Abstract
The paper deals with the determination of the cohesive zone parameters (separation energy, Γ, and cohesive strength, T max) for the 3D finite element modeling of the micro-ductile crack growth in thick, smooth-sided compact tension specimens made of a low-strength steel. Since the cohesive zone parameters depend, in general, on the local constraint conditions around the crack tip, their values will vary along the crack front and with crack extension. The experimental determination of the separation energy via automated fracture surface analysis is not accurate enough. The basic idea is, therefore, to estimate the cohesive zone parameters, Γ and T max, by fitting the simulated distribution of the local crack extension values along the crack front to the experimental data of a multi-specimen J IC-test. Furthermore, the influence of the cohesive zone parameters on the crack growth behavior is investigated. The point of crack growth initiation is determined only by the magnitude of Γ. Both Γ and T max affect the crack growth rate (or the crack growth resistance), but the influence of the cohesive strength is much stronger than that of the separation energy. It turns out that T max as well as Γ vary along the crack front. In the center of the specimen, where plane strain conditions prevail, the separation energy is lower and the cohesive strength is higher than at the side-surface.
Similar content being viewed by others
References
ABAQUS (1998). Version 5.8., H.K.S. Inc., Pawtucket, U.S.A.
Brocks, W. (2001) private communications.
de-Andrés, A., Pérez, J.L. and Ortiz, M. (1999). Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. International Journal of Solids and Structures 36, 2231–2258.
Chen, C.R., Scheider, I., Siegmund, T., Tatschl, A., Kolednik, O. and Fischer, F.D. (2001). Fracture initiation and crack growth-cohesive zone modeling and stereoscopic measurements. In: Advances in Fracture Research, Proceedings of ICF 10, K. Ravi-Chandar, B.L. Karihaloo, T. Kishi, R.O. Ritchie, A.T. Yokobori Jr., T. Yokobori, Eds., Paper ICF100409OR. Elsevier, Oxford, UK.
Elices, M., Guinea, G.V., Góomez, J. and Planas, J. (2002). The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics 69, 137–163.
ESIS P2-92 (1992). ESIS Procedure for determining the fracture behaviour of Materials, Delft, The Netherlands.
Foulk, J.W., Allen, D.H. and Helms, K.L.E. (2000). Formulation of a three-dimensional cohesive zone model for application to a finite element algorithm. Computer Methods in Applied Mechanics and Engineering 183, 51–66.
Hutchinson J.W. and Evans, A.G. (2000). Mechanics of materials: Top-down approaches to fracture. Acta materials 48, 125–135.
Knauss, W.G. (1993). Time dependent fracture and cohesive zones. Journal of Engineering Materials and Technology 115, 262–267.
Kolednik, O. (1981). A contribution to stereophotogrammetry with the scanning electron microscope. Practical Metallography 18, 562–573.
Kolednik, O. and Stüwe, H.P. (1982). Abschätzung der Rißzähigkeit eines duktilen Werkstoffes aus der Gestalt der Bruchfläche. Zeitschrift für Metallkunde 73, 1982, 219–223.
Kolednik, O. and Stüwe, H.P. (1985). The stereophotogrammetric determination of the critical crack tip opening displacement. Engineering Fracture Mechanics 21, 145–155.
Kolednik, O. (1991) On the physical meaning of the J-Δa-curves. Engineering FractureMechanics 38, 403–412.
Li, H., and Chandra, N. (2003). Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models. International Journal of Plasticity 19, 849–882.
Li, W., and Siegmund T. (2002). An analysis of crack growth in thin-sheet metal via a cohesive zone model. Engineering Fracture Mechanics 69, 2073–2093.
Lin, G. Cornec, A., and Schwalbe, K.-H. (1998). Three-dimensional finite element simulation of crack extension in aluminium alloy 2024FC. Fatigue & Fracture of Engineering Materials and Structures 21, 1159–1173.
Needleman, A. (1987). A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 54, 525–531.
Needleman, A. (1990). An analysis of decohesion along an imperfect interface. International Journal of Fracture 42, 21–40.
Nguyen, O., Repetto, E.A., Ortiz, M. and Radovitzky, R.A. (2001). A cohesive model of fatigue crack growth. International Journal of Fracture 110, 351–369.
Ortiz, M. and Pandolfi, A. (1999). Finite-deformation irreversible cohesive elements for three-dimensional crack propagation analysis. International Journal for Numerical Method in Engineering 44, 1267–1282.
Pandolfi, A., Guduru, P.R., Ortiz, M. and Rosakis, A.J. (2000). Three dimensional cohesive element analysis and experiments of dynamic fracture in C300 steel. International Journal of Solids and Structures 37, 3373–3760.
Rahulkumar, P., Jagota, A., Bennison, S.J. and Saigal, S. (2000). Cohesive element modeling of viscoelastic fracture: application to peel testing of polymers. International Journal of Solids and Structure 37, 1873–1897.
Roe, K.L. and Siegmund, T. (in press). An irreversible cohesive zone model for interface fatigue crack growth simulation. Engineering Fracture Mechanics, in press.
Roy, Y.A. and Dodds Jr, R.H. (2001). Simulation of ductile crack growth in thin aluminum panels using 3-D surface cohesive elements. International Journal of Fracture 110, 21–45.
Scheider, I. (2001). Bruchmechanische Bewertung von Laserschweißverbindungen durch numerische Simulation mit dem Kohäsivzonenmodell. Ph.D. Thesis, Technical University Hamburg-Harburg, Germany.
Scheider, I. And Brocks, W. (2003). The effect of the traction-separation law on the results of cohesive zone crack propagation analyses. In: Fracture and Damage Mechanics, Proceedings of the 3rd International Conference on Fracture and Damage Mechanics, Trans Tech Publications, Zurich, Switzerland.
Scherer, S. and Kolednik, O. (2001). A New system for automatic surface analysis in SEM. Microscopy and Analysis 70, 15–17.
Seshadri, B.R, and Newman Jr., J.C. (2000). Residual strength analysis of riveted lap-splice joints. ASTM STP 1389, 486–504.
Shan, G.X., Kolednik, O., Fischer, F.D. and Stuwe, H.P. (1993). A 2D model for numerical investigations of stable crack growth in thick smooth fracture mechanics specimens. Engineering Fracture Mechanics 45, 99–106.
Shan, G.X., Kolednik, O. and Fischer, F.D. (1995). A numerical study on the influence of geometry variations on stable crack growth in CT specimens for different materials. ASTM STP 1244, 71–87.
Shet, C., and Chandra N. (2002). Analysis of energy balance when using cohesive zone models to simulate fracture processes. Journal of Engineering Materials and Technology, Transactions of the ASME 124, 440–450.
Shih, C.F. (1981). Relationship between the J-integral and the crack tip opening displacement for staionary and extending cracks. Journal of the Mechanics and Physics of Solids 29, 305–326.
Siegmund, T. and Brocks, W. (1999). Prediction of the work of separation and implication to modeling. International Journal of Fracture 99, 97–116.
Siegmund, T. and Brocks, W. (2000a). The role of cohesive strength and separation energy for modeling of ductile fracture. ASTM STP 1360, 139–151.
Siegmund, T. and Brocks, W. (2000b). A numerical study on the correlation between the work of separation and the dissipation rate in ductile fracture. Engineering Fracture Mechanics 67, 139–154.
Siegmund, T. and Brocks, W. (2000c). Modeling crack growth in thin sheet aluminum alloys. ASTM STP 1389, 475–485.
Stampfl, J., Scherer, S., Gruber, M. and Kolednik, O. (1996a). Reconstruction of surface topographies by scanning electron microscopy for application in fracture research. Applied Physics A63, 341–346.
Stampfl, J., Scherer, S., Stüwe, H.P. and Kolednik, O. (1996b). The stereophotogrammetric determination of the plastic work for ductile fracture. In: Mechanisms and Mechanics of Damage and Failure, Proc. of ECF 11, (Edited by J. Petit), EMAS, U.K., Vol. 3, 271–276.
Stampfl, J. and Kolednik, O. (2000). The separation of the fracture energy in metallic materials. International Journal of Fracture 101, 321–345.
Stüwe, H.P. (1980). The work necessary to form a ductile fracture surface. Engineering Fracture Mechanics 13, 231–236.
Stüwe, H.P. (1981). The plastic work spent in ductile fracture. In: Three-dimensional Constitutive Relations and Ductile Fracture, (Edited by S. Nemat-Nasser), North-Holland, Amsterdam, 213–221.
Thomason, P.F. (1990). Ductile Fracture of Metals, Pergamon Press, Oxford.
Turner, C.E. (1990). A re-assessment of the ductile tearing resistance, Part I and II. In: Fracture Behavior and Design of Materials and Structures, Proc. of ECF8, (Edited by D. Firrao), EMAS, U.K., 933–949 and 951–968.
Turner, C.E. and Kolednik, O. (1994). A micro and macro approach to the energy dissipation rate model of stable ductile crack growth. Fatigue and Fracture of Engineering Materials and Structures 17, 1089–1107.
Tvergaard, V. and 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, 1377–1397.
Tvergaard, V. and Hutchinson, J.W. (ß). Effect of strain-dependent cohesive zone model on prediction of crack growth resistance. International Journal of Solids and Structures 33, 3297–3308.
Tvergaard, V. (2001). Resistance curves for mixed mode interface crack growth between dissimilar elastic-plastic solids. Journal of the Mechanics and Physics of Solids 49, 2689–2703.
Xia, L. and Shih, C.F. (1995). 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.
Yan, W.Y., Shan, G.X., Kolednik, O. and Fischer, F.D. (1998) A numerical simulation of the crack growth in a smooth CT-specimen. Key Engineering Materials 145–149, 179–184.
Yuan, H., Lin, G.Y. and Cornec, A. (1996). Verification of a cohesive zone model for ductile fracture. Journal of Engineering Materials and Technology 118, 192–200.
Ziehenberger, K., Stampfl, J., Brantner, H.P., Pippan, R. and Kolednik, O. (1997) The local fracture toughness of particle reinforced aluminium alloys. In: Proceedings of the International Conference Micro Materials’ 97, (Edited by B. Michel and T. Winkle), Druckhausverlag Dresden, 1121–1123.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper is dedicated to Prof. Wolfgang Brocks on the occasion of his 60s birthday.
Rights and permissions
About this article
Cite this article
Chen, C.R., Kolednik, O., Scheider, I. et al. On the determination of the cohesive zone parameters for the modeling of micro-ductile crack growth in thick specimens. International Journal of Fracture 120, 517–536 (2003). https://doi.org/10.1023/A:1025426121928
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1025426121928