Certain microalloyed steels contain small additions of vanadium or niobium that permit the grain size to be reduced to about 2 ?m if the processing of the steel is carefully controlled. Likewise, advanced aluminum alloys containing special types of particles can be produced to yield a grain size of about 2 ?m. Suppose we reduce the grain size of steel and aluminum to 2 ?m by such processing would a substantial increase in the strengths of these material result? To what levels should the grain size be reduced to obtain significant strength increase in the two materials?