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
Consequence 1. No change in dislocation shape = no effect on further slip 2. Formation of jog (1 Which could slip along with the remaining segments, but on different S P. the consequence depends on the height of jog a. Short jog(1-2A) is effect in slip b.Long jog(>100A) forming L-shaped dislocation sources Mediums jog(<100A) forming dislocation dipole
◆ Ⅲ.Consequence 1. No change in dislocation shape ＝> no effect on further slip. 2. Formation of jog. ① Which could slip along with the remaining segments, but on different S.P. the consequence depends on the height of jog. a. Short jog (1~2Å) is effect in slip. b. Long jog (>100Å) forming L-shaped dislocation sources. c. Mediums jog (<100Å) forming dislocation dipole
2 Which must climb along with the remaining segments The consequence is a. leaving point defects b. hardening
② Which must climb along with the remaining segments. The consequence is a. leaving point defects b. hardening
Examples and Discussions
Examples and Discussions
Exercise
Exercise
Thank you 23
Thank you ! 23