There is no fundamental relation between density and strength. Steel alloys with different strength have similar density. Aramid fibers have high strengths, but low density. With respect to fatigue, for instance steel and aluminium behave differently.
Thanks Mr Stephen for answering my question. Mr Yatindra, the material that i want to know is fibre reinforced composite. For an example, glass fibre reinforced epoxy and glass fibre reinforced polypropylene. Since the density of epoxy is higher than PP and hence glass fibre reinforced epoxy will have higher mechanical strength. Is this statement correct?