Wednesday, 13 October 2004 - 1:25 PM

This presentation is part of : Micromechanics and Physics of Materials

The Second-order Estimates for the Effective Behavior and Field Fluctuations in Viscoplastic Polycrystals

Yi Liu, Department of Radiology, University of Iowa, 3970 JPP, 200 Hawkins Drive, Iowa City, IA 52242, Pedro Ponte Castaneda, Ecole Polytechnique, Departement de Mecanique, Palaiseau, 91128, France, and Ricardo A. Lebensohn, Los Alamos National Laboratory, MST8 - MS G755, Los Alamos, NM 87545.

In this work, the newly developed “second-order” self-consistent (SOE) nonlinear homogenization method is applied to study the effective behavior, field fluctuation in nonlinear viscoplastic polycrystalline materials. The method is derived within the variational framework of Ponte Castañeda, with use of the averages and fluctuations of the stress field over the various grain orientations in an optimally selected “linear comparison polycrystal”.

The SOE method is implemented to estimate the macroscopic property of the cubic and HCP polycrystals, and generate the information on the heterogeneity of the stress and strain-rate fields. The results are compared with the full-field simulations using the recently developed technique based on the Fast Fourier Transform (FFT). For polycrystals with linear slip behaviors, accuracy of the self-consistent method is demonstrated, for the first time, by the excellent agreement with the FFT results for both the effective flow stress and statistical quantities field quantities.

For nonlinear polycrystals, the new second-order estimates for the effective flow stress satisfy all the existing bounds, even for cases with highly anisotropic/nonlinear crystal behaviors, where previous nonlinear homogenization models for polycrystals, like the Taylor, “tangent” and “incremental” self-consistent schemes, fail. It is found that the second-order method is the only micromechanics model to date that agrees consistently with the FFT estimates for the effective flow stress and the statistical quantities of the stress and strain-rate fields.

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