Exam I W10 solns - ME 382 W 2010 MIDTERM I SOLUTIONS...

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ME 382 W 2010 MIDTERM I SOLUTIONS Problem 1:______/20 Problem 2:______/30 Problem 3:______/25 Problem 4:______/25
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ME 382 W10 Midterm 1 Page 2 of 9 20 points Problem 1 : Consider the following engineering stress-strain curve for a metallic bar and answer the following questions. Show all your work a. What is the initial yield stress? For 0.2% offset yield stress, yield stress = 900 MPa (See black lines on stress-strain curve). Alternately yield stress = 800 MPa from the onset of nonlinearity in the curve. b. If the Poisson ratio is ν = 0.3, calculate the volumetric strain at yield. Volumetric strain ε v = ε x + ε y + ε z Assuming that the loading is in the z-direction, ε x = ε y = - ν x ε z = -0.3 x 1.5% = -0.45% Therefore, ε v = 1.5% - 0.45% - 0.45% = 0.6% c. If the bar is loaded to σ = 1000 MPa, and then unloaded to σ = 0 MPa, what are the elastic, and plastic strains? Elastic strain, ε elastic = 1 ° ( ± ?? ² ( ± ?? + ± ?? )) = 0 since the stresses are zero once the bar is unloaded. Plastic strain, ε pzz = 0.5%. (See second stress-strain curve) By the fact that x- and y-directions are equivalent, we have ε pxx = ε pyy, and since plastic straining happens at constant volume, ε pxx + ε pyy + ε pzz = 0, we have ε pxx = ε pyy = -0.25%. d. Re-draw the engineering stress-strain curve in the box provided, showing the unloading from σ = 1000 MPa to σ = 0 MPa. Shown on next page in second stress-strain curve
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ME 382 W10 Midterm 1 Page 2 of 9
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ME 382 W10 Midterm 1 Page 2 of 9 30 points Problem 2 : Answer the following questions briefly (3—4 sentences). The use of sketches or equations could significantly strengthen your response. a. Of the Tresca and von Mises yield criteria, which is more accurate, and which is more conservative from the point of view of design? The Tresca criterion considers slip only along the 45˚ max shear planes while the Von Mises criterion considers slip along four octahedral shear stress planes where the shear stress is only slightly lower than the max shear stress. The Tresca criterion is therefore more
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This note was uploaded on 05/12/2010 for the course MECHENG 382 taught by Professor Thouless during the Winter '08 term at University of Michigan.

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Exam I W10 solns - ME 382 W 2010 MIDTERM I SOLUTIONS...

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