lec19_notes - K I = 100 MP a m K I . After 60 , 000 cycles...

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a w t M M MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING CAMBRIDGE, MASSACHUSETTS 02139 2.002 MECHANICS AND MATERIALS II FATIGUE CRACK GROWTH EXAMPLE Distributed : Wednesday, April 14, 2004 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 σ y = 1255 MP a , and ultimate tensile strength UT S = 1295 MP a . Fatigue crack propagation in the alloy is well-represented by a Paris-type relation of the sort Δ K I ± m da = Δ a 0 , dN Δ K I 0 where the exponent is m = 3 . 24, and the reference constants can be taken as a growth rate of da/dN = 10 3 mm/ cycle Δ a 0 when the applied stress intensity range is Δ
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Unformatted text preview: K I = 100 MP a m K I . After 60 , 000 cycles of the loading describ ed, the bar fractures, with failure due to a through-thickness edge crack of [failure] length a f = 14 mm , emanating from the tensile side of the bending stress eld. 1 The stress intensity factor for a rectangular beam containing an edge crack of length a and subjected to bending moment M can be expressed as K I = Q b a, where b is the peak tensile bending stress in the uncracked beam, subjected to bending moment M , and the conguration correction factor can be taken as constant, Q = 1 . 12, providing the relative crack depth a/w < . 3. Estimate the initial crack size, a i , that grew to cause the nal fracture. 2...
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This note was uploaded on 02/23/2012 for the course MECHANICAL 2.002 taught by Professor Davidparks during the Spring '04 term at MIT.

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lec19_notes - K I = 100 MP a m K I . After 60 , 000 cycles...

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