K Variations and Anisotropy: Microstructure Effect and Numerical Predictions

[+] Author and Article Information
Xu-Dong Li

School of Materials Science and Engineering, Gansu University of Technology, 85 Lan Gong Ping, Lanzhou, Gansu Province, 730050, P. R. China

J. Eng. Mater. Technol 125(1), 65-74 (Dec 31, 2002) (10 pages) doi:10.1115/1.1525252 History: Received June 05, 2002; Revised August 20, 2002; Online December 31, 2002
Copyright © 2003 by ASME
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Ravichandran,  K. S., and Li,  Xu-Dong, 2000, “Fracture Mechanical Character of Small Cracks in Polycrystalline Materials: Concept and Numerical K Calculations,” Acta Mater., 48, pp. 525–540.
Lankford,  J., 1982, “The Growth of Small Fatigue Cracks in 7075-T6 Aluminum,” Fat. Eng. Mater. Struct.,5, pp. 233–248.
Suresh,  S., 1983, “Crack Deflection: Implications for the Growth of Long and Short Fatigue Cracks,” Metall. Mater. Trans. A, 14A, pp. 2375–2385.
The Short Fatigue Cracks, 1986, EGF Pub. 1. K. J., Miller and E. R. de los Rios, Mechanical Engineering Publication, London, UK.
Small Fatigue Cracks, 1986, Proc. Int. Workshop on Small Fatigue Cracks, R. O. Ritchie and J. Lankford, eds., The Metallurgical Society of AIME, Warrendale, PA.
Tokaji,  K., 1986, “Limitations of Linear Elastic Fracture Mechanics in Respect to Small Fatigue Cracks and Microstructure,” Fat. Fract. Eng. Mater. Struct.,9, pp. 1–14.
Ravichandran,  K. S., and Larsen,  J. M., 1997, “Effects of Crack Aspect Ratio on the Behavior of Small Surface Cracks in Fatigue: Part II—Experiments on a Titanium (Ti-8Al) Alloy,” Metall. Mater. Trans. A, 28A, pp. 157–169.
Müller,  C., and Exner,  H. E., 1998, “Influence of a Grain Size Gradient on the Profile and Propagation of Fatigue Cracks in Titanium,” Z. Metallkd., 89, pp. 338–342.
Teng,  N. J., and Lin,  T. H., 1995, “Elastic Anisotropy Effect of Crystals on Polycrystal Fatigue Crack Initiation,” ASME J. Eng. Mater. Technol., 117, pp. 470–477.
Wu,  M. S., and Guo,  J., 2000 “Analysis of a Sector Crack in a Three-Dimensional Voronoi Polycrystal With Microstructure Stresses,” ASME J. Appl. Mech., 67, pp. 50–58.
Li, Xu-Dong, and Ravichandran, K. S., 1999, “The Role of Grain-Induced Local Anisotropy on Stress Intensity Factor for Microstructurally-Small Cracks,” Small Fatigue Cracks: Mechanics and Mechanisms, K. S. Ravichandran, R. O. Ritchie, and Y. Murakami, eds., Elsevier Science Ltd., London, pp. 85–92.
Nemat-Nasser, S., 1999, Micromechanics: Overall Properties of Heterogeneous Materials, 1st ed., Elsevier, New York.
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.
Anderson,  M. P., , 1984, “Computer Simulation of Grain Growth—I. Kinetics,” Acta Metall., 32, pp. 783–791.
Humphreys,  F. J., and Hatherly,  M., 1992, “Modelling Mechanisms and Microstructures of Recrystallisation,” Mater. Sci. Technol., 8, pp. 135–143.
Anderson,  M. P., Grest,  G. S., and Srolovitz,  D. J., 1985, “Grain Growth in Three Dimension: A Lattice Model,” Scr. Metall., 19, pp. 225–230.
Mehnert, K., and Klimanek, P., 1998, Proceedings of an International Conference on Texture, Sept. 1997, Clausthal, Germany, R. Schwarzer and H. J. Bunge, eds., Trans. Tech. Publications, CH-Aedermannsdorf.
Okabe, A., Boots, B., and Sugihara, K., 1999, Spatial Tessellations Concepts and Applications of Voronoi Diagrams, John Wiley and Son, New York.
Roe,  R.-J., and Krigbaum,  W. R., 1964, “Description of Crystallite Orientation in Polycrystalline Materials Having Fiber Texture,” J. Chem. Phys., 40, 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.
Kröner,  E., 1958, “Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls,” Z. Phys., 151, pp. 504–518.
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.
Li,  Xu-Dong, 2001, “Computer Identification of Structural Weaknesses in Locally Anisotropic Polycrystalline Materials,” ASME J. Eng. Mater. Technol., 123, pp. 361–370.
Li,  X.-D., 2002, “Numerical Correlation of Material Structure Weaknesses in Anisotropic Polycrystalline Materials,” Acta Mech., 155, pp. 137–155.
Li,  X.-D., 2002, “Numerical Assessment of Composite Structure Weaknesses in Short-Fiber Reinforced MMCs,” Mech. Mater., 34, pp. 191–216.
Li,  Xu-Dong, 2002, “Computer Assessment of Material Structure Weaknesses in Polycrystalline Materials,” Arch. Appl. Mech., (in press).
Tvergaard,  V., and Hutchinson,  J. W., 1988, “Microcracking in Ceramics Induced by Thermal Expansion or Elastic Anisotropy,” J. Am. Ceram. Soc., 71, 157–166.
Nozaki,  H., and Taya,  M., 1997, “Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains,” ASME J. Appl. Mech., 64, pp. 495–502.
Waldvogel,  J., 1979, “The Newtonian Potential of Homogeneous Polyhedra,” Z. Angew. Math. Phys., 30, pp. 388–398.
Rodin,  G. J., 1996, “Eshelby’s Inclusion Problem for Polygons and Polyhedra,” J. Mech. Phys. Solids, 44, pp. 1977–1995.
Bueckner,  H. F., 1970, “A Novel Principle for the Computation of Stress Intensity Factors,” Z. Angew. Math. Mech., 50, pp. 529–546.
Oore,  M., and Burns,  D. J., 1980, “Estimation of Stress Intensity Factor for Irregular Cracks Subjected to Arbitrary Normal Stress Field,” ASME J. Pressure Vessel Technol., 102, pp. 202–211.
Desjardins,  J. L., Burns,  D. J., and Thompson,  J. C., 1991, “A Weight Function Technique for Estimating Stress Intensity Factors for Cracks in High Pressure Vessels,” ASME J. Pressure Vessel Technol., 113, pp. 10–21.
Beghini,  M., Bertini,  L., and Gentili,  A., 1997, “An Explicit Weight Function for Semi-Elliptical Surface Cracks,” ASME J. Pressure Vessel Technol., 119, pp. 216–223.
Zeng,  X.-H., and Ericsson,  T., 1996, “Anisotropy of Elastic Properties in Various Aluminum-Lithium Sheet Alloys,” Acta Mater., 44, pp. 1801–1812.
Simmons, G., and Wang, H., 1970, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd ed., The MIT Press, Cambridge, MA.
Yang,  S. W., 1985, “Elastic Constants of a Monocrystalline Nickel-Based Superalloy,” Metall. Mater. Trans. A, 16, pp. 661–665.
Bunge,  H. J., Kiewel,  R., Reinert,  Th, and Fritsche,  L., 2000, “Elastic Properties of Polycrystals—Influence of Texture and Stereology,” J. Mech. Phys. Solids, 48, pp. 29–66.


Grahic Jump Location
A simulated polycrystalline aggregate consisting of 2114 arbitrarily polygon-shaped grains. Planar microcracks of different sizes are embedded in the aggregate of infinite medium. D denotes average grain size of the aggregate (D=10 microns). The dashed lines within Fig. 1 indicate microcracks of different sizes.
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Schematic illustration of broken grains (a) of varying crystallographic orientation with respect to loading direction; (b) in which reference and local crystallite co-ordinate frames are defined.
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(a) Illustration of numerical grids and refinement of boundary elements used to mesh the crack domain. Locations of centroid of elements are presented; (b) Illustration of an element shared by grains and shared area
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Duplicated local microstructure and mesoscopic stress distribution. (a) a microcrack of 2c/D=5 and broken grains; (b) spatial grain modulus ratios in grains intersected by the crack front; (c) appearance of computationally-scanned image of distribution of grain anisotropy ratio in broken grains; and (d) image of distribution of mesoscopic stress the broken grains.
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Illustration of grain geometry effect on K-Ratio evolution along a microcrack front. (a) The geometry effect imposes strong disturbances if grain shapes are treated differently rather than identically. (b) The grain geometry effect increases if the crack size is smaller.
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Demonstration, by (a) and (b), of the dependence of K Variation on local mesoscopic stress in intersected grains for a smaller crack (2c/D=5). (c) the effect of crystal anisotropy on K variations and deviations of anisotropic K away from isotropic counterparts.
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Crack size effect on K variation along the crack front (Ni material)
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Quantitative assessment of local dependence of anisotropic K for a crack of 2c/D=48. (a,d) inhomogeneous mesoscopic stress distributions due respectively to random and local preferential crystallographic orientations in grains nearby the location Q; (b,e) indications of contribution of 200 broken grains, closer to the location Q, to the anisotropic K; (c,f) local contribution per broken-grain-area in the 200 grains (the grain ID is indicated in a pair of brackets).




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