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Assignment2_solution - Assignment#2 Solutions ME264...

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1 Assignment #2 Solutions ME264 Materials Science for Mechanical Engineering Spring 2009 Due Date: 25 February 2009 (3 pts) 1. (1.5pt) (a) Define Poisson’s ratio , ν , and dilatation , , in the straining of an elastic solid. (b) Calculate the dilatation in the uniaxial elastic extension of a bar of material, assuming strains are small, in terms of ν and the tensile strain, ε . Hence find the value of ν for which the volume change during elastic deformation is zero. (c) Poisson’s ratio for most metals is about 0.3. For cork it is close to zero; for rubber it is close to 0.5. What are the approximate volume changes in each of these materials during an elastic tensile strain of ε ? Solution: (b) The following figure shows the uniaxial elastic extension of a bar of material. The change in axial length : 0 l l l δ ε = The length of the bar under uniaxial elastic extension: ( ) 0 0 0 0 1 l l l l l l l l l l δ ε ε = + = + = + The cross sectional area of the bar under uniaxial elastic extension: ( ) 2 0 1 l A v A ε = - Proof: 2 0 0 A r π = :cross sectional area before elastic extension.
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