85.14 Pile up of Dislocation I Mode I Back stress exerted by obstacle on leading dislocation (It is supposed to be a short-range-force ncbdx= tpbdx dx: virtual displacement → BnT
§5.14 Pile up of Dislocation ◆ Ⅰ.Model ◆ Ⅱ.Back stress exerted by obstacle on leading dislocation. (It is supposed to be a short-range-force.) n n b x b x B B = d = d dx : virtual displacement
◆Ⅲ. Distribution of the dis locat ion n Gb b2+b1=0i=(2,3,……,n) 2(1-)x=x To leading dislocation Gb 1 =22n(1-1)(-x) ,+t6 -tB6=0
◆ Ⅲ.Distribution of the dislocation 0 (2,3, , ) 1 1 2 (1 ) b b i n x x G b i i i j n j i j j + = = − − = To leading dislocation : 0 ( ) 1 2 (1 ) 1 1 1 2 + − = − − = b b b x Gb B j n j j
◆ⅣV. Consequence ① Cut through obstacle by slip (2 Bypass by climbing by cross slip ③ Crack
◆ Ⅳ.Consequence ① Cut through obstacle ② Bypass ③ Crack by slip by climbing by cross slip
35.15 Inter section of Dislocations Rule: When two dislocation moving on intersecting slip planes meet together, their shape will in general change. This shape change can be determined by the macroscopic deformation of the crystal
§5.15 Intersection of Dislocations ◆ Ⅰ.Rule: When two dislocation moving on intersecting slip planes meet together, their shape will in general change. This shape change can be determined by the macroscopic deformation of the crystal
I. Examples: 1.⊥-⊥ Burgers vector forming jog 2.⊥-⊥ Burgers vector∥ forming kink 3. L-$ forming one jog, one kink, or two jogs 1. $- forming two jogs
◆ Ⅱ.Examples: 1. ⊥-⊥ Burgers vector ⊥ forming jog 2. ⊥-⊥ Burgers vector ∥ forming kink 3. ⊥-$ forming one jog, one kink, or two jogs 4. $-$ forming two jogs A B C D 1 b 2 b A B C D 1 b 2 b A B C D 1 b b2