K Variations and Anisotropy: Microstructure Effect and Numerical Predictions
Source abstract
Abstract
Computer experiments were performed on simulated polycrystalline material samples that possess locally anisotropic microstructures to investigate stress intensity factor (K) variations and anisotropy along fronts of microcracks of different sizes. The anisotropic K, arising from inhomogeneous stresses in broken grains, was determined for planar microcracks by using a weight function-based numerical technique. It has been found that the grain-orientation-geometry-induced local anisotropy produces large variations in K along front of microcracks, when the crack size is of the order of few grain diameters. Synergetic effect of grain orientation and geometry of broken grains control K variations and evolution along the microcrack front. The K variations may diminish at large crack sizes, signifying a shift of K calculation to bulk stress dependence from local stress dependence. Local grain geometry and texture may lead to K anisotropy, producing unusually higher/lower K at a segment of the crack front. Either K variation or anisotropy cannot be ignored when assessing a microcrack.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Fatigue and fracture mechanics · Hydrogen embrittlement and corrosion behaviors in metals · Rock Mechanics and Modeling
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Materials Science and Engineering, Gansu University of Technology, 85 Lan Gong Ping, Lanzhou, Gansu Province, 730050, P. R. China
References (40)
Show source-provided references
1. 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. 525–540.10.1016/S1359-6454(99)00348-1 ↗
2. Lankford, J. , 1982, “The Growth of Small Fatigue Cracks in 7075-T6 Aluminum,” Fat. Eng. Mater. Struct., 5, pp. 233–248.10.1111/j.1460-2695.1982.tb01251.x ↗
3. Suresh, S. , 1983, “Crack Deflection: Implications for the Growth of Long and Short Fatigue Cracks,” Metall. Mater. Trans. A, 14A, pp. 2375–2385.10.1007/BF02663313 ↗
4. The Short Fatigue Cracks, 1986, EGF Pub. 1. K. J., Miller and E. R. de los Rios, Mechanical Engineering Publication, London, UK.
5. 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.
6. Tokaji, K., et al., 1986, “Limitations of Linear Elastic Fracture Mechanics in Respect to Small Fatigue Cracks and Microstructure,” Fat. Fract. Eng. Mater. Struct., 9, pp. 1–14.10.1111/j.1460-2695.1986.tb01207.x ↗
7. 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. 157–169.10.1007/s11661-997-0091-9 ↗
8. Mu¨ller, 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.
9. 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. 470–477.10.1115/1.2804741 ↗
10. 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. 50–58.10.1115/1.321151 ↗
11. 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. 85–92.10.1016/B978-008043011-9/50009-0 ↗
12. Nemat-Nasser, S., 1999, Micromechanics: Overall Properties of Heterogeneous Materials, 1st ed., Elsevier, New York.
13. Kocks, U. F., Tome´, C. N., and Wenk, H.-R., 1998, Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties, Cambridge University Press.
14. Anderson, M. P., et al., 1984, “Computer Simulation of Grain Growth—I. Kinetics,” Acta Metall., 32, pp. 783–791.10.1016/0001-6160(84)90151-2 ↗
15. Humphreys, F. J., and Hatherly, M., 1992, “Modelling Mechanisms and Microstructures of Recrystallisation,” Mater. Sci. Technol., 8, pp. 135–143.10.1179/026708392790170324 ↗
16. Anderson, M. P., Grest, G. S., and Srolovitz, D. J., 1985, “Grain Growth in Three Dimension: A Lattice Model,” Scr. Metall., 19, pp. 225–230.10.1016/0036-9748(85)90187-5 ↗
17. 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.
18. Okabe, A., Boots, B., and Sugihara, K., 1999, Spatial Tessellations Concepts and Applications of Voronoi Diagrams, John Wiley and Son, New York.10.1002/9780470317013 ↗
19. Roe, R.-J., and Krigbaum, W. R., 1964, “Description of Crystallite Orientation in Polycrystalline Materials Having Fiber Texture,” J. Chem. Phys., 40, pp. 2608–2615.10.1063/1.1725571 ↗
20. Nye, J. F., 1985, Physical Properties of Crystals: Their Representation by Tensors and Matrices, Oxford Science Publications Ltd., Oxford, UK.
21. Eshelby, J. D. , 1957, “The Determination of elastic Field of an Ellipsoid and Related Problems,” Proc. R. Soc. London, Ser. A, 241A, pp. 376–396.10.1098/rspa.1957.0133 ↗
22. Kro¨ner, E. , 1958, “Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls,” Z. Phys., 151, pp. 504–518.10.1007/BF01337948 ↗
23. Kneer, G. , 1965, “Uber die Berechnung der Elastizita¨tsmoduln vielkristalliner Aggregate mit Textur,” Phys. Status Solidi, 9, pp. 825–838.10.1002/pssb.19650090319 ↗
24. Morris, P. , 1970, “Elastic Constants of Polycrystals,” Int. J. Eng. Sci., 8, pp. 49–61.10.1016/0020-7225(70)90014-5 ↗
25. Li, Xu-Dong , 2001, “Computer Identification of Structural Weaknesses in Locally Anisotropic Polycrystalline Materials,” ASME J. Eng. Mater. Technol., 123, pp. 361–370.10.1115/1.1375158 ↗
26. Li, X.-D. , 2002, “Numerical Correlation of Material Structure Weaknesses in Anisotropic Polycrystalline Materials,” Acta Mech., 155, pp. 137–155.10.1007/BF01176239 ↗
27. Li, X.-D. , 2002, “Numerical Assessment of Composite Structure Weaknesses in Short-Fiber Reinforced MMCs,” Mech. Mater., 34, pp. 191–216.10.1016/S0167-6636(02)00093-5 ↗
28. Li, Xu-Dong , 2002, “Computer Assessment of Material Structure Weaknesses in Polycrystalline Materials,” Arch. Appl. Mech., (in press).
29. Tvergaard, V., and Hutchinson, J. W., 1988, “Microcracking in Ceramics Induced by Thermal Expansion or Elastic Anisotropy,” J. Am. Ceram. Soc., 71, 157–166.10.1111/j.1151-2916.1988.tb05022.x ↗
30. Nozaki, H., and Taya, M., 1997, “Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains,” ASME J. Appl. Mech., 64, pp. 495–502.10.1115/1.2788920 ↗
31. Waldvogel, J. , 1979, “The Newtonian Potential of Homogeneous Polyhedra,” Z. Angew. Math. Phys., 30, pp. 388–398.10.1007/BF01601950 ↗
32. Rodin, G. J. , 1996, “Eshelby’s Inclusion Problem for Polygons and Polyhedra,” J. Mech. Phys. Solids, 44, pp. 1977–1995.10.1016/S0022-5096(96)00066-X ↗
33. Bueckner, H. F. , 1970, “A Novel Principle for the Computation of Stress Intensity Factors,” Z. Angew. Math. Mech., 50, pp. 529–546.
34. 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. 202–211.10.1115/1.3263321 ↗
35. 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. 10–21.10.1115/1.2928720 ↗
36. Beghini, M., Bertini, L., and Gentili, A., 1997, “An Explicit Weight Function for Semi-Elliptical Surface Cracks,” ASME J. Pressure Vessel Technol., 119, pp. 216–223.10.1115/1.2842287 ↗
37. Zeng, X.-H., and Ericsson, T., 1996, “Anisotropy of Elastic Properties in Various Aluminum-Lithium Sheet Alloys,” Acta Mater., 44, pp. 1801–1812.10.1016/1359-6454(95)00320-7 ↗
38. Simmons, G., and Wang, H., 1970, Single Crystal Elastic Constants and Calculated Aggregate Properties: A Handbook, 2nd ed., The MIT Press, Cambridge, MA.
39. Yang, S. W. , 1985, “Elastic Constants of a Monocrystalline Nickel-Based Superalloy,” Metall. Mater. Trans. A, 16, pp. 661–665.10.1007/BF02814240 ↗
40. 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. 29–66.10.1016/S0022-5096(99)00020-4 ↗