Research Papers

Two Objective and Independent Fracture Parameters for Interface Cracks

[+] Author and Article Information
Jia-Min Zhao

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: zhaojm12@mails.tsinghua.edu.cn

He-Ling Wang

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: heling.wang@northwestern.edu

Bin Liu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: liubin@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 9, 2017; final manuscript received February 5, 2017; published online February 23, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(4), 041006 (Feb 23, 2017) (10 pages) Paper No: JAM-17-1018; doi: 10.1115/1.4035932 History: Received January 09, 2017; Revised February 05, 2017

Due to the oscillatory singular stress field around a crack tip, interface fracture has some peculiar features. This paper is focused on two of them. One can be reflected by a proposed paradox that geometrically similar structures with interface cracks under similar loadings may have different failure behaviors. The other one is that the existing fracture parameters of the oscillatory singular stress field, such as a complex stress intensity factor, exhibit some nonobjectivity because their phase angle depends on an arbitrarily chosen length. In this paper, two objective and independent fracture parameters are proposed which can fully characterize the stress field near the crack tip. One parameter represents the stress intensity with classical unit of stress intensity factors. It is interesting to find that the loading mode can be characterized by a length as the other parameter, which can properly reflect the phase of the stress oscillation with respect to the distance to the crack tip. This is quite different from other crack tip fields in which the loading mode is usually expressed by a phase angle. The corresponding failure criterion for interface cracks does not include any arbitrarily chosen quantity and, therefore, is convenient for comparing and accumulating experimental results, even existing ones. The non-self-similarity of the stress field near an interface crack tip is also interpreted, which is the major reason leading to many differences between the interfacial fracture and the fracture in homogenous materials.

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Fig. 1

Schematic of an interface crack between two different linear elastic isotropic materials

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Fig. 2

Schematics of two bodies with interface cracks of different lengths (LA≠LB) subject to remote loading σyy∞ and σxy∞

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Fig. 3

Schematics of two identical specimens with interface cracks subject to different loadings and their subsystems

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Fig. 4

Simulation models: (a) finite element mesh and (b) a recursive computing scheme

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Fig. 5

The fracture toughness versus loading-mode curves (K*−LI) for glass/epoxy materials measured by different researchers

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Fig. 6

Schematic of the K*-dominant zone

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Fig. 7

Schematic of an infinite bimaterial body including an interface crack subject to remote uniaxial tension

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Fig. 8

The relative errors between the full-field solution and the asymptotic solution for the cases with different stiffness ratios

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Fig. 9

Schematics of the deformation for the elements at the interface: (a) the undeformed configuration, (b) the deformed configuration in general situations (zero interfacial shear stress only at a point), and (c) the deformed configuration in special situations (zero interfacial shear stress over a region)

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Fig. 10

Variation of the normalized hoop stress along the interface as a function of the normalized distance to the crack tip from simulations

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Fig. 11

Comparison of the stress angular distributions between simulations and theoretical predictions




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