Review Articles

Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces

[+] Author and Article Information
Kyoungsoo Park

School of Civil & Environmental Engineering,
Yonsei University,
50 Yonsei-ro, Seodaemun-gu,
Seoul, Korea
e-mail: k-park@yonsei.ac.kr

Glaucio H. Paulino

Department of Civil &
Environmental Engineering,
University of Illinois at Urbana-Champaign,
205 North Mathews Avenue,
Urbana, IL 61801
e-mail: paulino@illinois.edu

1Corresponding author.

Manuscript received July 14, 2011; final manuscript received November 15, 2012; published online February 5, 2013. Editor: Harry Dankowicz.

Appl. Mech. Rev 64(6), 060802 (Feb 05, 2013) (20 pages) doi:10.1115/1.4023110 History: Received July 14, 2011; Revised November 15, 2012

One of the fundamental aspects in cohesive zone modeling is the definition of the traction-separation relationship across fracture surfaces, which approximates the nonlinear fracture process. Cohesive traction-separation relationships may be classified as either nonpotential-based models or potential-based models. Potential-based models are of special interest in the present review article. Several potential-based models display limitations, especially for mixed-mode problems, because of the boundary conditions associated with cohesive fracture. In addition, this paper shows that most effective displacement-based models can be formulated under a single framework. These models lead to positive stiffness under certain separation paths, contrary to general cohesive fracture phenomena wherein the increase of separation generally results in the decrease of failure resistance across the fracture surface (i.e., negative stiffness). To this end, the constitutive relationship of mixed-mode cohesive fracture should be selected with great caution.

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Grahic Jump Location
Fig. 1

Schematics of the cohesive zone model

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Fig. 2

Effective traction-separation relationships: (a) cubic polynomial, (b) trapezoidal, (c) smoothed trapezoidal, (d) exponential, (e) linear softening, and (f) bilinear softening

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Fig. 3

Cohesive fracture separations along the local coordinate system (a) two-dimensions (Δ1, Δ2) and (b) three-dimensions (Δ1, Δ2, Δ3)

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Fig. 6

Freed and Banks-Sills [5] potential (Ψ) and its gradients (Tn, Tt) with respect to displacement separations (Δn, Δt); φn=100 N/m, and σmax=30 MPa. The gradients refer to a revisited cubic-linear model.

Grahic Jump Location
Fig. 5

Needleman [4] potential (Ψ) and its gradients (Tn, Tt) with respect to displacement separations (Δn, Δt); φn=100 N/m, σmax=30 MPa, and αs = 10. The gradients refer to a cubic-linear model.

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Fig. 4

Effective displacement-based model with a linear softening: (a) normal cohesive traction, and (b) its derivative with respect to the normal separation (Δn) for T¯=σmax(1-Δ¯) where φn=100 N/m and σmax=10 MPa

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Fig. 7

Needleman [7] exponential-periodic potential and its gradients; φn=100 N/m, and σmax=30 MPa

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Fig. 8

Beltz and Rice [8] generalized exponential-periodic potential and its gradients; φn=2γs=100 N/m, φt=γus=200 N/m, σmax=30 MPa, τmax=40 MPa, and r=0

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Fig. 11

Xu and Needleman [9] exponential-exponential potential and its gradients; φn=100 N/m, φt=100 N/m, σmax=30 MPa, and τmax=40 MPa

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Fig. 12

Unified mixed-mode potential (PPR) [3] and its gradients for the intrinsic cohesive zone model with φn=100 N/m, φt=200 N/m, σmax=40 MPa, τmax=30 MPa, α=5, β=1.3, λn=0.1, and λt=0.2

Grahic Jump Location
Fig. 9

Xu and Needleman [9] exponential-exponential potential and its gradients; φn=100 N/m, φt=200 N/m, σmax=30 MPa, τmax=40 MPa, and r=0

Grahic Jump Location
Fig. 10

Xu and Needleman [9] exponential-exponential potential and its gradients; φn=200 N/m, φt=100 N/m, σmax=30 MPa, τmax=40 MPa, and r=0

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Fig. 13

Description of each cohesive interaction (Tn, Tt) region defined by the final crack opening widths (δn, δt) and the conjugate final crack opening widths (δ¯n, δ¯t); (a) Tn versus (δn,δ¯t) space; (b) Tt versus (δ¯n,δt) space

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Fig. 16

Variation of the work-of-separation considering the PPR potential [3] (φn = 100 N/m, φt = 200 N/m); (a) nonproportional path 1; (b) nonproportional path 2

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Fig. 14

The PPR potential [3] and its gradients for the extrinsic cohesive zone model with φn=100 N/m, φt=200 N/m, σmax=40 MPa, τmax=30 MPa, α=5, and β=1.3

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Fig. 15

Two arbitrary separation paths for the material debonding process; (a) nonproportional path 1; (b) nonproportional path 2




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