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Effects of distributed Fe particles on low-cycle fatigue behavior of Cu–Fe alloy single crystals
Materials Science and Engineering A319– 321 (2001) 506– 510 www.elsevier.com/locate/msea
Effects of distributed Fe particles on low-cycle fatigue behavior of Cu–Fe alloy single crystals Chihiro Watanabe *, Toshiyuki Fujii, Susumu Onaka, Masaharu Kato Department of Inno6ati6e and Engineered Materials, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226 -8502, Japan
Abstract Low-cycle fatigue behavior of Cu–1.58mass.%Fe alloy single crystals with precipitated f.c.c. k-Fe particles was examined under plastic strain controlled tests. Specimens with large (about 100 nm in diameter) and small (30 nm) particles were prepared. Although the k-Fe particles are coherent and shearable, no cyclic softening was observed in specimens with large particles. On the other hand, in small-particle specimens, cyclic softening was observed particularly at lower strain amplitudes. Dislocation microstructures characteristic of cyclic deformation were more clearly developed in large-particle specimens. Magnetic measurements of fatigued specimens revealed that more particles had transformed martensitically into b.c.c. h-Fe in large-particle specimens than in small-particle specimens. The transformation changes the particle character from ‘coherent and shearable’ to ‘incoherent and nonshearable’. This change enhances the uniform deformation and the absence of cyclic softening in the large-particle specimens where the majority of the particles became h-Fe. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Cyclic deformation; Fatigue; Cu–Fe alloy; Dislocation structure; Precipitation; Martensitic transformation
1. Introduction Using Cu –Fe alloy polycrystals and single crystals with finely dispersed precipitate k-Fe particles, we have examined the low-cycle fatigue behavior and dislocation microstructure [1,2]. When the volume fraction and the size of the particles are about 1.4% and 50 nm, respectively, it has been found that the alloys show cyclic hardening to saturation despite the fact that the k-Fe particles are coherent and shearable. Stress-induced k h martensitic transformation was found to occur extensively during the cyclic deformation. The transformation changes the particle character from ‘coherent and shearable’ to ‘incoherent and nonshearable’. This change in the particle character was concluded to be responsible for the absence of the cyclic softening. It has been found from monotonic tensile tests [3] that the stress-induced transformation of the Fe particles in Cu depends strongly on the particle size. The larger particles are more prone to the transformation. If this is also the case for cyclic deformation, the low-cycle * Corresponding author. Tel.: + 81-459-245634; fax: +81-459245173. E-mail address: [email protected] (C. Watanabe).
fatigue behavior of the Cu –Fe alloy should be sensitive to the particle size. If the transformation into h-Fe occurs in the majority of k-Fe particles in the early stage of cyclic deformation, the alloy can be regarded as that containing nonshearable h-Fe particles. On the other hand, if the transformation is difficult, the particles may remain as shearable k-Fe even in the late stages of cyclic deformation. With the above in mind, we have examined the low-cycle fatigue behavior of Cu –Fe alloy single crystals with dispersed k-Fe particles of different sizes. Referring to the previous study where the average particle size was controlled to be about 50 nm [2], we have selected two particles sizes, i.e. 100 and 30 nm, in this study. Main foci were placed upon examination of (i) cyclic deformation behavior; (ii) development of dislocation structure; and (iii) transformability of Fe particles.
2. Experimental From as-rolled Cu –1.58mass.%Fe alloy plates, single crystal sheets of 3× 50× 150 mm were grown by the
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 0 5 9 - 0
C. Watanabe et al. / Materials Science and Engineering A319–321 (2001) 506–510
Bridgman technique. The orientation of single crystal was determined by the Laue back-reflection technique. They were cut into specimens for fatigue tests (with the gage dimensions of 3×6 × 20 mm) so that the stress axis becomes parallel to the [419] direction of the Cu matrix. With this stress direction, the primary slip system of the Cu matrix becomes (11( 1)[011]. These specimens were solution-treated at 1273 K for 1.44 × 104 s and water quenched. To obtain spherical and coherent k-Fe precipitate particles, the solutiontreated specimens were aged either at 973 K for 6.91× 105 s or at 1073 K for 1.8× 103 s. The former and latter ageing treatments produced k-Fe particles of about 100 and 30 nm in diameter. Hereafter, these specimens will be referred to as specimens L (for large particles) and S (for small particles), respectively. Judging from the Cu –Fe equilibrium phase diagram, the volume fractions of the k-Fe particles in specimens L and S are estimated as 1.4 and 1.3 vol.%, respectively. Fatigue tests were performed in symmetric tensioncompression at room temperature in air using a Saginomiya servo-hydraulic testing machine (Servopac 2). A triangular waveform signal with a constant strain rate of about 3×10 − 3 s − 1 was used for constant
Fig. 1. Cyclic hardening curves of (a) specimens L; and (b) specimens S obtained under various plastic-shear strain amplitudes kpl.
507
plastic strain control. The fatigued specimens were sliced into 3 mm discs parallel to (211( ) of the Cu matrix and were ground down to 0.2 mm thick using silicon-carbide paper. Thin foils for TEM (Hitachi H700: 200 kV) observations were prepared by electrolytic polishing. Similar to the previous study [2], the amount of transformed particles in cyclically deformed specimens were found by measuring the saturation magnetization using a vibrating sample magnetometer (VSM).
3. Results and discussion In the following, the results in the previous study [2] for Cu –Fe single crystals with about 50 nm k-Fe particles will be quoted, whenever appropriate. For easy quotation, these previous specimens will be referred to as specimens M (for middle-sized particles).
3.1. Fatigue tests Fig. 1(a) and (b) shows the cyclic-hardening curves of specimens L and S, respectively. Here, the resolved shear stress amplitude ~ was plotted against the cumulative resolved shear strain 4Nkpl, where N is the number of fatigue cycles and kpl is the plastic shear strain amplitude. We find that clear cyclic softening occurs only in specimens S under smaller plastic strain amplitudes (kpl B 7× 10 − 5). All other curves for both specimens L and S show cyclic hardening to saturation in the early stage of the cyclic deformation. Saturation stress (for specimens cyclic hardened to saturation) or peak stress (for specimens where cyclic softening was observed) amplitudes ~s and amount of transformed particles (the volume fraction of h-Fe particles in fully fatigued specimens) were plotted against the plastic-strain amplitude kpl in Fig. 2. For comparison, the curves for the pure Cu single crystals [4], and for specimens M [2] were also drawn. As is well known, the curve for the pure Cu single crystal exhibits a plateau region with the stress level of about 28 MPa. It can be seen that stress levels for the Cu–Fe single crystals are higher than those for the pure Cu single crystals, due obviously to the dispersion-hardening effect. Although the plateau regions appear narrower in the Cu –Fe single crystals, all the curves show quite similar shapes. Therefore, it is difficult to discuss further the difference in the cyclic deformation behavior just by looking at the cyclic stress-strain curves. The amount of transformed Fe particles shows that the transformability is an increasing function of the particle size and the strain amplitude. In specimens L, cyclic deformation till fracture induces the transformation of practically all the particles when kpl exceeds 1.0× 10 − 3. Contrary to this, less than one-half of the
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saturation dislocation structure changes from the PSB structure to the cell structure. In our specimen L, the formation of the cell structure was observed only near the fracture surface. Fig. 4 shows the example. Here, we can see the coexistence of the labyrinth structure (lefthand side) and the cell structure (right-hand side). This observation suggests that as strain amplitude increases further, the labyrinth structure is gradually destroyed
Fig. 2. Cyclic stress-strain curves and the fraction of transformed h-Fe particles with respect to total amount of Fe particles in various fatigued specimens. The curve for pure Cu was taken from Ref. [4] and the curves for specimens M was taken from Ref. [2].
particles transforms into h-Fe for specimen S at kpl = 1.0× 10 − 3.
3.2. Dislocation microstructure 3.2.1. Specimens L The (211( ) views of the cyclically deformed specimens L are shown in Fig. 3. In Fig. 3(a), two kinds of dislocations can be seen; individual dislocations nearly parallel to the [011] direction and tangled dislocations around some Fe particles. The g·b Burgers-vector analysis of the former has revealed that they are the primary (11( 1)[011] dislocations. Dislocations on other slip planes were very scarcely observed in Fig. 3(a). The existence of the tangled dislocations around the Fe particles is indicative of the occurrence of stress-induced k h martensitic transformation [1]. Therefore, some particles have already transformed into h-Fe. At the intermediate strain amplitude of kpl =1.4× 10 − 3 (Fig. 3(b)), the dislocation structure is similar to the well-known PSB (persistent slip band) structure in a pure Cu single crystal [5]. However, because of the existence of the Fe particles, the so-called ladder structure is not very clearly developed. On the other hand, at the highest strain amplitude of kpl =1.4 ×10 − 2 (Fig. 3(c)), a well-developed labyrinth structure [6,7] consisting of two kinds of dipole walls is observed. Although the existence of a similar labyrinth-like structure was also noted in specimen M [2], it was not so regularly and clearly arranged as that in Fig. 3(c). This is considered to be due to the difference in the inter-particle spacing and in the effectiveness of dispersed particles in preventing the formation of geometrically regular dislocation structure. It is known in Cu single crystals that when the strain amplitude kpl is above those in the plateau region, the
Fig. 3. TEM photographs taken from specimens L cycled to saturation under plastic strain amplitude of (a) kpl =1.4 × 10 − 4; (b) kpl = 1.4 ×10 − 3; and (c) kpl =1.4 × 10 − 2. Zone axis: [211( ].
C. Watanabe et al. / Materials Science and Engineering A319–321 (2001) 506–510
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where f is the volume fraction and d is the average diameter of the Fe particles. With the values of f= 0.014, d=100 nm (for specimen L), f= 0.013 and d = 30 nm (for specimen S), we obtain u= 5.7× 102 nm (for specimen L) and 1.8× 102 nm (for specimen S). Because of the smaller inter-particle spacing in specimen S, dislocation motion and rearrangement are more difficult and this causes the strong retardation effect on
Fig. 4. TEM photographs taken from specimens L cycled to saturation under plastic strain amplitude of kpl = 1.4× 10 − 2. Zone axis: [211( ].
by the newly formed cell structure. From the difference in the diffraction contrast among different cells, we find the development of some misorientation.
3.2.2. Specimens S The [211( ] views of the cyclically deformed specimens S are shown in Fig. 5. Different from Fig. 3, no dislocation walls were seen in specimen S at any plastic strain amplitude. Furthermore, dislocation microstructures at these three different plastic strain amplitudes exhibit no significant difference. The more uniform dislocation structure in specimen S compared with specimens M and L reflects the difficulty in dislocation motion and rearrangement due to the smaller inter-particle spacing. 3.3. The roles of dispersed k-Fe and h-Fe particles In the previous section, two major factors to control the low-cycle fatigue behavior of the present Cu– Fe alloy single crystals have been pointed out; (i) size and distribution of the Fe particles; and (ii) transformability of the particles. The former not only controls the stress levels but also determined the degree of difficulty in the formation and development of dislocation structure. The latter determines the mode of interaction with glide dislocations. In other words, although both the k-Fe and h-Fe particles act as barriers against the formation of dislocation structure, only the transformed h-Fe particles are considered responsible for the absence of cyclic softening. Let us roughly estimate the average inter-particle spacing u on a slip plane using the following equation [8]. u=
' ' 1 6
y −1 d. f
(1)
Fig. 5. TEM photographs taken from specimens S cycled to saturation under plastic strain amplitude of (a) kpl =1 × 10 − 4; (b) kpl = 1.4 ×10 − 3; and (c) kpl =1 × 10 − 2. Zone axis: [211( ].
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inter-particle spacing corresponds to the case of pure Cu. From this diagram, we can easily visualize how the development of dislocation structure is affected by the existence of Fe particles.
5. Conclusions
Fig. 6. Dislocation structure diagram for the Cu –Fe alloy fatigued under plastic strain control.
the development of a fatigue dislocation structure. The relatively uniform dislocation distribution observed in specimens S (Fig. 6) is in consistent with this discussion. From Fig. 2, it is reasonable to consider that the lower limit of the volume fraction of the h-Fe particles necessary for the absence of cyclic softening is about 20% of the total Fe particles. Then, using f =0.013× 0.2 and d =30 nm for specimen S, we have u= 4.1× 102 nm from Eq. (1). This value is still smaller than the above value of u for specimen L. Therefore, even at the lower limit, sufficient amount of h-Fe particles do exist to cause the cyclic hardening to saturation.
4. Construction of a dislocation structure diagram From the observations and discussions made above, we are now ready to propose a ‘dislocation structure diagram’ for the present alloy that was fatigue tested under plastic-strain control. Fig. 6 shows a diagram plotting the inter-particle spacing as an ordinate and plastic strain amplitude as an abscira. The infinite
Plastic-strain-controlled low-cycle fatigue tests of Cu –Fe alloy single crystals with Fe particles of about 30 and 100 nm in diameter were performed. The results and conclusions are summarized as follows. (1) Specimens with Fe particles of 30 nm in diameter show cyclic softening under smaller plastic strain amplitudes (kpl B 7×10 − 5). All other specimens show cyclic hardening to saturation. (2) Dislocations were very uniformly distributed in specimens with Fe particle of 30 nm in diameter. At higher strain amplitude, the dislocation wall structure and cell structure were observed in specimens with Fe particles of 100 nm in diameter. (3) The particles prevent the formation of fatigue-induced stable dislocation structure. If the volume fraction of the particles is fixed, the effect becomes more significant as inter-particle spacing becomes smaller.
References [1] M. Kato, A. Nishimuta, T. Matsuyama, S. Horie, Mater. Sci. Eng. A111 (1989) 17. [2] M. Kato, N. Honjo, T. Fujii, ISIJ Int. 37 (1997) 12. [3] R. Monzen, A. Sato, T. Mori, Trans. Jpn. Inst. Met. 22 (1981) 65. [4] H. Mughrabi, Mater. Sci. Eng. 33 (1978) 207. [5] J.M. Finney, C. Laird, Philos. Mag. 31 (1975) 339. [6] P. Charsley, D. Kuhlmann-Wisdorf, Philos. Mag. A44 (1981) 1351. ´ sperance, Mater. Sci. Eng. 81 [7] J.I. Dickson, L. Hanfield, G. L’E (1986) 477. [8] A. Kelly, R.B. Nicholson, Progress in Materials Science, vol. 10, no. 3, Peramon Press, New York, 1963.
Effects of distributed Fe particles on low-cycle fatigue behavior of Cu–Fe alloy single crystals Chihiro Watanabe *, Toshiyuki Fujii, Susumu Onaka, Masaharu Kato Department of Inno6ati6e and Engineered Materials, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226 -8502, Japan
Abstract Low-cycle fatigue behavior of Cu–1.58mass.%Fe alloy single crystals with precipitated f.c.c. k-Fe particles was examined under plastic strain controlled tests. Specimens with large (about 100 nm in diameter) and small (30 nm) particles were prepared. Although the k-Fe particles are coherent and shearable, no cyclic softening was observed in specimens with large particles. On the other hand, in small-particle specimens, cyclic softening was observed particularly at lower strain amplitudes. Dislocation microstructures characteristic of cyclic deformation were more clearly developed in large-particle specimens. Magnetic measurements of fatigued specimens revealed that more particles had transformed martensitically into b.c.c. h-Fe in large-particle specimens than in small-particle specimens. The transformation changes the particle character from ‘coherent and shearable’ to ‘incoherent and nonshearable’. This change enhances the uniform deformation and the absence of cyclic softening in the large-particle specimens where the majority of the particles became h-Fe. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Cyclic deformation; Fatigue; Cu–Fe alloy; Dislocation structure; Precipitation; Martensitic transformation
1. Introduction Using Cu –Fe alloy polycrystals and single crystals with finely dispersed precipitate k-Fe particles, we have examined the low-cycle fatigue behavior and dislocation microstructure [1,2]. When the volume fraction and the size of the particles are about 1.4% and 50 nm, respectively, it has been found that the alloys show cyclic hardening to saturation despite the fact that the k-Fe particles are coherent and shearable. Stress-induced k h martensitic transformation was found to occur extensively during the cyclic deformation. The transformation changes the particle character from ‘coherent and shearable’ to ‘incoherent and nonshearable’. This change in the particle character was concluded to be responsible for the absence of the cyclic softening. It has been found from monotonic tensile tests [3] that the stress-induced transformation of the Fe particles in Cu depends strongly on the particle size. The larger particles are more prone to the transformation. If this is also the case for cyclic deformation, the low-cycle * Corresponding author. Tel.: + 81-459-245634; fax: +81-459245173. E-mail address: [email protected] (C. Watanabe).
fatigue behavior of the Cu –Fe alloy should be sensitive to the particle size. If the transformation into h-Fe occurs in the majority of k-Fe particles in the early stage of cyclic deformation, the alloy can be regarded as that containing nonshearable h-Fe particles. On the other hand, if the transformation is difficult, the particles may remain as shearable k-Fe even in the late stages of cyclic deformation. With the above in mind, we have examined the low-cycle fatigue behavior of Cu –Fe alloy single crystals with dispersed k-Fe particles of different sizes. Referring to the previous study where the average particle size was controlled to be about 50 nm [2], we have selected two particles sizes, i.e. 100 and 30 nm, in this study. Main foci were placed upon examination of (i) cyclic deformation behavior; (ii) development of dislocation structure; and (iii) transformability of Fe particles.
2. Experimental From as-rolled Cu –1.58mass.%Fe alloy plates, single crystal sheets of 3× 50× 150 mm were grown by the
0921-5093/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 0 5 9 - 0
C. Watanabe et al. / Materials Science and Engineering A319–321 (2001) 506–510
Bridgman technique. The orientation of single crystal was determined by the Laue back-reflection technique. They were cut into specimens for fatigue tests (with the gage dimensions of 3×6 × 20 mm) so that the stress axis becomes parallel to the [419] direction of the Cu matrix. With this stress direction, the primary slip system of the Cu matrix becomes (11( 1)[011]. These specimens were solution-treated at 1273 K for 1.44 × 104 s and water quenched. To obtain spherical and coherent k-Fe precipitate particles, the solutiontreated specimens were aged either at 973 K for 6.91× 105 s or at 1073 K for 1.8× 103 s. The former and latter ageing treatments produced k-Fe particles of about 100 and 30 nm in diameter. Hereafter, these specimens will be referred to as specimens L (for large particles) and S (for small particles), respectively. Judging from the Cu –Fe equilibrium phase diagram, the volume fractions of the k-Fe particles in specimens L and S are estimated as 1.4 and 1.3 vol.%, respectively. Fatigue tests were performed in symmetric tensioncompression at room temperature in air using a Saginomiya servo-hydraulic testing machine (Servopac 2). A triangular waveform signal with a constant strain rate of about 3×10 − 3 s − 1 was used for constant
Fig. 1. Cyclic hardening curves of (a) specimens L; and (b) specimens S obtained under various plastic-shear strain amplitudes kpl.
507
plastic strain control. The fatigued specimens were sliced into 3 mm discs parallel to (211( ) of the Cu matrix and were ground down to 0.2 mm thick using silicon-carbide paper. Thin foils for TEM (Hitachi H700: 200 kV) observations were prepared by electrolytic polishing. Similar to the previous study [2], the amount of transformed particles in cyclically deformed specimens were found by measuring the saturation magnetization using a vibrating sample magnetometer (VSM).
3. Results and discussion In the following, the results in the previous study [2] for Cu –Fe single crystals with about 50 nm k-Fe particles will be quoted, whenever appropriate. For easy quotation, these previous specimens will be referred to as specimens M (for middle-sized particles).
3.1. Fatigue tests Fig. 1(a) and (b) shows the cyclic-hardening curves of specimens L and S, respectively. Here, the resolved shear stress amplitude ~ was plotted against the cumulative resolved shear strain 4Nkpl, where N is the number of fatigue cycles and kpl is the plastic shear strain amplitude. We find that clear cyclic softening occurs only in specimens S under smaller plastic strain amplitudes (kpl B 7× 10 − 5). All other curves for both specimens L and S show cyclic hardening to saturation in the early stage of the cyclic deformation. Saturation stress (for specimens cyclic hardened to saturation) or peak stress (for specimens where cyclic softening was observed) amplitudes ~s and amount of transformed particles (the volume fraction of h-Fe particles in fully fatigued specimens) were plotted against the plastic-strain amplitude kpl in Fig. 2. For comparison, the curves for the pure Cu single crystals [4], and for specimens M [2] were also drawn. As is well known, the curve for the pure Cu single crystal exhibits a plateau region with the stress level of about 28 MPa. It can be seen that stress levels for the Cu–Fe single crystals are higher than those for the pure Cu single crystals, due obviously to the dispersion-hardening effect. Although the plateau regions appear narrower in the Cu –Fe single crystals, all the curves show quite similar shapes. Therefore, it is difficult to discuss further the difference in the cyclic deformation behavior just by looking at the cyclic stress-strain curves. The amount of transformed Fe particles shows that the transformability is an increasing function of the particle size and the strain amplitude. In specimens L, cyclic deformation till fracture induces the transformation of practically all the particles when kpl exceeds 1.0× 10 − 3. Contrary to this, less than one-half of the
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saturation dislocation structure changes from the PSB structure to the cell structure. In our specimen L, the formation of the cell structure was observed only near the fracture surface. Fig. 4 shows the example. Here, we can see the coexistence of the labyrinth structure (lefthand side) and the cell structure (right-hand side). This observation suggests that as strain amplitude increases further, the labyrinth structure is gradually destroyed
Fig. 2. Cyclic stress-strain curves and the fraction of transformed h-Fe particles with respect to total amount of Fe particles in various fatigued specimens. The curve for pure Cu was taken from Ref. [4] and the curves for specimens M was taken from Ref. [2].
particles transforms into h-Fe for specimen S at kpl = 1.0× 10 − 3.
3.2. Dislocation microstructure 3.2.1. Specimens L The (211( ) views of the cyclically deformed specimens L are shown in Fig. 3. In Fig. 3(a), two kinds of dislocations can be seen; individual dislocations nearly parallel to the [011] direction and tangled dislocations around some Fe particles. The g·b Burgers-vector analysis of the former has revealed that they are the primary (11( 1)[011] dislocations. Dislocations on other slip planes were very scarcely observed in Fig. 3(a). The existence of the tangled dislocations around the Fe particles is indicative of the occurrence of stress-induced k h martensitic transformation [1]. Therefore, some particles have already transformed into h-Fe. At the intermediate strain amplitude of kpl =1.4× 10 − 3 (Fig. 3(b)), the dislocation structure is similar to the well-known PSB (persistent slip band) structure in a pure Cu single crystal [5]. However, because of the existence of the Fe particles, the so-called ladder structure is not very clearly developed. On the other hand, at the highest strain amplitude of kpl =1.4 ×10 − 2 (Fig. 3(c)), a well-developed labyrinth structure [6,7] consisting of two kinds of dipole walls is observed. Although the existence of a similar labyrinth-like structure was also noted in specimen M [2], it was not so regularly and clearly arranged as that in Fig. 3(c). This is considered to be due to the difference in the inter-particle spacing and in the effectiveness of dispersed particles in preventing the formation of geometrically regular dislocation structure. It is known in Cu single crystals that when the strain amplitude kpl is above those in the plateau region, the
Fig. 3. TEM photographs taken from specimens L cycled to saturation under plastic strain amplitude of (a) kpl =1.4 × 10 − 4; (b) kpl = 1.4 ×10 − 3; and (c) kpl =1.4 × 10 − 2. Zone axis: [211( ].
C. Watanabe et al. / Materials Science and Engineering A319–321 (2001) 506–510
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where f is the volume fraction and d is the average diameter of the Fe particles. With the values of f= 0.014, d=100 nm (for specimen L), f= 0.013 and d = 30 nm (for specimen S), we obtain u= 5.7× 102 nm (for specimen L) and 1.8× 102 nm (for specimen S). Because of the smaller inter-particle spacing in specimen S, dislocation motion and rearrangement are more difficult and this causes the strong retardation effect on
Fig. 4. TEM photographs taken from specimens L cycled to saturation under plastic strain amplitude of kpl = 1.4× 10 − 2. Zone axis: [211( ].
by the newly formed cell structure. From the difference in the diffraction contrast among different cells, we find the development of some misorientation.
3.2.2. Specimens S The [211( ] views of the cyclically deformed specimens S are shown in Fig. 5. Different from Fig. 3, no dislocation walls were seen in specimen S at any plastic strain amplitude. Furthermore, dislocation microstructures at these three different plastic strain amplitudes exhibit no significant difference. The more uniform dislocation structure in specimen S compared with specimens M and L reflects the difficulty in dislocation motion and rearrangement due to the smaller inter-particle spacing. 3.3. The roles of dispersed k-Fe and h-Fe particles In the previous section, two major factors to control the low-cycle fatigue behavior of the present Cu– Fe alloy single crystals have been pointed out; (i) size and distribution of the Fe particles; and (ii) transformability of the particles. The former not only controls the stress levels but also determined the degree of difficulty in the formation and development of dislocation structure. The latter determines the mode of interaction with glide dislocations. In other words, although both the k-Fe and h-Fe particles act as barriers against the formation of dislocation structure, only the transformed h-Fe particles are considered responsible for the absence of cyclic softening. Let us roughly estimate the average inter-particle spacing u on a slip plane using the following equation [8]. u=
' ' 1 6
y −1 d. f
(1)
Fig. 5. TEM photographs taken from specimens S cycled to saturation under plastic strain amplitude of (a) kpl =1 × 10 − 4; (b) kpl = 1.4 ×10 − 3; and (c) kpl =1 × 10 − 2. Zone axis: [211( ].
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inter-particle spacing corresponds to the case of pure Cu. From this diagram, we can easily visualize how the development of dislocation structure is affected by the existence of Fe particles.
5. Conclusions
Fig. 6. Dislocation structure diagram for the Cu –Fe alloy fatigued under plastic strain control.
the development of a fatigue dislocation structure. The relatively uniform dislocation distribution observed in specimens S (Fig. 6) is in consistent with this discussion. From Fig. 2, it is reasonable to consider that the lower limit of the volume fraction of the h-Fe particles necessary for the absence of cyclic softening is about 20% of the total Fe particles. Then, using f =0.013× 0.2 and d =30 nm for specimen S, we have u= 4.1× 102 nm from Eq. (1). This value is still smaller than the above value of u for specimen L. Therefore, even at the lower limit, sufficient amount of h-Fe particles do exist to cause the cyclic hardening to saturation.
4. Construction of a dislocation structure diagram From the observations and discussions made above, we are now ready to propose a ‘dislocation structure diagram’ for the present alloy that was fatigue tested under plastic-strain control. Fig. 6 shows a diagram plotting the inter-particle spacing as an ordinate and plastic strain amplitude as an abscira. The infinite
Plastic-strain-controlled low-cycle fatigue tests of Cu –Fe alloy single crystals with Fe particles of about 30 and 100 nm in diameter were performed. The results and conclusions are summarized as follows. (1) Specimens with Fe particles of 30 nm in diameter show cyclic softening under smaller plastic strain amplitudes (kpl B 7×10 − 5). All other specimens show cyclic hardening to saturation. (2) Dislocations were very uniformly distributed in specimens with Fe particle of 30 nm in diameter. At higher strain amplitude, the dislocation wall structure and cell structure were observed in specimens with Fe particles of 100 nm in diameter. (3) The particles prevent the formation of fatigue-induced stable dislocation structure. If the volume fraction of the particles is fixed, the effect becomes more significant as inter-particle spacing becomes smaller.
References [1] M. Kato, A. Nishimuta, T. Matsuyama, S. Horie, Mater. Sci. Eng. A111 (1989) 17. [2] M. Kato, N. Honjo, T. Fujii, ISIJ Int. 37 (1997) 12. [3] R. Monzen, A. Sato, T. Mori, Trans. Jpn. Inst. Met. 22 (1981) 65. [4] H. Mughrabi, Mater. Sci. Eng. 33 (1978) 207. [5] J.M. Finney, C. Laird, Philos. Mag. 31 (1975) 339. [6] P. Charsley, D. Kuhlmann-Wisdorf, Philos. Mag. A44 (1981) 1351. ´ sperance, Mater. Sci. Eng. 81 [7] J.I. Dickson, L. Hanfield, G. L’E (1986) 477. [8] A. Kelly, R.B. Nicholson, Progress in Materials Science, vol. 10, no. 3, Peramon Press, New York, 1963.