Spectral representation of higher-order localization relationships for elastic behavior of polycrystalline cubic materials

A computationally efficient higher-order spectral framework has been formulated for the calculation of the elastic localization tensors for polycrystalline material systems using the generalized spherical harmonics as the Fourier basis. This new approach offers tremendous potential for rapid analysis of the elastic performance of a very large set of microstructures in any selected polycrystalline material system. The spectral framework transforms the complex integral relations for local stress and strain fields (derived from established generalized composite theories) into relatively simple algebraic expressions involving polynomials of structure parameters and morphology-independent influence coefficients. These coefficients need to be established only once for a given material system. In this paper, we formulate and demonstrate a viable approach to establishing the values of the second-order influence coefficients for cubic polycrystals by calibration to the results of micromechanical finite element models.

[1]  John Hinde,et al.  Statistical Modelling in R , 2009 .

[2]  Surya R. Kalidindi,et al.  Fast computation of first-order elastic–plastic closures for polycrystalline cubic-orthorhombic microstructures , 2007 .

[3]  Surya R. Kalidindi,et al.  Calibration of elastic localization tensors to finite element models: Application to cubic polycrystals , 2007 .

[4]  David T. Fullwood,et al.  Generalized Pareto front methods applied to second-order material property closures , 2007 .

[5]  E. Kröner.  Bounds for effective elastic moduli of disordered materials , 1977 .

[6]  G. Proust,et al.  Procedures for construction of anisotropic elastic–plastic property closures for face-centered cubic polycrystals using first-order bounding relations , 2006 .

[7]  Mark J. Beran,et al.  Statistical Continuum Theories , 1968 .

[8]  I. Tadjbakhsh,et al.  The elastic tensor of given symmetry nearest to an anisotropic elastic tensor , 1963 .

[9]  K. Chawla,et al.  Mechanical Behavior of Materials , 1998 .

[10]  S. Kalidindi,et al.  Finite approximations to the second-order properties closure in single phase polycrystals , 2005 .

[11]  H. Garmestani,et al.  Microstructure-sensitive design of a compliant beam , 2001 .

[12]  S. Kalidindi,et al.  Microstructure sensitive design of an orthotropic plate subjected to tensile load , 2004 .

[13]  S. Torquato.  Random Heterogeneous Materials , 2002 .

[14]  G. Milton.  The Theory of Composites , 2002 .

[15]  David T. Fullwood,et al.  Elastic properties closures using second-order homogenization theories: Case studies in composites of two isotropic constituents , 2006 .

[16]  E. Kröner,et al.  Elastic moduli of perfectly disordered composite materials , 1967 .

[17]  T. A. Mason,et al.  Use of microstructural statistics in predicting polycrystalline material properties , 1999 .

[18]  Surya R. Kalidindi,et al.  Elastic–plastic property closures for hexagonal close-packed polycrystalline metals using first-order bounding theories , 2007 .