Large deformation simple compression of a copper single crystal
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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
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