Abstract
Various aspects on probabilistic modelling of cleavage fracture are discussed. The investigation involves consideration of a unit cell with an explicitly modelled void. The results from this model are compared with results for the case when the void content is accounted for in the sense of a Gurson-Tvergaard law. It is found that explicit modelling of the void can give substantially different results for the fracture probability. The effect depends on the exponent in the assumed Weibull distribution, the threshold stress, the constraint conditions and the hardening of the material.
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References
ABAQUS, Standard–User's manual, Version 5.5. Hibbit, Karlsson and Sorensen, Inc., Providence, RI (1995).
Bakker, A. and Koers, R.W.J. (1991). Prediction of cleavage fracture in the brittle–ductile transition region. ESIS/EGF9 (Edited by J.G. Blauel and K.–H. Schwalbe), Mechanical Engineering Publications, London, 613.
Curry, D.A. and Knott, J.F. (1976). Relationship between fracture toughness and microstructures in the cleavage fracture of mild steel. Metal Science 10, 1.
O'Dowd, N.P. and Shih, C.F. (1991). Family of crack–tip fields characterized by a triaxiality parameter – 1.
Structure of fields. Journal of the Mechanics and Physics of Solids 39, 989.
Faleskog, J. and Shih, C.F. (1997). Micromechanics of coalescence – I. Synergistic effects of elasticity, plastic yielding and multi–size–scale voids. Journal of the Mechanics and Physics of Solids 45, 21.
Faleskog, J., Gao, X. and Shih, C.F. (1998). Cell model for nonlinear fracture mechanics – I. Micromechanics calibration. International Journal of Fracture(in Press).
Isacsson, M. and Narström, T. (1998). Microscopic examination of crack growth in a pressure vessel steel. Materials Science and Engineering, A, 169.
Knott, J.F. (1980). Micromechanisms of fibrous crack extension in engineering alloys. Metal Science 14, 327.
Lin, T., Evans, A.G. and Ritchie, R.O. (1986). A statistical model of brittle fracture by transgranular cleavage. Journal of the Mechanics and Physics of Solids 34, 477.
McMahon Jr., C.J. and Cohen, M. (1965). Initiation of cleavage in polycrystalline iron. Acta Metallurgica 13, 591.
McMeeking, R.M. (1997). Finite deformation analysis of crack–tip opening in elastic–plastic materials and implications for fracture. Journal of the Mechanics and Physics of Solids 25, 357.
Ritchie, R.O., Knott, J.F. and Rice, J.R. (1973). On the relationship between critical tensile stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids 21, 395.
Wallin, K. (1984). The scatter in KIc–results. Engineering Fracture Mechanics 19, 1085.
Xia, L. and Shih, C.F. (1995a). Ductile crack growth – I. A numerical study using computational cells with microstructurally based length scales. Journal of the Mechanics and Physics of Solids 43, 233.
Xia, L. and Shih, C.F. (1995b). Ductile crack growth – II. Void nucleation and geometry effects on macroscopic fracture behaviour. Journal of the Mechanics and Physics of Solids 43, 1953.
Xia, L. and Shih, C.F. (1996). Ductile crack growth – III. Transition to cleavage fracture incorporating statistics. Journal of the Mechanics and Physics of Solids 44, 603.
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Isacsson, M., Nilsson, F. & Faleskog, J. Probabilistic cell modelling of cleavage fracture. International Journal of Fracture 92, 359–372 (1998). https://doi.org/10.1023/A:1007572816861
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DOI: https://doi.org/10.1023/A:1007572816861