Calculate the theoretical yield strength of aluminum. The Young's modulus of aluminum is 70 GPa, and Poisson's ratio is 0.3. You may assume a simple cubic lattice for aluminum crystals. Compare your result with the measured yield strength of pure aluminum (~40 MPa), and explain the main cause of the difference.

1-Can ceramics contain dislocations? Provide reasoning.

What is cold working process for metals? Why cold working can help improve strength of the metal? Use dislocation theory to explain.

(a) Why is the carbon concentration in austenite (y-Fe) higher than in ferrite (a-Fe)? (b) Determine the volume change accompanied by the transformation of y-Fe (FCC) to a-Fe (BCC) during cooling. Note that the atomic radii for a-Fe, y-Fe, and C are 0.124nm, 0.127mm, and 0.077mm, respectively. (HINT: Because the number of atoms in FCC and BCC differs, consider volume per atom in the calculation of volume change).

A hypothetical metal alloy has a grain diameter of 2.4 × 10-2 mm. After a heat treatment at 575°C for 500 min, the grain diameter has increased to 5.6 × 10-2 mm. Compute the time required for a specimen of this same material (i.e., do = 2.4 × 10-² mm) to achieve a grain diameter of 5.5 x 10-2 mm while being heated at 575°C. Assume the n grain diameter exponent has a value of 2.2. i min

2. Sketch: a. 3 stages of single crystal stress-strain curve under uniaxial stress b. Frank-Reed mechanism for dislocation multiplication.

A metal crystallizes in the face‑centered cubic (FCC) lattice. The density of the metal is 12020 kg/m3, and the length of a unit cell edge, ?, is 389.08 pm. Calculate the mass of one metal atom.

List the 12 slip systems for fcc. which of these will not be active if load is applied in [100] direction for a single crystal?

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The flow stress for an alloy is 115 Mpa when its dislocation density is 10^6 cm^-2 and 207 Mpa when its dislocation density is 10^8 cm^-2. When the flow stress is 359 Mpa, Find the dislocation density.