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A direct method for the determination of the mean orientation‐dependent elastic strains and stresses in polycrystalline materials from strain pole figures
Author(s) -
Bernier Joel V.,
Miller Matthew P.
Publication year - 2006
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889806009873
Subject(s) - intergranular corrosion , materials science , anisotropy , crystallite , elasticity (physics) , aggregate (composite) , orientation (vector space) , lattice (music) , inverse , composite material , condensed matter physics , mathematical analysis , mechanics , geometry , mathematics , optics , physics , microstructure , metallurgy , acoustics
A salient manifestation of anisotropy in the mechanical response of polycrystalline materials is the inhomogeneous partitioning of elastic strains over the aggregate. For bulk samples, the distributions of these intergranular strains are expected to have a strong functional dependence on grain orientations. It is then useful to formulate a mean lattice strain distribution function (LSDF) over the orientation space, which serves to characterize the micromechanical state of the aggregate. Orientation‐dependent intergranular stresses may be recovered from the LSDF via a constitutive assumption, such as anisotropic linear elasticity. While the LSDF may be determined directly from simulation data, its experimental determination relies on solving an inverse problem that is similar in character to the fundamental problem of texture analysis. In this paper, a versatile and robust direct method for determining an LSDF from strain pole figures is presented. The effectiveness of this method is demonstrated using synthetic strain pole figures from a model LSDF obtained from the simulated uniaxial deformation of a 1000‐crystal aggregate.