Estimating the correlation length of inhomogeneities in a polycrystalline material

This paper deals with the correlation length estimated from a mesoscopic model of a polycrystalline material. The correlation length can be used in some macroscopic material models as a material parameter that describes the internal length. It can be estimated directly from the strain and stress fields calculated from a finite-element model, which explicitly accounts for the selected mesoscopic features such as the random orientation, shape and size of the grains. A crystal plasticity material model was applied in the finite-element analysis. ent correlation lengths were obtained depending on whether the strain or the stress field was used. The correlation lengths also changed with the macroscopic load. If the load is below the yield strength the correlation lengths are constant, and are of the order of the average grain size. The correlation length can therefore be considered as an indicator of first plastic deformations in the material. Increasing the load above the yield strength creates shear bands that temporarily increase the values of the correlation lengths calculated from the strain fields. With a further load increase the correlation lengths decrease slightly below the average grain size. If displacement boundary conditions are used, the correlation length calculated from strain field is lower then the one calculated from the stress field. The opposite is true, if stress boundary conditions are applied. However, with the exception of the load region where significant shear bands appear, both seem to follow similar qualitative rules.