For any precipitation-hardened alloy, like an al-cu alloy, the strengthening of the alloy depends on the size and number of the precipitates.
a) Calculate the cross-sectional area of a single 10-micron (10-5 m) diameter spherical precipitate.
b) Determine how many 1-micron spherical precipitates would be needed to have the same volume as the 10-micron precipitate.
c) Calculate the cross-sectional area of the single 10 micron precipitate and the many 1-micron precipitates.
d) Based on your calculations of cross-sectional area, which alloy would be more effective at stopping dislocations, those with a few 10-micron precipitates or those with many 1-micron precipitates? Which would have the higher strength? Which would have the higher ductility?
e) For an al-cu alloy of 4 atomic percent copper, 96 atomic % aluminium, estimate the density of the al-cu alloy compared to pure aluminium. is this a significant change that an airline company would care about?