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Lecture Recap: 9/21/09 Lecture Recap: 9/21/09

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Page 1: Lecture Recap: 9/21/09 - MIT OpenCourseWare · Dislocation Energy 0 2 2 1 2 1 W E d τ γ τγ rz μγ rz γ ∫ = = = = 8 2 2 2 z r screw r b W π μ = ∫ ∫ 2 2 2 8 r b V W π

Lecture Recap: 9/21/09 Lecture Recap: 9/21/09

Dislocation Energy

21dEW rzrz μγτγγτ

==== ∫ 8 22

z rscrew rbW

πμ

= ∫ ∫

8 rb

πμ

= )ln(4

inner

outer

rrblW

πμ

=Screw

2bEdge

2~ bl

W μν

μ−1

~2b

Energy of dislocation proportional to lengthSame dimensions as F, “line tension”

Edge dislocation always higher energy(1-ν)<1

Crystals try to form long screw dislocationsy y gDislocations often zigzag to accommodate screw

http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/backbone/r5_2_3.html

Page 3: Lecture Recap: 9/21/09 - MIT OpenCourseWare · Dislocation Energy 0 2 2 1 2 1 W E d τ γ τγ rz μγ rz γ ∫ = = = = 8 2 2 2 z r screw r b W π μ = ∫ ∫ 2 2 2 8 r b V W π

Mixed Dislocations

Stress Edge ScrewStress

σxx

Edge Screw

0222

)(3

)1(2 yxyxb y

−−

νπμ

σyy

222

)()1(2 yxyxb y

+−

−νπμ

)(σzz

τxy

0222

)()1(2yxb x

+−μ

)( yyxx σσν +

τxz 0

222 )()1(2 yx +−νπ

Θcos2 r

bπμ

bτyz 0 Θsin2 r

bπμ

Page 4: Lecture Recap: 9/21/09 - MIT OpenCourseWare · Dislocation Energy 0 2 2 1 2 1 W E d τ γ τγ rz μγ rz γ ∫ = = = = 8 2 2 2 z r screw r b W π μ = ∫ ∫ 2 2 2 8 r b V W π

Stress Fields

Dislocations can interactImagine them like charges: similar dislocations repel, opposites attract

http://www.matter.org.uk/matscicdrom/manual/images/image109.gif

Image of stress fields around two dislocations removed due to copyright restrictions.

http://www.matter.org.uk/matscicdrom/manual/images/image109.gif

Page 5: Lecture Recap: 9/21/09 - MIT OpenCourseWare · Dislocation Energy 0 2 2 1 2 1 W E d τ γ τγ rz μγ rz γ ∫ = = = = 8 2 2 2 z r screw r b W π μ = ∫ ∫ 2 2 2 8 r b V W π

Dislocation Motion

Peach-Koehler Equation

Fx = bxσ

(xy + byσ yy + bzσ zy

)Fy = −(bxσ xx + byσ xy + bzσ xz )

Edge Dislocationσxx Fσyy F=0

Screw Dislocationσxx F= 0

= 00=0

σyy Fσzz F=0τxy F τxz F=0τyz F=0

σzz

τyz Fτyz F 0 τyz F*assumes pos Edge, RH Screw

http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/illustr/dislocation_3dim.jpg

τxy F= 0 τxz F

Image removed due to copyright restrictions.F= 0 Please see the cover of Nature Physics 5(April 2009).

http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/illustr/dislocation_3dim.jpg

http://www.nature.com/nphys/journal/v5/n4/covers/largecover.gif

Page 6: Lecture Recap: 9/21/09 - MIT OpenCourseWare · Dislocation Energy 0 2 2 1 2 1 W E d τ γ τγ rz μγ rz γ ∫ = = = = 8 2 2 2 z r screw r b W π μ = ∫ ∫ 2 2 2 8 r b V W π

Dislocation Motion

Dislocation moves along plane containing b, tg p g ,

Edge Screw

Page 7: Lecture Recap: 9/21/09 - MIT OpenCourseWare · Dislocation Energy 0 2 2 1 2 1 W E d τ γ τγ rz μγ rz γ ∫ = = = = 8 2 2 2 z r screw r b W π μ = ∫ ∫ 2 2 2 8 r b V W π

MIT OpenCourseWarehttp://ocw.mit.edu

3.40J / 22.71J / 3.14 Physical Metallurgy Fall 2009

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

http://ocw.mit.edu

http://ocw.mit.edu/terms

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