34.4 Rotation of Crystal dur ing Slip .I. The cause of rotation Due to constraints, or boundary conditions, imposed on the crystal The rule of rotation 1)axis of rotation R L=+(·n)b R‖L×团b×l
§4.4 Rotation of Crystal during Slip ◆ Ⅰ.The cause of rotation: Due to constraints, or boundary conditions, imposed on the crystal. ◆ Ⅱ.The rule of rotation : 1) axis of rotation ∥ ∥ R R L l b l L l l n b = + ( )
2)During slip, the S.D. tends to approach to loading direction in tension During slip, the S P. tends to approach to compression plane in compression
2) During slip, the S.D. tends to approach to loading direction in tension. During slip, the S.P. tends to approach to compression plane in compression. F F F F F F F F
Slip band (1000 atoms) Slip line(100 atoms) Distance between slip bands ( (b)
ll. The consequence of rotation 1. Change in length of the specimen ① n tension L=1+y(l·n)b L=I1+2y cos A cos o+r2 cos2 o L Xb sin Aon cos sin n ② In compression A=a-y(a·b)n
◆ Ⅲ.The consequence of rotation : 1. Change in length of the specimen 2 2 L = l 1+ 2 cos cos + cos ① In tension L l l n b = + ( ) cos cos sin sin 0 0 l L b n ② In compression A a a b n = − ( )
2. Change in orientation (1 Orientation change and multislip (2) Geometrical softening in tension Schmid's law [=o coS/ cos at the onset of slip: t=tc=const =0, coS n, cOS Fcosn F cos/ cOS COS y个→4→a√cos COS
② Geometrical softening in tension Schmid’s law at the onset of slip: = cos cos = = const. C y o o = cos cos o o o o A F A F cos cos ) cos ( cos = = o C cos cos = 2. Change in orientation ① Orientation change and multislip
Examp le Given: a FCC crystal held in tension F//[215 Determine: 1. Single slip system 2. Rule of rotation 3. r and orientation at the onset of duplex of slip 4. Rule of rotation during duplex slip 5. Final orientation, i. e. the state position
Example: Given: a FCC crystal held in tension ∥ Determine: 1. Single slip system 2. Rule of rotation 3. and orientation at the onset of duplex of slip 4. Rule of rotation during duplex slip 5. Final orientation, i.e. the state position F [215]
Solution slip system:(1 11)[0111 2. locus: F tend to[o11,R‖F×[011R[211 3.L=l+b(l·n)b let 1=[/ v3 6-a\1 7=[215] [nvw]=[215]+U([215 [111]、[011 [215]+√6U01 L=-2+0=-2p=-1-√6U=-2 F'∥[226]∥[13 duplex slip systems:(1111011+(111[101
1. slip system: 2. locus: F tend to , ∥ ∥ 3. ( 111)[ 0 1 1 ] [ 0 1 1 ] R F [ 0 1 1 ] R [211 ] 2 [011] 3 [111] [2 15]( ) = = = = + l n b L l l n b 6 66 2 0 2 1 6 2 [2 15] 6 [011] 2 [01 1] ) 3 [1 11] [ ] [2 15] ([2 15] let [ ] = = − + = − = − − = − = = + = + = wu v uvwl uvw F // [ 2 2 6 ]// [ 1 1 3 ] duplex slip systems : (111)[ 011]+ (111)[101] Solution:
4.R=R1+R2=[10 5. stable: F: u'v'wT R1=[nw×101R2=[avw]×[011 When R=R+R2=[000] stable and no rotation
4. 5. stable: [110] R = R1 + R2 = F : [u v w ] [ ] [101] [ ] [011] R1 = u v w R2 = u v w When R = R1 + R2 =[000] stable and no rotation
34.5 Sur face Morphology of Crystal After Sli The following deformation marks can be seen on the surface of the crystal after slip 1. Slip lines: the steps formed on surface due to slip 2. Slip bands 3. Deformation band formed due to inhomogeneous rotation 4. Kink bands
§4.5 Surface Morphology of Crystal After Slip The following deformation marks can be seen on the surface of the crystal after slip. 1. Slip lines: the steps formed on surface due to slip. 2. Slip bands. 3. Deformation band formed due to inhomogeneous rotation. 4. Kink bands
34.6 Strain Hardening (Work- harden ng I. What's strain harden ing (work ing hardening By strain hardening we means the increase in tensile stress for polycrystals or in shear stress(the flow stress) for single crystals necessary for keeking on plastic deformation
§4.6 Strain Hardening (Workhardening) ◆Ⅰ.What’s strain hardening ? (working hardening) By strain hardening we means the increase in tensile stress for polycrystals or in shear stress (the flow stress) for single crystals necessary for keeking on plastic deformation
