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Cyclic deformation behavior of double-slip-oriented copper single crystals I: coplanar double slip orientation on 011-1̄11 side of the stereographic triangle
Materials Science and Engineering A260 (1999) 132 – 138
Cyclic deformation behavior of double-slip-oriented copper single crystals I: coplanar double slip orientation on 011-1( 11 side of the stereographic triangle X.W. Li *, Z.G. Wang, S.X. Li State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Academia Sinica, 72 Wenhua Road, Shenyang 110015, People’s Republic of China Received 2 June 1998; received in revised form 7 September 1998
Abstract The cyclic deformation behaviors of [2( 33] coplanar double-slip-oriented and [4( 18 41] single-slip-oriented copper single crystals were investigated at constant plastic shear strain amplitude gpl in the range of about 10 − 4 –10 − 2 at ambient temperature in air. It was revealed that the cyclic deformation behavior of copper single crystal oriented on the 011-1( 11 side is distinctly dissimilar from that on the 001-1( 11 and 001-011 sides in the stereographic triangle. The plot of initial hardening rate u0.2 against gpl of [2( 33] crystal exhibits two regions as presented for single-slip-oriented crystals. The critical strain amplitude ( :3.5 ×10 − 3), corresponding to the occurrence of the secondary hardening stage in the cyclic hardening curve of the [2( 33] crystal, was found to be an intermediate value between that for single-slip-oriented single crystals and polycrystals. The result shows that the cyclic hardening behavior of the [2( 33] crystal, as compared with that of single-slip-oriented crystals, is more close to that of polycrystals. Instead of a clear plateau, the cyclic stress–strain (CSS) curves of the [2( 33] crystals shows a quasi-plateau over the range of about 3.0 ×10 − 4 –2.0× 10 − 3, which would be greatly attributed to the mode of dislocation interactions between slip systems operating in the crystal. The habit plane of two types of deformation bands DBI and DBII, formed in the cyclically deformed [2( 33] crystal, are perpendicular to each other strictly, and they develop with increasing applied strain amplitude. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Crystals; Double-slip-oriented; Cyclic deformation; Copper
1. Introduction In the past three decades, the interest has been focused on the investigation of cyclic deformation mechanisms in copper single crystals oriented for single slip in order to explore fatigue behavior of f.c.c. metals [1,2]. It is well known that three distinct regimes exist for the cyclic saturation stresses of single-slip-oriented crystals. In the second regime (6×10 − 5 5gpl 5 7.5× 10 − 3), the cyclic stress – strain (CSS) curve exhibits an extended plateau wherein the saturation stress is nearly independent of applied plastic strain amplitude gpl [3]. However, systematic work on the cyclic deformation behavior of double-slip-oriented crystals is still rather * Corresponding address. Tel.: + 86-2423-843531; fax: + 86-243891320; e-mail: [email protected].
limited. In the stereographic triangle shown in Fig. 1, the three sides correspond to quite different double-slip orientations with differently active slip systems and corresponding dislocation reactions during cyclic deformation. Jin and Winter [4,5] reported a preliminary
Fig. 1. Stereographic triangle showing the orientations of copper single crystals involved in this paper.
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X.W. Li et al. / Materials Science and Engineering A260 (1999) 132–138
result of the cyclic deformation response and dislocation structures of copper single crystals with [1( 12], [1( 22] and [012] double-slip orientations on the three sides of the stereographic triangle at one strain amplitude of 3.0×10 − 3. In recent years, Gong et al. [6,7] investigated the cyclic deformation behavior of [034] and [1( 17] oriented copper single crystals in a wide range of strain amplitude. An obviously different cyclic deformation behavior was found between [034] and [1( 17] crystals and single-slip-oriented crystals. Nevertheless, the cyclic deformation behavior of copper single crystal oriented for coplanar double slip on 011-1( 11 side is still not well understood. To comprehensively understand the effect of crystallographic orientation and dislocation interaction mode on the cyclic deformation behavior of copper single crystals oriented for double slip, the present work studied systematically the cyclic deformation behavior of [2( 33] coplanar double-slip-oriented copper single crystals at a wide range of plastic strain amplitude of 1.3× 10 − 4 –7.5×10 − 3. Single-slip-oriented [4( 18 41] copper single crystals were also studied for comparison.
2. Experimental procedures Single crystals were grown from OFHC copper of 99.999% purity by the Bridgman technique. The dimensions of the fatigue specimens are 7×7 ×70 mm3, with a gauge section of 7 × 5×16 mm3 for the [2( 33] crystals, and 6× 6 ×60 mm3, with a gauge section of 6×4×16 mm3 for the [4( 18 41] crystals. The orientation of the specimens was determined by the Laue back-reflection technique with an accuracy within 9 2°. Before the fatigue tests, the specimens were an-
Fig. 2. The cyclic hardening curves of the [2( 33] crystals at different strain amplitudes.
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nealed at 800°C for 2 h in vacuum, and then electro-polished to produce a strain-free and mirrorlike surface for microscopic observations. Fatigue tests were performed in symmetric tension– compression at room temperature in air using a Shimadzu servo–hydraulic testing machine. A triangular waveform signal with a frequency of 0.05–0.4 Hz was used for the constant plastic strain control. Stress– strain hysteresis loops were registered on an X –Y recorder. All specimens were deformed cyclically up to the occurrence of saturation. Some of the [4( 18 41] crystals were continuously cycled at successively increased gpl. After the fatigue tests, the slip features of the specimen surfaces were carefully observed by optical microscopy and scanning electron microscopy (SEM).
3. Results
3.1. Cyclic hardening Fig. 2 shows cyclic hardening curves of the [2( 33] copper single crystals deformed at different strain amplitudes. Fatigue testing conditions and data of cyclic hardening and saturation are listed in Table 1, where gpl,cum (gpl,cum = 4Ngpl, N is the total cyclic number) is the cumulative plastic strain, u0.2 is the initial hardening rate (u0.2 = Dt/Dgpl,cum, Dgpl,cum = 0.2), ts is the shear saturation stress, tmax is the maximum shear stress, and tmax/ts is a parameter describing cyclic softening behavior. It can be seen from Fig. 2 that, under a lower strain amplitude (gpl = 1.3× 10 − 4), the shear stress in the specimen increases slowly with increasing cyclic number and finally develops into a saturation state. For the intermediate strain amplitudes (gpl = 2.4×10 − 4 – 1.7× 10 − 3), the hardening curves exhibit a clear stress overshooting stage. The parameter tmax/ts in Table 1 does reflect the extent of overshooting. At higher strain amplitudes (gpl ] 3.5× 10 − 3), the hardening curves exhibit a slight softening after the stress reaches a first maximum, subsequently a slow secondary hardening process sustains to an occurrence of a pseudosaturation state. The plots of u0.2 against gpl of the [2( 33] and [4( 18 41] crystals are shown in Fig. 3. The results for the [034] and [1( 17] double-slip-oriented copper single crystals [6] are also included for comparison. It is clearly shown that the curve of u0.2 − gpl for the [2( 33] crystal obviously exhibits two ranges as presented for the [4( 18 41] and [034] crystals. The initial hardening rate, u0.2, of the [2( 33] crystals, which is nearly independent of gpl below 2.0× 10 − 3, is much lower than that of the [1( 17] crystals, but close to that of the [034] and [4( 18 41] crystals.
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Table 1 Fatigue testing conditions and data for [2( 33] and [4( 18 41] copper single crystals Orientation
Specimen No.
gpl
Cyclic No.
gpl,cum
u0.2 (MPa)
ts (MPa)
tmax (MPa)
tmax/ts
[2( 33]
1 2 3 4 5 6 7 8 9
1.3×10−4 2.4×10−4 3.4×10−4 6.2×10−4 9.2×10−4 1.7×10−3 3.5×10−3 5.3×10−3 7.5×10−3
65 000 45 600 32 000 22 250 12 000 6000 4700 10 200 17 500
33.8 43.8 43.5 55.2 44.2 40.8 65.8 216.2 526.8
10.2 10.5 12.8 13.9 14.6 15.1 24.9 38.2 46.1
25.0 28.9 30.1 30.9 31.7 32.5 33.5 35.4 37.2
25.0 30.4 31.4 34.3 34.5 34.6 33.5 35.4 37.8
1.00 1.05 1.04 1.11 1.09 1.06 1.00 1.00 1.02
[4( 18 41]
1
1.7×10−4 3.3×10−4 8.6×10−4 1.3×10−3 1.6×10−3 2.5×10−3 3.6×10−3 4.5×10−3 6.5×10−3 7.7×10−3
46 000 14 000 23 400 19 600 6500 9700 3500 3600 1400 2100
31.3 49.8 80.5 182.4 41.6 138.6 50.4 64.8 101.2 165.9
8.4 – 9.0 – 14.8 – 27.1 30.5 – –
27.4 27.2 28.0 28.2 27.6 27.6 27.5 29.0 29.8 31.2
31.2 – 31.0 – 27.6 – 27.7 31.9 – –
1.14 – 1.11 – 1.00 – 1.01 1.10 – –
2 3 4 5
An increase in gpl beyond 2.0× 10 − 3 causes a rapid increase in u0.2 for the four oriented crystals.
3.2. Cyclic stress– strain cur6e
corresponding stress is slightly higher than that of the average plateau stress (27.7 MPa) of the [034] crystal. The CSS curve for the [1( 17] crystal is quite different from that of the other three crystals. The saturation shear stress increases monotonously with increasing gpl.
The CSS curves of [4( 18 41], [2( 33], [034], and [1( 17] are shown in Fig. 4. The curve for the [4( 18 41] crystal shows a clear plateau in the range of 1.7× 10 − 4 B gpl B7.0× 10 − 3 with an average saturation stress of 28.0 MPa, very close to Mughrabi’s results [6]. For the [2( 33] crystal, strictly speaking, its CSS curve does not show a clear plateau, however, the saturation stress of the [2( 33] crystal does not increase strikingly with increasing gpl in the range of 3.0×10 − 4 – 2.0 ×10 − 3, wherein a quasi-plateau seems to be presented, and the
The surface slip features of the [2( 33] crystal specimens cycled to saturation at various plastic strain amplitudes are shown in Fig. 5. In the case of gpl = 1.3× 10 − 4, nearly no slip band was detected. With increasing strain amplitude to 2.4× 10 − 4, only very faint slip lines can be observed in local regions.
Fig. 3. Initial cyclic hardening rate u0.2 versus plastic shear strain amplitude gpl.
Fig. 4. The cyclic stress – strain curves of four differently oriented crystals.
3.3. Surface slip features
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Fig. 5. Surface slip features of the [2( 33] crystals cyclically deformed at various strain amplitudes. (a)gpl =3.4 × 10 − 4;(b) gpl =9.2 ×10 − 4;(c–d) gpl = 3.5 ×10 − 3 and (e–f) gpl = 5.3× 10 − 3.(a–e) viewed from (320) and (d – f) viewed from (6( 9 13).
Thus, a fatigue limit, defined as the critical strain amplitude below which slip bands do not form, can be determined to be about 1.8× 10 − 4 for the [2( 33] crystals. This value is roughly equal to the fatigue limit of 1.7× 10 − 4 for the [001] crystal [8], but much higher than that of 6.0×10 − 5 for single-slip-oriented copper single crystals [3]. When gpl =3.4 ×10 − 4 (see Fig. 5(a)), the primary PSBs begin to appear in some regions and distribute unhomogeneously on the specimen surface. As the strain amplitude increases to 9.2× 10 − 4, these primary PSBs tend to concentrate into a so-called macro-deformation band denoted by DBI, beyond which nearly no slip bands can be observed, as shown in Fig. 5(b). When gpl increases to 3.5× 10 − 3, another type of de-
formation band denoted by DBII, which is also concentrated with primary PSBs, was observed on the specimen surface. DBI develops almost along the primary PSBs while DBII makes a certain angle with the primary PSBs (see Fig. 5(c–d)). With gpl continuously increasing, DBI and DBII develop further and almost occupy the whole specimen surface (see Fig. 5(e–f)).
4. Discussion
4.1. Cyclic hardening Mughrabi [3] classified the curve of u0.2 − gpl into two ranges: when gpl B 10 − 3 (range I%), u0.2 is lower and
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almost independent of gpl; In the range II% (gpl \10 − 3), u0.2 increases notably with increasing gpl. Gong et al. [6] reported a quite similar hardening behavior for the [034] crystal. The present study showed that the initial cyclic hardening behavior of the [2( 33] crystal is similar to those of [4( 18 41] single-slip-oriented crystal and the [034] crystal (see Fig. 3). When gpl B2.0 ×10 − 3, the initial hardening rate u0.2 of the [2( 33] crystal is rather low and almost independent of gpl, indicating that the cyclic hardening of the [2( 33] crystal is mainly associated with the primary dislocation multiplication and their interactions. In the range of higher strain amplitude (gpl \2.0× 10 − 3), u0.2 increases rapidly with increasing gpl. Under these circumstances, the coplanar slip system might operate generously, leading to a large-scale dislocation interaction between primary and coplanar slip systems. Moreover, it is clear from Fig. 3 that the curve of u0.2 −gpl for the [2( 33] crystal is very close to that for the [034] crystal and much lower than that for the [1( 17] crystal, which may be attributed to the differences in active slip systems and their corresponding dislocation reactions in these three crystals. For the [1( 17] crystal, a strong interaction between primary and conjugate systems gives Lomer – Cottrell locks, causing a much higher value of u0.2, while the dislocation interactions in the [2( 33] and [034] crystals form new glissile coplanar dislocations and sessile jogs, respectively. These two kinds of dislocation interactions are relatively weak, thus leading to a lower value of u0.2.
4.2. Secondary cyclic hardening Wang and Mughrabi [9] have investigated the secondary cyclic hardening in fatigued copper monocrystals and polycrystals. They found that the occurrence of secondary cyclic hardening stage closely corresponds to the slow bulk microstructural changes, leading ultimately to the formation of a cell structure. In general, the secondary cyclic hardening stage in single-slip-oriented crystals is observable only when gpl ]4.2 × 10 − 3; while in polycrystals, secondary cyclic hardening becomes clearly evident at an earlier stage and a lower gpl of about 2.0×10 − 3. In the present [2( 33] crystals, it was noted that a slight secondary hardening already occurs after cycling for about 103 cycles at a plastic strain amplitude gpl of 3.5 × 10 − 3, and an increase in the shear stress amplitude reaches about 2.8% (see Fig. 2). It is obvious that the value of 3.5 ×10 − 3 is an intermediate one between that of single-slip-oriented crystals and polycrystals, which seems to show that the cyclic hardening behavior of the [2( 33] double-slip-oriented crystal is more close to those of polycrystals than those of single-slip-oriented crystals. When gpl ]5.3 × 10 − 3, the secondary cyclic hardening of the [2( 33] crystals becomes more notable, and the increase in the shear stress reaches about 7.5%, whereas an only 5.5% in-
crease in shear stress was observed for single-slip-oriented crystals at a strain amplitude gpl of 7.5×10 − 3 [9]. This comparison further indicated that the secondary cyclic hardening in the [2( 33] double-slip-oriented crystal appears to be more pronounced as compared to that in single-slip-oriented crystal. The secondary cyclic hardening should be associated with an increase in the activity of the secondary slip systems in single crystals. In the [2( 33] crystals, the coplanar secondary slip system is easy to operate especially at higher strain amplitudes. Besides, the interactions between primary and coplanar dislocations would result readily in the formation of cell structures. Therefore, the phenomenon mentioned above is likely to understand.
4.3. Cyclic stress–strain cur6e It is well known that the CSS curve of single-slip-oriented copper single crystals exhibits a plateau in the strain amplitude range of 6.0×10 − 5 –7.5×10 − 3, and the plateau saturation shear stress ts is about 28 MPa. Winter [10] has proposed a two-phase model to explain the existence of plateau region in the CSS curve for single-slip-oriented crystals. It is now generally accepted that the occurrence of saturation stress plateau is closely related to the formation of PSBs ladder structures. For the [2( 33] crystals, the second highest Schmid factor occurs on the (111)[1( 10] slip system, which has the same slip plane as the primary slip system. Accordingly, the coplanar slip system is likely to operate and participate in deformation together with the primary slip system, causing cell structures formation and suppressing the occurrence of PSBs ladder structures. In addition, the scale of the cell structures may change with varying plastic strain amplitude. These might be essential reasons for the non-existence of a clear plateau. Lepisto et al. [11,12] observed the dislocation structures in cyclically deformed [1( 11] multiple-slip-oriented copper single crystals at a plastic strain amplitude gpl of 1.4× 10 − 3. It was found that the cell structure formed in the [1( 11] crystals exhibits PSBs with ladder-like features. The dislocation structure formed in the [2( 33] crystals might show some similarities to that of the [1( 11] crystals because the [2( 33] orientation is close to the [1( 11] orientation. So, the occurrence of a cell structure with ladder-like features would be expected in cyclically deformed [2( 33] crystals. This type of cell structures is favorable for accommodating much more plastic strain so that the saturation stress does not increase notably with the increasing gpl, leading to the presence of a quasi-plateau. A detailed studies of dislocation structures in cyclically deformed [2( 33] is being undertaken and the results will be reported elsewhere.
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In summary, quite different plateau behaviors in the CSS curve are expected to be observed in cyclically deformed copper single crystals oriented for different double slips on the different sides (011/1( 11, 001/1( 11 and 001/011) of the stereographic triangle. The plateau region (10 − 4 –4.3× 10 − 3) for the [034] crystal becomes shorter as compared with that for single-slip-oriented crystals, while the CSS curve of the [1( 17] crystal shows almost no plateau region. In between the results of the [034] and [1( 17] crystals, a quasi-plateau in the CSS curve occurs for the [2( 33] crystal. Consequently, concerning different double-slip-oriented copper single crystals, the occurrence or disappearance of a plateau in CSS curve mainly depends upon the inherent slip characteristics and the mode of dislocation interaction between slip systems in the crystal. For the crystals with orientations located on the 011/1( 11 side of the stereographic triangle, the transition from the occurrence of a clear plateau region (1.1 × 10 − 4 – 7.2 × 10 − 3) in [011] multiple-slip-oriented crystals [13] to the disappearance of a plateau in [1( 11] multiple-slip-oriented crystals [14] is linked up through the presence of a quasi-plateau in coplanar double-slip-oriented crystals.
4.4. Deformation bands (I, II) Most of the previous work on deformation bands (DBs) are mainly based on unidirectional deformation [15–17]. In some of the recent investigations [6,8,13], it was found that DBs seems to be a general phenomenon in cyclically deformed copper single crystals oriented for double or multiple slip. Gong et al. [8] suggested that the poor reversibility of slip may be responsible for the formation of DBs. We [13] suggested that the formation of DBI and DBII in cyclically deformed [011] multiple-slip-oriented crystals results from the local irreversible rotation of crystal which exists during symmetrical push – pull loading. In the present work, as found out by SEM observation, the PSBs in DBII formed at gpl of 1.7× 10 − 3 extruded uniformly from the crystal surface, not producing a heavy plastic deformation (see Fig. 6(a)), while the PSBs in DBII formed at gpl of 5.3 ×10 − 3 caused serious disruption of the whole initially smooth surface, and some microcracks nucleated along the PSBs in DBs (see Fig. 6(b)). Accordingly, like PSBs, DBs develop with increasing applied strain amplitude. Fig. 7 shows schematically the surface orientations of the fatigue specimen and typical surface traces made by favorable slip planes as well as deformation bands observed in the [2( 33] crystal. The habit planes of DBI and DBII were determined by a simple crystallographic calculation from Fig. 7 to be (0.65 0.57 0.50) and ( − 0.44 − 0.25 0.86), respectively. It is obvious that the habit plane of DBI is close to the primary slip plane (111), and the habit plane of DBII is close to the
Fig. 6. SEM micrographs of PSB features in DBII at different strain amplitudes.(a) gpl =1.7 × 10 − 3; and (b) gpl =5.3 × 10 − 3. View from (6 9( 13).
conventional kink plane (1( 01). Both of them are strictly perpendicular to each other. The two types of DBs found here are quite similar to that found in [011] crystals [13]. Thus, it was believed that the formation of the two types of DBs formed in the [2( 33] crystals could also be interpreted as being the result of the local irreversible rotation of crystal, meanwhile the results above further confirmed the feasibility of the explanation to the formation of DBI and DBII in view of the classical crystallographic deformation geometry.
Fig. 7. Illustration of surface orientations, slip planes and deformation bands of [2( 33] crystal.
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local irreversible rotation of crystal which exists during symmetrical push–pull loading.
5. Conclusions Based on the experimental results and discussion above, the following conclusions can be drawn. 1. Similar to the result of the [4( 18 41] single-slip-oriented crystal, the plot of initial cyclic hardening rate u0.2 against plastic strain amplitude gpl for the [2( 33] double-slip-oriented copper single crystal exhibits obvious two ranges. For gpl B2.0 × 10 − 3, u0.2 of the [2( 33] crystal is rather low and almost independent of gpl. When gpl \2.0 ×10 − 3, u0.2 increases notably with increasing gpl. 2. The secondary cyclic hardening occurs during the cyclic hardening process of the [2( 33] crystal when gpl ]3.5× 10 − 3. This critical plastic strain amplitude of 3.5×10 − 3 corresponding to the occurrence of the secondary cyclic hardening for the [2( 33] crystal is lower than that of single-slip-oriented crystals and higher than that of polycrystals. It indicates that the cyclic hardening behavior of the [2( 33] crystal is more close to that of polycrystals as compared with that of single-slip-oriented crystals. 3. The CSS curve of [2( 33] crystal does not show a clear plateau, but a quasi-plateau over the range of about 3.0×10 − 4 −2.0 ×10 − 3. 4. Two types of deformation bands DBI and DBII form on the specimen surface of the [2( 33] crystal, and their habit planes are strictly perpendicular to each other. They develop with the increasing applied strain amplitude. The formation of DBI and DBII was considered as being the result of the
.
Acknowledgements This work was financially supported by the National Nature Science Foundation of China (NSFC) under Grant No. 19392300-4. The authors are grateful for this support. References [1] C. Laird, P. Charsley, H. Mughrabi, Mater. Sci. Eng. A81 (1986) 433. [2] Z.S. Basinski, S.J. Basinski, Prog. Mater. Sci. 36 (1992) 89. [3] H. Mughrabi, Mater. Sci. Eng. 33 (1978) 207. [4] N.Y. Jin, Philos. Mag. A 48 (1983) 33. [5] N.Y. Jin, A.T. Winter, Acta Metall. 32 (1984) 989. [6] B. Gong, Z.G. Wang, Y.W. Zhang, Mater. Sci. Eng. A 194 (1995) 171. [7] B. Gong, Z.R. Wang, Z.G. Wang, Y.W. Zhang, Mater. Sci. Eng. A 210 (1996) 94. [8] B. Gong, Z.R. Wang, Z.G. Wang, Acta Mater. 45 (1997) 1365. [9] R. Wang, H. Mughrabi, Mater. Sci. Eng. 63 (1984) 147. [10] A.T. Winter, Philos. Mag. 30 (1974) 715. [11] T.K. Lepisto, V.T. Kuokkala, P.O. Kettunen, Scripta Metall. 18 (1984) 245. [12] T.K. Lepisto, V.T. Kuokkala, P.O. Kettunen, Mater. Sci. Eng. 81 (1986) 457. [13] X.W. Li, Z.G. Wang, G.Y. Li, S.D. Wu, S.X. Li, Acta Mater. 46 (1998) 4497. [14] T.K. Lepiso, P.O. Kettunen, Mater. Sci. Eng. 83 (1986) 1. [15] C.S. Barrett, L.H. Levenson, Trans. Metall. Soc. AIME, 135 (1939) 327; 137 (1940) 112. [16] R.K.W. Honeycombe, J. Inst. Met. 80 (1951) 45. [17] E.A. Calnan, Acta Crystall. 5 (1952) 557.
Cyclic deformation behavior of double-slip-oriented copper single crystals I: coplanar double slip orientation on 011-1( 11 side of the stereographic triangle X.W. Li *, Z.G. Wang, S.X. Li State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Academia Sinica, 72 Wenhua Road, Shenyang 110015, People’s Republic of China Received 2 June 1998; received in revised form 7 September 1998
Abstract The cyclic deformation behaviors of [2( 33] coplanar double-slip-oriented and [4( 18 41] single-slip-oriented copper single crystals were investigated at constant plastic shear strain amplitude gpl in the range of about 10 − 4 –10 − 2 at ambient temperature in air. It was revealed that the cyclic deformation behavior of copper single crystal oriented on the 011-1( 11 side is distinctly dissimilar from that on the 001-1( 11 and 001-011 sides in the stereographic triangle. The plot of initial hardening rate u0.2 against gpl of [2( 33] crystal exhibits two regions as presented for single-slip-oriented crystals. The critical strain amplitude ( :3.5 ×10 − 3), corresponding to the occurrence of the secondary hardening stage in the cyclic hardening curve of the [2( 33] crystal, was found to be an intermediate value between that for single-slip-oriented single crystals and polycrystals. The result shows that the cyclic hardening behavior of the [2( 33] crystal, as compared with that of single-slip-oriented crystals, is more close to that of polycrystals. Instead of a clear plateau, the cyclic stress–strain (CSS) curves of the [2( 33] crystals shows a quasi-plateau over the range of about 3.0 ×10 − 4 –2.0× 10 − 3, which would be greatly attributed to the mode of dislocation interactions between slip systems operating in the crystal. The habit plane of two types of deformation bands DBI and DBII, formed in the cyclically deformed [2( 33] crystal, are perpendicular to each other strictly, and they develop with increasing applied strain amplitude. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Crystals; Double-slip-oriented; Cyclic deformation; Copper
1. Introduction In the past three decades, the interest has been focused on the investigation of cyclic deformation mechanisms in copper single crystals oriented for single slip in order to explore fatigue behavior of f.c.c. metals [1,2]. It is well known that three distinct regimes exist for the cyclic saturation stresses of single-slip-oriented crystals. In the second regime (6×10 − 5 5gpl 5 7.5× 10 − 3), the cyclic stress – strain (CSS) curve exhibits an extended plateau wherein the saturation stress is nearly independent of applied plastic strain amplitude gpl [3]. However, systematic work on the cyclic deformation behavior of double-slip-oriented crystals is still rather * Corresponding address. Tel.: + 86-2423-843531; fax: + 86-243891320; e-mail: [email protected].
limited. In the stereographic triangle shown in Fig. 1, the three sides correspond to quite different double-slip orientations with differently active slip systems and corresponding dislocation reactions during cyclic deformation. Jin and Winter [4,5] reported a preliminary
Fig. 1. Stereographic triangle showing the orientations of copper single crystals involved in this paper.
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 8 ) 0 0 9 7 4 - 5
X.W. Li et al. / Materials Science and Engineering A260 (1999) 132–138
result of the cyclic deformation response and dislocation structures of copper single crystals with [1( 12], [1( 22] and [012] double-slip orientations on the three sides of the stereographic triangle at one strain amplitude of 3.0×10 − 3. In recent years, Gong et al. [6,7] investigated the cyclic deformation behavior of [034] and [1( 17] oriented copper single crystals in a wide range of strain amplitude. An obviously different cyclic deformation behavior was found between [034] and [1( 17] crystals and single-slip-oriented crystals. Nevertheless, the cyclic deformation behavior of copper single crystal oriented for coplanar double slip on 011-1( 11 side is still not well understood. To comprehensively understand the effect of crystallographic orientation and dislocation interaction mode on the cyclic deformation behavior of copper single crystals oriented for double slip, the present work studied systematically the cyclic deformation behavior of [2( 33] coplanar double-slip-oriented copper single crystals at a wide range of plastic strain amplitude of 1.3× 10 − 4 –7.5×10 − 3. Single-slip-oriented [4( 18 41] copper single crystals were also studied for comparison.
2. Experimental procedures Single crystals were grown from OFHC copper of 99.999% purity by the Bridgman technique. The dimensions of the fatigue specimens are 7×7 ×70 mm3, with a gauge section of 7 × 5×16 mm3 for the [2( 33] crystals, and 6× 6 ×60 mm3, with a gauge section of 6×4×16 mm3 for the [4( 18 41] crystals. The orientation of the specimens was determined by the Laue back-reflection technique with an accuracy within 9 2°. Before the fatigue tests, the specimens were an-
Fig. 2. The cyclic hardening curves of the [2( 33] crystals at different strain amplitudes.
133
nealed at 800°C for 2 h in vacuum, and then electro-polished to produce a strain-free and mirrorlike surface for microscopic observations. Fatigue tests were performed in symmetric tension– compression at room temperature in air using a Shimadzu servo–hydraulic testing machine. A triangular waveform signal with a frequency of 0.05–0.4 Hz was used for the constant plastic strain control. Stress– strain hysteresis loops were registered on an X –Y recorder. All specimens were deformed cyclically up to the occurrence of saturation. Some of the [4( 18 41] crystals were continuously cycled at successively increased gpl. After the fatigue tests, the slip features of the specimen surfaces were carefully observed by optical microscopy and scanning electron microscopy (SEM).
3. Results
3.1. Cyclic hardening Fig. 2 shows cyclic hardening curves of the [2( 33] copper single crystals deformed at different strain amplitudes. Fatigue testing conditions and data of cyclic hardening and saturation are listed in Table 1, where gpl,cum (gpl,cum = 4Ngpl, N is the total cyclic number) is the cumulative plastic strain, u0.2 is the initial hardening rate (u0.2 = Dt/Dgpl,cum, Dgpl,cum = 0.2), ts is the shear saturation stress, tmax is the maximum shear stress, and tmax/ts is a parameter describing cyclic softening behavior. It can be seen from Fig. 2 that, under a lower strain amplitude (gpl = 1.3× 10 − 4), the shear stress in the specimen increases slowly with increasing cyclic number and finally develops into a saturation state. For the intermediate strain amplitudes (gpl = 2.4×10 − 4 – 1.7× 10 − 3), the hardening curves exhibit a clear stress overshooting stage. The parameter tmax/ts in Table 1 does reflect the extent of overshooting. At higher strain amplitudes (gpl ] 3.5× 10 − 3), the hardening curves exhibit a slight softening after the stress reaches a first maximum, subsequently a slow secondary hardening process sustains to an occurrence of a pseudosaturation state. The plots of u0.2 against gpl of the [2( 33] and [4( 18 41] crystals are shown in Fig. 3. The results for the [034] and [1( 17] double-slip-oriented copper single crystals [6] are also included for comparison. It is clearly shown that the curve of u0.2 − gpl for the [2( 33] crystal obviously exhibits two ranges as presented for the [4( 18 41] and [034] crystals. The initial hardening rate, u0.2, of the [2( 33] crystals, which is nearly independent of gpl below 2.0× 10 − 3, is much lower than that of the [1( 17] crystals, but close to that of the [034] and [4( 18 41] crystals.
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Table 1 Fatigue testing conditions and data for [2( 33] and [4( 18 41] copper single crystals Orientation
Specimen No.
gpl
Cyclic No.
gpl,cum
u0.2 (MPa)
ts (MPa)
tmax (MPa)
tmax/ts
[2( 33]
1 2 3 4 5 6 7 8 9
1.3×10−4 2.4×10−4 3.4×10−4 6.2×10−4 9.2×10−4 1.7×10−3 3.5×10−3 5.3×10−3 7.5×10−3
65 000 45 600 32 000 22 250 12 000 6000 4700 10 200 17 500
33.8 43.8 43.5 55.2 44.2 40.8 65.8 216.2 526.8
10.2 10.5 12.8 13.9 14.6 15.1 24.9 38.2 46.1
25.0 28.9 30.1 30.9 31.7 32.5 33.5 35.4 37.2
25.0 30.4 31.4 34.3 34.5 34.6 33.5 35.4 37.8
1.00 1.05 1.04 1.11 1.09 1.06 1.00 1.00 1.02
[4( 18 41]
1
1.7×10−4 3.3×10−4 8.6×10−4 1.3×10−3 1.6×10−3 2.5×10−3 3.6×10−3 4.5×10−3 6.5×10−3 7.7×10−3
46 000 14 000 23 400 19 600 6500 9700 3500 3600 1400 2100
31.3 49.8 80.5 182.4 41.6 138.6 50.4 64.8 101.2 165.9
8.4 – 9.0 – 14.8 – 27.1 30.5 – –
27.4 27.2 28.0 28.2 27.6 27.6 27.5 29.0 29.8 31.2
31.2 – 31.0 – 27.6 – 27.7 31.9 – –
1.14 – 1.11 – 1.00 – 1.01 1.10 – –
2 3 4 5
An increase in gpl beyond 2.0× 10 − 3 causes a rapid increase in u0.2 for the four oriented crystals.
3.2. Cyclic stress– strain cur6e
corresponding stress is slightly higher than that of the average plateau stress (27.7 MPa) of the [034] crystal. The CSS curve for the [1( 17] crystal is quite different from that of the other three crystals. The saturation shear stress increases monotonously with increasing gpl.
The CSS curves of [4( 18 41], [2( 33], [034], and [1( 17] are shown in Fig. 4. The curve for the [4( 18 41] crystal shows a clear plateau in the range of 1.7× 10 − 4 B gpl B7.0× 10 − 3 with an average saturation stress of 28.0 MPa, very close to Mughrabi’s results [6]. For the [2( 33] crystal, strictly speaking, its CSS curve does not show a clear plateau, however, the saturation stress of the [2( 33] crystal does not increase strikingly with increasing gpl in the range of 3.0×10 − 4 – 2.0 ×10 − 3, wherein a quasi-plateau seems to be presented, and the
The surface slip features of the [2( 33] crystal specimens cycled to saturation at various plastic strain amplitudes are shown in Fig. 5. In the case of gpl = 1.3× 10 − 4, nearly no slip band was detected. With increasing strain amplitude to 2.4× 10 − 4, only very faint slip lines can be observed in local regions.
Fig. 3. Initial cyclic hardening rate u0.2 versus plastic shear strain amplitude gpl.
Fig. 4. The cyclic stress – strain curves of four differently oriented crystals.
3.3. Surface slip features
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Fig. 5. Surface slip features of the [2( 33] crystals cyclically deformed at various strain amplitudes. (a)gpl =3.4 × 10 − 4;(b) gpl =9.2 ×10 − 4;(c–d) gpl = 3.5 ×10 − 3 and (e–f) gpl = 5.3× 10 − 3.(a–e) viewed from (320) and (d – f) viewed from (6( 9 13).
Thus, a fatigue limit, defined as the critical strain amplitude below which slip bands do not form, can be determined to be about 1.8× 10 − 4 for the [2( 33] crystals. This value is roughly equal to the fatigue limit of 1.7× 10 − 4 for the [001] crystal [8], but much higher than that of 6.0×10 − 5 for single-slip-oriented copper single crystals [3]. When gpl =3.4 ×10 − 4 (see Fig. 5(a)), the primary PSBs begin to appear in some regions and distribute unhomogeneously on the specimen surface. As the strain amplitude increases to 9.2× 10 − 4, these primary PSBs tend to concentrate into a so-called macro-deformation band denoted by DBI, beyond which nearly no slip bands can be observed, as shown in Fig. 5(b). When gpl increases to 3.5× 10 − 3, another type of de-
formation band denoted by DBII, which is also concentrated with primary PSBs, was observed on the specimen surface. DBI develops almost along the primary PSBs while DBII makes a certain angle with the primary PSBs (see Fig. 5(c–d)). With gpl continuously increasing, DBI and DBII develop further and almost occupy the whole specimen surface (see Fig. 5(e–f)).
4. Discussion
4.1. Cyclic hardening Mughrabi [3] classified the curve of u0.2 − gpl into two ranges: when gpl B 10 − 3 (range I%), u0.2 is lower and
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almost independent of gpl; In the range II% (gpl \10 − 3), u0.2 increases notably with increasing gpl. Gong et al. [6] reported a quite similar hardening behavior for the [034] crystal. The present study showed that the initial cyclic hardening behavior of the [2( 33] crystal is similar to those of [4( 18 41] single-slip-oriented crystal and the [034] crystal (see Fig. 3). When gpl B2.0 ×10 − 3, the initial hardening rate u0.2 of the [2( 33] crystal is rather low and almost independent of gpl, indicating that the cyclic hardening of the [2( 33] crystal is mainly associated with the primary dislocation multiplication and their interactions. In the range of higher strain amplitude (gpl \2.0× 10 − 3), u0.2 increases rapidly with increasing gpl. Under these circumstances, the coplanar slip system might operate generously, leading to a large-scale dislocation interaction between primary and coplanar slip systems. Moreover, it is clear from Fig. 3 that the curve of u0.2 −gpl for the [2( 33] crystal is very close to that for the [034] crystal and much lower than that for the [1( 17] crystal, which may be attributed to the differences in active slip systems and their corresponding dislocation reactions in these three crystals. For the [1( 17] crystal, a strong interaction between primary and conjugate systems gives Lomer – Cottrell locks, causing a much higher value of u0.2, while the dislocation interactions in the [2( 33] and [034] crystals form new glissile coplanar dislocations and sessile jogs, respectively. These two kinds of dislocation interactions are relatively weak, thus leading to a lower value of u0.2.
4.2. Secondary cyclic hardening Wang and Mughrabi [9] have investigated the secondary cyclic hardening in fatigued copper monocrystals and polycrystals. They found that the occurrence of secondary cyclic hardening stage closely corresponds to the slow bulk microstructural changes, leading ultimately to the formation of a cell structure. In general, the secondary cyclic hardening stage in single-slip-oriented crystals is observable only when gpl ]4.2 × 10 − 3; while in polycrystals, secondary cyclic hardening becomes clearly evident at an earlier stage and a lower gpl of about 2.0×10 − 3. In the present [2( 33] crystals, it was noted that a slight secondary hardening already occurs after cycling for about 103 cycles at a plastic strain amplitude gpl of 3.5 × 10 − 3, and an increase in the shear stress amplitude reaches about 2.8% (see Fig. 2). It is obvious that the value of 3.5 ×10 − 3 is an intermediate one between that of single-slip-oriented crystals and polycrystals, which seems to show that the cyclic hardening behavior of the [2( 33] double-slip-oriented crystal is more close to those of polycrystals than those of single-slip-oriented crystals. When gpl ]5.3 × 10 − 3, the secondary cyclic hardening of the [2( 33] crystals becomes more notable, and the increase in the shear stress reaches about 7.5%, whereas an only 5.5% in-
crease in shear stress was observed for single-slip-oriented crystals at a strain amplitude gpl of 7.5×10 − 3 [9]. This comparison further indicated that the secondary cyclic hardening in the [2( 33] double-slip-oriented crystal appears to be more pronounced as compared to that in single-slip-oriented crystal. The secondary cyclic hardening should be associated with an increase in the activity of the secondary slip systems in single crystals. In the [2( 33] crystals, the coplanar secondary slip system is easy to operate especially at higher strain amplitudes. Besides, the interactions between primary and coplanar dislocations would result readily in the formation of cell structures. Therefore, the phenomenon mentioned above is likely to understand.
4.3. Cyclic stress–strain cur6e It is well known that the CSS curve of single-slip-oriented copper single crystals exhibits a plateau in the strain amplitude range of 6.0×10 − 5 –7.5×10 − 3, and the plateau saturation shear stress ts is about 28 MPa. Winter [10] has proposed a two-phase model to explain the existence of plateau region in the CSS curve for single-slip-oriented crystals. It is now generally accepted that the occurrence of saturation stress plateau is closely related to the formation of PSBs ladder structures. For the [2( 33] crystals, the second highest Schmid factor occurs on the (111)[1( 10] slip system, which has the same slip plane as the primary slip system. Accordingly, the coplanar slip system is likely to operate and participate in deformation together with the primary slip system, causing cell structures formation and suppressing the occurrence of PSBs ladder structures. In addition, the scale of the cell structures may change with varying plastic strain amplitude. These might be essential reasons for the non-existence of a clear plateau. Lepisto et al. [11,12] observed the dislocation structures in cyclically deformed [1( 11] multiple-slip-oriented copper single crystals at a plastic strain amplitude gpl of 1.4× 10 − 3. It was found that the cell structure formed in the [1( 11] crystals exhibits PSBs with ladder-like features. The dislocation structure formed in the [2( 33] crystals might show some similarities to that of the [1( 11] crystals because the [2( 33] orientation is close to the [1( 11] orientation. So, the occurrence of a cell structure with ladder-like features would be expected in cyclically deformed [2( 33] crystals. This type of cell structures is favorable for accommodating much more plastic strain so that the saturation stress does not increase notably with the increasing gpl, leading to the presence of a quasi-plateau. A detailed studies of dislocation structures in cyclically deformed [2( 33] is being undertaken and the results will be reported elsewhere.
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In summary, quite different plateau behaviors in the CSS curve are expected to be observed in cyclically deformed copper single crystals oriented for different double slips on the different sides (011/1( 11, 001/1( 11 and 001/011) of the stereographic triangle. The plateau region (10 − 4 –4.3× 10 − 3) for the [034] crystal becomes shorter as compared with that for single-slip-oriented crystals, while the CSS curve of the [1( 17] crystal shows almost no plateau region. In between the results of the [034] and [1( 17] crystals, a quasi-plateau in the CSS curve occurs for the [2( 33] crystal. Consequently, concerning different double-slip-oriented copper single crystals, the occurrence or disappearance of a plateau in CSS curve mainly depends upon the inherent slip characteristics and the mode of dislocation interaction between slip systems in the crystal. For the crystals with orientations located on the 011/1( 11 side of the stereographic triangle, the transition from the occurrence of a clear plateau region (1.1 × 10 − 4 – 7.2 × 10 − 3) in [011] multiple-slip-oriented crystals [13] to the disappearance of a plateau in [1( 11] multiple-slip-oriented crystals [14] is linked up through the presence of a quasi-plateau in coplanar double-slip-oriented crystals.
4.4. Deformation bands (I, II) Most of the previous work on deformation bands (DBs) are mainly based on unidirectional deformation [15–17]. In some of the recent investigations [6,8,13], it was found that DBs seems to be a general phenomenon in cyclically deformed copper single crystals oriented for double or multiple slip. Gong et al. [8] suggested that the poor reversibility of slip may be responsible for the formation of DBs. We [13] suggested that the formation of DBI and DBII in cyclically deformed [011] multiple-slip-oriented crystals results from the local irreversible rotation of crystal which exists during symmetrical push – pull loading. In the present work, as found out by SEM observation, the PSBs in DBII formed at gpl of 1.7× 10 − 3 extruded uniformly from the crystal surface, not producing a heavy plastic deformation (see Fig. 6(a)), while the PSBs in DBII formed at gpl of 5.3 ×10 − 3 caused serious disruption of the whole initially smooth surface, and some microcracks nucleated along the PSBs in DBs (see Fig. 6(b)). Accordingly, like PSBs, DBs develop with increasing applied strain amplitude. Fig. 7 shows schematically the surface orientations of the fatigue specimen and typical surface traces made by favorable slip planes as well as deformation bands observed in the [2( 33] crystal. The habit planes of DBI and DBII were determined by a simple crystallographic calculation from Fig. 7 to be (0.65 0.57 0.50) and ( − 0.44 − 0.25 0.86), respectively. It is obvious that the habit plane of DBI is close to the primary slip plane (111), and the habit plane of DBII is close to the
Fig. 6. SEM micrographs of PSB features in DBII at different strain amplitudes.(a) gpl =1.7 × 10 − 3; and (b) gpl =5.3 × 10 − 3. View from (6 9( 13).
conventional kink plane (1( 01). Both of them are strictly perpendicular to each other. The two types of DBs found here are quite similar to that found in [011] crystals [13]. Thus, it was believed that the formation of the two types of DBs formed in the [2( 33] crystals could also be interpreted as being the result of the local irreversible rotation of crystal, meanwhile the results above further confirmed the feasibility of the explanation to the formation of DBI and DBII in view of the classical crystallographic deformation geometry.
Fig. 7. Illustration of surface orientations, slip planes and deformation bands of [2( 33] crystal.
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local irreversible rotation of crystal which exists during symmetrical push–pull loading.
5. Conclusions Based on the experimental results and discussion above, the following conclusions can be drawn. 1. Similar to the result of the [4( 18 41] single-slip-oriented crystal, the plot of initial cyclic hardening rate u0.2 against plastic strain amplitude gpl for the [2( 33] double-slip-oriented copper single crystal exhibits obvious two ranges. For gpl B2.0 × 10 − 3, u0.2 of the [2( 33] crystal is rather low and almost independent of gpl. When gpl \2.0 ×10 − 3, u0.2 increases notably with increasing gpl. 2. The secondary cyclic hardening occurs during the cyclic hardening process of the [2( 33] crystal when gpl ]3.5× 10 − 3. This critical plastic strain amplitude of 3.5×10 − 3 corresponding to the occurrence of the secondary cyclic hardening for the [2( 33] crystal is lower than that of single-slip-oriented crystals and higher than that of polycrystals. It indicates that the cyclic hardening behavior of the [2( 33] crystal is more close to that of polycrystals as compared with that of single-slip-oriented crystals. 3. The CSS curve of [2( 33] crystal does not show a clear plateau, but a quasi-plateau over the range of about 3.0×10 − 4 −2.0 ×10 − 3. 4. Two types of deformation bands DBI and DBII form on the specimen surface of the [2( 33] crystal, and their habit planes are strictly perpendicular to each other. They develop with the increasing applied strain amplitude. The formation of DBI and DBII was considered as being the result of the
.
Acknowledgements This work was financially supported by the National Nature Science Foundation of China (NSFC) under Grant No. 19392300-4. The authors are grateful for this support. References [1] C. Laird, P. Charsley, H. Mughrabi, Mater. Sci. Eng. A81 (1986) 433. [2] Z.S. Basinski, S.J. Basinski, Prog. Mater. Sci. 36 (1992) 89. [3] H. Mughrabi, Mater. Sci. Eng. 33 (1978) 207. [4] N.Y. Jin, Philos. Mag. A 48 (1983) 33. [5] N.Y. Jin, A.T. Winter, Acta Metall. 32 (1984) 989. [6] B. Gong, Z.G. Wang, Y.W. Zhang, Mater. Sci. Eng. A 194 (1995) 171. [7] B. Gong, Z.R. Wang, Z.G. Wang, Y.W. Zhang, Mater. Sci. Eng. A 210 (1996) 94. [8] B. Gong, Z.R. Wang, Z.G. Wang, Acta Mater. 45 (1997) 1365. [9] R. Wang, H. Mughrabi, Mater. Sci. Eng. 63 (1984) 147. [10] A.T. Winter, Philos. Mag. 30 (1974) 715. [11] T.K. Lepisto, V.T. Kuokkala, P.O. Kettunen, Scripta Metall. 18 (1984) 245. [12] T.K. Lepisto, V.T. Kuokkala, P.O. Kettunen, Mater. Sci. Eng. 81 (1986) 457. [13] X.W. Li, Z.G. Wang, G.Y. Li, S.D. Wu, S.X. Li, Acta Mater. 46 (1998) 4497. [14] T.K. Lepiso, P.O. Kettunen, Mater. Sci. Eng. 83 (1986) 1. [15] C.S. Barrett, L.H. Levenson, Trans. Metall. Soc. AIME, 135 (1939) 327; 137 (1940) 112. [16] R.K.W. Honeycombe, J. Inst. Met. 80 (1951) 45. [17] E.A. Calnan, Acta Crystall. 5 (1952) 557.