zhi wang1 xianyu jin nanguo jin abid a shah bei li1d h d h 1 tr( ) 3 1 1 1d 1 ()2 h i d 1 tr h 3 d d...
TRANSCRIPT
Zhi Wang1
Xianyu Jin*1
Nanguo Jin1
Abid A Shah2
Bei Li1
DHD
2(1 2 ) tr( ) 1tr( )
6 1- 2
D D
H
v v
E D E
σHσ Hσ
E v
Dσ H
HD
1tr( )
3
D σ σ σ
1
2( )
H I D1
tr3
HD D
1
2( )
I D ( )diagI D1( ) ( )diag
I D P I D P
1/ 2 1/ 2 1( ) ( )diag
I D P I D PijI P
( )I D
2 2
1 2
tr( ) tr( )(1 2 ) 1[ ] tr( )
6 1- 1- 2
D D
H H
v v
E D D E
σ σHσ Hσ
max(0, )x x
min(0, )x x
+ -
1 2
tr( ) tr( )(1 2 ) 1= [ ] ( )
3 1- 1-
D D
H H
v v
E D D E
σ σε I Hσ H
σ
I
1
2
3
1
1
1
1 1
1
2 2
1
3 3
11 2
13 1
1
1 121 13
1 1 1
31 1
1 13
1 1
e
e
He
D
v
E D
D D
E D D
D D
1(1 )HK D K
D
1 2 3, ,x x x
1
2
3
D
D
D
D
1 2 3
1( , , )D D D
E
ε B σ
B
1X B
12 1311 12 21 13 311 1 1
2322 23 32 332 2 3
, , ,
, , ,
E E EB B B v B B v
E E E
E E EB B B v B
E E E
iE i
1X 2X 1E 2E 12
1 1 1121
2
1 (1 )(2 )E E
DE E
2 2 1122
1
1 (1 )[2 (1 ) ]E E
DE E
1
12
1 21
1 2H
ED
E
:σ C ε 1 1: tr( )
v v
E E
ε C σ σ σ I C
σ σ
+ -
1 2
tr( ) tr( )1[ ] [( )]
3 1- 1-
D D D
H HD D
σ σσ I Hσ Hσ
1/ 2 1/ 2 2( ) : 1( ) ( ) ( ) [(1 tr ) tr (1 tr ) tr ]
3 tr 3 3
I - D σσ I - D σ I - D I - D D σ D σ I
D
eq eq
+
2
+ += =eq
ε ε ε:
= (tr ) 0eqf D
0tr(tr ) tan[ arctan( )]a
aA a
DD
0f 0f 0f
(tr ) D
(tr ) D0 (0)
(tr ) D
a A
E v0 (0)
( ; ) :F F
Y ε Y ε
tr( ) tr( )F
D ε D ε
Y
0f 0f
1tr ( )eq D
1( )tr( )
eqeq
eqd
D
1[ ( )]tr( )
tr( ) tr( )
eqeq
eq
d
d
D
ε ε
1( ( ))tr( )
tr( ) tr( )
eqeq
eq
d
d
D
D ε εε ε
2
2tr( ) ( )eq
ε eq
12
2
( ) eqeq
eq eq
Dd
ε
1X
1 0 0
0 0 0
0 0 0
ε
1
2
2
0 0
0 0 0
0 0 0
ε
1 0 0
0 0 0
0 0 0
D
D
1X
2
2
0 0 0
0 0
0 0
ε2
2
2 2
2
0 0 0
0 0
0 0
ε
2
2
0 0 0
0 0
0 0
D
D
D
E
1 2
tr trtr
3 (1 tr ) 3 (1 tr )3 3
K K
σ σε
D D
K
tr 1D
tr 0σ 3K
3 (1 tr )K D
1 2
tr trtr
3 3K K
σ σ
ε
1 tr3
cD
D
1 21 2(1 tr ), (1 tr )
3 3K K K K
D D
1
2
3tr
3
cc
DD
D
21 2(1 ), (1 )
3c cK K D K K D
2
3tr cD
D
1 2(1 ), (1 )c cK K D K K D
cD
2
D ε
( )D D D D cD n
n n
n n cD D n
2 (1 ) [(1 ) tr (1 ) tr ]D
c c cG D K D D
σ ε ε ε I
/ 2(1 )G E
( 1) 1 1:eq n n n ε ε
( 1) (tr )trial eq n nf D
0f 1n n D D 0f
2
2
1 1
1
2
( 1)
tr tr
n n n
n n
eq n
D D D ε
D D
D2
1 1n n n D D ε
1 1:n n σ C ε
11/ 2 1/ 2 111 1 1 1
1
21 11 1
( ) :( ) ( ) ( )
3 tr( )
1[(1 tr ) tr (1 tr ) tr ]
3 3
nnnn n n n
n
n nn n
I D σσ I D I D I D
D
D σ D σ I
2385m / kg
19.98μm
21 2 C
24GPa, 0.2,E v 1=3 2 0.5 2.88605e 4,a
7.7e3,A 0 1.35e 4,k E v
1 2 0, ,a A k
24MPa, 0.2E v
3.21MPa
3.21MPa
D
C
:σ C ε
tr 0,ε
1/ 2 1/ 2 ( ) ( )2 [( ) ( ) ] (1 tr )
3 trG K
I D I DC I D I D D I I
D
tr 0,ε
1/ 2 1/ 2 ( ) ( )2 [( ) ( ) ]
3 trG K
I D I DC I D I D I I
D
/[2(1 )]G E /[3(1 2 )]G K
A B ( )ijkl ik jlA B A B
B
11
1 2 3 1
(1 ) 4 1 1 1 2( )
9 1 1 1 3(1 )H
BD D D D
12 21
1 2 3 1
(1 ) 2 2 1 1 2( )
9 1 1 1 3(1 )H
B BD D D D
13 31
1 2 3 1
(1 ) 2 1 2 1 2( )
9 1 1 1 3(1 )H
B BD D D D
22
1 2 3 1
(1 ) 1 4 1 1 2( )
9 1 1 1 3(1 )H
BD D D D
23 32
1 2 3 1
(1 ) 1 2 2 1 2( )
9 1 1 1 3(1 )H
B BD D D D
33
1 2 3 1
(1 ) 1 1 4 1 2( )
9 1 1 1 3(1 )H
BD D D D
B
11
1 2 3 2
(1 ) 4 1 1 1 2( )
9 1 1 1 3(1 )H
BD D D D
12 21
1 2 3 2
(1 ) 2 2 1 1 2( )
9 1 1 1 3(1 )H
B BD D D D
13 31
1 2 3 2
(1 ) 2 1 2 1 2( )
9 1 1 1 3(1 )H
B BD D D D
22
1 2 3 2
(1 ) 1 4 1 1 2( )
9 1 1 1 3(1 )H
BD D D D
23 32
1 2 3 2
(1 ) 1 2 2 1 2( )
9 1 1 1 3(1 )H
B BD D D D
33
1 2 3 2
(1 ) 1 1 4 1 2( )
9 1 1 1 3(1 )H
BD D D D