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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.7 P.867~877


Towards fully automatic modelling of the fracture process in quasi-brittle and ductile materials: a unified crack growth criterion

Author(s):  Zhen-jun YANG, Guo-hua LIU

Affiliation(s):  College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   zjuliu@163.com

Key Words:  Finite element method (FEM), Crack propagation criterion, Cohesive zone model (CZM), Virtual crack extension (VCE), Arc-length method

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Zhen-jun YANG, Guo-hua LIU. Towards fully automatic modelling of the fracture process in quasi-brittle and ductile materials: a unified crack growth criterion[J]. Journal of Zhejiang University Science A, 2008, 9(7): 867~877.

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%T Towards fully automatic modelling of the fracture process in quasi-brittle and ductile materials: a unified crack growth criterion
%A Zhen-jun YANG
%A Guo-hua LIU
%J Journal of Zhejiang University SCIENCE A
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A071540

T1 - Towards fully automatic modelling of the fracture process in quasi-brittle and ductile materials: a unified crack growth criterion
A1 - Zhen-jun YANG
A1 - Guo-hua LIU
J0 - Journal of Zhejiang University Science A
VL - 9
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SP - 867
EP - 877
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A071540

Fully automatic finite element (FE) modelling of the fracture process in quasi-brittle materials such as concrete and rocks and ductile materials such as metals and alloys, is of great significance in assessing structural integrity and presents tremendous challenges to the engineering community. One challenge lies in the adoption of an objective and effective crack propagation criterion. This paper proposes a crack propagation criterion based on the principle of energy conservation and the cohesive zone model (CZM). The virtual crack extension technique is used to calculate the differential terms in the criterion. A fully-automatic discrete crack modelling methodology, integrating the developed criterion, the CZM to model the crack, a simple remeshing procedure to accommodate crack propagation, the J2 flow theory implemented within the incremental plasticity framework to model the ductile materials, and a local arc-length solver to the nonlinear equation system, is developed and implemented in an in-house program. Three examples, i.e., a plain concrete beam with a single shear crack, a reinforced concrete (RC) beam with multiple cracks and a compact-tension steel specimen, are simulated. Good agreement between numerical predictions and experimental data is found, which demonstrates the applicability of the criterion to both quasi-brittle and ductile materials.

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[1] ACI Report 446.3R-97, 1997. Finite Element Analysis of Fracture in Concrete Structures: State-of-the-Art. Reported by ACI Committee 446.

[2] Arrea, M., Ingraffea, A.R., 1982. Mixed-mode Crack Propagation in Mortar and Concrete. Report No. 81-13, Department of Structural Engineering, Cornell University, USA.

[3] Bocca, P., Carpinteri, A., Valente, S., 1991. Mixed-mode fracture of concrete. International Journal of Solid and Structures, 27(9):1139-1153.

[4] Bresler, B., Scordelis, A.C., 1963. Shear strength of reinforced concrete beams. Journal of the American Concrete Institute, 60(4):51-72.

[5] Dhar, S., Dixit, P.M., Sethuraman, R., 2000. A continuum damage mechanics model for ductile fracture. International Journal of Pressure Vessels and Piping, 77(6):335-344.

[6] Griffith, A.A., 1921. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London Series A, 221:163-198.

[7] 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 Technology-Transactions of ASME, 99:2-15.

[8] Hellen, T.K., 1975. On the method of virtual crack extension. International Journal for Numerical Methods in Engineering, 9(1):187-207.

[9] Hillerborg, A., Rots, J., 1989. Crack concepts and numerical modelling, Report of the Technical Committee 90-FMA Fracture Mechanics to Concrete––applications, Elfgren, L. (Ed.), RILEM. Chapman and Hall, London, p.128-150.

[10] Hillerborg, A., Modeer, M., Petersson, P.E., 1976. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 6(6):773-782.

[11] Li, H., Chandra, N., 2003. Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models. International Journal of Plasticity, 19(6):849-882.

[12] Li, W.Z., Siegmund, T., 2002. An analysis of crack growth in thin-sheet metal via a cohesive model. Engineering Fracture Mechanics, 69(18):2073-2093.

[13] May, I.M., Duan, Y., 1997. A local arc-length procedure for strain softening. Computers and Structures, 64(1-4):297-303.

[14] Petersson, P.E., 1981. Crack Growth and Development of Fracture Zone in Plain Concrete and Similar Materials. Report TVBM-1006, Division of Building Materials, Lund Institute of Technology, Lund, Sweden.

[15] Rots, J., 1991. Smeared and discrete representations of localized fracture. International Journal of Fracture, 51(1):45-59.

[16] Rots, J., de Borst, R., 1987. Analysis of mixed-mode fracture in concrete. Journal of Engineering Mechanics ASCE, 113(11):1739-1758.

[17] Siegmund, T., Brocks, W., 2000. Numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture. Engineering Fracture Mechanics, 67(2):139-154.

[18] Turner, C.E., Kolednik, O., 1994. A micro and macro approach to the energy-dissipation rate model of stable ductile crack-growth. Fatigue & Fracture of Engineering Materials and Structures, 17(9):1089-1107.

[19] Tvergaard, V., Hutchinson, J.W., 1992. The relation between crack-growth resistance and fracture process parameters in elastic plastic solids. Journal of the Mechanics and Physics of Solids, 40(6):1377-1397.

[20] Tvergaard, V., Hutchinson, J.W., 1996. Effect of strain-dependent cohesive zone model on predictions of crack growth resistance. International Journal of Solids and Structures, 33(20-22):3297-3308.

[21] Xie, M., 1995. Finite Element Modelling of Discrete Crack Propagation, Ph.D Thesis, University of New Mexico, USA.

[22] Xie, M., Gerstle, W.H., 1995. Energy-based cohesive crack propagation modelling. Journal of Engineering Mechanics ASCE, 121(12):1349-1458.

[23] Yang, Z.J., Chen, J.F., 2004. Fully automatic modelling of cohesive discrete crack propagation in concrete beams using local arc-length methods. International Journal of Solids and Structures, 41(3-4):801-826.

[24] Yang, Z.J., Proverbs, D., 2004. A comparative study of numerical solutions to nonlinear discrete crack modelling of concrete beams involving sharp snap-back. Engineering Fracture Mechanics, 71(1):81-105.

[25] Zhang, Z.L., Thaulow, C., Odegard, J., 2000. A complete Gurson model approach for ductile fracture. Engineering Fracture Mechanics, 67(2):155-168.

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