(Strengthening Mechanism, Yield Criteria, 16 Points) Let's Assume that a pure aluminum exhibits the shear yield strength (y) of 100MPa. (a) If a dislocation density becomes 25 times higher, what will be the shear yield strength? (4 Points) The Burgers vector of FCC aluminum is b=2a0110. Lattice parameter of aluminum (a0)=4.05A. Magnitude of Burgers vector =a022 Shear modulus ()=26GPa Taylor coefficient ()=0.5 The intrinsic lattice resistance for the Taylor equation (0)=20MPa Taylor equation: y=0+b (b) For a polycrystalline aluminum, determine the grain size that gives you the same strength with the answer in (a). To obtain the Hall-Petch equation, use the data below. (6 Points) (c) Assume that pure polycrystalline aluminum in (b) obeys the Tresca yield criteria. When an aluminum part is subjected to the principal stress, I=150MPa and II=150MPa, what is the maximum allowed grain size to avoid the plastic deformation? (6 Points)