Saturated dislocation structures of cyclic deformation Ni[110] single crystals

Materials' Science and Engineering, A 147 ( 1991 ) 155-160

155

Saturated dislocation structures of cyclic deformation Nil110] single

crystals Chen Xianfeng Department of Materials Science, Shanghai Jiao Tong University, Shanghai 200030 (China)

(Received July 20, 1990; in revised form April 24, 1991 )

Abstract The cyclic deformation of Ni[1 10] single crystals has been investigated in tension-compression under total strain control. The slip systems found by slip trace analysis are (101)[11 i], (112)[11 i] and (213)[ 11 i]. Transmission electron microscopy (TEM) observations showed that at the saturation stage of cyclic deformation the characteristic features of the dislocation structure are dislocation tangles and bands located in definite orientations parallel to the intersections of the slip planes and the projective planes. It is suggested that the formation of dislocation bands is due to highly concentrated dislocations on the planes which constitute the coarse slip bands, producing high elastic strain fields in these planes. Under diffraction conditions these highly strained planes appear as thick and dark bands in TEM images.

1. Introduction Cyclic deformation and its micromechanisms have been widely investigated in f.c.c, metals [1-9]. It has been found that the deformation of f.c.c, crystals in the saturation stage is heterogeneous and is concentrated in persistent slip bands (PSBs). A plateau appears in the cyclic stress-strain (CSS) curves. The corresponding dislocation structure is the dislocation ladder structure of the PSBs and the dislocation vein structure of the matrix, In contrast, a limited number of investigations on the cyclic deformation behaviour of b.c.c, crystals have been reported [10-16] because of the complexity of the dislocation slip properties of b.c.c, metals. Studies on a-Fe [10] and Fe-Si [12] showed that their saturated dislocation structures are two- and three-dimensional cell structures respectively. Sestak et al. [11] showed recently that the cyclic deformation of b.c.c. Fe-Si alloy crystals at 2 9 5 K exhibits similarly shaped CSS curves and similar strain localization in the PSBs, together with the development of a dislocation arrangement similar to that of f.c.c, metal crystals. However, there is appreciable secondary slip in Fe-Si crystals at the beginning of the saturation stage, leading to a cell structure in the PSBs. The cyclic deformation of iron is signifi0921-5093/91/$3.50

cantly different to that of Fe-Si crystals and f.c.c. metals. The CSS curves exhibit two plateaux and PSBs do not form. Observations of the dislocation substructures of deformed molybdenum crystals [15] showed that dislocation tangles occur at low plastic strain amplitude and that a typical wall structure on the primary plane and cell structure on the conjugate plane are formed under large cumulative strain. Studies on the cyclic deformation of niobium single crystals [13] showed a plateau in the CSS curves at low amplitude, the length of this plateau depending on the temperature and strain rate. The dislocation structures of niobium single crystals during cyclic deformation were studied recently [16]. In this paper, results on the formation of dislocation bands in cyclically deformed N b [ l l 0 ] single crystals are reported and the cause of the formation of dislocation bands is discussed.

2. Experimental details Nb[110] single crystals 7 mm in diameter were prepared in an electron bombardment furnace. The chemical composition is given in Table 1. Specimens were chemically polished. Cyclic deformation was conducted in a symmetrical, © Elsevier Sequoia/Printed in The Netherlands

156 TABLE 1 Chemical composition of niobium single crystals (weight per cent) Si

Fe

AI

Cr

Ti

Mg

Mn

C

O

Nb

<0.0015

<0.0014

<0.001

<0.0003

<0.001

<0.001

<0.001

0.007

0.007

Balance

uniaxial push-pull mode with an Instron 1251 machine under conditions of total strain control and constant plastic strain. Triangular wave strain signals were employed. All tests were conducted in air at room temperature at a constant strain rate ~ = 6 x 10 - 4 s -1. The gauge length was 12.5 mm. The test procedure was as follows: (1) a group of crystals were cyclically deformed to saturation at selected strain amplitudes; (2) one crystal was tested in a multistep mode with gradually increased strain amplitudes; (3) a group of crystals were cyclically deformed with equal strain amplitudes but different numbers of cycles. The slip line directions were measured on the cylindrical surface of specimens and the slip planes were determined from stereographic plots of these directions, Discs 0.5 mm thick were cut from the deformed specimens along the longitudinal axis and carefully ground with fine abrasive paper, They were then electropolished using a doublejet technique until perforation, at which time they were ready for transmission electron microscopy (TEM).

v~ •pQ 11o 91E-3 edE-

~ 9o ~

" _ ~

5o

,

=

~ z

0

,

k 2 ec~,~

,

~ 3

,

i 4

Fig. 1. Selected cyclic hardening curves, with plastic strain amplitude indicated on each curve.

rs / •Po 11o loo 90 80

. / ]

7o I

3.1. Cyclic hardening and cyclic stress-strain curves A group of Nb[110] single crystals were cyclically deformed to saturation. Figure 1 shows the cyclic hardening curves for various plastic strain amplitudes. These were obtained by plotting the axial peak stress (mean value of tensile and compressive stresses) against the cumulative plastic strain Ecum 4Nep~, where N is the number of cycles and epl is the plastic strain amplitude, In Fig. 2 the saturation stress from a singleamplitude test is plotted against the plastic strain amplitude. The result is a semilogarithmic CSS curve. It can be seen that the curve may be separated into two distinctly different regimes according to the value of the slope. Nevertheless,

1.6 E - 3

7o

10 -5

3. Results and discussion

4~E-3 " 5G~--4

I

I

I I III]

I

i

i

i

10 "~1

i i i l[

10-3

i

I

i

I

i i i iI

10-2

Ep~

Fig. 2. Cyclic stress-strain curve of Nb[110] single crystal.

without doing a lower amplitude test it is difficult to judge whether the plateau will appear or not. The saturation stresses obtained by the multistep method are similar to that in Fig. 2.

3.2. Slip trace analysis Only a few slip traces appeared on the specimen surfaces when cyclic deformation was carried out at low plastic strain amplitude, e.g. ep~= 5 x 10 -5. The number of slip traces increases with increasing epl. The morphology of the slip traces is shown in Fig. 3. Stereographic plots of surface slip traces of Nb[110] crystals are shown in Fig. 4. They were tested in (a) tension,

157

(b) compression, (c) cyclic deformation and (d) multistep cyclic deformation. It may be seen that the operative slip systems in N b [ l l 0 ] crystals during larger deformation in tension, compression and cyclic deformation are all the same. The slip direction is [11]] and the slip planes are (101), (112)and (213). 3.3. Dislocation structures

.....~

'/z~ - : ..... , I ;I Fig. 3. Surface strain distribution of cyclically deformed zrystal,

f

Dislocation structures of cyclically deformed crystals were observed with a J E O L 100CX electron microscope. The results are summarized in Table 2. It can be seen that the substructure of crystals cyclically deformed at low total strain amplitude

i:'..a

a

b

e

d

Fig. 4. Stereographic plots of slip bands on the specimen surfaces of deformed crystals: (a) tensed; (b) compressed; (c) cyclically deformed; (d) multistep cyclically deformed.

158 TABLE 2 Dislocation s t r u c t u r e s o b s e r v e d in n i o b i u m crystals cyclically d e f o r m e d at selected strain a m p l i t u d e s No. 1

Strain a m p l i t u d e

C u m u l a t i v e strain

Dislocation s t r u c t u r e

Fig.

eto t = 0.38 × 1 0 - 3

£toLcum= 0.95

Tangles

5

eto t = 0.68 x 1 0 - 3

etot. . . . = 1.5

Tangles

6

epl = 5 x 1 0 - 5 epl = 5 x 10 -5 epl = 5.6 × 10 4 epl = 1.6 × 10 -3 eo~ = 4.1 x 10 3 Col = 6.6 × 1 0 - 3 epl = 9.1 × 10 - 3 epl = 9.1 x 1 0 - 3 Multistep

ecum = 0 . 0 0 2 2 ecum = 0 . 2 5 eCum= 1.5 ecum = 3.2 ec,m = 1.6 ecum = 3.6 gcum = 0.018 ecum = 3.6 e~um = 4.3

Tangles Tangles Tangles Tangles Tangles Tangles Tangles Tangles Tangles

(%1=0) 2

(%,=0)

3 4 5 6 7 8 9 10 11

~

~ii~i~ i~i! !iiiii!'~¸

i!~!i ¸¸i!i~;!!iii i

~ ;~ii ~

and and and and and and and and and

bands bands bands bands bands bands bands bands bands

7 11 8

9 10

~ ii~i~il

Fig. 5. Dislocation s t r u c t u r e in cyclically d e f o r m e d crystal, e t o t = 0 . 3 8 x 1 0 3, ecum=O.95, B=[ill],g=[llO ].

consists of dislocation tangles (Figs. 5 and 6). When the crystals are deformed at medium plastic strain amplitude, dislocation tangles and bands are revealed (Figs. 7-11 ). In the case of Figs. 5 and 6 the total amplitude did not reach the value at which plastic deformation occurred, but dislocations had already been generated in some regions of the crystal by the occurrence of localized plastic flow. This may be attributed to heterogeneous deformation in the crystal under the push-pull mode. The dislocation structures shown in Figs. 7-11 were observed in specimens cyclically deformed at medium plastic strain amplitude. In addition to the dislocation tangles, dislocation bands are evident. When observed on the (i 11) projective plane, the directions of the bands were found to be perpendicular to [101], [110], [01]] and [12i]

Fig. 6. Dislocation B=[ill],g={ll0}.

bands,

etot=0.68

× 10 -3,

ecu m = 1 . 5 ,

"x~77 Vt~-~'~'x

Fig. 7. Dislocation B = [i 11], g = [101].

bands,

ep~ = 5 x 1 0 - 5,

ecurn= 0.0022,

respectively (Figs. 7, 8, 9(a)and 10(a)). On the (011) projective plane they are perpendicular to [01 i], [2il] and [21 i] respectively (Figs. 9(b) and 10(b)). On the (001) projective plane the bands

159

%,,,

\

I

[o1~j Fig. 8. Saturated dislocation ecu m = 3.2, B=[i 1 11, g=[12i].

structure, tp~= 1.6 x 10 -3,

m ~

~z.~ ~'~o

<.5/ \ ~

t:

I

Q

i~ [110]

pm

Fig. 10. Dislocation bands in a specimen multistep tested with a gradually increasing (a) B = [ i l l ] , g=[101]; (b) B = [011 ], g = [2(I(I].

"

(o11)11

i

I

I IJm

~

%':

~

~~

(a)

g

[01~1

~m[21iJ 1 pm '~ll Fig. 9. Dislocation

bands, %1 = 9.1 x I O_ ~, ecu m = 0.018: (a)

B=[i l 1],g=[O1 i];(b)B=[OI 1], g=[O1 l].

are pependicular to each other and perpendicular to [010] and [100] respectively (Fig. 11). There are also parallel dislocation lines in the [110] direction which take an angle of 45 ° with respect to the bands. According to the analysis of the slip traces, these directions of the dislocation bands are just the normals of the operative {101} and {112} slip planes which are located at the edge-on position under the corresponding observation conditions, Therefore the observed dislocation bands indicate the intersections between the slip planes and the projective planes. On the ( i l l ) plane the orientations of the dislocation bands are the intersections beween the slip planes ( 101 ), ( 1 l 0), (011) and (121) and the image plane (i 11) (Figs. 7, 8, 9(a) and 10(a)). On the (011) plane the orientations of the dislocation bands are the inter-

(b)

~ ~.~ k~ /

~;:'~ ,..,..~/ ~ !~

~'¢ ...... Fig. 11. Dislocation configuration, %,= 5.6 x 10-4, tcu~= 1.5: (a) b a n d s perpendicular to each other, g = [ l l 0 ] ,

B=[001]; (b) dislocation lines oriented at 45 ° to bands, g= [110], B= [001].

sections between the slip planes (011), ( 2 i l ) and (21i) and the image plane (011) (Figs. 9(b) and 10(b)). According to the above analysis, we would expect that the dislocation bands perpendicular to each other should be found when B = [001],

160 e.g. the dislocation bands should be along the intersecting lines of the (011 ) and ( 101 ) slip planes with the (011 ) projective plane. This is verified by Fig. 11. Therefore the occurrence of dislocation bands may be related to the heterogeneity of cyclic deformation, which is concentrated on crystallographic planes showing coarse slip bands. Concentrated dislocation lines and tangles existing in these slip bands result in strong elastic strain fields. When the TEM image was taken with such a plane under diffraction conditions, thick and dark bands appeared, Both the cyclic deformation tested at different strain amplitudes and at constant strain amplitude but different deformation cycles verified that the slip traces on the specimen surfaces are in correspondence with the observed dislocation bands in the TEM images. When cyclic deformation was carried out at a strain amplitude lower than the plastic deformation amplitude, no slip trace appeared on the specimen surface and dislocation bands were not found in the crystal. At lower £pl a few slip traces appeared and fewer dislocation bands could be found in some areas. With increasing epl the slip traces increase and the dislocation bands can be found readily.

4. C o n c l u s i o n s (1) P S B d i s l o c a t i o n s t r u c t u r e s a n d cell s t r u c -

tures were not observed in Nb[110] crystals after cyclic deformation at constant plastic strain amplitude. (2) At constant plastic strain amplitude the operative slip systems in Nb[110] crystals are mainly (110)[11i] followed by (112)[11i] and (213)[11i]. (3) D i s l o c a t i o n b a n d s w i t h d e f i n i t e o r i e n t a -

tions were observed in the specimens tested.

Variation of the plastic strain amplitude does not affect the dislocation structure. These dislocation bands are due to the image contrast caused by highly concentrated dislocation tangles in the coarse slip bands. Acknowledgments This work was supported by the Chinese National Science Foundation. The author is grateful to Professor Lin Dongliang for his support and encouragement and to Dr. Han Kuanding for his valuable contribution at the beginning of this work. References 1 C. Laird, Mater. Sci. Eng., 25(1976) 187. 2 C. Laird, Fatigue and Microstructure, American Society

for Metals,Metals Park, OH, 1978, p. 149. 3 H. Mughrabi, Mater. Sci. Eng., 33(1978)207.

4 D. Kuhlmann-Wilsdorf and C. Laird, Mater. Sci., 27

(1977) 137.

5 Z. S. Basinski, A. S. Korbel and J. Basinski, Acta Metall., 28(1980) 991. 6 K. Mecke, C. Blochwitz and U. Kremling, Cryst. Res. Technol., 17(1982)1557. 7 R. Wang and H. Mughrabi, Mater. Sci. Eng., 65 (1984)

219.

8 N.Y. Jin and A. T. Winter, Acta Metall., 32 (1984) 1173. 9 N.Y. Jin, Acta Metall., 37(1989) 2055. 10 H. Mughrabi, K. Herz and X. Stark, Acta Metall., 24 (1976) 659; Int. J. Fract., 17(1981) 193. 11 B. Sestak, V. Novak and S. Libovicky, Phil. MaR. A, 57 (1988) 353. 12 H. Mori, M. Tokuwame and T. Migazaki, Phil. MaR. A, 40 (1979)409. 13 M. Anglada and E Guiu, Phil. MaR. A, 44 (198 l) 499,

523. 14 EGuiuandM.Anglada, Phil. Mag. A, 46(1982)881. 15 F'Guiu'J'A'PlanellandM'Anglada'inDisl°cati°nin Real Materials, Institute of Metals, London, 1985, p. 263. 16 Lin Dongliang, Wu Jiansheng and Chen Xianfeng, Mater. Sci. Eng., 85 (1987) 19.