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and Slip Bands with Compressive Strains during Tensile Deformation ...... 44) S. Miura, J. Takamura and N. Narita: Supplement of Trans. JIM 9. (1968) 555–561.
Materials Transactions, Vol. 51, No. 4 (2010) pp. 597 to 606 Special Issue on Crystallographic Orientation Distribution and Related Properties in Advanced Materials II #2010 The Japan Institute of Metals

Relationship between h111i Rotation Recrystallization Mechanism and Slip Bands with Compressive Strains during Tensile Deformation in Aluminum Single Crystals Fukuji Inoko1; * , Keizo Kashihara2 , Minoru Tagami3 and Tatsuya Okada3 1

The University of Tokushima, Tokushima 770-8506, Japan Wakayama National College of Technology, Gobo 644-0023, Japan 3 Department of Mechanical Engineering, Faculty of Engineering, The University of Tokushima, Tokushima 770-8506, Japan 2

The h111i rotation recrystallization mechanism, that is the slip band intersection model, presents that a h111i rotation recrystallization nucleus is formed in an intersection part of two kinds of slip bands. The nucleus is obtained by the rotation of the deformed matrix around h111i axis normal to the common cross slip plane of these slip systems. Eight kinds of nuclei are composed of four h111i axes with clockwise and counterclockwise rotations. For these formations in tensile deformation, the operation of slip bands with compressive strain plays an important role. So the operation of twenty-four slip systems including plus and minus directions should be estimated. In tensile deformation, the recrystallization nuclei of h001i, h112i, h111i, and Schmid factor m ¼ 0:5 with kink bands in aluminum single crystals have been estimated and compared with the experimental results, and good relations have been found between them in terms of the selection of kinds of nuclei and their frequency. [doi:10.2320/matertrans.MG200905] (Received October 1, 2009; Accepted January 25, 2010; Published March 10, 2010) Keywords: aluminum single crystals, tensile deformation, h111i rotation recrystallization mechanism, slip band intersection model, twentyfour slip systems, compressive slip, kink band, vortex in couette flow

1.

Introduction D5 110

The h111i rotation recrystallization mechanism proposed by Inoko,1) and Inoko and Fujita2) using four types of aluminum bicrystals with each 10 {111} twist boundary and different tensile axes deformed in tension to 30% strain shows that a recrystallized grain (RG) is formed by the rotation of adjoining deformed matrix (ADM) around the h111i normal to the common cross slip plane of two activated slip bands in their intersection. As each 10 {111} twist boundary corresponds to the cross slip plane of primary slip systems in both component crystals of the bicrystals, the number of RGs with the rotation around the h111i normal to the twist boundary is maximum. Especially, in the bicrystal with tensile axes of component crystals A and B shown by the stereographic projection in Fig. 1, many RGs were formed along the boundary parallel to P4 (11 1) in the back face normal to near D5 [110] with six kinds of RGs except to the clockwise and counterclockwise rotations around normal [111] to the primary slip plane P1 (111), and no RG did along the boundary of the front face. The shapes of the RGs are different with rotation axes. The RGs rotated around normal to P4 (11 1) grow along the boundary parallel to P4 plane to become longitudinal shape, while those of RGs normal to P2 (1 11) and P3 (1 1 1) do into both component crystals to become lozenge shapes. During tensile deformation, the twist angle in the bicrystal decreases to zero to become a single crystal with [1 12] tensile axis. Successively, in four types of aluminum bicrystals with each 28 {111} twist boundary by Inoko and Mima3) and bicrystals with a 90 {112} twist boundary by Inoko, Fujita and Akizono,4) the result of the above bicrystal was reaffirmed. *Professor

Emeritus, The University of Tokushima

P1 111 010

D2

101

D6

011

-Y

111 P2

P4 111 110

D3

A

112

111

001

B

P4

Y

D1 101

D4 P3

100

011

111

D5 110

Fig. 1 Stereographic projection of tensile directions of component crystals A and B in an aluminum bicrystal with a (11 1) 10 twist boundary. Grain boundary is normal to Y axis [11 1]. The twist angle decreases with increasing tensile strain for the bicrystal to become a single crystal with [1 12] tensile direction.

Figure 2 shows a stereographic projection in which slip systems of aluminum single crystals with the tensile axes of Schmid factor m ¼ 0:5, [001], [1 12] and [1 11] are indicated, for example P1 (111): primary, P2 (1 11): critical, P3 (1 1 1): conjugate, P4 (11 1): cross slip planes, and D1 [1 01]D6 [011]: six possible slip directions. The sign P1D1 (111)[1 01] indicates primary slip system on plane P1 (111) to direction D1 [1 01], and P1D-1 (111)[101 ] the slip system to inverse (minus) direction of D1 [1 01]. In this figure for the cases of tensile axes within triangle [1 11]-[1 12]-[011], the plane P4 (11 1) should be altered to P-4 (11 1) because Schmid factors of the slip systems on plane P4 (1 11 ) should be plus.

598

F. Inoko, K. Kashihara, M. Tagami and T. Okada Rotation axis P4

100 D3 110

P1D1

P4 plane

Screw dislocation network: Twist boundary

D5 110 P2D5

D1 101 P3111 010

P2 111 112 m=0.5

D4 011

001

P4 111

010 D6 011

Edge dislocation network: Tilt boundary

P1 111 D2 101 D5 110

D3 110

100

Fig. 2 Stereographic projection of tensile axes of Schmid factor m ¼ 0:5, h001i, h112i and h111i in aluminum single crystals. m ¼ 0:5 crystal forms kink bands (KBs), and h001i, h112i and h111i crystals form multiple slip bands without deformation band.

In the kink bands (KBs) of aluminum single crystals with Schmid factor m ¼ 0:5, eight kinds of RGs which were composed of eight kinds of clockwise and counterclockwise rotations around each normal to four {111} planes (P1P4) were detected by Inoko, Kurimoto and Kashihara,5) and Inoko and Kashihara.6) The authors7) found with surprise and expectation that in the kink band (KB) the slip on the critical slip plane P2 (1 11) remarkably operates toward minus (compressive) direction, which can be decided from the change in the slope of the primary slip bands P1D1 (111)[1 01] in the KB. From this fact, the intersection of two kinds of slip bands in which one is the primary slip band P1D1 (111)[1 01] and another is the critical slip band P2D-5 (1 11)[1 1 0] can be rotated counterclockwise around the normal [11 1] to their common cross slip plane P4 as shown in Fig. 3 and Fig. 4. These figures indicate the same mechanism with two kinds of expressions for the h111i rotation recrystallization nucleus (RN). Figure 3 is our h111i rotation recrystallization mechanism1,2,7) and presents a cylindrical nucleus formed by the counterclockwise rotation of the adjoining deformed matrix (ADM) around the normal to the common cross slip plane P4 (11 1) of primary slip system P1D1 (111)[1 01] and critical slip system P2D-5 (1 11)[1 1 0]. It is surrounded by two kinds of dislocation networks. One is twist boundaries composed of screw dislocations of P1D1 (111)[1 01] and P2D-5 (1 11)[1 1 0] on upper plane P4 (11 1) and lower one P-4 (1 11 ). Another is tilt boundaries of side face composed of their edge dislocations. Also Fig. 4 is our ‘‘slip bands intersection model’’7) called by Humphrys,8) and presents the formation of a nucleus in KB due to the intersection of two kinds of activated slip systems (bands) P1D1 (111)[1 01] with tensile strain, and P2D-5 (1 11)[1 1 0] with compressive strain. Figure 4(c) shows two dimensional expression for the formation of a nucleus due to the intersection of two activated slip bands (systems) of P1D1 and P2D-5. Figure 4(d) gives a schematic diagram of a parallelepiped nucleus by three

Fig. 3 Schematic illustration showing the h111i rotation recrystallization mechanism. A cylindrical (or parallelepiped) nucleus is formed by the counterclockwise rotation of the adjoining deformed matrix (ADM) around the normal to the common cross slip plane P4 (11 1) of two kinds of activated slip systems (bands) P1D1 (111)[1 01] and P2D-5 ð1 11Þ½1 1 0] in their intersection.

dimensional expression. During tensile deformation such operation of slip bands P2D-5 (1 11)[1 1 0] and P2D-2 (1 11)[1 01 ] with compressive strains can form many kinds of RGs. And also, Fig. 5 shows whether cross slip of primary slip system promotes tensile strain or compressive strain for tensile axis of FCC single crystal within the standard triangle [001]-[011]-[1 11]. When a tensile axis is situated within the red region [001]-[011]-[1 12] of the standard triangle, cross slip promotes tensile strain with the maximum value of +1 in [001], while in the blue one [1 12]-[011]-[1 11] cross slip promotes compressive strain with the minimum value of 1 in pole P2 [1 11]. The value expresses the rate of Schmid factor of cross slip system per that of primary slip system for any tensile axes in the standard triangle. The original of this figure for FCC was calculated by Diehl et al.9) for estimating the capability of forming Lomer-Cottrell-sessiledislocations. Mori and Fujita10) used it for judging the easiness and difficulty of cross slip. Kashihara et al.11) and Tagami et al.12,13) found that during tensile deformation of [1 11] aluminum single crystal toward normal to P2 plane, all cross slips of six kinds of primary slip systems operated toward minus (compressive) directions to produce complex-fine-wavy slip bands and very dense dislocation cell walls. In h1 11i specimens deformed in tension to 30% and then annealed we observed eight kinds of many RGs. On tensile deformation of h011i aluminum single specimens Kashihara et al.14,15) found the special type of band of secondary slip (SBSS) and Wert et al.16) studied it in detail by using EBSD, which was different from KB, and BSS (band of secondary slip) which was called by Honeycombe.17) In SBSS the quasi-primary slip systems of P2D2 and P2D5 become active instead of the primary slip systems of P1D1 and P1D3 at the initial stage. With increasing strain the tensile orientation of deformed matrix (DM) slipped on P1 plane moved toward P2 pole, while that of SBSS slipped on P2 plane toward P1 pole. So each boundary between DMs and SBSSs forms large angle tilt boundary with small distortion. It is different from the case of the boundaries

Relationship between h111i Rotation Recrystallization Mechanism and Slip Bands with Compressive Strains during Tensile Deformation

P1 (DM)

599

P2 (KB)

P3 (DM)

P1 (KB)

50µm

(a)

(c)

(b)

(d)

Fig. 4 (a) SEM micrograph showing a kink band (KB). (b) TEM micrograph showing that KB is composed of cell structures. Straight cell walls corresponding to slip bands parallel to critical slip plane P2 (1 11) are formed. (c) Schematic illustration showing that in the intersection of two kinds of activated slip bands P1D1 (111)[1 01] with tensile strain and P2D-5 (1 11)[1 1 0] with compressive strain a nucleus is formed by the counterclockwise rotation of adjoining deformed matrix (ADM) around normal to P4 plane (11 1). P4 plane is roughly parallel to the free surface or this sheet. (d) A parallelepiped RN composed of three kinds of six slip planes P1s, P2s, and P4s in the interior of specimen, while in the surface layer P1s, P2s, and P4 and free surface.

111

112

-1 -0.8 -0.6 -0.4 -0.2

001

1 0.8 0.6 0.4

0.2

0

011

Fig. 5 The rate of Schmid factor of cross slip system per that of primary slip system is calculated for tensile directions in the standard triangle. In red region of h001i-h011i-h1 12i, cross slip of any primary slip system promotes tensile strain more and more, while in blue region of h1 11ih011i-h1 12i cross slip with compressive strain occurs.

between KBs and DMs having strong distortion.6) In such SBSSs, eight kinds of many RGs were formed because the above minus cross slips would play an important role. Also Okada et al.18) studied with different type of SBSS in which the tensile axes of DMs moved toward near P2 pole and those of SBSSs followed at about 10 behind them with the same direction. The h011i in tension is very unstable orientation. The difference with a few degrees changes easily the mode of deformation. In SBSS studied by Okada et al.18) four kinds of many RGs were observed, which indicated almost four kinds of clockwise and counterclockwise rotations around P1 and P2 axes by EBSD. Therefore, we should understand still more that the operation of slip bands with compressive strain during tensile deformation is very important for the formation of h111i rotation recrystallization nuclei due to the h111i rotation recrystallization mechanism (that is, the slip band

F. Inoko, K. Kashihara, M. Tagami and T. Okada

intersection model). Till then, the formation of RGs and texture has been explained by many researchers standing by the nucleation theory or/and the growth theory. As the former ones Burgers and Louwerse19) expanded the theory of ‘‘local distortion’’ into a theory of recrystallization textures. They considered that the nucleus was rotated around h112i axis. Also, Cahn20) indicated the nucleation of RGs by the polygonization in the local distortion. However they have not explained the mechanism of h111i rotation RGs. The latter ones standing by the theory of growth, for example by Barrett,21) Beck, Sperry and Hu,22) Kohara, Parthasarathi and Beck,23) Yoshida, Liebmann and Lu¨cke,24) and Senna and Lu¨cke,25) have asserted that h111i rotation RGs are formed by the easy growth of the RGs with approximately 40 h111i rotation relation to each adjoining deformed matrix (ADM). However, in our experimental results the h111i rotation ‘‘recrystallization nuclei (RNs)’’ do form already with high dislocation density after deformation as the h111i rotation of ADM around the normal to the common cross slip plane of each two activated slip bands in their intersections. After annealing with moderate temperatures and times, the RNs appear as RGs with the same orientation of each RNs. Therefore, the authors do stand by the nucleation theory, but do not always deny the growth theory. In this paper, for the importance on the operation of compressive slip bands during tensile deformation, the activity of twelve (twenty-four) slip systems (bands) are estimated with the results of the observation of activated slip bands, dislocation structures and orientation relationship between ADMs and RGs by the etch pit method,1–4) Scanning Electron Microscopy/Electron Channeling Pattern/Electron Back Scattering Diffraction (SEM/ECP/EBSD), Transmission Electron Microscopy (TEM) etc.,5–7,11–16,18,26) and the calculation values of Schmid factors before and after deformation in ADMs, the probability of minus cross slips with compressive strains, the shear stress along KB produced by the moment due to the operation of primary slip system and the constrain by the chucks. The estimations are compared with those of the above real data1–7,11–15,26) obtained on the kinds and the number of RGs in aluminum single crystals with tensile directions of m ¼ 0:5, [001], [1 12] and [1 11]. So we would confirm still more that the h111i rotation recrystallization (nucleus) mechanism, that is the slip band intersection model, is rightful and effective, and newly from the model the active slip systems would be derived more precisely to apply it to the control of textures. 2.

Experimental

The results of 99.99 mass% aluminum single crystals with tensile directions of m ¼ 0:5,5–7) h001i,12,13) h112i by Tagami et al.26) and h111i11–13) were used. Their final tensile strains were 30% (m ¼ 0:5), 25% (h001i), 22% (h112i) and 22% (h111i). The annealing conditions for getting initial stages of recrystallization were 733 K-80 min (fifty-eight RGs)5) and 713 K-6 min (eighty-five RGs)6) for m ¼ 0:5 specimens, 753 K903 K-8 min for h001i (no RG that is no RN),12,13) 753 K873 K-3 min for h112i (eight RGs that is few RNs),26) and 753-25 min (forty-five RGs)11) and 753 K-15.5 min (twenty RGs)12,13) for h111i.

Stress,σ /MPa

600

75

111 293K 71MPa

50 112 293K

32MPa

25 001 293K 22MPa m=0.5 293K 15MPa

0

5

10

15

20 25 Strain ε (%)

Fig. 6 Nominal stress-strain curves of m ¼ 0:5, h001i, h112i and h111i aluminum single crystals deformed in tension.

3.

Results and Discussion

The nominal stress-strain curves of aluminum single crystals with tensile axes of m ¼ 0:5, h001i, h112i and h111i are shown in Fig. 6. The nominal stress of h111i specimen shows very high work hardening with 71 MPa at 22% strain, while that of h001i indicates no work hardening over 10% strain at low stress level of 22 MPa at 25% strain, but at initial stage of strain it shows high value as it has eight kinds of primary slip systems. As specimen m ¼ 0:5 glides on the single slip plane P1, at very first stage of strain the stress is very low, but in aluminum at room temperature at low strain it moves to second stage of work hardening. Although KBs in which work hardening would be very high are formed, the stress is not so high because it is understood that the rate of KB per cross section of specimen is very low below approximately 1/10. 3.1 Single crystals with KBs (m ¼ 0:5)5,6) Figure 7(a) shows a plate of KB formed throughout thickness of aluminum single crystal with m ¼ 0:5 after tensile strain 30% by the operation of the slip bands of P2D-2 (1 11)[1 01 ] and P2D-5 (1 11)[1 1 0] with compressive strains in KB including the vicinities of boundaries between DMs and KB. Figure 7(b) explains that the shear stress  acts on KB plate parallel to the direction along KB.  is produced by a pair of moments Ms occurred due to single slips of P1D1 in DMs and the chuck constrain, and operates slip systems (bands) P2D-2 and P2D-5 with compressive strains. As shown in Figs. 3 and 4 the intersection of P1D1 and P2D-5 is rotated counterclockwise around [11 1] normal to their common cross slip plane P4. Examples on the formation of these nuclei are observed in the figures of the intersections of two activated slip bands on the surfaces of deformed aluminum and silver by the fine work of Kuhlmann-Wilsdorf and Wilsdorf.27) As shown in the figures of various slip bands observed by Mitchell et al.28) using extensively interference microscopy, and carbon replica in single crystals of  phase copper-

Relationship between h111i Rotation Recrystallization Mechanism and Slip Bands with Compressive Strains during Tensile Deformation

601

U

θ H

u

D

C

A

B

D’ C’ B’

A’

Defromation and rotation (θ ) of element in Couette flow30) or in slip band

(a)

U: Velocity in Couette flow30) or in slip band

TA DM

(KB) P2D2 B) (K P2D5

ban d)

P1

y

(K

(u +

B)

)

u dy dt y dx AD

udt

M)

(K

C’

KB

(D

D1

P1

ink

M

D1

Fig. 8 Schematic illustration showing rotation  of element in Couette flow.30) u is velocity in flow. U and H are difference of velocity and distance between upper and lower walls, respectively. Shear in a slip band is similar to Couette flow.

dθ AD

M DM

D

D’

B’

C

(b)

A’

dy

dy AB

dθ AB dθAB vdt

(v +

)

v dx dt x

B A

Fig. 7 (a) SEM photograph of kink band (KB) formed at 30% strain in m ¼ 0:5 crystal. (b) The mechanism of the formation of KB by shear stress  produced by moments due to operation of primary slip P1D1 (111)[1 01] and constrain of chucks.  operates slip bands P2D-5 (1 11)[1 1 0] with compressive strains.

aluminum alloys deformed in tension, the shear deformation of a slip band due to the motion of a group of dislocations is similar to one dimensional Couette flow as shown in Fig. 8.29,30) We would understand that the formation of a recrystallization nucleus RN in an intersection part by special pair of activated slip bands is similar to the vortex (rotation) in the two dimensional (2D) Couette flow as shown in Fig. 9.29,30) In it the rotation of element with dotted lines shows the vortex (rotation), while the distortion of element with solid lines is the deformation. A number of latent RN would be formed in deformation bands of KBs and SBSSs, in h111i specimen and near grain boundaries, etc. Their size would be smaller than 0.5 mm. In the vortex (rotation), that is latent RN, there would occur a number of dislocations just after the plastic deformation. During annealing it is recovered to polygonization not with low angle grain boundaries but with high angle ones, and would become a real RN. Table 1 shows that for twelve slip systems Schmid factor m before deformation, and mA (DM) in deformed matrix and mA (KB) in kink band after deformation, and stress transmission factor, that is orientation factor, Nij 4,31–34) are calculated. The Nij is given by the following equation:

dx x

Rotation (vortex) in 2D Couette flow Strength of vortex : ω z = 1/2 ( v/ x − u/ y) Fig. 9 Schematic illustration presenting a rotation (vortex) of element drown by dotted lines in two dimensional Couette flow.30) The rotation (vortex) corresponds to a h111i rotation recrystallization nucleus.

Table 1 Three kinds of Schmid factors m, mA (DM), mA (KB), and transmission factor Nij , for twelve slip systems in a single crystal with m ¼ 0:5. mA : Schmid factor after 30% strain. Slip system

m

mA (DM)

mA (KB)

Nij

P1D1

0.50

0.43

0.43

1:00

P1D3

0.24

0.22

0.24

0:50

P1D4

0.25

0.22

0.19

0:50

P2D2

0.47

0.38

0.49

0:67

P2D4

0.29

0.38

0.16

0:17

P2D5

0.18

0.02

0.29

0:50

P3D2

0.19

0.22

0.09

0:67

P3D3

0.11

0.22

0.03

+0.17

P3D6

0.30

0.44

0.12

0:50

P4D1

0.17

0.15

0.14

0:34

P4D5

0.05

0.02

0.12

+0.17

P4D6

0.23

0.15

0.26

0:17

602

F. Inoko, K. Kashihara, M. Tagami and T. Okada Table 2 The estimation and experimental results of RG (RN) in m ¼ 0:5 specimen. After final annealing at temperatures of 713733 K, it has eight types of clockwise and counterclockwise rotations (RNs) around the each normal to four slip planes P1P4. They are composed of each set of three slip systems including one or two minus slip systems in twenty-four (twelve) slip systems, and the activity and the note are indicated. The estimation chooses eight kinds of many RNs whose results correspond to the kinds and the number of RGs formed really.

Rotation axis

Pole P1 [111]

Clockwise direction Slip system

Activity

Note

RG

P2D4 (1 11)[01 1]

P3D3 (1 1 1)[1 10]

P3D-3 (1 1 1)[11 0]

Coplanar slip

17

Cross of

P4D-1 (11 1)[101 ]

P1D1

P1D4 (111)[01 1]

Coplanar slip

P3D-2 (1 1 1)[1 01 ]

Shear stress 

P1D-4 (111)[011 ] 20

P4D-5 (11 1)[1 1 0]

P1D3

Shear stress 

(111)[11 0] P2D2

(111)[1 10]

mA

(1 11)[101]

6

P4D-6 (11 1)[01 1 ]

P2D-2 (1 11)[1 01 ]

P1D1

Shear stress 

(111)[1 01]

P2D5

25

(1 11)[110] Quasi-pri. slip sys.

P3D6 (1 1 1)[011] : Normal,

: Some,

P1D4 7 Cross of P1D-1 Shear stress  Coplanar slip

17

Coplanar slip Shear stress 

26

Pri. slip sys.

P2D-5 (1 11)[1 1 0]

Shear stress 

P3D-6 (1 1 1)[01 1 ]

Shear stress 

25

: Scarcely

Nij ¼ ðei  ej Þðgi  gj Þ þ ðei  gj Þðej  gi Þ: Here,

RG

P4D6

(111)[101 ]

: Remarkable,

Note Cross of

(11 1)[011]

P1D-1 Pole P4 [11 1]

P3D2 (1 1 1)[101]

Activity

P4D5 (11 1)[110]

P1D-3 Pole P3 [1 1 1]

Slip System

P2D-4 (1 11)[011 ]

P4D1 (11 1)[1 01]

Pole P2 [1 11]

Counterclockwise direction

ð1Þ

ei : gi : ej : gj :

unit vector normal to kink band, unit vector parallel to kink band, unit vector normal to slip plane j ( j ¼ 14), unit vector parallel to slip direction j ( j = three from 16). Shear stress s acted on the slip system j by the shear stress  is obtained as a following equation: s ¼ Nij :

ð2Þ

From the experimental results of slip bands in KB observed by SEM, s operates slip systems of P2D5 and P2D2 to the inverse directions, that is P2D-5 and P2D-2 was confirmed. The shear stress total acted for the operation of the slip system j is given in the following equation: total ¼ m þ s ¼ m þ Nij ;

ð3Þ

where m is the shear stress on the slip system j by the applied tensile stress. In order to operate the slip system P2D5 against the forest dislocations on the primary slip P1 plane in KB to the inverse directions, that is P2D-5 with compressive strain, it would be necessary for total to be not

smaller than the absolute value of a compressive shear stress of 0:5 whose value operates the primary slip system P1D-1 in DM in compression. Assuming that  ¼ f , and substituting m and Nij in eq. (3) by the values of m (¼ 0:18) and Nij (¼ 0:5), respectively, for P2D5 in Table 1, the value of f in the early stage of KB formation is given by 0:5 5 0:18  0:5 f  f = 1:36 Also we obtain at 30% strain that f = 0:90 for m ¼ 0:43 and mA ðDMÞ ¼ 0:02 in DM, and f = 1:44 for m ¼ 0:43 and mA ðKBÞ ¼ 0:29 in KB. So the value of f would not be smaller than approximately 1:31:5. As the results of it, we should consider for the minus (compressive) slip systems of P1D-1, P1D-3, P1D-4, P3D-2, P3D-6 and P4D-1 to be operated. Table 2 indicates that eight types of rotations around the normal to each four slip planes P1P4 to two directions clockwise and counter-clockwise are produced by the composition of each three slip systems including one or two minus slip systems in twenty-four (twelve) slip systems, and the activity and the note of them. The number of RGs for each kind of the rotation is also listed. Therefore, the operation of minus slip systems much increases the

Relationship between h111i Rotation Recrystallization Mechanism and Slip Bands with Compressive Strains during Tensile Deformation

probability of the formation of RGs in the kind and the number. The activity of twenty-four slip systems and the number of RGs for each kind of the rotation were measured. From Table 2, both of the estimation and the experimental results on the formation of eight kinds of RGs and the number of them are consistent with each other. h001i, h112i and h111i specimens with multiple slip systems without deformation band Table 3 shows Schmid factors on [001], [1 12] and [1 11] specimens. [001] specimen has eight kinds of primary slip systems with the same Schmid factor of m ¼ 0:41 and the rest of four slip systems with m ¼ 0. [1 12] specimen has two kinds of primary slip systems with m ¼ 0:41, four kinds of secondary slip systems with m ¼ 0:27, and four kinds of ones with m ¼ 0. [1 11] specimen has six kinds of primary slip systems with m ¼ 0:27 and six kinds of ones with m ¼ 0. 3.2.1 [001] specimen12,13) From Fig. 2 and Table 3, [001] specimen has eight kinds of primary slip systems, which have four pairs of cross slip systems P1D1-P4D1, P1D4-P2D4, P2D2-P3D2 and P3D6P4D6. So the activation of the cross slips promotes tensile strains more and more. During tensile deformation the tensile axis maintains stable. Therefore as shown in Fig. 6 at the stage less than 0.2% strain work hardening is very high due to the multiple slips with eight kinds of slip systems, but over

603

10% work hardening hardly occurs. In the whole region of the surface of the crystal, prominent cross slips can be observed easily. The dislocation density of cell walls is very low. As shown in Table 4, although eight kinds of primary slips occur remarkably, they do not intersect each other for the formation of RN. In addition, for example, the operation of P2D-4 and P3D3 is not expected as their Schmid factors

3.2

Table 3 Schmid factors in h001i, h112i and h111i multiple slip specimens for each twelve slip systems. Slip system

h001i

h112i

h111i

P1D1

0.41

0.41

0.27

P1D3

0.00

0.27

0.27

P1D4

0.41

0.14

0.00

P2D2

0.41

0.27

0.00

P2D4

0.41

0.27

0.00

P2D5

0.00

0.00

0.00

P3D2

0.41

0.14

0.00

P3D3

0.00

0.27

0.27

P3D6

0.41

0.41

0.27

P4D1

0.41

0.00

0.27

P4D5

0.00

0.00

0.00

P4D6

0.41

0.00

0.27

Table 4 The estimation and experimental results of RG (RN) in h001i specimen. No RG were formed even after final annealing at high temperature of 903 K, although it has eight kinds of primary slip bands with prominent cross slips. And also the estimation judged no RG (RN), that is, no vortex. Rotation axis

Clockwise direction Slip system

Activity

Counterclockwise direction Note

RG

P2D-4 (1 11)[011 ] Pole P1 [111]

P2D4 (1 11)[01 1]

P3D3 (1 1 1)[1 10]

0

P4D1 P1D4

Pole P3 [1 1 1]

Pole P4 [11 1]

P3D-2

P3D2 (1 1 1)[101]

P1D-3

P1D3

(111)[11 0]

(111)[1 10] Pri. slip sys.

0

P4D-6

P4D6 (11 1)[011]

P1D-1

P1D1

(111)[101 ]

(111)[1 01]

P2D5

0

P3D6

Pri. slip sys.

(1 1 1)[011] : Remarkable,

: Normal,

: Some,

: Scarcely

Pri. slip sys.

0

P2D-2 (1 11)[1 01 ]

(11 1)[01 1 ]

(1 11)[110]

0

(111)[011 ]

P4D5 (11 1)[110]

P2D2

Pri. slip sys.

P3D-3 (1 1 1)[11 0]

P4D-5 (11 1)[1 1 0]

(1 11)[101]

RG

P1D-4

0

(1 1 1)[1 01 ]

Note

(11 1)[101 ]

Pri. slip sys.

(111)[01 1]

Activity

P4D-1

Pri. slip sys.

(11 1)[1 01]

Pole P2 [1 11]

Slip System

P2D-5 (1 11)[1 1 0] P3D-6 (1 1 1)[01 1 ]

0 Pri. slip sys. Pri. slip sys. 0

604

F. Inoko, K. Kashihara, M. Tagami and T. Okada Table 5 The estimation and experimental results of RG (RN) in [1 12] specimen. Some large RGs were formed after final annealing at high temperature of 873 K, because two kinds of primary slip systems P1D1 (111)[1 01] and P3D6 (1 1 1)[011] have low probability of cross slips, but with clockwise and counterclockwise directions. The estimation is reasonable to understand the experimental result.

Rotation axis

Clockwise direction Slip system

Activity

Note

Counterclockwise direction RG

P2D-4 (1 11)[011 ] Pole P1 [111]

P3D3 (1 1 1)[1 10]

Coplanar slip

1

Cross of P1D1

P1D4 P3D-2 (1 1 1)[1 01 ]

0

Cross of

P4D-1 (11 1)[101 ]

Cross of

P1D3

2

P1D1

P3D2 (1 1 1)[101]

Coplanar slip

0

P4D5 Cross of

(111)[11 0]

P1D3 (111)[1 10]

P3D3

P2D2 (1 11)[101]

1

P4D-6 (11 1)[01 1 ]

Cross of

P1D-1

Cross of

P4D6 P1D1 (111)[1 01]

P4D1/D-1

P2D5

1

(1 11)[110] P3D6

Pri. slip sys.

(1 1 1)[011] : Some,

Coplanar slip

P2D-2 (1 11)[1 01 ] (11 1)[011]

P3D6

(111)[101 ]

: Normal,

P3D-3 (1 1 1)[11 0]

(11 1)[110]

P1D-3

: Remarkable,

RG

(111)[011 ]

P4D-5 (11 1)[1 1 0]

Pole P4 [11 1]

Note

P1D-4

Coplanar slip

(111)[01 1]

Pole P3 [1 1 1]

Activity

P2D4 (1 11)[01 1]

P4D1 (11 1)[1 01]

Pole P2 [1 11]

Slip System

0 Cross of P3D6 Pri. slip sys.

P2D-5 (1 11)[1 1 0] P3D-6 (1 1 1)[01 1 ]

1 Cross of P4D6/D-6

: Scarcely

are m ¼ 0:41 and 0.00. To our surprise, the intersection parts between their primary slip bands do form no vortex (no RN). Also, in the experiment no RG was observed. 3.2.2 [1 12] specimen26) This specimen has two kinds of primary slip systems P1D1 and P3D6 with m ¼ 0:41, their coplanar slip systems of P1D3 and P3D3 with m ¼ 0:27 and four slip systems of P2D5, P4D1, P4D5 and P4D6 with m ¼ 0. The cross slips of the primary P1D1 and P3D6 are not easy because tensile axis [1 12] is situated on the boundary [1 12]-[011] between the red region and the blue one in Fig. 5. So, after deformation, slip bands of P1D1 and P3D6 are almost straight. Few short cross slips on P4 are observed. However, the cross slip of this specimen could do plus and/or minus directions. It means the capability of two kinds of clockwise and counterclockwise rotations. Table 5 shows the estimation and experimental results of the formation of RGs (RNs) using the activity of twentyfour slip systems. In [1 12] specimen, some large RGs form at higher annealing temperature of 873 K than that of 713733 K in m ¼ 0:5 specimens. It indicates that the formation of RNs is a few and difficult. The estimation is almost reasonable except at least one RN with the counterclockwise rotation around the normal [1 1 1] to P3 plane. 3.2.3 [1 11] specimen11–13) This [1 11] specimen has six kinds of primary slip systems

with m ¼ 0:27 and six kinds of slip systems with m ¼ 0. Figure 5 shows that the cross slips in this specimen are relatively difficult as they become slip bands with compressive strains even during tensile deformation. However the cross slips do occur over the whole regions with wavy and fine cross slips. In TEM micrographs cell walls with very high density of dislocations probably composed of a number of latent RNs or vortexes are observed.11–13) So, Fig. 6 indicates that h111i specimen has very high work hardening. From Table 6 it is understood that the cross slip bands with compressive strains play an important role on the formation of RNs with clockwise and counterclockwise rotations around P1, P3 and P4 poles. The RNs of clockwise and counterclockwise rotations around P2 pole can not be estimated only at the zero values of Schmid factors for P1D  4, P3D  2 and P4D  5, but after deformation layers of cell walls with very dense dislocations parallel to P2 plane were observed by TEM micrographs.11–13) From these results the operation of those slip systems on the RNs with P2 pole rotation would be understood. On activated slip systems in kink bands (KBs) in tensile deformation many researchers35–42) have judged to be the critical slip bands with high Schmid factors and tensile strains. For example, Jaoul35) showed a figure of a single crystal with KBs during tensile deformation. He drew it as if

Relationship between h111i Rotation Recrystallization Mechanism and Slip Bands with Compressive Strains during Tensile Deformation

605

Table 6 The estimation and experimental results of RG (RN) in h111i specimen. All eight kinds of many RGs were formed after final annealing at temperature of 753 K, because it has six kinds of primary slip systems whose active cross slip bands have compressive strains. As the result of it, all eight kinds of RGs were formed. And also the estimation gives eight kinds of many RGs (RNs). Rotation axis

Clockwise direction Slip system

Activity

Note

Counterclockwise direction RG

P2D-4 (1 11)[011 ] Pole P1 [111]

P3D3 (1 1 1)[1 10]

Pri. slip sys.

P1D-4

Cell walls//P2

P3D-2 (1 1 1)[1 01 ]

Cell walls//P2

P4D5 (1 11 )[110]

Cell walls//P2

(111)[011 ] P3D2

6

(1 1 1)[101] P4D-5 (1 11 )[1 1 0]

Cross of

P1D-3 (111)[11 0]

P1D3 (111)[1 10]

P3D3

P2D2 (1 11)[101]

P4D-6 (1 11 )[01 1 ]

Pri. slip sys. Cross of

P1D-1 (111)[101 ]

P1D1 (111)[1 01]

P4D1

P2D5 (1 11)[110]

13

P3D6 : Some,

Cross of P1D3

RG

(1 1 1)[01 1 ]

6

Pri. slip sys. Cell walls//P2 Cell walls//P2

9

Cell walls//P2 Pri. slip sys. 14 Cross of P3D6 Pri. slip sys.

P2D-5 (1 11)[1 1 0] P3D-6

Pri. slip sys.

(1 1 1)[011] : Normal,

Note

P2D-2 (1 11)[1 01 ]

7

P4D6 (1 11 )[011]

: Remarkable,

P4D1 (1 11 )[1 01]

P1D1

(111)[01 1]

Pole P4 [1 11 ]

P3D-3 (1 1 1)[11 0]

1

Cross of

P1D4

Pole P3 [1 1 1]

Activity

P2D4 (1 11)[01 1]

P4D-1 (1 11 )[101 ]

Pole P2 [1 11]

Slip System

5 Cross of P4D6

: Scarcely

in the KBs the critical slip with tensile strain had occurred, but from the photographs by Jaoul35) and Jaoul et al.,36) we can see that critical and/or conjugate slip bands with compressive strain occurred. Takamura37) got the experimental result of the rotation of KB showing compressive deformation. However he said that as if compressive deformation had occurred in KB. But he chose the critical slip systems with high and plus Schmid factors, and tensile strains as the activated slip. The primary slip system P1D1 and its coplanar slips P1D3 and P1D4 are active before the formation of KBs, and after it P1D-1, P1D-3 and P1D-4 on the primary slip plane, P2D-2 and P2D-5 on the critical, P3D-2 and P3D-6 on the conjugate, and P4D-1 on the cross with all compressive strains would be active. Therefore all eight kinds of a number of RGs (RNs) are formed. The Fig. 5 on the rates of Schmid factor of the cross slip system per the primary slip system was originally calculated by Diehl et al.9) for estimating the probability on the formation of the Lomer-Cottrell-sessile-dislocations. But for the formation it was not important whether the values of the rate are plus or minus. Ramaswami et al.43) observed that acute cross slip was the predominant mode of cross slip in crystals of the h1 11i orientation unlike the h001i orientation where only obtuse cross slip was observed. Miura et al.44) mentioned that in red region screw dislocations tended to

make obtuse cross slip while in blue region acute cross slip was expected. The authors11–13) found that cross slip in the blue region of the triangle h011i-h1 12i-h1 11i, especially near h1 11i, had compressive strain. So we judged that acute cross slip was compressive (minus) cross slip. In general, it is recognized that cross slip plays an important role on work softening. However, just after the operation of compressive cross slip does stress relief, it would produce strong work hardening. It should be reason that h111i specimen has wavy-fine slip bands, cell walls with very high dislocation density, very high work hardening as shown in Fig. 6, and eight kinds of many RGs (RNs). 4.

Conclusions

The main conclusions obtained are the following. (1) The h111i rotation mechanism, that is slip band intersection model, is similar to the formation of vortex (rotation) in two dimensional Couette flow. (2) By estimating the activation of twenty-four slip systems, the mechanism is useful to know kinds of h111i rotation recrystallized grains (nuclei), and in some detail the number. Especially operation of slip bands with compressive strains increases the kinds and the number of the nuclei.

606

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(3) In kink bands of m ¼ 0:5 crystal, critical slip bands, etc. with compressive strains occur due to the shear stress acted on the kink band to compressive direction by the moments produced by the rotation of primary slip bands and the constrain of both chucks. So eight kinds of many RGs form along the kink bands. (4) h001i cube crystals do not form any nucleus, because although eight kinds of primary slips and their cross slips are activated very remarkably, the other sixteen slip systems are not active. As the result of it, there is no intersection of slip bands to form nucleus. (5) Crystals in triangle h011i-h1 12i-h1 11i, especially h1 11i, have minus (acute) fine-wavy cross slips with compressive strains. So all eight kinds of many RGs (RNs) are formed in the whole surface. (6) If we know kinds of rotations of RGs, kinds of activated slip systems in the place could be estimated. REFERENCES 1) F. Inoko: Proc. 7th Riso Int. Symp., Ed. by N. Hansen et al., (Roskilde, Denmark, 1986) pp. 373–378. 2) F. Inoko and T. Fujita: Proc. JIMIS-4 (1986) Minakami, Japan, (Supplement to Trans. JIM) pp. 435–442. 3) F. Inoko and G. Mima: Scr. Metall. 21 (1987) 1039–1044. 4) F. Inoko, T. Fujita and K. Akizono: Scr. Metall. 21 (1987) 1399–1404. 5) F. Inoko, M. Kurimoto and K. Kashihara: J. Japan Inst. Metals 54 (1990) 642–649. 6) F. Inoko and K. Kashihara: J. Japan Inst. Metals 56 (1992) 361–370. 7) F. Inoko, T. Okada, M. Tagami and K. Kashihara: Proc. 21th Riso Int. Symp., Eds. N. Hansen et al., (Roslilde, Denmark, 2000) pp. 365–370. 8) F. J. Humphrys: Mater. Sci. Forum 447–470 (2004) 107–116. 9) V. J. Diehl, M. Kause, W. Offenha¨user and W. Staubwasser: Z. Metallk. 45 (1954) 489–492. 10) T. Mori and H. Fujita: Phil. Mag. 46 (1982) 91–104. 11) K. Kashihara, M. Tagami, T. Okada and F. Inoko: Mater. Sci. Eng. A 291 (2000) 207–217. 12) M. Tagami, K. Kashihara, T. Okada and F. Inoko: J. Japan Inst. Metals 64 (2000) 535–542. 13) M. Tagami, K. Kashihara, T. Okada and F. Inoko: Mater. Trans. 42 (2001) 2013–2020. 14) K. Kashihara, T. Tagami and F. Inoko: Mater. Trans. JIM 37 (1996) 564–571.

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