Problem 2: Determine the Factor of Safety for the following condition: (a) Using distortion-energy theory, determine the factor of safety of a AISI 1040 hot-rolled steel for the following plane stress states: 6, =-50 MPa, o, = 40 MPa, Ty=-80 MPa (b) Using Coulomb-Mohr and Modified mohr theory, determine the factor of safety of a ASTM 50 cast iron for the following principal stress states: G,- 10 kpsi, a, =-15 kpsi, Ty-20 kpsi

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(ii) The turbine blade root is found to contain a surface fatigue crack of 3.3 mm during a routine maintenance inspection. The major stop-start load cycle is experienced twice per day with a minimum stress of 34 MPa and a maximum stress of 195 MPa. The turbine blade has a KIC of 75 MPa√m. Fatigue crack growth rate data for this alloy is given by: the Paris law constant, A = 4.5 x 10-11 and the Paris law exponent, m = 3.8. How many more stop-starts would you recommend be used? Explain your reasoning. You can assume the shape factor Q = 1.2, K is in MPaNm and a (crack length) is in m

b-Yield strength using 0.006 extension strain method (in psi). Answer: c- If the yield stress is considered failure stress, what is the maximum working stress (psi) to be applied to this material if a factor of safety of 1.25 is used? Answer: