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Research Papers

Two Objective and Independent Fracture Parameters for Interface Cracks

[+] Author and Article Information
Jia-Min Zhao

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

He-Ling Wang

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

Bin Liu

AML, CNMM,
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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References

Xie, J. W. , and Waas, A. M. , 2015, “ Predictions of Delamination Growth for Quasi-Static Loading of Composite Laminates,” ASME J. Appl. Mech., 82(8), p. 081004. [CrossRef]
Huang, Y. , Yuan, J. H. , Zhang, Y. C. , and Feng, X. , 2016, “ Interfacial Delamination of Inorganic Films on Viscoelastic Substrates,” ASME J. Appl. Mech., 83(10), p. 101005. [CrossRef]
Williams, M. L. , 1959, “ The Stresses Around a Fault or Crack in Dissimilar Media,” Bull. Seismol. Soc. Am., 49(2), pp. 199–204.
Erdogan, F. , 1963, “ Stress Distribution in a Nonhomogeneous Elastic Plane With Cracks,” ASME J. Appl. Mech., 30(2), pp. 232–236. [CrossRef]
Erdogan, F. , 1965, “ Stress Distribution in Bonded Dissimilar Materials With Cracks,” ASME J. Appl. Mech., 32(2), pp. 403–410. [CrossRef]
Sih, G. C. , and Rice, J. R. , 1964, “ The Bending of Plates of Dissimilar Materials With Cracks,” ASME J. Appl. Mech., 31(3), pp. 477–482. [CrossRef]
Rice, J. R. , and Sih, G. C. , 1965, “ Plane Problems of Cracks in Dissimilar Media,” ASME J. Appl. Mech., 32(2), pp. 418–423. [CrossRef]
England, A. H. , 1965, “ A Crack Between Dissimilar Media,” ASME J. Appl. Mech., 32(2), pp. 400–402. [CrossRef]
Suo, Z. , 1989, “ Singularities Interacting With Interfaces and Cracks,” Int. J. Solids Struct., 25(10), pp. 1133–1142. [CrossRef]
Rice, J. R. , Suo, Z. , and Wang, J.-S. , 1990, “ Mechanics and Thermodynamics of Brittle Interfacial Failure in Bimaterial System,” Metal-Ceramics Interfaces, M. Rühle , A. G. Evans , M. F. Ashby , and J. P. Hirth , eds., Pergamon Press, New York, pp. 269–294.
Comninou, M. , 1977, “ The Interface Crack,” ASME J. Appl. Mech., 44(4), pp. 631–636. [CrossRef]
Comninou, M. , 1978, “ The Interface Crack in a Shear Field,” ASME J. Appl. Mech., 45(2), pp. 287–290. [CrossRef]
Comninou, M. , and Schmueser, D. , 1979, “ The Interface Crack in a Combined Tension-Compression and Shear Field,” ASME J. Appl. Mech., 46(2), pp. 345–348. [CrossRef]
Atkinson, C. , 1977, “ On Stress Singularities and Interfaces in Linear Elastic Fracture Mechanics,” Int. J. Fract., 13(6), pp. 807–820. [CrossRef]
Knowles, J. K. , and Sternberg, E. , 1983, “ Large Deformations Near a Tip of an Interface-Crack Between Two Neo-Hookean Sheets,” J. Elasticity, 13(3), pp. 257–293. [CrossRef]
Rice, J. R. , 1988, “ Elastic Fracture Mechanics Concepts for Interfacial Cracks,” ASME J. Appl. Mech., 55(1), pp. 98–103. [CrossRef]
Comninou, M. , 1990, “ An Overview of Interface Cracks,” Eng. Fract. Mech., 37(1), pp. 197–208. [CrossRef]
Hutchinson, J. W. , and Suo, Z. , 1991, “ Mixed Mode Cracking in Layered Materials,” Adv. Appl. Mech., 29, pp. 63–191.
Agrawal, A. , and Karlsson, A. M. , 2007, “ On the Reference Length and Mode Mixity for a Bimaterial Interface,” J. Eng. Mater. Technol., 129(4), pp. 580–587. [CrossRef]
Ikeda, T. , Miyazaki, N. , and Soda, T. , 1998, “ Mixed Mode Fracture Criterion of Interface Crack Between Dissimilar Materials,” Eng. Fract. Mech., 59(6), pp. 725–735. [CrossRef]
Yuuki, R. , Liu, J. Q. , Xu, J. Q. , Ohira, T. , and Ono, T. , 1994, “ Mixed Mode Fracture Criteria for an Interface Crack,” Eng. Fract. Mech., 47(3), pp. 367–377. [CrossRef]
Ji, X. , 2016, “ SIF-Based Fracture Criterion for Interface Cracks,” Acta Mech. Sin., 32(3), pp. 491–496. [CrossRef]
Wang, J.-S. , and Suo, Z. , 1990, “ Experimental Determination of Interfacial Toughness Curves Using Brazil-Nut-Sandwiches,” Acta Metall. Mater., 38(7), pp. 1279–1290. [CrossRef]
Banks-Sills, L. , 2015, “ Interface Fracture Mechanics: Theory and Experiment,” Int. J. Fract., 191(1–2), pp. 131–146. [CrossRef]
Liechti, K. M. , and Chai, Y. S. , 1992, “ Asymmetric Shielding in Interfacial Fracture Under in-Plane Shear,” ASME J. Appl. Mech., 59(2), pp. 295–304. [CrossRef]
Swadener, J. G. , and Liechti, K. M. , 1998, “ Asymmetric Shielding Mechanisms in the Mixed-Mode Fracture of a Glass/Epoxy Interface,” ASME J. Appl. Mech., 65(1), pp. 25–29. [CrossRef]
Banks-Sills, L. , and Ashkenazi, D. , 2000, “ A Note on Fracture Criteria for Interface Fracture,” Int. J. Fract., 103(2), pp. 177–188. [CrossRef]
Reedy, E. D. , and Emery, J. M. , 2014, “ A Simple Cohesive Zone Model That Generates a Mode-Mixity Dependent Toughness,” Int. J. Solids Struct., 51(21), pp. 3727–3734. [CrossRef]
O'Dowd, N. P. , Shih, C. F. , and Stout, M. G. , 1992, “ Test Geometries for Measuring Interfacial Fracture Toughness,” Int. J. Solids Struct., 29(5), pp. 571–589. [CrossRef]
Becker, T. , McNaney, J. , Cannon, R. , and Ritchie, R. , 1997, “ Limitations on the Use of the Mixed-Mode Delaminating Beam Test Specimen: Effects of the Size of the Region of K-Dominance,” Mech. Mater., 25(4), pp. 291–308. [CrossRef]
Chen, F. H. K. , and Shield, R. T. , 1977, “ Conservation Laws in Elasticity of the J-Integral Type,” Z. Angew. Math. Phys., 28(1), pp. 1–22. [CrossRef]
Yau, J. F. , Wang, S. S. , and Corten, H. T. , 1980, “ A Mixed-Mode Crack Analysis of Isotropic Solids Using Conservation Laws of Elasticity,” ASME J. Appl. Mech., 47(2), pp. 335–341. [CrossRef]
Yau, J. F. , and Wang, S. S. , 1984, “ An Analysis of Interface Cracks Between Dissimilar Isotropic Materials Using Conservation Integrals in Elasticity,” Eng. Fract. Mech., 20(3), pp. 423–432. [CrossRef]
Bank-Sills, L. , Travitzky, N. , Ashkenazi, D. , and Eliasi, R. , 1999, “ A Methodology for Measuring Interface Fracture Properties of Composite Materials,” Int. J. Fract., 99(3), pp. 143–161. [CrossRef]
Wu, L. Z. , Yu, H. J. , Guo, L. C. , He, Q. L. , and Du, S. Y. , 2011, “ Investigation of Stress Intensity Factors for an Interface Crack in Multi-Interface Materials Using an Interaction Integral Method,” ASME J. Appl. Mech., 78(6), p. 061007. [CrossRef]
Chen, S. H. , Wang, T. C. , and Kao-Walter, S. , 2003, “ A Crack Perpendicular to the Bimaterial Interface in Finite Solid,” Int. J. Solids Struct., 40(11), pp. 2731–2755. [CrossRef]
Chen, S. H. , Wang, T. C. , and Kao-Walter, S. , 2005, “ Finite Boundary Effects in Problem of a Crack Perpendicular to and Terminating at a Bimaterial Interface,” Acta Mech. Sin., 21(1), pp. 56–64. [CrossRef]

Figures

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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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