Abstract
A computational approach based on a cell model of material offers real promise as a predictive tool for nonlinear fracture analysis. A key feature of the computational model is the modeling of the material in front of the crack by a layer of similarly-sized cubic cells. Each cell of size D contains a spherical void of initial volume fraction f 0. The microseparation characteristics of the material in a cell, a result of void growth and coalescence, is described by the Gurson–Tvergaard constitutive relation; the material outside the layer of cells can be modelled as an elastic- plastic continuum. The success of this computational model hinges on developing a robust calibration scheme of the model parameters. Such a scheme is proposed in this study. The material-specific parameters are calibrated by a two-step micromechanics/fracture-process scheme. This article describes the micromechanics calibration of void growth taking into account both the strain hardening and the strength of the material. The fracture-process calibration is addressed in a companion paper.
Similar content being viewed by others
References
ABAQUS (1995). StandardUser's Manual, Version 5.5. Hibbit, Karlsson and Sorensen, Inc., Providence, RI.
Aravas, N. (1987). On the numerical integration of a class of pressure-dependent plasticity models. International Journal for Numerical Methods in Engineering 24, 1395-1416.
Becker, R. and Needleman, A. (1988). Effect of yield surface curvature on necking and failure in porous plastic solids. Journal of Applied Mechanics 53, 491-499.
Begley, J.A. and Landes, J.D. (1976). Serendipity and the J integral. International Journal of Fracture 12, 764-766.
Broberg, B.B. (1997). The cell model of materials. Computational Mechanics 19, 447-452.
Broberg, B. (1982). The foundation of fracture mechanics. Engineering Fracture Mechanics 16, 497-515.
Brocks, W., Klingbeil, D., Kuenencke, G. and Sun, D.Z. (1995). Applications of the Gurson model to ductile tearing. (Edited by M. Kirk and A. Bakker), Constraint Effects in Fracture, Theory and Applications, ASTM STP 1244. American Society for Testing and Materials, 232-254.
Bilby, B.A., Howard, I.C. and Li, Z.H. (1993). Prediction of the first spinning cylinder test using ductile damage theory. Fatigue and Fracture of Engineering Materials and Structures 16, 1-20.
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, 21-50.
Garwood, S.J. (1979). Effect of specimen geometry on crack growth resistance. (Edited by C.W. Smith), Fracture Mechanics, ASTM-STP 667. American Society for Testing and Materials, 511-532.
Gao, X., Faleskog, J. and Shih, C.F. (1998a). Cell model for nonlinear fracture analysis - II. Fractureprocess calibration and verification. International Journal of Fracture.
Gao, X., Faleskog, J., Dodds, R.H. and Shih, C.F. (1998b). Ductile tearing in part-through cracks: Experiments and cell-model prediction. Engineering Fracture Mechanics 59, 761-777.
Gurson, A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth: Part I - Yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology 99, 2-15.
Hancock, J.W., Reuter, W.G. and Parks, D.M. (1993). Constraint and toughness parameterized by T. (Edited by E.M. Hackett, K.H. Schwalbe and R.D. Dodds), Constraints Effects in Fracture. American Society for Testing and Materials, 21-40.
Hill, R. (1967). The essential structure of constitutive laws for metal composites and polycrystals. Journal of the Mechanics and Physics of Solids 15, 79-95.
Huang, Y. (1991). Accurate dilatation rates for spherical voids in triaxial stress fields. Journal of AppliedMechanics 58, 1084-1086.
Koplik, J. and Needleman, A. (1988). Void Growth and Coalescence in Porous Plastic Solids. International Journal of Solids and Structures 24, 835-853.
Leblond, J.B., Perrin, G. and Devaux, J. (1995). An improved Gursontype model for hardenable ductile metals. European Journal of Mechanics A/Solids 14, 499-527.
McClintock, F.A. (1968). A criterion for ductile fracture by growth of holes. Journal of Applied Mechanics 35, 363-371.
McMeeking, R.M. (1977). Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture. Journal of the Mechanics and Physics of Solids 25, 357-381.
Needleman, A., Tvergaard, V. and Hutchinson, J.W. (1992). Void growth in plastic solids (Edited by A.S. Argon), Topics in Fracture and Fatigue, Springer Verlag, New York, 145-178.
O'Dowd, N.P. and Shih, C.F. (1991). Family of crack-tip fields characterized by a triaxiality parameter - I. Structure of fields. Journal of the Mechanics and Physics of Solids 39, 989-1015.
Rice, J.R. and Tracey, D.M. (1969). On the ductile enlargement of voids in triaxial stress fields. Journal of the Mechanics and Physics of Solids 17, 201-217.
Rousselier, G. (1987).Ductile fracturemodels and their potential in local approach of fracture. Nuclear Engineering and Design 105, 97-111.
Ruggieri, C., Panontin, T.L. and Dodds, R.H. (1996). Numerical modeling of ductile crack growth in 3D using computational cell elements. International Journal of Fracture 82, 67-96.
Shih, C.F. and Xia, L. (1995). Modeling crack growth resistance using computational cells with microstructurallybased length scales. (Edited by M. Kirk and A. Bakker), Constraint Effects in Fracture, Theory and Applications, ASTM STP 1244. American Society for Testing and Materials, 163-190.
Tracey, D.M. (1971). Strain-hardening and interaction effects on the growth of voids in ductile fracture. Engineering Fracture Mechanics 3, 301-315.
Tvergaard, V. (1981). Influence of voids on shear band instabilities under plane strain conditions. International Journal of Fracture 17, 389-407.
Tvergaard, V. (1982). Ductile fracture by cavity nucleation between larger voids. Journal of the Mechanics and Physics of Solids 30, 265-286.
Tvergaard, V. and Hutchinson, J.W. (1992). The relation between crack growth resistance and fracture process parameters in elasticplastic solids. Journal of the Mechanics and Physics of Solids 40, 1377-1397.
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, 233-259.
Xia, L. and Shih, C.F. (1995b). Ductile crack growth - II. Void nucleation and geometry effects on macroscopic fracture behavior. Journal of the Mechanics and Physics of Solids 43, 1953-1981.
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, 603-639.
Xia, L., Shih, C.F. and Hutchinson, J.W. (1995). A computational approach to ductile crack growth under large scale yielding conditions. Journal of the Mechanics and Physics of Solids 43, 389-413.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Faleskog, J., Gao, X. & Shih, C.F. Cell model for nonlinear fracture analysis – I. Micromechanics calibration. International Journal of Fracture 89, 355–373 (1998). https://doi.org/10.1023/A:1007421420901
Issue Date:
DOI: https://doi.org/10.1023/A:1007421420901