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Homework 1 - uniform cross section is loaded in tension...

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HOMEWORK 1 Due date: Wed, Jan 13 th 2010 Problem 1 : Below is a true stress versus true strain curve from an ME395 lab, in which a tensile test is conducted on an annealed sample of brass. What is the yield strength for this brass after it has been work-hardened to a true strain of 10%? Plot the engineering (nominal) stress-strain curve for this work-hardened brass. (You may neglect the small effects of elastic deformation in your answer.) Problem 2: (Ashby & Jones, Vol. 1, 3e, Problem 11.4a) Discuss the assumption that, when a piece of metal is deformed at constant temperature, its volume is unchanged. Note: You need to discuss whether the question is talking about elastic deformation or plastic deformation, and why is it necessary to include the assumption of constant temperature. Problem 3: (Ashby & Jones, Vol. 1, 3e, Problem 11.4b) A ductile metal wire of
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Unformatted text preview: uniform cross section is loaded in tension until it just begins to neck. Assuming that volume is conserved, derive a differential expression relating the true stress to the true strain at the onset of necking. Note: You need to remember that the onset of necking is given by the maximum in the nominal stress - nominal strain curve. Think of a mathematical expression in terms of nominal stress and nominal strain that defines this point—then re-express the nominal stress and strain in terms of the true stress and strain to get your answer. Problem 4: (Ashby & Jones, Vol. 1, 3e, Problem 11.5) The curve of true stress versus true strain for the metal wire approximates to σ = 350 ε 0.4 MN m-2 . Estimate the tensile strength of the wire and the work required to take 1 m 3 of the wire to the point of necking....
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