1. A plate fatigue test specimen made from 7005-T53 aluminum contains a semi-circular surface crack (a/c = 1) and is subjected to R = 0.1 uniaxial loading with a stress range, AS,, of 250 MPa. You can use the K solutions from the Dowling textbook (2nd Ed.) provided below. You can also assume that the crack size is negligibly small compared to the thickness (t) and width (b) and the shape remains semi-circular throughout the life of the test specimen to enable analytical integration of the crack growth relationship. ж K-15/1 Case & $ F for small a Limits for £:10% on F P (a) -0.637 - 05 AM л 75 P 3M (b) 0.728 2b <04.03 P 6M (c) 0.722 지 035, 02 4P 32M (d) 0.728 <0.2 or 0.35 Note: 'Different limits for tension or bending, respectively. Figure 8.17 Stress intensity factors for (a) an embedded circular crack under uniform tension normal to the crack plane, and related cases: (b) half-circular surface crack, (c) quarter-circular corner crack, and (d) half-circular surface crack in a shaft, where the latter is more precisely a portion of a circular are with center on the surface. (Based on [Newman 86] and [Raju 86]) The following crack growth data were obtained in laboratory air environment. Using these data: (a) Plot crack length, a (mm), versus cycles, N. (b) Plot da/dN versus AK. Identify the three regions of crack growth. (c) Determine the Paris equation constants, C and m, for the linear region of crack growth. N (cycles) a (mm) da/dN (mm) 95,000 0.244 100,000 0.246 7.00 x 10-7 105,000 0.251 3.920 x 10-6 110,000 0.285 9.665 x 10-6 115,000 0.347 1.053 x 10-5 125,000 0.414 1.230 x 10- 130,000 0.490 2.063 x 10-5 135,000 0.621 4.661 x 10-5 140,000 0.956 9.565 x 10-5 145,000 1.577 3.964 x 10 147,000 2.588 1.105 x 10-³ 147,400 3.078 1.554 x 10- 147,500 3.241 8.758 x 10- 147,500 3.445

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