3. A simply supported beam of length 400 mm is shown in the figure below. The beam has a circular cross section with a diameter of 20 mm. An oscillating bending couple moment is applied at the center with M varying between -800 Nm and +800 Nm, at a frequency of 100 Hz. As shown below, there is a semi-circular crack with initial depth of a= 3.0 mm on the bottom surface of the beam at a distance of 150 mm from one end. The yield strength of the beam is 600 MPa, Kic = 35 MPam. The threshold for cyclic crack growth, AKth, is 15 MPam 150 mm A d M:-800-800 Nm B 250 mm a) semi-circular crack of depth a Will the beam fail in any form (e.g. yield, fatigue, fast fracture)? Please justify your answer. b) Crack growth follows a Paris Law of da/dN=1.4210 (AK,)4 m/cycle, where AK, has units of MPam. Calculate the life time of the beam (1.6 s)