Computer Identification of Structural Weaknesses in Locally Anisotropic Polycrystalline Materials

[+] Author and Article Information
Xu-Dong Li

MatCom, 86 Iroquois Rd., West Hartford, CT 06117

J. Eng. Mater. Technol 123(3), 361-370 (Mar 09, 2001) (10 pages) doi:10.1115/1.1375158 History: Received July 07, 2000; Revised March 09, 2001
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.


Sunder,  S. S., and Wu,  M. S., 1990, “Crack nucleation due to elastic anisotropy in polycrystalline ice,” Cold Regions Sci. Tech. , 18, pp. 29–47.
Ghahremani,  F., and Hutchinson,  J. W., 1990, “Three-dimensional effects in microcrack nucleation in brittle polycrystals,” J. Am. Ceram. Soc., 73, pp. 1548–1554.
Lebensohn,  R. A., and Tomé,  C. N., 1993, “A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys,” Acta Metall. Mater., 41, No. 9, pp. 2611–2624.
Teng,  N. J., and Lin,  T. H., 1995, “Elastic anisotropy effect of crystals on polycrystal fatigue crack initiation,” ASME J. Eng. Mater. Technol., 117, No. 10, pp. 470–477.
Dunn,  M. L., and Ledbetter,  H., 1997, “Elastic-plastic behavior of textured short-fiber composites,” Acta Metall., 45, No. 8, pp. 3327–3340.
Lu,  Z. K., and Weng,  G. J., 1998, “A self consistent model for the stress-strain behavior of shape-memory alloy polycrystals,” Acta Mater., 46, No. 15, pp. 5423–5433.
González,  C., and Llorca,  J., 2000, “A self-consistent approach to the elasto-plastic behavior of two phase materials including damage,” J. Mech. Phys. Solids, 48, pp. 675–692.
Wu,  M. S., and Guo,  J., 2000, “Analysis of a sector crack in a three-dimensional Voronoi polycrystal with microstructural stresses,” ASME J. Appl. Mech., 67, pp. 50–58.
Kocks, U. F., Tomé, C. N., and Wenk, H.-R., 1998, Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties, Cambridge University Press.
Okabe, A., Boots, B., and Sugihara, K., 1992, Spatial Tessellations Concepts and Applications of Voronoi Diagrams, J. Wiley, New York.
Roe,  R.-J., and Krigbaum,  W. R., 1964, “Description of crystallite orientation in polycrystalline materials having fiber texture,” J. Chem. Phys., 40, No. 9, pp. 2608–2615.
Nye, J. F., 1985, Physical Properties of Crystals: Their Representation By Tensors and Matrices, Oxford Science Publications Ltd., Oxford, UK.
Eshelby,  J. D., 1957, “The determination of elastic field of an ellipsoid and related problems,” Proc. R. Soc. London, Ser. A, 241A, pp. 376–396.
Eshelby,  J. D., 1959, “The elastic field outside an elliptical inclusion,” Proc. R. Soc. London, Ser. A, 252A, pp. 561–569.
Eshelby, J. D., 1961, “Elastic inclusions and inhomogeneities,” Prog. in Solid Mech., Vol. 2, I. N. Snedden, and R. Hill, eds., North-Holland, Amsterdam, pp. 89–140.
Kröner,  E., 1958, “Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls,” Z. Phys., Band,151, pp. 504–518.
Kröner,  E., 1961, “Zur plastischen verformung des vielkristalls,” Acta Metall., 9, pp. 155–161.
Kneer,  G., 1965, “Uber die Berechnung der Elastizitätsmoduln vielkristalliner Aggregate mit Textur,” Phys. Status Solidi,9, pp. 825–838.
Morris,  P., 1970, “Elastic constants of polycrystals,” Int. J. Eng. Sci., 8, pp. 49–61.
Bunge,  H. J. , 2000, “Elastic properties of polycrystals—influence of texture and stereology,” J. Mech. Phys. Solids, 48, pp. 29–66.
Aernoudt, E. et al., 1993, Deformation and textures of Metals at Large Strain, Ser. eds., R. W. Cahn, P. Haasen, and E. J. Krämer, VCH, Weinheim.
Van Houtte, P., 1996, in Proceedings of the 11th International Conference on Texture of Materials, Sept., Xian, China, Vol. eds., Z. Liang, L. Zuo, and Y. Chu, Vol. 1, pp. 236, International Academic, Beijing.
Raabe, D., 1998, Computational Materials Science, Wiley-VCH, New York.
Tvergaard,  V., and Hutchinson,  J. W., 1988, “Microcracking in ceramics induced by thermal expansion or elastic anisotropy,” J. Am. Ceram. Soc., 71, No. 3, pp. 157–166.
Oritz,  M., and Suresh,  S., 1993, “Statistical properties of residual stresses and intergranular fracture in ceramic materials,” ASME J. Appl. Mech., 60, No. 3, pp. 77–84.
Zisman,  A. A., and Rybin,  V. V., 1998, “Mesoscopic stress field arising from the grain interaction in plastically deformed polycrystals,” Acta Mater., 46, pp. 457–464.
Nozaki,  H., and Taya,  M., 1997, “Elastic fields in a polygon-shaped inclusion with uniform eigenstrains,” ASME J. Appl. Mech., 64, No. 9, pp. 495–502.
Jasiuk,  I., Chen,  J., and Thorpe,  M. F., 1994, “Elastic moduli of two dimensional materials with polygonal and elliptic holes,” Appl. Mech. Rev., 47, pp. 18–28.
Jasiuk,  I., 1995, “Various vis-a-vis rigid inclusions: elastic moduli of materials with polygonal inclusions,” Int. J. Solids Struct., 32, pp. 407–422.
Rodin,  G. J., 1996, “Eshelby’s inclusion problem for polygons and polyhedra,” J. Mech. Phys. Solids, 44, No. 12, pp. 1977–1995.
Wu,  L. Z., and Du,  S. Y., 1999, “The elastic field with a hemispherical inclusion,” Proc. R. Soc. London, Ser. A, 455A, pp. 879–891.
Mura, T. 1999, “A theory of fracture with a polygonal shape crack,” Small Fatigue Cracks: Mechanics and Mechanisms, eds. by K. S. Ravichandran, R. O. Ritchie and Y. Murakami, Elsevier Science, London, pp. 3–15.
Ru,  C. Q., 1999, “Analytic solution for Eshelby’s problem of an inclusion of arbitrary shape in a plane or half-plane,” ASME J. Appl. Mech., 66, No. 2, pp. 315–322.
Waldvogel,  J., 1979, “The Newtonian potential of homogeneous polyhedra,” Z. Angew. Math. Phys., 30, pp. 388–398.
Simmons, G., and Wang, H., 1970, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd. edn., The MIT Press, Cambridge, MA.
Zeng,  X.-H., and Ericsson,  T., 1996, “Anisotropy of elastic properties in various aluminium-lithium sheet alloys,” Acta Mater., 44, No. 5, pp. 1801–1812.
Yang,  S. W., 1985, “Elastic constants of a monocrystalline nickel-based superalloy,” Metall. Mater. Trans. A, 16A, pp. 661–665.
Bunge, H. J., 1982, Texture Analysis in Materials Science, Butterworths, London.
Adams,  B. L. , 1987, “Description of orientation coherence in polycrystalline materials,” Acta Metall., 35, No. 12, pp. 2935–2946.
Pospiech,  J., Lucke,  K., and Sztwiertnia,  K., 1993, “Orientation distribution and orientation correlation functions for description of microstructure,” Acta Metall., 41, No. 1, pp. 305–321.


Grahic Jump Location
Typical distribution of peak SVI (I ≥2.0) occurring in grains in the simulated polycrystalline material samples
Grahic Jump Location
Fundamental relations of the Relevance Parameter with the Orientation-Geometry Factor ∅ for (a) stress ratio R≥2.0; (b) energy ratio ℵ≥2.0 and (c) SVI ratio J ≥2.0 at applied stress level 1.0 MPa
Grahic Jump Location
Evolution of Variation Intensity Factor for (a) mesoscopic stress, (b) SVI, and (c) amount of absorbed energy over conjoining grains in the simulated polycrystalline material samples
Grahic Jump Location
Sketch of geometric relations. (a) Reference frame in polycrystalline material sample subjected to uniform tension loading; (b) definition of Euler parameterization; (c) crystallite frame for cubic crystal structure
Grahic Jump Location
Typical distribution of peak stress (R≥2.0 and R<0.0) occurring in grains in the simulated Ni polycrystalline aggregate consisting of 1317 arbitrarily polygon-shaped grains
Grahic Jump Location
Typical distribution of peak energy (ℵ ≥2.0) absorbed in grains in the simulated polycrystalline material samples



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In