hw3sol - Materials Science and Engineering 765 mechanical...

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1/3 Anderson G4:Users:peterand:Central files:Courses:MSE 765:2005:hw3sol.doc Materials Science and Engineering 765 mechanical behavior of materials Spring 2005 Homework 3 Solutions (updated May10) Due: On Tuesday, May 3, 2005 at 5pm. Please show all work necessary to arrive at your answers. Slide under my office door (345 Fontana). 1. Construction of a Burgers circuit Using the SF /RH (note the corrected typo in green) rule discussed in class, determine the Burgers vector and line sense of the dislocation in the figure below (Figure 4.7 in McClintock and Argon). As part of your answer, submit a copy of the figure showing your circuit. We choose the dislocation line direction ξ to point out of the plane of the paper and then construct a right-handed circuit as shown above. The circuit reveals a Burgers vector b pointing from left to right. A square or other circuit reveals the same b . The only requirement is that the circuit would be closed in a perfect crystal. 2. Independent slip systems In class, we derived an expression for the average plastic strain produced when a dislocation with slip plane normal n and Burgers vector b slips an area A s of a crystal with volume V. A fcc crystal with {111} type slip planes and <110> slip directions has 12 distinct slip systems (4 {111} slip planes and 3 <110> slip directions in each plane). A set of slip systems is said to be independent when the plastic strain
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