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Dislocation structures in fatigued critical and conjugate double-slip-oriented copper single crystals
Materials Science and Engineering A333 (2002) 51 – 59 www.elsevier.com/locate/msea
Dislocation structures in fatigued critical and conjugate double-slip-oriented copper single crystals X.W. Li a,b,*,1, Y. Umakoshi b, B. Gong a, S.X. Li a, Z.G. Wang a a
State Key Laboratory for Fatigue and Fracture of Materials, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China b Department of Materials Science and Engineering, Graduate School of Engineering, Osaka Uni6ersity, 2 -1, Yamada-oka, Suita, Osaka 565 -0871, Japan Received 26 July 2001; received in revised form 30 August 2001
Abstract The dislocation structures induced by cyclic deformation of [017] critical and, [1( 12], [1( 17] conjugate double-slip-oriented Cu single crystals were investigated using transmission electron microscopy (TEM) and electron channeling contrast (ECC) technique in scanning electron microscopy (SEM). It was found that the crystallographic orientation has a notable effect on the dislocation structures in cyclically saturated critical and (or) conjugate double-slip-oriented Cu single crystals. Such an orientation dependence of dislocation structure can account well for the corresponding orientation dependence of the plateau behavior in the cyclic stress–strain (CSS) curve. In cyclic deformation of the [1( 12] crystal, the formation of persistent slip band (PSB) ladder structures is a general phenomenon; PSBs occur even under the low strain amplitude, which is below the plateau region in the CSS curve. The experimental result above indicates that there is not a complete one-to-one correlation between the formation of PSBs and the presence of a plateau region of the CSS curve. In certain double-slip oriented Cu single crystals investigated here, the actual size of microstructures is in fact, found to be changeable with varying strain amplitude, which is one of the main reasons for the disappearance of a clear plateau in the CSS curve of these crystals. For example, the decrease in the width of vein channels with increasing strain amplitude and the absence of PSB ladder structure are the major reason for non-existence of a clear plateau region in the CSS curve of the [1( 17] crystal, while the joint effects of the scale change of the labyrinth structure and the formation of PSB ladder-like structures lead to the occurrence of only a narrow quasi-plateau in the CSS curve of the [017] crystal. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Cu single crystal; Dislocation structure; Conjugate double slip; Critical double slip; Cyclic deformation; Crystallographic orientation
1. Introduction Dislocation structures of fcc crystals created during cyclic deformation have been a subject of strong interest over many years, particularly, since Winter [1] discovered the well-known two-phase structure of dislocation ladders of persistent slip bands (PSBs) and dislocation veins of the matrix in cyclically deformed Cu single crystals oriented for single slip. The dislocation structure in the cyclically deformed Cu single * Corresponding author. Tel.: +81-6-6879-7527; fax: + 81-6-68797495. E-mail address: [email protected] (X.W. Li). 1 Tel.: +86-24-23843531; fax: +86-24-23891320; E-mail: [email protected]
crystals with single-slip orientation has been reported in great numbers and the conclusive results were well reviewed by several investigators [2–5]. It is now commonly recognized that the cyclic saturation dislocation structure of single-slip Cu crystals depends strongly on the applied strain amplitude kpl. As kpl falls in the plateau region of the cyclic stress –strain (CSS) curve, dislocation configuration consists of PSB ladders and matrix veins, namely so-called ‘two phase’ structure [1]. At kpl below the lower end of the plateau, the dislocation structure is occupied entirely by veins, whereas the dislocation features are characterized by the development of labyrinths and cells at kpl near the upper end of the plateau or beyond the plateau [6,7]. The cyclic deformation behavior and dislocation features of Cu single crystals was extensively investigated
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Table 1 Fatigue testing conditions and data for [017], [1( 17] and [1( 12], copper single crystals selected for ECC or TEM observations Orientation
kpl
Cyclic number
kpl, cum
~s (MPa)
Corresponding ECC and TEM images
[017]
1.2×10−4 9.4×10−4 1.1×10−4 3.0×10−3 5.0×10−3 3.7×10−4 7.1×10−4 1.4×10−3 2.3×10−3
84 100 24 000 60 000 9540 1290 30 000 22 000 9100 7100
40.3 90.2 26.4 114.5 25.8 44.4 62.5 51.0 65.3
28.6 37.1 28.1 38.3 49.6 26.9 28.7 28.6 28.7
Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig.
[1( 17] [1( 12]
with the purpose of clarifying further cyclic plasticity of actual polycrystals, in which the grains are oriented randomly and double- or multiple-slip can be frequently seen to operate due to elastic and plastic strain incompatibility between adjacent grains [8]. A comprehensive knowledge of the orientation-dependent dislocation arrangements in cyclically deformed single crystals is thus of particular importance for a better understanding of the fatigue deformation micro-mechanisms of polycrystals. For instance, Buque et al. [9] recently examined the dislocation structures in cyclically deformed nickel polycrystals using the electron back scattering patterns (EBSP) and electron channeling contrast (ECC) techniques. Their results demonstrated that the dislocation pattern in a certain grain of polycrystals is governed by its axial orientation and the observed structure types are similar to those observed in single crystals of corresponding orientations. In recent years, the cyclic deformation behavior of Cu single crystals with various slip orientations has been revealed and summarized in a systematic way [10–12]. More recently, Li et al. [13] observed the cyclic dislocation structures of some multiple-slip-oriented Cu single crystals and found a strong orientation dependence of dislocation structures in those crystals. However, the knowledge on the dislocation structure of cyclically deformed double-slip-oriented Cu single crystals is still of imperfection. Jin [14] and Jin and Winter [15] studied preliminarily the dislocation structures of Cu single crystals with different double-slip orientations on the three sides of the stereographic triangle only at one relatively high strain amplitude of 3.0× 10 − 3. To fully understand the dislocation behavior in doubleslip-oriented Cu single crystals during cyclic deformation, Li et al. [16] explored the dislocation structures of cyclically deformed coplanar double-slip-oriented Cu single crystals in a wide range of strain amplitudes and found that the crystallographic orientation has nearly no effect on the dislocation structures of this type of double-slip crystals, which consist primarily of dislocation cells. The emphasis of the present work was placed on the influence of the crystallographic orientation on
3(a) 3(b) 4(a and b) 4(c and d) 4(e and f) 5(a) 5(b) 6(a–c) 5(c)
dislocation structures in cyclically deformed critical and conjugate double-slip-oriented Cu single crystals.
2. Experimental procedures All of the single crystals investigated were grown from OFHC copper of 99.999% purity by the Bridgman or Czochralski technique. The detailed description of preparation of the fatigue specimens and cyclic fatigue experiments can be found in our previous papers [17– 19]. Fatigue testing conditions and data for the, [1( 12], [1( 17] and [017] crystal specimens selected for TEM or ECC-SEM observations are listed in Table 1, where kpl, cum (kpl, cum = 4Nkpl, N is the total number of cycles) is the cumulative plastic strain and ~s, is the shear saturation stress. Fig. 1 shows the location of the orientations of Cu single crystals involved in this paper in the stereographic standard triangle and the classification of different types of slip orientations. Thin foils for TEM studies were first sliced from the gauge part of the fatigued specimens by spark-cutting parallel to some specific crystallographic planes (111), (11( 1) and (12( 1), then mechanically thinned down to dozens of micron thick and finally polished by a conventional twin-jet method. TEM observations were performed using JEOL-2000FX II and JEOL 3010 electron microscope operated at 200 and 300 kV, respectively. In
Fig. 1. Stereographic triangle showing the orientations of Cu single crystals involved in this paper (full circles) and the classification of orientations with different slip types. The cyclic dislocation structures of orientations indicating by open circles were reported in [15,24].
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addition, ECC-SEM technique was also employed to observe the dislocation arrangements on the specimen surfaces of fatigued [017] and [1( 12] crystals. The observed surfaces are (2( 71( ) for the [017] crystal and (201) and (2( 01( ) for the [1( 12] crystal, respectively. Concerning the detailed introduction to this technique, please see [7].
3. Experimental results
3.1. Cyclic stress– strain beha6ior
Fig. 2. The cyclic stress – strain (CSS) curves of four differently oriented crystals. For comparison, the CSS curve of single-slip-oriented copper single crystals is also depicted as shown in the dotted line taken from Mughrabi’s [20] work.
The CSS curves of the [1( 12], [1( 17] and [017] crystals are shown in Fig. 2. The results obtained with the [034] crystal [17] and single-slip crystals [20] are also included in this figure for comparison. Evidently, the CSS curve for the [1( 12] conjugate double-slip crystal shows a clear shorter plateau in the range of 5.0×10 − 4 B kpl B4.0× 10 − 3 with an average saturation stress of 28.6 MPa, as compared with the result of single-slip crystals shown in the dotted line in Fig. 2. However, the CSS curve for the [1( 17] crystal, which is also conjugate double-slip oriented, is quite different from that of the [1( 12] crystal; it does not show a clear plateau region, and the saturation shear stress increases monotonously with increasing kpl. The curve for the [034] critical double-slip crystal exhibits a plateau in the strain range of 1.0× 10 − 4 –4.3×10 − 3, which is also narrower than that of single-slip crystals but wider than that of the [1( 12] crystal. Instead of a clear plateau, the curve for the [017] crystal appears to show a narrow quasi-plateau over the range of 5.0×10 − 4 – 1.5× 10 − 3. Apparently, the crystallographic orientation has a strong effect on the CSS behavior of these oriented crystals, which has been reported in detail in [17–19].
3.2. Cyclic saturation dislocation structure 3.2.1. [017] Cu single crystal Fig. 3 shows the dislocation structures in the [017] crystal cyclically saturated at different plastic strain amplitudes obtained by the ECC technique. The observed plane is (2( 71( ). At a lower strain amplitude kpl of 1.2× 10 − 4, a basically observed feature of the dislocation structure is irregular labyrinths as shown in Fig. 3(a). The widths of labyrinth channels were determined roughly to be 0.8–1.3 mm. As kpl increases to 9.4×10 − 4, which is within the quasi-plateau region in the CSS curve (see Fig. 2), the major area is covered by regular labyrinth structures, and the average width of channels is reduced to about 0.5 mm. Besides, some narrow PSB ladder-like structures are embedded in the labyrinths, as shown in Fig. 3(b). Fig. 3. ECC-SEM images of dislocation structures in the [017] crystals cyclically saturated at different strain amplitudes. (a) kpl =1.2 × 10 − 4, irregular labyrinth structure; and (b) kpl = 9.4× 10 − 4, regular labyrinth and PSB ladder-like structures; viewed from (2( 71( ).
3.2.2. [1( 17] Cu single crystal Fig. 4 presents the variation of dislocation structure in the [1( 17] crystal with the applied plastic strain ampli-
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tude. Fig. 4(a and b) show the dislocation structures of a [1( 17] crystal specimen cycled at a lower strain amplitude of 1.1×10 − 4. It can be seen from (111) and (12( 1) sections that the dislocation structure consists mainly of veins under this strain amplitude. The average width of vein channels was determined roughly to be about 1.7 mm. As kpl increases to 3.0×10 − 3, the dislocation structure is also occupied by veins in the major area with the exception of dislocation wall-like structure occurring in some local regions, as shown in Fig. 4(c and d). It should be noted that the average width of vein channels is reduced to about 1.2 mm in this case. For strain amplitude up to 5.0×10 − 3, the dislocation
arrangement develops greatly, consisting of labyrinth and cell structures. Fig. 4(e and f) show the dislocation arrangement observed from a (11( 1) section. The average width of labyrinth channels and the diameter of cells were measured to be about 0.4 and 0.5 mm, respectively.
3.2.3. [1( 12] Cu single crystal Fig. 5 shows the characteristic dislocation structure observed in the [1( 12] single crystal by the ECC technique. It is interesting to note from Fig. 5(a) that PSB ladder structures already occur even in a lower strain amplitude of 3.7×10 − 4 below the plateau region in the CSS curve of the [1( 12] crystal. As kpl increases to 7.1× 10 − 4 and 2.3× 10 − 3, which fall, respectively, in the lower end and middle of the plateau in the CSS curve of the [1( 12] crystal, the well-developed PSB ladder structures form, as shown in Fig. 5(b and c). TEM observation on a (111) section further shows that numerous short PSB wall structure was frequently observed to embed in the matrix vein structure at kpl = 1.4× 10 − 3. A typical example is given in Fig. 6(a). In addition, in very few of local regions, irregular PSB walls were found together with dislocation cells forming in the matrix vein structure, as shown in Fig. 6(b). In cell interiors some individual dislocations, dislocation dipoles and dislocation loops can be clearly seen, as presented in Fig. 6(c).
4. Discussion
4.1. Correlation between change of dislocation scale and CSS beha6ior
Fig. 4. Dislocation structures in the [1( 17] crystals cyclically saturated at different strain amplitudes. (a) kpl = 1.1× 10 − 4, (111) foil, vein structure; (b) kpl =1.1 ×10 − 4, (12( 1) foil, vein structure; (c) kpl = 3.0× 10 − 3, (12( 1) foil, vein structure; (d) kpl = 3.0× 10 − 3, (12( 1) foil, dislocation wall-like structure; (e) kpl = 5.0× 10 − 3, (11( 1) foil, labyrinth structure and (f) kpl = 5.0× 10 − 3, (11( 1) foil, cell structure.
It is well known that for single-slip crystals the dimension of the PSB ladder structures is a kpl-independent quantity at room temperature [21], but the volume fraction of PSB ladder structures increases really with increasing kpl. The plateau behavior in the CSS curve is accomplished by adjusting the volume ratio of the two phases (PSBs and the matrix) to correspond with the applied strain amplitude. However, experimental results in the present study have indicated that the scales of labyrinth structure and vein structure decrease with increasing strain amplitude for the [017] and [1( 17] crystals, respectively. Brown [22,23] and Pederson [24] have discussed quantitatively the correlations between the height of the screw dipole (or the spacing of dislocation walls and veins) and the corresponding bowing stress (or passing stress) in fatigued crystals. For a Cu single crystal oriented for single slip, the cyclic hardening takes place due to significant dislocation multiplication by way of the bowing out of dislocations by a Frank–Read mechanism. In this way, the diameter of the channel areas
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Fig. 5. ECC-SEM images of dislocation structures in the [1( 12] crystals cyclically saturated at different amplitudes. (a) kpl =3.7 × 10 − 4, veins, walls and PSB ladders; (b) kpl = 7.1× 10 − 4, PSB ladders and veins; and (c) kpl =2.3 × 10 − 3, PSB ladders and veins. (a and c) viewed from (2( 01( ); (b) viewed from (201).
Fig. 6. TEM photograph showing the dislocation structure from a (111) section of the [1( 12] crystal cycled at kpl =1.4 × 10 − 3; (a) short PSB walls and matrix veins, (b) irregular PSR walls and loose cells and (c) high-magnification cell structure.
adjacent to the veins should be equal to the Orowan– Frank–Read length, [5]: dOr 1.5
Gb ~s
(1)
where G is the shear modulus, b the magnitude of the Burgers vector and ~s is the saturation stress. The channel diameter in Eq. (1) represents the maximum distance over which two ends of a semi-circle dislocation arc can be separated under a stress ~s. Apparently, the scale of the vein channel is roughly inversely proportional to the saturation stress ~s. For single-slip Cu single crystals, the saturation stress ~s corresponding to the plateau region of the CSS curve is nearly constant, i.e. ~s = 28 MPa, and the width of the vein channels is
comparable to that of the veins ( 1.5 mm) [5,21]. In the present study, as for the [1( 17] crystal, the average width of vein channels is found to be about 1.7 mm at kpl = 1.1× 10 − 4. This value is quite close to that of single-slip crystals. When kpl = 3.0× 10 − 3, the average width of vein channels is reduced to about 1.2 mm. The ratio of the average width of vein channels and the saturation stresses at these two strain amplitudes are, respectively: d1 1.7 = : 1.42 d2 1.2 ~s2 38.3 = : 1.36 ~s1 28.1
(2)
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where d1 and ~s1 are the average width of vein channels and the saturation stress at kpl =1.1 ×10 − 4, respectively, and d2 and ~s2 are the average width of vein channels and the saturation stress at kpl =3.0 ×10 − 3, respectively. It is clear that the value of dl/d2 is quite close to that of ~s2/~s1. This rough evaluation implies that the decrease in width of vein channels leads straightly to the increase in saturation stress, and thus to the disappearance of a plateau region in the CSS curve. Similarly, the scale change of the labyrinth structure in the [017] crystal is also an important factor causing the non-existence of a clear plateau region in its CSS curve. Quite analogous phenomena about dislocation scale changes were also previously found in the [001] multiple-slip and coplanar double-slip oriented Cu single crystals by Wang et al. [25] and by Li et al. [16], respectively. They all state that the change of dislocation scale is one of the main reasons for the disappearance of a clear plateau in the CSS curve of their crystals. By and large, one can contend that in certain multiple- or double-slip oriented Cu single crystals, the actual size of microstructures is in fact changeable for accommodating varying strains.
4.2. Correlation between PSB formation and CSS beha6ior As is well known, the CSS curve of single-slip-oriented Cu single crystals exhibits three distinct regimes, and the second regime (6.0×10 − 5 – 7.5 × 10 − 3) shows a clear plateau. Winter [21] raised a ‘two-phase’ model to explain the existence of the plateau region in the CSS curve for single-slip-oriented crystals. The formation of PSBs is now generally regarded as a main reason for the occurrence of the plateau. This ‘two-phase’ model seems to be also feasible to the case of [1( 12] crystals. As shown in Fig. 5(b and c) and Fig. 6(a), PSB ladders and PSB walls were observed clearly in the [1( 12] crystal cycled under the plateau strain amplitudes. Jin and Winter [15] also reported two separate sets of PSB ladder structures in a [1( 12] crystal cyclically deformed at a plastic strain amplitude 3.0× 10 − 3 exactly within the plateau region (see Fig. 2). It is thus reasonable to believe that the formation of PSB ladder structures might be the basic reason for the occurrence of plateau region in the CSS curve of the [1( 12] crystal. It is worth mentioning that dislocation cells were found in a very few of local regions as shown in Fig. 6(b and c). A possible reason for the formation of such cell structures is that PSBs in the primary and secondary (conjugate) slip directions intersect in local areas and combine to form cell walls. The occurrence of these cells has almost no effect on the plateau behavior of the very crystal. A more distinct cell structure was reported by Lisiecki and Weertman [26] on the crystal oriented quite near [1( 12]
orientation cyclically deformed at a high temperature (523 K) with a plastic strain amplitude of 3.5×10 − 3. In regard to the [017] crystal, a distinctive ‘twophase’ structure, i.e. labyrinth structure of the matrix and PSB ladder-like structure was detected as shown Fig. 3(a), which is somewhat different from the ‘twophase’ structure obtained with single-slip crystals over the plateau region in the CSS curve. Wang et al. [25] found a similar structure in cyclically deformed [001] crystals; however, they called the ladder-like structure ‘strip’-like structure, which only occupies a very small volume fraction (B 5% at gpl = 1.8× 10 − 3), whereas in the [017] crystal such a ladder-like structure accounts for a much greater volume fraction (see Fig. 3(b)). Although the scale of the labyrinth structure increases with the decreasing strain amplitude, the CSS curve of the [017] crystal still show a narrow quasi-plateau region primarily due to the formation of PSB ladder-like structures, which carry a considerable part of the cyclic plastic strain. The formation of this kind of PSB ladder-like structure might be promoted by the involvement of a critical (secondary) slip [27]. Accordingly, the occurrence of a quasi-plateau region in the CSS curve of the [017] crystal results from the joint effects of the scale change of the labyrinth structures and the formation of PSB ladder-like structures. In contrast, no PSB ladder structures were observed in cyclically deformed [1( 17] crystals, the saturation dislocation structures of which are mainly composed of vein structures at low strain amplitudes, and develop into labyrinth-like and cell structures with increasing gpl. Therefore, the scale change of the vein channels and non-existence of PSBs bring about the disappearance of a clear plateau in the CSS curve of the [1( 17] crystal. In light of the above results, it is clear that the formation of PSBs is a necessary condition for the occurrence of a plateau region in the CSS curve. That is to say, the presence of a plateau region is inexorably accompanied with the formation of PSBs. Does a oneto-one correlation exist between a plateau region and PSBs as a consequence? This question may be answered if the dislocation structure in cyclically deformed [1( 12] crystals was further inspected. Interestingly, PSB ladder structure does occur even at the strain amplitude below the plateau region of the CSS curve for the [1( 12] crystal, as indicated in Fig. 5(a). This result is greatly different from that obtained with single-slip crystals [20], for which PSBs form only in the plateau region in the CSS curve. In the recent work [28], we detected systematically the changes of hysteresis loop shape parameter VH with number of cycles N in the [1( 12] Cu single crystals during cyclic deformation. It was found that, when the strain amplitude kpl is even below the plateau region in the CSS curve (e.g. kpl = 3.7× 10 − 4), the curve of VH –N shows obvious minimum, implying the possible formation of PSBs in these lower strain
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range in terms of the definition of VH [20,28,29]. The present experimental results are in good agreement with the VH analysis. However, it deserves to be mentioned that the PSB ladder structure (Fig. 5(a)) are just in the initial stage of formation and are not well developed when the applied strain amplitude is below the plateau region in the CSS curve. As is well known, if the applied strain amplitude is in excess of a certain value, the transformation from the matrix vein structure to the PSB ladder structure must take place to accommodate high values of plastic strains. Winter [30] suggested that this transformation occurs at the soft centers of veins wherein exist small dislocation-poor areas surrounded by a harder vein shell of higher dislocation density, and then the surviving vein shell segments develop the first dislocation walls. Subsequently, the walls shift at a certain rate with cycling and gradually form the typical ladder pattern in the PSBs. These results are based only on single-slip Cu single crystals; however, whether and how such a transformation would happen in cyclically deformed Cu single crystals oriented for double slip was not reported. In the present study, it can be perceived from Fig. 5(a) that there really exists an obvious transition region (i.e. walls) in the process of the transformation from the vein structure to the PSB ladder structure, which is essentially similar to the case for single-slip crystals. Nevertheless, the main distinction is that the transformation occurs only in the plateau regime for single-slip crystals, whereas the transformation can occur even below the plateau regime for the [1( 12] crystal, and the PSB ladder structure and the transitional wall structure coexist. Such difference is believed to be associated with different geometrical relationships between crystal orientations and corresponding slip systems for these oriented crystals. In view of the above observations and analyses, one can reach the fact that the PSBs do form, as the case stands, not necessarily in the plateau region of the CSS curve. Putting the case in another way, the formation of PSBs is just a necessary but not a sufficient condition for the presence of a plateau region of the CSS curve. Blochwitz and Veit [31] summarized and analyzed systematically the plateau behavior of fatigued Ni single crystals and deduced a conclusion that the PSB structure should also exist at stresses and strain higher than the plateau stress and the upper end of the plateau strain range if certain premises are satisfied, which further provided a convincing support for the results above.
4.3. Orientation dependence of dislocation structures The dislocation structure of cyclically deformed Cu single crystals oriented for single slip was well known to be almost independent of the crystallographic orienta-
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tion [2,4,20]. Recently, Li et al. [13] summarized that the cyclic dislocation structures in cyclically deformed multiple-slip-oriented Cu single crystals hinge strongly upon the crystallographic orientation. Three kinds of representative dislocation arrangements, such as labyrinths, cells and PSB ladders are typical for the [001], [1( 11] and [011] multiple-slip crystals. Similar results obtained with multiple-slip Ni single crystals have been also reported recently by Buque [32]. More recently, Li et al. [16] investigated systematically the dislocation structures of coplanar double-slip oriented Cu single crystals. The dislocation structure of coplanar double-slip crystals is nearly orientation-independent and composed mainly of dislocation cells. In the present study, the crystallographic orientation for critical or conjugate double-slip crystals has a strong effect on the dislocation structures. For the conjugate double-slip crystals, PSB ladder structures was found in the [1( 12] crystal cycled at strain amplitudes below and within the plateau region of the CSS curve, while no PSB ladders occur in the [1( 17] crystal over the strain range investigated, and veins, labyrinths and cells are its characteristic dislocation patterns. For the [1( 12] and [1( 17] crystals, which are on the same [001]/[1( 11] side of the stereographic triangle, their primary and conjugate slip systems are non-coplanar and non-collinear systems with [110] plane symmetry, so the dislocation interactions would engender immobile Lomer – Cottrell locks. Why do their dislocation structures show different characteristics? It may be in fact understood if the geometrical relationship between crystal orientation (i.e. loading direction) and corresponding slip systems is checked. For the [1( 12] crystal, the direction of vectorial resultant between [1( 01] primary and [011] secondary slip directions is exactly the loading direction [1( 12], i.e. [1( 01]+ [011] [1( 12]. Therefore, the primary and secondary slip systems are strictly symmetrical with regard to the [1( 12] loading direction. During cycling, the formed Lomer–Cottrell locks would impede notably the motion of follow-up dislocations, and impel dislocations in these two systems to tend to glide and multiply in separated zones due to the high symmetry of these two slip systems. In each of zones, independent slip deformation, i.e. single-slip-type deformation is expected, leading to a similar dislocation structures including PSB ladders with that observed in single-slip crystals [15]. However, for the [1( 17] crystal, the disappearance of this kind of high slip symmetry is believed to be the main reason for the nonexistence of PSB ladder structures. Regarding the critical double-slip crystals, Gong et al. [27] reported that PSB ladders, veins and labyrinths constitute the main dislocation features in the critical double-slip crystal cycled at intermediate amplitudes and cell structures developed at higher strain ampli-
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tudes. Jin and Winter [15] also found PSB ladders and veins in the [012] critical double-slip crystal cycled at an intermediate strain amplitude of 3.0× 10 − 3. The present work revealed that the labyrinth structure becomes the main dislocation configuration in cyclically deformed [017] critical double-slip crystals and that some narrow PSB ladder-like structures are embedded in the labyrinth structures. Gong et al. [27] asserted that the effect of the operation of critical slip system on cyclic deformation behavior in the [034] critical double-slip crystal is analogous to that of the increase in strain amplitude on single-slip crystals’ behavior. It can thus be inferred that the formation of PSB ladder structures is promoted by the involvement of a critical (secondary) slip. Certainly, since there is little difference of the geometrical relationship between crystal orientation and corresponding slip systems among these critical double-slip crystals, their dislocation structures still present distinctive features to a certain extent. To sum up, the PSB ladders structure is a common dislocation feature for the critical double-slip crystals, and its role playing during cyclic deformation tend to become weaker as the orientation varies from the [011] orientation to the [001] orientation along the [001]/[011] side of the stereographic standard triangle. Two extreme cases are as follows, first, in cyclically deformed crystals with [011] orientation, the PSB ladders structure is a main deformation microstructure [13], causing a clear plateau region of the CSS curve [33]; secondly, for crystals with [001] orientation, no PSBs were found and the labyrinth structure was considered to accommodate the applied strains during cycling [25], causing a complete disappearance of a plateau region in the CSS curve [34]. Therefore, the dislocation structure of critical doubleslip crystals changes gradually with the variation in crystallographic orientation along the [001]/[011] boundary. Consequently, such an orientation dependence of dislocation structure was believed to result not only from the different modes of dislocation interactions among slip systems operating in the crystals but also from different slip deformation characteristics induced by the different geometrical relationships between orientations and corresponding slip systems in the differently oriented crystals. The orientation dependence of dislocation structure accounts well for the corresponding orientation dependence of the plateau behavior in the CSS curve of Cu single crystals reported previously, [10].
5. Conclusions Based on the experimental results and discussion above, the following conclusions can be drawn. (1)
There exists an obvious crystallographic orientation dependence of the dislocation structures induced by cyclic deformation of critical and (or) conjugate double-slip-oriented Cu single crystals, which can explain well the corresponding orientation dependence of the plateau behavior in the CSS curve. (2) The formation of well-developed PSB ladder structures is a basic reason for the occurrence of a plateau region in the CSS curve of the [1( 12] crystal. PSB ladder structure, which developed from vein and then wall structures, does occur in the lower strain amplitude below the plateau region in the CSS curve for the very crystal despite the fact that it is just in the initial stage of formation and is not well developed in this instance. This experimental result indicates that the formation of PSBs is only a necessary but not a sufficient condition for the presence of a plateau region of the CSS curve. (3) The saturation dislocation structures of [1( 17] crystals are mainly composed of vein structures at low strain amplitudes, and developed into labyrinth-like and cell structures at high strain amplitudes. The decrease in the scale of vein structure with increasing strain amplitude and the absence of PSB ladder structure was believed to cause the disappearance of a plateau region in the CSS curve of the [1( 17] crystal. (4) The saturation dislocation structure of the [017] crystal consists primarily of irregular labyrinth structure at a low strain amplitude of 1.2× 10 − 4. A distinctive ‘two-phase’ structure, i.e. labyrinth structure and PSB ladder-like structure was found to form at a comparatively higher strain amplitude of 9.4×10 − 3. The average width of labyrinth channel decreases with increasing strain amplitude. The occurrence of a quasi-plateau in the CSS curve of the [017] crystal was considered as being the result of the joint effects of the scale change of the labyrinth structure and the formation of PSB ladder-like structures.
Acknowledgements This work was financially supported by the Special Funds for the Major State Basic Research Project of China under Grant No. G19990680 and a grant-in-aid for Scientific Research and Development from the Ministry of Education, Science, Sports and Culture of Japan. This support is gratefully acknowledged. Dr X.W. Li would like to acknowledge the Japan Society for the Promotion of Science (JSPS) for a postdoctoral fellowship for Foreign Researchers, and to give his loving thanks to his wife Yang Liu and daughter Ruo Xuan Li for their whole-hearted love and support. Also, Dr X.W. Li is grateful to Professor C. Blochwitz and Dr C. Buque for providing their manuscripts for perusal.
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References [1] A.T. Winter, Phil. Mag. 30 (1974) 719. [2] C. Laird, Dislocation in Solid, in: F.R.N. Nabarro (Ed.), North Holland, 6 (1983) 1. [3] C. Laird, P. Charsley, H. Mughrabi, Mater. Sci. Eng. 81 (1986) 433. [4] Z.S. Basinski, S.J. Basinski, Prog. Mater. Sci. 36 (1992) 89. [5] S. Suresh, Fatigue of Materials, Cambridge University Press, London, 1998. [6] F. Ackemann, L.P. Kubin, J. Lepinoux, H. Mughrabi, Acta Metall. 32 (1984) 715. [7] X.W. Li, Y.M. Hu, Z.G. Wang, Mater. Sci. Eng. A248 (1998) 299. [8] Y.D. Chung, H. Margolin, Metall. Trans. 4 (1973) 1905. [9] C. Buque, J. Bretschneider, A. Schwab, C. Holste, Mater. Sci. Eng. A300 (2001) 254. [10] X.W. Li, Z.G. Wang, S.X. Li, Phil. Mag. Lett. 79 (1999) 715. [11] X.W. Li, Z.G. Wang, S.X. Li, Phil. Mag. Lett. 79 (1999) 869. [12] Z.G. Wang, X.W. Li, Z.F. Zhang, S.X. Li, J. Mater. Sci. Technol. 15 (1999) 489. [13] X.W. Li, Y. Umakoshi, S.X. Li, Z.G. Wang, Z. Metallkd. 92 (2001) 1222 –1226. [14] N.Y. Jin, Phil. Mag. A 48 (1983) 33. [15] N.Y. Jin, A.T. Winter, Acta Metall. 32 (1984) 989.
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[16] X.W. Li, Z.G. Wang, Y.W. Zhang, S.X. Li, Y. Umakoshi, Phys. Stat. Sol. (a) (2002) in press. [17] B. Gong, Z.G. Wang, Y.W. Zhang, Mater. Sci. Eng. A194 (1995) 171. [18] X.W. Li, Z.G. Wang, S.X. Li, Mater. Sci. Eng. A265 (1999) 18. [19] X.W. Li, Z.G. Wang, S.X. Li, Mater. Sci. Eng. A269 (1999) 166. [20] H. Mughrabi, Mater. Sci. Eng. 33 (1978) 207. [21] Z.S. Basinski, A.S. Korbel, S.J. Basinski, Acta Metall. 28 (1980) 191. [22] L.M. Brown, Metall. Trans. A 22 (1991) 1693. [23] L.M. Brown, Mater. Sci. Eng. A285 (2000) 35. [24] O.B. Pedersen, Phil. Mag. A 73 (1996) 829. [25] Z.R. Wang, B. Gong, Z.G. Wang, Acta Mater. 45 (1997) 1379. [26] L.L. Lisiecki, J.R. Weertman, Acta Metall. Mater. 38 (1990) 509. [27] B. Gong, Z.R. Wang, Z.G. Wang, Y.W. Zhang, Mater. Sci. Eng. A210 (1996) 94. [28] X.W. Li, Z.G. Wang, S.X. Li, Mater. Sci. Eng. A271 (1999) 315. [29] J. Polak, J. Helesic, K. Obrlik, Mater. Sci. Eng. A271 A101 (1988) 7. [30] A.T. Winter, Phil. Mag. 37 (1978) 457. [31] C. Blochwitz, U. Veit, Crystallogr. Res. Technol. 17 (1982) 529. [32] C. Buque, Int. J. Fatigue 23 (2001) 671. [33] X.W. Li, Z.G. Wang, G.Y. Li, S.D. Wu, S.X. Li, Acta Mater. 46 (1998) 4497. [34] B. Gong, Z.R. Wang, Z.G. Wang, Acta Mater. 45 (1997) 1365.
Dislocation structures in fatigued critical and conjugate double-slip-oriented copper single crystals X.W. Li a,b,*,1, Y. Umakoshi b, B. Gong a, S.X. Li a, Z.G. Wang a a
State Key Laboratory for Fatigue and Fracture of Materials, Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China b Department of Materials Science and Engineering, Graduate School of Engineering, Osaka Uni6ersity, 2 -1, Yamada-oka, Suita, Osaka 565 -0871, Japan Received 26 July 2001; received in revised form 30 August 2001
Abstract The dislocation structures induced by cyclic deformation of [017] critical and, [1( 12], [1( 17] conjugate double-slip-oriented Cu single crystals were investigated using transmission electron microscopy (TEM) and electron channeling contrast (ECC) technique in scanning electron microscopy (SEM). It was found that the crystallographic orientation has a notable effect on the dislocation structures in cyclically saturated critical and (or) conjugate double-slip-oriented Cu single crystals. Such an orientation dependence of dislocation structure can account well for the corresponding orientation dependence of the plateau behavior in the cyclic stress–strain (CSS) curve. In cyclic deformation of the [1( 12] crystal, the formation of persistent slip band (PSB) ladder structures is a general phenomenon; PSBs occur even under the low strain amplitude, which is below the plateau region in the CSS curve. The experimental result above indicates that there is not a complete one-to-one correlation between the formation of PSBs and the presence of a plateau region of the CSS curve. In certain double-slip oriented Cu single crystals investigated here, the actual size of microstructures is in fact, found to be changeable with varying strain amplitude, which is one of the main reasons for the disappearance of a clear plateau in the CSS curve of these crystals. For example, the decrease in the width of vein channels with increasing strain amplitude and the absence of PSB ladder structure are the major reason for non-existence of a clear plateau region in the CSS curve of the [1( 17] crystal, while the joint effects of the scale change of the labyrinth structure and the formation of PSB ladder-like structures lead to the occurrence of only a narrow quasi-plateau in the CSS curve of the [017] crystal. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Cu single crystal; Dislocation structure; Conjugate double slip; Critical double slip; Cyclic deformation; Crystallographic orientation
1. Introduction Dislocation structures of fcc crystals created during cyclic deformation have been a subject of strong interest over many years, particularly, since Winter [1] discovered the well-known two-phase structure of dislocation ladders of persistent slip bands (PSBs) and dislocation veins of the matrix in cyclically deformed Cu single crystals oriented for single slip. The dislocation structure in the cyclically deformed Cu single * Corresponding author. Tel.: +81-6-6879-7527; fax: + 81-6-68797495. E-mail address: [email protected] (X.W. Li). 1 Tel.: +86-24-23843531; fax: +86-24-23891320; E-mail: [email protected]
crystals with single-slip orientation has been reported in great numbers and the conclusive results were well reviewed by several investigators [2–5]. It is now commonly recognized that the cyclic saturation dislocation structure of single-slip Cu crystals depends strongly on the applied strain amplitude kpl. As kpl falls in the plateau region of the cyclic stress –strain (CSS) curve, dislocation configuration consists of PSB ladders and matrix veins, namely so-called ‘two phase’ structure [1]. At kpl below the lower end of the plateau, the dislocation structure is occupied entirely by veins, whereas the dislocation features are characterized by the development of labyrinths and cells at kpl near the upper end of the plateau or beyond the plateau [6,7]. The cyclic deformation behavior and dislocation features of Cu single crystals was extensively investigated
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Table 1 Fatigue testing conditions and data for [017], [1( 17] and [1( 12], copper single crystals selected for ECC or TEM observations Orientation
kpl
Cyclic number
kpl, cum
~s (MPa)
Corresponding ECC and TEM images
[017]
1.2×10−4 9.4×10−4 1.1×10−4 3.0×10−3 5.0×10−3 3.7×10−4 7.1×10−4 1.4×10−3 2.3×10−3
84 100 24 000 60 000 9540 1290 30 000 22 000 9100 7100
40.3 90.2 26.4 114.5 25.8 44.4 62.5 51.0 65.3
28.6 37.1 28.1 38.3 49.6 26.9 28.7 28.6 28.7
Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig. Fig.
[1( 17] [1( 12]
with the purpose of clarifying further cyclic plasticity of actual polycrystals, in which the grains are oriented randomly and double- or multiple-slip can be frequently seen to operate due to elastic and plastic strain incompatibility between adjacent grains [8]. A comprehensive knowledge of the orientation-dependent dislocation arrangements in cyclically deformed single crystals is thus of particular importance for a better understanding of the fatigue deformation micro-mechanisms of polycrystals. For instance, Buque et al. [9] recently examined the dislocation structures in cyclically deformed nickel polycrystals using the electron back scattering patterns (EBSP) and electron channeling contrast (ECC) techniques. Their results demonstrated that the dislocation pattern in a certain grain of polycrystals is governed by its axial orientation and the observed structure types are similar to those observed in single crystals of corresponding orientations. In recent years, the cyclic deformation behavior of Cu single crystals with various slip orientations has been revealed and summarized in a systematic way [10–12]. More recently, Li et al. [13] observed the cyclic dislocation structures of some multiple-slip-oriented Cu single crystals and found a strong orientation dependence of dislocation structures in those crystals. However, the knowledge on the dislocation structure of cyclically deformed double-slip-oriented Cu single crystals is still of imperfection. Jin [14] and Jin and Winter [15] studied preliminarily the dislocation structures of Cu single crystals with different double-slip orientations on the three sides of the stereographic triangle only at one relatively high strain amplitude of 3.0× 10 − 3. To fully understand the dislocation behavior in doubleslip-oriented Cu single crystals during cyclic deformation, Li et al. [16] explored the dislocation structures of cyclically deformed coplanar double-slip-oriented Cu single crystals in a wide range of strain amplitudes and found that the crystallographic orientation has nearly no effect on the dislocation structures of this type of double-slip crystals, which consist primarily of dislocation cells. The emphasis of the present work was placed on the influence of the crystallographic orientation on
3(a) 3(b) 4(a and b) 4(c and d) 4(e and f) 5(a) 5(b) 6(a–c) 5(c)
dislocation structures in cyclically deformed critical and conjugate double-slip-oriented Cu single crystals.
2. Experimental procedures All of the single crystals investigated were grown from OFHC copper of 99.999% purity by the Bridgman or Czochralski technique. The detailed description of preparation of the fatigue specimens and cyclic fatigue experiments can be found in our previous papers [17– 19]. Fatigue testing conditions and data for the, [1( 12], [1( 17] and [017] crystal specimens selected for TEM or ECC-SEM observations are listed in Table 1, where kpl, cum (kpl, cum = 4Nkpl, N is the total number of cycles) is the cumulative plastic strain and ~s, is the shear saturation stress. Fig. 1 shows the location of the orientations of Cu single crystals involved in this paper in the stereographic standard triangle and the classification of different types of slip orientations. Thin foils for TEM studies were first sliced from the gauge part of the fatigued specimens by spark-cutting parallel to some specific crystallographic planes (111), (11( 1) and (12( 1), then mechanically thinned down to dozens of micron thick and finally polished by a conventional twin-jet method. TEM observations were performed using JEOL-2000FX II and JEOL 3010 electron microscope operated at 200 and 300 kV, respectively. In
Fig. 1. Stereographic triangle showing the orientations of Cu single crystals involved in this paper (full circles) and the classification of orientations with different slip types. The cyclic dislocation structures of orientations indicating by open circles were reported in [15,24].
X.W. Li et al. / Materials Science and Engineering A333 (2002) 51–59
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addition, ECC-SEM technique was also employed to observe the dislocation arrangements on the specimen surfaces of fatigued [017] and [1( 12] crystals. The observed surfaces are (2( 71( ) for the [017] crystal and (201) and (2( 01( ) for the [1( 12] crystal, respectively. Concerning the detailed introduction to this technique, please see [7].
3. Experimental results
3.1. Cyclic stress– strain beha6ior
Fig. 2. The cyclic stress – strain (CSS) curves of four differently oriented crystals. For comparison, the CSS curve of single-slip-oriented copper single crystals is also depicted as shown in the dotted line taken from Mughrabi’s [20] work.
The CSS curves of the [1( 12], [1( 17] and [017] crystals are shown in Fig. 2. The results obtained with the [034] crystal [17] and single-slip crystals [20] are also included in this figure for comparison. Evidently, the CSS curve for the [1( 12] conjugate double-slip crystal shows a clear shorter plateau in the range of 5.0×10 − 4 B kpl B4.0× 10 − 3 with an average saturation stress of 28.6 MPa, as compared with the result of single-slip crystals shown in the dotted line in Fig. 2. However, the CSS curve for the [1( 17] crystal, which is also conjugate double-slip oriented, is quite different from that of the [1( 12] crystal; it does not show a clear plateau region, and the saturation shear stress increases monotonously with increasing kpl. The curve for the [034] critical double-slip crystal exhibits a plateau in the strain range of 1.0× 10 − 4 –4.3×10 − 3, which is also narrower than that of single-slip crystals but wider than that of the [1( 12] crystal. Instead of a clear plateau, the curve for the [017] crystal appears to show a narrow quasi-plateau over the range of 5.0×10 − 4 – 1.5× 10 − 3. Apparently, the crystallographic orientation has a strong effect on the CSS behavior of these oriented crystals, which has been reported in detail in [17–19].
3.2. Cyclic saturation dislocation structure 3.2.1. [017] Cu single crystal Fig. 3 shows the dislocation structures in the [017] crystal cyclically saturated at different plastic strain amplitudes obtained by the ECC technique. The observed plane is (2( 71( ). At a lower strain amplitude kpl of 1.2× 10 − 4, a basically observed feature of the dislocation structure is irregular labyrinths as shown in Fig. 3(a). The widths of labyrinth channels were determined roughly to be 0.8–1.3 mm. As kpl increases to 9.4×10 − 4, which is within the quasi-plateau region in the CSS curve (see Fig. 2), the major area is covered by regular labyrinth structures, and the average width of channels is reduced to about 0.5 mm. Besides, some narrow PSB ladder-like structures are embedded in the labyrinths, as shown in Fig. 3(b). Fig. 3. ECC-SEM images of dislocation structures in the [017] crystals cyclically saturated at different strain amplitudes. (a) kpl =1.2 × 10 − 4, irregular labyrinth structure; and (b) kpl = 9.4× 10 − 4, regular labyrinth and PSB ladder-like structures; viewed from (2( 71( ).
3.2.2. [1( 17] Cu single crystal Fig. 4 presents the variation of dislocation structure in the [1( 17] crystal with the applied plastic strain ampli-
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tude. Fig. 4(a and b) show the dislocation structures of a [1( 17] crystal specimen cycled at a lower strain amplitude of 1.1×10 − 4. It can be seen from (111) and (12( 1) sections that the dislocation structure consists mainly of veins under this strain amplitude. The average width of vein channels was determined roughly to be about 1.7 mm. As kpl increases to 3.0×10 − 3, the dislocation structure is also occupied by veins in the major area with the exception of dislocation wall-like structure occurring in some local regions, as shown in Fig. 4(c and d). It should be noted that the average width of vein channels is reduced to about 1.2 mm in this case. For strain amplitude up to 5.0×10 − 3, the dislocation
arrangement develops greatly, consisting of labyrinth and cell structures. Fig. 4(e and f) show the dislocation arrangement observed from a (11( 1) section. The average width of labyrinth channels and the diameter of cells were measured to be about 0.4 and 0.5 mm, respectively.
3.2.3. [1( 12] Cu single crystal Fig. 5 shows the characteristic dislocation structure observed in the [1( 12] single crystal by the ECC technique. It is interesting to note from Fig. 5(a) that PSB ladder structures already occur even in a lower strain amplitude of 3.7×10 − 4 below the plateau region in the CSS curve of the [1( 12] crystal. As kpl increases to 7.1× 10 − 4 and 2.3× 10 − 3, which fall, respectively, in the lower end and middle of the plateau in the CSS curve of the [1( 12] crystal, the well-developed PSB ladder structures form, as shown in Fig. 5(b and c). TEM observation on a (111) section further shows that numerous short PSB wall structure was frequently observed to embed in the matrix vein structure at kpl = 1.4× 10 − 3. A typical example is given in Fig. 6(a). In addition, in very few of local regions, irregular PSB walls were found together with dislocation cells forming in the matrix vein structure, as shown in Fig. 6(b). In cell interiors some individual dislocations, dislocation dipoles and dislocation loops can be clearly seen, as presented in Fig. 6(c).
4. Discussion
4.1. Correlation between change of dislocation scale and CSS beha6ior
Fig. 4. Dislocation structures in the [1( 17] crystals cyclically saturated at different strain amplitudes. (a) kpl = 1.1× 10 − 4, (111) foil, vein structure; (b) kpl =1.1 ×10 − 4, (12( 1) foil, vein structure; (c) kpl = 3.0× 10 − 3, (12( 1) foil, vein structure; (d) kpl = 3.0× 10 − 3, (12( 1) foil, dislocation wall-like structure; (e) kpl = 5.0× 10 − 3, (11( 1) foil, labyrinth structure and (f) kpl = 5.0× 10 − 3, (11( 1) foil, cell structure.
It is well known that for single-slip crystals the dimension of the PSB ladder structures is a kpl-independent quantity at room temperature [21], but the volume fraction of PSB ladder structures increases really with increasing kpl. The plateau behavior in the CSS curve is accomplished by adjusting the volume ratio of the two phases (PSBs and the matrix) to correspond with the applied strain amplitude. However, experimental results in the present study have indicated that the scales of labyrinth structure and vein structure decrease with increasing strain amplitude for the [017] and [1( 17] crystals, respectively. Brown [22,23] and Pederson [24] have discussed quantitatively the correlations between the height of the screw dipole (or the spacing of dislocation walls and veins) and the corresponding bowing stress (or passing stress) in fatigued crystals. For a Cu single crystal oriented for single slip, the cyclic hardening takes place due to significant dislocation multiplication by way of the bowing out of dislocations by a Frank–Read mechanism. In this way, the diameter of the channel areas
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Fig. 5. ECC-SEM images of dislocation structures in the [1( 12] crystals cyclically saturated at different amplitudes. (a) kpl =3.7 × 10 − 4, veins, walls and PSB ladders; (b) kpl = 7.1× 10 − 4, PSB ladders and veins; and (c) kpl =2.3 × 10 − 3, PSB ladders and veins. (a and c) viewed from (2( 01( ); (b) viewed from (201).
Fig. 6. TEM photograph showing the dislocation structure from a (111) section of the [1( 12] crystal cycled at kpl =1.4 × 10 − 3; (a) short PSB walls and matrix veins, (b) irregular PSR walls and loose cells and (c) high-magnification cell structure.
adjacent to the veins should be equal to the Orowan– Frank–Read length, [5]: dOr 1.5
Gb ~s
(1)
where G is the shear modulus, b the magnitude of the Burgers vector and ~s is the saturation stress. The channel diameter in Eq. (1) represents the maximum distance over which two ends of a semi-circle dislocation arc can be separated under a stress ~s. Apparently, the scale of the vein channel is roughly inversely proportional to the saturation stress ~s. For single-slip Cu single crystals, the saturation stress ~s corresponding to the plateau region of the CSS curve is nearly constant, i.e. ~s = 28 MPa, and the width of the vein channels is
comparable to that of the veins ( 1.5 mm) [5,21]. In the present study, as for the [1( 17] crystal, the average width of vein channels is found to be about 1.7 mm at kpl = 1.1× 10 − 4. This value is quite close to that of single-slip crystals. When kpl = 3.0× 10 − 3, the average width of vein channels is reduced to about 1.2 mm. The ratio of the average width of vein channels and the saturation stresses at these two strain amplitudes are, respectively: d1 1.7 = : 1.42 d2 1.2 ~s2 38.3 = : 1.36 ~s1 28.1
(2)
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where d1 and ~s1 are the average width of vein channels and the saturation stress at kpl =1.1 ×10 − 4, respectively, and d2 and ~s2 are the average width of vein channels and the saturation stress at kpl =3.0 ×10 − 3, respectively. It is clear that the value of dl/d2 is quite close to that of ~s2/~s1. This rough evaluation implies that the decrease in width of vein channels leads straightly to the increase in saturation stress, and thus to the disappearance of a plateau region in the CSS curve. Similarly, the scale change of the labyrinth structure in the [017] crystal is also an important factor causing the non-existence of a clear plateau region in its CSS curve. Quite analogous phenomena about dislocation scale changes were also previously found in the [001] multiple-slip and coplanar double-slip oriented Cu single crystals by Wang et al. [25] and by Li et al. [16], respectively. They all state that the change of dislocation scale is one of the main reasons for the disappearance of a clear plateau in the CSS curve of their crystals. By and large, one can contend that in certain multiple- or double-slip oriented Cu single crystals, the actual size of microstructures is in fact changeable for accommodating varying strains.
4.2. Correlation between PSB formation and CSS beha6ior As is well known, the CSS curve of single-slip-oriented Cu single crystals exhibits three distinct regimes, and the second regime (6.0×10 − 5 – 7.5 × 10 − 3) shows a clear plateau. Winter [21] raised a ‘two-phase’ model to explain the existence of the plateau region in the CSS curve for single-slip-oriented crystals. The formation of PSBs is now generally regarded as a main reason for the occurrence of the plateau. This ‘two-phase’ model seems to be also feasible to the case of [1( 12] crystals. As shown in Fig. 5(b and c) and Fig. 6(a), PSB ladders and PSB walls were observed clearly in the [1( 12] crystal cycled under the plateau strain amplitudes. Jin and Winter [15] also reported two separate sets of PSB ladder structures in a [1( 12] crystal cyclically deformed at a plastic strain amplitude 3.0× 10 − 3 exactly within the plateau region (see Fig. 2). It is thus reasonable to believe that the formation of PSB ladder structures might be the basic reason for the occurrence of plateau region in the CSS curve of the [1( 12] crystal. It is worth mentioning that dislocation cells were found in a very few of local regions as shown in Fig. 6(b and c). A possible reason for the formation of such cell structures is that PSBs in the primary and secondary (conjugate) slip directions intersect in local areas and combine to form cell walls. The occurrence of these cells has almost no effect on the plateau behavior of the very crystal. A more distinct cell structure was reported by Lisiecki and Weertman [26] on the crystal oriented quite near [1( 12]
orientation cyclically deformed at a high temperature (523 K) with a plastic strain amplitude of 3.5×10 − 3. In regard to the [017] crystal, a distinctive ‘twophase’ structure, i.e. labyrinth structure of the matrix and PSB ladder-like structure was detected as shown Fig. 3(a), which is somewhat different from the ‘twophase’ structure obtained with single-slip crystals over the plateau region in the CSS curve. Wang et al. [25] found a similar structure in cyclically deformed [001] crystals; however, they called the ladder-like structure ‘strip’-like structure, which only occupies a very small volume fraction (B 5% at gpl = 1.8× 10 − 3), whereas in the [017] crystal such a ladder-like structure accounts for a much greater volume fraction (see Fig. 3(b)). Although the scale of the labyrinth structure increases with the decreasing strain amplitude, the CSS curve of the [017] crystal still show a narrow quasi-plateau region primarily due to the formation of PSB ladder-like structures, which carry a considerable part of the cyclic plastic strain. The formation of this kind of PSB ladder-like structure might be promoted by the involvement of a critical (secondary) slip [27]. Accordingly, the occurrence of a quasi-plateau region in the CSS curve of the [017] crystal results from the joint effects of the scale change of the labyrinth structures and the formation of PSB ladder-like structures. In contrast, no PSB ladder structures were observed in cyclically deformed [1( 17] crystals, the saturation dislocation structures of which are mainly composed of vein structures at low strain amplitudes, and develop into labyrinth-like and cell structures with increasing gpl. Therefore, the scale change of the vein channels and non-existence of PSBs bring about the disappearance of a clear plateau in the CSS curve of the [1( 17] crystal. In light of the above results, it is clear that the formation of PSBs is a necessary condition for the occurrence of a plateau region in the CSS curve. That is to say, the presence of a plateau region is inexorably accompanied with the formation of PSBs. Does a oneto-one correlation exist between a plateau region and PSBs as a consequence? This question may be answered if the dislocation structure in cyclically deformed [1( 12] crystals was further inspected. Interestingly, PSB ladder structure does occur even at the strain amplitude below the plateau region of the CSS curve for the [1( 12] crystal, as indicated in Fig. 5(a). This result is greatly different from that obtained with single-slip crystals [20], for which PSBs form only in the plateau region in the CSS curve. In the recent work [28], we detected systematically the changes of hysteresis loop shape parameter VH with number of cycles N in the [1( 12] Cu single crystals during cyclic deformation. It was found that, when the strain amplitude kpl is even below the plateau region in the CSS curve (e.g. kpl = 3.7× 10 − 4), the curve of VH –N shows obvious minimum, implying the possible formation of PSBs in these lower strain
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range in terms of the definition of VH [20,28,29]. The present experimental results are in good agreement with the VH analysis. However, it deserves to be mentioned that the PSB ladder structure (Fig. 5(a)) are just in the initial stage of formation and are not well developed when the applied strain amplitude is below the plateau region in the CSS curve. As is well known, if the applied strain amplitude is in excess of a certain value, the transformation from the matrix vein structure to the PSB ladder structure must take place to accommodate high values of plastic strains. Winter [30] suggested that this transformation occurs at the soft centers of veins wherein exist small dislocation-poor areas surrounded by a harder vein shell of higher dislocation density, and then the surviving vein shell segments develop the first dislocation walls. Subsequently, the walls shift at a certain rate with cycling and gradually form the typical ladder pattern in the PSBs. These results are based only on single-slip Cu single crystals; however, whether and how such a transformation would happen in cyclically deformed Cu single crystals oriented for double slip was not reported. In the present study, it can be perceived from Fig. 5(a) that there really exists an obvious transition region (i.e. walls) in the process of the transformation from the vein structure to the PSB ladder structure, which is essentially similar to the case for single-slip crystals. Nevertheless, the main distinction is that the transformation occurs only in the plateau regime for single-slip crystals, whereas the transformation can occur even below the plateau regime for the [1( 12] crystal, and the PSB ladder structure and the transitional wall structure coexist. Such difference is believed to be associated with different geometrical relationships between crystal orientations and corresponding slip systems for these oriented crystals. In view of the above observations and analyses, one can reach the fact that the PSBs do form, as the case stands, not necessarily in the plateau region of the CSS curve. Putting the case in another way, the formation of PSBs is just a necessary but not a sufficient condition for the presence of a plateau region of the CSS curve. Blochwitz and Veit [31] summarized and analyzed systematically the plateau behavior of fatigued Ni single crystals and deduced a conclusion that the PSB structure should also exist at stresses and strain higher than the plateau stress and the upper end of the plateau strain range if certain premises are satisfied, which further provided a convincing support for the results above.
4.3. Orientation dependence of dislocation structures The dislocation structure of cyclically deformed Cu single crystals oriented for single slip was well known to be almost independent of the crystallographic orienta-
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tion [2,4,20]. Recently, Li et al. [13] summarized that the cyclic dislocation structures in cyclically deformed multiple-slip-oriented Cu single crystals hinge strongly upon the crystallographic orientation. Three kinds of representative dislocation arrangements, such as labyrinths, cells and PSB ladders are typical for the [001], [1( 11] and [011] multiple-slip crystals. Similar results obtained with multiple-slip Ni single crystals have been also reported recently by Buque [32]. More recently, Li et al. [16] investigated systematically the dislocation structures of coplanar double-slip oriented Cu single crystals. The dislocation structure of coplanar double-slip crystals is nearly orientation-independent and composed mainly of dislocation cells. In the present study, the crystallographic orientation for critical or conjugate double-slip crystals has a strong effect on the dislocation structures. For the conjugate double-slip crystals, PSB ladder structures was found in the [1( 12] crystal cycled at strain amplitudes below and within the plateau region of the CSS curve, while no PSB ladders occur in the [1( 17] crystal over the strain range investigated, and veins, labyrinths and cells are its characteristic dislocation patterns. For the [1( 12] and [1( 17] crystals, which are on the same [001]/[1( 11] side of the stereographic triangle, their primary and conjugate slip systems are non-coplanar and non-collinear systems with [110] plane symmetry, so the dislocation interactions would engender immobile Lomer – Cottrell locks. Why do their dislocation structures show different characteristics? It may be in fact understood if the geometrical relationship between crystal orientation (i.e. loading direction) and corresponding slip systems is checked. For the [1( 12] crystal, the direction of vectorial resultant between [1( 01] primary and [011] secondary slip directions is exactly the loading direction [1( 12], i.e. [1( 01]+ [011] [1( 12]. Therefore, the primary and secondary slip systems are strictly symmetrical with regard to the [1( 12] loading direction. During cycling, the formed Lomer–Cottrell locks would impede notably the motion of follow-up dislocations, and impel dislocations in these two systems to tend to glide and multiply in separated zones due to the high symmetry of these two slip systems. In each of zones, independent slip deformation, i.e. single-slip-type deformation is expected, leading to a similar dislocation structures including PSB ladders with that observed in single-slip crystals [15]. However, for the [1( 17] crystal, the disappearance of this kind of high slip symmetry is believed to be the main reason for the nonexistence of PSB ladder structures. Regarding the critical double-slip crystals, Gong et al. [27] reported that PSB ladders, veins and labyrinths constitute the main dislocation features in the critical double-slip crystal cycled at intermediate amplitudes and cell structures developed at higher strain ampli-
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tudes. Jin and Winter [15] also found PSB ladders and veins in the [012] critical double-slip crystal cycled at an intermediate strain amplitude of 3.0× 10 − 3. The present work revealed that the labyrinth structure becomes the main dislocation configuration in cyclically deformed [017] critical double-slip crystals and that some narrow PSB ladder-like structures are embedded in the labyrinth structures. Gong et al. [27] asserted that the effect of the operation of critical slip system on cyclic deformation behavior in the [034] critical double-slip crystal is analogous to that of the increase in strain amplitude on single-slip crystals’ behavior. It can thus be inferred that the formation of PSB ladder structures is promoted by the involvement of a critical (secondary) slip. Certainly, since there is little difference of the geometrical relationship between crystal orientation and corresponding slip systems among these critical double-slip crystals, their dislocation structures still present distinctive features to a certain extent. To sum up, the PSB ladders structure is a common dislocation feature for the critical double-slip crystals, and its role playing during cyclic deformation tend to become weaker as the orientation varies from the [011] orientation to the [001] orientation along the [001]/[011] side of the stereographic standard triangle. Two extreme cases are as follows, first, in cyclically deformed crystals with [011] orientation, the PSB ladders structure is a main deformation microstructure [13], causing a clear plateau region of the CSS curve [33]; secondly, for crystals with [001] orientation, no PSBs were found and the labyrinth structure was considered to accommodate the applied strains during cycling [25], causing a complete disappearance of a plateau region in the CSS curve [34]. Therefore, the dislocation structure of critical doubleslip crystals changes gradually with the variation in crystallographic orientation along the [001]/[011] boundary. Consequently, such an orientation dependence of dislocation structure was believed to result not only from the different modes of dislocation interactions among slip systems operating in the crystals but also from different slip deformation characteristics induced by the different geometrical relationships between orientations and corresponding slip systems in the differently oriented crystals. The orientation dependence of dislocation structure accounts well for the corresponding orientation dependence of the plateau behavior in the CSS curve of Cu single crystals reported previously, [10].
5. Conclusions Based on the experimental results and discussion above, the following conclusions can be drawn. (1)
There exists an obvious crystallographic orientation dependence of the dislocation structures induced by cyclic deformation of critical and (or) conjugate double-slip-oriented Cu single crystals, which can explain well the corresponding orientation dependence of the plateau behavior in the CSS curve. (2) The formation of well-developed PSB ladder structures is a basic reason for the occurrence of a plateau region in the CSS curve of the [1( 12] crystal. PSB ladder structure, which developed from vein and then wall structures, does occur in the lower strain amplitude below the plateau region in the CSS curve for the very crystal despite the fact that it is just in the initial stage of formation and is not well developed in this instance. This experimental result indicates that the formation of PSBs is only a necessary but not a sufficient condition for the presence of a plateau region of the CSS curve. (3) The saturation dislocation structures of [1( 17] crystals are mainly composed of vein structures at low strain amplitudes, and developed into labyrinth-like and cell structures at high strain amplitudes. The decrease in the scale of vein structure with increasing strain amplitude and the absence of PSB ladder structure was believed to cause the disappearance of a plateau region in the CSS curve of the [1( 17] crystal. (4) The saturation dislocation structure of the [017] crystal consists primarily of irregular labyrinth structure at a low strain amplitude of 1.2× 10 − 4. A distinctive ‘two-phase’ structure, i.e. labyrinth structure and PSB ladder-like structure was found to form at a comparatively higher strain amplitude of 9.4×10 − 3. The average width of labyrinth channel decreases with increasing strain amplitude. The occurrence of a quasi-plateau in the CSS curve of the [017] crystal was considered as being the result of the joint effects of the scale change of the labyrinth structure and the formation of PSB ladder-like structures.
Acknowledgements This work was financially supported by the Special Funds for the Major State Basic Research Project of China under Grant No. G19990680 and a grant-in-aid for Scientific Research and Development from the Ministry of Education, Science, Sports and Culture of Japan. This support is gratefully acknowledged. Dr X.W. Li would like to acknowledge the Japan Society for the Promotion of Science (JSPS) for a postdoctoral fellowship for Foreign Researchers, and to give his loving thanks to his wife Yang Liu and daughter Ruo Xuan Li for their whole-hearted love and support. Also, Dr X.W. Li is grateful to Professor C. Blochwitz and Dr C. Buque for providing their manuscripts for perusal.
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