Lecture Recap: 9/21/09 Dislocation Energy γ 1 W = E = ∫ τ d γ = τγ 2 0 W μb 2 = V 8π 2 r 2 rz 1 = μγ 2 2 rz Screw W 2 ~ μb l W screw Edge W μb ~ l 1 −ν 2 Same dimensions as F, “line tension” y Edge dislocation always higher energy { (1-ν)<1 y Crystals y tryy to form long g screw dislocations { Dislocations often zigzag to accommodate screw http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/backbone/r5_2_3.html ∫ ∫ z r 2 μb2 r W = l ln( outer ) 4π r inner y Energy of dislocation proportional to length { = μb2 8π 2 r Mixed Dislocations Stress σxx σyy Edge Screw μby 3x2 + y2 − 2 π (1 − ν ) ( x 2 + y 2 ) 2 μby x2 − y2 2 π (1 − ν ) ( x 2 + y 2 ) 2 σzz ν (σ τxyy μbx xx +σ yy ) x2 − y2 2 π (1 − ν ) ( x 2 + y 2 ) 2 τxz 0 τyz 0 0 0 0 0 μb cos Θ 2πr μb sin Θ 2πr Stress Fields y Dislocations can interact y Imagine them like charges: similar dislocations repel, opposites attract Image of stress fields around two dislocations removed due to copyright restrictions. http://www.matter.org.uk/matscicdrom/manual/images/image109.gif Dislocation Motion y Peach-Koehler Equation Fx = bxσ xy + byσ yy + bzσ zy Fy = −(bxσ xx + byσ xy + bzσ xz ) Edge Dislocation σxx F σyy F=0 σzz F=0 0 F τxy τxz F=0 τyz F 0 F=0 Screw Dislocation σxx F= 0 σyy F= 0 Image removed due to copyright restrictions. σzz =0 00 Please see the cover of Nature Physics 5 F= τxy F= =00 (April 2009). F τxz F τyz *assumes pos Edge, RH Screw http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_5/illustr/dislocation_3dim.jpg Dislocation Motion y Dislocation moves along gp plane containing g b,, t Edge Screw S S t b MIT OpenCourseWare http://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.