MSE113-HW5 - Fall 2009 UNIVERSITY OF CALIFORNIA College of...

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Unformatted text preview: Fall 2009 UNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering MSE 113 Mechanical Behavior of Materials PROBLEM SET 5 Assigned 10/27/09 Due 11/3/09 Prof. Ritchie Go to library and locate the ASTM Standards. Find and read the standard on Test Method for Linear‐Elastic Plane‐Strain Fracture Toughness K Ic of Metallic Materials (E‐ 399). Problem 1 Explain, as quantitative as possible (but preferably brief), the difference between plane stress and plane strain deformation? Why is the fracture toughness of a metallic material invariably lower in plane strain? Problem 2 You are the metallurgist for a design group which is working on cars for the proposed Maglev (magnetic levitation) high‐speed train route between Pittsburgh and Philadelphia. The structural engineer for the project asks you to help select a material for the car underframe. She has several candidate materials in mind, all of which have adequate yield strength, and which have varying densities (reduced weight of the cars will improve performance). She also reminds you that the design stress for the parts must not exceed 1/3 of the yield stress. She then hands you the following data which she has tabulated from her handbooks: Base Alloy Form σys (ksi) Density (lb/m3) σys/E Al A357‐T6 Cast and Machined 55 0.0966 0.00505 Al 7075‐T6 Forged 75 0.0966 0.00725 Ti Ti‐6Al‐4V Forged 145 0.164 0.00746 Steel 4340 Rolled 215 0.284 0.00602 Steel HSLA Rolled 175 0.284 0.00344 The structural engineer has just been to a conference where she saw examples of design procedures based on linear elastic fracture mechanics. She would like to use this approach if possible and wants to know if the candidate materials are appropriate. You look up the following data: Alloy σys (ksi) KIC (ksi√ඃඃ) A357‐T6 55 11 7075‐T6 75 20 Ti‐6Al‐4V 145 70 4340 215 100 HSLA 175 125 If the structural sections of the underframe will be about 0.25 in. thick, answer the following: a) Which material do you recommend? Why? For which of these will a linear elastic fracture mechanics (LEFM) approach be reasonable, i.e., is the small scale yielding requirement satisfied? b) How does your choice affect car weight? c) What will be the critical crack size in service for each material at stress of 1/3 of yield stress? d) What would be your reaction to the suggestion that the 4340 also be considered with a change in heat treatment, to achieve a yield strength of 220 ksi and a KIC of 35 ksi√ඃඃ? e) What other material properties might also be important, in addition to the ones considered in this problem? Problem 3 After all of your hard work on the Maglev high‐speed train project, you decide you need some fun in the sun! As you board Fight 113, headed for a winter break in Hawaii, you notice cracks emanating both sides of a round window in the passenger compartment. A nervous glance reveals that they approximately 3in. in either direction along the longitudinal axis of the aircraft. Fortunately you brought a calculator and you favorite mechanics book (for those long afternoons relaxing under the Hawaiian sun). You quickly look up the following information for the aluminum alloy 7075‐T6: σy = 64 ksi, Kc ≈ 25 ksi√ඃඃ (a reasonable plane stress value). Panic inspires you to simplify the problem by treating the airplane as a thin walled cylindrical pressure vessel with radius r = 10ft., thickness t = 0.15in., and length L = 200ft., with a maximum pressure of P = 1 atm. Should you run from the aircraft or just relax and enjoy the in‐flight movie, confident that your engineering skills have averted near tragedy? Treat the problem as two cracks emanating from a hole in an infinite body, where the hole (window) radius is 6 in. (See Stress Intensity Factor handout) You need only concern yourself with the maximum normal stress. Show all the work necessary to justify your conclusion. ...
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