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Void nucleation behavior of single-crystal high-purity iron specimens subjected to tensile deformation
Author’s Accepted Manuscript Void Nucleation Behavior of Single-Crystal HighPurity Iron Specimens Subjected to Tensile Deformation Osamu Furukimi, Chatcharit Kiattisaksri, Yuji Takeda, Masatoshi Aramaki, Satoshi Oue, Shinji Munetoh, Masaki Tanaka www.elsevier.com/locate/msea
PII: DOI: Reference:
S0921-5093(17)30851-1 http://dx.doi.org/10.1016/j.msea.2017.06.084 MSA35222
To appear in: Materials Science & Engineering A Received date: 22 March 2017 Revised date: 20 June 2017 Accepted date: 21 June 2017 Cite this article as: Osamu Furukimi, Chatcharit Kiattisaksri, Yuji Takeda, Masatoshi Aramaki, Satoshi Oue, Shinji Munetoh and Masaki Tanaka, Void Nucleation Behavior of Single-Crystal High-Purity Iron Specimens Subjected to Tensile Deformation, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2017.06.084 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Void Nucleation Behavior of Single-Crystal High-Purity Iron Specimens Subjected to Tensile Deformation
Osamu Furukimi*, Chatcharit Kiattisaksri1, Yuji Takeda, Masatoshi Aramaki, Satoshi Oue, Shinji Munetoh, Masaki Tanaka
Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Nishi-ku,
Fukuoka 819-0395, Japan
*Corresponding author at: Department of Materials Science and Engineering, Faculty of
Engineering, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan, Tel.: +81 92-802-2949.
[email protected]
1
Present address: Department of Materials Science and Engineering, Kyoto University, Honcho, Yoshida, Sakyo-ku, Kyoto 606-8501, Japan
1
Abstract Void nucleation plays an important role for determining local deformation properties of ductile materials. In this study, the void nucleation behavior of single-crystal iron was examined in tensile tests. Two micrometer-size single crystals having a different type of slip extracted from electrodeposited pure iron were used to investigate the fracture mechanics during tensile deformation. Scanning electron microscopy (SEM) and high voltage electron microscopy (HVEM) images verified the existence of only a single slip system in the smaller specimen (cross-sectional area A = 16 µm2) and furthermore, no voids were observed. However, multiple slips and voids were observed in the larger specimen (A = 28 µm2). These findings allowed us to reveal that multiple slips are a necessary criterion for void nucleation in single-crystal iron.
Keywords: Electrodeposited pure iron, Micrometer-size single crystal, Tensile deformation, Void nucleation, Slip system
1. Introduction Understanding fracture mechanics is important to determine the reasons for failures in metals. Most types of metal failures can be categorized as brittle and ductile fractures; the type depends on the ability of a metal to undergo large plastic deformation before fracture [1]. In the fracture process of ductile metals, the plastic deformation in tensile tests can be categorized as uniform deformation and local deformation. During uniform deformation, a metal experiences slip deformation and rotation via the movement of dislocations. During local deformation, voids nucleate and grow following an increase in stress triaxiality and a simultaneous increase in dislocation density. In 1978, Goods and Brown introduced a simple model to predict void nucleation during 2
the deformation of metals which contain a dispersion of hard second phase particles, such as Fe3C in Fe and SiO2 in Cu [2]. The model describes the conditions required for void nucleation during plastic deformation. The critical stress can be calculated as shown in equation (1). 𝜎𝑓 + 𝜎𝑐 + 𝑝 ≥ 𝜎1
(1)
where σf is the flow stress related to the microstructure, σc the local stress, p the triaxial stress, and σ1 the particle-matrix interface strength. When the combined action of the superimposed stresses ( 𝜎𝑓 + 𝜎𝑐 + 𝑝 ) reaches the magnitude of 𝜎1 , the nucleation of voids will occur. It should be noted that σf reflects various contributions of the microstructures, such as dislocations induced by cutting precipitates or inclusions (Orowan stress), the increase in dislocation density (forest hardening), and the internal stress in the plastic matrix. It can be seen that 𝜎𝑓 is associated with the existence of dislocation. In other words, in a specimen which contains a high number of dislocations, there is a high possibility that voids form in regions characterized by a high dislocation density. Void nucleation mechanisms are broadly categorized into homogeneous and heterogeneous nucleation: the former mostly involves an increase of the dislocation density
and vacancy migration, whereas heterogeneous
nucleation occurs at sites which contain particles such as inclusions, precipitates, or other discontinuous structures [3]. In homogeneous nucleation, voids can be formed by the condensation of vacant lattice sites. However, this mechanism
cannot occur below
approximately 300 K, because the vacancy diffusion rate is extremely low under those conditions. In addition, voids can also be formed by dislocation interactions. Dodd and Bai [4] proposed that a crack can be considered as a void formed by the pile-up of dislocations against a boundary. Moreover, they suggest that another kind of dislocation interaction could occur in such a situation as follows: when under shear deformation an edge dislocation interferes with another edge dislocation, which has a Burgers vector with an 3
opposite sign, a micro-crack is formed. This micro-crack can also be considered as a void. Finally, Dodd and Bai showed that a third mechanism is observed in certain cases: two dislocations travelling on intersecting paths on different planes may merge and thus result in the formation of a void. We studied the sites of heterogeneous void nucleation in duplex stainless steel [5], 16 %Cr ferritic steel [6], and commercial-grade pure iron (Fe: 99.82 mass%) [7]. These studies revealed that voids nucleate at the grain boundaries between different phases, e.g., between ferrite and austenite phases, between Cr23C6 or Cr2N precipitated particles and ferrite phases, at ferrite grain boundaries, respectively. For Ti-added interstitial free (IF) steel, León-García et al. recently identified TiN precipitates as the void nucleation sites during tensile deformation [8]. Toda et al., in addition, observed void nucleation at ferrite-austenite grain boundaries by using the synchrotron X-ray computer tomography method [9]. In tensile tests of commercial-grade pure iron specimens with thicknesses ranging from 0.2 to 2 mm, further results revealed that the local deformation energy obtained from stress–strain curves decreases with a decrease in specimen thickness. This phenomenon is caused by the nucleation behavior of voids, since the stress triaxiality depends on the specimen thickness [7]. In addition, Kato [10] previously analyzed ductile fracture properties by using the deformation energy obtained from stress–strain curves. Nagumo et al., finally, discussed void growth and crack formation in terms of the deformation energy [11]. The results of these studies indicate that the stress triaxiality factor should be considered when evaluating the ductile fracture property as well as the void nucleation and growth. The above-mentioned findings show that void nucleation depends on the microstructure, including the grain boundaries and particles, and on stress triaxiality. However, to the best of our knowledge, experimental studies of the void nucleation behavior in metal specimens that contain neither particles nor grain boundaries have not been reported so far. 4
Many researchers have studied the tensile deformation process for small, round specimens with diameters of up to 10 µm of, e.g., Mo [12] and Cu [13]. The results of these studies have revealed that the strength of a metal increases for specimens which have a cross-sectional area of less than 64 µm2 due to the flow stress and stress triaxiality. It has been hypothesized that screw dislocations play a lesser role in governing plasticity in smaller specimens. Thus, specimens with only a small number of screw dislocations can reach a higher strength. Additionally, the result revealed that the specimen with diameters of less than 1 μm exhibit stair-like hardening characteristic during tensile deformation, while the specimen with diameters greater than 1 μm exhibit a more continuous post-yield strain hardening. The hardening characteristic in smaller-size specimen can be attributed to the anomalous slip in BCC metals, which clearly influences the yield strength. Although screw dislocations and anomalous slip are the main causes for the higher strength of smaller specimens, the dependence of void nucleation and growth, which play an important role in local deformation, has not been elucidated yet for smaller size specimens. Notably, an improvement of the elongation properties during local deformation is required to develop high strength nano-wires. Despite extensive studies on void nucleation under various conditions, there have been no experimental studies on void nucleation in single-crystal metals, especially for smaller specimens. Therefore, the aim of this study is to provide fundamental information on the void nucleation during tensile testing for single-crystal iron specimens of smaller sizes with no precipitated particles or grain boundaries. Specimens with cross-sectional areas of 16 and 28 µm2 were used to examine the influence of different types of slip on the void nucleation mechanism.
2. Experimental 2.1
Experimental Specimens 5
Single-crystal high-purity iron samples (Fe: 99.98 mass%) were prepared from commercial polycrystalline electrodeposited pure iron (MAIRON Grade SHP; TOHO ZINC CO., LTD, Annaka, Japan) with a chemical composition as shown in Table 1. The polycrystalline electrodeposited pure iron was inserted into a carbon resin and polished with emery papers, followed by a sequential polishing with αalumina and colloidal silica solutions to allow the observation of the crystal orientation by electron backscatter diffraction (EBSD) mapping. Based on -
these EBSD results, micro-tensile test specimens with a [10 1 ] normal direction (ND) and [111] axial direction (AD) for tensile loading were prepared using focused ion beam (FIB) processing (Quanta 3d 200i, FEI, Hillsboro, USA), as shown in Fig.1. The acceleration voltage was kept at 30 kV, while the ion current was adjusted from 5 to 60 nA depending on the size of the milling volume. In this experiment, two types of single-crystal iron specimens were prepared to observe how plastic deformation, which depends on the size of the tensiletest specimen, influences the void nucleation behavior. The first specimen had a gauge width of 4 µm and thickness of 4 µm, while the second specimen had a gauge width of 14 µm and thickness of 2 µm. In both specimens, slight curvatures were applied to give the samples the shape of standard flat test samples for a good control of the fracture points. For convenience, the first specimen (cross-sectional area A = 16 µm2) is called the smaller specimen in the remainder of this study, while the second specimen (A = 28 µm2) is called the larger specimen. In order to perform tensile tests, a FIB probe was welded to the sample by W deposition in the FIB setup, as shown in Fig. 2. Subsequently, the samples were pulled by the holder until fracture.
6
Fig. 1 Preparation of a single-crystal tensile test specimen (b) from polycrystalline electrodeposited pure iron (a).
Table. 1. Chemical compositions of impurities in the electrodeposited iron. (ppm)
C 9
P 5
S 13
Si 5
Mn 1
Cu 1
Co 1
7
Ni 1
Cr 1
O 120
N 5
Fig. 2 Tensile test of a single-crystal iron sample in a FIB setup.
2.2 Field emission scanning electron microscopy, highvoltage electron microscopy, and EBSD analysis After tensile tests, the topography of the fractured specimens was observed using a field emission scanning electron microscope (FE-SEM) (Ultra 55, Carl Zeiss AG, Oberkochen, Germany) at an accelerating voltage of 5 kV. Voids in the inner part of the specimens could be observed after cutting the specimens in half perpendicular to their transverse direction (TD), as shown in Fig. 3.
Fig. 3 FE-SEM image of a void observed on the surface of a specimen after tensile testing.
8
Additionally, an EBSD detector installed within the FE-SEM was used to examine the crystallographic orientation before and after tensile testing and subsequently, the results were analyzed using the Orientation Imaging Microscopy Analysis Software (OIM™; AMETEK CO., LTD, Mahwah, USA). The dislocation features before tensile tests and those along the fracture surface after tensile tests were observed using a high-voltage electron microscope (HVEM) (JEM-1250NFE; JEOL CO., LTD, Akishima, Japan). Samples for HVEM observation were prepared by FIB processing to reduce the sample thickness down to 400 nm. For HVEM observations, dark-field images were used to obtain a better contrast between the samples and dislocation features. The applied acceleration voltage was 1250 kV.
3. Results A HVEM image of the as-received electrodeposited iron specimen is shown in Fig. 4. In this figure, dark contrast enables the identification of two types of dislocations. First, lines appearing on the specimen indicate existing dislocations which originate from the electrodeposited process. Secondly, the circular marks with a dark contrast are considered to correspond to FIBinduced dislocations, which are a result from Ga ion damage induced by FIB sample preparation [14].
9
Fig. 4 HVEM image of an as-received electrodeposited iron sample before tensile tests.
10
FE-SEM images of the sample surfaces in normal direction of the smaller and larger specimen after fracture are shown in Figs. 5 (a) and (b), respectively. Figure 5 (a) shows that slip bands are located near the fracture surface, indicating a significant localized plastic deformation. Straight slip bands were also observed on the fracture surface, suggesting the activation of a single slip system. In Fig. 5 (b), it can be seen that the topography of the larger specimen differed substantially from that of the smaller specimen. First, the larger specimen underwent severe shearing, which can be attributed to the accumulation of slip bands. Secondly, the slip bands in the larger specimen were wavy, indicating a multiple slip system.
Fig. 5 FE-SEM images of smaller (a) and larger specimens (b). RA: reduction of area.
11
The reduction of area (RA) values after tensile tests were calculated for the specimens at the locations indicated in Figs. 5 (a) and (b). The RA values were 22 and 30 % for the smaller and larger specimen, respectively. This result revealed that the plastic deformation of the larger specimen was greater than that of the smaller specimen. A top-view FE-SEM image of the fractured surface of the smaller specimen is shown in Fig. 6. Slip bands are observed, but there is no evidence of voids that nucleated during the tensile test.
Fig. 6 Top-view FE-SEM images of the fracture surface for the smaller specimen.
12
Top-view and cross-sectional view FE-SEM images of the fracture surface of the larger specimen are shown in Figs. 7 (a) and (b), respectively. The topview image reveals a number of voids with diameters between 50 and 100 nm on the fracture surface. The cross-sectional view, in addition, reveals that the voids nucleated internally. It can be seen that the voids grew along the deformed surface and coalesced and this way elongated to approximately 240 nm. Moreover, at about 11 µm from the fracture surface, the whole specimen experienced severe shearing. However, in these images, the presence of voids was not clearly visible. Hence, we used HVEM to verify the presence of voids.
Fig. 7 Top-view (axial direction) (a) and cross-sectional view (transverse direction) (b) FE-SEM images of the fracture surface of the larger specimen.
13
Figure 8 (a) shows the HVEM image of the smaller specimen after fracture, revealing that no voids existed near the fracture surface; instead, dislocations accumulated in lines, which were expected to be slip bands. The slip analysis will be further discussed below. Figure 8 (a) further shows that dislocations accumulated along a single slip plane in the smaller specimen, while dislocations accumulated along several slip planes for the larger specimen, as shown in Fig. 8 (b). This observation suggests the presence of multiple slip systems in the larger specimen. Moreover, in the larger specimen, voids could be clearly identified, as marked in Fig. 8 (b).
Fig. 8 Dark-field HVEM images of the fracture surface for smaller (a) and larger (b) specimens.
14
In order to confirm whether the encircled region (white circle) in Fig. 7 (b) is a void, under-focused and over-focused images were taken, shown in Figs. 9 (a) and (b), respectively. In electron microscopy, a Fresnel fringe is often seen near a void [15]. In Fig. 9 (a), a white Fresnel fringe (indicated by an arrow) appeared in the vicinity of the encircled area. On the other hand, in the overfocused image (Fig. 9 (b)), a black Fresnel fringe (indicated by an arrow) was observed. Thus, it was concluded that the encircled area in Fig. 8 (b) is indeed a void.
Fig. 9 Fresnel fringe around voids (encircled area in Fig. 8) observed in underfocused (a) and over-focused (b) images of the larger specimen.
15
4. Discussion The above experimental results show that voids nucleated in the larger singlecrystal iron specimen during the tensile tests. On the other hand, no voids nucleated in the smaller specimen. Furthermore, both specimens were deformed by single and multiple slip systems. Here, the difference in the slip system between the smaller and larger specimens will be discussed on the basis of plastic deformation during tensile testing. Crystallographic rotation analysis results for the smaller specimen are shown in Fig. 10. The inverse pole figure (IPF) map in Fig. 10 (b) was obtained for the same area as shown in Fig. 10 (a). As seen from the IPF in a standard triangle, this specimen rotated along a great circle, indicating that the tensile direction rotated in a single axis from the <111> to <101> direction. This rotation due to slip deformation resulted in the formation of a new grain boundary, as shown in Fig. 10(b). This observation was once again an indication of the activation of only a single slip system in the smaller sample.
16
Fig. 10 Inverse pole figure (IPF) maps in the cross-sectional direction and IPF triangles in axial and normal directions for the smaller specimen. In the case of the larger specimen, EBSD results showed variations in the color, as shown in Fig. 11. This change in color relates to a strain gradient which is the rate at which the strain changes through a specimen. Thus, the EBDS analysis indicates that a large region of the sample underwent plastic deformation. From the results shown in Figs. 10 and 11, it is clear that both specimens exhibited different strain hardening characteristic. This difference was mainly due to different types of slip systems, which can easily be seen from the axial IPF triangle. The deviation in the tensile direction suggested a concurrent activation of competitive slip systems. This observation is an indication of the occurrence of multiple slip systems. These results agree well with the wavy slip patterns observed on the surface in normal direction, as shown in Fig. 5 (b).
17
Fig. 11 IPF map in cross-sectional direction, and IPF triangles in the axial and normal directions for the larger specimen.
Moreover, the aforementioned results reveal that, in the smaller specimen, single slip occurred because of the larger plastic deformation (see Fig. 5), while in the larger specimen, multiple slip occurred because of the smaller plastic deformation, which was accompanied by a different crystal rotation.
4. Conclusion The aim of this study was to explore the mechanism of void nucleation during tensile deformation for single-crystal iron specimens of small size containing no microstructural defects, such as grain boundaries or precipitated particles. In our experiments, electrodeposited high-purity iron was used. Single-crystal specimens were prepared by focused ion beam processing in [101] normal 18
direction and [111] axial direction. Two specimens with different sizes were used to observe the plastic deformation and void nucleation. Scanning electron microscopy observations revealed that the smaller specimen (cross-sectional area A = 16 µm2) exhibited straight slip patterns. In the larger specimen (A = 28 µm2), on the other hand, a number of shear bands and wavy slip patterns were observed. Based on the plotted orientations obtained from the inverse pole figure triangle, it was concluded that the smaller specimen exhibited single slip, while the larger specimen exhibited multiple slip system. A significant finding in these experiments was the nucleation behavior of voids in single-crystal iron specimens. Voids with diameters of 50 to 100 nm were observed along the slip band in the larger specimen. This observation suggested that, upon deformation, voids nucleate even in single-crystal materials, which naturally have no precipitates or grain boundaries. However, in the smaller sample with single-slip occurrence, no voids existed. Therefore, it can be concluded that multiple slip is necessary for the nucleation of voids.
References [1]
J. R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. of Appl. Mech., 35(1968), 379-386.
[2]
S. H. Goods and L. M. Brown, The nucleation of cavities by plastic deformation, Acta Metall., 27(1979) 1–15.
[3]
B. Dodd and Y. Bai, Ductile fracture and ductility, ACADEMIC PRESS INC. (LONDON) LTD., (1987) 85–91.
[4]
B. Dodd and Y. Bai, Ductile fracture and ductility, ACADEMIC PRESS INC. (LONDON) LTD., (1987) 152–159.
[5]
T. Hirashima, M. Aramaki, M. Yamamoto, K. Yasuda, S. Munetoh, O. 19
Furukimi, Effect of tensile test specimen thickness on deformation energy for duplex stainless steel, Tetesu-To-Hagané, 101(2015) 308– 314. [6]
O. Furukimi, S. Niigaki, N. Yamada, M. Aramaki, S. Oue, Y. Funakawa, Local deformation energy and void formation behavior in 16%Cr ferritic steel, Tetesu-To-Hagané, 99(2013) 60–60.
[7]
Y. Takeda, C. K. M. Aramaki, S. Munetoh, O. Furukimi, Effects of tensile test specimen thickness on elongation and deformation energy for industrial pure iron, Tetesu-To-Hagané, 102(2016), 599–606.
[8]
O. León-García, R. Petrov and L. A. I. Kestens, Void initiation at TiN precipitates in IF steels during tensile deformation, Mater. Sci. Eng. A, 527(2010), 4202-4209.
[9]
H.Toda, F. Tomizato, R. Harasaki, D. Seo, M. Kobayashi, A. Takeuchi and K. Uesugi, 3D fracture behaviours in dual-phase stainless steel, ISIJ Int., 56(2016), 883–892.
[10] M. Kato: Materia Jpn., Selected topics in strength of materials II Thermodynamics and kinetics of Deformation-; 6(2008), 317–322. [11] M. Nagumo, A criterion of ductile fracture on the tensile testing of a perforated mild steel sheet, Acta Mater., 21(1973), 1661–1667 [12] J. Y. Kim, D. Jang, and J. R. Greer, Crystallographic orientation and size dependence of tension–compression asymmetry in molybdenum nanopillars, Int. J. Plast., 28(2012), 46–52. [13] D. Kiener, W. Grosinger, G. Dehm, and R. Pippan, A further step towards an understanding of size-dependent crystal plasticity: In situ tension experiments of miniaturized single-crystal copper samples, Acta Mater., 56(2008), 580–592. [14] D. Kiener, C. Motz, M. Rester, M. Jenko and G. Dehm, FIB damage of Cu and possible consequences for miniaturized mechanical tests, Mater. 20
Sci. Eng. A, 459(2007), 262-272. [15] M. Ruhle and M. Wilkens, Defocusing Contrast of Cavities, Theory Crystal Lattice Defects, 6(1975),129–140.
21
PII: DOI: Reference:
S0921-5093(17)30851-1 http://dx.doi.org/10.1016/j.msea.2017.06.084 MSA35222
To appear in: Materials Science & Engineering A Received date: 22 March 2017 Revised date: 20 June 2017 Accepted date: 21 June 2017 Cite this article as: Osamu Furukimi, Chatcharit Kiattisaksri, Yuji Takeda, Masatoshi Aramaki, Satoshi Oue, Shinji Munetoh and Masaki Tanaka, Void Nucleation Behavior of Single-Crystal High-Purity Iron Specimens Subjected to Tensile Deformation, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2017.06.084 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Void Nucleation Behavior of Single-Crystal High-Purity Iron Specimens Subjected to Tensile Deformation
Osamu Furukimi*, Chatcharit Kiattisaksri1, Yuji Takeda, Masatoshi Aramaki, Satoshi Oue, Shinji Munetoh, Masaki Tanaka
Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Nishi-ku,
Fukuoka 819-0395, Japan
*Corresponding author at: Department of Materials Science and Engineering, Faculty of
Engineering, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan, Tel.: +81 92-802-2949.
[email protected]
1
Present address: Department of Materials Science and Engineering, Kyoto University, Honcho, Yoshida, Sakyo-ku, Kyoto 606-8501, Japan
1
Abstract Void nucleation plays an important role for determining local deformation properties of ductile materials. In this study, the void nucleation behavior of single-crystal iron was examined in tensile tests. Two micrometer-size single crystals having a different type of slip extracted from electrodeposited pure iron were used to investigate the fracture mechanics during tensile deformation. Scanning electron microscopy (SEM) and high voltage electron microscopy (HVEM) images verified the existence of only a single slip system in the smaller specimen (cross-sectional area A = 16 µm2) and furthermore, no voids were observed. However, multiple slips and voids were observed in the larger specimen (A = 28 µm2). These findings allowed us to reveal that multiple slips are a necessary criterion for void nucleation in single-crystal iron.
Keywords: Electrodeposited pure iron, Micrometer-size single crystal, Tensile deformation, Void nucleation, Slip system
1. Introduction Understanding fracture mechanics is important to determine the reasons for failures in metals. Most types of metal failures can be categorized as brittle and ductile fractures; the type depends on the ability of a metal to undergo large plastic deformation before fracture [1]. In the fracture process of ductile metals, the plastic deformation in tensile tests can be categorized as uniform deformation and local deformation. During uniform deformation, a metal experiences slip deformation and rotation via the movement of dislocations. During local deformation, voids nucleate and grow following an increase in stress triaxiality and a simultaneous increase in dislocation density. In 1978, Goods and Brown introduced a simple model to predict void nucleation during 2
the deformation of metals which contain a dispersion of hard second phase particles, such as Fe3C in Fe and SiO2 in Cu [2]. The model describes the conditions required for void nucleation during plastic deformation. The critical stress can be calculated as shown in equation (1). 𝜎𝑓 + 𝜎𝑐 + 𝑝 ≥ 𝜎1
(1)
where σf is the flow stress related to the microstructure, σc the local stress, p the triaxial stress, and σ1 the particle-matrix interface strength. When the combined action of the superimposed stresses ( 𝜎𝑓 + 𝜎𝑐 + 𝑝 ) reaches the magnitude of 𝜎1 , the nucleation of voids will occur. It should be noted that σf reflects various contributions of the microstructures, such as dislocations induced by cutting precipitates or inclusions (Orowan stress), the increase in dislocation density (forest hardening), and the internal stress in the plastic matrix. It can be seen that 𝜎𝑓 is associated with the existence of dislocation. In other words, in a specimen which contains a high number of dislocations, there is a high possibility that voids form in regions characterized by a high dislocation density. Void nucleation mechanisms are broadly categorized into homogeneous and heterogeneous nucleation: the former mostly involves an increase of the dislocation density
and vacancy migration, whereas heterogeneous
nucleation occurs at sites which contain particles such as inclusions, precipitates, or other discontinuous structures [3]. In homogeneous nucleation, voids can be formed by the condensation of vacant lattice sites. However, this mechanism
cannot occur below
approximately 300 K, because the vacancy diffusion rate is extremely low under those conditions. In addition, voids can also be formed by dislocation interactions. Dodd and Bai [4] proposed that a crack can be considered as a void formed by the pile-up of dislocations against a boundary. Moreover, they suggest that another kind of dislocation interaction could occur in such a situation as follows: when under shear deformation an edge dislocation interferes with another edge dislocation, which has a Burgers vector with an 3
opposite sign, a micro-crack is formed. This micro-crack can also be considered as a void. Finally, Dodd and Bai showed that a third mechanism is observed in certain cases: two dislocations travelling on intersecting paths on different planes may merge and thus result in the formation of a void. We studied the sites of heterogeneous void nucleation in duplex stainless steel [5], 16 %Cr ferritic steel [6], and commercial-grade pure iron (Fe: 99.82 mass%) [7]. These studies revealed that voids nucleate at the grain boundaries between different phases, e.g., between ferrite and austenite phases, between Cr23C6 or Cr2N precipitated particles and ferrite phases, at ferrite grain boundaries, respectively. For Ti-added interstitial free (IF) steel, León-García et al. recently identified TiN precipitates as the void nucleation sites during tensile deformation [8]. Toda et al., in addition, observed void nucleation at ferrite-austenite grain boundaries by using the synchrotron X-ray computer tomography method [9]. In tensile tests of commercial-grade pure iron specimens with thicknesses ranging from 0.2 to 2 mm, further results revealed that the local deformation energy obtained from stress–strain curves decreases with a decrease in specimen thickness. This phenomenon is caused by the nucleation behavior of voids, since the stress triaxiality depends on the specimen thickness [7]. In addition, Kato [10] previously analyzed ductile fracture properties by using the deformation energy obtained from stress–strain curves. Nagumo et al., finally, discussed void growth and crack formation in terms of the deformation energy [11]. The results of these studies indicate that the stress triaxiality factor should be considered when evaluating the ductile fracture property as well as the void nucleation and growth. The above-mentioned findings show that void nucleation depends on the microstructure, including the grain boundaries and particles, and on stress triaxiality. However, to the best of our knowledge, experimental studies of the void nucleation behavior in metal specimens that contain neither particles nor grain boundaries have not been reported so far. 4
Many researchers have studied the tensile deformation process for small, round specimens with diameters of up to 10 µm of, e.g., Mo [12] and Cu [13]. The results of these studies have revealed that the strength of a metal increases for specimens which have a cross-sectional area of less than 64 µm2 due to the flow stress and stress triaxiality. It has been hypothesized that screw dislocations play a lesser role in governing plasticity in smaller specimens. Thus, specimens with only a small number of screw dislocations can reach a higher strength. Additionally, the result revealed that the specimen with diameters of less than 1 μm exhibit stair-like hardening characteristic during tensile deformation, while the specimen with diameters greater than 1 μm exhibit a more continuous post-yield strain hardening. The hardening characteristic in smaller-size specimen can be attributed to the anomalous slip in BCC metals, which clearly influences the yield strength. Although screw dislocations and anomalous slip are the main causes for the higher strength of smaller specimens, the dependence of void nucleation and growth, which play an important role in local deformation, has not been elucidated yet for smaller size specimens. Notably, an improvement of the elongation properties during local deformation is required to develop high strength nano-wires. Despite extensive studies on void nucleation under various conditions, there have been no experimental studies on void nucleation in single-crystal metals, especially for smaller specimens. Therefore, the aim of this study is to provide fundamental information on the void nucleation during tensile testing for single-crystal iron specimens of smaller sizes with no precipitated particles or grain boundaries. Specimens with cross-sectional areas of 16 and 28 µm2 were used to examine the influence of different types of slip on the void nucleation mechanism.
2. Experimental 2.1
Experimental Specimens 5
Single-crystal high-purity iron samples (Fe: 99.98 mass%) were prepared from commercial polycrystalline electrodeposited pure iron (MAIRON Grade SHP; TOHO ZINC CO., LTD, Annaka, Japan) with a chemical composition as shown in Table 1. The polycrystalline electrodeposited pure iron was inserted into a carbon resin and polished with emery papers, followed by a sequential polishing with αalumina and colloidal silica solutions to allow the observation of the crystal orientation by electron backscatter diffraction (EBSD) mapping. Based on -
these EBSD results, micro-tensile test specimens with a [10 1 ] normal direction (ND) and [111] axial direction (AD) for tensile loading were prepared using focused ion beam (FIB) processing (Quanta 3d 200i, FEI, Hillsboro, USA), as shown in Fig.1. The acceleration voltage was kept at 30 kV, while the ion current was adjusted from 5 to 60 nA depending on the size of the milling volume. In this experiment, two types of single-crystal iron specimens were prepared to observe how plastic deformation, which depends on the size of the tensiletest specimen, influences the void nucleation behavior. The first specimen had a gauge width of 4 µm and thickness of 4 µm, while the second specimen had a gauge width of 14 µm and thickness of 2 µm. In both specimens, slight curvatures were applied to give the samples the shape of standard flat test samples for a good control of the fracture points. For convenience, the first specimen (cross-sectional area A = 16 µm2) is called the smaller specimen in the remainder of this study, while the second specimen (A = 28 µm2) is called the larger specimen. In order to perform tensile tests, a FIB probe was welded to the sample by W deposition in the FIB setup, as shown in Fig. 2. Subsequently, the samples were pulled by the holder until fracture.
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Fig. 1 Preparation of a single-crystal tensile test specimen (b) from polycrystalline electrodeposited pure iron (a).
Table. 1. Chemical compositions of impurities in the electrodeposited iron. (ppm)
C 9
P 5
S 13
Si 5
Mn 1
Cu 1
Co 1
7
Ni 1
Cr 1
O 120
N 5
Fig. 2 Tensile test of a single-crystal iron sample in a FIB setup.
2.2 Field emission scanning electron microscopy, highvoltage electron microscopy, and EBSD analysis After tensile tests, the topography of the fractured specimens was observed using a field emission scanning electron microscope (FE-SEM) (Ultra 55, Carl Zeiss AG, Oberkochen, Germany) at an accelerating voltage of 5 kV. Voids in the inner part of the specimens could be observed after cutting the specimens in half perpendicular to their transverse direction (TD), as shown in Fig. 3.
Fig. 3 FE-SEM image of a void observed on the surface of a specimen after tensile testing.
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Additionally, an EBSD detector installed within the FE-SEM was used to examine the crystallographic orientation before and after tensile testing and subsequently, the results were analyzed using the Orientation Imaging Microscopy Analysis Software (OIM™; AMETEK CO., LTD, Mahwah, USA). The dislocation features before tensile tests and those along the fracture surface after tensile tests were observed using a high-voltage electron microscope (HVEM) (JEM-1250NFE; JEOL CO., LTD, Akishima, Japan). Samples for HVEM observation were prepared by FIB processing to reduce the sample thickness down to 400 nm. For HVEM observations, dark-field images were used to obtain a better contrast between the samples and dislocation features. The applied acceleration voltage was 1250 kV.
3. Results A HVEM image of the as-received electrodeposited iron specimen is shown in Fig. 4. In this figure, dark contrast enables the identification of two types of dislocations. First, lines appearing on the specimen indicate existing dislocations which originate from the electrodeposited process. Secondly, the circular marks with a dark contrast are considered to correspond to FIBinduced dislocations, which are a result from Ga ion damage induced by FIB sample preparation [14].
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Fig. 4 HVEM image of an as-received electrodeposited iron sample before tensile tests.
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FE-SEM images of the sample surfaces in normal direction of the smaller and larger specimen after fracture are shown in Figs. 5 (a) and (b), respectively. Figure 5 (a) shows that slip bands are located near the fracture surface, indicating a significant localized plastic deformation. Straight slip bands were also observed on the fracture surface, suggesting the activation of a single slip system. In Fig. 5 (b), it can be seen that the topography of the larger specimen differed substantially from that of the smaller specimen. First, the larger specimen underwent severe shearing, which can be attributed to the accumulation of slip bands. Secondly, the slip bands in the larger specimen were wavy, indicating a multiple slip system.
Fig. 5 FE-SEM images of smaller (a) and larger specimens (b). RA: reduction of area.
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The reduction of area (RA) values after tensile tests were calculated for the specimens at the locations indicated in Figs. 5 (a) and (b). The RA values were 22 and 30 % for the smaller and larger specimen, respectively. This result revealed that the plastic deformation of the larger specimen was greater than that of the smaller specimen. A top-view FE-SEM image of the fractured surface of the smaller specimen is shown in Fig. 6. Slip bands are observed, but there is no evidence of voids that nucleated during the tensile test.
Fig. 6 Top-view FE-SEM images of the fracture surface for the smaller specimen.
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Top-view and cross-sectional view FE-SEM images of the fracture surface of the larger specimen are shown in Figs. 7 (a) and (b), respectively. The topview image reveals a number of voids with diameters between 50 and 100 nm on the fracture surface. The cross-sectional view, in addition, reveals that the voids nucleated internally. It can be seen that the voids grew along the deformed surface and coalesced and this way elongated to approximately 240 nm. Moreover, at about 11 µm from the fracture surface, the whole specimen experienced severe shearing. However, in these images, the presence of voids was not clearly visible. Hence, we used HVEM to verify the presence of voids.
Fig. 7 Top-view (axial direction) (a) and cross-sectional view (transverse direction) (b) FE-SEM images of the fracture surface of the larger specimen.
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Figure 8 (a) shows the HVEM image of the smaller specimen after fracture, revealing that no voids existed near the fracture surface; instead, dislocations accumulated in lines, which were expected to be slip bands. The slip analysis will be further discussed below. Figure 8 (a) further shows that dislocations accumulated along a single slip plane in the smaller specimen, while dislocations accumulated along several slip planes for the larger specimen, as shown in Fig. 8 (b). This observation suggests the presence of multiple slip systems in the larger specimen. Moreover, in the larger specimen, voids could be clearly identified, as marked in Fig. 8 (b).
Fig. 8 Dark-field HVEM images of the fracture surface for smaller (a) and larger (b) specimens.
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In order to confirm whether the encircled region (white circle) in Fig. 7 (b) is a void, under-focused and over-focused images were taken, shown in Figs. 9 (a) and (b), respectively. In electron microscopy, a Fresnel fringe is often seen near a void [15]. In Fig. 9 (a), a white Fresnel fringe (indicated by an arrow) appeared in the vicinity of the encircled area. On the other hand, in the overfocused image (Fig. 9 (b)), a black Fresnel fringe (indicated by an arrow) was observed. Thus, it was concluded that the encircled area in Fig. 8 (b) is indeed a void.
Fig. 9 Fresnel fringe around voids (encircled area in Fig. 8) observed in underfocused (a) and over-focused (b) images of the larger specimen.
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4. Discussion The above experimental results show that voids nucleated in the larger singlecrystal iron specimen during the tensile tests. On the other hand, no voids nucleated in the smaller specimen. Furthermore, both specimens were deformed by single and multiple slip systems. Here, the difference in the slip system between the smaller and larger specimens will be discussed on the basis of plastic deformation during tensile testing. Crystallographic rotation analysis results for the smaller specimen are shown in Fig. 10. The inverse pole figure (IPF) map in Fig. 10 (b) was obtained for the same area as shown in Fig. 10 (a). As seen from the IPF in a standard triangle, this specimen rotated along a great circle, indicating that the tensile direction rotated in a single axis from the <111> to <101> direction. This rotation due to slip deformation resulted in the formation of a new grain boundary, as shown in Fig. 10(b). This observation was once again an indication of the activation of only a single slip system in the smaller sample.
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Fig. 10 Inverse pole figure (IPF) maps in the cross-sectional direction and IPF triangles in axial and normal directions for the smaller specimen. In the case of the larger specimen, EBSD results showed variations in the color, as shown in Fig. 11. This change in color relates to a strain gradient which is the rate at which the strain changes through a specimen. Thus, the EBDS analysis indicates that a large region of the sample underwent plastic deformation. From the results shown in Figs. 10 and 11, it is clear that both specimens exhibited different strain hardening characteristic. This difference was mainly due to different types of slip systems, which can easily be seen from the axial IPF triangle. The deviation in the tensile direction suggested a concurrent activation of competitive slip systems. This observation is an indication of the occurrence of multiple slip systems. These results agree well with the wavy slip patterns observed on the surface in normal direction, as shown in Fig. 5 (b).
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Fig. 11 IPF map in cross-sectional direction, and IPF triangles in the axial and normal directions for the larger specimen.
Moreover, the aforementioned results reveal that, in the smaller specimen, single slip occurred because of the larger plastic deformation (see Fig. 5), while in the larger specimen, multiple slip occurred because of the smaller plastic deformation, which was accompanied by a different crystal rotation.
4. Conclusion The aim of this study was to explore the mechanism of void nucleation during tensile deformation for single-crystal iron specimens of small size containing no microstructural defects, such as grain boundaries or precipitated particles. In our experiments, electrodeposited high-purity iron was used. Single-crystal specimens were prepared by focused ion beam processing in [101] normal 18
direction and [111] axial direction. Two specimens with different sizes were used to observe the plastic deformation and void nucleation. Scanning electron microscopy observations revealed that the smaller specimen (cross-sectional area A = 16 µm2) exhibited straight slip patterns. In the larger specimen (A = 28 µm2), on the other hand, a number of shear bands and wavy slip patterns were observed. Based on the plotted orientations obtained from the inverse pole figure triangle, it was concluded that the smaller specimen exhibited single slip, while the larger specimen exhibited multiple slip system. A significant finding in these experiments was the nucleation behavior of voids in single-crystal iron specimens. Voids with diameters of 50 to 100 nm were observed along the slip band in the larger specimen. This observation suggested that, upon deformation, voids nucleate even in single-crystal materials, which naturally have no precipitates or grain boundaries. However, in the smaller sample with single-slip occurrence, no voids existed. Therefore, it can be concluded that multiple slip is necessary for the nucleation of voids.
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