# Assignment2 - the value of the constant A ~ for each metal....

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1 Assignment #2 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 ? 2. (1.5pt) The table below gives the Young’s module, E , the atomic volume, , and the melting temperature, T M , for a number of metals. If Ω M T k A E ~ (where k is Boltzmann’s constant and A ~ is a constant), calculate and the tabulate

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Unformatted text preview: the value of the constant A ~ for each metal. Hence find an arithmetic mean of A ~ for these metals. Use the equation, with average A ~ , to calculate he approximate Young’s modulus of (a) diamond and (b) ice. Compare these with the experimental values of 12 10 . 1 × N m-2 and 9 10 7 . 7 × N m-2 , respectively. Watch the units. Material Ω x 10 29 (m 3 ) T M (K) E ( GN m-2 ) Nickel 1.09 1726 214 Copper 1.18 1356 124 Silver 1.71 1234 76 Aluminum 1.66 933 69 Lead 3.03 600 14 Iron 1.18 1753 196 Vanadium 1.40 2173 130 Chromium 1.20 2163 289 Niobium 1.80 2741 100 Molybdenum 1.53 2883 360 Tantalum 1.80 3271 180 Tungsten 1.59 3683 406 2 Data for ice and diamond. Ice Diamond Ω = 29 10 27 . 3-× m 3 Ω = 30 10 68 . 5-× m 3 T M = 273 K T M = 4200 K E = 9 10 7 . 7 × N m-2 E = 12 10 . 1 × N m-2...
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## This note was uploaded on 11/17/2009 for the course MECHANICAL ME 264 taught by Professor Asst.prof.a.fethiokyar during the Spring '09 term at Yeditepe Üniversitesi.

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Assignment2 - the value of the constant A ~ for each metal....

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