Past exam of the materials science course of the University of Cambridge / 2016 / Paper 1 / 5 / b / i / Solution

For a coarse-grained, approximately untextured polycrystal undergoing general plastic flow, use the conventional orientation-and-compatibility estimateWith the supplied ${\tau }_c=27.5\mathrm{MPa}$,The round $M=3$ result is a conventional estimate for an unspecified coarse polycrystal, not a material-independent exact conversion. The most favorably oriented individual grains can first slip at $2{\tau }_c=55\mathrm{MPa}$; that is not the same event as compatible macroscopic yielding throughout the aggregate.

There is no single crystallographic tensile axis for all grains. Individual grains rotate and can develop crystallographic texture, while the macroscopic bar remains loaded along its tensile axis. A specified initial texture or yield criterion would be needed for a more exact numerical prediction.