Large deformation analysis of axisymmetric inhomogeneities including coupled elastic and plastic anisotropy

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A mathematical framework is developed for the study of materials containing axisymmetric inclusions or flaws such as ellipsoidal voids, penny-shaped cracks, or fibers of circular cross-section. The general case of nonuniform statistical distributions of such heterogeneities is attacked by first considering a spatially uniform distribution of flaws that are all oriented in the same direction. Assuming an isotropic substrate, the macroscopic material properties of this simpler microstructure naturally should be transversely isotropic. An orthogonal basis for the linear subspace consisting of all double-symmetric transversely-isotropic fourth-order tensors associated with a given material vector is applied to deduce the explicit functional dependence ... continued below

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11 p.

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Brannon, R.M. December 31, 1996.

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  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM (United States)
    Place of Publication: Albuquerque, New Mexico

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Description

A mathematical framework is developed for the study of materials containing axisymmetric inclusions or flaws such as ellipsoidal voids, penny-shaped cracks, or fibers of circular cross-section. The general case of nonuniform statistical distributions of such heterogeneities is attacked by first considering a spatially uniform distribution of flaws that are all oriented in the same direction. Assuming an isotropic substrate, the macroscopic material properties of this simpler microstructure naturally should be transversely isotropic. An orthogonal basis for the linear subspace consisting of all double-symmetric transversely-isotropic fourth-order tensors associated with a given material vector is applied to deduce the explicit functional dependence of the material properties of these aligned materials on the shared symmetry axis. The aligned and uniform microstructure seems geometrically simple enough that the macroscopic transversely isotropic properties could be derived in closed form. Since the resulting properties are transversely isotropic, the analyst must therefore be able to identify the appropriate coefficients of the transverse basis. Once these functions are identified, a principle of superposition of strain rates ay be applied to define an expectation integral for the composite properties of a material containing arbitrary anisotropic distributions of axisymmetric inhomogeneities. A proposal for coupling plastic anisotropy to the elastic anisotropy is presented in which the composite yield surface is interpreted as a distortion of the isotropic substrate yield surface; the distortion directions are coupled to the elastic anisotropy directions. Finally, some commonly assumed properties (such as major symmetry) of the Cauchy tangent stiffness tensor are shown to be inappropriate for large distortions of anisotropic materials.

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11 p.

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OSTI as DE97001388

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  • 1997 international conference on computational engineering science, San Jose (Costa Rica), 4-9 May 1997

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  • Other: DE97001388
  • Report No.: SAND--96-2846C
  • Report No.: CONF-970558--1
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 463643
  • Archival Resource Key: ark:/67531/metadc677677

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  • December 31, 1996

Added to The UNT Digital Library

  • July 25, 2015, 2:21 a.m.

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  • April 14, 2016, 8:36 p.m.

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Brannon, R.M. Large deformation analysis of axisymmetric inhomogeneities including coupled elastic and plastic anisotropy, article, December 31, 1996; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc677677/: accessed December 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.