1. Consider a single crystal of nickel oriented such that a tensile stress is applied along a [001] direction. If slip occurs on a (111) plane and in a [101] direction, and is initiated at an applied tensile stress of 13.9 MPa (2020 psi), compute the critical resolved shear stress.

2. A single crystal of a metal that has the FCC crystal structure is oriented such that a ten- sile stress is applied parallel to the [100] di- rection. If the critical resolved shear stress for this material is 0.5 MPa, calculate the magni- tude(s) of applied stress(es) necessary to cause slip to occur on the (111) plane in each of the [110], [101], and [011] directions.

3. (a) A single crystal of a metal that has the strengthening, and strain hardening). Be sure to explain how dislocations are involved in each of the strengthening techniques.