The Correlation Length: A Measure of Inhomogeneities in Polycrystalline Materials

Abstract

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. The crystal plasticity material model was applied during the finite-element analysis. Different correlation lengths were obtained depending on whether the strain or the stress field was used. The correlation lengths also changed with the macroscopic load. While the load is below the yield strength the correlation lengths are constant, and of the order of the average grain size. 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. The correlation lengths calculated from the stress field are smaller than the ones calculated from the strain field. However, with the exception of the load region where significant shear bands appear, both seem to follow the same qualitative rules.