Research Papers

Investigating Some Technical Issues on Cohesive Zone Modeling of Fracture

[+] Author and Article Information
John T. Wang

NASA Langley Research Center, Hampton,
VA, 23681
e-mail: john.t.wang@nasa.gov

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received May 2, 2012; final manuscript received August 28, 2012; published online December 21, 2012. Assoc. Editor: Joost Vlassak.

J. Eng. Mater. Technol 135(1), 011003 (Dec 21, 2012) (10 pages) Paper No: MATS-12-1083; doi: 10.1115/1.4007605 History: Received May 02, 2012; Revised August 28, 2012

This study investigates some technical issues related to the use of cohesive zone models (CZMs) in modeling the fracture of materials with negligible plasticity outside the fracture process zone. These issues include: (1) why cohesive laws of different shapes can produce similar fracture predictions, (2) under what conditions CZM predictions have a high degree of agreement with linear elastic fracture mechanics (LEFM) analysis results, (3) when the shape of cohesive laws becomes important in the fracture predictions, and (4) why the opening profile along the cohesive zone length (CZL) needs to be accurately predicted. Two cohesive models were used in this study to address these technical issues. They are the linear softening cohesive model and the Dugdale perfectly plastic cohesive model. Each cohesive model uses five cohesive laws of different maximum tractions. All cohesive laws have the same cohesive work rate (CWR) defined by the area under the traction–separation curve. The effects of the maximum traction on the cohesive zone length and the critical remote applied stress are investigated for both models. The following conclusions from this study may provide some guidelines for the prediction of fracture using CZM. For a CZM to predict a fracture load similar to that obtained by an LEFM analysis, the cohesive zone length needs to be much smaller than the crack length, which reflects the small-scale yielding condition requirement for LEFM analysis to be valid. For large-scale cohesive zone cases, the predicted critical remote applied stresses depend on the shape of the cohesive models used and can significantly deviate from LEFM results. Furthermore, this study also reveals the importance of accurately predicting the cohesive zone profile for determining the critical remote applied load.

© 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Barenblatt, G. I., 1962, “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture,” Advances in Applied Mechanics, 7, pp. 55–129. [CrossRef]
Dugdale, D. S., 1960, “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids, 8, pp. 100–104. [CrossRef]
Camacho, G. T., and Ortiz, M., 1996, “Computational Modelling of Impact Damage in Brittle Materials,” Int. J. Solids Struct., 33, pp. 2899–2938. [CrossRef]
Needleman, A., 1987, “A Continuum Model for Void Nucleation by Inclusion Debonding,” ASME J. Appl. Mech., 54, pp. 525–531. [CrossRef]
Needleman, A., 1990, “An Analysis of Decohesion Along an Imperfect Interface,” Int. J. Fract., 42, pp. 21–40. [CrossRef]
Xu, X. P., and Needleman, A., 1993, “Void Nucleation by Inclusion Debonding in a Crystal Matrix,” Modell. Simul. Mater. Sci. Eng., 1, pp. 111–132. [CrossRef]
Tvergaard, V., and Hutchinson, J. W., 1992, “The Rbetween Crack Growth Resistance and Fracture Process Parameters in Elastic–Plastic Solids,” J. Mech. Phys. Solids, 40, pp. 1377–1397. [CrossRef]
Tvergaard, V., 1990, “Effect of Fibre Debonding in a Whisker-Reinforced Metal,” Mater. Sci. Eng. A, 125, pp. 203–213. [CrossRef]
Park, K., Paulino, G. H., and Roesler, J. R., 2009, “A Unified Potential-Based Cohesive Model for Mixed-Mode Fracture” J. Mech. Phys. Solids, 57(6), pp. 891–908. [CrossRef]
Rice, J. R., 1978, “Thermodynamics of the Quasi-Static Growth of Griffith Cracks,” J. Mech. Phys. Solids, 26, pp. 61–78. [CrossRef]
Gurtin, M. E., 1979, “Thermodynamics and Cohesive Zone in Fracture,” J. Appl. Math. Phys. (ZAMP), 30, pp. 991–1003. [CrossRef]
Gurtin, M. E., 1979, “Thermodynamics and the Griffith Criterion for Brittle Fracture,” Int. J. Solids Struct., 15, pp. 553–560. [CrossRef]
Costanzo, F., and Allen, D. H., 1995, “A Continuum Thermodynamic Analysis of Cohesive Zone Models,” Int. J. Eng. Sci., 33, pp. 2197–2219. [CrossRef]
Li, Y. N., and LiangR. Y., 1993, “The Theory of the Boundary Eigenvalue Problem in the Cohesive Crack Model and Its Application,” J. Mech. Phys. Solids, 41, pp. 331–350. [CrossRef]
Park, K., Paulino, G. H., and Roesler, J. R., 2008, “Determination of the Kink Point in the Bi-Linear Softening Model for Concrete,” Eng. Fract. Mech., 75, pp. 3806–3818. [CrossRef]
Rice, J. R., 1968, “A Path Independent Integral and Approximate Analysis of Strain Concentration by Notches and Cracks,” ASME J. Appl. Mech., 35, pp. 379–386. [CrossRef]
Hutchinson, J. W., 1979, A Course on Nonlinear Fracture Mechanics, Department of Solid Mechanics, The Technical University of Denmark, Lyngby, Denmark, pp. 12–13.
Bao, G., and Suo, Z., 1992, “Remarks on Crack-Bridging Concepts,” Appl. Mech. Rev., 45(8), pp. 355–366. [CrossRef]
ChandraN., Li.H., Shet, C., and Ghonem, H., 2002, “Some Issues in the Application of Cohesive Zone Models for Metal Ceramic Interfaces,” Int. J. Solids Struct., 39, pp. 2827–2855. [CrossRef]
Shet, C., and Chandra, N., 2004, “Effect of the Shape of Traction–Displacement Cohesive Zone Curves on the Fracture Response,” Mech. Adv. Mater. Struct., 11, pp. 249–275. [CrossRef]
Li, H., and Chandra, N., 2003, “Analysis of Crack Growth and Crack-Tip Plasticity in Ductile Materials Using Cohesive Zone Models,” Int. J. Plast., 19, pp. 849–882. [CrossRef]
Alfano, M., Furgiuele, F., Leonardi, A., Maletta, C., and Paulino, G. H., 2009, “Mode I Fracture of Adhesive Joints Using Tailored Cohesive Zone Models,” Int. J. Fract., 157, pp. 193–204. [CrossRef]
Rots, J. G., 1986, “Strain-Softening Analysis of Concrete Fracture Specimens,” Fracture Toughness and Fracture Energy of Concrete, F. H.Wittmann, ed., Elsevier Science Publishers, Amsterdam, The Netherlands, pp. 137–148.
de Borst, R., 2003, “Numerical Aspects of Cohesive-Zone Models,” Eng. Fract. Mech., 70, pp. 1743–1757. [CrossRef]
van Mier, J. G. M., and van Vliet, M. R. A., 2002, “Uniaxial Tension for the Determination of Fracture Parameters of Concrete: State of the Art,” Eng. Fract. Mech., 69, pp. 235–247. [CrossRef]
Abanto-Bueno, J., and Lambros, J., 2005, “Experimental Determination of Cohesive Failure Properties of a Photodegradable Copolymer,” Exp. Mech., 45, pp. 144–152. [CrossRef]
Kandula, S. S. V., Abanto-Bueno, J., Geubelle, P. H., and Lambros, J., 2006, “Cohesive Modeling of Quasi-Static Fracture in Functionally Graded Materials,” J. Appl. Mech., 73, pp. 783–791. [CrossRef]
Elices, M., Guinea, G. V., Gomez, J., and Planas, J., 2002, “The Cohesive Zone Model: Advantages, Limitations and Challenges,” Eng. Fract. Mech., 69, pp. 137–163. [CrossRef]
Li, V. C., Chan, C. M., and Leung, K. Y., 1987, “Experimental Determination of the Tension-Softening Relations for Cementitious Composites,” Cem. Concr. Res., 17, pp. 441–452. [CrossRef]
Sørensen, B. F., and Jacobsen, T. K., 2003, “Determination of Cohesive Laws by the J Integral Approach,” Eng. Fract. Mech., 70, pp. 1841–1858. [CrossRef]
Gain, A. L., Carroll, J., Paulino, G. H., and Lambros, J., 2011, “A Hybrid Experimental/Numerical Technique to Extract Cohesive Fracture Properties for Mode-I Fracture of Quasi-Brittle Materials,” Int. J. Fract., 169, pp. 113–131. [CrossRef]
Shen, B., and Paulino, G. H., 2011, “Identification of Cohesive Zone Model and Elastic Parameters of Fiber-Reinforced Cementitious Composites Using Digital Image Correlation and a Hybrid Inverse Technique,” Cem. Concr. Compos., 33, pp. 572–585. [CrossRef]
Jin, Z. H., and Sun, C. T., 2005, “Cohesive Fracture Model Based on Necking,” Int. J. Fract., 134, pp. 91–108. [CrossRef]
Jin, Z. H., and Sun, C. T., 2006, “A Comparison of Cohesive Zone Modeling and Classical Fracture Mechanics Based on Near Tip Stress Field,” Int. J. Solids Struct., 43, pp. 1047–1060. [CrossRef]
matlab®, The Language of Technical Computing, Version (R2010b), The MathWorks, Inc.
Kanninen, M. F., and Popelar, C. H., 1985, Advanced Fracture Mechanics, Oxford University Press, New York.
Cox, B. N., and Marshall, D. B., 1994, “Concepts for Bridged Cracks in Fracture and Fatigue,” Acta Metall. Mater., 42(2), pp. 341–363. [CrossRef]
Planas, J., and Elices, M., 1992, “Asymptotic Analysis of Cohesive Crack: 1. Theoretical Background,” Int. J. Fract., 55, pp. 153–177. [CrossRef]
Broek, D., 1986, Elementary Engineering Fracture Mechanics, 4th revised ed., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, pp. 247–248.
Davila, C. G., Camanho, P. P., and de Moura, M. F., 2001, “Mixed-Mode Decohesion Elements for Analyses of Progressive Delamination,” 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Seattle, WA, April 16–19, Paper No. AIAA-2001-1486.
Camanho, P. P., Davila, C. G., and de Moura, M. F., 2003, “Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials,” J. Compos. Mater., 37, pp. 1415–1438. [CrossRef]
Yang, Q., and Cox, B., 2005, “Cohesive Models for Damage Evolution in Laminated Composites,” Int. J. Fract., 133, pp. 107–137. [CrossRef]
Xie, D., and Waas, A. M., 2006, “Discrete Cohesive Zone Model for Mixed-Mode Fracture Using Finite Element Method,” Eng. Fract. Mech., 73, pp. 1783–1796. [CrossRef]
Tada, H., Paris, P. C., and Irwin, G. R., 2000, The Stress Analysis of Cracks Handbook, ASME Press, New York, p. 141.
Hillerborg, A., Modeer, M., and Petersson, P. E., 1976, “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements,” Cem. Concr. Res., 6, pp. 773–782. [CrossRef]
Moës, N., and Belytschko, T., 2002, “Extended Finite Element Method for Cohesive Crack Growth,” Eng. Fract. Mech., 69, pp. 813–833. [CrossRef]
Turon, A., Davila, C. G., Camanho, P. P., and Costa, J., 2007, “An Engineering Solution for Mesh Size Effects in the Simulation of Delamination Using Cohesive Zone Models,” Eng. Fract. Mech., 74, pp. 1665–1668. [CrossRef]
Geubelle, P. H., and Baylor, J., 1998, “Impact-Induced Delamination of Composites: A 2D Simulation,” Composites Part B, 29, pp. 589–602. [CrossRef]
Jin, Z. H., 2009, The University of Maine, Orono, Mechanical Engineering Department, personal communication, September 4.
Planas, J., and Elices, M., 1991, “Nonlinear Fracture of Cohesive Materials,” Int. J. Fract., 51, pp. 139–157. [CrossRef]


Grahic Jump Location
Fig. 1

Fracture analysis of a cracked infinite plate using a cohesive zone model

Grahic Jump Location
Fig. 2

Linear softening and Dugdale models

Grahic Jump Location
Fig. 3

Cohesive zone fully developed at crack growth initiation and unchanged during growth for linear elastic material

Grahic Jump Location
Fig. 4

Five cohesive laws with different maximum tractions but the same cohesive work rate for both the linear softening and the Dugdale models

Grahic Jump Location
Fig. 5

J-integral paths around a cohesive zone

Grahic Jump Location
Fig. 6

Iterative solution procedure

Grahic Jump Location
Fig. 7

Cohesive zone opening displacements along the cohesive zone length for cohesive laws with different maximum tractions (a=1l¯ch)

Grahic Jump Location
Fig. 8

Cohesive zone length as a function of maximum traction for different crack lengths

Grahic Jump Location
Fig. 9

Cohesive zone length as a function of crack length for cohesive laws with different maximum tractions

Grahic Jump Location
Fig. 10

Critical remote applied stress as a function of maximum traction for different crack lengths

Grahic Jump Location
Fig. 11

Critical remote applied stress as a function of the scale of cohesive zone length

Grahic Jump Location
Fig. 12

LEFM energy release rate as a function of maximum traction

Grahic Jump Location
Fig. 13

LEFM energy release rate as a function of the scale of cohesive zone length

Grahic Jump Location
Fig. 14

Changes of critical remote applied stress due to modifying the cohesive zone opening profile from a cusp shape to a triangular shape




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In