A simple method of analysis of stress transmission in polycrystals with frictionless grain boundaries is presented. This method applies to a large class of two-dimensional and three-dimensional polycrystals which can be modeled as either periodic or disordered arrays of polyhedra. Calculations are performed for the periodic arrays of rhombic dodecahedra and truncated octahedra, and for arrays generated by the Voronoy tessellation of disordered point lattices. Results of these calculations show that normal stresses transmitted by frictionless grain boundaries are significantly different from applied stresses. In particular, it is predicted that, in disordered polycrystals subjected to uniaxial compression, 45 percent of grain boundaries are in tension and the maximum tensile stress is one half of the applied stress.

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