4020-F2011-HW9Solutions - 1 MSE 4020 HW9-SOLUTION...

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Unformatted text preview: 1 MSE 4020 HW9-SOLUTION 10/26/2011 Problem 1 1. For two parallel edge dislocations with antiparallel Burgers vectors (shown in the figure above), the force F(Glide force F x and Climing force F y ) can be written as: F x = ! Gb 2 2 " (1 ! # ) x(x 2 ! y 2 ) (x 2 + y 2 ) 2 (1) F y = ! Gb 2 2 " (1 ! # ) y(3x 2 + y 2 ) (x 2 + y 2 ) 2 (2) (a) x = -2, y = 1 From Eq. 1 F x = 2.28 ! 10 " 3 dym / cm (b) x = -y F x = 0 dym / cm (c) x = 0 F x = 0 dym / cm (d) x y F x F y r A B 2 x = y F x = 0 dym / cm (e) dF x dx = ! 9.502 " 10 ! 7 ( ) " (x 2 + y 2 ) 2 " (3x 2 ! y 2 ) ! 4x 2 " (x 2 ! y 2 ) " (x 2 + y 2 ) (x 2 + y 2 ) 4 # $ % & ' ( = ) (x 2 + y 2 ) 2 " (3x 2 ! y 2 ) ! 4x 2 " (x 2 ! y 2 ) " (x 2 + y 2 ) = ) (x 2 + y 2 ) " (3x 2 ! y 2 ) ! 4x 2 " (x 2 ! y 2 ) = ) x 4 ! 6x 2 y 2 + y 4 = ) x 2 = ! ! 6y 2 36y 4 ! 4y 4 2 = 3 2 2 ( ) y 2 y = 1 m ) x 2 ( ) 1 = 5.83 m ) x 1 = 2.414 m ) F x = 2.4 " 10 ! 3 dyn / cm x 2 = ! 2.414 m ) F x = ! 2.4 " 10 ! 3 dyn / cm * + ,- , x 2 ( ) 2 = 0.410....
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This note was uploaded on 12/05/2011 for the course MSE 4020 at Cornell University (Engineering School).

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4020-F2011-HW9Solutions - 1 MSE 4020 HW9-SOLUTION...

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