E 45 - Fall 2010 - Gronsky - Midterm 1 (solution)

E 45 - Fall 2010 - Gronsky - Midterm 1 (solution) -...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science & Engineering Professor R. Gronsky Fall Semester 2010 Engineering 45 Midterm 01 Solutions INSTRUCTIONS ................................ PATIENCE Do not open pages until “START” is announced. .............................. PRUDENCE Position yourself with occupied seats directly in front of you and vacant seats to your left / right, when possible, unless instructed by exam proctors. .............................. PROTOCOL Only writing instruments / eraser / straightedge are allowed. Remove all other materials, including books / reference materials / calculators / PDAs / cell phones (disable all sounds) / other electronic devices / headphones / ear buds / hats from your person / workplace. ........................... POLITENESS Asking and answering questions during the exam are very disruptive and discourteous to your classmates. So there will be no questions during the exam. Instead, please include your concerns or alternative interpretations in your written answers. ............. PROFESSIONALISM The engineering profession demands strict ethical standards of honesty and integrity. Engineers do not cheat on the job, and there will be no cheating on this exam. 1. Mechanical Properties The stress-strain plots at right are obtained from a single uniaxial tensile test, by varying load ( P ) and measuring elongation ( Δ l = l–l ) of a test sample before converting to this format. One curve results from a conversion to engineering stress σ e = P/A and engineering strain ε e = Δ l/l , the other, true stress σ t = P/A i and true strain ε t = Δ l/l i where the subscripts 0 and i refer to "original" and "instantaneous" values of cross-sectional area ( A ) and length ( l ). a . Label the curves as σ e – ε e and σ t – ε t and explain the differences in their appearances. (See labels superimposed on figure above). The σ e – ε e curve exhibits an inflection point when the cross-sectional area of the sample begins to decrease ("necking"). This decrease is not taken into account in the definition of engineering stress, which assumes a constant (original) area. By contrast, there can be no inflection point in the σ t – ε t curve because each increment of area reduction is included in the definition. Both true stress (load divided by instantaneous cross-sectional area) and true strain (change in length divided by instantaneous length) add incrementally as deformation proceeds. Both increase monotonically, as exhibited by the shape of the σ t – ε t curve. b . The uniaxial tensile test is conducted according to ASTM standards using a constant crosshead speed . Explain the significance of this requirement and how it influences the curves shown above....
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This note was uploaded on 01/27/2011 for the course BIOE 104 taught by Professor Various during the Spring '10 term at Berkeley.

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E 45 - Fall 2010 - Gronsky - Midterm 1 (solution) -...

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