清华大学：《材料科学基础》课程教学资源（PPT课件讲稿）Chapter 5. 8 The Stress Around a Dislocation

85. 8 The Stress Around a Dislocation I. Screw dis location D i sp l acement l=0un,=0 b 2丌2兀 d Strain:a =0 0 a dx

§5.8 The Stress Around a Dislocation ◆ Ⅰ. Screw dislocation: Displacement: Strain: ( ) 2 2 0 0 1 x y t g b b u u u x y z − = = = =    0 d d 0 d d 0 d d = = = = = = z u y u x u z z y y x x   

=0 Oy a b M b-- Ox dz 2T( +y-) x y2 Oy az y Stresses:o、=o,=o,=0 Gb y Gb x 2nx2+ x-+

( 1 2) = 0   +   = = x u y ux y xy   z 2 ( ) 2 2 z x y u b y x u x xz +  = −   +   =   z 2 ( ) 2 2 z x y u b x y u y yz +  =   +   =   Stresses: 0  x = y = z = ( ) 2 ( ) 2 0 z 2 2 z 2 2 x y G b x x y G b y x y x y + = + = = −     

I. Edge dislocation Gb y3x-+y 2(1-v)(x2+y Gb y(x2 y-2x(1-)(x2+y 女 z=(0x+o1) Gb x =0 2m(1-v)(x2+

◆ Ⅱ.Edge dislocation 2 2 2 2 2 ( ) (3 ) 2 (1 ) x y Gb y x y x + + − = −    2 2 2 2 2 ( ) ( ) 2 (1 ) x y Gb y x y y + − − =    ( )  z =  x + y 0 ( ) ( ) 2 (1 ) 2 2 2 z z 2 2 = = + − − xy = x y x y Gb x x y     

fy=0,ox=0y=02=0 Gb Gb 2m(1-U)x2z(1-U)r For either edge or screw dislocation shear stress on slip plane along SD G edge dislocation n b screw dislocation n

if y=0 , 0  x = y = z = r Gb x Gb xy 2 (1 ) 2 (1 )  − = − = For either edge or screw dislocation shear stress on slip plane along S.D.        − = = screw dislocatio n 2 edge dislocatio n 2 (1 ) s       G G r b  

35.9 Elastic Energy and Line Tension of dislocation I M tot W core elast s misfit P

§5.9 Elastic Energy and Line Tension of Dislocation ◆ Ⅰ. Wtot = Wcore+ Welast = Wmisfit+ We l P  

1. We of an edge dislocation Model: see fiqure consider an area element x-x+dx which displaced from b’→b+db then M We=S x,( x)db IGb 1 dxd b 2(1-y)x Glb--In(R)=aGb? +dx 4m(1-y)

1. We of an edge dislocation. Model: see figure. consider an area element x→x+dx which displaced from b'→ b'+db'. then Gb l r Glb R x b x lGb W l x b R r e xy 2 2 b 0 ln( ) 4 (1 ) d d 1 2 (1 ) ( d )d o       = − =  −  = =     

2. W of a screw dislocation Glb R We=4丌r 3.W of a mixed dislocation bsin a b a G(bsin a) 1 G(b cos a)LlIn( R mIX 4m(1+y) 4丌

2. We of a screw dislocation: ln( ) 4 2 e  r Glb R W  = 3. We of a mixed dislocation: l bcos bsin  b   ]ln( ) 4 ( cos ) 4 (1 ) ( sin ) [ 2 2 mix  r G b l G b l R W      + + =

◆‖l. Line tension line tension ≈d dl @Gb2

◆ Ⅱ.Line tension e 2 d d line tension Gb l W T = =

Examples and Discussions

Examples and Discussions

Exercise

Exercise