Abstract
When a material exhibits large amounts of plastic deformation before failure, with a continuous evolution of the elastic-plastic boundaries around the crack tip the assumptions made by all criteria based on linear fracture mechanics (LEFM) are no longer valid.
The necessary modifications of the T-criterion, for adapting it to elastic-plastic solutions, are presented here together with an illustrative example, comprising the case of the definition of the T-criterion by means of the singular plastic solutions of Hutchinson, Rice and Rosengren, henceforth denoted HRR, together with its mixed-mode extension studied by Shih [1–4]. It was shown that the T-criterion is still valid for elastic-plastic cases provided the components of energy are appropriately defined
Résumé
Lorsqu'un matériau fait état de grandes déformations plastiques avant rupture, accompagnées d'une évolution continue des frontières entre élasticité et plasticité autour de l'extrémité de la fissure, les hypothèses associées à tous les critères basés sur la théorie de la mécanique de la rupture linéaire et élastique ne sont plus guère valables.
Les modifications nécessaires à apporter au critère T pour l'adapter aux solutions élasto-plastiques sont présentées et sont illustrées par un exemple. Ces modifications portent sur la définition du critère T à l'aide des solutions plastiques singulières de Hutchinson, Rice et Rosengren, dénommées HRR, et sur leur extension pour un mode mixte, telle qu'étudiée par Shih.
On montre que le critère T est encore valable pour les cas d'élasto-plasticité pour autant que les composantes de l'énergie soient bien définies
Similar content being viewed by others
References
J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 16 (1968) 13–31.
J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 16 (1968) 337–347.
J.R. Rice and G.F. Rosengren, Journal of the Mechanics and Physics of Solids 16 (1968) 1–12.
C.F. Shih, in Fracture Analysis, ASTM STP 560 (1974) 187–210.
P.S. Theocaris and N.P. Andrianopoulos, Engineering Fracture Mechanics 16 (1982) 425–432.
P.S. Theocaris and N.P. Andrianopoulos, International Journal of Fracture 20 (1982) 125–130.
P.S. Theocaris, Engineering Fracture Mechanics 19 (1984) 975–991.
A.H. Cottrell, Proceedings of the Royal Society (London), A285 (1967) 10–21.
C.F. Shih, Elastic-Plastic Analysis of Combined Mode Crack Problems, Ph.D. thesis, Harvard University (1973).
P.S. Theocaris, Engineering Fracture Mechanics 24 (1986).
J.R. Rice and M.A. Johnson, in Inelastic Behavior of Solids, M.F. Kanninen, W.F. Adler, A.R. Rosenfield and R.I. Jaffee (eds.), McGraw-Hill, New York (1970) 641–671.
R.M. McMeeking, Journal of the Mechanics and Physics of Solids 25 (1977) 357–381.
C.F. Shih and M.D. German, International Journal of Fracture 17 (1981) 27–43.
C.F. Shih, Journal of the Mechanics and Physics of Solids 29 (1981) 305–306.
C.F. Shih, “Tables of Hutchinson-Rice-Rosengren Singular Field Quantities”, MRL E-147, Materials Research Laboratory, Brown University (1983).
L.P. Pook, Engineering Fracture Mechanics 3 (1971) 205–218.
J.G. Williams and P.D. Ewing, International Journal of Fracture Mechanics 8 (1972) 441–446.
R.C. Shah, Fracture Analysis, ASTM STP 560 (1974) 29–52.
P.S. Theocaris and D. Pazis, International Journal of Mechanical Sciences 25 (1983) 121–136.
P.S. Theocaris, International Journal of Fracture 32 (1986) R51-R58.
P.S. Theocaris, International Journal of Fracture (1987) submitted for publication.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Theocaris, P.S., Philippidis, T.P. The T-criterion for ductile fractures in HRR plastic singular fields. Int J Fract 35, 21–37 (1987). https://doi.org/10.1007/BF00034532
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00034532