Answer these mechanic questions.

Describe the four types of stress cycles in the context of fatigue mechanics. Illustrate your answer with diagram(s) where necessary. (b) A material conforms to the Coffin-Mason law: PN0.4 f = 0.25 A sample made of this material is subjected to P = 0.015 for 250 cycles then P = 0.0075 for the remainder of its life, calculate the number of cycles it can endure by Miners rule: X n N = 1 2. (a) A thick-walled closed cylinder has an outside-to-inside diameter ratio of K. Derive expressions for the pressure P to initiate yield in the bore of the cylinder according to the Tresca and von Mises yield criteria. (b) Determine the pressure P for closed cylinder with an internal diameter of 30 mm, an external diameter of 50 mm and the material of the cylinder has a yield stress of Y = 250 MPa. Tresca: 1 3 = Y von Mises: (1 2)2 + (2 3)2 + (1 3)2 = 22 Y For a closed cylinder: h = P r 2 i r 2 o r 2 i 1 + r 2 o r 2 ! ; r = P r 2 i r 2 o r 2 i 1 r 2 o r 2 ! ; z = P r 2 i r 2 o