Grain size effects on the texture evolution of α-Zr

A c l a metall, mazer. Voh 4Z, No. 2, pp. 485 498, 1995

Pergamon

0956-7151(94)00238-X

Copyright ~ 1995 Elsevier Science Ltd Printed in Great Britain. All righls reserved 0956-7151/95 $9.50 + 0.00

G R A I N SIZE EFFECTS ON THE T E X T U R E EVOLUTION OF c~-Zr A. SALINAS-RODRIGUEZ Centro de lnvestigacidn y de Estudios Avanzados, Unidad Saltillo, Coahuila, Mexico (Received 14 January 1994: in revisedjbrm 18 May I994)

Abstract The texture evolution during the plastic deformation at room temperature of Zr 2.5Nb round bars was studied in specimens with two different ~-Zr grain sizes. It was found that during axisymmetric compression the strain producing mechanisms active during deformation depended on the grain size. In fine grained specimens there are two main phenomena characterizing the evolution of texture: (i) a rapid rotation of the grains about their (c) axis to form a <1120> fiber at strains below 0.20 and, (ii) a slow and progressive reorientation of the axes of the grains towards the compression axis to form a [0001] fiber texture tilted approx. 20'. The latter process takes strains larger than -0,80. In coarse grained material, the texture evolution is characterized by a sudden rotation of the axes to become aligned parallel to the compression axis at strains as low as -0.05. It is shown using a self-consistent viscoplaslic model of texture evolution that the type of texture obtained depends on the mechanism controlling slip acting as complementary deformation modes, control the texture evolution process. In coarse grained material twinning is responsible for the final texture observed.

INTRODUCTION During the plastic deformation of ~-Zr, glide on {10T0} planes of dislocations with 3<11_50) Burgers vectors is responsible for accommodating strains perpendicular to the axis of the h.c.p, crystallite. However, the number of available slip systems of this type is not sufficient to allow a crystallite in a polycrystalline aggregate to accommodate an arbitrarily imposed strain. Thus, other types of deformation modes, such as twinning and slip, must be activated to permit the grains in a polycrystal to deform parallel to <0001>. Reed-Hill [1] showed that, in coarse grained unalloyed Zr, {T012}<1101> "tensile twinning" and {1122} axis deformation. MacEwen et al. [3] have shown that the evolution of texture and residual stresses during the compression at room temperature of Zircaloy-2 can be explained in terms of the effects of {]'012}<1101> tensile twinning. The uniaxial compression of coarse grained Zircaloy-2, with a < 10]'0) initial fiber texture, causes a 90 ~ reorientation of the axes of the grains [1-3] resulting in the formation of a <0001 > fiber texture. The origin of this texture has been attributed to the activation of {10121<110l) tensile twins in grains 485

with <0001 } nearly perpendicular to the compression axis [1 3]. Tenckhoff [4] studied experimentally the mechanisms leading to the development of textures in coarse grained unalloyed Zr during plane strain rolling. This work showed that the final texture obtained, (0001)<10i0> tilted 30-40 about the rolling direction, was the result of the interaction of the reorientation tendencies produced by the activation of {T012} and {11_52I < i i 2 3 ) twins in conjunction with glide of ~<11~,0> dislocations. Recently, Tom6 et al. [5] introduced the Volume Fraction Transfer scheme to incorporate twinning systems into texture evolution simulations. This approach allowed them to predict correctly the reorientation tendencies observed in Zircaloy-2 deformed at room temperature. At temperatures higher than 850 K, 7-Zr single crystals deform primarily via glide mechanisms [6-9]. The reduced ability of the material to deform by twinning at high temperatures requires thc activation of slip systems with Burgers vectors of the type to accommodate the imposed deformation components parallel to the <0001> directions of the crystallites. Salinas-Rodriguez and Jonas [10] studied the high temperature texture development in Zr 2.5Nb using the full and relaxed constraints models of texture evolution. It was demonstrated that the activity of ( c + a ) slip systems, such as {i011}<1123>, was overestimated by these models. When the CRSS for slip was assumed to vary in the range 1-10 times the CRSS for slip, the activity of < c + a> slip dominated the texture

486

SALINAS-RODRIGUEZ:

TEXTURE EVOLUTION OF ~-Zr

development process and lead to rcoricntation tendencies and final textures opposite to what is normally found experimentally. Recently, gebensohn el al. [11] attempted to incorporate the effect of temperature into the simulation of rolling of h.c.p. polycrystals using full constraints and self-consistent viscoplastic models by varying the CRSS for pyramidal (c + a ) , basal ( a ) and prismatic ( a ) slip. They concluded that the experimental texture, i.e. (0002) poles in the plane perpendicular to the rolling direction, can only be predicted correctly by the self-consistent viscoplastic model. However, SalinasRodriguez [12] showed that similar results can be obtained using the so-called "pancake" relaxed constraints model of texture evolution, as long as (0001)(11_50) basal slip is considered to contribute significantly to the texture evolution. Furthermore, in this work it was shown that the (0002) pole figures predicted by the relaxed constraints model were independent of the CRSS for the active slip systems as long as r<'+ "' >- z b,&~ <"' > z ~;~,m~tJ~.. ~" The relevance of this work is the recognition of basal slip as an important deformation mode for h.c.p, polycrystals with a low c/a ratio. Unfortunately, there has not been much experimental work regarding the activity of basal slip in 3{-Zr. Akhtar [9] produced TEM evidence that shows that basal slip becomes an active deformation mode in Zr single crystals deformed at temperatures greater than 800 K. Levine [13] determined the low temperature CRSS for basal slip in 3{-Ti and studied in detail the rate controlling mechanism for this typc of slip at room temperature. TEM evidence for (c + a ) slip in deformed 3{-Zr is abundant and the occurrence of this deformation mode at low and high temperatures is now wen established [14, 15]. However, this type o1"dislocation is generated during deformation to maintain compatibility between crystallites which differ in their ability to accommodate the applied strain by the easier ( a ) type deformation modes [14] or in grains unfavorably oriented for this type of slip [15]. In general, (c + a ) dislocations are found in deformed polycrystalline ~-Zr near grain and twin boundaries and other regions of the microstructure where stress concentrations are high [14]. These observations support the results of the calculations reported by Tom6 et al. [5] and Salinas-Rodriguez and Jonas [10] for uniaxial deformation, and by Salinas-Rodriguez [12] and Lebensohn et al. [11] for the case of plane strain rolling. Furthermore, they indicatc as well that (c + a ) slip cannot be considered as a primary deformation mode during the plastic deformation of ~-Zr. In all these calculations, agreement between the predicted and the experimental textures is obtained when basal slip is incorporated into the models and the activity of pyramidal (c + a ) slip is limited to less than 10% of the overall average slip activity. The relaxed constraints and the selfconsistent viscoplastic models both have the same

effect of decreasing the activity of (c + a ) slip during the simulation of the plastic deformation of 3{-Zr.

From the discussion presented above it appears that the plastic deformation of 3{-Zr follows two different patterns depending on the temperature of deformation. At room temperature and up to 800 K, mechanical twinning plays an important role as a strain producing mechanism. Twinning controls the evolution of textures as a result of the massive and abrupt orientation changes produced when a twin is formed in a crystallite. At higher temperatures, however, the twinning activity is expected to decrease as the stresses required for the activation of (c + a ) slip mechanisms also decrease. As a result, the deformation and the texture evolution behaviors in this material must change accordingly. Grain size affects the nucleation of mechanical twins z,ia the Hall Petch relationship [16 18] with slip usually preceding the nucleation of twins [18]. Thus, as the grain size decreases the probability of twin nucleation decreases and, for the case of 3{-Zr deformed at room temperature, (c + a ) slip mechanisms must become increasingly important to allow generalized plastic flow of a polycrystalline specimen. Most of the research work carried out up to now on the plastic deformation and texture evolution of c~-Zr has been performed on coarse grained materials where twinning plays an important role in controlling the deformation. It was therefore decided to investigate the effect of grain size on the compressive deformation of Zr 2.5Nb at room temperature. This alloy is used in the fabrication of pressure tubes for Canadian nuclear reactors (CANDU) and is usually characterized by a microstructure of very narrow 3{-Zr grains (~< 1 pm) elongated in the axial direction of the tubes.

EXPERIMENTAL

Compression texture q/coarse grahwd Zircaloy-2 Figure I illustrates the inverse pole figures for the compression axis of Zircaloy-2 (1.5% Sn, 1200 ppm O) and Z~2.5Nb (2.5% Nb, 1100 ppm O) deformed to a compressive strain of -0.20. Apart from the differences in chemical composition and the occurrence of approx. 10% fl-Zr in the Zr 2.5Nb alloy as a grain boundary second phase, the two alloys differ by about 65% in the size of the 3{-Zr grains. The initial textures for both alloys were typical (10T0) fibers commonly observed in round bar zirconium alloys. Since the macroscopic deformation in these alloys is accommodated mainly in the ~-Zr phase, it is significant that the textures produced by compressive detbrmation at room temperature are considerably different. In Zircaloy-2 the compression texture is essentially a [0001] fiber while in Zr-2.5Nb the inverse pole figure indicates a (11-~0) fiber. The type of compression texture observed in Fig. 1 for

487

SALINAS-RODRIGUEZ: TEXTURE EVOLUTION OF ~-Zr

4.6 0001~

0.2

0001L

ao]se1.7 \

to~5

,0~1,0.5 0.2~24

IOT3110.2k!H~4

10i4~~ , ~

2o~3~,0~I

IoT4ql0.5

poT2qiO.l 0 . I ~

\ nS.z O.q,= 0.6 "_ 0121~3" ~" \

oratE\

IO/l,,O.1 0.2/\"k emma \

2o ,, °o:' 1 . 2 r -. ~ "

IoTo~~ - 2 1 3 0 o.2

I

2,9 toro~ ~

COMPRESSION

AXiS

2 J 3 0

03

Fig. 1. Inverse pole figures of the compression axis for (a) Zircaloy-2 (20/lm average :~-Zr grain size) and (b) Z~2.5Nb (10/lm average ~-Zr grain size).

Z r - 2 . 5 N b has never been reported previously. It was therefore decided to investigate in detail the effect of ~-Zr grain size on the compressive deformation of Z r - 2 . 5 N b and evaluate the results in terms of the known behavior of Zircaloy-2.

reference direction in the plane of the specimen. Pole figures were plotted using a standard stereographic projection with the compression axis ( Z ) at the center and the transverse reference direction at the north pole. Pole density contours were plotted in units of multiples of the pole density in a random distribution

Experimental materials and techniques Z ~ 2 . 5 N b bar stock, 12.7ram in diameter, was employed as starting material. Cylindrical specimens, 8 mm in diameter with an aspect ratio of 1.5, were machined to have their axial direction parallel to the axis of the bar. Two batches of specimens were vacuum annealed for 24 h at two different temperatures, 1073 and 1123 K, and then furnace cooled. Figure 2 illustrates the typical microstructures observed in the specimens. The heat treatments produced equiaxed e - Z r grains with average grain sizes of" 5 and 10 gin, respectively. In what follows, these will be referred to as fine and coarse grained materials, respectively. Isolated regions of b.c.c./%Zr were observed mainly at the corners of the ~ grains. The chemical composition of this phase has been measured using X-ray diffraction techniques by Aldridge and Cheadle [19] and has been reported as Z~20%Nb. Compression testing was carried out at constant true strain rate of - 5 x 10 4 s ~to true strains of up to - 0 . 8 0 . After deformation, texture was measured by neutron diffraction. The wavelength of the incident beam was 1.398 dt and was obtained from the (331) planes of a Si crystal m o n o c h r o m a t o r at a diffraction angle of 6 8 . Intensity data were collected for the (0002), (10T0) and (112-0) reflections of ~-Zr. These data were obtained as a function of the tilt angle (0 9 0 ) from the axial direction of the specimen and the azimuth angle (0 360") from a

Fig. 2. Microstructure of Zr 2.5Nb after annealing at 1073 and 1123 K for 24 h followed by furnace cooling.

488

SALINAS-RODRIGUEZ:

T E X T U R E EVOLUTION OF ct-Zr

of orientations (mrd). Most of the texture data, however, is reported in the form of volume fractions of grains with a given {uvtw ) direction tilted an angle Z from the compression axis. By taking into account the rotational symmetry of the uniaxial compression

(a)

X

Zr-2.5

test, the volume fractions were calculated, as a function of Z, from the measured pole densities averaged over the azimuth angle from 0"*to 360 °. The evolution of microstructure with deformation was followed using standard metallographic techniques.

Nb

X

Hot Swaged Round Bar (0002)

"n

~ ~1

x

-n

Y

Nb

Ho'~ Swaged Round Bar (10TO)

x

y

CENTRE IS Z CONTOUR INTERVAL:

(b)

Zr-2.5

X ?

CENTRE IS Z 0.500

rnrd

Zr-2.5

Nb

CONTOUR INTERVAL:

X

(c¢+~) Annealecl (0002)

~'~

2.500

Zr-2.5

mrd

Nb

((c¢+/3) 10TO) Annealed

E'----- x

Y

Y

CENTRE IS Z CONTOUR INTERVAL:

CENTRE IS Z 1.000

mrd

CONTOUR INTERVAL:

5.000

mrd

Fig. 3. (0002) and (I0]'0) pole figures for Zr 2.5Nb specimens (a) before and (b) after annealing for 24 h at I073 K.

SAL1NAS-RODRIGUEZ: TEXTURE EVOLUTION OF :¢-Zr

(b)

(a)

[~

-~

0.5 ¸

grain

-0.20

size:

5 #m

0.5~

iI

I

-0.40

~

-0.20

t .~

-0.40

~

-0.80

-0.80 0.4 V O L U M E

0.4 ~ 4 ~

ANNEALED V O

i / !

L

grain

size:

5 #m

ANNEALED

I 0.3

¢

0.3

F R A C T I O N

489

/ I i /

F R A

c o.2~

0.2

T I 0 N

/

÷

/ i 0.1 ~

// /. . , . ~ ,.~

0

10

20

30

40

50

60

70

O.

80

0

90

10

20

30

40

50

60

70

80

90

A N G L E F R O M C O M P R E S S I O N A X I S T O ,1010~'

A N G L E F R O M C O M P R E S S I O N A X I S TO ~0002)

Fig. 41 Distribution of the volume fractioD of grains with (a) (0002) and (b) (10i0) tilted from the compression axis in fine grained Zr 2.5Nb as a function of strain.

has been shown by Cheadle and Ells [20] to be associated with the characteristics of the (~ +/3)/'e transformation.

RESULTS

Annealing texture in Zr--2.5Nb Figure 3 shows the (0002) and (1010) pole figures obtained before and after annealing the compression specimens at 1073 K. Similar results were obtained after annealing at 1123K. As can be seen, (~ + f i ) annealing of Zr 2.5Nb only produces the sharpening of the initial texture. This texture "'memory" effcct

(a)

Texture and microstructure et,olution in .fine grained material Figure 4(a, b) illustrates the effect of compressive strain on the volume fraction of grains with (00025

(b) 0.5

0.5 grain -~

0.4 V O L U M E F R A C T I O N

size

grain

5 LLm

.

-0.20 -0.40

:::

-0.05

-0.80

'~-

-0.10

"~

-0.15

0.4

ANNEALED V O L U M E

0"3~

F R A C T I O N

0.2F

p~ , 0.1

0

10

20

30

40

50

L£

~

60

70

t~;~"G

80

A N G L E F R O M C O M P R E S S I O N A X I S T O <1120~

.

90

size:

10 ~ m

~'~ ANNEALED

0.3

0.2 ~

//, ~ O. 1

~ _ . ,.

0

10

20

30

40

50

60

70

80

A N G L E F R O M C O M P R E S S I O N A X I S TO <11'20>

Fig. 5. Distribution of the volume fraction of grains with (1120) tilted from the compression axis in (a) fine g r a i n e d a n d (b} c o a r s e g r a i n e d Z r 2 . 5 N b as a f u n c t i o n o f s t r a i n .

90

490

SALINAS-RODRIGUEZ:

TEXTURE EVOLUTION OF c~-Zr

and (10T0) tilted from O to 9 0 from the compression axis. A similar graph is illustrated in Fig. 5(a) for the volume fraction of grains with (1120) tilted from 0 to 90 from the compression axis. There are two interesting observations in these figures. First, before deformation the majority of the grains are oriented with (10101 direction between 0 and 15 from the compression axis. These correspond to the maxima observed at 9 0 in Fig. 4(a), and at 5" and 60' in Fig. 4(b) for the annealed material (corresponding to the (10T0) fiber). After a compressive strain of -0.20, the grains rotate approx. 30 ' about an axis nearly parallel to (0001) producing a 30' shift in the maxima observed in Fig. 4(b). It should be noted that the shift takes place in the opposite direction in Fig. 5(a), i.e. when the rotation of the grains during deformation is followed using the orientation of their (11501 direction. These results indicate that during the compression of Zr-2.5Nb there is a very rapid rotation of the ~-Zr grains about their ( c ) axis from (10]'01 to (11501 nearly parallel to the compression axis. The second important observation concerns the evolution with strain of the (0002) directions of the grains [Fig. 4(a)]. As can be seen, the volume fraction of grains with (0002) at 9 0 from the compression axis decreases progressively with strain until at E = - 0 . 8 0 about 80% of the grains have their ( c ) axes tilted between 15 and 9 0 from the compression axis. The data in Fig. 4(a) indicate that the distribution of the normal to the basal planes evolves in a continuous manner with strain and becomes random at compressive strains of about - 0 . 5 . At ~ = - 0 . 8 0 there is a small, well defined maximum at about 2 0 from the compression axis which is expected to increase as deformation proceeds. This result is consistent with the evolution of the (10i01 axes observed in Fig. 4(b); the maxima observed at 30': and 90 ~ decrease and increase, respectively, for strains greater than -0.20. Figure 6 illustrates the microstructure of fine grained Zr-2.5Nb after compressive strains of - 0 . 2 and -(/.4. As can be seen, only few grains reveal the presence of mechanical twins. It can therefore be concluded that a slow rotation of the normal to the (0002) planes, from the plane of compression towards the compression axis [Fig. 4(a)], can be associated with the reorientation tendencies produced by the activity of glide dislocations. The process of deformation of fine grained material appears to involve a low frequency of twinning which is delayed until the orientation of the grains becomes unfavorable for slip at large deformations. Texture and microstrueture evolution in coarse grained material

Figures 5(b) and 7(a, b) illustrate the effect of strain on the distributions of (112.01, (0002) and (IOTO) after compression of coarse grained

Fig. 6. Effect of compressive deformation on the microstructure of fine grained Zr 2.5Nb.

Zr 2.5Nb. It should be noted that the maximum compressive strain in this case is only -0.15. The evolution with strain of the texture in these specimens appears to be simpler than in the case of the fine grained material. Figure 5(b) shows that the (11501 direction of the majority of the grains remains fixed in space; this implies that the grains rotate about a (11501 direction as a result of deformation. Careful comparison of Fig. 7(a) and 7(b) shows that, as deformation proceeds, there is an increase in the volume fraction of grains with ( c ) axes between 0" and 15 which takes place concurrently with the decrease in the volume fraction of grains with (10i01 directions in the same range of orientations. However, Fig. 7(a) also shows that compressive deformation has only a limited effect on the volume fraction of grains with ( c ) axes normal to the compression axis. It will be shown later that the change in texture produced by compressive deformation of coarse grained Z>2.5Nb is associated with the formation of "tensile" twins. Since during twinning only a fraction of a given crystallite is transformed into the twin orientation which then grows with continued straining, it is not surprising that the volume fraction of grains with ( e ) axes normal to the compression axis decreases about the same amount as the increase in the volume fraction of grains with (0002) between 0° and 15:: from the compression axis.

SALINAS-RODRIGUEZ:

T E X T U R E E V O L U T I O N OF ~-Zr

(a)

491

(b) 0.5

0.5-

ANNEALED E-

0.4-

-~

grain size: 10

g r a i n size: 10 #m

ANNEALED

-0.05

-0.05

-0.10

~7 -0.10 0.4

-0.15

V O L U M 0.3 E

V O L U M 0.3 E

F R A C 0.2 T I O N

F R A C 0.2 T I O N

-0.15

0.1

,/:¢d-

'

/

I , @

o k > >

-

o i

_

30 ANGLE FROM COMPRESSION AXIS TO ,0002~

40

50

60

70

80

90

ANGLE FROM COMPRESSION AXIS TO <1010~

Fig. 7. Distribution of the volume Fraction of grains with (a) (0002) and (b) ( 1 0 i 0 ) tilted from the compression axis in coarse grained Zr 2.5Nb as a function of strain.

Summarizing the observations described above, it may be concluded that during the compression of coarse grained Zr 2.SNb, a significant volume fraction of material changes rapidly its orientation so that the [0001] direction of the grains becomes aligned nearly parallel to the compression axis. The axis of rotation for this reorientation is a (1120} direction which remains fixed in space after compressive strains as large as -0.15. The rate of evolution of this texture component is very large as indicated by the small compressive strains required to induce the reorientation of the normal to the (0002) planes. Figure 8 illustrates the microstructure of the coarse grained material after compressive strains of - 0 . 0 5 and -0.15. As can be seen, at strains as small as -0.05, most of the c~-Zr grains reveal the presence of thin twins with a lenticular morphology. The thickness and number of these twins increase with deformation. These observations are entirely consistent with the texture evolution behavior described above. Figure 9 compares the strain dependence of the volume fraction of twins in the present coarse grained specimens with that observed by MacEwen et al. [3] in Zircaloy-2 deformed in compression. The graph also shows the variation with strain of the volume fraction of grains with {0002} between 0 and 15 from the compression axis. It is evident that there is a strong correlation between the occurrence of mechanical twins in coarse grained Zr-2.5Nb and the formation of the [0001] texture component during compressive deformation. This observation is consistent with the ( c ) axis reorientation produced when

a Zr single crystal is loaded in tension parallel to the (0001} and deforms plastically by {1012}{1011) twinning [1].

Fig. 8. Effect of compressive deformation on the microstructure of coarse grained Zr 2.SNb.

492

SALINAS-RODRIGUEZ: TEXTURE EVOLUTION OF e-Zr 0.5 (~) T W I N V 0 L U M E F R A C T I 0 N

@ 0.4

ZIRCALOY [3] metall. Zr-2.SNb metall.

-@- Zr-2.5Nb texture

0.3

f 0.2

0.1

o~ 0.00

0.05

0.10

0.15

0.20

STRAIN

Fig. 9. Effect of compressive strain on the volume fraction of twins in thc :~-Zr grains of coarse grained Zircaloy-2 [3] and Zr 2.5Nb.

Microstructure o f fine and coarse grained Zr 2.SNb under the T E M Figure 10 shows two T E M micrographs obtained from thin foils prepared from cross sections of fine and coarse grained specimens, respectively, coinpressed to a strain of - 0 . 0 5 . The operating reflection in both cases was g = [0002] which, according to the invisibility criterion g. b = 0, should result in contrast due to dislocations with (c + a ) Burgers vectors. As can be seen, the fine grained specimen shows an array of nearly parallel (c + a ) dislocations, some of which are clearly straight. This type of characteristic arrangement of (c + a ) dislocations has been reported by Minonishi and Morozumi [21] in deformed Ti single crystals and by Holt et al. [22] in cold worked Zr-2.5Nb. In contrast, the T E M micrograph obtained from the coarse grained specimen under the same diffraction conditions, shows the presence of three mechanical twins with some dislocations near the twin and grain boundaries. In this case, the foil normal was determined to be a direction nearly parallel to the [1i'00] of the matrix and the [0001] direction of the wider twin. This indicates that the formation of the twin produced a lattice rotation of nearly 90 which brings the ( c ) direction of the twin to an orientation nearly parallel to the compression axis of the specimen. This behavior is similar to the reorientation of the ( c ) axis produced in an c~-Zr single crystal deformed in tension parallel to its ( c ) axis [1] and with the texture evolution observed in Fig. 7 in coarse grained Zr-2.5Nb. The lattice reorientation observed is consistent with that associated to the

Fig. 10. TEM micrographs of (a) fine and (b) coarse grained Zr 2.5Nb deformed in compression to a strain of 0.05. g = [00011, B ~ [1ioo].

SALINAS-RODRIGUEZ:

TEXTURE EVOLUTION OF :~-Zr

formation of {~012}(]'01T) "tensile" twins in ~-Zr [1]. It is noteworthy that the twins in the coarse grained specimen exhibit an internal substructure consisting of fine parallel lamellae and some isolated dislocations near the twin boundaries. Considering that during continued deformation the twin must accommodate compressive strains in a direction nearly parallel to its (c)-axis, it is probable that these lamellae are {1122}(1T23) compressive twins. The occurence of re-twinning in coarse grained Zr was first reported by Reed-Hill [1]. DISCUSSION

Self-consistent viscoplastic model of polyerystalline plasticity Molinari et al. [23] proposed a model for the simulation of large strain polycrystalline deformation. This approach consists in assuming a viscoplastic constitutive law for the plastic deformation by slip of the single crystals in the polycrystal. The microscopic strain rate tensor, 7~i, is related to the microscopic stress tensor, or,s, through the following equation

7-sr<

t

493

which characterize the microscopic hardening of the crystallite. The exponent m is the strain rate sensitivity for slip. The stress, ~r, and the strain rate, ~, in every grain are allowed to be different from one another and from the macroscopic strain rate, I~, and stress, S. The main assumption of the model is that the average microscopic strain rate, & and stress, u, are coupled to the macroscopic strain rate, 1~, and stress, S, through an interaction equation of the form ( S ~ - 60.) = (G ,ikl + A &,) (~7~ , - ~:k,). The terms (S g - 6) and (1~-~) are the deviations from the average of the stress and strain rate in a given grain• A ~ represents the viscoplastic response of the matrix and its symmetry properties are determined by the nature of the imposed deformation and the symmetry of the initial texture• The tensor G depends on the shape of the grains in the polycrystal. The above equation must be solved self-consistently for the whole set of orientations building the polycrystal. This approach to texture evolution modeling appears to be a better description of the plastic behavior of strongly anisotropic materials such as h.c.p. ~-Zr [5, 21].

Simulation of texture evolution controlled by slip in -Zr

•

The r ~ are orientation factors which change with deformation and the ~ are reference shear stresses

A theoretical polycrystal was constructed with a distribution of 400 ~-Zr grains with basal planes

2

2

~ > - . .

": !:

1-7; ;.':

-....-". i:

/:

-

.

."

f- ".- :.:.

.,".~-L\"

!;;,

" "'. " i

.

?.

""

•

•

-

"

•

'.

""

../

i"".:7,"!/'!, !

.

. : 7

.-"

"/- ."

':"

.

""

.

i .~

-

...,.~/

I~= - 0 . 5 0

I~= 0 . 2 5

2

2

I

/

:

\

..., ,~"v: .':" "; .." '

- ~ , "

"

k\.,\:: ""

.

.

.. . . .

.. •

~.

_

. " i ..

, "J'"

--

-,i

.. " "

-:

j

"

;: ; :.7!:

.:

/

. ./

:¢t ~%.'~.

I~ = - 0 . 7 5

~L t

1l."

.~.~7 /

E = -1.0

Fig. I I. Evolution with applied strain of the (0002) plane normal distribution in h.c.p.-Zr deformed in compression according to the self-consistentviscoplastic model• The plastic deformation in the individual crystallites was assumed to take place solely by
/

t

494

SALINAS-RODRIGUEZ:

TEXTURE EVOLUTION OF e-Zr

nearly parallel to the compression axis and axes randomly distributed about it. The development of texture was simulated assuming that { 10T0), (0001)<1120), and {1011 }<1123) slip systems were active with relative CRSS's of 0.1, 0.2 and 1.0, respectively. The strain rate sensitivity of slip was assumed to be the same for all three slip modes and was set to 0.05 which corresponds to room temperature deformation conditions. The changes produced by compressive deformation on this orientation distribution are illustrated in the form of (0002) pole figures in Fig. 11. The compression axis in these pole figures is plotted at the origin. It is evident that, as deformation proceeds, the (0002) poles rotate progressively towards the compression axis. At a compressive strain of - 0 . 5 the distribution becomes random and at a strain of - 1.0 there is clearly a rotationally symmetric concentration of basal planes tilted about 18' from the compression axis. This angle is very close to that observed in Fig. 4(a) for the maximum in the curve for E = - 0 . 8 0 . It is noteworthy that in Fig. 4(a) the distribution of the normal to the (0002) planes becomes random at some intermediate strain between - 0.40 and - 0.60. The agreement between the calculated (0002) pole figures and the observed texture evolution behavior in fine grained Zr-2.5Nb supports the initial hypothesis that the strain producing mechanism in fine grain -Zr is primarily dislocation glide. This result is most surprising since mechanical twinning is generally acknowledged to play a rate controlling role during deformation of h.c.p.-Zr at room temperature [1-3]. Dependence (~/ the slip distribution on strain rate sensitit,i O' During the plastic detbrmation of a polycrystalline aggregate the distribution of microscopic shears on

(a)

2

the active slip systems required to accommodate the imposed deformation depends on the evolution of the microscopic hardening of the individual crystallites and the orientation distribution of the polycrystalline sample. These two parameters determine the interaction during deformation among crystallites of differing orientations. Under viscoplastic conditions of deformation, the shear strain distribution also depends on the strain rate sensitivity, m, of the material. As deformation proceeds, the orientation distribution changes due to texture evolution and the shear stresses required to activate slip also change due to strain hardening. The microscopic shear strain distribution must therefore vary during the course of plastic deformation. In the absence of twinning, prismatic slip is the predominant deformation mode in e-Zr at room temperature. Thus, although the self-consistent viscoplastic model predicts correctly the evolution with strain of the (0002) pole figures of fine grained Z>2.SNb, it remains to show that the model also predicts the correct microscopic shear strain distribution. From the reorientation tendencies observed in the calculations, one would expect an increased activity of pyramidal slip as the (0002) poles rotate towards their final orientation. However, this would not be consistent with the predominance of prismatic slip during the deformation of ~-Zr. Figure 12(a, b) shows the (0002) pole figures calculated using the full-constraints (FC) and the selfconsistent (SC) viscoplastic models, respectively, after an imposed strain of - 1 . 0 on a collection of 100 grain orientations. The axes of these grains were initially randomly distributed at 90 from the compression axis. The CRSS's and the strain rate sensitivity employed in these calculations were the same as those employed in the calculations described in 2

(b)

I

•

"t,

Fig. 12. Predicted (0002) pole figures for a collection of 100 h.c.p.-Zr grain orientations with axes initially perpendicular to the compression axis. (a) Full-constraints and (b) self-consistent viscoplastic models. ~ = - 1.0.

SALINAS-RODRIGUEZ:

TEXTURE EVOLUTION OF c~-Zr

the previous section. As can be seen, b o t h models predict similar final distributions of basal planes. Figures 13 a n d 14 show the effect o f m on the slip distribution for two o r i e n t a t i o n distributions: t h a t c o r r e s p o n d i n g to the initial (1010> fiber texture of the annealed specimens, a n d t h a t c o r r e s p o n d i n g to the texture observed in fine grained Z r - 2 . 5 N b

495

compressed to E = - 0 . 8 [scc Fig. 4(a)] a n d predicted by b o t h the SC and F C viscoplastic models (see Fig. 12). As can be seen, for strain rate sensitivities characteristic o f r o o m t e m p e r a t u r e deformation, m ~< 0.05, a n d a distribution of (0002) poles m a k i n g a large angle with the pole o f the compression axis, the SC model predicts a p r e d o m i n a n c e o f prismatic

(a) SLIP ACTIVITY 1 . 0 0

SELF-CONSISTENT, VISCOPLASTIC

\\\

PRISMATIC

(D BASAL

~

PYRAMIDAL

4" =-o.ol

0.80

0.60

0.40 /

©

/

(

0.20

0.00 0.00

0.20

I

I

L

0.40

0.60

0.80

1.00

STRAIN RATE SENSITIVITY

(b) 1.00

0.80

SLIP ACTIVITY FULL- CONSTtL~INTS, VISCOPLASTIC

1

PRISMATIC

O

BASAL

@

4`

PYRAMIDAL

=-0.01

0.60

0.40

A

0.20

I

0.00 0.00

0.20

I_

0.40

I

--

0.60

I

0.80

- -

1.00

STRAIN RATE SENSITIVITY Fig. 13. Effect of strain rate sensitivity on the average slip activity after a compressive strain of E = --0.01 on a collection of 400 h.c.p.-Zr grain orientations with @)-axes distributed randomly between 80 ° and 9if' from the compression axis. AM .13/2--43

496

SALINAS-RODRIGUEZ:

TEXTURE EVOLUTION OF c~-Zr

(a) SLIP i

ACTIVITY

.00

SELF-CONSISTENT, VISCOPLASTIC PRISMATIC

0

BASAL

~=

PYRAMIDAL

~'=-1.0

0.80

O. 6 0

~:~

~

0.40

]

/'

2T]

I

0.20

jJ

-] ~ - - ~

o. 00

0.00

J-

/

J

J

~

2

I

I

J

0.20

0.40

0.60

o.8o

S T R A I N RATE

1 .o0

SENSITIVITY

(b) SLIP

ACTIVITY

1.00

FULL CONSTRAINTS, VISCOPLASTIC A PRISMATIC

O BASAL

~]= PYRAMIDAL

=-1.0

0.80

0.60

0.40 -

0.20 0.00

I

j

i

I

I

I

0.00

0.20

0.40

0.60

0.80

STRAIN

RATE

1.00

SENSITIVITY

Fig. 14. Effect of strain rate sensitivity on the average slip activity after a compressive strain of e = - 1.0 on a collection of 400 h.c.p.-Zr grain orientations with -axes distributed randomly between 15<' and 25 ~ from the compression axis.

slip. In contrast, the FC model predicts a uniform distribution of microscopic shears on all the active slip systems and the shear strain distribution does not depend on the strain rate sensitivity. W h e n the orientation distribution is such that basal plane n o r m a l s are tilted closer to the compression axis, the full-

constraints model predicts t h a t the activity of ( c + a ) slip controls the d e f o r m a t i o n o f the polycrystal. As m increases, the SC model predicts t h a t the average basal slip activity increases rapidly to a m a x i m u m t h a t depends on the o r i e n t a t i o n distribution. A t small strains, when [0001] directions of

SALINAS-RODRIGUEZ:

TEXTURE EVOLUTION OF :~-Zr

the grains make a large angle with the compression axis, prismatic slip is the main deformation mode. With increased strain the [0001] directions approach the compression axis and, for m values greater than 0.05, the average basal slip activity becomes greater than the prismatic activity. This result is not supported by the usual observations in :~-Zr deformed at room temperature where dislocations with ( a ) Burgers vectors are found to glide mainly on prismatic planes with limited slip activity on basal planes. On the other hand, the average pyramidal slip activity increases with m at a rate that depends on the characteristics of the orientation distribution of the polycrystal. It is evident, however, that the average pyramidal slip activity is always lower that the activities of prismatic and basal slip. It is then possible to argue that the twinning observed in fine grained Zr 2.5Nb at large strains (see Fig. 6) is needed to accommodate the imposed deformation when the activity of prismatic slip decreases due to the evolution of the compression texture. The significance of the results described to above is that they show that for m values of up 0.1, the model predicts that prismatic slip is the principal strain producing mechanism in ~-Zr regardless of the orientation distribution of the polycrystal. Basal and pyramidal slip must therefore be considered as secondary slip modes. These deformation modes are required to initiate the plastic flow of cyrstallites with unfavorable orientations for prismatic slip and to maintain compatibility among crystallites of differing orientations in a polycrystalline aggregate. The average slip activities of these two types of slip systems depend strongly on the initial texture and its evolution during deformation.

497

Effect o f grain size on the plastic yielding o f h.c.p.-Zr The symmetry of the initial texture in the present material and the imposed strain path require accommodation of tensile strains parallel to the [0001] axes of the majority of the grains at the beginning of the deformation. {i012}~1011) twins are formed when a tensile strain is imposed parallel to the @)-axis of an ~-Zr crystallite. The orientation of the ( c ) axis in the twin is related to the [0001] direction in the matrix by an 85:: rotation about a (1120) direction. This is entirely consistent with the compression texture developed in coarse grained Zr-2.5Nb (Fig. 7). Thus, generalized plastic flow must be established in the coarse grained polycrystalline material when the stresses are high enough to activate the twin systems. Twinning is not generally observed in fine grained Zr 2.5Nb at small strains, thus, the preceding discussion suggests that there is a competition between (c + a ) slip and tensile twinning to control the initial yielding of the specimens. Since these two mechanisms require larger stresses to be activated than ( a ) slip [3], generalized plastic flow and the texture development will depend on the preferred mode of ( c ) axis deformation. The results obtained in coarse grained ~-Zr and the results of the calculations presented in the previous section, strongly suggest that the ~ grain size controls which mechanism is preferred for ( c ) axis deformation. MacEwen et al. [3] showed that the compression flow curve of coarse grained Zircaloy-2 exhibits an elasto-plastic transition during which only prismatic slip is responsible for plastic flow. Pyramidal (c + a ) slip and twinning are not activated until plastic flow is fully established at total strains larger than -0.03.

800

S

T R E S S

M P a

600

40o

200

#m iN ~--

COARSE GRAIN

5

10

0 0

0.05

0.1

0.15

0.2

STRAIN Fig. 15. Room temperature flow curves for fine and coarse grained Zr 2.5Nb measured in axisymmetric compression at a strain rate of - 5 x 10 5s ~.

498

SALINAS-RODRIGUEZ and ROOT:

The flow curve for coarse grained Zr-2.5 Nb (Fig. 15) exhibited an elasto-plastic transition with a proportional limit of 280 MPa and a flow stress of 350 MPa at end of the transition. Fine grained specimens did not show an elasto-plastic transition and twinning was delayed to much greater strains. The onset of fully plastic flow was defined by a sharp yield point at 420 MPa. The observations described above suggest that the activation of slip determines the onset of fully plastic deformation in fine grained Zr 2.5Nb. In coarse grained material, the more extensive planar arrays of dislocations with slip is activated. This effect may also be reinforced by the compatibility stresses developed to accommodate the mismatch between the grains and the metastable fi phase present in Zr-2.5Nb. The reason why this should have a bigger effect in the coarse grained material remains still unclear. One further effect contributing to the preference of twinning in coarse grained material may be associated with a higher content of oxygen in solid solution due to the higher annealing temperature. This excess oxygen can lock up the dislocations which would therefore require a higher activation stress allowing twinning to take place first. The occurrence of a sharp yield point in the fine grained material strongly supports this argument. The lattice reorientation associated with twinning requires axes of the twins. This causes an increasing work hardening rate as more material becomes reoriented with fiber texture at compressive strains of about - 0 . 2 . With increased deformation the normal to the basal planes of the h.c.p, grains rotates continuously towards the compression axis and the final

TEXTURE EVOLUTION OF ~-Zr tcxturc is a fiber tilted - 2 0 °. These later results were correctly predicted by the self-consistent, viscoplastic model of Molinari et al., indicating that this approach to texture evolution modeling provides a better description of the plastic behavior of strongly anisotropic materials deforming by slip. The preference of twinning in coarse grained Z r - 2 . 5 N b was attributed to oxygen atoms locking the dislocations which then would require higher activation stresses than in fine grained material produced by annealing at lower temperatures. Acknowledgements--The technical assistance of Dr. John

H. Root and J. F. Mecke are gratefully acknowledged. Special thanks are due to Professor G. Canova, the University of Metz, France and the Consejo Nacional de Ciencia y Tecnologia of M~xico. REFERENCES

l. R. E. Reed-Hill, in Deformation Twinning (edited by R. E. Reed-Hill, J. P. Hirth and H. Rogers). The Metallurgical Society of AIME, Gordon & Breech (1964). 2. R. G. Ballinger, G. E. Lucas and R. M. Pelloux, J. nucl. Mater. l, 1353 (1984). 3. S. R. MacEwen, N. Christodoulou, C. N. Tom6, J. Jackman, T. M. Holden, J. Faber and R. L. Hitterman, ICOTOM-8 Conf. Proc. (edited by J. S. Kallend and G. Gottstein), p. 825. The Metallurgical Society (1988). 4. E. Tenckhoff, Metall. Trans. 9A, 1401 (I978). 5. C. Topm& C. Lebensohn and U. F. Kocks, Acta metall. 39, 2667 (1991). 6. A. Akhtar, Metall. Trans. 6A, 1 (1975). 7. A. Akhtar and A. Teghtsoonian, Acta metall. 19, 655 (1971). 8. A. Akhtar, Acta metall. 21, 1 (1973). 9. A. Akhtar, J. nucl. Mater. 47, 79 (1973). 10. A. Salinas-Rodriguez and J. J. Jonas, Metall. Trans. 23A, 271 (1992). ll. C. Lebensohn, P. V. Sanchez and A. A. Pochettino, Scripta metall. In press. 12. A. Salinas-Rodriguez, Ph.D. thesis, McGill Univ. (1988). 13. E. D. Levine, Trans. Metall. Soc. A1ME 236, 1558 (1966). 14. O. T. Woo, G. J. C. Carpenter and S. R. MacEwem J. nuel. Mater. 87, 70 (1979). 15. A. A. Pochettino, N. Gannio, C. V. Edwards and R. Penelle, Scripta metall. 27, 1859 (1992). 16. M. J. Marcinkowski and H. A. Lipsitt, Acta metall. 10, 95 (1962). 17. D. Hull, Acta metall. 9, I91 (1961). 18. S. Mahajan and D. F. Williams, Int. Metall. Rec. 18, 43 (1973). 19. S. A. Aldridge and B. A. Cheadle, J. nucl. Mater. 42, 32 (1972). 20. B. A. Cheadle and C. E. Ells, Electrochem. Technol. 4, 329 (1962). 2l. Y. Minonishi and S. Morozumi, Scripta metall. 16, 427 (1982). 22. R. A. Holt, M. Griffiths and R. W. Gilbert, J. nucl. Mater. 149, 51 (1987). 23. A. Molinari, G. R. Canova and S. Ahzi, Acta metall. 35, 2983 (1987).