by Yang, Z. J.; Deeks, A. J.

A two-step method, coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM), is developed in this paper for modelling cohesive crack growth in quasi-brittle normal-sized structures such as concrete beams. In the first step, the crack trajectory is fully automatically predicted by a recently-developed simple remeshing procedure using the SBFEM based on the linear elastic fracture mechanics theory. In the second step, interfacial finite elements with tension-softening constitutive laws are inserted into the crack path to model gradual energy dissipation in the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the proposed method. The numerical results demonstrate that this two-step SBFEM-FEM coupled method can predict both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for crack growth problems with strong snap-back phenomenon. The effects of the tensile strength, the mode-I and mode-II fracture energies on the predicted load-displacement relations are also discussed.

DOI: 10.1007/s10704-007-9065-6
Online Date: 4/27/2007
Print publication date: 2/1/2007
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by Hillig, William Bruno

The time rate of extension of a single slit-like flaw in glass is modeled assuming the same corrosion mechanism as previously invoked for modeling delayed failure in glass containing a multiplicity of microscopic scratches or flaws. The rate of extension is expressible in terms of the stress intensity K and is in good agreement with the experimental results reported by Wiederhorn and Bolz and others. The model considers a moisture-induced corrosive attack occurring on the exposed flaw surfaces to be governed by local chemical kinetic and thermodynamic considerations, producing a rounding of the flaw tip. This mechanism accounts for the possibility of threshold behavior. The remotely applied stress becomes magnified as shown by Inglis to require the combined effect of the flaw length and tip curvature. These geometric factors in combination with the remotely applied stress mutually interact through the corrosion kinetics to define the net rate of flaw extension.

DOI: 10.1007/s10704-006-9020-y
Online Date: 4/24/2007
Print publication date: 2/1/2007
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by Rozenburg, Keith; Berger, J. R.; Martin, Paul A.; Reimanis, Ivar

The analysis of moiré data obtained in bimaterials with near-interface cracks is examined. To extract stress intensity factors, a collocation-type method is developed where Westergaard crack-tip expansions are used for displacements in the cracked portion of the bimaterial, expansions from the method of fundamental solutions are used for displacements in the uncracked portion of the bimaterial, and continuity conditions at the interface are used to couple the two expansions. Proof-of-principle numerical experiments performed on synthetic data from a boundary element analysis of a cracked bimaterial successfully demonstrated the analysis method. Mixed-mode stress intensity factors were then determined from actual moiré data obtained in a copper–tungsten specimen.

DOI: 10.1007/s10704-006-9016-7
Online Date: 4/17/2007
Print publication date: 2/1/2007
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by Lee, Hyungyil; Kim, Yun-Jae

This paper investigates interfacial crack tip stress fields and the J-integral for bi-materials with plastic hardening mismatch via detailed elastic-plastic finite element analyses. For small scale yielding, the modified boundary layer formulation with the elastic T-stress is employed. For fully plastic yielding, plane strain single-edge- cracked specimens under pure bending are considered. Interfacial crack tip stress fields are explained by modified Prandtl slip-line fields. It is found that, for bi-materials consisting of two elastic-plastic materials, increasing plastic hardening mismatch increases both crack-tip stress constraint in the lower hardening material and the J-contribution there. The implication of asymmetric J-integral in bi-materials is also discussed.

DOI: 10.1007/s10704-006-9025-6
Online Date: 4/17/2007
Print publication date: 2/1/2007
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by Moran, Brian; Kulkarni, Salil S.; Reeves, Howard W.

A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis–Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis–Menten kinetics.

DOI: 10.1007/s10704-007-9067-4
Online Date: 4/17/2007
Print publication date: 2/1/2007
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by Kulchytsky-Zhyhailo, Roman; Matysiak, Stanisław Jan

The paper deals with the asymptotic analysis of stresses near interface crack tips in the periodically two-layered elastic composites. The problem is investigated for the plane state of strain within the framework of the homogenized model with microlocal parameters. The angular dependence of stresses at the crack tip is presented for different mechanical and geometrical properties of the composite.

DOI: 10.1007/s10704-007-9064-7
Online Date: 4/17/2007
Print publication date: 2/1/2007
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by Graciani, Enrique; Mantič, Vladislav; París, Federico

A general expression for estimating the location of the first interpenetration point in the open model of interface cracks that, for a fixed reference system, can be directly applied to all material combinations is presented.

DOI: 10.1007/s10704-007-9066-5
Online Date: 4/13/2007
Print publication date: 2/1/2007
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by Gunderson, Joshua D.; Brueck, John F.; Paris, Anthony J.

Two methods of determining the mode I interlaminar fracture toughness for fiber-reinforced polymer matrix (FRPM) composites using a double cantilever beam (DCB) test are compared. The standard method of determining G

_IC
is based in linear-elastic fracture mechanics theory and requires a visual measurement of the crack length, presenting data acquisition and analysis difficulties. The proposed method makes use of elastic–plastic fracture mechanics theory and an analytical closed form solution to the J-integral to relate the fracture toughness J

_IC
, load, and angular displacement at the load application points. This method has the advantage of replacing visually acquired data with data easily obtained using inexpensive transducers as well as being applicable to a broader class of materials.

DOI: 10.1007/s10704-007-9063-8
Online Date: 4/13/2007
Print publication date: 2/1/2007
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by Katzav, E.; Adda-Bedia, M.; Arias, R.

The problem of dynamic symmetric branching of a tensile crack propagating in a brittle material is studied within Linear Elastic Fracture Mechanics theory. The Griffith energy criterion and the principle of local symmetry provide necessary conditions for the onset of dynamic branching instability and for the subsequent paths of the branches. The theory predicts a critical velocity for branching and a well defined shape described by a branching angle and a curvature of the side branches. The model rests on a scenario of crack branching based on reasonable assumptions and on exact dynamic results for the anti-plane branching problem. Our results reproduce within a simplified 2D continuum mechanics approach the main experimental features of the branching instability of fast cracks in brittle materials.

DOI: 10.1007/s10704-007-9061-x
Online Date: 4/11/2007
Print publication date: 2/1/2007
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by Lucht, T.; Aliabadi, M. H.

In order to avoid introduction of an error when a local crack growth criterion is used in an incremental crack growth formulation, each straight crack extension would have to be infinitesimal or have its direction corrected. In this paper a new procedure to correct the crack extension direction is proposed in connection with crack growth analyzed by the Dual Boundary Element Method (DBEM). The proposed correction procedure and a reference correction procedure already described in the literature are evaluated by solving two different computational crack growth examples. In the two examples it is found that analyses of the crack paths performed with the proposed crack correction procedure using big increments of crack extension are in excellent agreement with analyses of the crack paths performed by using very small increments of crack extension. Furthermore, it is shown that the reference correction procedure has a tendency to overcorrect the crack growth direction if the stop criterion for the iterative correction procedure is not calibrated in each new crack growth analysis.

DOI: 10.1007/s10704-007-9057-6
Online Date: 4/11/2007
Print publication date: 1/1/2007
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