The evolution of the anisotropy of a polycrystalline aggregate.

*(English)*Zbl 0786.73067(From authors’ abstract and introduction.) The macroscopic properties of a polycrystalline aggregate depend upon the orientational distribution of the single crystals. Firstly, the authors derive the equation of evolution for the orientation of a single crystal of arbitrary type that deforms through the mechanism of rate independent crystallographic slip. Then they introduce an orientational distribution function \(f(\phi)\) to describe the distribution of orientations of the single crystals in the aggregate, and derive the evolutionary equation for this function.

An approximate representation of the orientational distribution function applied to cubic crystals and the differential equations for the evolution of the coefficients associated with the anisotropic term of the representation are given. Solutions of these equations can be obtained numerically. This work is an attempt to extend the results obtained by V. C. Prantil [Ph.D. Thesis, Cornell Univ. Ithaca, New York (1992)] for the texture, plastic spin and yield of two-dimensional polycrystalline aggregates to three dimensions.

An approximate representation of the orientational distribution function applied to cubic crystals and the differential equations for the evolution of the coefficients associated with the anisotropic term of the representation are given. Solutions of these equations can be obtained numerically. This work is an attempt to extend the results obtained by V. C. Prantil [Ph.D. Thesis, Cornell Univ. Ithaca, New York (1992)] for the texture, plastic spin and yield of two-dimensional polycrystalline aggregates to three dimensions.

Reviewer: V.Gheorghiţă (Iaşi)

##### MSC:

74A60 | Micromechanical theories |

74M25 | Micromechanics of solids |

74E10 | Anisotropy in solid mechanics |

##### Keywords:

macroscopic properties; crystallographic slip; orientational distribution function; cubic crystals
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\textit{Y. Zhang} and \textit{J. T. Jenkins}, J. Mech. Phys. Solids 41, No. 7, 1213--1243 (1993; Zbl 0786.73067)

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##### References:

[1] | Advani, S.G.; Tucker, C.L., The use of tensors to describe and predict fiber orientation in short fiber composites, J. rheol., 31, 751-784, (1987) |

[2] | Aifantis, E.C., Contemporary topics in plastic deformation : anisotropy, texture, voids,and shear bands, (), 319-333 |

[3] | Bishop, J.F.W.; Hill, R., A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, Phil. mag., 42, 414-427, (1951) · Zbl 0042.22705 |

[4] | Bishop, J.F.W.; Hill, R., A theoretical derivation of the plastic properties of a polycrystalline face-centered metal, Phil. mag., 42, 1298-1307, (1951) · Zbl 0044.45002 |

[5] | Bishop, J.F.W., A theory of the tensile and compressive textures of face-centered cubic metals, J. mech. phys. solids, 3, 130-142, (1954) |

[6] | Bunge, H.J., Texture analysis in material science, (1982), Butterworths London |

[7] | Canova, G.R.; Fressengeas, C.; Molinari, A.; Kocks, U.F., Effect of rate sensitivity on slip system activity and lattice rotation, Acta metall., 36, 1961-1970, (1988) |

[8] | Dafalias, Y.F., The plastic spin, J. appl. mech., 52, 865-871, (1985) · Zbl 0587.73052 |

[9] | Goldstein, H., Classical mechanics, (1980), Addison-Wesley Cambridge, MA · Zbl 0491.70001 |

[10] | Kanatani, K.-I., Distribution of directional data and fabric tensors, Int. J. engng sci., 22, 149-164, (1984) · Zbl 0586.73004 |

[11] | Kocks, U.F.; Canova, G.R.; jonas, J.J., Yield vectors in F.C.C. crystals, Acta metall., 31, 1243-1252, (1983) |

[12] | Mandel, J., Director vectors and constitutive equations for plastic and visco-plastic media, (), 135-143 |

[13] | Onat, E.T.; Leckie, F.A., Representation of mechanical behavior in the presence of changing internal structure, J. appl. mech., 55, 1-10, (1988) |

[14] | Prantil, V.C., An analytical description of macroscopic anisotropy for planar polycrystalline aggregate, () |

[15] | Prantil, V.C.; Jenkins, J.T.; Dawson, P., An analysis of texture and plastic spin for planar polycrystals, J. mech. phys. solids, 41, (1993), (in press) · Zbl 0780.73067 |

[16] | Truesdell, C.; Noll, W., The nonlinear field theories of mechanics, () · Zbl 0779.73004 |

[17] | Voyiadjis, G.Z.; Kattan, P.I., Eulerian constitutive model for finite deformation plasticity with anisotropic hardening, Mech. mater., 7, 279-293, (1989) |

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