Sommario
Viene presentato uno studio agli elementi finiti con un approccio allo strato limite del caricamento monotono seconda il Modo I di una fessura stazionaria in condizioni di stato di tensione piana e plasticità contenuta. Viene esaminata in particolare l'influenza che la componente tensionale elastica trasversale nonsingolare (i.e. T-stress) delle condizioni al contorno ha sullo stato di sollecitazione elasto-plastica all'apice della fessura. Si osserva che questo parametro dello stato di biassialità all'apice di fessure controlla sia l'estensione della zona plastica che lo stato deformativo al suo interno. Le soluzioni numeriche vengono inoltre impiegate per simulare sistemi di frange moirè interferometriche fornendo così un utile strumento di confronto con precedenti risultati sperimentali.
Summary
A plane stress, finite element analysis of the monotonic loading of a Mode I stationary crack under small scale yielding using a boundary layer approach is presented. A small-strain,J 2 plasticity theory is used in conjunction with a linear hardening material model. The effects due to the inclusion of the non-singular elastic T-stress in the asymptotic boundary conditions on the elastic-plastic fields near the tip are investigated. This parameter, which accounts for the inherent biaxial stress state at a crack tip, is found to control extension and state of deformation of the plastic zone. The full-field numerical solutions are also used to simulate moirè interferometric fringe patterns in order to assess earlier detailed experimental observations.
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References
Kanninen M.F., Popelar C.H.,Advanced Fracture Mechanics, Oxford University Press, New York, 1985.
Rice J.R., “Mathematical Analysis of the Mechanics of Fracture”, in Liebowitz H. (ed)Fracture — An Advanced Treatise. Vol. II, Academic Press, 1968, pp. 191–311.
Rice J.R., “Mechanics of Crack Tip Deformation and Extension by Fatigue”, inFatigue Crack Propagation, ASTM STP 415, Am. Soc. for Test. and Matls., Philadelphia, 1967, pp. 247–311.
Gangloff R.P., Ritchie R.O., “Environmental Effects novel to the Propagation of Short Fatigue Cracks”, in Bilby B.A., Miller K.J. and Willis J.R. (eds.),Fundamental of Deformation and Fracture, Cambridge University Press, Cambridge, 1985, pp. 529–558.
Nicoletto G., “Fatigue Crack Tip Strains in 7075-T6 Aluminum Alloy”,Fat. and Fract. of Engng Matls and Structs, 10, 1987, pp. 37–49.
Nicoletto G., “Plastic Zone Sizes about Fatigue Cracks in Metals”,Int. J. of Fatigue, 11, 1989, pp. 107–115.
Atluri S.N. (Ed.),Computational Methods in the Mechanics of Fracture, North-Holland, Amsterdam, 1986.
Williams M.L., “On the Stress Distribution at the Base of a Stationary Crack”,Trans. ASME, J. Appl. Mech., 24, 1957, pp. 109–114.
Larsson S.G., Carlsson A.J., “Influence of Non-singular Stress Terms and Specimen Geometry on Small-scale Yielding at Crack Tips in Elastic-plastic Materials”,J. Mech. and Phys. of Solids, 21, 1973, pp. 263–277.
Leevers P.S., Radon J.C., “Inherent Stress Biaxiality in Various Fracture Specimen Geometries”,Int. J. of Fract., 19, 1982, pp. 311–325.
Kfouri A.P., “Some Evaluation of the Elastic T-term using Eshelby's Method”,Int. J. Fract, 1986, pp. 301–315.
Smith E.W., Pascoe K.J., “The Behaviour of Fatigue Cracks subject to Applied Biaxial Stress: A Review of Experimental Evidence”,Fat. of Eng. Matls and Structs., 6, 1983, pp. 201–224.
Brown M.W., Miller K.J., “Mode I Fatigue Crack Growth under Biaxial Stress at Room and Elevated Temperature”, inMultiaxial Fatigue, ASTM STP 853, American Society for Testing and Materials, Philadelphia, 1985, pp. 135–152.
Vecchio R.S., Crompton J.S., Hertzberg R.W., “The Influence of Specimen Geometry on Near-threshold Fatigue Crack Growth”,Fat. Fract. of Eng. Mater. and Struct., 10, 1987, pp. 333–347.
Narasimhan R., Rosakis A.J., “A Finite Element Analysis of Small-scale Yielding near a Stationary Crack under Plane Stress”,J. of Mech. Phys. Solids, 36, 1988, pp. 77–117.
Owen D.R.J., Hinton E.,Finite Elements in Plasticity: Theory and Practice, Pineridge Press, Swansea, U.K., 1980.
Rice J.R., “Stresses due to a Sharp Notch in a Work-hardening Elastic-plastic Material Loaded by Longitudinal Shear”,Trans. ASME, J. of Appl. Mech., 34, 1967, pp. 287–294.
Nicoletto G., “Moirè-interferometric Fringe Patterns about Crack Tips: Experimental observations and Numerical simulation”,Optics and Lasers in Engineering, 12, 1990, in press.
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Portions of this paper are included in the Proceedings of 9.th Congress of AIMETA, Bari, 1988.
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Nicoletto, G. Biaxial stress effects on the elastic-plastic crack-tip displacement fields. Meccanica 25, 99–106 (1990). https://doi.org/10.1007/BF01566209
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DOI: https://doi.org/10.1007/BF01566209