Can you define part materials with a global variable at the assembly level?

I would like to setup an assembly template to automate design on variable crate sizes using global variables by defining things such as ID in XYZ and material size.  I can manage the equations for XYZ to adjust all my parts' sizes, but I cannot figure out how to set up a Global Material.  It would be great if I can enter something like "Cleat Size" as the variable name and then enter the "Value/Equation" as "1X4" or "1X6" or "2X4" etc. - the goal of this operation would be to have my many cleats across multiple subassemblies change the material type to "1X4" or "1X6" or "2X4" etc. and then I can use a nested IIF to define my cross-sections.

Is something like this possible?  Can a part file reach into an assembly to determine its material like it can with dimensions?