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texture on the cyclic stress–strain behavior of polycrystalline copper
Materials Science and Engineering A256 (1998) 18 – 24
Effect of grain size/texture on the cyclic stress–strain behavior of polycrystalline copper T. Luoh, C.P. Chang * Institute of Materials Science and Engineering, Sun Yat-Sen Uni6ersity, Kaohsiung 80424, Taiwan, ROC Received 15 May 1998; received in revised form 21 July 1998
Abstract The cyclic stress–strain behavior of copper with different grain sizes/textures has been studied. The results show that at high plastic strain amplitudes, secondary hardening occurs after the primary hardening stage in small-grained specimens; and cyclic softening occurs after the primary hardening stage in large-grained specimens. At low plastic strain amplitudes, the effect of grain size/texture is small, saturation occurs after the primary hardening stage in all specimens. The secondary hardening found in small-grained specimens is associated with the formation of equiaxed cells. In a small-grained specimen, it contains more twin and grain boundaries and twin steps than a large-grained specimen; these boundaries and twin steps in particular promote secondary slip activity, therefore enhance the formation of equiaxed cells. The cyclic softening found in large-grained specimens is mainly associated with the condensation of loop patches into dense dislocation walls. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Cyclic stress–strain; Grain size/texture; Strain amplitudes
1. Introduction The cyclic stress – strain behavior of fcc metals, especially pure copper, has been intensively studied over the last few decades. When copper single crystals are cyclically deformed along single-slip orientation, at a resolved plastic strain amplitude less than 10 − 2, the stress–strain curve, the so called hardening curve, exhibits a primary hardening stage followed by a saturation stage [1–4]. A short and small amount of softening stage, also called overshooting, prior to saturation has been found by several authors [5 – 7]. Some investigators reported a secondary hardening stage occurred late in the saturation stage prior to fatigue failure [8–10]. Secondary hardening rate is lower than the primary hardening rate. Abel [8] reported softening occurred after the primary hardening stage at several plastic strain amplitudes. When copper single crystals were tested along multiple-slip orientations, the cyclic stress – strain behavior is complicated. Jin and Winter [11] and Jin [12] reported that [1( 12], [012], [1( 22] and [011] oriented crystals show * Corresponding author. [email protected]
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similar stress–strain response as that of single-slip oriented crystals. Villechaise et al. [13] and Lepisto¨ and Kettunen [14] reported that a significant softening stage occurs after the primary hardening stage, when the crystals were cyclically deformed along 111 direction. Villechaise et al. [13] also found prior to fatigue failure, a secondary hardening stage occurred after the softening stage. No saturation stage was found by these authors when copper was tested along 111 direction. The stress–strain behavior of [001] oriented crystals reported by Gong et al. [15] is quite complicated. Their results show that when the crystals were tested at a nominal plastic strain amplitude less than 2.4×10 − 4, only primary hardening and saturation stages exist; when tested at 4.8–6.0× 10 − 4, a significant softening stage occurs after the primary hardening stage, which is followed by a secondary hardening stage; when tested at above 2.4 × 10 − 4, a primary hardening stage is followed by an overshooting softening stage before reaching a saturation stage. Compared to single crystals, research on the cyclic stress–strain behavior of polycrystalline copper appears to be less active. Research on the cyclic behavior of polycrystalline copper has been concentrated on the construction of cyclic stress–strain curve (CSSC), in an
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T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
attempt to correlate it with the CSSC of single crystals. In order to construct a CSSC, most investigators used the so-called incremental step [16], or multiple-step [17] method to obtain the cyclic stress – strain response at several strain amplitudes on one specimen. By this kind of test, the detailed cyclic stress – strain behavior at one strain amplitude cannot be obtained, although it does save a lot of testing time and materials for the construction of a CSSC. Even though, there have been several reports on the cyclic stress – strain behavior of copper polycrystals. Using a grain size of about 150 mm, Rasmussen and Pedersen [18] reported that the cyclic stress–strain behavior of copper polycrystals is similar to that of copper single crystals tested along single-slip orientation, i.e. a saturation stage occurs after the primary hardening stage. The plastic strain amplitudes used by them were between 2.5 ×10 − 4 and 3.0 ×10 − 3. Using a small grain size of 25 mm, Wang and Mughrabi [9] reported that primary hardening and saturation stages were found when tested at plastic strain amplitudes of 1.0–5.0×10 − 4; secondary hardening was found to follow the primary hardening stage when these specimen were tested at plastic strain amplitudes of 1.0–2.0× 10 − 3. Using an exceptionally large grain size of 2 mm, Kuokkala and Kettunen [19] reported the occurrence of primary hardening and saturation stages for specimens tested at a plastic strain amplitude below 8.0 ×10 − 3. When tested at a plastic strain amplitude above 1.5 × 10 − 3, a long term softening stage occurred after the primary hardening stage prior to fatigue failure. Pola´k et al. [20,21] reported the cyclic stress–strain behavior of copper tested at a wide range of plastic strain amplitude, from 3.0 ×10 − 6 to 1.0 ×10 − 2, with a grain size of 50 mm. They found that when the amplitude is below 2.0×10 − 4, primary hardening stage is followed by a softening stage prior to failure; when the amplitude is 5.0×10 − 4, primary hardening stage is followed by a saturation stage prior to failure; when the amplitudes are 1.0 – 2.0×10 − 3, primary hardening stage is followed by a saturation stage, and the saturation stage is followed by a secondary hardening stage prior to failure; when the amplitudes are 5.0 × 10 − 3 and 1.0× 10 − 2, primary hardening stage is followed by a secondary hardening stage prior to failure. Pola´k and Klesnil [22] found similar cyclic stress – strain behavior in copper with 30 mm grain size. From above discussion, it is clear that five kinds of deformation stages, namely primary hardening, overshooting, saturation, softening and secondary hardening, have been identified during cyclic deformation of copper under varies conditions. The dislocation mechanisms responsible for the primary hardening, overshooting and saturation in copper single crystals deformed along single-slip orientation have been thoroughly discussed in some review papers [23 –25]. In
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brief, the primary hardening stage is caused by the accumulation of edge dipole loops into loop patches (veins) which act as obstacles to the motion of dislocations. During cycling, both the number and the size of loop patches increases therefore causing rapid hardening. The overshooting softening is caused by the generation of persistent slip bands (PSBs) which is the result of condensation of loop patches into dipolar walls, a softer structure than the vein structure. The mechanism responsible for the saturation behavior varies at different applied amplitudes. For plastic strain amplitudes less than 6.0× 10 − 5, saturation is caused by the shuttling of screw dislocations in the channels between loop patches and Taylor flipping of edge dislocations in the loop patches; for plastic strain amplitudes between 6.0× 10 − 5 and 8.0× 10 − 3, cyclic deformation localized into PSBs, saturation is caused by a dynamic equilibrium between dislocation multiplication and annihilation in PSBs. The multiplication of dislocations is caused by bowing out of edges from the ladder walls and the dragging-out of edges of glissile screws in the channels. The annihilation of dislocations is the result of cross slip of both screw and edge dislocations. The reason for the occurrence of secondary hardening in both single crystals and ploycrystals has been given by Wang and Mughrabi [9]. Their transmission electron microscopy (TEM) results suggested that the occurrence of secondary hardening was accompanied by an increase of secondary slip activity, which cause the gradual transformation of PSB ladder walls into cells with increasing misorientation. The cell structure is harder than the PSB structure. Villechaise et al. [13] pointed out also that the secondary hardening found in their 111 crystals was associated with the transformation of walls or labyrinth structures into cell structure. Pola´k et al. [20] suggested that either a build up of the forest dislocation density or an activation of slip systems with a lower Schmid factor may cause the secondary hardening found in their polycrystalline copper. They gave no reason for the activation of the slip systems with a lower Schmid factor in the late stage of cyclic deformation. The idea that a build up of the forest dislocation can cause secondary hardening is in line with the conclusion drawn by Wang and Mughrabi [9], since the increase of forest dislocations will lead to the formation of cells. Although cyclic softening has been found in both single crystals and polycrystals, the reason for the occurrence of cyclic softening is not quite clear. Villechaise et al. [13] found {100} slip lines were associated with cyclic softening in the surfaces of their 111 copper crystals, they therefore suggested that cyclic softening is due to the breakdown of the Lomer–Cottrell locks and the subsequent {100} slip. The cyclic softening found in [001] copper crystals by Gong et al. [15] was attributed to the formation of a kind of slip
T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
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bands found on their specimen surfaces. The structure of this band was not identified. Several mechanisms have been proposed by Pola´k et al. [20–22] for the cyclic softening found in their finegrained copper at very low plastic strain amplitudes. They suggested that (a) the localization of slip into PSBs, or (b) the condensation of dislocation structure, or (c) the reduction of slip systems within a grain may cause the cyclic softening. Mechanism (b) was later excluded by Pola´k et al. [21] as a possible softening mechanism, since they failed to find the change of dislocation structure during the softening stage. It is intuitively believed that the cyclic stress–strain behavior of a polycrystal should depend on its grain size, however from above discussion, it appears to us that studies on the effect of grain size on the cyclic stress–strain behavior of polycrystals is lacking. The aim of the present paper is to report some of our results in this field.
2. Experimental details Standard fatigue test specimens with 6.25 mm gauge diameter, 27 mm gauge length for low plastic strain amplitudes (opl B 10 − 4), and 15 mm gauge length for other plastic strain amplitudes, were machined from extruded rods of oxygen-free high conductivity copper with 99.99% purity. Before fatigue test, specimens were annealed under vacuum to give grain sizes of 30, 120 and 260 mm. Grain size was measured by standard intersection method, twin boundaries were included in the counting of intersections. After annealing, the specimens were first mechanically-polished then chemicallypolished in a solution of equal parts of HNO3, HPO4, and CH3COOH at room temperature. Fatigue tests were carried out under constant plastic strain control mode by a servohydraulic Instron 1332 fitted with an external computer-controlled system. Strain was measured by an extensometer of 10 mm (for opl \10 − 4) or 25 mm (for opl B10 − 4) gauge length. A strain rate of 2×10 − 3 s − 1 was used. The plastic strain amplitude is equal to half the width of the hysteresis loop, and the range used is between 4.0× 10 − 5 and 8.0×10 − 3. TEM thin foils were first sliced from the gauge part of the test pieces, then mechanically thinned down to about 200 mm thick and polished by the standard twin-jet method. The electro-polishing solution used was the Struers D-2 electrolyte, polished at 8°C, 7 V. Transmission electron microscopy was carried out using a Jeol 3010 TEM operated at 300 KV.
Fig. 1. Cyclic stress – strain response of pure copper with a grain size of 30 mm at several plastic strain amplitudes.
specimens with grain sizes of 30, 120 and 260 mm, respectively. Fig. 1 shows that for specimens with a grain size of 30 mm, when opl B 6.4× 10 − 4, the primary hardening stage is followed by a saturation stage; when opl = 1.5× 10 − 3, a short saturation stage can be found after the primary hardening, and a secondary hardening stage after the saturation stage; when opl = 4.0×10 − 3, the primary hardening stage is followed by a secondary hardening stage before failure occurs. For specimens with a grain size of 120 mm, Fig. 2 shows that when opl B 8.0× 10 − 4, only primary hardening and saturation stages occur, when the amplitude is increased, at opl = 2.5× 10 − 3, significant softening occurs after the primary hardening stage. No secondary hardening was found before fatigue failure. When the grain size is 260 mm, at opl B 1.0× 10 − 3, as in specimens with smaller grain sizes, the primary hardening stage is followed by a saturation stage; with increasing amplitude, similar to the 120 mm specimens, significant softening occurs after the primary hardening stage as shown in Fig. 3. In summary, the cyclic stress–strain behavior found in our specimens shows that at low plastic strain amplitudes,
3. Results Figs. 1–3 show the cyclic stress – strain response of
Fig. 2. Cyclic stress – strain response of pure copper with a grain size of 120 mm at several plastic strain amplitudes.
T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
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4. Discussion
Fig. 3. Cyclic stress – strain response of pure copper with a grain size of 260 mm at several plastic strain amplitudes.
the primary hardening stage is followed by a saturation stage; at high plastic strain amplitudes, the primary hardening is followed by a secondary hardening stage in small-grained specimens, and by a softening stage in large-grained specimens. In order to understand the reason for the difference in cyclic stress–strain response of copper with different grain size, dislocation structures were studied by TEM. All observations were carried out in specimens tested until fatigue failure. Fig. 4 shows the dislocation structure of a specimen which has a grain size of 30 mm, tested at opl =1.5 ×10 − 3. In Fig. 4, the specimen has gone through the secondary hardening stage, and cell structure has been developed. Fig. 4(a) shows that a large area is covered by the cell structure, and Fig. 4(b) shows the cells are nearly equiaxed and have misorientation across cell boundaries. Fig. 5 shows the dislocation structure of a specimen which has a grain size of 120 mm, tested at opl =2.5 ×10 − 3. This specimen has gone through the softening stage. From Fig. 5, it can be seen that dense dislocation walls were developed from loop patches, and these walls are virtually parallel to each. In some other areas, this type of walls were found to have misorientation across them. Only a small fraction of the area was found to be covered by cell structure in this specimen. Similar structure was found in specimens with 260 mm grain size, tested at opl = 2× 10 − 3, as shown in Fig. 6(a). Areas which covered by fully developed dense dislocation walls were also found, as shown in Fig. 6(b). These walls have already developed into elongated cells with sharp boundaries, and have misorientation across them. The apparent width of these elongated cells is about the same size as the cells found in Fig. 4(b); however the length of these elongated cells is about 5 – 10 times larger than those cells size. Similar findings of elongated cells were found in specimens with 260 mm grain size, tested at opl = 5.0× 10 − 3, as shown in Fig. 7. Some stains in Fig. 7 are just artifacts produced during polishing.
Mughrabi and Wang [26] have pointed out earlier that textures are easily introduced by the thermomechanical treatments employed to obtain specimens with different grain sizes. In the literature, several authors [16,26] reported 111 –100 fiber texture in their copper specimens. We have checked our specimens by X-ray, and indeed found that the intensity of 111 –100 fiber texture increases with increasing grain size. In the following discussion, the effect of specimens with different grain sizes on the cyclic stress–strain behavior is therefore the effect of both texture and grain size.
Fig. 4. TEM micrographs showing the formation of nearly equiaxed cells which are associated with the occurrence of the secondary hardening stage in specimens with a grain size of 30 mm; opl = 1.5× 10 − 3. Many beam imaging condition.
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T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
Fig. 5. TEM micrograph showing the condensation of loop patches into dense dislocation walls, which are associated with the occurrence of the softening stage in specimens with a grain size of 120 mm; opl = 2.5 × 10 − 3.
From the present results, it can be seen that the effect of grain size/texture on the cyclic stress – strain behavior of polycrystals is profound at high strain amplitudes, opl \ 10 − 3, and has small effect at low strain amplitudes. Our discussion will therefore concentrate on high strain amplitude range. Figs. 1 – 3 show that secondary hardening occurs in specimens with 30 mm grain size, and cyclic softening occurs in specimens with 120–260 mm grain size. The reasons for this will be discussed in term. Our TEM results, Fig. 4, show that secondary hardening is associated with the formation of equiaxed cells in small-grained specimens. This is in agreement with the view of Wang and Mughrabi [9]. The question now is why equiaxed cells are easier to be formed in smallgrained specimens than in large-grained specimens. We believe this is mainly due to small-grained specimens contain more twin and grain boundaries and twin steps. These boundaries and twin steps in particular promote secondary slip activity [27 – 29], so that the formation of cells is easier. Fig. 8 shows an example of the promotion of cell formation at a twin step. In large-grained specimens, the number of twin and grain boundaries and twin step reduces, therefore the formation of equiaxed cells, the hardening factor, becomes less favorable, and secondary hardening is diminished. The condensation of loop patches into dense dislocation walls, as shown in Figs. 5 – 7, starts to cause softening, since dense dislocation walls occupy less volume fraction than loop patches. We notice that the condensation of loop patches into dense dislocation walls occurred over a wide region, rather than localized into a band as in the case of PSB formation. Softening occurs when the condensation of loop patches starts,
softening continues with increasing proportion of loop patches is condensed into walls, meanwhile the misorientation across these walls is gradually built up. In the late softening stage, secondary slip activity increases, the long dislocation-free channels between the walls are subdivided, the walls structure is gradually transformed into elongated cells, as shown in Fig. 6(b). We expect that if the fatigue life is prolonged, the elongated cells will eventually be transformed into equiaxed cells. This means that the softening stage would be followed by a secondary hardening stage before failure, providing the fatigue life is long enough. The formation of PSBs is also a kind of condensation process, and will contribute to softening, as been suggested by Pola´k et al. [21], however we do not think the contribution of this term is significant in the present case, since we found thevolume fraction occupied by PSBs in our specimens was not high.
Fig. 6. TEM micrographs showing the condensation of loop patches into (a) dense dislocation walls and (b) elongated cells, which are associated with the occurrence of the softening stage in specimens with a grain size of 260 mm; opl =2 × 10 − 3. Many beam imaging condition in (b).
T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
Fig. 7. TEM micrograph showing the formation of elongated cells, which are associated with the occurrence of the softening stage in specimens with a grain size of 260 mm, opl = 5.0× 10 − 3. Many beam imaging condition. Note some stains in the micrograph are just artifacts produced during polishing.
When polycrystalline copper is cyclically deformed, grains are often divided into regions containing different primary dislocations, each region is called a ‘vein block’ [30]. Pola´k et al. [21] suggested that during
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cycling, the number of vein blocks reduces, and this may cause softening. We did not find the reduction of vein blocks during cycling in our specimens. It seems difficult to understand why the number of vein blocks would reduce during cycling. Since our large-grained specimens have 111 –100 fiber texture, the softening mechanisms proposed in the literature for 111 and 100 oriented crystals need to be examined. Villechaise et al. [13] proposed that the breakdown of the Lomer–Cottrell locks and the subsequent {100} slip can cause softening. In another paper, the present authors [31] found {100} slip activity during the formation of dislocation-free zones beside grain boundaries in similar fatigued specimens. Since the {100} slip activity found in those specimens was low, if cube slip would cause softening in the present case, it cannot be the dominant mechanism. Wang et al. [32] reported that in [001] oriented crystals, dislocation walls on (001) plane and labyrinth structure were found at opl = 1.8–3.0× 10 − 3, and solely labyrinth structure was found at opl = 4.8–7.2× 10 − 4. We found only small amount of labyrinth structure, and no {100} walls. This indicates that the grains which contribute to the 100 fiber texture in our specimens are not precisely aligned along the cube directions. The crystals used by Gong et al. [15] and Wang et al. [32] are within 9 2° along [001]. The formation of a kind of slip band which cause the softening in 100 crystals suggested by Gong et al. [15] is unlikely to be able to operate in our specimens. The cyclic stress–strain behavior of our 30 mm specimens is similar to the results of Pola´k et al. [20–22] at opl \ 5.0× 10 − 4. For 6.0×10 − 5 B opl B 5.0× 10 − 4, we found saturation after the primary hardening stage, but they found softening after the primary hardening stage. The discrepancy may due to different texture in their specimens and/or some other metallurgical factors, since our fatigue specimens were machined from extruded rods, and theirs were from cold rolled specimens. It need to be emphasized that in the present research, specimens with different grain sizes are associated with different annealing textures; the different cyclic stress– strain behaviors found in specimens with different grain sizes are therefore the effect of both grain size and texture.
5. Conclusions
Fig. 8. TEM micrographs showing that the formation of cell structure is promoted at a twin step. opl = 4.0× 10 − 4, the cumulative plastic strain is 10.
The cyclic stress–strain behavior of polycrystalline copper has been found to be dependent on grain size/ texture. At high plastic strain amplitudes, opl \ 10 − 3, secondary hardening occurs after the primary hardening stage in small-grained specimens; and cyclic soften-
T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
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ing occurs after the primary hardening stage in largegrained specimens. At low plastic strain amplitudes, 10 − 5 B opl B 10 − 3, the effect of grain size/texture is small, saturation occurs after the primary hardening stage in all specimens. The secondary hardening found in small-grained specimens is associated with the formation of equiaxed cells. In a small-grained specimen, it contains more twin and grain boundaries and twin steps than a largegrained specimen, these boundaries and twin steps in particular promote secondary slip activity, therefore enhance the formation of equiaxed cells. The cyclic softening found in large-grained specimens is mainly associated with the condensation of loop patches into dense dislocation walls.
Acknowledgements The authors would like to express their thanks to the National Science Council for the financial support of this work through contracts NSC-81-0405-E-110-520 and NSC-83-0405-E-110-013.
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[6] Z.S. Basinski, R. Pascual, S.J. Basinski, Acta Metall. 31 (1983) 591. [7] H. Mughrabi, Mater. Sci. Eng. 33 (1978) 207. [8] A. Abel, Mater. Sci. Eng. 36 (1978) 117. [9] R. Wang, H. Mughrabi, Mater. Sci. Eng. 63 (1984) 147. [10] R. Wang, H. Mughrabi, S. McGovern, M. Rapp, Mater. Sci. Eng. 65 (1984) 219. [11] N.J. Jin, A.T. Winter, Acta Metall. 32 (1984) 989. [12] N.J. Jin, Phil. Mag. Lett. 56 (1987) 23. [13] P. Villechaise, J. Mendez, P. Violan, Acta Metall. Mater. 39 (1991) 1683. [14] T.K. Lepisto¨, P.O. Kettunen, Mater. Sci. Eng. 83 (1986) 1. [15] B. Gong, Z. Wang, Z. Wang, Acta Mater. 45 (1997) 1365. [16] L. Llanes, A.D. Rollett, C. Laird, J.L. Bassani, Acta Metall. Mater. 41 (1993) 2667. [17] H. Mughrabi, R. Wang, in: N. Hansen, A. Horsewell, T. Leffers, H. Lilholt (Eds.), Deformation of Polycrystals, Riso National Laboratory, Roskilde, Denmark, 1981, p. 87. [18] K.V. Rasmussen, O.B. Pedersen, Acta Metall. 28 (1980) 1467. [19] V.T. Kuokkala, P. Kettunen, Acta Metall. 33 (1985) 2041. [20] J. Pola´k, K. Obrtlı´k, M. Ha´jek, A. Vas' ek, Mater. Sci. Eng. A151 (1992) 19. [21] J. Pola´k, K. Obrtlı´k, M. Ha´jek, A. Vas' ek, Mater. Sci. Eng. A154 (1992) 15. [22] J. Pola´k, M. Klesnil, Mater. Sci. Eng. 63 (1984) 189. [23] Z.A. Basinski, S.J. Basinski, Prog. Mat. Sci. 36 (1992) 89. [24] H. Mughrabi, in: M.H. Loretto (Ed.), Dislocations and Properties of Real Materials, The Institute of Metals, London, 1985, p. 244. [25] C. Laird, in: F.R.N. Nabarro (Ed.), Dislocations in Solids, vol. 6, North-Holland, Amsterdam, 1983, p. 56. [26] H. Mughrabi, R. Wang, in: P. Lukas, J. Pola´k (Eds.), Basic Mechanisms in Fatigue of Metals, Elsevier, UK, 1988, p. 1. [27] R.C. Boettner, J.A. Liu, Y.C. Liu, Phil. Mag. 10 (1964) 95. [28] L. Llanes, C. Laird, Mater. Sci. Eng. A157 (1992) 21. [29] P. Peralta, L. Llanes, C. Laird, Phil. Mag. 70A (1994) 219. [30] T. Luoh, H.T. Tai, C.P. Chang, Phil. Mag. (1998) (in press). [31] T. Luoh, C.P. Chang, Acta Mater. 44 (1996) 2683. [32] Z. Wang, B. Gong, Z. Wang, Acta Mater. 45 (1997) 1379.
Effect of grain size/texture on the cyclic stress–strain behavior of polycrystalline copper T. Luoh, C.P. Chang * Institute of Materials Science and Engineering, Sun Yat-Sen Uni6ersity, Kaohsiung 80424, Taiwan, ROC Received 15 May 1998; received in revised form 21 July 1998
Abstract The cyclic stress–strain behavior of copper with different grain sizes/textures has been studied. The results show that at high plastic strain amplitudes, secondary hardening occurs after the primary hardening stage in small-grained specimens; and cyclic softening occurs after the primary hardening stage in large-grained specimens. At low plastic strain amplitudes, the effect of grain size/texture is small, saturation occurs after the primary hardening stage in all specimens. The secondary hardening found in small-grained specimens is associated with the formation of equiaxed cells. In a small-grained specimen, it contains more twin and grain boundaries and twin steps than a large-grained specimen; these boundaries and twin steps in particular promote secondary slip activity, therefore enhance the formation of equiaxed cells. The cyclic softening found in large-grained specimens is mainly associated with the condensation of loop patches into dense dislocation walls. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Cyclic stress–strain; Grain size/texture; Strain amplitudes
1. Introduction The cyclic stress – strain behavior of fcc metals, especially pure copper, has been intensively studied over the last few decades. When copper single crystals are cyclically deformed along single-slip orientation, at a resolved plastic strain amplitude less than 10 − 2, the stress–strain curve, the so called hardening curve, exhibits a primary hardening stage followed by a saturation stage [1–4]. A short and small amount of softening stage, also called overshooting, prior to saturation has been found by several authors [5 – 7]. Some investigators reported a secondary hardening stage occurred late in the saturation stage prior to fatigue failure [8–10]. Secondary hardening rate is lower than the primary hardening rate. Abel [8] reported softening occurred after the primary hardening stage at several plastic strain amplitudes. When copper single crystals were tested along multiple-slip orientations, the cyclic stress – strain behavior is complicated. Jin and Winter [11] and Jin [12] reported that [1( 12], [012], [1( 22] and [011] oriented crystals show * Corresponding author. [email protected]
Fax:
+886
7
5254099;
e-mail:
similar stress–strain response as that of single-slip oriented crystals. Villechaise et al. [13] and Lepisto¨ and Kettunen [14] reported that a significant softening stage occurs after the primary hardening stage, when the crystals were cyclically deformed along 111 direction. Villechaise et al. [13] also found prior to fatigue failure, a secondary hardening stage occurred after the softening stage. No saturation stage was found by these authors when copper was tested along 111 direction. The stress–strain behavior of [001] oriented crystals reported by Gong et al. [15] is quite complicated. Their results show that when the crystals were tested at a nominal plastic strain amplitude less than 2.4×10 − 4, only primary hardening and saturation stages exist; when tested at 4.8–6.0× 10 − 4, a significant softening stage occurs after the primary hardening stage, which is followed by a secondary hardening stage; when tested at above 2.4 × 10 − 4, a primary hardening stage is followed by an overshooting softening stage before reaching a saturation stage. Compared to single crystals, research on the cyclic stress–strain behavior of polycrystalline copper appears to be less active. Research on the cyclic behavior of polycrystalline copper has been concentrated on the construction of cyclic stress–strain curve (CSSC), in an
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T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
attempt to correlate it with the CSSC of single crystals. In order to construct a CSSC, most investigators used the so-called incremental step [16], or multiple-step [17] method to obtain the cyclic stress – strain response at several strain amplitudes on one specimen. By this kind of test, the detailed cyclic stress – strain behavior at one strain amplitude cannot be obtained, although it does save a lot of testing time and materials for the construction of a CSSC. Even though, there have been several reports on the cyclic stress – strain behavior of copper polycrystals. Using a grain size of about 150 mm, Rasmussen and Pedersen [18] reported that the cyclic stress–strain behavior of copper polycrystals is similar to that of copper single crystals tested along single-slip orientation, i.e. a saturation stage occurs after the primary hardening stage. The plastic strain amplitudes used by them were between 2.5 ×10 − 4 and 3.0 ×10 − 3. Using a small grain size of 25 mm, Wang and Mughrabi [9] reported that primary hardening and saturation stages were found when tested at plastic strain amplitudes of 1.0–5.0×10 − 4; secondary hardening was found to follow the primary hardening stage when these specimen were tested at plastic strain amplitudes of 1.0–2.0× 10 − 3. Using an exceptionally large grain size of 2 mm, Kuokkala and Kettunen [19] reported the occurrence of primary hardening and saturation stages for specimens tested at a plastic strain amplitude below 8.0 ×10 − 3. When tested at a plastic strain amplitude above 1.5 × 10 − 3, a long term softening stage occurred after the primary hardening stage prior to fatigue failure. Pola´k et al. [20,21] reported the cyclic stress–strain behavior of copper tested at a wide range of plastic strain amplitude, from 3.0 ×10 − 6 to 1.0 ×10 − 2, with a grain size of 50 mm. They found that when the amplitude is below 2.0×10 − 4, primary hardening stage is followed by a softening stage prior to failure; when the amplitude is 5.0×10 − 4, primary hardening stage is followed by a saturation stage prior to failure; when the amplitudes are 1.0 – 2.0×10 − 3, primary hardening stage is followed by a saturation stage, and the saturation stage is followed by a secondary hardening stage prior to failure; when the amplitudes are 5.0 × 10 − 3 and 1.0× 10 − 2, primary hardening stage is followed by a secondary hardening stage prior to failure. Pola´k and Klesnil [22] found similar cyclic stress – strain behavior in copper with 30 mm grain size. From above discussion, it is clear that five kinds of deformation stages, namely primary hardening, overshooting, saturation, softening and secondary hardening, have been identified during cyclic deformation of copper under varies conditions. The dislocation mechanisms responsible for the primary hardening, overshooting and saturation in copper single crystals deformed along single-slip orientation have been thoroughly discussed in some review papers [23 –25]. In
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brief, the primary hardening stage is caused by the accumulation of edge dipole loops into loop patches (veins) which act as obstacles to the motion of dislocations. During cycling, both the number and the size of loop patches increases therefore causing rapid hardening. The overshooting softening is caused by the generation of persistent slip bands (PSBs) which is the result of condensation of loop patches into dipolar walls, a softer structure than the vein structure. The mechanism responsible for the saturation behavior varies at different applied amplitudes. For plastic strain amplitudes less than 6.0× 10 − 5, saturation is caused by the shuttling of screw dislocations in the channels between loop patches and Taylor flipping of edge dislocations in the loop patches; for plastic strain amplitudes between 6.0× 10 − 5 and 8.0× 10 − 3, cyclic deformation localized into PSBs, saturation is caused by a dynamic equilibrium between dislocation multiplication and annihilation in PSBs. The multiplication of dislocations is caused by bowing out of edges from the ladder walls and the dragging-out of edges of glissile screws in the channels. The annihilation of dislocations is the result of cross slip of both screw and edge dislocations. The reason for the occurrence of secondary hardening in both single crystals and ploycrystals has been given by Wang and Mughrabi [9]. Their transmission electron microscopy (TEM) results suggested that the occurrence of secondary hardening was accompanied by an increase of secondary slip activity, which cause the gradual transformation of PSB ladder walls into cells with increasing misorientation. The cell structure is harder than the PSB structure. Villechaise et al. [13] pointed out also that the secondary hardening found in their 111 crystals was associated with the transformation of walls or labyrinth structures into cell structure. Pola´k et al. [20] suggested that either a build up of the forest dislocation density or an activation of slip systems with a lower Schmid factor may cause the secondary hardening found in their polycrystalline copper. They gave no reason for the activation of the slip systems with a lower Schmid factor in the late stage of cyclic deformation. The idea that a build up of the forest dislocation can cause secondary hardening is in line with the conclusion drawn by Wang and Mughrabi [9], since the increase of forest dislocations will lead to the formation of cells. Although cyclic softening has been found in both single crystals and polycrystals, the reason for the occurrence of cyclic softening is not quite clear. Villechaise et al. [13] found {100} slip lines were associated with cyclic softening in the surfaces of their 111 copper crystals, they therefore suggested that cyclic softening is due to the breakdown of the Lomer–Cottrell locks and the subsequent {100} slip. The cyclic softening found in [001] copper crystals by Gong et al. [15] was attributed to the formation of a kind of slip
T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
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bands found on their specimen surfaces. The structure of this band was not identified. Several mechanisms have been proposed by Pola´k et al. [20–22] for the cyclic softening found in their finegrained copper at very low plastic strain amplitudes. They suggested that (a) the localization of slip into PSBs, or (b) the condensation of dislocation structure, or (c) the reduction of slip systems within a grain may cause the cyclic softening. Mechanism (b) was later excluded by Pola´k et al. [21] as a possible softening mechanism, since they failed to find the change of dislocation structure during the softening stage. It is intuitively believed that the cyclic stress–strain behavior of a polycrystal should depend on its grain size, however from above discussion, it appears to us that studies on the effect of grain size on the cyclic stress–strain behavior of polycrystals is lacking. The aim of the present paper is to report some of our results in this field.
2. Experimental details Standard fatigue test specimens with 6.25 mm gauge diameter, 27 mm gauge length for low plastic strain amplitudes (opl B 10 − 4), and 15 mm gauge length for other plastic strain amplitudes, were machined from extruded rods of oxygen-free high conductivity copper with 99.99% purity. Before fatigue test, specimens were annealed under vacuum to give grain sizes of 30, 120 and 260 mm. Grain size was measured by standard intersection method, twin boundaries were included in the counting of intersections. After annealing, the specimens were first mechanically-polished then chemicallypolished in a solution of equal parts of HNO3, HPO4, and CH3COOH at room temperature. Fatigue tests were carried out under constant plastic strain control mode by a servohydraulic Instron 1332 fitted with an external computer-controlled system. Strain was measured by an extensometer of 10 mm (for opl \10 − 4) or 25 mm (for opl B10 − 4) gauge length. A strain rate of 2×10 − 3 s − 1 was used. The plastic strain amplitude is equal to half the width of the hysteresis loop, and the range used is between 4.0× 10 − 5 and 8.0×10 − 3. TEM thin foils were first sliced from the gauge part of the test pieces, then mechanically thinned down to about 200 mm thick and polished by the standard twin-jet method. The electro-polishing solution used was the Struers D-2 electrolyte, polished at 8°C, 7 V. Transmission electron microscopy was carried out using a Jeol 3010 TEM operated at 300 KV.
Fig. 1. Cyclic stress – strain response of pure copper with a grain size of 30 mm at several plastic strain amplitudes.
specimens with grain sizes of 30, 120 and 260 mm, respectively. Fig. 1 shows that for specimens with a grain size of 30 mm, when opl B 6.4× 10 − 4, the primary hardening stage is followed by a saturation stage; when opl = 1.5× 10 − 3, a short saturation stage can be found after the primary hardening, and a secondary hardening stage after the saturation stage; when opl = 4.0×10 − 3, the primary hardening stage is followed by a secondary hardening stage before failure occurs. For specimens with a grain size of 120 mm, Fig. 2 shows that when opl B 8.0× 10 − 4, only primary hardening and saturation stages occur, when the amplitude is increased, at opl = 2.5× 10 − 3, significant softening occurs after the primary hardening stage. No secondary hardening was found before fatigue failure. When the grain size is 260 mm, at opl B 1.0× 10 − 3, as in specimens with smaller grain sizes, the primary hardening stage is followed by a saturation stage; with increasing amplitude, similar to the 120 mm specimens, significant softening occurs after the primary hardening stage as shown in Fig. 3. In summary, the cyclic stress–strain behavior found in our specimens shows that at low plastic strain amplitudes,
3. Results Figs. 1–3 show the cyclic stress – strain response of
Fig. 2. Cyclic stress – strain response of pure copper with a grain size of 120 mm at several plastic strain amplitudes.
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4. Discussion
Fig. 3. Cyclic stress – strain response of pure copper with a grain size of 260 mm at several plastic strain amplitudes.
the primary hardening stage is followed by a saturation stage; at high plastic strain amplitudes, the primary hardening is followed by a secondary hardening stage in small-grained specimens, and by a softening stage in large-grained specimens. In order to understand the reason for the difference in cyclic stress–strain response of copper with different grain size, dislocation structures were studied by TEM. All observations were carried out in specimens tested until fatigue failure. Fig. 4 shows the dislocation structure of a specimen which has a grain size of 30 mm, tested at opl =1.5 ×10 − 3. In Fig. 4, the specimen has gone through the secondary hardening stage, and cell structure has been developed. Fig. 4(a) shows that a large area is covered by the cell structure, and Fig. 4(b) shows the cells are nearly equiaxed and have misorientation across cell boundaries. Fig. 5 shows the dislocation structure of a specimen which has a grain size of 120 mm, tested at opl =2.5 ×10 − 3. This specimen has gone through the softening stage. From Fig. 5, it can be seen that dense dislocation walls were developed from loop patches, and these walls are virtually parallel to each. In some other areas, this type of walls were found to have misorientation across them. Only a small fraction of the area was found to be covered by cell structure in this specimen. Similar structure was found in specimens with 260 mm grain size, tested at opl = 2× 10 − 3, as shown in Fig. 6(a). Areas which covered by fully developed dense dislocation walls were also found, as shown in Fig. 6(b). These walls have already developed into elongated cells with sharp boundaries, and have misorientation across them. The apparent width of these elongated cells is about the same size as the cells found in Fig. 4(b); however the length of these elongated cells is about 5 – 10 times larger than those cells size. Similar findings of elongated cells were found in specimens with 260 mm grain size, tested at opl = 5.0× 10 − 3, as shown in Fig. 7. Some stains in Fig. 7 are just artifacts produced during polishing.
Mughrabi and Wang [26] have pointed out earlier that textures are easily introduced by the thermomechanical treatments employed to obtain specimens with different grain sizes. In the literature, several authors [16,26] reported 111 –100 fiber texture in their copper specimens. We have checked our specimens by X-ray, and indeed found that the intensity of 111 –100 fiber texture increases with increasing grain size. In the following discussion, the effect of specimens with different grain sizes on the cyclic stress–strain behavior is therefore the effect of both texture and grain size.
Fig. 4. TEM micrographs showing the formation of nearly equiaxed cells which are associated with the occurrence of the secondary hardening stage in specimens with a grain size of 30 mm; opl = 1.5× 10 − 3. Many beam imaging condition.
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T. Luoh, C.P. Chang / Materials Science and Engineering A256 (1998) 18–24
Fig. 5. TEM micrograph showing the condensation of loop patches into dense dislocation walls, which are associated with the occurrence of the softening stage in specimens with a grain size of 120 mm; opl = 2.5 × 10 − 3.
From the present results, it can be seen that the effect of grain size/texture on the cyclic stress – strain behavior of polycrystals is profound at high strain amplitudes, opl \ 10 − 3, and has small effect at low strain amplitudes. Our discussion will therefore concentrate on high strain amplitude range. Figs. 1 – 3 show that secondary hardening occurs in specimens with 30 mm grain size, and cyclic softening occurs in specimens with 120–260 mm grain size. The reasons for this will be discussed in term. Our TEM results, Fig. 4, show that secondary hardening is associated with the formation of equiaxed cells in small-grained specimens. This is in agreement with the view of Wang and Mughrabi [9]. The question now is why equiaxed cells are easier to be formed in smallgrained specimens than in large-grained specimens. We believe this is mainly due to small-grained specimens contain more twin and grain boundaries and twin steps. These boundaries and twin steps in particular promote secondary slip activity [27 – 29], so that the formation of cells is easier. Fig. 8 shows an example of the promotion of cell formation at a twin step. In large-grained specimens, the number of twin and grain boundaries and twin step reduces, therefore the formation of equiaxed cells, the hardening factor, becomes less favorable, and secondary hardening is diminished. The condensation of loop patches into dense dislocation walls, as shown in Figs. 5 – 7, starts to cause softening, since dense dislocation walls occupy less volume fraction than loop patches. We notice that the condensation of loop patches into dense dislocation walls occurred over a wide region, rather than localized into a band as in the case of PSB formation. Softening occurs when the condensation of loop patches starts,
softening continues with increasing proportion of loop patches is condensed into walls, meanwhile the misorientation across these walls is gradually built up. In the late softening stage, secondary slip activity increases, the long dislocation-free channels between the walls are subdivided, the walls structure is gradually transformed into elongated cells, as shown in Fig. 6(b). We expect that if the fatigue life is prolonged, the elongated cells will eventually be transformed into equiaxed cells. This means that the softening stage would be followed by a secondary hardening stage before failure, providing the fatigue life is long enough. The formation of PSBs is also a kind of condensation process, and will contribute to softening, as been suggested by Pola´k et al. [21], however we do not think the contribution of this term is significant in the present case, since we found thevolume fraction occupied by PSBs in our specimens was not high.
Fig. 6. TEM micrographs showing the condensation of loop patches into (a) dense dislocation walls and (b) elongated cells, which are associated with the occurrence of the softening stage in specimens with a grain size of 260 mm; opl =2 × 10 − 3. Many beam imaging condition in (b).
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Fig. 7. TEM micrograph showing the formation of elongated cells, which are associated with the occurrence of the softening stage in specimens with a grain size of 260 mm, opl = 5.0× 10 − 3. Many beam imaging condition. Note some stains in the micrograph are just artifacts produced during polishing.
When polycrystalline copper is cyclically deformed, grains are often divided into regions containing different primary dislocations, each region is called a ‘vein block’ [30]. Pola´k et al. [21] suggested that during
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cycling, the number of vein blocks reduces, and this may cause softening. We did not find the reduction of vein blocks during cycling in our specimens. It seems difficult to understand why the number of vein blocks would reduce during cycling. Since our large-grained specimens have 111 –100 fiber texture, the softening mechanisms proposed in the literature for 111 and 100 oriented crystals need to be examined. Villechaise et al. [13] proposed that the breakdown of the Lomer–Cottrell locks and the subsequent {100} slip can cause softening. In another paper, the present authors [31] found {100} slip activity during the formation of dislocation-free zones beside grain boundaries in similar fatigued specimens. Since the {100} slip activity found in those specimens was low, if cube slip would cause softening in the present case, it cannot be the dominant mechanism. Wang et al. [32] reported that in [001] oriented crystals, dislocation walls on (001) plane and labyrinth structure were found at opl = 1.8–3.0× 10 − 3, and solely labyrinth structure was found at opl = 4.8–7.2× 10 − 4. We found only small amount of labyrinth structure, and no {100} walls. This indicates that the grains which contribute to the 100 fiber texture in our specimens are not precisely aligned along the cube directions. The crystals used by Gong et al. [15] and Wang et al. [32] are within 9 2° along [001]. The formation of a kind of slip band which cause the softening in 100 crystals suggested by Gong et al. [15] is unlikely to be able to operate in our specimens. The cyclic stress–strain behavior of our 30 mm specimens is similar to the results of Pola´k et al. [20–22] at opl \ 5.0× 10 − 4. For 6.0×10 − 5 B opl B 5.0× 10 − 4, we found saturation after the primary hardening stage, but they found softening after the primary hardening stage. The discrepancy may due to different texture in their specimens and/or some other metallurgical factors, since our fatigue specimens were machined from extruded rods, and theirs were from cold rolled specimens. It need to be emphasized that in the present research, specimens with different grain sizes are associated with different annealing textures; the different cyclic stress– strain behaviors found in specimens with different grain sizes are therefore the effect of both grain size and texture.
5. Conclusions
Fig. 8. TEM micrographs showing that the formation of cell structure is promoted at a twin step. opl = 4.0× 10 − 4, the cumulative plastic strain is 10.
The cyclic stress–strain behavior of polycrystalline copper has been found to be dependent on grain size/ texture. At high plastic strain amplitudes, opl \ 10 − 3, secondary hardening occurs after the primary hardening stage in small-grained specimens; and cyclic soften-
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ing occurs after the primary hardening stage in largegrained specimens. At low plastic strain amplitudes, 10 − 5 B opl B 10 − 3, the effect of grain size/texture is small, saturation occurs after the primary hardening stage in all specimens. The secondary hardening found in small-grained specimens is associated with the formation of equiaxed cells. In a small-grained specimen, it contains more twin and grain boundaries and twin steps than a largegrained specimen, these boundaries and twin steps in particular promote secondary slip activity, therefore enhance the formation of equiaxed cells. The cyclic softening found in large-grained specimens is mainly associated with the condensation of loop patches into dense dislocation walls.
Acknowledgements The authors would like to express their thanks to the National Science Council for the financial support of this work through contracts NSC-81-0405-E-110-520 and NSC-83-0405-E-110-013.
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