1. A thin-walled Cylinder with closed ends (Sy = 200,000 psi) is to be subjected to a maximum internal pressure of 5,000 psi in service. The mean radius of the cylinder is to be 12 in. What the minimum wall thickness, t, should be used to avoid failure in yielding according to both Tresca and von Mises criteria? Assume that the factor of safety is 2.
2. For a material whose flow curve is given by , show that the tensile strength is: Su = K(n/2.718)n
3. The true stress-true strain of a material is given by , where K is a constant and n is the strain-hardening exponent.
(a) Describe a method to determine n.
(b) Derive the relationship for toughness
4. An aluminum thin-walled tube (radius/thickness = 10) is closed at each end pressurized to 2,000 psi to cause plastic deformation. The plastic stress-strain curve is given by ¯ ¯ . If the elastic strain is neglected and if the radial stress, , find:
(a) The tangential and the longitudinal stresses
(b) The value of the effective stress, ¯
(c) The value of the effective strain, ¯
(d) The tangential, the longitudinal and the radial strains. ( ¯ in ksi)
5. Assume that the composition of a U.S. penny is 100% Cu. If the diameter of this coin is 1.9 cm, determine the approximate number of vacancies in a (100) plane parallel to the face of the coin at a temperature of 1080 °C.
(Burgers vector in Cu = 0.2556 nm, ff = 2x104 cal/mol, R = 2 cal/mol. K)
6. The total dislocation length in a crystal is 25x107 cm. If the dimensions of the crystal are 1 cm x 2.5 cm x 1cm, what is the average spacing between two dislocations?