow and α0 -martensite (b.c.c.) in blue colour; and (c, f) crystallographic orientation map of the b.c.c. phase in the inverse pole figure colouring code according to the surface normal direction. Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
transformation and dislocation slip mechanisms even when these were operating concurrently. The major results can be summarized as follows: (1) Multiple deformation mechanisms, which involve complex interactions between dislocation slip, mechanical twinning, motion of partial dislocations associated with stacking fault formation and α0 -martensite formation, operate in metastable austenitic stainless steels throughout the entire deformation process. (2) The individual deformation mechanisms were related to different clusters of AE signals grouped statistically by the similarity in their power spectral density. The contribution of these individual mechanisms to AE was found different on different deformation stages, depending primarily on the austenite stability controlled by the Ni content and testing temperature. (3) The results of the AE cluster analysis regarding the kinetics of the individual deformation mechanisms appear in good agreement with the post-mortem microstructural investigations. (4) The possibility to utilize different types of AE sensors has been demonstrated in attempt to distinguish between operating source mechanisms, using the ASK clustering procedure. The presented results for all three steel variants after tensile deformation at RT appeared in good agreement with previous results obtained for the same steels tested with the other type of AE transducer [18]. (5) The present investigation demonstrated that the increase in testing temperature leads to significant changes in the microstructure evolution in all three steel variants. The possibility to
follow the activity of different deformation processes during the loading history is demonstrated by means of the appropriate AE cluster analysis. (6) Mechanical twinning is still operative in the steel variant with 9% nickel at elevated temperature (373 K), though with a reduced activity. The AE cluster analysis shows that in replace for twinning, the activity of dislocation glide increased with increasing temperature. (7) The AE cluster analysis paired by microstructural investigations revealed that transition occurs in the dominating deformation mechanism from martensitic phase transformation at RT to mechanical twinning at 373 K in the steel variant with 6% nickel. (8) The same analysis shows that the martensitic phase transformation occurs even at the elevated temperature up to 373 K in the steel variant with 3% nickel, but with a reduced intensity.
Acknowledgements Financial support of the CRC 799 research project by the German Research Foundation (DFG) and by the Russian Ministry of Education and Science (Grant-in-aid 11.G34.31.0031) is greatly acknowledged. One of the authors (ML) gratefully acknowledges the hospitality of the Institute of Materials Engineering, Technische Universität Bergakademie Freiberg. Special thanks go to Dipl.-Ing. G. Schade for his skilful and enthusiastic assistance with experiments and to Mrs. K. Zuber for careful preparation of the specimens for the EBSD measurements.
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References [1] H.K.D.H. Bhadeshia, ISIJ Int. 42 (2002) 1059–1060. [2] S. Allain, J.P. Chateau, O. Bouaziz, S. Migot, N. Guelton, Mater. Sci. Eng. A 387– 389 (2004) 158–162. [3] B.C. De Cooman, K.-G. Chin, J. Kim, in: M. Chiaberge (Ed.), New Trends and Developments in Automotive System Engineering, New York, USA, 2011, pp. 101–102. [4] P. Mangonon, G. Thomas, Metall. Trans. 1 (1970) 1577–1586. [5] H. Biermann, J. Solarek, A. Weidner, Steel Res. Int. 83 (2012) 512–520. [6] A. Weidner, S. Martin, V. Klemm, U. Martin, H. Biermann, Scr. Mater. 64 (2011) 513–516. [7] S. Martin, C. Ullrich, D. Imek, U. Martin, D. Rafaja, J. Appl. Crystallogr. 44 (2011) 779–787. [8] A. Dumay, J.P. Chateau, S. Allain, S. Migot, O. Bouaziz, Mater. Sci. Eng. A 483– 48l (2008) 184–187. [9] L. Krüger, S. Wolf, U. Martin, S. Martin, P.R. Scheller, A. Jahn, A. Weiß, J. Phys. 240 (2010) 012098. [10] S. Martin, S. Wolf, U. Martin, L. Krüger, Solid State Phenom. 172–174 (2011) 172–177. [11] A. Jahn, A. Kovalev, A. Weiß, S. Wolf, L. Krüger, P.R. Scheller, Steel Res. Int. 82 (2011) 39–44. [12] J. Talonen, H. Hänninen, Acta Mater. 55 (2007) 6108–6118. [13] L. Remy, A. Pineau, Mater. Sci. Eng. 28 (1977) 99–107.
193
[14] A. Weiß, H. Gutte, M. Radke, P.R. Scheller, Patent WO002008009722A1. [15] A. Weiß, H. Gutte, A. Jahn, P.R. Scheller, Materialwiss. Werkst. 40 (2009) 606–611. [16] A. Jahn, A. Kovalev, A. Weiβ, P. Scheller, R.S. Wolf, L. Krüger, S. Martin, U. Martin, ESOMAT (2009) 05013, http://dx.doi.org/10.1051/esomat/ 200905013. [17] V. Tsakiris, D.V. Edmonds, Mater. Sci. Eng. A 273–275 (1999) 430–436. [18] A. Vinogradov, A. Lazarev, M. Linderov, A. Weidner, H. Biermann, Acta Mater. 61 (2013) 2434–2449. [19] S. Lazarev, A. Mozgovoi, A. Vinogradov, A. Lazarev, A. Shvedov, J. Acoust. Emiss. 27 (2009) 215–223. [20] E. Pomponi, A. Vinogradov, Mech. Syst. Signal Proc. 40 (2013) 791–804. [21] A. Vinogradov, D. Orlov, A. Danyuk, Y. Estrin, Acta Mater. 61 (2013) 2044–2056. [22] A. Vinogradov, M. Nadtochiy, S. Hashimoto, S. Miura, Mater. Trans. JIM 36 (1995) 426–431. [23] A. Vinogradov, D.L. Merson, V. Patlan, S. Hashimoto, Mater. Sci. Eng. A 341 (2003) 57–73. [24] A. Vinogradov, V. Patlan, S. Hashimoto, Philos. Mag. A 81 (2001) 1427–1446. [25] F.P. Higgens, S.H. Carpenter, Acta Metall. 26 (1978) 133–139. [26] R. Takeda, Y. Kaneko, D.L. Merson, A. Vinogradov, Mater. Trans. 54 (2013) 532–539. [27] A. Lazarev, A. Vinogradov, J, Acoust. Emiss. 27 (2009) 144–156. [28] A. Weidner, A. Glage, H. Biermann, Proc. Eng. 2 (2010) 1961–1971.
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Deformation mechanisms in austenitic TRIP/TWIP steels at room and elevated temperature investigated by acoustic emission and scanning electron microscopy M. Linderov a, C. Segel b, A. Weidner b, H. Biermann b, A. Vinogradov a,n a b
Laboratory of Physics of Strength of Materials and Intelligent Diagnostic Systems, Togliatti State University, Togliatti 445667, Russia Institute of Materials Engineering, Technische Universität Bergakademie Freiberg, 09599 Freiberg, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 9 November 2013 Received in revised form 23 December 2013 Accepted 28 December 2013 Available online 7 January 2014
The modern austenitic stainless TRIP/TWIP steels have an outstanding combination of strength and ductility, depending on their chemical composition and loading conditions. A critical factor, which strongly affects all deformation-induced processes in metastable austenitic steels, is the temperature. To get a better insight into the effect of temperature on the deformation kinetics and transformation processes in high-alloy CrMnNi TRIP/TWIP steels with different austenite stability due to a varied content of Ni (3, 6 and 9 wt%), an acoustic emission (AE) technique was used during uniaxial tension at two different temperatures – ambient and 373 K. The in-situ AE results were paired with detailed SEM investigations using the electron backscattered diffraction (EBSD) technique to identify the deformationinduced phase transformations and mechnical twinning. The cluster analysis of the AE signals has revealed an excellent correlation of AE features with synergistic complexity of deformation mechanisms involved in various combinations: dislocation glide, stacking faults, martensitic phase transformation and twinning. & 2014 Elsevier B.V. All rights reserved.
Keywords: Ferrous alloy Phase transformation Electron microscopy EBSD Mechanical characterization
1. Introduction Strength and ductility are primary characteristics of virtually any engineering material, which largely affect the other properties of interest, e.g. fatigue resistance and toughness. The ideal structural material should combine high strength with sufficient ductility along with other functional properties. However, high strength and good ductility are often mutually exclusive, and improving both at the same time is a very challenging task, which can be hardly accomplished by conventional strain hardening techniques aiming at limiting dislocation mobility. The improved ductility can be associated with “delayed necking”, which can be achieved by activating deformation mechanisms other than dislocation-based ones, cf. phase transformations or twinning. These well-known mechanisms, which are broadly utilized in modern austenitic steels, are referred to as transformation induced plasticity (TRIP) [1] and twinning induced plasticity (TWIP) [2]. Since recently the high-alloy steels enjoy increasing popularity due to their outstanding combination of functional properties including excellent strength and ductility, extended strain hardening and high deformation energy absorption [3]. These properties result from a specific combination of multiple microstructural processes activated
n
Corresponding author. Tel.: þ 7 8482 546303 E-mail addresses: [email protected], [email protected] (A. Vinogradov).
0921-5093/$ - see front matter & 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2013.12.094
during plastic deformation. These processes include primarily (i) dislocation glide, (ii) formation of stacking faults, (iii) mechanical twinning and (iv) martensitic phase transformation. Occurring in a variety of combinations and/or almost always largely overlapping, these mechanisms govern the overall mechanical response of this class of austenitic steels. The root cause of the TRIP effect is a diffusionless deformationinduced martensitic phase transformation. This transformation from the metastable austenitic γ phase (f.c.c.) into the α0 -martensite (b.c.c.) often occurs via the intermediate so-called ε-martensite, which appears as a result of dense arrangement of significantly extended and overlapping stacking faults forming a specific h.c.p. atomic structure [4–7]. Steels exhibiting the TRIP effect are characterized by concurrently high strength and high ductility. The dominating deformation process substantiating the TWIP effect is mechanical twinning. The boundaries of microtwin bundles act as strong barriers for gliding dislocations, thus leading to a dynamic Hall–Petch effect promoting strain hardening and delaying necking [8]. It has long been recognized that dominating deformation mechanisms in TRIP and TWIP steels are controlled by the chemical composition and the deformation temperature since both these factors strongly affect the stacking fault energy (SFE) and the austenite stability [9–12]. Both the SFE and the austenite stability increase with increasing temperature. Krüger et al. [9] and Martin et al. [10] showed that the preferred deformation mechanism in the
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cast high alloyed CrMnNi steels at room temperature is associated with the deformation-induced α0 -martensite transformation due to low austenite stability as well as low SFE. Increasing temperature leads to reduction in the stacking faults formation rate due to the increasing austenite stability and SFE. In conjunction with evidence for the increased microstructural stability, the increased activation stress for the martensitic phase transformation, reduction of the overall amount of the α0 -martensite and preponderance for other deformation modes such as twinning and dislocation glide is observed at elevated temperatures [13]. It has been demonstrated in Refs. [14–16] that the desired control over the austenite stability and, therefore over the deformation mechanisms of high-alloy CrMnNi cast TRIP/TWIP steels can be achieved through a judicious variation of the nickel content. Deformation twinning, formation of stacking faults and deformation-induced martensitic phase transformation are similar microstructural processes in that they all involve fast diffusionless cooperative motion of large groups of atoms resulting in shear of a constrained plate-shaped region of a parent crystal [17]. To tailor deformation microstructures and develop materials with novel enhanced properties it is essential to know the details of the kinetics of different deformation processes. However, despite the significant amount of experimental data collected to date, we are still far from comprehensive understanding of the synergistic interplay between the primary mechanisms involved into complexity of plastic deformation – dislocation glide, formation of stacking faults, twinning and martensitic phase transformation, particularly at higher temperatures. Therefore, the aim of the present investigation is to get a better insight into the evolution of different deformation processes in TRIP/TWIP steels at ambient and elevated temperatures. A powerful means which can shed light on the development of deformation microstructures in real time scale is the acoustic emission (AE) technique complementing conventional mechanical testing. The AE method provides highly time-resolved information on the microstructural processes in the bulk of the material because it is fundamentally based on recording of surface displacements caused by local stress relaxations associated with different sources (deformation mechanisms) during plastic deformation and fracture. The present investigation is focused on the effect of temperature on the deformation behaviour of metastable austenitic stainless steels. To attain the goal, the quantitative AE analysis is coupled with the detailed microstructural characterization. The general methodology based on the statistical and cluster analysis of the AE time-series in real time scale in this work was borrowed from an earlier paper [18].
2. Experimental details A chemical design of high-alloy CrMnNi steels promoted by Weiß et al. [14] with a low carbon content of 0.05–0.08, Cr – 16%, Mn 6% and the varied nickel amount to be of 3%, 6% and 9% (all in wt%), respectively, was used for the present study. Details of the chemical composition and other relevant characteristics including Cr and Ni equivalents, martensitic start temperature and stacking fault energy are given in Ref. [18]. Flat tensile specimens with a rectangular cross section of 8 4 mm2 and a gauge length of 35 mm were machined from cast plates of 20 mm thickness. The cast plates were solution annealed at 1273 K for 0.5 h followed by N2-gas quenching. Tensile deformation of the specimens was performed at room temperature (RT) and 373 K under crosshead displacement control with a nominal initial strain rate of 3 10 3 s 1 on a screw-driven testing frame (Zwick 1476, Germany). The experimental setup for AE measurements based on the 18 bit PCI-2 data acquisition board
(Physical Acoustic Corporation, USA) operating in a continuous mode with 2 M Samples/s data rate has been described in Ref. [18]. The WDFS63 (Physical Acoustic Corporation, USA) AE sensor was fixed at the shoulder part of the specimen using machine oil as a coupling media ensuring a good acoustic contact between the surface and the sensor. The actual frequency response of the sensor verified by a primary calibration technique [19] revealed two strong resonant peaks at 260 kHz and 700 kHz. Because of this resonant nature of the sensor, the application of the recently developed so-called adaptive sequential k-means (ASK) technique [20] has become a challenging task: aiming at distinction between underlying deformation mechanisms we applied the categorization procedure to a set of AE power spectral densities (PSD), which inevitably inherited the sensor resonances having little to do with the actual microstructural development. The ASK algorithm, which has been tested successfully in several studies [18,21], is a nonsupervised version of the conventional k-means procedure, which does not require to specify the number of clusters to be extracted in advance and which is capable of working in real time. The AE signal from the sensor output was amplified by 60 dB using a lownoise PAC 2/4/6 preamplifier and passed through the 30–1000 kHz band-pass filter before acquisition. A thermocouple was fixed on the gauge part of the specimen to control the deformation temperature during tensile testing at 373 K. The continuously streamed data were sectioned into consecutive individual realizations of 4096 readings. After Fast Fourier Transformation (FFT) of the AE data stream the power spectral density (PSD) function Gðf Þ was calculated using a Welch technique. The average AE energy (or average power related to the duration of the realization) and the median frequency fm of the PSD Rf R fm function were computed by definition as E ¼ f max Gðf Þdf ; 0 R1 min Gðf Þdf ¼ f Gðf Þdf , respectively. Further details of the procedures m employed for AE signal processing can be found in Ref. [22]. The time duration of the deformation tests was depending on the material, the deformation temperature and mostly on the nominal strain rate of 1 10 3 s 1 in a range between 110 and 240 s. Because of the relatively high data acquisition rate, the amount of data received in a single continuously recorded AE stream was in the range of 0.5–1 Gb resulting in time consuming calculations involving millions of Fourier transforms and data manipulation during clustering. Therefore, the above described ASK procedure was applied only to the first 60 s of the test. Actually, this region is of greatest interest since all major structural transformations occur during this time. The results of the AE cluster analysis were corroborated by post-mortem SEM investigations with backscattered electron (BSE) imaging and electron backscattered diffraction (EBSD). In order to avoid any preparation influence on the material state, the gauge parts of the specimens were vibration-polished for 24 h with 0.02 μm grade colloidal silica. The SEM investigations were performed using the field emission scanning electron microscope (MIRA 3 XMU, TESCAN, Czech Republic) equipped with the OIMTMtechnology from EDAX/TSL.
3. Results and discussion 3.1. Mechanical testing and acoustic emission behaviour The AE events in all steel variants appear as a random timeseries consisting of high-amplitude bursts overlapping with a lowamplitude continuous signal, which is very similar to a background noise in visual appearance but is different in amplitude and spectral features, thus making it possible to separable one from the other as shown in Ref. [18] for the same steel variants at room temperature. Typically for pure f.c.c. metals and alloys,
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Fig. 1. Stress–strain (time) curves plotted together with the average AE energy E and the median frequency fm measured during tensile straining of high-alloy CrMnNi cast TRIP/TWIP steels with varying Ni content of 9% (a, b), 6% (c, d) and 3% (e, f), tested at room temperature (a, c, e) and at 373 K (b, d, f) at a nominal strain rate of 3 10 3 s–1.
the AE level rapidly increases after the beginning of loading around the yield stress and then reduces smoothly until fracture. Fig. 1 shows the AE diagrams synchronized with the loading curves, revealing noticeable differences in the mechanical behaviour as well as in the AE history of the studied steels with 3%, 6% and 9% of nickel at both temperatures (RT and 373 K). The steel with 9% Ni shows the highest elongation to failure but the lowest tensile strength at room temperature. In contrast, the steel with 3% Ni shows a pronounced secondary hardening resulting in the highest tensile strength and the shortest elongation to failure at RT; its stress–strain curve is sigmoidal, which is indicative of the martensitic phase transformation. A temperature increase up to 373 K exerts a very strong effect on the hardening mechanisms altering the stress–strain curves of all steels under investigation. However, this influence is most significant in the steels with 3% and 6% of nickel. Considering the AE diagrams, it is important to notice that the behaviour of the spectrum median frequency fm is quite specific in the investigated steels and is different from what is typically observed during hardening of pure f.c.c. metals. The fm vs. time (strain) curve exhibits a clearly pronounced maximum on the early deformation stage of the steels with 9% and 6% Ni, respectively, at
both testing temperatures as shown in Fig. 1a–d. The opposite trend is observed in pure f.c.c. metals such as Cu [23,24] where the AE spectrum commonly shifts to higher frequencies due to the reduction of the dislocation mean free path during uniform deformation hardening stage mediated by dislocation slip and interaction between dislocations. The specific behaviour of the AE PSD function in the investigated steel variants is a clear indicator of the active deformation mechanisms (dominating AE sources) other than dislocation glide. The most obvious candidates for those sources are mechanical twins and martensitic phase transformations. The distinction between active deformation mechanisms has been done with an aid from the AE cluster analysis using the ASK algorithm. In the steel variant with 3% Ni, the trends in the fm behaviour at RT and 373 K appear to be opposite to those seen in the other two steels. As shown in Fig. 1e and f, a pronounced fm maximum at the onset of deformation is followed by graduate reduction in fm at RT, whereas at 373 K the fm value shifts to a higher frequency domain before dropping when strain localization sets in on the late deformation stage. Thus, it is evident that the deformation mechanism changes substantially at the elevated temperature and this will be demonstrated below by direct microstructural observations. Furthermore, the AE energy
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reflecting the dynamics at the source is by order of magnitude higher at RT than at 373 K in the steel variant with 3% Ni content. This is associated with the massive diffusionless martensitic phase transformation, which is obviously more pronounced at ambient than at elevated temperature. The issue regarding the role of the other possible mechanisms involved into the deformation process has yet to be addressed.
3.2. Acoustic emission cluster analysis and microstructural observations A generally reasonable assumption based on fundamental theoretical considerations is that different sources produce AE signals with different waveforms and, therefore, PSDs. Since AE is
actually a random process with inevitable scatter in descriptive variables, it is difficult, or impossible, to distinguish between different sources by visual comparison of waveforms and PSDs. However, such distinction can become possible through the quantitative grouping of signals of a similar kind if a certain statistical criterion of similarity/dissimilarity is met. Using a data processing methodology described in early works in detail [20,21], the ASK clustering procedure, comparing individual PSD functions in order of their appearance in time, returned the indexed AE series with the clustered AE patterns shown in Fig. 2 in terms of bi-variant E vs. fm distributions for different steels and temperatures. Two different clusters were identified in the steels with 9% and 3% nickel, respectively, whereas in the steel with 6% nickel four different clusters were distinguishable at room temperature. In the steel with 9% nickel, no significant change in the
Fig. 2. Scatter-plots showing bi-variate distributions of AE descriptive variables – average energy E and median frequency fm – for austenitic stainless steels with different Ni content tested at room temperature and at 373 K. Parameters related to individual realizations assigned to different AE clusters (i.e. to different deformation mechanisms) are shown in different colours, corresponding to those in Figs. 3, 5 and 7: (a, b) 9% Ni, (c, d) 6% Ni and (e, f) 3% Ni.
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identified clusters was observed at higher temperature (373 K). However, significant changes occurred in the steel variants with 6% and 3% nickel, respectively. This indicates that the identified clusters as well as their changes depending on temperature correlate well with the underlying microstructural processes. In what follows, the time evolution of the identified AE clusters in each steel variant at two temperatures (RT and 373 K) will be highlighted with support from detailed microstructure analysis.
3.2.1. Steel variant with 9% nickel Fig. 3a–d shows the evolution of two AE clusters (shown in green and red, respectively) in terms of their cumulative energy (a, b) and the number of cluster members (c, d) at RT (a, c) and 373 K (b, d). As has been shown in previous investigations [5], no martensitic phase transformation is observed in this steel variant. However, profuse mechanical twinning does occur leading to the TWIP effect. At room temperature the first cluster (red), starts at the very beginning of deformation and is characterized by a low AE energy, cf. Figs. 2 and 3a. The large body of investigations shows that the low amplitude AE in pure iron or stable steels [25–27] is typical for materials without any phase transformations or mechanical twinning. This type of low amplitude and relatively low frequency cluster is correlated with the ordinary dislocation slip. The second identified cluster (green) starts later on the deformation history. The high-energy burst type AE with reasonably high frequency content (see Fig. 2a) is specific to this cluster. The number of AE cluster elements is increasing over the whole deformation range up to failure, however the rate of AE signal accumulation is more pronounced at the beginning of deformation. Signals of this kind are commonly associated with mechanical twinning [21].
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The same primary deformation mechanisms – dislocation slip and mechanical twinning – were identified by means of the AE cluster analysis at 373 K. However, at this temperature the intensity of twinning decreased and regularly dislocation slip becomes more pronounced. This is reflected by the relative number of AE cluster elements were a significant increase in the “dislocation” cluster members is observed clearly. In contrast, the cluster corresponding to mechanical twinning loses its members significantly and the cumulative AE energy reduces concurrently. These findings agree nicely with the direct, but post-mortem, microstructural observations. Fig. 4 shows the results of EBSD investigations performed after specimen failure on the steel with 9% nickel at RT (a–c) and 373 K (d–f). As expected, no martensitic phase transformation was detected in this steel variant at both temperatures. However, intensive mechanical twinning becomes evident on OIM maps. Both, the image quality map with indicated twin boundaries in red (601 〈111〉 misorientation) (a, d) as well as the surface normal-projected inverse pole figure orientation map (b, e) reveal the dense populations of mechanical twins on two different twin systems. Individual twin lamellae can have a thickness of few nanometres. Due to the limited resolution of EBSD measurements (step size is 100 nm), the nanometre thick twin lamellae cannot be resolved. Twin bundles on the primary twin system were identified as large areas consisting of many individual twins and extending over a whole grain. Shorter and thinner twins on a secondary twin system were observed in between the primary twin bundles. The length and thickness of these secondary twin bands were much less than on the primary system. At higher temperature (373 K), significant changes in the twinning activity are observed: the density of twins decreases remarkably with increasing temperature. Nevertheless, the thicker twins on the primary twin system are characterized by a higher strain level both at RT and at 373 K, which is evident from the kernel
Fig. 3. Results of the AE cluster analysis for the steel variant with 9% nickel tested in tension at RT (a, c) and 373 K (b, d): (a, b) time-evolution of the cumulative AE energy and (c, d) time-evolution of the number of AE cluster elements.
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Fig. 4. Summary of microstructure observations and EBSD measurements on the steel variant with 9% nickel after tensile test at RT (a–c) and 373 K (d–f): (a, d) band contrast images with twin boundaries indicated in red; (b, e) crystallographic orientation map in the inverse pole figure colouring code according to the surface normal direction; and (e, f) kernel average misorientation. Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1 Twin fraction of the steel variant with 9% nickel after tensile tests at RT and 373 K calculated using the primary and secondary twin orientation from the inverse pole figure colouring of the EBSD orientation maps. 16% Cr–6% Mn–9% Ni
RT 373 K
Therefore, the large scatter in the results obtained on the specimen deformed at 373 K is reasonable. In spite of these limitations, the determined values show favourable agreement with the AE findings.
Twin fraction [%] from EBSD orientation maps AOI 1
AOI 2
AOI 3
average
37 35
29 2
29 9
31.7 15.3
average misorientation shown in Fig. 4c and f. In order to quantify the volume fraction of mechanical twins, the area fraction of twinned regions was determined from the crystallographic orientation map. The twin orientation relationship between adjacent crystal domains is described by a misorientation angle/axis pair of 601 around a 〈111〉 direction. In the inverse pole figure crystallographic orientation map this relation is seen in different specific colours for the matrix and the twinned areas. Performing EBSD measurements on three commensurable and randomly chosen areas of interest (AOI) at RT and 373 K, respectively, it was found that the area fraction of mechanical twins decreased from of 31% at RT to 15% at 373 K on average. Results of three individual measurements at both temperatures are summarized in Table 1. We should notice that this is a lower-bound estimate due to the fact that nano-twins are not detectable by EBSD measurements and are not included into statistics. On the other hand, it is well known that the crystallographic orientation of the grains is decisive for the appearance of mechanical twins. The large grain size of the as-cast material is another limiting factor for the estimation of the area fraction of mechanically twinned regions.
3.2.2. Steel variant with 6% nickel Fig. 5 shows the results of the AE cluster analysis at RT (a, c) and 373 K (b, d) obtained for the steel containing 6% of nickel. Fig. 5a and b demonstrates the evolution of the cumulative AE energy, whereas Fig. 5c and d represents the kinetics of AE cluster members accumulation. The steel variant with 6% nickel is a metastable austenitic steel, which exhibits a pronounced deformation-induced martensitic phase transformation at room temperature [11]. The phase transformation occurs from the metastable austenitic phase (f.c.c.) via the intermediate state termed commonly “ε-martensite” (h.c.p.) into the α0 -martensite (b.c.c.) [4]. The hexagonal structure of the ε-martensite results from the stacking faults, which are densely packed in deformation bands [8]. The AE cluster analysis revealed at least four different microstructural processes operating more or less at the same time at RT. The first cluster (shown in red) is pretty much the same as the corresponding cluster in the steel with 9% nickel. It is attributed to the conventional dislocation slip and its behaviour is quite similar to what we have discussed in the preceding section. The second cluster (shown in green) is also similar to that in the steel with 9% Ni and is attributed to mechanical twinning starting around the yield point. However, the smaller number of cluster elements was detected (N o500) in this steel variant. This means that mechanical twinning is observed only occasionally and locally due to chemical inhomogeneity, but it is not the dominating deformation mechanism. To the contrast with the steel containing 9% nickel, a
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Fig. 5. Results of the AE cluster analysis for the steel variant with 6% nickel tested in tension at RT (a, c) and 373 K (b, d): (a, b) time-evolution of the cumulative AE energy and (c, d) time-evolution of the number of AE cluster elements.
third cluster (shown in blue) was distinguished its features appear to be similar to those of the cluster caused by mechanical twinning in terms of AE energy and median frequency, Fig. 2c. This cluster is also composed of high-energy pulses with a broad frequency range from 250 kHz up to 700 kHz. However, according to the basics of the categorization procedure, these classes should be regarded as statistically different and thus they describe populations of different AE sources. Therefore, the latter cluster is most likely associated with the motion of Shockley-partial dislocations forming stacking faults. This cluster starts to develop immediately as the yield point is reached; it then increases significantly before saturation already on the early deformation stage. This finding is in good agreement with microstructural investigations performed in situ or during interrupted tests reported in Refs. [5,28], where it was shown that the hexagonal phase inside the deformation bands composed of densely packed stacking faults (ε-martensite) transforms into the α0 -martensite during deformation. The fourth identified cluster (shown in pink) is obviously related to the dominant deformation mechanism in this steel variant – the martensitic phase transformation. It comes into force at the same moment as the so-called ε-martensite starts to form by motion of partial dislocations. The number of elements contributing to this type of cluster increases significantly over the whole deformation range. A significant change in the kinetics of the identified clusters is observed at the elevated temperature. As has been reported in Ref. [8], a transition from the martensitic phase transformation to mechanical twinning occurs in the steel variant with 6% nickel around deformation temperature of 353 K. Pronounced mechanical twinning becomes evident from the AE cluster analysis at 373 K as shown by the well developed cluster corresponding to twins (shown in green, Fig. 5b and d). This cluster starts around the yield point of the material. The number of elements contributing to this cluster increases
progressively with deformation. The third cluster composed of the signals originated from martensitic phase transformation (shown in pink) was identified too. In view of the two-step γ 4 ε 4 α0 nature of the martensitic transformation, the stacking faults should be present in the microstructure since they serve as the prerequisites for the α0 -martensite. However, only few signals related to the possible stacking faults were identified by the AE analysis, because they were hardly separable from the twin cluster. In order to achieve a better discrimination between the twins and stacking faults, a signal acquisition chain with a substantially improved wideband sensor response should be helpful. The microstructural observations corroborate the deformation scenario proposed by the AE analysis. Fig. 6a–f shows the results of EBSD-measurements at RT (a–c) and 373 K (d–f), where a and d visualize the phase transformation in the respective EBSD maps, b and e show the crystallographic orientation of the f.c.c. phase and c and f illustrate the appearance of twin boundaries in the microstructure. The change in the operating deformation mechanisms becomes clearly evident. Whereas the martensitic phase transformation, which occurs through the intermediate ε-martensite, dominates in the deformation patterns at RT, mechanical twinning substitutes for it at 373 K to a large extent. Fig. 6a illustrates clearly the formation of deformation bands, which were indexed as a hexagonal phase (yellow) due to the high density of stacking faults. Inside these bands, the α0 -martensite nuclei form. The mechanical twins were observed sporadically near the stacking faults, Fig. 6b and c, cf. Ref. [5]. No massive martensitic phase transformation occurred at 373 K. Nevertheless, small areas of ε- and α0 -martensite were detected very locally by the EBSD measurements as shown in Fig. 6d, while Fig. 6e and f demonstrates clearly the prevalence of mechanical twinning at this temperature.
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Fig. 6. Summary of microstructure observations and EBSD measurements on the steel variant with 6% nickel after tensile test at RT (a–c) and 373 K (d–f). (a, d) Phase map with austenitic phase (f.c.c.) in red, ε-martensite (h.c.p.) in yellow and α0 -martensite (b.c.c.) in blue colour (b, e). Crystallographic orientation map in the inverse pole figure colouring code according to the surface normal direction; (e, f) band contrast images with indicated twin boundaries (red). Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3.2.3. Steel variant with 3% nickel Main results of the AE cluster analysis are summarized in Fig. 7 for the steel variant with 3% nickel. The deformation process in this steel is mediated entirely by intensive deformation-induced and/or stress-assisted martensitic phase transformation [11]. Two major types of AE signals were distinguished at room temperature by the ASK procedure. At the onset of straining, the first cluster (shown in blue) of AE signals emerge. The signals belonging to this cluster possess a remarkably high energy. This cluster has boosted its membership significantly in the first fifth part of the deformation process. This cluster, as discussed above, is originated from the motion of partial dislocations and, consequently, is related to the formation of ε-martensite within the deformation bands, which shows a progressive development during deformation. This agrees well with results reported by Jahn et al. [11] who showed that the formation of ε-martensite goes through an intermediate concentration maximum. The second massive cluster (shown in pink) correlates obviously with the martensitic phase transformation. This cluster appears reasonably and starts to grow after the sharp accumulation of the stacking faults signified by a respective AE cluster. AS signals originated from the formation of α0 -martensite are characterized by the high energy and steep increase in membership during deformation. The increase in the testing temperature exerts a significant effect on the behaviour of this steel with unstable microstructure. Although, this steel shows signatures of the two-stage γ 4 ε 4 α0 martensitic transformation even at 373 K, the activity of the underlying AE sources drops substantially, leading to significant reduction in the cumulative energy of corresponding AE clusters; notice the different scales in Fig. 7a and b. On the other hand, the contribution of the dislocation glide to the resultant strain and corresponding AE increases sharply with increasing temperature.
The steel variant with 3% nickel exhibits the lowest austenite stability. The initial microstructure of this steel variant consists of three phases: (i) austenite, (ii) roughly 12 vol% δ-ferrite inherited from processing and (iii) a small volume fraction of athermal martensite resulting from rapid cooling. The δ-ferrite has the same b.c.c. crystallographic structure as the α0 -martensite. Therefore, distinction between these two phases by EBSD analyses is not straightforward. The specific morphology as well as the better band contrast of Kikuchi patterns originated from the δ-ferrite are the main microstructural features essential for a good separation between the δ-ferrite and α0 -martensite. Fig. 8 shows the microstructure (a) and the phase distribution (b) in the steel with 3% nickel after tensile test at RT interrupted at 33% elongation. The SEM micrograph taken in the BSE contrast (a) reveals clearly an arrangement of numerous deformation bands along different activated slip systems; the α0 -martensite nuclei appear in dark contrast. The EBSD-analysis clarifies the phase distribution in the deformation bands as illustrated in Fig. 8b. The deformationinduced α0 -martensite (blue) originates inside deformation bands with a hexagonal lattice structure (yellow) as well as at the band intersections. The high strain level in the material caused some amount of non-indexed Kikuchi patterns (zero solutions coloured in black) during EBSD measurement. The influence of temperature on the martensitic phase transformation in the steel with 3% nickel is convincingly demonstrated by results of SEM investigations summarized in Fig. 9a–c at RT and d–e at 373 K. The blue coloured b.c.c. phase fraction is constituted by two major phases: the δ-ferrite and deformation induced α0 -martensite. Using the BSE contrast images (a, d) the clear identification of the δ-ferrite is possible. The EBSD measurements reveal a significant decrease in the total b.c.c. phase fraction from 65% to 30% with increasing temperature
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Fig. 7. Results of the AE cluster analysis for the steel variant with 3% nickel tested in tension at RT (a, c) and 373 K (b, d): (a, b) time-evolution of the cumulative AE energy and (c, d) time-evolution of the number of AE cluster elements. Please, note the different scales in Fig. 7a and b for the cumulative AE energy.
Fig. 8. SEM mages showing a deformation microstructure of the steel variant with 3% nickel strianed in tension at RT up to 33% elongation: (a) BSE contrast image showing formation of deformation bands on two different activated slip systems and (b) EBSD phase map with austenitic phase (f.c.c.) in red, ε-martensite (h.c.p.) in yellow and α0 -martensite (b.c.c.) in blue colour. Black colour corresponds to zero solutions. Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from RT to 373 K. With account to the amount of δ-ferrite, this means that the fraction of the deformation-induced α0 -martensite reduced from 28.7% after deformation at RT (cf. data obtained by FerritscopeTM [18]; an excellent quantitative agreement has been found for the α0 -martensite volume fraction assessed by AE and by magnetic measurements) to 8.8% at 373 K. The orientation map of the b.c.c. phases is displayed in the inverse pole figure (IPF) colours (Fig. 9c and f), confirming the reduction in the α0 -martensite phase fraction with increasing temperature.
4. Summary and conclusions Motivated by the need for better understanding of the deformation mechanisms underlying complex mechanical behaviour of metastable austenitic stainless steels with TRIP/TWIP effects facilitating their strength and ductility, the relative roles of primary deformation mechanisms were investigated at ambient and elevated temperature. The advanced AE technique employed was shown to be well suited for discrimination in between mechanical twinning, stacking fault formation, martensitic phase
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Fig. 9. Summary of microstructure observations and EBSD investigations for the steel variant with 3% nickel after tensile test at RT (a–c) and 373 K (d–f): (a, d) SEM images in BSE contrast showing formation of deformation bands on different slip systems; δ-ferrite in dark contrast is clearly distinguished within the microstructure (see arrows); (b, e) EBSD phase maps with austenitic phase (f.c.c.) in red, ε-martensite (h.c.p.) in yellow and α0 -martensite (b.c.c.) in blue colour; and (c, f) crystallographic orientation map of the b.c.c. phase in the inverse pole figure colouring code according to the surface normal direction. Stress axis is horizontal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
transformation and dislocation slip mechanisms even when these were operating concurrently. The major results can be summarized as follows: (1) Multiple deformation mechanisms, which involve complex interactions between dislocation slip, mechanical twinning, motion of partial dislocations associated with stacking fault formation and α0 -martensite formation, operate in metastable austenitic stainless steels throughout the entire deformation process. (2) The individual deformation mechanisms were related to different clusters of AE signals grouped statistically by the similarity in their power spectral density. The contribution of these individual mechanisms to AE was found different on different deformation stages, depending primarily on the austenite stability controlled by the Ni content and testing temperature. (3) The results of the AE cluster analysis regarding the kinetics of the individual deformation mechanisms appear in good agreement with the post-mortem microstructural investigations. (4) The possibility to utilize different types of AE sensors has been demonstrated in attempt to distinguish between operating source mechanisms, using the ASK clustering procedure. The presented results for all three steel variants after tensile deformation at RT appeared in good agreement with previous results obtained for the same steels tested with the other type of AE transducer [18]. (5) The present investigation demonstrated that the increase in testing temperature leads to significant changes in the microstructure evolution in all three steel variants. The possibility to
follow the activity of different deformation processes during the loading history is demonstrated by means of the appropriate AE cluster analysis. (6) Mechanical twinning is still operative in the steel variant with 9% nickel at elevated temperature (373 K), though with a reduced activity. The AE cluster analysis shows that in replace for twinning, the activity of dislocation glide increased with increasing temperature. (7) The AE cluster analysis paired by microstructural investigations revealed that transition occurs in the dominating deformation mechanism from martensitic phase transformation at RT to mechanical twinning at 373 K in the steel variant with 6% nickel. (8) The same analysis shows that the martensitic phase transformation occurs even at the elevated temperature up to 373 K in the steel variant with 3% nickel, but with a reduced intensity.
Acknowledgements Financial support of the CRC 799 research project by the German Research Foundation (DFG) and by the Russian Ministry of Education and Science (Grant-in-aid 11.G34.31.0031) is greatly acknowledged. One of the authors (ML) gratefully acknowledges the hospitality of the Institute of Materials Engineering, Technische Universität Bergakademie Freiberg. Special thanks go to Dipl.-Ing. G. Schade for his skilful and enthusiastic assistance with experiments and to Mrs. K. Zuber for careful preparation of the specimens for the EBSD measurements.
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References [1] H.K.D.H. Bhadeshia, ISIJ Int. 42 (2002) 1059–1060. [2] S. Allain, J.P. Chateau, O. Bouaziz, S. Migot, N. Guelton, Mater. Sci. Eng. A 387– 389 (2004) 158–162. [3] B.C. De Cooman, K.-G. Chin, J. Kim, in: M. Chiaberge (Ed.), New Trends and Developments in Automotive System Engineering, New York, USA, 2011, pp. 101–102. [4] P. Mangonon, G. Thomas, Metall. Trans. 1 (1970) 1577–1586. [5] H. Biermann, J. Solarek, A. Weidner, Steel Res. Int. 83 (2012) 512–520. [6] A. Weidner, S. Martin, V. Klemm, U. Martin, H. Biermann, Scr. Mater. 64 (2011) 513–516. [7] S. Martin, C. Ullrich, D. Imek, U. Martin, D. Rafaja, J. Appl. Crystallogr. 44 (2011) 779–787. [8] A. Dumay, J.P. Chateau, S. Allain, S. Migot, O. Bouaziz, Mater. Sci. Eng. A 483– 48l (2008) 184–187. [9] L. Krüger, S. Wolf, U. Martin, S. Martin, P.R. Scheller, A. Jahn, A. Weiß, J. Phys. 240 (2010) 012098. [10] S. Martin, S. Wolf, U. Martin, L. Krüger, Solid State Phenom. 172–174 (2011) 172–177. [11] A. Jahn, A. Kovalev, A. Weiß, S. Wolf, L. Krüger, P.R. Scheller, Steel Res. Int. 82 (2011) 39–44. [12] J. Talonen, H. Hänninen, Acta Mater. 55 (2007) 6108–6118. [13] L. Remy, A. Pineau, Mater. Sci. Eng. 28 (1977) 99–107.
193
[14] A. Weiß, H. Gutte, M. Radke, P.R. Scheller, Patent WO002008009722A1. [15] A. Weiß, H. Gutte, A. Jahn, P.R. Scheller, Materialwiss. Werkst. 40 (2009) 606–611. [16] A. Jahn, A. Kovalev, A. Weiβ, P. Scheller, R.S. Wolf, L. Krüger, S. Martin, U. Martin, ESOMAT (2009) 05013, http://dx.doi.org/10.1051/esomat/ 200905013. [17] V. Tsakiris, D.V. Edmonds, Mater. Sci. Eng. A 273–275 (1999) 430–436. [18] A. Vinogradov, A. Lazarev, M. Linderov, A. Weidner, H. Biermann, Acta Mater. 61 (2013) 2434–2449. [19] S. Lazarev, A. Mozgovoi, A. Vinogradov, A. Lazarev, A. Shvedov, J. Acoust. Emiss. 27 (2009) 215–223. [20] E. Pomponi, A. Vinogradov, Mech. Syst. Signal Proc. 40 (2013) 791–804. [21] A. Vinogradov, D. Orlov, A. Danyuk, Y. Estrin, Acta Mater. 61 (2013) 2044–2056. [22] A. Vinogradov, M. Nadtochiy, S. Hashimoto, S. Miura, Mater. Trans. JIM 36 (1995) 426–431. [23] A. Vinogradov, D.L. Merson, V. Patlan, S. Hashimoto, Mater. Sci. Eng. A 341 (2003) 57–73. [24] A. Vinogradov, V. Patlan, S. Hashimoto, Philos. Mag. A 81 (2001) 1427–1446. [25] F.P. Higgens, S.H. Carpenter, Acta Metall. 26 (1978) 133–139. [26] R. Takeda, Y. Kaneko, D.L. Merson, A. Vinogradov, Mater. Trans. 54 (2013) 532–539. [27] A. Lazarev, A. Vinogradov, J, Acoust. Emiss. 27 (2009) 144–156. [28] A. Weidner, A. Glage, H. Biermann, Proc. Eng. 2 (2010) 1961–1971.