ELASTIC STATE AND ORIENTATION OF NEEDLE-SHAPED INCLUSIONS

The inclusion problem of linear isotropic elasticity is applied to ana lyze the elastic strain energies of coherent, semicoherent and incoher ent needle-shaped inclusions. Misfit strains of a general tetragonal t ype, elastic constants and orientation of the needle are treated as va riables. The strain-energy minimization criterion is adopted to find t he optimum orientation. Several new and general conclusions are derive d for the elastic state of the needle inclusions. The predicted optimu m orientation is compared with that obtained by the purely geometrical invariant-line criterion. It is found that the two criteria predict t he identical orientation only under special cases.