MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 02139 2.002 MECHANICS AND MATERIALS II HOMEWORK # 5 Distributed: Wednesday, April 7, 2004 Due: Wednesday, April 14, 2004 Problem 1 The typical properties of several steels that are being considered for use in bridges in Alaska, and therefore will have service temperatures as low as −60oF , are as follows: Steel (ASTM Grade) Minimum Yield Strength (ksi) Yield Strength at 60oF ,(ksi) KIc at −60oF , (ksi √in) A36 36 44 60 A441 50 69 53 A572 50 57 100 A514 100 110 60 For a design stress of 0.6 of the minimum yield strength [to be encountered in service], compare the critical crack sizes for fast fracture at the design stress for each steel. Use an edge crack in a large plate for your analysis (note: for this geometry, the numerical value of the configuration correction factor is Q = 1.12). With which material would you choose to design? Discuss the tradeoffs you are aware of, including how your inspection technology might influence your decision. 1awtMMProblem 2 A large thick plate of 7075-T651 aluminum alloy is examined by nondestructive techniques and is found to contain no detectable cracks. In current engineering practice, flaws less than 5 mm in length are not usually reliably detected in large engineering components. Assume that the plate contains an edge crack of length at this limit (5 mm) of detection, and determine if the plate will undergo general yielding or fail by fast fracture before general yielding occurs when subject to tensile loading normal to the presumed crack. What is the stress at which failure would occur? σy = 503 MPa, KIc = 27 MPa√m. Problem 3 Dowling text, problem 8.15, page 352 (Second Edition). Problem 4 A bar of 4340 steel, of thickness t = 12 mm and width w = 60 mm, is subjected to a cyclic bending moment that ranges from maximum value M(max) = 4 kNm to minimum value M(min) = 0.8 kNm. Figure 1: Schematic of edge-cracked specimen under bending. The steel has Young’s modulus E = 208 GP a, Poisson ratio ν = 0.3, tensile yield strength σy = 1255 MP a, and ultimate tensile strength UT S = 1295 MP a. After 60, 000 cycles of the loading describ ed, the bar fractures, with failure due to a through-thickness edge crack of [failure] length af = 14 mm, emanating from the “tensile side” of the bending stress field. 2The stress intensity factor for a rectangular beam containing an edge crack of length “a” and subjected to bending moment “M ” can be expressed as KI = Q σb √πa, where σb is the peak tensile bending stress in the uncracked beam, subjected to bending moment M , and the configuration correction factor can be taken as constant, Q = 1.12, providing the relative crack depth a/w <∼ 0.3. • Estimate the fracture toughness of the 4340 steel. • Based on your estimate, do you think that final failure took place under small-scale yielding conditions? Under crack-front plane strain conditions? Discuss.
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