Neighborhood effect on the strain distribution in linearly elastic polycrystals: Part 1 – Finite element study of the interaction between grains

Polycrystals are full of all kinds of heterogeneities which introduce stress concentrations. The local stress field in a grain does not depend solely on its crystallographic orientation. In fact, its neighborhood has also been shown to play a significant role. A definition and quantification method of the neighborhood effect was proposed and a finite element study was performed to evaluate the elastic strain variations of a given grain surrounded by a heterogeneous neighborhood composed of one or several grains inserted in an infinite homogeneous matrix. A regular structure was used to generate the aggregates and annihilate any grain size and shape ratio. Grains crystallographic orientations influences on a grain’s strain tensor were studied with respect to their relative positions and the loading axis. A grain strain variations due to its neighborhood were found to be independent of its orientation, and a grain’s influence on another grain’s mean strain tensor was shown to be independent of other neighboring grains. From these observations, some simplifications were proposed to better describe the neighborhood effect in order to develop the analytic model presented in a second part of the paper.