HW2 - EN222: Mechanics of Solids Homework 2: Dislocations...

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EN222: Mechanics of Solids Homework 2: Dislocations Due Thursday February 16, 2006 Division of Engineering Brown University 1. Using the method of images, calculate the stress fields induced by a screw dislocation near the interface between an elastic solid and a very stiff (rigid) solid. Assume that the two solids are perfectly bonded. Calculate the configurational force acting on the dislocation, and state whether the dislocation is attracted to or repelled from the interface. 2. The complex potentials generating the solution to an edge dislocation at the origin of an infinite solid were given in class as () 12 00 22 ( ) log( ) ( ) log( ) 8( 1 ) 1 ) Eb i b Eb ib zi z z i z ω πν + Ω= = −− where are the burgers vector components. Using whatever symbolic manipulation program you like, check the formulas given below for the displacement and stress state. If you find an error, please give the correct solution! i b 1 12 2 2 21 1 1 log( ) cos2 sin 2 2 4 (1 ) 8 ) 1 log( ) sin 2 2 4 ) 8 ) b ub r b b b r
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