Research Papers

A Crack Close to and Perpendicular to an Interface: Resolution of Anomalous Behavior With a Cohesive Zone

[+] Author and Article Information
George G. Adams

Department of Mechanical Engineering, Northeastern University,
Boston, MA 02115
e-mail: adams@coe.neu.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 6, 2018; final manuscript received December 10, 2018; published online January 8, 2019. Assoc. Editor: Haleh Ardebili.

J. Appl. Mech 86(3), 031008 (Jan 08, 2019) (7 pages) Paper No: JAM-18-1628; doi: 10.1115/1.4042289 History: Received November 06, 2018; Revised December 10, 2018

In this investigation, we consider a crack close to and perpendicular to a bimaterial interface. If the crack tip is at the interface then, depending on material properties, the order of the stress singularity will be equal to, less than, or greater than one-half. However, if the crack tip is located any finite distance away from the interface the stress field is square-root singular. Thus, as the crack tip approaches the interface, the stress intensity factor approaches zero (for cases corresponding to a singularity of order less than one-half) or infinity (for a singularity of order greater than one-half). The implication of this behavior is that for a finite applied pressure the crack will either never reach the interface or will reach the interface with vanishing small applied pressure. In this investigation, a cohesive zone model is used in order to model the crack behavior. It is found that the aforementioned anomalous behavior for the crack without a cohesive zone disappears and that the critical value of the applied pressure for the crack to reach the interface is finite and depends on the maximum stress of the cohesive zone model, as well as on the work of adhesion and the Dundurs' parameters.

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Grahic Jump Location
Fig. 1

A crack of length 2a perpendicular to and terminating a distance δ from a bimaterial interface

Grahic Jump Location
Fig. 2

Bounded part of stress along y =0 between the interface and crack tip for μ21 = 2, ν1 = ν2 = ¼ (α = 1/3, β = 1/9) and various values of δ/a (0.001, 0.005, 0.01, 0.05, 0.1)

Grahic Jump Location
Fig. 3

A crack of length 2a perpendicular to a bimaterial interface. A cohesive zone extends from the crack tip to the interface.

Grahic Jump Location
Fig. 4

The stress field so that Fig. 1 is the superposition of the stress fields from Figs. 3 to 4. The crack is subject to a cohesive zone stress and to the stress field of Fig. 1

Grahic Jump Location
Fig. 5

Asymptotic configuration corresponding to Fig. 4 in the immediate vicinity of the crack tip

Grahic Jump Location
Fig. 6

Variation of the critical crack tip-to-interface distance versus work of adhesion parameter for various values of the modulus ratio

Grahic Jump Location
Fig. 7

Variation of the critical internal crack pressure versus work of adhesion parameter for various values of the modulus ratio

Grahic Jump Location
Fig. 8

Variation of the critical internal crack pressure versus crack tip-to-interface distance for various values of the modulus ratio. Valid for any δ<δC.

Grahic Jump Location
Fig. 9

For a semi-infinite crack, the variation of the order of the singularity λ (when δ = 0), the dimensionless stress intensity factor at which the notional tip reaches the interface, (KI/σ0δ1/2) the ratio (γ) of the critical stress intensity factor to that of a homogeneous material, and the dimensionless cohesive zone length (wδ/μ1h02), with respect to the Dundurs parameter (α)



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