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displacements in the e3 direction and (c) no tractions on the lateral surfaces. The elasticity tensor ~ f o r an fcc crystal requires three material parameters C1~, C12, and C44, w h i c h for copper are taken to have valuestg~ C~I = 170 GPa, C~2 = 124 GPa, and C44 = 75 GPa. W e take the reference value o f slip rate to be 4/0 = 0.001 s -~. The slip-rate sensitivity parameter is taken to be equal to the macroscopic strain-rate sensitivity measured from a strain-rate jump experiment in simple compression on annealed oxygen-free high-conductivity polycrystalline copper at r o o m temperature. Such an experiment l~ yields rn = 0.012. W e assume that latent hardening is adequately described [4,5~ by Eqs. [5] with q = 1.4. W e recognize this to be a gross simplification o f actual circumstances, but different choices o f values o f q , o r indeed different forms f o r q~#, do not significantly affect the macroscopic shape change o r lattice reorientation in the experiment under consideration. The slip system hardening parameters ho, a , ss, and the initial value o f slip resistance So, were found

ho = 250 MPa,

a = 2.5,

ss = 190 MPa,

So = 16 M P a

[6]

Figure 2 shows the correspondence between the s i m u lated stress-strain response and the experimental data. The curve fit is reasonable. The measured crystal orientation after a true strain o f - 0 . 5 3 in simple compression and the corresponding numerical prediction are compared in Figure 3(a) in terms o f {110} equal-area pole figures. These pole figures are identical to the initial pole figures shown in Figure 1(b). F o r this particular geometry o f deformation, there is no change in the orientation o f the crystal lattice. The macroscopic shape o f the deformed sample from

T a b l e I . S l i p S y s t e m s , R e s o l v e d S h e a r Stresses, and S h e a r i n g R a t e s d u r i n g S i m p l e C o m p r e s s i o n i n [ 0 1 1 ] Direction o n a fcc S i n g l e C r y s t a l *

a

[mo~]c 1

1

[no~]c

1

X/2

1

X/20 1

1

I

1

3 1

5

V~

6

1 0V~

1

1

I

1

V~ 0 1 X/2

1

7

1

1

1

1

11

1

1

1

1

l

1

1

1

1

1

1

1

X/i

1

[ 7

1

1

11

1

V~

X/i

1

1

1

1

1

1

V~0~ 1

V3 V~

1

1

or

2

- ~ 0

~

~/("

1 .,/2 - 3 0

0

0

0

0

0

0

0

0

/~ "~3 0

0

0

/~ ~/3 0

0

0

0

0

010 1

1 1

1

X/2

22

~

1

0

1 x/3

1 1 1

V'222

1

V~V"3 1

1

~/3V~ 1

[ 7

"~/3 0 ] 7

1

] 7

3 - ~/3 0

1 1 1

1

X/222

V~

1

11

1

V~

22

N/3

t

vSx/3

or

1

1 1

o

2

1

N/'3 V'3

~(1,

or

o

1

1

0

or

X/6

1

1

X/-3N/3

X/i

5e

(Eq. [4a])

V2

1 1 1 - ~ ~"3 X/3

~

V2V~ 0

12

1

~ 0 ---,

00-1

9

11

1

2

1

0

10

1

~

1

V~ X/3 V~

(Eq. [4b])

1

o 1o

Mr3

[no~]

V2

v3v3

1

~Ov~

1

1

1

1

8

1

V"5V"3 V~

v

4

[mo~]

1 00-1

- 3 -

[~

*[mo°]c and no~]~ are the components of the slip direction and slip plane normal with respect t o the crystal b a s i s {eT}, w h i l e [too"] and [no~] are the components of the same vectors with respect to the global b a s i s {ei}. METALLURGICAL TRANSACTIONS A

VOLUME 24A, APRIL 1993--9