Calculation And Use Of Intragranular Field Fluctuations In Non-Linear Homogenization Schemes For The Prediction Of The Mechanical Behavior Of Viscoplastic Polycrystals

Abstract

In this contribution we present an implementation of the calculation of the average
field fluctuations inside the grains of a thermoelastic aggregate, in terms of the derivatives of
the stress potential given by the self-consistent (SC) approximation for linear polycrystals.
Similar expressions are applicable to non-linear viscoplastic polycrystals, whose behavior
can be estimated by means of the different non-linear homogenization schemes, which require
linearization of the constitutive behavior at grain level. These statistical indicators are in turn
used to calculate the standard deviations (SD) of the mechanical fields, considering both
intergranular and intragranular fluctuations. The SDs corresponding to different first-order
non-linear SC extensions are then compared, for the case of a non-linear hcp polycrystal.
Finally, we show how to use the above statistical information to generate more refined nonlinear
SC estimates, taking into account both first- and second-order moments to define the
local linearized behavior of the grains