Modelling of stresses in polycrystalline materials

The present work deals with stress redistributions and their subsequent influence on the precipitation in NiTi based shape memory alloys. Two mechanisms which may result into the stress redistribution are selected. The calculations based on the linear elasticity theory are performed using three simple models of microstructures with increasing complexity. The obtained results clearly show that the selected mechanisms give rise to the stress redistribution in the microstructures. The interaction energy between redistributed stress field and the precipitate-matrix misfit strain is calculated. The selection of crystallographic precipitate variants as a result of the minimum interaction energy criterion is demonstrated. A comparison of the calculated results with the experimental data suggests that it is possible to explain qualitatively the selective precipitation by means of the mechanisms of stress redistributions. The concepts described here are general, and can be easily adopted for modelling other strain/stress problems in polycrystalline materials.