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Microtension behaviour of lenticular martensite structure of Fe–30 mass% Ni alloy
Materials Science & Engineering A 618 (2014) 359–367
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Microtension behaviour of lenticular martensite structure of Fe–30 mass% Ni alloy Yoji Mine n, Hiroki Takashima, Mitsuhiro Matsuda, Kazuki Takashima Department of Materials Science and Engineering, Kumamoto University Kurokami, Chuo-ku, Kumamoto 860-8555, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 20 June 2014 Received in revised form 29 August 2014 Accepted 5 September 2014 Available online 16 September 2014
Microtension testing of an Fe–30Ni alloy revealed that yielding in the lenticular martensite plates is not necessarily caused by the slip system with the highest Schmid factor. Dislocation gliding likely occurred on the slip system parallel to the plane of nanotwins in the lenticular martensite plate. The martensite plate exhibited a critical resolved shear stress of 190 MPa. Strain accumulation at the variant interfaces between the primary plate and the aggregated fragments led to a unique faceted fracture. This is attributed to anisotropic plasticity in the lenticular martensite plates owing to the interaction of the mobile dislocations with the nanotwins. & 2014 Elsevier B.V. All rights reserved.
Keywords: Mechanical characterisation Ferrous alloy Martensite Crystal plasticity Fracture Interfaces
1. Introduction Martensite is the most important phase for steels in order to attain high strength and high resistance to fatigue and wear [1]. It is accepted that in ferrous alloys, four distinct morphologies of martensitic microstructures, namely, lath, butterfly, lenticular, and thin plate, are observed depending on alloy composition and transformation temperature [2]. Recent advances in electron backscatter diffraction (EBSD) analysis techniques have helped clarify the details of the martensitic microstructures [3–7]. Each martensitic microstructure has a hierarchical structure. In particular, the substructure of lenticular martensite, which appears in highcarbon steels and Fe–Ni alloys, consists of three regions, namely, midrib, twinned, and untwinned regions. The midrib lies in the middle of the lenticular martensite plate and is characterised by a high density of nanoscale twins with a low density of dislocations. It was also reported that the substructure and crystallographic features of the midrib are identical to those of thin-plate martensite [8]. A nano-indentation study by Zhang et al. revealed that the nanohardness of the midrib was higher than that of the other regions [9]. They concluded that the very fine twin structure had two roles in hardening: it acts as a stress-concentration site to generate dislocations and as a strong obstacle to dislocation
n
Corresponding author. Tel./fax: þ 81 96 342 3713. E-mail address: [email protected] (Y. Mine).
http://dx.doi.org/10.1016/j.msea.2014.09.027 0921-5093/& 2014 Elsevier B.V. All rights reserved.
gliding [9]. However, the impact of the midrib on the macroscopic strength is small because its volume fraction is limited. Micromechanical testing techniques have developed rapidly, along with microelectronic mechanical systems (MEMS) technology. Nano-indentation, although commonly used [9], is not appropriate for analysing the deformation process that leads to the final fracture. On the other hand, microtension testing has recently been applied to the analyses of mechanical characteristics on the scale of a few tens of micrometres [10–13]. If the specimen size is reduced to the scale of the lenticular martensite plate, i.e., a few tens of micrometres, the intrinsic effects of the substructure on the strength and plasticity of the lenticular martensite can be observed. This study used microtension testing to characterize the uniaxial stress–strain behaviour of the lenticular martensite structure, with particular focus on the impact of the nanotwins on the plastic deformation and fracture.
2. Material and experimental methods The material used in this study was an Fe–29.7Ni (mass%) alloy (hereafter denoted as Fe–30Ni), supplied in the form of a coarsegrained austenite with an average grain size of approximately 5 mm. Platelets with dimensions of approximately 1 mm 5 mm 10 mm were cut from this alloy. A lenticular martensite microstructure was obtained by cooling in liquid nitrogen (77 K). The platelets were thinned down to a thickness of 20 μm by grinding both surfaces with emery paper. Specimens with a gauge section of
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20 μm 20 μm 50 μm were fabricated using focused ion beam (FIB) machining after their surfaces were polished using colloidal silica for EBSD analysis. Three specimens were obtained such that their loading directions (LDs) were parallel to the midrib of the lenticular martensite plate. The three specimens are denoted as the P1, P2, and P3 specimens. A specimen transverse to the midrib, which is denoted as the T specimen, was also prepared. Fig. 1 shows the schematic drawing of the lenticular martensite structure in the four specimens used in this study. A field emission gun-scanning electron microscope with an EBSD analyser was used for observing the gauge sections of the specimens. The crystal orientation was determined by automatic beam scanning with a step size of 0.1– 0.6 μm at an accelerating voltage of 20 kV. EBSD analysis was carried out using the TexSEM Laboratories orientation imaging microscopy (OIM) software (v. 7.0.1). A clean-up procedure was applied to all EBSD images to adjust single points with misorientations of more than 51 to their neighbours. A tensile test with a micro-gluing grip was performed at a crosshead speed of 0.1 μm s 1, which is equivalent to a strain rate of 2 10 3 s 1, at room temperature in laboratory atmospheric conditions. The test was interrupted at predetermined displacements to monitor the length of the elongated gauge part and measure the surface undulation by scanning white-light interferometry (SWLI) with a high resolution of 0.1 nm in the depth direction. Based on the analysis of the shifts of 45 points selected on the SWLI image, the distributions of the maximum in-plane shear strain were determined. The details of the method are described in another paper [14]. Some failure specimens were fabricated using FIB, and then their longitudinal cross sections were observed by OIM or transmission electron microscopy (TEM). The TEM examination was conducted with a JEOL JEM-2000FX transmission electron microscope operated at an accelerating voltage of 200 kV.
Fig. 1. Schematic drawing showing lenticular martensite structure in (a) P1, (b) P2, (c) P3, and (d) T specimens.
3. Results 3.1. Stress–strain behaviour Fig. 2 illustrates the stress–strain behaviour obtained using micrometre-sized specimens of the lenticular martensite structures. The LDs of the P1, P2, and P3 specimens were arranged within an angle of 111 to the [110] direction, as shown in the standard stereographic triangle in Fig. 2. The LD of the T specimen was inclined at an angle of 201 with respect to the [100] direction. After yielding occurred at a stress of 400–560 MPa, an ultimate tensile strength, σUTS, of 520–670 MPa was attained at a strain of several per cent, where the yield stress, σys, is defined as the stress obtained just after plastic deformation commenced in the stress–strain plots. These values were somewhat lower than σys ¼ 650 MPa and σUTS ¼ 730 MPa obtained for the bulk specimen [15]. The stress– strain curves of the P1 and P2 specimens showed good reproducibility, whereas the P3 specimen exhibited the highest yield stress and ultimate tensile strength through significant strain hardening. The yield stress and ultimate tensile strength in the T specimen were slightly higher than those in the P1 and P2 specimens. The local elongation in the T specimen was highest, whereas the uniform elongations were similar among all the specimens.
3.2. Deformation and fracture morphologies in parallel specimens Fig. 3 shows the positions from which the microtension specimens were cut out and the crystallographic orientation maps in the P1, P2, and P3 specimens. Fig. 3(a), (c), and (e) was taken by scanning ion microscopy (SIM) and Fig. 3(b), (d), and (f) was obtained by EBSD analysis. The unit triangle represents the inverse pole figure colour-coded according to the crystallographic orientation corresponding to the projection of the LD of the tensile specimens. Black points in the OIM maps represent the measuring error due to contamination on the specimen surface. The symbols Vx are assigned to each martensite variant on the basis of an N–W orientation relationship. The OIM maps of the P1 and P2 specimens show that the gauge section mainly consisted of four martensite variants: the fragments V1, V7, and V9 embedded in the primary plate V3 (Fig. 3b and d). In the P3 specimen, the gauge part consisted of multiple martensite variants (Fig. 3f). Fig. 3(a), (c), and (e) shows that the midrib lay nearly parallel to the LD. In particular, the traces of nanotwins are visible in the SIM image of the P2 specimen (Fig. 3c). Fig. 4 shows typical TEM micrographs
Fig. 2. Stress–strain behaviours obtained using microtension specimens of lenticular martensite plates.
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Fig. 3. SIM images of sectioning regions and OIM maps of microtension specimens: (a, b) P1, (c, d) P2, and (e, f) P3. LD and TD represent the loading and transverse directions of the specimens, respectively. Vx represents the variant type, which is assigned on the basis of an N–W orientation relationship.
indicative of the orientation relationship between the nanotwins and the midrib in the lenticular martensite plate. Fig. 5 shows the surface undulation during tensile straining of the P1 specimen by SWLI (a–d) and the distribution of the maximum shear strain (e–g), which was constructed from the SWLI images. The protrusion became pronounced at a strain of 2% (Fig. 5b). At a strain of 3.8%, furrows appeared (Fig. 5c), and then the crack was opened at a strain of 8.3% (Fig. 5d). At a macrostrain
of 2%, where the flow stress was saturated through some strain hardening (Fig. 2), strain localisation occurred (Fig. 5e). The crack was formed at the highest local strain region at a macrostrain of 3.8% and then local strain was further localised ahead of the crack tip at a macrostrain of 8.3% (Fig. 5f and g). Fig. 6(a) and (b) shows the side view after failure and the fracture surface of the P1 specimen, respectively. The fracture morphologies indicate that the facets were formed, and a shear-type fracture finally
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Fig. 4. TEM micrographs showing the orientation relationship between nanotwins and midrib: (a) bright-field image, (b) electron diffraction pattern, and (c) key diagram of (b) (subscripts M and T represent matrix and twin, respectively).
Fig. 5. (a–d) SWLI images indicating surface undulation and (e–g) distribution of the maximum in-plane shear strain, γmax, during the plastic straining process of the P1 specimen.
occurred. The faceted fracture was repeated in the other specimens. The plane of the facet was not consistent with the typical {001} cleavage plane. A close observation shows that the traces are visible on the facet surface (Fig. 6c).
Fig. 7 shows the microstructure beneath the faceted fracture surface of the P1 specimen, extracted from the cross section marked in Fig. 6(b). Fig. 7(a), taken by SIM, shows the lamellar structures beneath the faceted fracture surface. It was also
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Fig. 6. (a) Side view and (b) overall view of fracture surface of the P1 specimen. (c) Enlarged micrograph of facet. LD, TD, and ND represent the loading, transverse and normal directions of the specimens, respectively.
Fig. 7. (a) SIM and (b, c) bright-field TEM images with selected area electron diffraction patterns of the microstructure beneath the faceted fracture surface in the P1 specimen.
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Fig. 8. (a) Side view and (b) overall view of the fracture surface of the P2 specimen.
Fig. 9. (a) Side view, (b) overall view of fracture surface, and (c) SIM image of microstructure beneath the fracture surface in the P3 specimen.
confirmed that such a microstructure was not visible in the counterpart of the faceted fracture surface. Fig. 7(b) and (c) shows TEM bright-field images with selected area electron diffraction (SAED) patterns. The SAED analysis confirms that some lamellar variants (V7 and V8) were formed from the same parent crystal as V3. It is therefore concluded that the faceted fracture occurred at the interfaces between the primary variant and the aggregated variant fragments embedded in it. Fig. 8(a) and (b) shows the side view of fracture morphology and the fracture surface in the P2 specimen, respectively. A sheartype fracture concurrent with facets was observed again. It is
noteworthy that the slip traces on the side surface (Fig. 8a) were in the direction parallel to the nanotwins (Fig. 3c). The in situ SWLI observation of the P3 specimen revealed that plastic deformation arose in the primary plate and then faceted cracking occurred in the vicinity of the aggregated variant fragments. Fig. 9 shows the fracture morphologies and the microstructure beneath the fracture surface in the P3 specimen. Although the primary plate V4 was predominant on the specimen surface (Fig. 3f), the transverse cross section of the gauge part (Fig. 9c), which was cut out from the marked region in Fig. 9(a), exhibits a complex microstructure with multiple variants. Like the
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Fig. 10. (a) SIM image at initial state and (b–f) SWLI images indicating surface undulation during the plastic straining process of the T specimen.
Fig. 11. (a) SIM image and (b) OIM map of the T specimen after failure.
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P1 specimen, the aggregated variant fragments are visible beneath the faceted fracture surface in the P3 specimen. 3.3. Deformation and fracture morphologies in transverse specimen Fig. 10(a) and (b–f) shows the initial microstructure taken by SIM and SWLI during tensile straining of the T specimen, respectively. The T specimen was cut out so that the LD could traverse the midrib of the primary plate. Surface undulation owing to plastic deformation commenced in the primary plate at a strain of 0.85% (Fig. 10b). The plastic deformation process shown in Fig. 10(c–f) indicates that local strain was accumulated at the aggregated variant interfaces and then cracking occurred at those interfaces. Fig. 11(a) and (b) presents the SIM and OIM images, respectively, of the longitudinal cross section of the T specimen after failure. There are aggregated variant fragments neighbouring the facets in the left part of the specimen, whereas the right part exhibits an intensely deformed primary plate.
operative. Note that the lenticular martensite plate has nanotwins at the middle of it. In the P2 specimen, the operative slip plane was parallel to the plane of the nanotwins (compare Figs. 3c and 12b). Although the traces of the nanotwins could not be observed in the other specimens, the operative slip systems in all the specimens correspond to one of the possible nanotwin planes inferred from the orientation relationship with the midrib, as shown in Fig. 4. Therefore, if the slip system parallel to the nanotwin plane is favoured, it is reasonable that the definite CRSS value can be obtained (Table 1). This value was significantly lower than the CRSS of 300–360 MPa for the in-lath-plane slip that was activated parallel to the habit plane of the lath martensite structures of carbon steel [13]. In both cases, dislocation gliding was hardly hindered by the obstacles, i.e., the nanotwins for the lenticular martensite and the block boundaries for the lath martensite. Thus, the difference in the CRSS is anticipated to reflect the difference in the strength of the matrix between both martensite structures. 4.2. The formation of faceted cracks
4. Discussion 4.1. Effect of nanotwin orientation on plastic deformation Fig. 12 shows the stereographic projection of the primary plate in each specimen, indicative of the operative slip system (112) ½1 11 inferred from the slip traces and/or the crystal rotation during the tensile straining. These stereographic projections show that the slip system exhibiting the highest Schmid factor in each specimen was not activated. Table 1 summarises the yield stress, Schmid factors for the slip system exhibiting the highest value among {112} 〈1 11〉 and the operative slip system, and the critical resolved shear stress (CRSS). The CRSS for the operative slip system was determined to be 182–200 MPa, despite the fact that the slip system exhibiting the highest Schmid factor was not
In all the specimens, faceted and shear-type fractures appeared, as shown in Figs. 6, 8, and 9. Beneath the faceted fracture surfaces, aggregated variant fragments were observed in one half of the Table 1 Yield stress, Schmid factors for slip system exhibiting the highest value and operative slip system, and critical resolved shear stress (CRSS). Yield stress (MPa)
P1 P2 P3 T
441 404 556 490
Schmid factor
CRSS (MPa)
Highest value
Operative slip system
0.493 0.469 0.495 0.469
0.441 0.452 0.360 0.393
Fig. 12. Stereographic projection figures showing operative slip system in (a) P1, (b) P2, (c) P3, and (d) T specimens.
195 182 200 192
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failure specimens, whereas the other half exhibited severe deformation of the coarse variant (Figs. 7 and 11). Anisotropic deformation in the primary plate due to the activation of the slip system that was parallel to the nanotwin plane was followed by the strain accumulation at the variant interfaces (Figs. 5 and 10). The orientation of the nanotwin plane can be greatly rotated at some variant interfaces. It is therefore hypothesised that the interaction of the mobile dislocations with the nanotwins can promote strain localisation at the variant interfaces to form the faceted fracture. On the other hand, the P3 specimen exhibited significant strain hardening after yielding at somewhat higher stress. Indeed, the SIM examination of the cross section confirmed that the gauge section of the P3 specimen comprised the multiple variants beneath the primary plate (Fig. 9c). This suggests that the variant boundaries also contribute to hardening in the bulk specimen. 5. Conclusions Microtension testing of an Fe–30Ni alloy was conducted to clarify the effect of the nanotwins on the plastic deformation in a lenticular martensite structure. Yielding in the lenticular martensite plates did not occur by the slip system exhibiting the highest Schmid factor. Dislocation gliding likely occurred on the slip system parallel to the plane of the nanotwins. The CRSS was determined to be 182–200 MPa. A unique faceted fracture, in which the plane was not consistent with the typical {001} cleavage plane, was observed after microtension straining of the lenticular martensite plates. The faceted crack was initiated due to strain localisation at the variant interfaces between the primary plate and the aggregated fragments. It is suggested that the anisotropic plasticity and the formation of the faceted fracture are related to the interaction of dislocations with nanotwins.
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Acknowledgements The authors are indebted to Mr. N. Ohara, Dr. M. Tsushida and Dr. T. Yamamuro, Kumamoto University for their assistance with the TEM observation. This work was supported by a Grant-in-Aid for Scientific Research (B) 24360293 from the Japan Society for the Promotion of Science (JSPS).
References [1] G. Krauss, Mater. Sci. Eng. A 273–275 (1999) 40–57. [2] M. Umemoto, E. Yoshitake, I. Tamura, J. Mater. Sci. 18 (1983) 2893–2904. [3] S. Morito, H. Tanaka, R. Konishi, T. Furuhara, T. Maki, Acta Mater. 51 (2003) 1789–1799. [4] H. Kitahara, R. Ueji, M. Ueda, N. Tsuji, Y. Minamino, Mater. Character 54 (2005) 378–386. [5] H. Kitahara, R. Ueji, N. Tsuji, Y. Minamino, Acta Mater. 54 (2006) 1279–1288. [6] H. Sato, S. Zaefferer, Acta Mater. 57 (2009) 1931–1937. [7] T. Chiba, G. Miyamoto, T. Furuhara, Scr. Mater. 67 (2012) 324–327. [8] A. Shibata, T. Murakami, S. Morito, T. Furuhara, T. Maki, Mater. Trans. 49 (2008) 1242–1248. [9] L. Zhang, T. Ohmura, A. Shibata, K. Tsuzaki, Mater. Sci. Eng. A 527 (2010) 1869–1874. [10] Y. Mine, H. Fujisaki, M. Matsuda, M. Takeyama, K. Takashima, Scr. Mater. 65 (2011) 707–710. [11] Y. Mine, K. Hirashita, M. Matsuda, M. Otsu, K. Takashima, Corros. Sci. 53 (2011) 529–533. [12] Y. Mine, K. Hirashita, M. Matsuda, K. Takashima, Metall. Mater. Trans. A 42 (2011) 3567–3571. [13] Y. Mine, K. Hirashita, H. Takashima, M. Matsuda, K. Takashima, Mater. Sci. Eng. A 560 (2013) 535–544. [14] T. Ito, Y. Mine, M. Otsu, K. Takashima, Kumamoto University, Kumamoto, Japan, 2014 (unpublished research). [15] H. Kitahara, N. Tsuji, Y. Minamino, Mater. Sci. Forum 503–504 (2006) 913–918.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Microtension behaviour of lenticular martensite structure of Fe–30 mass% Ni alloy Yoji Mine n, Hiroki Takashima, Mitsuhiro Matsuda, Kazuki Takashima Department of Materials Science and Engineering, Kumamoto University Kurokami, Chuo-ku, Kumamoto 860-8555, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 20 June 2014 Received in revised form 29 August 2014 Accepted 5 September 2014 Available online 16 September 2014
Microtension testing of an Fe–30Ni alloy revealed that yielding in the lenticular martensite plates is not necessarily caused by the slip system with the highest Schmid factor. Dislocation gliding likely occurred on the slip system parallel to the plane of nanotwins in the lenticular martensite plate. The martensite plate exhibited a critical resolved shear stress of 190 MPa. Strain accumulation at the variant interfaces between the primary plate and the aggregated fragments led to a unique faceted fracture. This is attributed to anisotropic plasticity in the lenticular martensite plates owing to the interaction of the mobile dislocations with the nanotwins. & 2014 Elsevier B.V. All rights reserved.
Keywords: Mechanical characterisation Ferrous alloy Martensite Crystal plasticity Fracture Interfaces
1. Introduction Martensite is the most important phase for steels in order to attain high strength and high resistance to fatigue and wear [1]. It is accepted that in ferrous alloys, four distinct morphologies of martensitic microstructures, namely, lath, butterfly, lenticular, and thin plate, are observed depending on alloy composition and transformation temperature [2]. Recent advances in electron backscatter diffraction (EBSD) analysis techniques have helped clarify the details of the martensitic microstructures [3–7]. Each martensitic microstructure has a hierarchical structure. In particular, the substructure of lenticular martensite, which appears in highcarbon steels and Fe–Ni alloys, consists of three regions, namely, midrib, twinned, and untwinned regions. The midrib lies in the middle of the lenticular martensite plate and is characterised by a high density of nanoscale twins with a low density of dislocations. It was also reported that the substructure and crystallographic features of the midrib are identical to those of thin-plate martensite [8]. A nano-indentation study by Zhang et al. revealed that the nanohardness of the midrib was higher than that of the other regions [9]. They concluded that the very fine twin structure had two roles in hardening: it acts as a stress-concentration site to generate dislocations and as a strong obstacle to dislocation
n
Corresponding author. Tel./fax: þ 81 96 342 3713. E-mail address: [email protected] (Y. Mine).
http://dx.doi.org/10.1016/j.msea.2014.09.027 0921-5093/& 2014 Elsevier B.V. All rights reserved.
gliding [9]. However, the impact of the midrib on the macroscopic strength is small because its volume fraction is limited. Micromechanical testing techniques have developed rapidly, along with microelectronic mechanical systems (MEMS) technology. Nano-indentation, although commonly used [9], is not appropriate for analysing the deformation process that leads to the final fracture. On the other hand, microtension testing has recently been applied to the analyses of mechanical characteristics on the scale of a few tens of micrometres [10–13]. If the specimen size is reduced to the scale of the lenticular martensite plate, i.e., a few tens of micrometres, the intrinsic effects of the substructure on the strength and plasticity of the lenticular martensite can be observed. This study used microtension testing to characterize the uniaxial stress–strain behaviour of the lenticular martensite structure, with particular focus on the impact of the nanotwins on the plastic deformation and fracture.
2. Material and experimental methods The material used in this study was an Fe–29.7Ni (mass%) alloy (hereafter denoted as Fe–30Ni), supplied in the form of a coarsegrained austenite with an average grain size of approximately 5 mm. Platelets with dimensions of approximately 1 mm 5 mm 10 mm were cut from this alloy. A lenticular martensite microstructure was obtained by cooling in liquid nitrogen (77 K). The platelets were thinned down to a thickness of 20 μm by grinding both surfaces with emery paper. Specimens with a gauge section of
360
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20 μm 20 μm 50 μm were fabricated using focused ion beam (FIB) machining after their surfaces were polished using colloidal silica for EBSD analysis. Three specimens were obtained such that their loading directions (LDs) were parallel to the midrib of the lenticular martensite plate. The three specimens are denoted as the P1, P2, and P3 specimens. A specimen transverse to the midrib, which is denoted as the T specimen, was also prepared. Fig. 1 shows the schematic drawing of the lenticular martensite structure in the four specimens used in this study. A field emission gun-scanning electron microscope with an EBSD analyser was used for observing the gauge sections of the specimens. The crystal orientation was determined by automatic beam scanning with a step size of 0.1– 0.6 μm at an accelerating voltage of 20 kV. EBSD analysis was carried out using the TexSEM Laboratories orientation imaging microscopy (OIM) software (v. 7.0.1). A clean-up procedure was applied to all EBSD images to adjust single points with misorientations of more than 51 to their neighbours. A tensile test with a micro-gluing grip was performed at a crosshead speed of 0.1 μm s 1, which is equivalent to a strain rate of 2 10 3 s 1, at room temperature in laboratory atmospheric conditions. The test was interrupted at predetermined displacements to monitor the length of the elongated gauge part and measure the surface undulation by scanning white-light interferometry (SWLI) with a high resolution of 0.1 nm in the depth direction. Based on the analysis of the shifts of 45 points selected on the SWLI image, the distributions of the maximum in-plane shear strain were determined. The details of the method are described in another paper [14]. Some failure specimens were fabricated using FIB, and then their longitudinal cross sections were observed by OIM or transmission electron microscopy (TEM). The TEM examination was conducted with a JEOL JEM-2000FX transmission electron microscope operated at an accelerating voltage of 200 kV.
Fig. 1. Schematic drawing showing lenticular martensite structure in (a) P1, (b) P2, (c) P3, and (d) T specimens.
3. Results 3.1. Stress–strain behaviour Fig. 2 illustrates the stress–strain behaviour obtained using micrometre-sized specimens of the lenticular martensite structures. The LDs of the P1, P2, and P3 specimens were arranged within an angle of 111 to the [110] direction, as shown in the standard stereographic triangle in Fig. 2. The LD of the T specimen was inclined at an angle of 201 with respect to the [100] direction. After yielding occurred at a stress of 400–560 MPa, an ultimate tensile strength, σUTS, of 520–670 MPa was attained at a strain of several per cent, where the yield stress, σys, is defined as the stress obtained just after plastic deformation commenced in the stress–strain plots. These values were somewhat lower than σys ¼ 650 MPa and σUTS ¼ 730 MPa obtained for the bulk specimen [15]. The stress– strain curves of the P1 and P2 specimens showed good reproducibility, whereas the P3 specimen exhibited the highest yield stress and ultimate tensile strength through significant strain hardening. The yield stress and ultimate tensile strength in the T specimen were slightly higher than those in the P1 and P2 specimens. The local elongation in the T specimen was highest, whereas the uniform elongations were similar among all the specimens.
3.2. Deformation and fracture morphologies in parallel specimens Fig. 3 shows the positions from which the microtension specimens were cut out and the crystallographic orientation maps in the P1, P2, and P3 specimens. Fig. 3(a), (c), and (e) was taken by scanning ion microscopy (SIM) and Fig. 3(b), (d), and (f) was obtained by EBSD analysis. The unit triangle represents the inverse pole figure colour-coded according to the crystallographic orientation corresponding to the projection of the LD of the tensile specimens. Black points in the OIM maps represent the measuring error due to contamination on the specimen surface. The symbols Vx are assigned to each martensite variant on the basis of an N–W orientation relationship. The OIM maps of the P1 and P2 specimens show that the gauge section mainly consisted of four martensite variants: the fragments V1, V7, and V9 embedded in the primary plate V3 (Fig. 3b and d). In the P3 specimen, the gauge part consisted of multiple martensite variants (Fig. 3f). Fig. 3(a), (c), and (e) shows that the midrib lay nearly parallel to the LD. In particular, the traces of nanotwins are visible in the SIM image of the P2 specimen (Fig. 3c). Fig. 4 shows typical TEM micrographs
Fig. 2. Stress–strain behaviours obtained using microtension specimens of lenticular martensite plates.
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Fig. 3. SIM images of sectioning regions and OIM maps of microtension specimens: (a, b) P1, (c, d) P2, and (e, f) P3. LD and TD represent the loading and transverse directions of the specimens, respectively. Vx represents the variant type, which is assigned on the basis of an N–W orientation relationship.
indicative of the orientation relationship between the nanotwins and the midrib in the lenticular martensite plate. Fig. 5 shows the surface undulation during tensile straining of the P1 specimen by SWLI (a–d) and the distribution of the maximum shear strain (e–g), which was constructed from the SWLI images. The protrusion became pronounced at a strain of 2% (Fig. 5b). At a strain of 3.8%, furrows appeared (Fig. 5c), and then the crack was opened at a strain of 8.3% (Fig. 5d). At a macrostrain
of 2%, where the flow stress was saturated through some strain hardening (Fig. 2), strain localisation occurred (Fig. 5e). The crack was formed at the highest local strain region at a macrostrain of 3.8% and then local strain was further localised ahead of the crack tip at a macrostrain of 8.3% (Fig. 5f and g). Fig. 6(a) and (b) shows the side view after failure and the fracture surface of the P1 specimen, respectively. The fracture morphologies indicate that the facets were formed, and a shear-type fracture finally
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Fig. 4. TEM micrographs showing the orientation relationship between nanotwins and midrib: (a) bright-field image, (b) electron diffraction pattern, and (c) key diagram of (b) (subscripts M and T represent matrix and twin, respectively).
Fig. 5. (a–d) SWLI images indicating surface undulation and (e–g) distribution of the maximum in-plane shear strain, γmax, during the plastic straining process of the P1 specimen.
occurred. The faceted fracture was repeated in the other specimens. The plane of the facet was not consistent with the typical {001} cleavage plane. A close observation shows that the traces are visible on the facet surface (Fig. 6c).
Fig. 7 shows the microstructure beneath the faceted fracture surface of the P1 specimen, extracted from the cross section marked in Fig. 6(b). Fig. 7(a), taken by SIM, shows the lamellar structures beneath the faceted fracture surface. It was also
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Fig. 6. (a) Side view and (b) overall view of fracture surface of the P1 specimen. (c) Enlarged micrograph of facet. LD, TD, and ND represent the loading, transverse and normal directions of the specimens, respectively.
Fig. 7. (a) SIM and (b, c) bright-field TEM images with selected area electron diffraction patterns of the microstructure beneath the faceted fracture surface in the P1 specimen.
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Fig. 8. (a) Side view and (b) overall view of the fracture surface of the P2 specimen.
Fig. 9. (a) Side view, (b) overall view of fracture surface, and (c) SIM image of microstructure beneath the fracture surface in the P3 specimen.
confirmed that such a microstructure was not visible in the counterpart of the faceted fracture surface. Fig. 7(b) and (c) shows TEM bright-field images with selected area electron diffraction (SAED) patterns. The SAED analysis confirms that some lamellar variants (V7 and V8) were formed from the same parent crystal as V3. It is therefore concluded that the faceted fracture occurred at the interfaces between the primary variant and the aggregated variant fragments embedded in it. Fig. 8(a) and (b) shows the side view of fracture morphology and the fracture surface in the P2 specimen, respectively. A sheartype fracture concurrent with facets was observed again. It is
noteworthy that the slip traces on the side surface (Fig. 8a) were in the direction parallel to the nanotwins (Fig. 3c). The in situ SWLI observation of the P3 specimen revealed that plastic deformation arose in the primary plate and then faceted cracking occurred in the vicinity of the aggregated variant fragments. Fig. 9 shows the fracture morphologies and the microstructure beneath the fracture surface in the P3 specimen. Although the primary plate V4 was predominant on the specimen surface (Fig. 3f), the transverse cross section of the gauge part (Fig. 9c), which was cut out from the marked region in Fig. 9(a), exhibits a complex microstructure with multiple variants. Like the
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Fig. 10. (a) SIM image at initial state and (b–f) SWLI images indicating surface undulation during the plastic straining process of the T specimen.
Fig. 11. (a) SIM image and (b) OIM map of the T specimen after failure.
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P1 specimen, the aggregated variant fragments are visible beneath the faceted fracture surface in the P3 specimen. 3.3. Deformation and fracture morphologies in transverse specimen Fig. 10(a) and (b–f) shows the initial microstructure taken by SIM and SWLI during tensile straining of the T specimen, respectively. The T specimen was cut out so that the LD could traverse the midrib of the primary plate. Surface undulation owing to plastic deformation commenced in the primary plate at a strain of 0.85% (Fig. 10b). The plastic deformation process shown in Fig. 10(c–f) indicates that local strain was accumulated at the aggregated variant interfaces and then cracking occurred at those interfaces. Fig. 11(a) and (b) presents the SIM and OIM images, respectively, of the longitudinal cross section of the T specimen after failure. There are aggregated variant fragments neighbouring the facets in the left part of the specimen, whereas the right part exhibits an intensely deformed primary plate.
operative. Note that the lenticular martensite plate has nanotwins at the middle of it. In the P2 specimen, the operative slip plane was parallel to the plane of the nanotwins (compare Figs. 3c and 12b). Although the traces of the nanotwins could not be observed in the other specimens, the operative slip systems in all the specimens correspond to one of the possible nanotwin planes inferred from the orientation relationship with the midrib, as shown in Fig. 4. Therefore, if the slip system parallel to the nanotwin plane is favoured, it is reasonable that the definite CRSS value can be obtained (Table 1). This value was significantly lower than the CRSS of 300–360 MPa for the in-lath-plane slip that was activated parallel to the habit plane of the lath martensite structures of carbon steel [13]. In both cases, dislocation gliding was hardly hindered by the obstacles, i.e., the nanotwins for the lenticular martensite and the block boundaries for the lath martensite. Thus, the difference in the CRSS is anticipated to reflect the difference in the strength of the matrix between both martensite structures. 4.2. The formation of faceted cracks
4. Discussion 4.1. Effect of nanotwin orientation on plastic deformation Fig. 12 shows the stereographic projection of the primary plate in each specimen, indicative of the operative slip system (112) ½1 11 inferred from the slip traces and/or the crystal rotation during the tensile straining. These stereographic projections show that the slip system exhibiting the highest Schmid factor in each specimen was not activated. Table 1 summarises the yield stress, Schmid factors for the slip system exhibiting the highest value among {112} 〈1 11〉 and the operative slip system, and the critical resolved shear stress (CRSS). The CRSS for the operative slip system was determined to be 182–200 MPa, despite the fact that the slip system exhibiting the highest Schmid factor was not
In all the specimens, faceted and shear-type fractures appeared, as shown in Figs. 6, 8, and 9. Beneath the faceted fracture surfaces, aggregated variant fragments were observed in one half of the Table 1 Yield stress, Schmid factors for slip system exhibiting the highest value and operative slip system, and critical resolved shear stress (CRSS). Yield stress (MPa)
P1 P2 P3 T
441 404 556 490
Schmid factor
CRSS (MPa)
Highest value
Operative slip system
0.493 0.469 0.495 0.469
0.441 0.452 0.360 0.393
Fig. 12. Stereographic projection figures showing operative slip system in (a) P1, (b) P2, (c) P3, and (d) T specimens.
195 182 200 192
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failure specimens, whereas the other half exhibited severe deformation of the coarse variant (Figs. 7 and 11). Anisotropic deformation in the primary plate due to the activation of the slip system that was parallel to the nanotwin plane was followed by the strain accumulation at the variant interfaces (Figs. 5 and 10). The orientation of the nanotwin plane can be greatly rotated at some variant interfaces. It is therefore hypothesised that the interaction of the mobile dislocations with the nanotwins can promote strain localisation at the variant interfaces to form the faceted fracture. On the other hand, the P3 specimen exhibited significant strain hardening after yielding at somewhat higher stress. Indeed, the SIM examination of the cross section confirmed that the gauge section of the P3 specimen comprised the multiple variants beneath the primary plate (Fig. 9c). This suggests that the variant boundaries also contribute to hardening in the bulk specimen. 5. Conclusions Microtension testing of an Fe–30Ni alloy was conducted to clarify the effect of the nanotwins on the plastic deformation in a lenticular martensite structure. Yielding in the lenticular martensite plates did not occur by the slip system exhibiting the highest Schmid factor. Dislocation gliding likely occurred on the slip system parallel to the plane of the nanotwins. The CRSS was determined to be 182–200 MPa. A unique faceted fracture, in which the plane was not consistent with the typical {001} cleavage plane, was observed after microtension straining of the lenticular martensite plates. The faceted crack was initiated due to strain localisation at the variant interfaces between the primary plate and the aggregated fragments. It is suggested that the anisotropic plasticity and the formation of the faceted fracture are related to the interaction of dislocations with nanotwins.
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Acknowledgements The authors are indebted to Mr. N. Ohara, Dr. M. Tsushida and Dr. T. Yamamuro, Kumamoto University for their assistance with the TEM observation. This work was supported by a Grant-in-Aid for Scientific Research (B) 24360293 from the Japan Society for the Promotion of Science (JSPS).
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