{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment2_solution

# Assignment2_solution - Assignment#2 Solutions ME264...

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}