Elastic properties of dislocation 上清充通大￥ SANCEAI JUO TO阳UY Strain energy of edge dislocation The elastic energy for edge dislocation per unit length Gb2 R U。=4π1-v In >Us (N=1/3) Yo For ro=2b,R-2000b(subgrain size) Gb2,R U。= U; ln4≈0.5Gb2Ue=1l 30 4π Strain energy of mixed dislocation The elastic energy for mixed dislocation stored in this volume per unit length U=U,+0。- R 4πk ≈CGb2 ro where:0.5≤a≤0.75 Institute of Forming Technology Equipment 17
Elastic properties of dislocation Institute of Forming Technology & Equipment 17 The elastic energy for edge dislocation per unit length Strain energy of edge dislocation ln 4 (1 ) 0 2 r Gb R U e >U (ν＝1/3) s UU U s e where：0.5≤α≤0.75 2 0 2 ln 0.5 4 Gb r Gb R U s 0 2 ln 4 r R k Gb 2 Gb 1 3 1 2 U UU e ss Strain energy of mixed dislocation For r0＝2b，R＝2000b (subgrain size) The elastic energy for mixed dislocation stored in this volume per unit length
Elastic properties of dislocation 上济充通大米 SHEAMGRAI DUD TONO UHTVEREETTY Dissociation of dislocations 口 Dislocations may dissociate to reduce their energy Consider the reaction*: 2b→b+b L业 Change in energy: Initial energy before splitting into partials:G(2b)2/2=2Gb2 Energy after splitting into partials:2[G(b)2/2]=G(b)2 Reduction in energy =2Gb2-Gb2=Gb2. The reaction would be favorable. Institute of Forming Technology Equipment 18
Elastic properties of dislocation Institute of Forming Technology & Equipment 18 Dissociation of dislocations Consider the reaction*: 2b → b + b Change in energy: Initial energy before splitting into partials: G(2b)2/2 = 2Gb2 Energy after splitting into partials: 2[G(b)2/2] = G(b)2 Reduction in energy = 2Gb2 – Gb2 = Gb2. The reaction would be favorable. Dislocations may dissociate to reduce their energy
Elastic properties of dislocation 上产克大睾 SHEAMGHAI DUD TONO UHTVEREETTY Line tension A dislocation has a line tension,which is similar to the surface tension of a soap bubble or a liquid. This is because the strain energy of a dislocation is proportional to its length. an increase in length results in an increase in energy. The line tension is defined as the increase in energy per unit increase in the length of a dislocation line: T=a.Gb2 Institute of Forming Technology Equipment 19
Elastic properties of dislocation Institute of Forming Technology & Equipment 19 A dislocation has a line tension, which is similar to the surface tension of a soap bubble or a liquid. This is because the strain energy of a dislocation is proportional to its length. an increase in length results in an increase in energy. The line tension is defined as the increase in energy per unit increase in the length of a dislocation line: Line tension T T 2 T Gb
Elastic properties of dislocation 上清充通大￥ SHEAMGHAI DUD TONO UHTVEREETTY Force acting on a dislocation o External work done by t to move the dislocation through the crystal: W=t.(lds).b Internal work done against the resistance fis(note that the dislocation moved by a distance /) W=F.ds from which we conclude that: F ds- =t.b External work done by t Where f is the glide force on a unit length of a dislocation;t is the shear stress in the glide plane resolved in the direction of b. Virtual work principle Institute of Forming Technology Equipment 20
Elastic properties of dislocation Institute of Forming Technology & Equipment 20 • External work done by τ to move the dislocation through the crystal: • Internal work done against the resistance f is (note that the dislocation moved by a distance l): from which we conclude that: Where f is the glide force on a unit length of a dislocation; τ is the shear stress in the glide plane resolved in the direction of b. Force acting on a dislocation ┴ ┴ l ds ┴ ┴ b τ τ W lds b ( ) W F ds F f b l F ┴ ┴ ┴ ┴ Virtual work principle External work done by τ
Elastic properties of dislocation 上产克大睾 SHEAMGHAI DUD TONO UHTVEREETTY Force between two parallel screw dislocations Consider two parallel screw dislocations,the stress field of first dislocation b Gb 70:= 2πr ,t9⊥b2 P(x.y) For t,e,no forces act on b2 f=tg:·b2= Gbb2∝1 Two parallel screw dislocations 2π·r 0 0 0 The force is repulsive for screw of the same sign and attractive for 0 0 screws of opposite sign. Institute of Forming Technology Equipment 21
Elastic properties of dislocation Institute of Forming Technology & Equipment 21 Force between two parallel screw dislocations Two parallel screw dislocations 2 b 2 z y x 1 b 1 P(x,y) rθ f 0 0 0 0 0 0 0 z z z z r Gb 2 1 r r Gb b f b z 1 2 1 2 2 2 b z Consider two parallel screw dislocations, the stress field of first dislocation b1, The force is repulsive for screw of the same sign and attractive for screws of opposite sign. For τzθ, no forces act on b2