6. A uniaxial tension test with a bar made of each of the materials shown below

Question

6. A uniaxial tension test with a bar made of each of the materials shown below is to be conducted. For small strain testing (within the linear elastic limit) the "volumetric strain (change in volume per unit initial volume) of the uniaxially stressed material is of interest since it relates to the material "compressibility". Which two materials in the table would be expected to have the greatest and least'(volumetric strain), at a given axial strain level, based on the rovided data? Stiffness Properties of Selected Materials Young's Modulus of Shear Modulus of Elasticity, E (10 ps Elasticity, G (10° psi) Ratio, v Poisson's Material Tungsten carbide Titanium carbide Titanium carbide Molybdenum Molybdenum Molybdenum Steel (mos) Stainless steel Iron base superalloy (A-286) 95 42-65 (77) 33-48 (1600-1800°F) 47 (RT)1 33 (1600 °F) 20 (2400 °F) 30 28 29.1 (RT) 23.5 (1000 °F) 22.2 (1200 ) 19.8 (1500°F) 29 31 13-24 17 16 16 10.3 6.5 6.0 0.4 0.20 0.19 0.29 11.5 10.6 0.30 0.31 0.31 Cobalt base superalloy Inconel Cast iron Commercial bronze (C 22000) Titanium Phosphor bronze Aluminum Magnesium Graphite-epoxy composite Acrylic thermoplastic Room temperature. 11.0 5.2-8.5 6.3 6.2 6.0 0.21-0.27 0.31 0.35 0.33 0.29 0.4 The smallest volumetric strain will occur in the Acrulic Thermoplastic (Explain why)

Explanation / Answer

Volumetric strain is given by = linear strain * (1-2v) where 'v' is poisson's ratio. From the data given you can see Acrylic thermoplastic has highest poisson's ratio value of 0.4. Therefore, (1-2v) will be least for it and so will be volumetric strain.

Based on similar explanation titanium carbide has the least poisson's ratio so it should have highest volumetric strain.

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