Consider a sheet of an fcc metal that has a {110} texture. That is, a {110} plane is parallel to the plane of the sheet and a direction is parallel to the prior rolling direction.
A. Predict the value of Ro (the strain ratio measured in a rolling direction tension test). [Hint: Let x , y, and z be the rolling, transverse, and sheet-normal direc- tions. Assign speci?c indices [hkl ] to the rolling, transverse, and sheet-normal directions. Find the speci?c indices of the transverse direction, y. Then sketch a standard cubic projection showing these directions. (It is convenient to choose x, y, and z so that they lie in the hemisphere of the projection.) For uniaxial tension along x, determine which slip systems will be active, and assume an equal shear strain, γ i , on each. For each system, calculate the resulting strains, εx , εy , and εz in terms of γ i and sum these over all slip systems. Assume equal amounts of slip on all the equally favored slip systems. Now predict the strain ratio Ro.]
B. Predict R90.