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Unformatted text preview: MSE 2610 Introduction to the Mechanical Properties of Materials Fall 2008 Homework #4 Solutions Due: 02 October 2008 1.) A true stress vs. true strain curve modeled as the function ⎩ ⎨ ⎧ < < < = ε ε ε ε σ 002 . ) 58 . 3 ( 002 . ) 80 ( 3 . GPa GPa The original unloaded sample had a diameter of 10 mm. a.) What is the ultimate tensile strength of this material? ( ) ( ) GPa 49 . 2 3 . GPa 58 . 3 UTS 3 . m UTS @ ε 3 . T = = = = b.) What is the reduced crosssectional area of the sample at strains of 0.01, 0.05, and 0.1? ( ) 2 5 2 2 o T o m 10 85 . 7 ) m 005 . ( π r π A ε exp A A − × = = = − = A o (m 2 ) ε T (no units) A (m 2 ) 7.85 x 105 0.01 7.78 x 105 7.85 x 105 0.05 7.47 x 105 7.85 x 105 0.1 7.11 x 105 2.) An extremely long hollow steel tube has an internal pressure of 1 MPa. The internal pressure is increased to some amount P2 such that the circumference of the tube increases by 0.06%. The modulus of the material is 200 GPa and the thickness of the tube is 0.5 cm. The thickness of the tube is 1 % of the diameter [Note: This allows for treatment of the problem as a thinwalled tube.] From an uniaxial tension test of the same material, it was found that the steel had a yield strength of 180 MPa. a.) Find P 2 .  A 0.06% increase in circumference corresponds to a strain in the material of 0.0006. Neglecting Poisson strain in the thickness of the pressure vessel wall, one can write: 6 1 1 2 1 1 1 10 5 . 2 ) cm 5 . )( GPa 200...
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This note was uploaded on 12/24/2008 for the course MSE 261 taught by Professor Sass during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 SASS

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