4.26 (a) Iron (r = 0.124 nm, G = 70 GPa) is being deformed to a shear strain of 0.3. Assuming a constant dislocation density equal to 1010 cm−2, what is the average distance each dislocation has to move? (b) Assuming that the strain rate is 10−2 s−1, what is the average dislocation velocity?

Consider a single crystal of a hypothetical metal that has the BCC crystal structure. A stress of 50 MPa is applied in the [101] direction of the BCC unit cell.a. Determine the most favourable slip direction for the (011) slip plane of the BCC unit cell. ⟨111⟩ is the family of directions with the highest linear density in the BCC unit cell.b. If τcrss = 27.5 MPa, determine if the single crystal yields. If not, what stress level is required?c. What is the minimum stress at which the BCC single crystal yields?

Consider a single crystal of some hypothetical metal that has the BCC crystal structure and is oriented such that a tensile stress is applied along a [2 2 1] direction. If slip occurs on a (2 1 1) plane and in a [-1 1 1] direction, compute the stress at which the crystal yields if its critical resolved shear stress is 2.4 MPa.

6.31 The flow stress for an alloy is 100 MPa when its dislocation density is 106 cm-2, and 150 MPa when its dislocation density is 108 cm-². When the flow stress is 190 MPa, what is the dislocation density?