1) Crack Propagation: . A 7075 aluminum alloy aircraft component in the form a 100 mm wide plate with a central elliptical hole that is twice as long as its width as shown in figure 1, is subjected to far field uniform uniaxial stress of 50 MPa during pressurization of the aircraft cabin. a) Lookup the appropriate stress concentration factor for this geometry using the attached formula For a infinite plate the solution is: max 1 2 nom ab ? ? ? ? ? ? ? ? ? ? For a plate with finite width D, the solution is b) Conduct finite element analysis of the part to find the maximum stress and compare this to the stress computed using the stress concentration factor determined in (a) c) Determine the critical crack length for this geometry assuming that the crack is located at the location of maximum stress Hint: For the worst scenario calculation you can assume that the crack is subjected to a uniform loading of the maximum stress. d) Determine the number of pressurization cycles required for the smallest detectable flaw of 0.2 mm to grow to critical size. Assuming that the smallest detectable flaw is located at the location of maximum stress. Relevant material properties of 7075 Aluminum: E = 70 GPa, Sy = 505 MPa, K1C= 29 MPav ; Paris law ( ) where C = 6.9 x 10-12 m/cycle (MPav )-2.5 and m =2.5. 50 mm ? ? 100 mm 25 mm
2) Shafts in Speed Reducer: . A shaft is used to support pinion in a speed reducer. Due to the force, F, applied by pinion gear, the shaft undergoes fully reversed cyclic loading during the each rotation. Due to the facewidth of the pinion gear, the shaft is constrained to be of length l and is supported at the ends by bearings. The gear is mounted such that the center of the gear coincides with the center of the shaft. Diameter and material of the shaft needs to be chosen such that cost of the shaft is minimized and shaft does not fail due to fatigue loading. In addition, proper meshing of pinion and gear teeth requires that shaft deflection can not be larger…