Problem 2 (33 points) A large plate is subjected to an applied stress S in the y- direction, and another applied stress (0.5)$ in the x-direction. This plate has an inclined crack in it. If S keeps increasing, the inclined crack is risking mixed-mode fracture (Mode I + Mode II). A handbook gives the stress intensity factors K, and K,, for a crack of half-length a inclined at an angle to the x-axis in a large plate subjected to a stress S applied in in the y-direction and another stress as applied in the x-direction (where a is a number such as 0.5, 1.0, 2.0, ... etc.): S K = S (cos20 + a sin0) as KII = S (1) sine cose The angle of inclination is the angle formed by the x-axis and the crack line and is measured counterclockwise from the positive half of the x-axis. The Mixed-Mode Facture Criterion of the material is: 2 + KIC KII KIC = 1 (KIC = 30 MPam, Kc= KIC = 3 ). For an inclined crack with a = 0.003 m and angle of inclination 0 = 45, determine the magnitude of S that gives a safety factor against mixed-mode fracture of XK = 4 x