Research Papers

Investigation of Stress Intensity Factors for an Interface Crack in Multi-Interface Materials Using an Interaction Integral Method

[+] Author and Article Information
Linzhi Wu

 Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, Chinawlz@hit.edu.cn

Hongjun Yu

 Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, Chinayuhongjun@hit.edu.cn

Licheng Guo, Qilin He, Shanyi Du

 Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, China

J. Appl. Mech 78(6), 061007 (Aug 24, 2011) (11 pages) doi:10.1115/1.4003906 History: Received September 14, 2009; Revised March 24, 2011; Published August 24, 2011

A new interaction integral formulation is derived for obtaining mixed-mode stress intensity factors (SIFs) of an interface crack with the tip close to complicated material interfaces. The method is a conservation integral that relies on two admissible mechanical states (actual and auxiliary fields). By a suitable selection of the auxiliary fields, the domain formulation does not contain any integral related to the material interfaces, which makes it quite convenient to deal with complicated interface problems. The numerical implementation of the derived expression is combined with the extended finite element method (XFEM). According to the numerical calculations, the interaction integral shows good accuracy for straight and curved interface crack problems and exhibits domain-independence for material interfaces. Finally, an interfacial fracture problem is investigated for the representative centrosymmetric structure formed by two constituent materials.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Interfacial fracture of ZrB2 -SiC-AlN ceramic composite [19]

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Figure 2

An interface crack located between two homogeneous materials

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Figure 3

Schematic of the contour integrals and related domain integrals. (The domain A is divided into four parts by two bimaterial interfaces ΓA=ΓA12+ΓA34 and ΓJ=ΓJ13+ΓJ24. Domains A, A1, A2, A3 and A4 are enclosed by Γ0, Γ01, Γ02, Γ03 and Γ04, respectively, when Γ→0. Here A=∑i=14Ai, ΓI=ΓA, Γ0=ΓB+ΓC++Γ-+ΓC-, ΓB=∑i=14ΓBi, Γ=∑i=12Γi, Γ01=ΓB1+ΓC++Γ1-+ΓA12+ΓJ13, Γ02=ΓB2+ΓJ24+ΓA12-+Γ2-+ΓC-, Γ03=ΓB3+ΓJ13-+ΓA34 and Γ04=ΓB4+ΓA34-+ΓJ24-.).

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Figure 4

A curvilinear coordinate system based on a curved interface

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Figure 5

Schematic of two curved interfaces in the integral domain (the material properties are same for the domain with same color). (a) ΓI and ΓA do not overlap; (b) ΓI and ΓA overlap partially.

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Figure 6

Integral domains for a curved crack face

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Figure 7

An edge crack and an elliptical inclusion placed on a mesh: (a) finite element mesh and refined mesh around crack tip; (b) distribution of integration points

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Figure 8

A center crack located between two dissimilar materials (example 1): (a) geometry and boundary conditions; (b) complete finite element mesh; (c) integral domain to compute the interaction integral

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Figure 9

A rectangular plate with a center interface crack under tension load (example 2): (a) geometry and boundary conditions; (b) complete finite element mesh; (c) integral domains to verify the convergence of the interaction integral; (d) integral domains around the crack tip

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Figure 10

A circular-arc crack along the interface of a circular inclusion embedded in a plate (example 3): (a) geometry and boundary conditions; (b) finite element mesh

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Figure 11

Normalized SIFs at the crack tip A varying with angle θ0 (example 3)

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Figure 12

The mesh around the inclusion and the refined mesh around the crack tip (example 3): (a) the mesh around the inclusion for the XFEM (Mesh 1); (b) refined mesh for the XFEM (Mesh 1); (c) the mesh around the inclusion for the FEM (Mesh 2); (d) refined mesh for the FEM (Mesh 2)

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Figure 13

A circular-arc crack between an inclusion and matrix (example 4)

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Figure 14

Normalized SIFs at the crack tip A varying with angle θ0 (example 4)

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Figure 15

Normalized SIFs and phase angles of a center interface crack varying with crack length 2a/L: (a) K1(a)/K0 for E1/E2=0.1; (b) K1(a)/K0 for E1/E2=10; (c) K2(a)/K0 for E1/E2=0.1; (d) K2(a)/K0 for E1/E2=10; (e) ψ(a)/π for E1/E2=0.1; (f) ψ(a)/π for E1/E2=10



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