Dislocations and Cracks 1
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1 Disloctions nd Ccs st Apil 003 c 003, Michel Mde
2 Definitions Bittle Ductile Disloction Buges Vecto Glide Plne Fenel Kontoov Model Hextic Phses Oienttionl Ode, Memin Wgne Theoem Kostelitz Thouless Beezinsii Tnsition Ccs Confoml Mpping Stess Intensity Fcto st Apil 003 c 003, Michel Mde
3 4 cm Definitions 3 Given sufce enegy of J/m, height h t which it pys to split object in two is h 4 g (L) st Apil 003 c 003, Michel Mde
4 Filue in She 4 F F L A L A L L (A) F (B) F G L L F A (L) st Apil 003 c 003, Michel Mde
5 Filue in She 5 F A G 5 Y 5 she tension. (L3) Mteil She modulus G/5 Yield stength (0 egs cm 3 ) (0 egs cm Ion Coppe Titnium ) st Apil 003 c 003, Michel Mde
6 Filue in Tension 6 F A Y L L G 5 Y 5 F A she tension. (L4) (L5) Mteil Young s Theoeticl Pcticl Rtio Modulus Y 5 Stength Stength (0 egscm 3 ) (0 egscm 3 ) (0 egscm Ion Titnium Silicon Glss ) st Apil 003 c 003, Michel Mde
7 Complete Cohesive Enegy Cuve 7 P 4 W W W (L6) ) Pessue P (0 egscm Wigne-Seitz dius, W (Å) st Apil 003 c 003, Michel Mde
8 Disloctions 8 b (A) (B) (C) b b (A) Edge (B) Scew st Apil 003 c 003, Michel Mde
9 Buges Vecto 9 F ext y z x b F ext st Apil 003 c 003, Michel Mde
10 Expeimentl Obsevtions of Disloctions 0 (A) (B) (A) (B) (C) st Apil 003 c 003, Michel Mde
11 Expeimentl Obsevtions of Disloctions [Souce: Amelincx (964)] st Apil 003 c 003, Michel Mde
12 Expeimentl Obsevtions of Disloctions (A) (B) (A) Coutesy of J. Humpheys, Mncheste Univesity.) [(B) Cullis et l. (985)] st Apil 003 c 003, Michel Mde
13 Foce to Move Disloction 3 f x xyb x (L7) xy F ext N (L8) f b L (L9) Pech Kohle foce st Apil 003 c 003, Michel Mde
14 One-Dimensionl Disloctions: Fenel Kontoov Model 4 F Fcit (A) FFcit (B) Find foce needed to move disloction in simple one dimensionl model. st Apil 003 c 003, Michel Mde
15 n One-Dimensionl Disloctions: Fenel Kontoov Model 5 U x x int x f x (L0) f n x n xn x n xn U x (L) f n x n xn x n xn x n xn x n xn f f x n n x n n fo fo n n 0 0 (L) x n f n A l e qn (L3) e q q e 0(L4) x n f qn A e (L5) st Apil 003 c 003, Michel Mde
16 One-Dimensionl Disloctions: Fenel Kontoov Model 6 Al A l e q A(L6) q A e (L6b) A l A e q e q (L7) (L7b) x 0 f c Al(L8) f c tnh q (L9) q (L0) st Apil 003 c 003, Michel Mde
17 One-Dimensionl Disloctions: Fenel Kontoov Model 7 f c 4 (L) st Apil 003 c 003, Michel Mde
18 Impossibility of Cystlline Ode in Two Dimensions 8 Peiels nd Lndu showed tht two dimensionl cystls e destoyed by theml fluctutions. U d C u u (L) u e i u (L3) u 0 fo (L4) U d C e i u u (L5) C u (L6) st Apil 003 c 003, Michel Mde
19 u u Impossibility of Cystlline Ode in Two Dimensions 9 u d u (L7) u (L8) u u (L9) u du du du du du i du u e u du du i e ui ui e e C u e C C e C u u C u u (L30) (L3) C u u i (L3) st Apil 003 c 003, Michel Mde
20 Impossibility of Cystlline Ode in Two Dimensions 0 B T (L33) C u B T C d B T C (L34) (L35) 0 d B T C (L36) st Apil 003 c 003, Michel Mde
21 Oienttionl Ode u u dx dy (L37) tn dy dx (L38) u nd u (L39) st Apil 003 c 003, Michel Mde
22 Oienttionl Ode tn dy dx dxdy dx dy uy ux xdx xdx uy y uy ux ux x ydy ydy dx dy uy x dy dx ux y (L40) (L4) cos sin uy y ux x cos uy x sin ux y (L4) uy x ux y (L43) ixuy iyux e i (L44) d (L45) 4 x ux y uy xy ux u y uy u x (L46) st Apil 003 c 003, Michel Mde
23 Oienttionl Ode 3 4 B T C x y (L47) B T 4C 0 d 0 d B T 6 C (L48) st Apil 003 c 003, Michel Mde
24 Kostelitz Thouless Beezinsii Tnsition 4 Liquid Hextic Cystl t 0 s t 0 05 s t 0 s st Apil 003 c 003, Michel Mde
25 Kostelitz Thouless Beezinsii Tnsition 5 [Muy nd Gie (996)] st Apil 003 c 003, Michel Mde
26 y y u y Kostelitz Thouless Beezinsii Tnsition 6 u x 0 uy 0 u x uz x (L49) U d (L50) u 0 (L5) u x Imln x iy (L5) U d x y y x x y (L53) st Apil 003 c 003, Michel Mde
27 y Kostelitz Thouless Beezinsii Tnsition R ln R d (L54) (L55) u x Im ln x iy ln x x 0 iy (L56) q ln x 0 with q 3 4 (L57) st Apil 003 c 003, Michel Mde
28 Kostelitz Thouless Beezinsii Tnsition 8 S B ln L (L58) st Apil 003 c 003, Michel Mde
29 Kostelitz Thouless Beezinsii Tnsition 9 q ln L (L59) B T c q (L60) i j U i j with U q ln (L6) d e d e q q U U (L6) (L63) Z g e U (L64) st Apil 003 c 003, Michel Mde
30 sin U U U U d d Kostelitz Thouless Beezinsii Tnsition 30 n d R d e d R e (L65) (L66) p Eq d e cos Eq cos q cos sin (L67) (L68) q E(L69) d n q d e (L70) 4 d 4 d n (L7) st Apil 003 c 003, Michel Mde
31 Kostelitz Thouless Beezinsii Tnsition 3 d d d x dx 4 4 q 3 4 e q x 3 q x U e (L7) (L73) st Apil 003 c 003, Michel Mde
32 Kostelitz Thouless Beezinsii Tnsition 3 0 q q 6 0 q 0 0 q xln st Apil 003 c 003, Michel Mde
33 Fctue of Stip 33 (A) L dl (B) dl L y x U Y L (L74) du dl Y L (L75) st Apil 003 c 003, Michel Mde
34 Fctue of Stip 34 dl dl L Y Y L nd yy Y L Y L (L76) (L77) st Apil 003 c 003, Michel Mde
35 Fctue of Stip 35 Rdius of cuvtue R l z y x Stess yz, long y yz 3 4 Distnce x st Apil 003 c 003, Michel Mde
36 Fctue of Stip 36 Mximum stess pplied stess l R (L78) st Apil 003 c 003, Michel Mde
37 y xz Stesses Aound n Ellipticl Hole 37 u 0 (L79) u (L80) yz u y i fo i xiy i xiy (L8) (L8) x t t (L83) T x t y t nd N y t x t (L84) yz N0(L85) st Apil 003 c 003, Michel Mde
38 Stesses Aound n Ellipticl Hole 38 u x ix u y ix x t y t x t iy 0 iy u x yt y t u y xt 0(L86) (L87) t t (L88) (L89) p (L90) ei (L9) (L9) 4p (L93) st Apil 003 c 003, Michel Mde
39 Stesses Aound n Ellipticl Hole 39 i fo (L94) i fo (L95) i i fo fo 0(L96) 0 (L97) i i (L98) i 4p i p 4p (L99) st Apil 003 c 003, Michel Mde
40 Stess Intensity Fcto 40 yz u y x x x x s x (L00) K lim 0 yz (L0) st Apil 003 c 003, Michel Mde
41 Atomic Aspects of Fctue Wve numbe t R(L0) t (L0b) st Apil 003 c 003, Michel Mde
42 Atomic Aspects of Fctue 4 e i e i R i K R i t ei i t (L03) (L04) (L05) (L06) st Apil 003 c 003, Michel Mde
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