Dislocation emission criterion for a wedge crack under mixed mode loading
Source abstract
Abstract
Dislocation emission criterion for a wedge crack under mixed mode loading was investigated using Airy stress function. The order of singularity at the wedge crack tip due to remote loading was found to vary with the loading mode. The plastic zones for plane stress and plane strain were studied based on von Mises' and Tresca criteria. The dislocation emission criterion was examined for both loading modes. The mechanism of crack propagation was believed to be controlled by dislocation emission. Under an action of Mode I loading, the wedge tip movement occurred when a pair of edge dislocations of Burgers vectors be iθ and −be −iθ were emitted from the wedge tip where b and θ were the magnitude of Burgers vector and the angle between the positive x axis and the line connecting from the tip to dislocation. Similarly, under an action of Mode II loading, the wedge crack tip moved as soon as either an edge dislocation of Burgers vector along the x direction was emitted from its tip or a pair of edge dislocations of Burgers vectors be iθ and be −iθ were emitted from the wedge tip. The conventional mechanism of crack propagation based on the energy release rate was not expected to occur. The calculated results for a few special cases were presented and compared with those reported in the literature.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Fatigue and fracture mechanics · Ultrasonics and Acoustic Wave Propagation · Numerical methods in engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (25)
Show source-provided references
1. Broek, D. (1986). Elementary Engineering Fracture Mechanics, 4th ed., Martinus Nijhoff Publishers, Boston, MA, Chap. 3.
2. Cottrell, A.H. (1965). in: Fracture, (Edited by Osborn, C. J.) (Butterworths, London), p. 1.
3. Dieter, G.E. (1988). Mechanical Metallurgy, 3rd ed., McGraw-Hill, London, Chap. 4.
4. Huang, C.C., Yu, C.C. and Lee, S. (1995). The behavior of a screw dislocations dynamically emitted from the tip of a surface crack during loading and unloading. Journal of Materials Research 10, 183–189.10.1557/JMR.1995.0183 ↗
5. Irwin, G.R. (1948). Fracture dynamics, in Fracturing of Metals, ASM publ., Cleveland, Ohio, 147–166; (1958). Fracture I, in Handbuch der Physik VI, (Edited by Flügge, S.), Springer, Berlin, 551–590.
6. Lakshmanan, V. and Li, J.C.M. (1988). Edge dislocations emitted along inclined planes from a Mode I crack. Materials Science and Engineering A104, 95–104.10.1016/0025-5416(88)90410-7 ↗
7. Lin, I.H. and Thomson, R. (1986). Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Metallurgica 34, 187–206.10.1016/0001-6160(86)90191-4 ↗
8. Muskhelishvili, N.I. (1977). Some Basic Problems of the Mathematical Theory of Elasticity, (4th ed., Moscow 1954) Noordhoff, Leyden, translated by Radok, J.R.M.10.1007/978-94-017-3034-1 ↗
9. Ohr, S.M. (1984). Electron microscope observation of crack propagation and a dislocation model of fracture, in: The structure and Properties of Crystal Defects, (Edited by Paider, V. and Lejcek, L.) (Elsevier, New York), 438–458.
10. Ohr, S.M. (1985). An electron microscope study of crack tip deformation and its impact on the dislocation theory of fracture. Material Science and Engineering 72, 1–35.10.1016/0025-5416(85)90064-3 ↗
11. Ohr, S.M., Chang, S.J. and Thomson, R. (1985). Elastic interaction of a wedge crack with a screw dislocation. Journal of Applied Physics 57, 1839–1834.10.1063/1.334412 ↗
12. Rice, J.R. (1992). Dislocation nucleation from a crack tip – an analysis based on the Peierls concept. Journal of the Mechanics and Physics of Solids 40, 239–271.10.1016/S0022-5096(05)80012-2 ↗
13. Rice, J.R. and Thomson, R. (1974). Ductile versus brittle behavior of crystals. Philosophical Magazine 29, 73–97.10.1080/14786437408213555 ↗
14. Shastry, V., Anderson, P.M. and Thomson, R. (1994). Nonlocal effects of existing dislocations on crack tip emission and cleavage. Journal of Materials Research 9, 812–827.10.1557/JMR.1994.0812 ↗
15. Shieu, S.T. and Lee, S. (1988). The elastic interaction between screw dislocations and cracks emanating from an elliptic hole. Journal of Applied Physics 64, 129–139; (1990). The dislocation-free zone model of Mode III fracture: a discrete dislocation approach. Philosophical Magazine A61, 85–97.10.1063/1.341456 ↗
16. Shieu, S.T., Zhang, T.Y. and Lee, S. (1993). An edge dislocation near a macrocrack with a microcrack. Journal of Applied Physics 74, 6079–6087; (1995). Elastic analysis of an edge dislocation and two collinear cracks of different length, International Journal of Fracture 68, 333–350.10.1063/1.355192 ↗
17. Schoeck, G. (1991). Dislocation emission from crack tips. Philosophical Magazine A63, 111–120.10.1080/01418619108204596 ↗
18. Sih, G.C. (1973). Handbook of Stress Intensity Factor, Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, PA.
19. Sternberg, E. and Koiter, W.T. (1958). The wedge under a concentrated couple: A paradox in the two-dimensional theory of elasticity. ASME Journal of Applied Mechanics 25, 575–581.10.1115/1.4011875 ↗
20. Tsai, Y.Z. and Lee, S. (1997). Dynamic emission of screw dislocations from a propagating crack tip. Journal of Applied Physics 81, 2089–2093.10.1063/1.364260 ↗
21. Vehoff, H. and Neumann, P. (1979). In situSEM experiments concerning the mechanism of ductile crack growth. Acta Metallurgica 27, 915–920.10.1016/0001-6160(79)90126-3 ↗
22. Wang, S.D. and Lee, S. (1990). An analysis of the elastic interaction between an edge dislocation and an internal crack. Materials Science Engineering A130, 1–10; (1993). Edge dislocation dipoles near a semi-infinite crack tip. Engineering Fracture Mechanics 46, 297–309.10.1016/0921-5093(90)90074-D ↗
23. Williams, M.L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics 74, 526–528; (1957). On the stress distribution at the base of a stationary crack. ASME Journal of Applied Mechanics 24, 109–114.10.1115/1.4010553 ↗
24. Zhang, T.Y. (1990). Computer simulation of semibrittle fracture. Zeitschrift für Metallkunde 81, 63–69.
25. Zhang, T.Y., Tong, P., Ouyang, H. and Lee, S. (1995). Interaction of an edge dislocation with a wedge crack. Journal of Applied Physics 78, 4873–4880.10.1063/1.359775 ↗